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Rafter without fly brace?17

Rafter without fly brace?

(OP)
I am designing rafters to AS4100 and wondering what if I don't use fly brace. I understand that with fly brace it will give you full restraint. But if I don't use fly brace, will the purlin above be considered as lateral restraint for rafter under uplift? If so. can I take the purlin spacing as segment and the only factor that changes without fly brace is kt?
I have the same question when it comes the continuous steel floor beam design where Z/C floor joints sit on top of the beam. What segment should I take for the beam near the support? Can I take the floor joists spacing as segment with lateral restraint? Can anyone give me some examples? I have read some manuals but the examples they have are simply supported beams only. Thank you.

RE: Rafter without fly brace?

A purlin only provides lateral restraint when connected to the critical flange. Under uplift the bottom flange becomes critical, and thus purlins alone do not provide restraint. Hence the need for fly braces.

Under gravity load in continuous members the bottom flange can be critical too, i.e. you can need fly braces for gravity loading.

You should familiarise yourself with AS4100. It's all spelled out there.

RE: Rafter without fly brace?

(OP)
HI Tomfh. Thank you for your reply. So if I have a two spans continuous floor beam (6m+8m) supporting Z section floor joints above. The segment length under gravity for the beam will be 8m (the longer span) without any lateral restraint for checking negative moment near the support considering the critical flange will be at the bottom flange? If this is the case, why would people still use continuous beams instead of two simply supported beam of which the critical flange will be on top (under gravity) and lateral restraint will be provided?

RE: Rafter without fly brace?

Only a portion of the bottom flange is critical in continuous beam, so it's not nearly as bad as an 8m long beam with the whole bottom flange in compression.

RE: Rafter without fly brace?

(OP)

Quote (Only a portion of the bottom flange is critical in continuous beam, so it's not nearly as bad as an 8m long beam with the whole bottom flange in compression. )

Sorry but I don't quite understand. Does that mean I should take the length of the bottom flange in compression (say L/3 max = 2.7m) as the segment length?

RE: Rafter without fly brace?

When you run the analysis of your beam, the critical flange is the one in compression. We can't tell you from here how much of the bottom or top flange that is.

RE: Rafter without fly brace?

(OP)
Thanks jay. I understand the critical flange is in compression but I have problem understanding how long should the segment length be. For a continuous beam with floor joists on top under gravity load, which means joists can not provide restraint for negative moment area. Can I take the length from the column below to the point where moment becomes 0 (negative to positive) as the segment length to check if the bending capacity is okay for the negative moment at supports?

RE: Rafter without fly brace?

Generally speaking, I would take from inflection point to inflection point because I do not feel that the column to beam connection is a brace point unless the joint is detailed for out of plane moment. Otherwise it's technically a hinge in my eyes.

Edit: I do not consider inflection points as brace points per se. I do feel that if I design a beam for the maximum negative moment, assuming an unbraced length of inflection point to inflection point, while also being conservative with my loading, analysis, lengths, and unity checks, that the beam is adequate. I would bet my house on the answer being the same as if I took it from the first brace point past the inflection point as others have described below but was less conservative on the rest of my numbers.

RE: Rafter without fly brace?

Quote:

When you run the analysis of your beam, the critical flange is the one in compression

It's actually defined in As4100 as the flange that laterally deflects the furthest. Usually the compression flange though, but not always.

The inflection point isn't a point of restraint (see this blog post I wrote as an an example demonstrating this aspect). It's something I see people doing from time to time, and it's the wrong way to think about the restraint issue.

The next purlin past the inflection point is possibly an 'L' restraint, possibly 'F' depending on your connections to the top flange. Keep in mind the fly brace braces the beam by preventing the twist (if your purlin meets the stiffness required) so is able to increase the capacity without needing to support the 2.5% flange force by some external horizontal support. For an 'L' type restraint the 2.5% force turns into an axial load in the purlin, so you need some external load path to support this force to achieve the requirement to prevent lateral deflection of the critical flange.

RE: Rafter without fly brace?

It’s a bit murky. The floor joists can be counted as a lateral restraint once the top flange becomes the critical flange. As agent666 says, the critical flange is defined as the one which will deflect the furthest in the absence of restraint, which is typically though not necessarily the compression flange. In practice people often just take the compression flange as the critical flange, which allows you to take the first restraint past the point of contraflexure as a restraint (or indeed the point of contraflexure itself as a restraint). I’m don’t know how conservative/unconservative that approach is. Maybe it’s close enough in practice.

RE: Rafter without fly brace?

(OP)
Many many thanks guys. I will take the first floor joist outside each injection point in positive moment area as the segment length for negative moment capacity check.
Just one more question regarding the 2.5% force that Agent666 mentioned.

Quote (For an 'L' type restraint the 2.5% force turns into an axial load in the purlin)

As it is a beam instead of a column, how do I work out the equivalent force? (the compressive stress times the area of critical flange?) Can you please give me an example? (I have read Agent666's reference but it is regarding column too).

RE: Rafter without fly brace?

Quote (fourpm)

how do I work out the equivalent force? (the compressive stress times the area of critical flange?)

Yes the force in the flange. The flange is akin to a horizontal column. It's under compression and wants to buckle (sideways) same as how a column wants to buckle, so you need to grab it to restrain it. 2.5% is a commonly accepted figure, although as agent666 points out, buckling is more to do with stiffness, not strength. The idea is that if something can carry 2.5% of the load it's probably stiff (and strong) enough to prevent buckling.

RE: Rafter without fly brace?

Often in calculations it's simplified as restraint force = F* = M*/(d-t_f) x 2.5/100.

Don't forget about parallel restraint forces and tracking the cumulative force to something that is stiff/can take the load. Typically for say a roof because of this requirement I'd only say the purlins that align with the roof bracing system are actually effective. Older AS1250 steel standard used to have the provision at the end of my link relating to stiffness. So basically span/400.

In reality you can do a buckling analysis to see at what point (i.e. What stiffness) something that's providing the bracing/restraint forces a higher mode of buckling.

RE: Rafter without fly brace?

Quote (fourpm)

I will take the first floor joist outside each injection point in positive moment area as the segment length for negative moment capacity check.

I object strongly to this approach unless:

1) you've got fly bracing in play or;

2) your joist to beam connections provides real rotational restraint to the beam.

3) use the beam span between supports (8m) as your effective, lateral torsional buckling length for the negative moment.

4) Use stiffeners, fly braces, or whatever the heck you've gotta do to call the beam to column connection a point of full restraint for lateral buckling.

The key to understanding the appropriate unbraced length lies in the concept shown below. Think of your bottom flange as:

5) A strut/column whose lateral, buckled shape will have no inflection points between beam support points.

6) A strut/column whose axial load is a funky, linearly varying thing rather than just end loads.

When looking at column Euler buckling, the [L] value is squared. In comparison, the axial load is linear. As result, the length of the buckling mode shape between inflection points matters vastly more than does the particular axial load being applied. So the fact that your axial load in your beam flange is distributed, linearly varying, and sometimes tension does not offset the impact of the buckling mode between beam supports not having any inflection points.

RE: Rafter without fly brace?

Quote (jayrod12)

Generally speaking, I would take from inflection point to inflection point because I do not feel that the column to beam connection is a brace point unless the joint is detailed for out of plane moment.

If the interior column cannot be considered to LTB brace the beam, then I believe that your effective length for negative moments is actually the full length of the two span beam, outer column to outer column. At which point the moral of the story becomes find a way to make the interior column an LTB brace point.

RE: Rafter without fly brace?

Quote (KootK)

3) use the beam span between supports (8m) as your effective, lateral torsional buckling length for the negative moment.

4) Use stiffeners, fly braces, or whatever the heck you've gotta do to call the beam to column connection a point of full restraint for lateral buckling.

This is certainly a safe approach, however quite conservative as it ignores the restraining effect of the floor against lateral torsional buckling.

My reading of AS4100 is that you can treat restraints on the compression flange as lateral restraints, which reduces your effective length.

RE: Rafter without fly brace?

Quote:

My reading of AS4100 is that you can treat restraints on the compression flange as lateral restraints, which reduces your effective length.

I concur, this is the intent of the 'L' restraint, provided you are preventing via external means deflection of the critical flange. It can rotate, but no lateral deflection of the flange.

RE: Rafter without fly brace?

Quote (Agent666)

provided you are preventing via external means deflection of the critical flange.

What I find a bit murky is AS4100 initially defines the critical flange as the flange which will deflect the furthest if the beam was fully unrestrained, however it also allows you to simply take the compression flange as the critical flange.

In our example here the bottom flange will deflect the furthest in the unrestrained situation, but at the middle of the beam the top flange is in compression, thus you could take either the top flange or the bottom flange as the critical flange in the middle portion of the beam.

Is that the intent you think? Is it saying that in such a location you can happily restrain either top or bottom and achieve an L restraint?

RE: Rafter without fly brace?

I have known other engineers to use full depth stiffeners both sides, along with a 4 bolt cleat connection to the purlin, all in lieu of fly braces. This was apparently because a client or architect objected to the fly braces. It might work, but is not as good, and is more expensive.

RE: Rafter without fly brace?

Hokie,

Yes we do that on occasion.

RE: Rafter without fly brace?

An interesting discussion. I had a reply mostly typed up a couple of days ago but must have gotten distracted with work.... As well as being difficult to justify why you can just reduce the effective length simply because there is a moment inflection. An important bit to remember is that with live load you don't know where that moment inflection will be.

As an aside. I've been looking at fly brace economies and they don't seem that cheap where access is more difficult. Counting the number of members that need to be fabricated and installed and you can quickly find that going for a heavier section beam might work out in your favour. Of course cost of labour etc varies on region.

RE: Rafter without fly brace?

I'll elaborate on all of this stuff in a second post but, to begin with, the following.

Quote (Tomfh)

This is certainly a safe approach, however quite conservative as it ignores the restraining effect of the floor against lateral torsional buckling.

I would characterize the approach as:

1) Appropriately conservative and;

2) The only, rational approach that can be shown to be safe.

Quote (Tomfh)

My reading of AS4100 is that you can treat restraints on the compression flange as lateral restraints, which reduces your effective length.

Quote (Agent666)

I concur, this is the intent of the 'L' restraint, provided you are preventing via external means deflection of the critical flange. It can rotate, but no lateral deflection of the flange.

I believe that you're both incorrect in that interpretation on the basis that the bottom flange is the critical flange and therefor the [L] restraint provided by the floor joist is not efficient in restraining negative moment LTB (lateral torsional buckling).

Quote (Tomfh)

What I find a bit murky...Is that the intent you think? Is it saying that in such a location you can happily restrain either top or bottom and achieve an L restraint.

3) I don't believe that is the intent.

4) Regardless of the intent, I'm confident that interpretation is out of step with fundamental, LTB stability principles.

5) I think that I can de-murkify this by adding some custom commentary to the AS4100 provisions based on the fundamentals. Next post.

My feeling is that the way AS4100 is set up for LTB tends to cause designer confusion in instances where there is moment reversal within a segment/sub-segment. I sympathize.

RE: Rafter without fly brace?

So here's how I think that this should be approached with respect to AS 4100 LTB provisions. Please keep in mind that my access to the standard is limited and outdated. Patience and understanding...

1) I think that it's critical to recognize that, with moment reversal, the design effort has to bifurcate into two paths:

a) LTB rotation about a point in space below the shear center which is used for the positive moment / top flange check (sketch B below).

b) LTB rotation about a point in space above the shear center which is used for the negative moment / bottom flange check (sketch C below).

Recognizing this bifurcation is important because, for the two paths, both of the following may be different:

c) the definition of the "segment". Going forward, I'll use "segment" as being equivalent to "segment/sub-segment".

d) the definition of which flange is the critical flange. (foreshadow hint: it's always the flange furthest from the center of LTB rotation).

Path [a] is trivial for OP's situation given the tightly spaced, translational bracing [L-bracing]. As such, everything that follows pertains to path [b], negative moment LTB.

2) For negative moment checking, it must be recognized that the bottom flange is the critical flange. As shown in sketch [A] below, it's the only flange capable of meaningful lateral movement.

3) For negative moment LTB checks, "segment" = "distance between beam supports" which I assume are fully braced such that both flanges are effectively, if indirectly, braced against lateral translation. "segment" <> the spaces between joists because, for negative moment LTB, the transnational restraints provided by the floor joists do not provide efficient translational restraint to the bottom flange which is the critical flange.

4) Because "segment" = "distance between beam supports" for the bottom/critical flange, the entire bottom flange must be considered to be the "compression flange" for the purpose of negative moment LTB checking. This is not changed by the fact that the bottom flange is not in compression, and is in fact in tension, over some of its length. Viewed this way, I believe that this addresses Tomfh's "murky" problem because the bottom flange is now both:

a) The flange that would experience the most lateral translation under unrestrained, negative moment LTB checking and;

b) The compression flange under negative moment LTB checking.

5) This winding road takes us back to "unbraced LTB tength" = "span between supports" for the negative moment check.

6) As shown in sketch D below, our real world expectation is actually constrained axis buckling about the top of the beam. This usually has a higher capacity than sketch C but is a serious pain the the butt to calculate so we just go with sketch C and call that good enough.

RE: Rafter without fly brace?

Quote (Kootk )

I believe that you're both incorrect in that interpretation on the basis that the bottom flange is the critical flange and therefor the [L] restraint provided by the floor joist is not efficient in restraining negative moment LTB (lateral torsional buckling).

Floors are good at preventing overall lateral torsional buckling of continuous beams. A continuous beam with a floor attached to the top flange has a much higher buckling load than a beam with no such restraints.

Presumably that’s why AS4100 allows you to take the compression flange as the critical flange.

RE: Rafter without fly brace?

Quote (kootk)

I believe that you're both incorrect in that interpretation on the basis that the bottom flange is the critical flange and therefor the [L] restraint provided by the floor joist is not efficient in restraining negative moment LTB (lateral torsional buckling).

Maybe I'm getting the wrong end of the stick here, but I thought we were talking about the first joist into the positive moment region after a negative moment region so the top flange (the one in compression and being restrained at the point of restraint) is the critical flange? Totally agree with what you are saying if the original poster meant the first joist in the negative moment region where the bottom flange is in compression. An 'L' restraint to the non critical flange is basically 'nothing' with respect to restraint in terms of NZS3404 & AS4100.

EDIT, this is what was said, first joist in the positive region, as we'd interpreted it?

Quote (OP)

I will take the first floor joist outside each injection point in positive moment area as the segment length for negative moment capacity check.

A sketch from OP would help here!

To those of you noting the AS4100 definition is a bit wonky, take a look at the definition in NZS3404, it attempts to clarify the non compression flange being the critical flange in some instances.

RE: Rafter without fly brace?

Quote (agent666)

Maybe I'm getting the wrong end of the stick here, but I thought we were talking about the first joist into the positive moment region after a negative moment region so the top flange (the one in compression and being restrained at the point of restraint) is the critical flange?

Yes we are talking about the first joist in the positive moment region, ie where the top flange goes into compression.

Kootk is saying that the bottom flange will deflect the farthest in the unrestrained situation even in the positive moment region (he is correct about that), and he is saying therefore that the top flange can never be considered the critical flange(since it never buckles further than the bottom flange), and therefore it can’t count as a lateral restraint point. This is where our opinions part ways.

AS4100 says we may take the compression flange as the critical flange, which is suspect is the codes way of recognising that floors etc do indeed provide reliable resistance against buckling.

So the argument here is down to whether the top flange may be considered the critical flange in the positive moment region. You and I (and I believe AS4100) are saying yes. kootk is saying no, hence him saying the effective length is 8m

Any chance you could post the NZ3404 definition?

RE: Rafter without fly brace?

As far as I can tell who cares whats going on between the restraints, the restraint clarification is only based on the location of the restraint.

Having said that the critical flange is strictly defined as the flange which moves the furthest in the absence of the restraint. To determine this for sure you need to do some buckling analyses. So totally impractical for day to day design. But I see where the discrepancy is coming from now.

In terms of applying this for practical design (Keep in mind these provisions are from NZS3404 and the last time I looked at it in another thread a while back there were subtle differences when compared with AS4100), basically for the purposes of defining the critical flange for a segment with restraints at both ends the code says it is simply taken as the compression flange, end of story.

Edit - Commentary clause to go with this

RE: Rafter without fly brace?

Quote (Agent666)

To those of you noting the AS4100 definition is a bit wonky, take a look at the definition in NZS3404, it attempts to clarify the non compression flange being the critical flange in some instances.

If anybody would be willing to post snips of either the AU or NZ definitions on this, that would be peachy.

EDIT: my dream has come true...

Quote (Tomfh)

Kook is saying (correctly) that the bottom flange will deflect the farthest in the unrestrained situation, and he is saying therefore that the top flange can never be considered the critical flange(since it never buckles further than the bottom flange), and therefore it can’t count as a lateral restraint.

Not too shabby. I'll try a quick and dirty summary myself:

1) Assume fully braced (F) supports each segment end and only top flange, transnational only braced points in between (L).

2) For negative moment LTB checks, no top flange bracing will make a lick of difference to calculated capacity no matter where it's placed. The only exception is if one gives detailed consideration to constrained axis LTB which, to my knowledge, is not a part of anyone's base code/standard/software.

RE: Rafter without fly brace?

Quote (Agent66)

Having said that the critical flange is strictly defined as the flange which moves the furthest in the absence of the restraint. To determine this for sure you need to do some buckling analyses. So totally impractical for day to day design.

Or you could just follow this simple procedure.

Quote (KootK)

1) I think that it's critical to recognize that, with moment reversal, the design effort has to bifurcate into two paths:

a) LTB rotation about a point in space below the shear center which is used for the positive moment / top flange check (sketch B below).

b) LTB rotation about a point in space above the shear center which is used for the negative moment / bottom flange check (sketch C below).

Quote (Tomfh)

AS4100 says we may take the compression flange as the critical flange, which is suspect is the codes way of recognising that floors etc do indeed provide reliable resistance against buckling.

Quote (Agent666)

basically for the purposes of defining the critical flange for a segment with restraints at both ends the code says it is simply taken as the compression flange, end of story.

Yes, the critical flange here will be a compression flange. The trouble, I believe, is with the definition that you guys are using for what is a compression flange.

Quote (KootK)

4) Because "segment" = "distance between beam supports" for the bottom/critical flange, the entire bottom flange must be considered to be the "compression flange" for the purpose of negative moment LTB checking. This is not changed by the fact that the bottom flange is not in compression, and is in fact in tension, over some of its length.

For the negative bending checks, the bottom flange is the compression flange in this context, even in the middle where the moment is positive. It is a strut subject to compression and compression buckling over a length equal to the span between supports.

RE: Rafter without fly brace?

Quote (agent666)

Having said that the critical flange is strictly defined as the flange which moves the furthest in the absence of the restraint

Yes. And this is generally not the top compression flange in these types of situations. The bottom flange buckles the most within the positive bending zone.

Yet for practical design purposes (no buckling analysis) the code says take the compression (top) flange as the critical flange. This contradicts the “flange which moves furthest” premise.

Thanks for supplying NZ3404. It seems essentially the same?

RE: Rafter without fly brace?

Quote (kootk)

2) no top flange bracing will make a lick of difference to calculated capacity no matter where it's placed

These codes allows you to take the compression flange as a critical flange (clause 5.5.2), which reduces effective length and thus enhances capacity.

Rational buckling analysis also show significantly enhanced buckling capacity with restraints on the top flange.

RE: Rafter without fly brace?

Here are the AS4100 provisions for comparison Kootk:-

The definition of what is the compression flange is simply the flange under compression due to flexure at the location of a restraint.

I.e. nothing in between in terms of the moment distribution matters, nor does axial load (dealt with separately via combined actions checks and the like), the moment distribution is taken care of by the alpha_m factor, similar to Cb factor in AISC.

All the restraints give you as a factoring up or down of the length to give an equivalent effective length over which buckling occurs.

RE: Rafter without fly brace?

Thanks for posting the 4100 commentary.

It’s strange that it refers to 5.5.2 as being a “more specific” version of 5.5.1, when in reality 5.5.2 contradicts 5.5.1. I’d thought 5.5.2 was an override of 5.5.1 rather than a refinement of 5.5.1

If you follow 5.5.1 then you can’t count a laterally restrained top flange anywhere (which is what kootk is arguing). But if you follow 5.5.2 you can use a laterally restrained top flange when it goes into compression, which is what pretty much everyone does, and what the design packages do.

RE: Rafter without fly brace?

Quote (Agent666)

basically for the purposes of defining the critical flange for a segment with restraints at both ends the code says it is simply taken as the compression flange, end of story.

Right, but to view "compression" flange in the correct fashion, you first have to view "segment" in the right fashion. In our case, it plays out like this for negative bending LTB checking:

1) "segment" = the bottom flange between the beam support points where there is full rotational restraint.

2) "compression flange" = the bottom flange, spanning from support to support, because:

a) that is the flange that moves the most during bucking (constrained axis buckling about the top flange) and, practically, is the only flange capable of moving here and;

b) the bottom flange has compression in it over the length of the segment which is not changed appreciably by the fact that the level of compression varies across the segment.

Once "segment" is viewed properly, all of the provisions become internally consistent which, frankly, ought to be taken as something of a sign.

Quote (Agent666)

The definition of what is the compression flange is simply the flange under compression due to flexure at the location of a restraint.

Note that, with segment properly defined, the bottom flange satisfies this definition.

Thanks for posting the AS4100 stuff, that's a great help.

RE: Rafter without fly brace?

Quote (Tomfh)

..and what the design packages do.

I'd not put much stock in that. The clip below is from an older version of RAM S-Beam. Software follows designer practices rather than leading them.

RE: Rafter without fly brace?

Quote (Tomfh)

Rational buckling analysis also show significantly enhanced buckling capacity with restraints on the top flange.

Yes, they do. The graphs below quantify that effect for any interested parties. Cliff notes:

1) EQ2 is the north american version of the moment gradient.
2) EQ3 is a modified version of EQ2 suggested for when inflection points occur within a segment.
3) Fig6 quantifies the improvement associated with having inflection points within a segment.
4) Fig9 quantifies the benefit accrued from the slight rotational restraint supplied by a typical joist seat connection.

So, yes, there absolutely are improvements associated with these things. From my perspective, the question really becomes:

A) Do we qualitatively take these things to simply mean that the buckling mode shown in the last sketch below is impossible/impractical OR;
B) Do we use a Cb based approach to rationally asses the buckling mode shown in the last sketch below?

For me, it's path B without question.

RE: Rafter without fly brace?

Kootk, at the middle of the beam the top flange is in compression. At any section of the beam the code allows you to take the compression flange as the critical flange.

RE: Rafter without fly brace?

Quote (Tomfh)

Kootk, at the middle of the beam the top flange is in compression. At any section of the beam the code allows you to take the compression flange as the critical flange

a) I wholeheartedly believe that you are misinterpreting that code provision and;

b) At the end of the day, I don't care what any code says. A first principle understanding trumps all else for me.

In fact, I believe that it is the lack of a first principle understanding on this that is leading you and Agent666 astray.

Quote (Tomfh)

What I find a bit murky is AS4100 initially defines the critical flange as the flange which will deflect the furthest if the beam was fully unrestrained, however it also allows you to simply take the compression flange as the critical flange.

Is that the intent you think? Is it saying that in such a location you can happily restrain either top or bottom and achieve an L restraint?

Frankly, your stance on this confuses me. You yourself clearly question either:

a) What the code says and/or;
b) Your interpretation of what the code says.

Given that, I don't understand your dogged resistance to my alternate interpretation.

RE: Rafter without fly brace?

The code says you can take the compression flange to be the critical flange. The "compression flange" is invariably understood to mean the flange in compression, which is the top flange in the positive bending zone in our example.

Allowing the use of the compression flange contradicts the code’s original definition of the critical flange (the flange which buckle farther), because sometimes the compression flange does not deflect the furthest, eg our example here. As you point out, the bottom flange always buckles the farthest at every point along the beam.

I can see two possibilities:

1. Compression flanges, whilst not necessarily always being the best place to brace, are nonetheless good enough places to brace that the code allows us to consider them critical flange.

2. The code is wrong allow the use of the compression flange as the critical flange, and doesn't properly consider that the compression flange isn't always critical.

You are offering a third possibility, and saying that by “compression flange” the code writers don’t actually mean the flange in compression, they simply mean the flange which will deflect the farthest, and they never intended us to use the top compression flange in examples like this one. If that’s what they mean, then reference to “compression flange” is entirely circular and redundant, as it reduces back to the original definition of critical flange as being the flange which deflects the furthest. It would also be an extremely misleading clause as most everyone understands “compression flange” to mean the flange under compression.

RE: Rafter without fly brace?

@Tomfh/Agent666,

Quote (Tomfh)

It would also be an extremely misleading clause as most everyone understands “compression flange” to mean the flange under compression.

And indeed it is.

I have a dream. And I propose that we do it together. First I need to bash the Aussie steel code however. Please forgive me that as, no doubt, there is some national pride involved.

When I look at the Aussie steel code on LTB, this is what I see:

1) Code provisions that do a good deal more designer spoon feeding than you see in North American codes. Is that good? Bad? Prudent? Insulting?

2) On balance, I would have to say that the spoon feeding is prudent. Structural engineers are notoriously bad at stability because, frankly, the math is well above our comfort zone on average. I've worked with a wide variety of designers in Canada in the US and my experience is that mistakes get made often. And I suspect that an Aussie style spoon feeding would improve that situation a great deal.

3) In my opinion, the Aussie code falls on it's face with respect to exactly this issue: beams with inflection points. Good for simple spans; uncommonly good for cantilevers; misleading for for beams with moment reversals. The trouble with spoon feeding is that it's near impossible to make it perfectly applicable to all situations. It is, after all, an attempt to make a very complex thing simpler than it really is.

So here's my my dream:

4) I convince you guys that my way is the right way from a purely theoretical standpoint. Maybe I pull that off and maybe I don't. I feel that my odds are pretty good if you guys give me some room to run and make of point of being flexible. And, if I can't convince you guys, that will be appropriate vetting to prevent me from pursuing what would come next.

5) We attempt a rewrite of the Aussie LTB provisions to sort this out. I expect this will be quite a challenge given that a) some smart cookies obviously composed the original and b) it would require great linguistic precision and the ability to anticipate the ways in which things may be misinterpreted by designers.

6) We put our proposed rewrite in front of the Aussie steel code steering committee, whomever the heck they be.

7) For the rest of our days, we vaingloriously point to the Aussie LTB provisions and say "hell yeah, we're the dudettes that got that written properly".

Any takers?

RE: Rafter without fly brace?

Quote (Tomfh)

You are offering a third possibility, and saying that by “compression flange” the code writers don’t actually mean the flange in compression...

Not quite. What I'm saying is really that you and Agent666 are misinterpreting what the code writers intended in their reference to the flange in compression. I think that what they really meant was something along these lines:

STEP 1: define "segment" for your LTB check being mindful of whether you're checking LTB rotation about a point in space above the shear center or a point in space below the shear center. For a point in space below the shear center, the segment(s) are the gaps between the joist connections. For a point in space above the shear center, the segment is the distance between the columns.

STEP 2: define "compression flange" for each segment being LTB checked as any flange exposed to compression force anywhere along its length. In the context of our negative bending check, this will make both flanges "compression flanges" for the segment defined as the bottom flange between columns. In support of this definition, see the first sketch below. Clearly, either flange could be taken as the compression flange. And that makes sense because what really matters is, just as we expect, which flange would move the most laterally. After all, it is that lateral motion that is the "buckling". The compression flange definition is, and always was, just a convenient and imperfect mnemonic to help us properly identify the critical flange.

STEP 3: define "critical flange" keeping in mind the definitions of "segment" and "compression flange" described above. Obviously, the segment that we're interested in here is the bottom flange segment between columns that will govern for a negative bending check where the point of LTB rotation is above the shear center. Following Aussie code logic, you've got two choices:

3a) define the critical flange as that which would move the most. We're all in agreement that this would be the bottom flange. Check.

3b) define the critical flange as the flange in compression. Per the definition in step 2, both flanges are in compression for this segment and this definition solves nothing. So back to 3a it is.

Viewing things this way leads to the following improvements in this situation:

1) The two critical flange definitions -- displacement vs compression - are no longer in conflict. The compression flange definition is just useless for beams with inflection points which I propose is nothing more than a shortcoming of the Aussie steel code.

2) The code writers no longer appear to be incompetent.

3) Nothing in cyclical/recursive.

These things strike me as circumstantial evidence loosely supporting my hypothesis that the code writers saw things defined as I've defined them above.

RE: Rafter without fly brace?

@Agent666/Tomfh:

Knowing a detail of how LTB is checked in your part of the world for beams with inflection points would help me greatly here. For me, it proceeds like this:

1) If my beam has inflection points, I accept that I'll have to do two separate LTB checks.

a) LTB rotation about a point in space below the shear center. Usually this is the positive bending check where top flange faux buckling is the name of the game.

b) LTB rotation about a point in space above the shear center. Usually this is the negative bending check where bottom flange faux buckling" is the name of the game.

2) I work out the segment definitions and bracing conditions for each of the two paths, acknowledging that they may be different.

4) I do the LTB check that would have the top flange faux buckling.

5) I do the LTB check that would have the bottom flange faux buckling.

Do you guys do a similar, bifurcated check where negative bending LTB and positive bending LTB are checked separately? Or do you tackle it in a single checking procedure?

RE: Rafter without fly brace?

If you can prove theoretically that the top flange in our example may not be used as a lateral bracing point to reduce effective length then you would of course be fully justified in criticising clause 5.5.2 (or at the very least how it’s universally interpreted), as it’s precisely where designers use the clause. If you are right, maybe the clause should forbid allowing the compression flange as critical flange if moment reverses within the segment?

All that being said, merely showing that the bottom flange buckles farthest as you have been doing is a long way short of proving your case that the top flange within the positive bending zone is an ineffective point to brace, ie that designers shouldn’t be taking it as critical flange.

Remember too, the whole “critical flange” thing is just spoon feeding in the first place. In reality there’s no such thing as “critical flanges” and “non critical ages”. They’re just design rules telling designers where to brace.

If however you prove your case that means everyone is doing it wrong, and that should be rectified in the code.

RE: Rafter without fly brace?

Quote (Tomfh)

All that being said, merely showing that the bottom flange buckles farthest as you have been doing is a long way short of proving your case that the top flange within the positive bending zone is an ineffective point to brace, ie that designers shouldn’t be taking it as critical flange.

Agreed. As a next step, when you have some free time, please review the attached article by Yura. You'll find that it agrees with my stance. And that's no accident given that much of my understanding of LTB has come from reading Yura's other works. So it's a bit incestuous in that way. Still, if you digest that article and still find yourself not agreeing with my position on this, please report back so that we might reconcile our respective opinions. Who knows, perhaps all this time while I've been claiming that you've been misinterpreting your code, I've actually been misinterpreting Yura.

I've included some samples of the article below to whet your appetite for more. Among other things, they suggest the use of Cb = 1.14 as a simple way to deal with most every practical inflection point beam bracing situation out there. Good stuff. Also, while much of the article deals with designers inappropriately using IP's as brace points, the article really is about a great deal more than that. Namely, the bracing and buckling of beams with moment reversals in general.

RE: Rafter without fly brace?

Quote (Tomfh)

If you are right, maybe the clause should forbid allowing the compression flange as critical flange if moment reverses within the segment?

Yeah, that would be a simple fix. You've kinda made short work of what I had expected to be a difficult exercise in rewriting.

RE: Rafter without fly brace?

Just to clarify though, no one here is saying to the take the inflexion point as a brace point per se (as agent666’s blog shows, it provides no actual restraint), we are taking about talking about using purlins and joists BEYOND the inflexion point as lateral restraints, which is a quite a different concept.

RE: Rafter without fly brace?

Quote (Tomfh)

..we are taking about talking about using purlins and joists BEYOND the inflexion point as lateral restraints, which is a quite a different concept.

From my perspective, these things are very similar concepts.

Concept #1: assume IP points represent full LTB brace points. False because the cross section can rotate about the shear center at such points.

Concept #2: assume lateral braces just beyond IP points represent full LTB brace points. False because the cross section can rotate about the lateral braces at such points.

#2 is obviously an improvement in that any capacity short coming will be lessened. It appears to be very much the same conceptual misunderstanding however.

RE: Rafter without fly brace?

Quote (Tomfh)

as agent666’s blog shows, it provides no actual restraint

Interestingly, you'll find that Yura tackles the exact same scenario that Agent's blog post does. A salient takeaway from that example is that a lateral brace placed at the IP also does little to restrain LTB. More precisely, LTB is greatly improved for rotation about a point above the shear center and improved about 10% for rotation about a point below the shear center.

RE: Rafter without fly brace?

Hi All,

This is an awesome discussion, I truly am learning a ridiculous amount as a 2nd year graduate.

AS4100 is currently under revision and maybe this 'murky' clause will be rewritten or clarified. Coming out of uni, they are teaching the points that Tomfh and Agent666 are putting forward in regards to designing the critical flange as the compression flange.

What do the other design codes around the world say on this matter? Yes we've looked at AS and NZS but they might as well be the same code except for the few differences pointed out above.

RE: Rafter without fly brace?

All -

I just want to pipe in here briefly.... The concept of whether "point of inflection" should be used as a point of bracing or not is a question that I dealt with for years and years. My thoughts on the subject:

1) The software company I worked for did NOT consider point of inflection as a point of bracing. This is because of lectures from Yura and such that members of our team had attended over the years. It is now explicitly codified in the AISC codes.

2) I would speak to a number of practicing engineers who were frustrated by this. And, they wanted us to automate the point of inflection as a brace point. I would point out the code references (or the notes from stability bracing seminars that were the basis for our company's decision). They'd get annoyed at the "code geeks", "academics", or young engineers (like me at the time) who thought they knew better than them who had been designing like this for years.

3) At first, I would merely point out that they could override the default values in the program if they wished. Eventually, once I'd really researched the topic better, I would point out the same seminar notes also addressed the issue. Joe Yura (if I remember correctly) wrote in the notes, a good explanation for why the "rule of thumb" of using the point of inflection hadn't been a problem in the past and why some older engineers where so attached to it. He had pointed out that if this is done while using a Cb = 1.0, then that conservatism would negate much of the unconservatism in the unbraced length. Therefore, I would kindly suggest to the users who complained about this that if they chose to still consider the point of inflection (based on their personal engineering judgment) that they should probably check to see if the program was using a Cb of greater than 1.0. If so, then probably should use a value equal to 1.0 to offset.

I'm not an expert on what the code provisions where before the Cb factor came into use as my engineering knowledge began with the 1989 green book. However, my impression was that some of the older engineers had the attitude of "great... the code writers added lots of extra complexity with the Cb. This, in turn, requires us to add more complexity with how determine unbraced lengths for the bottom flange".

RE: Rafter without fly brace?

Hey Kookt,

We are back on this topic again. Which I see as a good thing as I believe there is plenty of misunderstand around. And certainly a bunch of learning for me needed. From what I can see you have are fairly on top of things, but I do have one question about one of your statements. (And I believe you made a statement of similar effect in the last thread on a simlar topic.)

Re critical flanges:

Quote (Kookt)

a) that is the flange that moves the most during bucking (constrained axis buckling about the top flange) and, practically, is the only flange capable of moving here and;
The latter part of "practically, is the only flange capable of moving here" seems to assume the top flange is restrained which goes against the definition:
"The critical flange at any cross-section is the flange which in the absence of any restraint at that section would deflect the farther during buckling.

Your statement seems to mistinterpret the code and is a little bit recursive if you determine the critical flange in the context of existing restraints. Could you possibly elaborate? Am I just misinterpretting your statement. Thanks in advance.

RE: Rafter without fly brace?

Quote (Kootk)

From my perspective, these things are very similar concepts.

In my opinion they are fundamentally different. An inflection point provides no actual physical lateral restraint. A lateral restraint however - whilst not providing twist restraint - nonetheless significantly inhibits the lateral component of the lateral torsional buckle. It is harder for the beam to buckle. The beam can non longer just kick out sideways.

Quote (kootk)

A salient takeaway from that example is that a lateral brace placed at the IP also does little to restrain LTB.

I don't agree with that either. It inhibits the overall lateral component of the buckle, and forces the beam into a more difficult buckling mode. Run some buckling analyses....

RE: Rafter without fly brace?

Tomfh -

I agree that inflection point and brace point are two very different concepts. Though they have been (historically) mixed together in the past. I think the current codes have them pretty separate. However, in the thinking of many engineers they're similar.... Not because of first principles, but because of past design practice.

Now, we're probably getting to the point where engineers who were educated in the mid 80's or earlier may no longer be practicing. However, there are LOTS of people who worked under them for years that still conflate the two concepts. Again, not because of first principles, but because they learned under people who mixed the two concepts together.

Also, when the code calls the variable the "unbraced length of compression flange", there is an obvious reason why folks would mix the two concepts. Because the terminology suggests that when the flange ceases to be in compression, then it may not contribute to the unbraced length. Now, that's merely a terminology issue that doesn't have to do with first principles. But, I can see how that leads to confusion.

RE: Rafter without fly brace?

Quote (Tomfh)

I don't agree with that either. It inhibits the overall lateral component of the buckle, and forces the beam into a more difficult buckling mode. Run some buckling analyses....

What's there to disagree with? Yura did the buckling analysis in the article that I provided and arrived at the conclusion that IP bracing for that example amounted to a paltry, 10% improvement. Perhaps you should run some buckling analyses and report back. So far, this is all just me digging up the quantitative stuff.

RE: Rafter without fly brace?

Quote (kootk)

What's there to disagree with?

It's more than 10%. But put that aside for one second - Jura says it's not effective to laterally brace a flange without providing twist restraint. He (and you) say you can only count points of twist restraint. If that's true, then AS4100 is wrong to allow lateral bracing (without twist restraint) of any flange, regardless of whether it's the critical flange. The question of which flange is the critical flange is surely a moot point if a lateral (pin) brace alone fixed to a flange is assumed to provide no reduction of effective length?

RE: Rafter without fly brace?

Quote (JP)

Joe Yura (if I remember correctly) wrote in the notes, a good explanation for why the "rule of thumb" of using the point of inflection hadn't been a problem in the past and why some older engineers where so attached to it.

Cb = 1 surely is one reason for the dearth of consequences and dovetails nicely into the stuff in the Yura article suggesting that one could safely cover most any case with Cb = 1.14.

Along similar lines, consider:

1) When the top flange is restrained laterally, LTB is basically the bottom flange kicking sideways.

2) The bottom flange kicking sideways is substantially resisted by the bottom flange acting as a girt.

3) We assume that the bottom flange is pinned at the ends for girt action. Often, it's not.

4) We assume that the cross section is free to warp at thee ends for girt action. Often it's not.

These things introduce a lot of conservatism into the mix and aren't usually accounted for in non-FEM analyses. Basically, the only way to get a top braced, multi-span member to LTB is:

5) have adjacent spans both go critical for LTB and;

6) have adjacent spans LTB buckle in opposite directions.

That's a pretty tall order of course. My gut feel is that it's next to impossible to get a multi-span continuous beam to LTB buckle if it has full restraint at the supports and closely spaced lateral restraint anywhere on either flange.

RE: Rafter without fly brace?

Quote (Tomfh)

He (and you) say you can only count points of twist restraint

Not quite. What we're saying is this:

1) You can only count on points of twist restraint to define the end points of the "segment" that undergoes LTB buckling. Without this, the whole thing breaks down mathematically because you lose the boundary conditions fundamental to the problem. Technically, you can go full restraint on only one end and still be in compliance but that's introducing an extra layer of fanciness that we can surely do without for this discussion.

2) You can absolutely count on points of lateral, non-twist restraint to shift the point of LTB rotation closer to the member shear center and thereby improve capacity, if not eliminate twist altogether. This is the constrained axis buckling that I must have mentioned a half dozen times by now. In terms of Yura's work, this is the graph shown below and its brethren from the article where the benefit of lateral only bracing is acknowledged and quantified.

Quote (Tomfh)

The question of which flange is the critical flange is surely a moot point if a lateral (pin) brace alone fixed to a flange is assumed to provide no reduction of effective length?

This is an interesting question / observation. I'll attempt to answer this in my next post, in response to a question from human909.

RE: Rafter without fly brace?

Quote (KootK)

Not quite.

in summary Yura says this:

Quote (Yura)

The unbraced length that should be utilized in design should be the spacing between points with zero twist.

It seems to agree with your approach

RE: Rafter without fly brace?

Quote (KootK)

My gut feel is that it's next to impossible to get a multi-span continuous beam to LTB buckle if it has full restraint at the supports and closely spaced lateral restraint anywhere on either flange.

Initially you said laterally bracing the top flange provides negligible increase in capacity unless you also provide twist restraint, hence your advice for OP to take 8m as the buckling length. Now you say such lateral bracing makes it next to impossible for the beam to LTB buckle?

RE: Rafter without fly brace?

Quote (human909)

Your statement seems to mistinterpret the code and is a little bit recursive if you determine the critical flange in the context of existing restraints. Could you possibly elaborate? Am I just misinterpretting your statement. Thanks in advance.

I believe that the confusion has come about because the Aussi-clause below is also in serious need of an overhaul. More so, actually, than even the "compression flange" business because this clause will be egregiously misleading, in a theoretical sense, 100% of the time. That it will often lead designers to make the right choice anyhow is little more than coincidence.

Quote (AS4100)

The critical flange at any cross-section is the flange which in the absence of any restraint at that section would deflect the farther during buckling.

I've been reticent to get into this part of things because it requires going deep, deep into the theoretical weeds of the stability swamp. Now that you've asked the question, however, it's time.

1) As designers, we tend to think that there exist a handful of buckling possibilities for any particular member and that, once those have been checked, buckling is no longer possible. This is true in a practical/functional sense but is not true in a theoretical sense. Theoretically, there are an infinite number of possible buckling modes. Like a buckling multi-verse of sorts.

2) Each possible buckling mode is associated with a particular strain energy that is required for the member to assume the proposed buckled shape. What we mean by "critical buckling mode", is the next buckling mode in the infinite series that would be associated with the lowest strain energy. As in all things, nature strives to minimize energy.

This is complicated by the fact that the intervals between different buckling modes is not uniform. The 902 nd buckling mode might require 20X the strain energy of the 901 st buckling mode. But, then, the 903 rd buckling mode might require only 1.05X the strain energy of the 902 nd buckling mode. This is why I use the dual path, bifurcated checking approach that I mentioned previously for beams with inflection points. For such beams, I can't tell by inspection whether positive bending LTB or negative bending LTB governs. So I check both. And I pray to the powers that be that the 904 th buckling mode is miles off in the distance as far as strain energy goes.

3) For the purpose of this discussion, the important takeaway of #2 is that all buckling checks must start with the designer assuming a critical buckling mode. Not knowing... assuming (hopefully based on good judgement). This is what I did with the sketch below, taken from the beginning of this thread.

4) The assumed buckling mode shape from #3 must pay homage to the physical restraints that form the boundary conditions of the problem (lateral top flange braces here). Otherwise, we're no longer discussing an LTB mode shape that has any bearing on our real world situation. Again, this is what I did with the sketch below, taken from the beginning of this thread.

5) In the AS4100 procedure, they end with finding the assumed LTB mode shape (critical flange) rather than starting with it. And, in my opinion, this is a serious mistake and is what leads to things having a recursive, chicken and egg feel to them. There's just nothing meaningful to check in the world of LTB until AFTER an LTB buckling mode shape has been assumed.

6) The AS4100 business about the "absence of any restraint" seems to lead designers to examining a case where all restraints are removed as a means of establishing the LTB buckling shape for a case when all of the physical restraints are present. How much sense does that make? None. And, in spite of the way that the provision is written, I'm sure that it's not what anyone actually intended.

7) The AS4100 provision could be revised, quite easily, as follows:

a) The critical flange at any cross-section segment is the flange which in the absence of any restraint at that section would deflect the farther during buckling given the lateral and torsional restraints present. OR;

b) The critical flange at any cross-section segment is the flange which, in the absence of any additional restraint at that section contemplated by the designer would deflect the farther during buckling. given the lateral and torsional restraints present.

Modest changes but enormous implications. It's minor but we also shouldn't be speaking in terms of "cross sections". Rather, we should be speaking in terms of "segments" because LTB is a linear phenomenon rather than a point phenomenon.

RE: Rafter without fly brace?

Quote (Kootk)

6) The AS4100 business about the "absence of any restraint" seems to lead designers to examining a case where all restraints are removed as a means of establishing the LTB buckling shape for a case when all of the physical restraints are present. How much sense does that make? None. And, in spite of the way that the provision is written, I'm sure that it's not what anyone actually intended.

What is intended then?

RE: Rafter without fly brace?

Quote (KootK)

My gut feel is that it's next to impossible to get a multi-span continuous beam to LTB buckle if it has full restraint at the supports and closely spaced lateral restraint anywhere on either flange.

Quote (tomfh)

Initially you said laterally bracing the top flange provides negligible increase in capacity unless you also provide twist restraint, hence your advice for OP to take 8m as the buckling length. Now you say such lateral bracing makes it next to impossible for the beam to LTB buckle?

1) The buckling length for calculation purposes should be taken as 8m, the length between points of twist retraint.

2) In terms of theory and standard calculation procedures:

a) Normal code procedures usually do not take account of constrained axis LTB and, thus, offer no calculation benefit associated with the top flange lateral restraints.

b) If one desired additional capacity at the expense of additional complexity, one could consider constrained axis buckling to get more capacity as a result of the top flange lateral restraints.

3) In terms of real world behavior for the system at hand, I am indeed skeptical that LTB poses a real threat. That said, the name of the engineering game is what we can prove, not what we suspect.

I see all this as being internally consistent.

RE: Rafter without fly brace?

Quote (Tomfh)

What is intended then?

It's always dangerous to attempt to read minds but my guess is as shown below. I also speculate that this was introduced as a way to deal with the usual confusion at cantilevers. And then, as always, came the unintended consequences...

Quote (KootK)

a) The critical flange at any cross-section segment is the flange which in the absence of any restraint at that section would deflect the farther during buckling given the lateral and torsional restraints present. OR;

b) The critical flange at any cross-section segment is the flange which, in the absence of any additional restraint at that section contemplated by the designer would deflect the farther during buckling. given the lateral and torsional restraints present.

RE: Rafter without fly brace?

Quote (Kootk)

3) In terms of real world behavior for the system at hand, I am indeed skeptical that LTB poses a real threat. That said, the name of the engineering game is what we can prove, not what we suspect.

It’s easy enough to prove with a finite element buckling analysis. Or a real world test.

Quote (Kootk)

It's always dangerous to attempt to read minds but my guess is as shown below

I don’t agree with second guessing the code like this and arguing that by black they really mean white. I think that by “compression flange” they simply mean the flange in compression, and that by “absence of restraint” they mean just that, as opposed to the opposite - the presence of the restraints.

RE: Rafter without fly brace?

Black vs white seems an extreme characterization. I'd say that it's the same fundamental intents articulated with greater precision.

RE: Rafter without fly brace?

Thanks for your reply KootK. That answers my question and I think we are largely on the same page.

Quote (KootK)

b) The critical flange at any cross-section segment is the flange which, in the absence of any additional restraint at that section contemplated by the designer would deflect the farther during buckling. given the lateral and torsional restraints present.
KootK for AS4100 revision!

That would be a big change in the general approach of AS4100 but it makes much more sense.

Quote (KootK)

Modest changes but enormous implications. It's minor but we also shouldn't be speaking in terms of "cross sections". Rather, we should be speaking in terms of "segments" because LTB is a linear phenomenon rather than a point phenomenon.
Very true and very odd that this terminology is present.

Quote (KootK)

6) The AS4100 business about the "absence of any restraint" seems to lead designers to examining a case where all restraints are removed as a means of establishing the LTB buckling shape for a case when all of the physical restraints are present. How much sense does that make? None. And, in spite of the way that the provision is written, I'm sure that it's not what anyone actually intended.
Wow. I was going to disagree with you and agree with Tomfh. But now I'm second guessing myself. Your intepretation seems to turns a fair bit of the interpretation of AS4100 on its head IMO. But like you argue, it makes more sense from real engineering perspective. I'm going to have to dwell on this one.

RE: Rafter without fly brace?

Quote (Human909)

Very true and very odd that this terminology is present.

Either that or the code simply means what it says.

RE: Rafter without fly brace?

Quote (Tomfh)

Either that the code simply means what it says.
But what it says isn't entirely clear. As has been exhibitted in this thread. But you could be right here. Determining the force requirements for the critical flange restraints requires defining a critical flange at a cross section not a segment.

Sorry that I'm sitting on the fence a bit here. (When I've been in doubt over buckling, I jump over to buckling anaylsis software to help check my concerns.)

RE: Rafter without fly brace?

Quote (human909)

Determining the force requirements for the critical flange restraints requires defining a critical flange at a cross section not a segment.

I disagree with that as a defense of the original verbiage. You could have just as easily said:

Determining the force requirements for the critical flange restraints requires defining a critical flange at a cross section within the segment being braced.

In fact, I would argue that this would be more rational given that any meaningful determination of a brace force has to give consideration to the length of the thing (segment) being braced. Even the ridonkulously simplified 2.5% business is really something similar to:

[anticipated misalignment over segment length]/[segment length] = 0.025

Quote (human909)

Sorry that I'm sitting on the fence a bit here.

Jump the fence until your pants split and apologize for nothing. The largest impediment to productive discourse is folks holding their tongues until they're 107% confident in their opinions. I say jump in the pool at 60%, act like you own the place at 85%.

Quote (mrlm)

This is an awesome discussion...

Right?? It's like the Thrilla in Manilla of 2019 LTB discussions. And it is that because you've got some bold people here willing to put their egos at risk to defend their beliefs vigorously. Welcome to the conversation.

RE: Rafter without fly brace?

Quote (KootK)

The largest impediment to productive discourse is folks holding their tongues until they're 107% confident in their opinions. I say jump in the pool at 60%, act like you own the place at 85%.
I definately agree with you on this one. I've learn by vigorous debate and exploration. I make claims based on my gut and then dig up the evidence to prove it! But I'm going to have to give this more pondering than I currently have time for before I get off this uncomfortable fence.

Don't worry. I'll remember this post of yours for the future and I'll endevour to point out your mistakes when I'm only 60% sure.

RE: Rafter without fly brace?

Quote (KootK)

Right?? It's like the Thrilla in Manilla of 2019 LTB discussions.

Maybe for 2019, but this is no "Concrete Retaining Wall - Opening Corner R/F" or "Concrete Shear Friction Black-Box/Magic Voodoo".

RE: Rafter without fly brace?

Good one, winelandv. Maybe after the NTSB report on the Florida bridge, we should have another brawl about the elusive magic of shear-friction.

RE: Rafter without fly brace?

Quote (hokie66)

Maybe after the NTSB report on the Florida bridge, we should have another brawl about the elusive magic of shear-friction.

Can you give me a brief rundown on show shear friction is related that? Sounds like something I might be interested in.

RE: Rafter without fly brace?

KootK,

You don't want to read through 13 threads of over 200 posts? Curious.

But I kid. Long story short - Design was using shear-friction to pass horizontal component of truss web member through a cold joint. At least, that's my understanding. But I'll be honest, I've only been skimming the numbers/analysis posts for the last 3 months. hokie66 can hopefully describe it better.

RE: Rafter without fly brace?

Just heading back to this thread and catching up after a break and missing like 100 replies it seems, not all the way through it yet but need to point out that the following interpretation is actually incorrect.

Quote (kootk)

1) "segment" = the bottom flange between the beam support points where there is full rotational restraint.

This is not how a segment is defined in the code. A segment is just the part of a member (member is the entire member consisting of several segments potentially), defined as follows between any type of restraint be it L/F/P/U. In a positive flexure region with L restraints the segment is between the two L restraints.

I'll get through the remainder of the thread at some point...

RE: Rafter without fly brace?

Quote (Agent666)

...need to point out that the following interpretation is actually incorrect.

Prove it. I believe that it is in fact your interpretation that is in error. And I've supplied a good deal of material above to substantiate that claim.

Moreover, after all that has transpired here, is it really appropriate for us to be taking the verbiage of any of this AS4100 section as gospel? I feel that we're already a couple of light years past having concluded that this bit of AS4100 is flawed in a number of respects. To borrow from your blog: engineers vs sheep.

Quote (Agent666)

I'll get through the remainder of the thread at some point...

At the least, I'd recommend reading the Yura article if you haven't already.

RE: Rafter without fly brace?

Don't have time right now before work. But something someone above said set off a eureka moment in my brain & made it perfectly clear how the 5.5.1 clause and subsequent clause is to be interpreted with respect to the cross section (as opposed to segment vs member) nomenclature it uses, no need to change it to suit your interpretations. It's perfectly clear as it's written if you think about how its taught, documented in literature from this part of the world, and interpreted/used etc. This is the intent of the authors, because some of them are still writing and teaching it (like Charles Clifton). I'll post back after work when I have more time, hopefully you can hold your excitement till then.

I don't disagree with many of the other theories put forward, but this is about the exact interpretation and hence intent of these clauses.

RE: Rafter without fly brace?

Quote (Agent666)

I'll post back after work when I have more time, hopefully you can hold your excitement till then.

No rush. My excitement will hold for months.

RE: Rafter without fly brace?

Kootk, you really should read AS4100 before you explain it to everyone.

RE: Rafter without fly brace?

Quote (Tomfh)

Kootk, you really should read AS4100 before you explain it to everyone.

1) I have an older version of AS4100 and have read that.

2) I have some steel texts based on newer version of AS4100 and have read those.

3) I asked you and Agent666 to share the recent versions of the AS4100 so that I could participate more meaningfully in this discussion. So, if I'm missing information, that's on you.

4) If your version of AS4100 has some magic bullet clause that I haven't seen yet, and would refute my arguments, produce it. Something tells me that you already would have if it existed.

5) I think that it's poor form to deny my right to participate in this discussion just because:

b) I'm not writing from Canberra and;

a) You're unable to settle this debate as you'd like by way of logical argument.

6) It kinda feels as though we're heading back into this territory again, as shown below: Link.

7) If you don't value my input here, then stop engaging with me. I'm happy to continue the conversation with only those who would wish to continue it with me.

RE: Rafter without fly brace?

Quote (Kootk)

1) I have an older version of AS4100 and have read that.

2) I have some steel texts based on newer version of AS4100 and have read those.

3) I asked you and Agent666 to share the recent versions of the AS4100 so that I could participate more meaningfully in this discussion. So, if I'm missing information, that's on you.

4) If your version of AS4100 has some magic bullet clause that I haven't seen yet, and would refute my arguments, produce it. Something tells me that you already would have if it existed.

The relevant clauses, definitions, and underlying principles have been around since the first edition of AS4100, and indeed well before that, so your "old" copy should allow you to contribute.

Quote (Kootk5)

5) I think that it's poor form to deny my right to participate in this discussion just because:

No-one's denying your right to contribute. I'm merely asking that you familiarise yourself with AS4100 before telling us all what's wrong with it, and before telling us what's wrong with how it's taught, understood, and practised.

AS4100 does not view segments (and sub segments) the way you do. It is not wedded to Yura's (very general) advice to only count points of full twist restraint.

If you feel AS4100 is "flawed", then show how it is. You would need to show that AS4100 as written overestimates buckling capacity. If you can do that it would be a very important contribution.

Quote (Kootk)

You're unable to settle this debate as you'd like by way of logical argument.

The argument is that lateral restraints, whilst inferior to full restraints, do nonetheless enhance lateral torsional buckling capacity and that therefore AS4100 is justified in allowing designers to consider them.

RE: Rafter without fly brace?

This post will concentrate on stating exactly how the code requirements are intended to be interpreted. They might not reflect other realities, but they are a set of rules that is intended to result in a lower bound capacity being determined.

Firstly I wanted to say, there are some people who are fundamentally misinterpreting the AS4100/NZS3404 provisions in this thread and twisting the words to their own related but incorrect interpretations. I suspect this reply will maybe be meet with further disagreement and requiring endless proofs, which is fine.

I feel sometimes threads on lateral stability sometimes devolve into an argument a little like trying to convince a flat-earther that the world is round or vice versa, despite the common knowledge and education systems and so forth (including real proof) having known for a few centuries that the world is in fact round. No matter of proofs will convince the other side of the argument, this is a fact. I don't mean this to be derogatory at all to those on the alternative side of the debate, but sometimes everyone is wrong about something and this is one of those times I feel with people who have never used the AS/NZS standards trying to say we're applying the provisions which we have grown up with all wrong.

First a bit of background, I was taught steel design by John Butterworth, who was on the original NZS3404 1997 standards committee, he died a few years ago so I cannot ask him for clarification/proof/confirmation or other such things that people contributing to the thread are asking for. More recently I've also worked with a lot of people who have been taught steel design by Charles Clifton who was also on the 1997 standards committee when he was working for HERA. He currently teaches at the University of Auckland.

Now I like to think those guys therefore know what they are on about, and teach the standard in the intent it was meant to be interpreted without any twisting of words being required. After all they wrote and contributed to the standard as it is today. Now while those names might not mean anything to anyone outside of New Zealand, they were and are quite well respected in NZ, having taught generations of Engineers.

No doubt as other Aussies/NZ'ers who have contributed can attest to having been taught, and interpreted the provisions of the standard in the same manner I'm outlining below by other eminent people from this part of the world in the steel/stability world like Nicholas Trahair or Mark Bradford, etc, etc.

TLDR - Believe people who study and work in NZ and AU would know how to correctly apply their own code provisions.

Firstly some background/clarification on definitions so we are talking AS/NZS nomenclature (note all taken from NZS3404, but I'm sure they are similarly defined in AS4100).

Firstly let's look at a support, basically boils down to F or P restraint.

Definition of a member, basically boils down to a segment or number of segments:-

Role and definition of a segment (please note the use of 'cross section' here, more on this later when we get to the critical flange definition):-

Definition of a cross section:-
Well one isn't included, but it's fairly obvious based on the segment definition and the language in the entire remainder of the standard that 'cross section' is actually simply a point along the member where you may apply a restraint or evaluate the member or section capacity.

Definition of critical flange

THE IMPORTANT BITS OF INTERPRETATION ON THE ROAD TO CRITICAL FLANGE DEFINITION IN ACCORDANCE WITH AS4100/NZS3404:-

1 - A member is the physical member between supports with F or P restraints, or basically also saying you need F or P restraint at supports

2 - A member can be made up of a number of segments with F, R, L or U restraints at segment ends

3 - The member capacity is determined on a segment by segment basis

4 - Cross section means a point/location at the ends of a segment where a restraint is applied

5 - Critical flange is defined as the flange at any cross section (i.e. at the exact location of the restraint) which in the absence of a restraint at that cross section would deflect the furthest, which one deflects the furthest is determined usually by applying either the requirements of 5.5.2 or 5.5.3. Basically 5.5.2 says at that particular location of the restraint, if the top flange is in compression (for a segment with restraint at both ends) then the critical flange is the top flange. What goes on beyond the location of the restraint is irrelevant for assessing this (I feel this is the point people are missing for applying these provisions).

This is how the requirements are applied and intended to be applied and how they are taught by the people who wrote the standard, etc, etc. You can have an alternative view, but in this particular case you would not be correct.

I'm guilty of not using the correct terminology, the reference to the cross section in the definition means just that. Consider a small slice of the members length as the cross section. So the definition of the critical flange is not based on looking at a member or segment and seeing if it were to buckle as an entire member or segment to see which flange goes furthest. I'm guilty of saying this I think earlier on in the thread (I didn't read back through the first bit as its pretty heavy going!).

For application of the requirement for defining the critical flange all you are doing is looking at the location of the restraint in isolation and classifying the cross section based on the clause 5.5 criteria based on which flange is the compression flange typically as noted in 5.5.2 (though can be both the tension and compression flange for a restraint on a cantilevered end as noted in 5.5.3).

This is the way it is taught, interpreted, used, a theme noted by several posters here. There is no magic about it or mystery. I think in my brain when I read the criteria for critical flange I convert cross section to mean segment as some others have in an effort to understand how to apply the provisions. But this isn't the case if you fully want to apply it as intended. It says cross section for a specific reason.

I certainly always apply it based on the actual cross section and forces present only at the location of the restraint, as does everyone else who I've ever run into who actually practices in AS/NZS. I'm sure the other posters will back me up if I say this is it, anything else is incorrect. Tomfh and others have tried to explain how to interpret, or at least say other interpretations are not correct.

The rest of the length of the segment could be in a big black box for all I care for applying these provisions, you don't need to know what is going on along the segment. It is 100% irrelevant for application of the restraint/critical flange requirements. You only need to know the compression flange at the point of restraint.

What goes on along the member is allowed for elsewhere as is member imperfections/residual stresses/moment distribution in the form of the alpha_m and alpha_s factors.

I would point out when making comparison regarding different codes and people saying we're all doing it wrong down in this part of the world. The AS4100/NZS3404 curves are far more conservative than AISC curves for lateral torsional buckling, or alternatively the AISC curves are far less conservative than the AS/NZS capacities. So maybe you nothern types are doing it wrong, a debate for another day perhaps..... All I know is if designed correctly following your code of choice, shit shouldn't fall down.

My understanding is that this is because the AS/NZS curves are scaled to all be lower than experimental results (the 0.6 factor in the alpha_s calculation is responsible for this). As opposed to AISC which takes more or less an average path through all the experimental data, accepting that some real members could in fact have a lower capacity than predicted by the code. For example, here's something I prepared earlier comparing the capacity between AS\NZS and AISC codes for the same member/situation:-

Quote (Tom...)

You would need to show that AS4100 as written overestimates buckling capacity. If you can do that it would be a very important contribution.

RE: Rafter without fly brace?

Agent,

Good post.

Yes Australian practice is to assess the cross section at the location of the lateral restraint. The flange can be considered laterally restrained if it would buckle farthest in the absence of that restraint, or if that flange is the compression flange. These L restraints define your segments (“sub segments” in AS4100 terminology), which defines your effective length. So we appear to be in full agreement here.

The part I find murky is the critical flange definitions. Sometimes the flange which will buckle farthest is not the compression flange.

I’m not sure if this is deliberate and the code is saying that it’s fine to take either flange as critical on these situations, or if something else is going on. It would be interesting to see some buckling charts comparing the effectiveness of

1. Restraining the flange which will deflect farthest

And,

2. Restraining the compression flange.

Maybe both are perfectly adequate. I’ve run a few buckling analyses and it seems like much of the time it really doesn’t matter where you brace the cross section as far as preventing lateral torsional buckling.

So maybe the critical flange logic isn’t so much about identifying which of the two flanges will prevent buckling, and which one won’t, but is about weeding out especially crappy points of restraint.

RE: Rafter without fly brace?

All the code is saying is restrain the compression flange at the point of the restraint, because it defines this as the critical flange being the one that would deflects the furthest at that point. It defines this 'deflecting the furthest' thing as being satisfied if you basically restrai whichever flange is the compression flange for a segment with restraint at both ends, or both flanges for free at one end.

It's not expecting you to do some fancy analysis to prove it which I think others are getting bogged down on, its just a criteria that you apply directly. Whether the flange at that location really does deflect the furthest in reality is irrelevant, as you say even a 'L' restraint to the non-critical flange actually does something if you go through the buckling analysis route (i'd ignore it though, but just saying), even if it's not relied on in terms of the code.

Providing the right type of restraint to the non-critical flange like twist restraint still results in a P restraint at that cross section. Which for all intents and purposes is no different to direct restraint of the critical flange. Providing restraint to the flange in compression irrespective of where the restraint is improves the effective length.

I would point out under reversing moment, at one end of the segment you'll have the top flange critical, at the other the bottom. Again, nothing to do with what might be going on in between as far as the interpretation goes for which flange you are considering as being critical and requiring/having restraint.

Quote (Tomfh)

The part I find murky is the critical flange definitions. Sometimes the flange which will buckle farthest is not the compression flange.

In NZS3404 this is much clearer in our NZ code. Where it states for a cantilever both flanges are critical. I believe AS4100 says only the tension flange is critical. Any other situations you were thinking of particularly? AS4100 doesn't clarify this aspect at all.

There are a few subtle differences in NZS3404 that are not contained in AS4100, for example some of our local plate slenderness limits are subtly different, our angle member design provisions are quite different, and we don't for some reason have the block shear provisions that are in AS4100. Plus obviously we have all the multitude of seismic provisions, including quite a few other limitations on sections and some unique combined actions checks that are not present in AS4100.

RE: Rafter without fly brace?

Quote (Agent)

All the code is saying is restrain the compression flange at the point of the restraint, because it defines this as the critical flange being the one that would deflects the furthest at that point

Yes I understand. But in reality the compression flange is often not the flange which will deflect the furthest. Eg in our original example here it is the bottom flange which will buckle the farthest in the absence of restraints. Thus at midspan you could take the bottom flange as critical, given that it will deflect farthest in the absence of restraint, OR you could take the top flange as critical, given it is the compression flange.

It is interesting that in Nz3404 both flanges are critical for a cantilever. Are they saying you must restrain both? Or are they saying you may take your pick which one to restrain?

RE: Rafter without fly brace?

That's the thing, maybe not out in the span, but at that particular point of the restraint if you considered that little slice of the beam then I think it's interpreted as the compression flange is more likely going to deflect further than the tension flange at that particular point forgetting about anything else going on beyond that point. This is how you need to apply the provision, it's how you were taught to do it whether it was explicitly explained or not.

You're still thinking about buckling in the span though with your explaination/thinking in the last post. That's not how you interpret the code requirement. You need to stop thinking like that. Whats going on in the span has nothing to do with applying the provisions. It's all about the cross section at the point of the restraint.

RE: Rafter without fly brace?

Quote (Tomfh)

Kootk, you really should read AS4100 before you explain it to everyone.

Quote (KootK)

I think that it's poor form to deny my right to participate in this discussion just because...

Quote (Tomfh)

No-one's denying your right to contribute. I'm merely asking that you familiarise yourself with AS4100 before telling us all what's wrong with it, and before telling us what's wrong with how it's taught, understood, and practised.

Ah...I see. When I initially read your comment, I mistakenly interpreted it as a petty attempt to diminish my contributions here because I'm non-Aussie. But now I realize that you really just wanted to help promote the success of my efforts by ensuring that I'm well prepared going forward. Thanks. It is, however, a bit presumptuous of you to assume that I'm not already familiar with AS4100. That, particularly, given that most of the relevant provisions are already posted within this thread and I've been commenting on them in detail for weeks now.

Quote (Tomfh)

If you feel AS4100 is "flawed", then show how it is. You would need to show that AS4100 as written overestimates buckling capacity.

I would not need to do that and your thinking otherwise makes it evident that your missing the point of my arguments entirely. It's like is:

1) Theoretically, I believe that AS4100 is in complete agreement with the principles that I've been espousing. So there's no need for me to prove a numerical discrepancy because I've no cause whatsoever to believe that one exists.

2) I believe that you and Agent666 may be misinterpreting AS4100 and, as a result, overestimating LTB capacity. My concern is not that AS4100 is technically amiss, my concern is the you two are tehcnially amiss.

This will mix and match posts a bit awkwardly but, I think, is the ideal time to address this misconception:

Quote (Agent666)

...and people saying we're all doing it wrong down in this part of the world.

I have not said that ALL Australians are doing it wrong. I've only said that you and Tomfh are doing it wrong. There's an important difference there. Whether or not this as a systemic issue affecting many Aussies, I couldn't say (can't seem 'em from here). Rather, I'd be relying on you guys to tell me if this is a systemic issue.

3) The flaws that I feel I have identified in AS4100 are linguistic flaws, not technical ones. I feel that it is such linguistic flaws that have created the fertile ground into which all of these technical misconceptions have taken root. I sympathize with Aussie designers who struggle with interpreting these provisions because I know that I would struggle as well were our roles reversed.

RE: Rafter without fly brace?

Quote (Agent)

It's all about the cross section at the point of the restraint.

I’m not following you. Maybe I’m misunderstanding it?

Your saying that even though the bottom tension flange buckles the furthest (in the absence of the restraint we are considering), that in terms of the cross section itself it’s the compression flange which buckles further?

RE: Rafter without fly brace?

Quote (Kootk)

I have not said that ALL Australians are doing it wrong. I've only said that you and Tomfh are doing it wrong

Agent is a kiwi. He is using NZ version, but the AU and NZ codes are quite similar.

In day to day practice we both design the same as most other aussies/kiwis - we take lateral restraints of the compression flange to be the defining points of effective length. This is what our codes say and what they intend to say.

RE: Rafter without fly brace?

Quote (Tomfh)

Kootk, you really should read AS4100 before you explain it to everyone.

Quote (Agent666)

...people who have never used the AS/NZS standards trying to say we're applying the provisions which we have grown up with all wrong

Quote (Agent666)

...Believe people who study and work in NZ and AU would know how to correctly apply their own code provisions.

Quote (Agent666)

...as does everyone else who I've ever run into who actually practices in AS/NZS

Yeah, just look at all that hostility and resistance. And all, it seems, because you perceive me as an outsider because I don't own an Aussie passport. I get it though. It's not an easy thing to feel as though your long held, long cherished beliefs are being threatened by someone coming from the outside. In fact, I believe that it is one of the most difficult and impressive feats of a strong mind/ego to be able to allow itself to be changed in the face of new information that challenges old beliefs. I struggle with this constantly.

Consider however:

1) The AS4100 provisions that we've been debating are clearly causing confusion among designers and, therefore, could stand to be improved.

2) It's always difficult to assess things clearly when you're immersed in the dogma and group think of your own, day to day environment. In this sense, who better than an outsider to help sort things out?

In would encourage you both to take a glass half full approach to this and consider my involvement in this conversation a positive thing rather than a hostile threat from the outside. Tomfh suggested that I read up AS4100. I did that, in spades, weeks ago. And why would I do that? Because I'm genuinely interested in helping with this. It's tough for me to help, though, if you refuse to recognize the opportunity that my help represents.

RE: Rafter without fly brace?

Quote (Agent66)

Agent is a kiwi.

My bad, I knew that. You get the idea though. Antipodeans in general.

RE: Rafter without fly brace?

Quote (Agent666)

..need to point out that the following interpretation is actually incorrect.

Quote (KootK)

Prove it. I believe that it is in fact your interpretation that is in error. And I've supplied a good deal of material above to substantiate that claim.

@Agent666: this post will be in response to the post of yours that began with this statement:

Quote (Agent666)

This post will concentrate on stating exactly how the code requirements are intended to be interpreted.

Some preliminaries:

1) Because of the sequence of how this has unfolded, I'm assuming that you meant for that to be the proof that I requested. That said, I found very little in your post resembling meaningful proof so it's difficult for me to tell. If I critique the proofiness of some sections of your post when, in fact, you never meant for those sections to be proof of anything, please forgive the error.

2) Your post was looong. And, as a frequent purveyor of long posts myself, I dig that. However, the length of your post made it a challenge for me to parse it an a manner that was a) efficient and b) short enough that other thread participants would actually bother to read it. To address this, I printed out your post and color coded it into sections that I felt represented different attempts at "proof". Going forward, I'll speak to each color coded section in turn. A copy of the PDF is attached.

3) The effort that you put into the response is apparent. And I'm grateful for that.

CRITIQUE OF THE PROOF

4) The RED section. This reads as "My professors, my colleagues, my dog, and my fish all do this my way. Therefore my way is probably the right way". This is a weak form of proof as opposed to, say, proof based on theory and physical reasoning. That said, I agree, it's a little something. There are some possible flaws to be considered however:

a) Mass delusions do in fact happen. The inflection point business of yore is a perfect example of this. It is in fact possible that all antipodeans believe as you do and are, none the less, wrong anyhow. Obviously, the odds of this are slim.

b) Far more likely, you may be misinterpreting the intent of your professors, your colleagues, your dog, and your fish in exactly the same way that you may have been misinterpreting AS4100. You are tainted, across the board, by your own preconceived notions. As are we all.

5) The YELLOW section. Frankly, I wasn't really sure what you were up to there. Yes, AS4100 and AISC are based on different curve fits. What does that tell us about how the AS4100 LTB provisions should be interpreted? Maybe you never intended to prove anything with this section and it's just an interesting factoid that you felt like sharing? Or maybe, like Tomfh, you mistakenly assumed that I challenge the validity of the AS4100 provisions on technical grounds. As I told Tom, that's not case. AS4100 and I are sympatico on the technical front. We only disagree with regard to what constitutes good technical writing.

6) The GREEN section. Here, it appears that you've simply restated your interpretations without offering up any particular proof in support of them. Moreover, you've presumptuously presented your interpretations as fact and mine as patently incorrect. Bold statements such as:

Quote (Agent666)

This post will concentrate on stating exactly how the code requirements are intended to be interpreted.

Quote (quote)

This is how the requirements are..intended to be applied...

Quote (quote)

You can have an alternative view, but in this particular case you would not be correct.

Ballsy stuff. It's like trying to debate with HAL9000. But, again, maybe you never intended for this section to prove anything. Maybe you just meant to demonstrate that you had a cohesive story to tell regarding the interpretation of AS4100. And a cohesive story is certainly better than a non-cohesive story.

RE: Rafter without fly brace?

So I got to thinkin'... if this wonky design method that Tomfh and Agent666 keep going an about is so ubiquitous, it must show up all over the place in Australian steel text books and design guides, right? And if that's the case, surely such documents would be worthwhile examples for us to ponder. So I set about trying to find such an example in my limited, antipodean library.

My quest was not an easy one. I have a text by the legend Trahair that, somehow, contained not a single example of an LTB check on a beam with an inflection point. But I hit pay dirt with a publication titled Steel Structures Design Manual to AS4100. In the preface, the authors describe the manual as "a self-instruction manual for beginners". Now we're speaking my language. I've attached an excerpt the relevant section of the manual to this post as a PDF.

So, when I read the example below, here's what I see:

1) And example from an authoritative, Australian source, dealing specifically with AS4100.

2) An example prepared by real antipodes rather than sketchy foreigners who don't know what they're talking about.

3) An example prosecuted according to the methods that I've espoused, verbatim.

4) An example prosecuted in a fundamentally different way to the methods espoused by Tomfh and Agent666

5) An example demonstrating that there's at least one Australian walking the face of the earth that sees things as I do.

RE: Rafter without fly brace?

Kootk.

That example contradicts everything you’ve been saying. It considers lateral restraints to be effective when they are attached to the compression flange. That is we’ve been saying from the start, and what you have been condemning.

RE: Rafter without fly brace?

Edit: Thanks KootK for posting you example above. But I don't see how this contradicts Agent666's previous posts. His 'interpretation' does not seem to contradict mine. But to be honest I'm now all a little confused about where the disagreements between people here exist. (But maybe I just get confused easily.) Either way am reading all posts with interest.

Quote (Tomfh)

Yes I understand. But in reality the compression flange is often not the flange which will deflect the furthest. Eg in our original example here it is the bottom flange which will buckle the farthest in the absence of restraints.
Sorry. Which example is this? In the rafter example the compression flange does defelect the most. In the continous beam example again the compression flange seems to defect the most.

Quote (Tomfh)

Thus at midspan you could take the bottom flange as critical, given that it will deflect farthest in the absence of restraint
How do you figure this?

Quote (KootK)

I believe that you and Agent666 may be misinterpreting AS4100 and, as a result, overestimating LTB capacity
Could you please give an example where the (mis)interpretation results in overestimating LTB capacity?

RE: Rafter without fly brace?

Quote (Human)

Sorry. Which example is this?

Continuous beam under gravity load. In the absence of the lateral restraints the bottom tension flange often buckles further than the top compression flange. Eg at midspan the bottom tension flange will often kick out the most during buckling, in the absence of intermediate lateral restraints, despite it being the tension flange at midspan.

Agent seems to be saying I’m doing it wrong to consider it that way, but I don’t really understand why. I thought that’s what the code meant by running a buckling analysis to see which flange buckles furthest in the unrestrained situation.

In any case I otherwise agree with Agent, and we approach it the same way in practice - by taking the compression flange to be critical. Eg the standard situation of counting purlins and joists as L restraints when they are attached to the compression flange.

RE: Rafter without fly brace?

Quote (Tomfh)

Continuous beam under gravity load. In the absence of the lateral restraints the bottom tension flange often buckles further than the top compression flange. Eg at midspan the bottom tension flange will often kick out the most during buckling, in the absence of intermediate lateral restraints, despite it being the tension flange at midspan.
Ok. I'm not seeing this in various buckling anaylisies that I'm looking at. But that isn't to say that the small range of scenarios I'm looking at are representative. Anyway debating this is probably distracting from the point. The simple rules regarding determinining critical flange can never be perfect. Hence the clause "The critical flange may be determined by an elastic buckling analysis.".

One would hope though that the simple rules regarding determinining critical flange remain conservative.

Quote (Tomfh)

In any case I otherwise agree with Agent, and we approach it the same way in practice - by taking the compression flange to be critical. Eg the standard situation of counting purlins and joists as L restraints when they are attached to the compression flange.
I am wondering if everyone is in furious agreement here.

RE: Rafter without fly brace?

Quote (Tomfh)

Eg at midspan the bottom tension flange will often kick out the most during buckling, in the absence of intermediate lateral restraints, despite it being the tension flange at midspan.
Do you have an example of this. I believe if you look at the mechanics of an unrestrained beam in positive bending it is the compression flange that buckles laterally, the tension flange is affected only by the buckling of the compression flange. Or are you meaning when the top flange is restrained but the bottom is not?

RE: Rafter without fly brace?

Quote (Human)

I am wondering if everyone is in furious agreement here.

No, because kootk has been arguing from the start that you cannot count L restraints to reduce your effective length.

RE: Rafter without fly brace?

Quote (Jayrod)

Do you have an example of this. I believe if you look at the mechanics of an unrestrained beam in positive bending it is the compression flange that buckles laterally, the tension flange is affected only by the buckling of the compression flange. Or are you meaning when the top flange is restrained but the bottom is not?

I am not talking about when the top flange is restrained. I am taking about the case with no restraints, except the full restraints at the supports.

When a beam buckles it tends to do so globally, it doesn’t necessarily buckle in and out as flanges change from compression to tension. In these examples it’s often the bottom flange which buckles the most at every location (in the unrestrained case), even where the bottom flange is the tension flange.

RE: Rafter without fly brace?

Perhaps the example that I posted can serve as a focal point for us to iron out some misunderstandings. Something a little more tangible too pick apart.

Quote (Tomfh)

That example contradicts everything you’ve been saying.

That's interesting because, in my opinion, it contradicts absolutely nothing that I've been saying. Can you point to a specific example or three that I can attempt to speak to?

In the morning, I'll:

1) Try to demonstrate how the example contradicts what you and Agent666 have been saying.

2) Address Human909's request that I contrast the example to Agents666's statements.

Quote (Human909)

Could you please give an example where the (mis)interpretation results in overestimating LTB capacity?

This one's easy. The original OP example where I say the unbraced length is the length between supports and Agent666 says that it would be a value less than that.

Quote (Human909)

His 'interpretation' does not seem to contradict mine.

I'm not clear on what your interpretation actually is Human909. Did you state that someplace? Can you reproduce or restate it here?

It's 9pm in Canadia and my inlaws are in town. That's all I've got in the tank for tonight.

RE: Rafter without fly brace?

Quote (Tomfh)

No, because kootk has been arguing from the start that you cannot count L restraints to reduce your effective length.

This needs greater precision to represent my position. KootK argues that:

1) You absolutely CAN count top flange L restraints for checking LTB represented by rotation about a point in space below the shear center.

2) You cannot count top flange L restraints for checking LTB represented by rotation about a point in space above the shear center, particularly one located at the intersection between the beam web and beam top flange.

Quote (KootK)

Do you guys do a similar, bifurcated check where negative bending LTB and positive bending LTB are checked separately? Or do you tackle it in a single checking procedure?

I asked this question of Tomfh and Agent666 long ago and received no response. Can one or both of answer this simple question for me now? It's complicated but I've got a hunch that this may be important in getting this sorted. For reference, this is what I mean by a bifurcated checking procedure:

Quote (KootK)

1) I think that it's critical to recognize that, with moment reversal, the design effort has to bifurcate into two paths:

a) LTB rotation about a point in space below the shear center which is used for the positive moment / top flange check (sketch B below).

b) LTB rotation about a point in space above the shear center which is used for the negative moment / bottom flange check (sketch C below).

RE: Rafter without fly brace?

Quote (kootk)

Can you point to a specific example or three that I can attempt to speak to?

...

Quote (Kootk)

3) use the beam span between supports (8m) as your effective, lateral torsional buckling length for the negative moment.

Quote (Kootk)

I say the unbraced length is the length between supports

In these examples there are lateral restraints attached to the compression flanges. According to AS4100 that counts as an L restraint, which reduces your segment length. You do NOT need to take the full length between fully restrained supports as your segment length.

It’s not a matter of “interpretation”, it’s what the code says, it’s what the writers meant, and it’s been part of Australian design logic for 50 years at least.

RE: Rafter without fly brace?

Quote (KootK)

It's 9pm in Canadia and my inlaws are in town. That's all I've got in the tank for tonight.
Well thanks for contributing.

Quote (KootK)

I'm not clear on what your interpretation actually is Human909. Did you state that someplace? Can you reproduce or restate it here?
I haven't really stated it. I've been a bit non comittal and probably even inconsistent. (sorry, its a bit weak) I've read your posts with interest, agreed with some things. I do agree that 4100 could be clearer. But I don't believe that Agent666's interpretation devitates from the intention. I don't have a clear view on the whole discussion which is why I am interested.

Quote (KootK)

"Could you please give an example where the (mis)interpretation results in overestimating LTB capacity?" This one's easy. The original OP example where I say the unbraced length is the length between supports and Agent666 says that it would be a value less than that.
Thanks. I'm going crunch the numbers using buckling analysis and see what I come out with....

Quote (KootK)

Do you guys do a similar, bifurcated check where negative bending LTB and positive bending LTB are checked separately? Or do you tackle it in a single checking procedure?
It is tackled in the single checking proceduce and supposably sufficiently caputured by the defintions of segment lengths and critical flange restraints. It does seem to be a simplification, but is it unconservative? I'll try to let the computer crunch the numbers and get back to you.

RE: Rafter without fly brace?

Quote (KootK)

That example contradicts everything you’ve been saying.

Nope, turns out your were absolutely right about that. I mistakenly thought that there was F-restraint at 3. So now I'm utterly confused by the manual statement that the bottom flange will buckle between 1 & 3 when every bone in my body tells me that makes no physical sense. With no bottom flange restraint between supports, I just don't see it doing the voodoo that I've shown in the sketch below. I am however starting see how the AS4100 dogma has made the rounds.

Do you have any additional published examples of LTB on beams with inflection points? This one is the sum total of what I can find in my stuff.

RE: Rafter without fly brace?

Quote (Human909)

It is tackled in the single checking proceduce and supposably sufficiently caputured by the defintions of segment lengths and critical flange restraints. It does seem to be a simplification, but is it unconservative?

Yeah, I was worried that it would turn out to be a single procedure. That is a significant difference and points to something being fundamentally different in the treatment that doesn't yet make sense to me. I don't know how to cover both top flange and bottom flange LTB in a single check without getting into fancy computer stuff.

Is there a definitive, very theoretical steel text that folks refer to in Australia? Something like Salmon & Johnson in the US? Both of the Aussie book that I've got are pretty lightweight in their treatment of LTB, including the Trahair one unfortunately. They're most just cookbook, how you do stuff manuals.

RE: Rafter without fly brace?

Quote (Kootk)

Do you have any additional published examples of LTB on beams with inflection points?

They’re all like that.

It’s how it’s done.

You have this idea that everyone’s misinterpreting it and there must be some authority who understands it correctly, and who simply must agree with you.

Forget that. We don’t do it your way.

RE: Rafter without fly brace?

There are a few worked examples from ASI and standards Australia and lecture notes that I'm aware of, but they just reinforce what Tomfh is saying and what I've said previously and the example that kootk provided (I haven't looked at it too hard, but I gather from the replies from others that it supports our side of the conversation).

I'll fish them out so we can either settle it or go another round.

RE: Rafter without fly brace?

Failing that, working towards getting some resolution I suggest we provide a detailed design on a beam and loading scanerio, kootk then does a counter design using his interpretation so we can appreciate exactly how he's going about applying the provisions.

RE: Rafter without fly brace?

Agent,

Can you respond to my comment 10 Nov 19 00:42.

I’d like to get to the bottom of this “buckles the furthest” thing. If I’m misunderstanding it I’d like to know.

Still struggling to understand how the compression flange can be considered to always buckle the furthest, even at cross sections where the tension flange buckles the most.

RE: Rafter without fly brace?

I'll try tomorrow, but in the interim I and others want to know what situation you are interpreting the tension flange as wanting to buckle the furthest at a point of restraint?

RE: Rafter without fly brace?

Quote (Kookt)

Yeah, I was worried that it would turn out to be a single procedure. That is a significant difference and points to something being fundamentally different in the treatment that doesn't yet make sense to me. I don't know how to cover both top flange and bottom flange LTB in a single check without getting into fancy computer stuff.
I recognise and agree with you concern that AS4100 does seem to take a few simplifying shortcuts. Though I've yet to determine how conservative or unconservative they are. I'm working on a variety of scenarios and putting some comparisons together compared to buckling analysis. Bare in my I am pretty ignorant of other codes and pretty ignorant of deeper LTB theory. But I figure this is a good approach to become less ignorant.

Quote (Kookt)

Is there a definitive, very theoretical steel text that folks refer to in Australia? Something like Salmon & Johnson in the US? Both of the Aussie book that I've got are pretty lightweight in their treatment of LTB, including the Trahair one unfortunately. They're most just cookbook, how you do stuff manuals.
I've only seen lightweight. Most of the teaching that I've seen is pretty light weight too (prosciptive follow the code stuff).

RE: Rafter without fly brace?

Quote (Kootk)

This one's easy. The original OP example where I say the unbraced length is the length between supports and Agent666 says that it would be a value less than that.
However I crunch the numbers using buckling analysis software I get greater movements on the top flange. I also get higher buckling resistance with the top flange laterally restrained. Ignoring top lateral restrains seems unnecessarily conservative.

Quote (Tomfh)

I’d like to get to the bottom of this “buckles the furthest” thing. If I’m misunderstanding it I’d like to know.

Still struggling to understand how the compression flange can be considered to always buckle the furthest, even at cross sections where the tension flange buckles the most.
It isn't being considered like that. In the code you have two choices, perform an elastic buckling analysis to determine which flange will buckle the furthest. OR the choices given which manages to cover most scenerios with closely enough.

RE: Rafter without fly brace?

Quote (Human)

In the code you have two choices

I know. I keep saying as much.

The point is you can get two different answers for a given cross section - eg. top flange critical based on compression flange check, vs bottom flange critical via an elastic buckling check.

Quote (Human)

However I crunch the numbers using buckling analysis software I get greater movements on the top flange

This is interesting. What software are you using? What sort of beam setup? How are you restraining the beam?

RE: Rafter without fly brace?

Quote (Agent666)

There are a few worked examples from ASI
Do you mean this?
https://www.steel.org.au/ASI/media/Australian-Stee...

Please do fish out section 5.12 if you have it. I inherited an older version (1990ish) from a retiring engineer, scanned it, threw out the paper and now find I've lost the scan. Very disappointed in myself. Found it online so I can live with myself again. The comment at the end of example 5.8 might actually be more relevant to how the AS buckling gurus (Trahair & Bradford, not sure who Bridge is) meant the code to be applied. But it's late and I haven't thought it through - attached for discussion.

https://files.engineering.com/getfile.aspx?folder=...

I haven't read the whole thread in detail yet (only opened it based on the number of replies) but it seems the two viewpoints may have an order of magnitude difference in final capacity based on the difference in effective length being discussed, unless something compensates along the way of the calculation. That would mean failures left, right & centre which of course we don't experience.

RE: Rafter without fly brace?

That was one of the examples I was thinking of that demonstrates the application of the code requirements. Will find more tonight.

The other references I thought of are HB48 (I think) by standards Australia, simplified design of steel members by SESOC, probably a multitude of publications by HERA and SCNZ as well.

RE: Rafter without fly brace?

Is a fly brace anything like a rat run?

Mike McCann, PE, SE (WA, HI)

RE: Rafter without fly brace?

Quote (Agent)

but in the interim I and others want to know what situation you are interpreting the tension flange as wanting to buckle the furthest at a point of restraint?

The continuous beam scenario. Continuous beam with full restraint each end, but no lateral restraints.

Look at kootks post on 17 Oct 19 22:56. like that with no lateral restraints. Just F restraints at the supports.

The bottom flange has varying stresses, ranging from compression at the ends, to tension in the middle.

The top flange has the opposite stresses.

I think the bottom flange will deflect further at every cross section when the beam buckles. Even where the bottom flange is in tension.

On the other hand human is saying his buckling runs show the opposite, and always show the top flange buckling more (which in itself would contracdict the compression flange always being critical, since much of the top flange is in tension).

And you're saying I'm completely misunderstanding it because you need to take the cross section in isolation.

So I'm not really sure what to make of it..

RE: Rafter without fly brace?

Quote (Tomfh)

The point is you can get two different answers for a given cross section - eg. top flange critical based on compression flange check, vs bottom flange critical via an elastic buckling check.
Yep. And there where is the problem with that. The code allows you to perform buckling analysis OR follow the suggested guideslines. It doesn't suggest that the results will be identical.

RE: Rafter without fly brace?

I'd need to do a buckling analysis, but I'd tend to agree with human on expecting the compression flange at any particular cross section being the one that deflected the furthest.

Edit - never seen the effect you're noting to be fair, it's always the compression flange moving further at any cross section unless you're dealing with cantilevers.

RE: Rafter without fly brace?

Quote (Human)

The code allows you to perform buckling analysis OR follow the suggested guideslines. It doesn't suggest that the results will be identical.

Yes I’ve discussed that above, and mentioned reasons why it may be the case. See my post 9 Nov 19 22:30

Agent replied that I was simply misunderstanding it, and the two approaches should give the same answer when you view the problem correctly. Also, the code commentary refers to the compression flange guideline as a “more specific” version of the buckling check. That suggests it should give the same answer, which would agree with Agent.

But I tend to agree a compression flange need not deflect farthest. That assumption ascribes magical stabilising forces to the tension flange, similar in many ways to the idea that a tension flange cannot buckle, and that therefore an inflexion point alone can stabilise a beam.

RE: Rafter without fly brace?

I've done some buckling analysis with Nastran In-Cad with various loading scenarios, simply supported and continuous. Top flange loaded and centre of beam loading. I've been getting the top flange buckling every time as the first buckling mode. I haven't really thought much was worth posting... AS4100 seems to be consevative by at least 50% for the scenarios being discussed on the particular model I chose. (8m long 250UB31)

Of course you can always resort to LTB theory or simply run ask yourself which buckled shape has lower energy under gravitational load.

RE: Rafter without fly brace?

Interesting.

So you’re getting top flange moving most, even when top flange in tension?

RE: Rafter without fly brace?

Quote (Tomfh)

Interesting.

So you’re getting top flange moving most, even when top flange in tension?
Buckling isn't only a compression phenomenon. It is better thought of as the system moving to a lower energy equilibrium. When the load is gravitational expect the buckling to result in lowering the potential energy of the load.

You can evern have tensile buckling on axial loading! (Though it is fairly contrived.)
https://youtu.be/EKngs1vvcJU?t=241

RE: Rafter without fly brace?

Human, what type of analysis are you performing an elastic critical buckling analysis? And what is the loading and restrain conditions for the model picture you posted? You say you tried a whole lot of different things in the post but didn't make it clear what scenario you posted (just so we are all on the same page)?

RE: Rafter without fly brace?

Hey Agent. I've been performing linear buckling analysis. Non-linear is slower and seems to be virtually identical so I've stuck with linear for speed.
-Loading in the model picture was centre point load located central to the web. Fixed restraints at the end.

All the scenarios displayed similar top flange buckling as would be normally expected under gravitational load.
(Though you can get potentially get bottom flange bucking if you have no lateral or rotational at a support.)

Quote (Agent666)

You say you tried a whole lot of different things in the post but didn't make it clear what scenario you posted (just so we are all on the same page)?
Sorry for the lack of detail. I just posted the picture more as an example to people rather than evidence of anything. Like I have said nothing was surprising so there isn't much to post. But if you want a scenrio run I can do that. When I say nothing is surprising I mean it buckles as expected and as indicated by AS4100. When restraints are placed on a cross section of the critical flange the buckling load significantly increases.

Quote (Tomfh)

I’m just trying to get some agreement here, as Agent as far as I can tell is saying compression flange has to buckle the furthest, ie the two checks are the same check...
{QUOTED FROM BELOW}
Fair enough. Sorry if I misunderstood. Yep tensions flange certainly buckle, cantilevers are a case in point.

RE: Rafter without fly brace?

Quote (Agent)

Buckling isn't only a compression phenomenon. It is better thought of as the system moving to a lower energy equilibrium

Yea I know. The system takes the easiest path at every turn. At a certain point it’s easier for the beam to twist and kick out sideways than keep bending downwards....

I’m just trying to get some agreement here, as Agent as far as I can tell is saying compression flange has to buckle the furthest, ie the two checks are the same check...

RE: Rafter without fly brace?

Human,

If you have a chance could you do one with no lateral rotational restraint.

RE: Rafter without fly brace?

Sure. But you are going to have to be more specific. We need some rotational restrain otherwise it is unstable.

RE: Rafter without fly brace?

I mean without lateral rotational restraint at the supports. I.e. make the beam pin ended in plan. Currently it appears fully fixed against lateral rotation, ie the supports are providing very significant restraint to the lateral part of the buckle.

RE: Rafter without fly brace?

Does anyone have time to run a beam through Microstran/Space Gass code check. That would show how thousands of engineers are applying the code, consciously or not. I won't have access for a little while where I am.

Is the inflection point a particularly bad place for a brace? Re Yura's 10% increase in capacity. Would a brace to the compression flange (AS/NZS terminology: only one flange braced) further along the beam be more effective?

How do you all visualise which flange will move further without computer analysis?

RE: Rafter without fly brace?

Is the AISC code routinely applied by checking different top and bottom flange unbraced lengths, eg full length of span for bottom flange as discussed in this topic? I wouldn't have read that from the Lb definition in F2.2. Seems pretty similar to AS/NZS: "braced against lateral displacement of the compression flange".

I did see the Yura article posted by KootK summarised in the commentary but it's not clear to me that it has been brought into the code itself.

RE: Rafter without fly brace?

Quote (steveh49)

Does anyone have time to run a beam through Microstran/Space Gass code check. That would show how thousands of engineers are applying the code, consciously or not. I won't have access for a little while where I am.
Yep. I've tested it on SpaceGass as requested. It applies the codes as I believe is literally written. Specifically when it comes to lateral restraints:

5.4.2.4 Laterally restrained
A cross-section of a segment whose ends are fully or partially restrained may be considered
to be laterally restrained when the restraint effectively prevents lateral deflection of the
critical flange (see Clause 5.5) but is ineffective in preventing twist rotation of the section,
as for example in Figure 5.4.2.4.

EG A fixed end an beam of length L with a single load in the middle will with restraints on the top flange at 24% and 76% of L will have an effective length bending length of L. Whereas the same beam with restraints at 26% and 74% will have segments of effective lenth of 0.26L, 0.48L and 0.26L. The effect of the restraint is determined whether the flange is critical, aka in compression.

This is to code but is quite perverse.

Quote (steveh49)

Is the inflection point a particularly bad place for a brace? Re Yura's 10% increase in capacity. Would a brace to the compression flange (AS/NZS terminology: only one flange braced) further along the beam be more effective?
If we are talking about the code then yes. If we are talking about reality it can get complicated but I would say braces close to the load is more effective.

Quote (steveh49)

How do you all visualise which flange will move further without computer analysis?
You load is being pulled by gravity. Imagine the buckling shape that will lower the lower (reduce the potential energy).

Quote (Tomfh)

I mean without lateral rotational restraint at the supports. I.e. make the beam pin ended in plan. Currently it appears fully fixed against lateral rotation, ie the supports are providing very significant restraint to the lateral part of the buckle.
No matter how you spin it. With a single span you still have top flange buckling. There is no scenario that I'm aware of where the bottom flange buckles that reduces the potential energy.
Anyway here you go...

RE: Rafter without fly brace?

Thanks very much to everyone who supplied links to additional examples following my last post. Good stuff.

Quote (Tomfh)

They’re all like that.

Gotcha. I feel compelled to voice a minor grievance here however. If similar examples abound, it sure would have been nice if somebody had posted one rather than letting me spin for 5000 posts until I dug one up myself.

Quote (Agent666)

I haven't looked at it too hard, but I gather from the replies from others that it supports our side of the conversation

Indeed it does, at least from the "how does everybody in AU apply this" perspective. As I mentioned, in my last post, this raises unanswered theoretical questions for me about the method itself. More that more later though.

Quote (Tomfh)

..and there must be some authority who understands it correctly, and who simply must agree with you.

I never said this, you're putting words into my mouth. I thought that it would be rational, and productive, to seek out some published examples to help support one perspective or the other. So I took the initiative and did that.

RE: Rafter without fly brace?

Quote (Tomfh)

You have this idea that everyone’s misinterpreting it..

Not everyone, just you and Agent. And I feel that was a rational approach. In the interest of dialing down the antagonism and defensiveness that plagues this thread, perhaps there would be benefit in my explaining my approach to this debate so far. If nobody cares... feel no pressure to read further. This will be off topic.

Having spotted something that I fundamentally disagreed with at the beginning of the thread, I saw the possible outcomes here being as follows, listed from most probable to least probable:

1) KootK is wrong. Most likely.
2) Tomfh and Agent are wrong. In between likely.
3) All of Australia is wrong. Least likely (mass delusion that I referred to earlier).

It would have been very convenient to just stop at #1 given that my being incorrect is the most likely outcome here. But, then, this thread would be five posts long instead of 75 posts long. And all of the value that we've jointly created here simply would not exist. And I would neither learn nor grow. So I chose to take #1 off of the table and assume that I was correct until someone (possibly myself) was able to convince me otherwise. I simply don't know how to conduct a debate without first assuming that I hold a valid opinion.

Next, I moved on to #2, given that I feel that is the second most likely outcome. Surely Tomfh and Agent being wrong is more probable than all of Australia being wrong. So I challenged your interpretations. Similar to #1, I simply don't know how to prosecute a debate where nobody challenges anybody on anything. Obviously, challenging people on things inevitably ruffles some feathers. While I can't control how others perceive my challenges, I can assure everyone that I mean no disrespect -- and minimal hostility -- when I issue them.

Lastly, I proceed to the least likely outcome which is that all of Australia is wrong about lateral torsional buckling. Now that I consider possibility #2 sufficiently vetted and eliminated, this is where I'm at. At present, I now do disagree with AS4100 on a theoretical level. That said, I still acknowledge that the most likely outcome here is #1: I'm wrong and/or simply lack understanding somewhere.

RE: Rafter without fly brace?

Quote (Tomfh)

Failing that, working towards getting some resolution I suggest we provide a detailed design on a beam and loading scanerio, kootk then does a counter design using his interpretation so we can appreciate exactly how he's going about applying the provisions.

I like this idea. However:

1) Before I start, I'd like to agree on the best example. I'm thinking either OP's original one or the manual example that I posted.

2) I'd like someone to run the example via software first and then provide me with a meaningful beam size and loading to check.

3) It's quite likely that I wont get to this until Xmas break. From now until Dec 31, I'm stuck in PDH Armageddon.

RE: Rafter without fly brace?

Choose your poison via an appropriate sketch (beam geometry, loading scenario, restraint locations, etc so it demonstrates whatever differences you are looking for with regard to the reversal of moment/inflection point), I'll choose some random magnitude of load and size an appropriate beam. Also I believe I said that not Tomfh.

It'll be interesting as well if you can compare to aisc or equivalent to see if any fundamental differences in capacity come out of it at the end of the day.

RE: Rafter without fly brace?

Quote (Human909)

Could you please give an example where the (mis)interpretation results in overestimating LTB capacity?

Quote (Human909)

This one's easy. The original OP example where I say the unbraced length is the length between supports and Agent666 says that it would be a value less than that.

Quote (Human)

However I crunch the numbers using buckling analysis software I get greater movements on the top flange. I also get higher buckling resistance with the top flange laterally restrained. Ignoring top lateral restrains seems unnecessarily conservative.

For this, I submit that you're using incorrect assumptions. The "next in line" buckling mode for the beam under consideration is section rotation about the intersection of the web and top flange. So there should be no lateral movement of the top flange to consider. And yes, the lateral restraints to the top flange do improve capacity. That's what changes the buckling mode from:

1) Rotation about a point in space above the shear center and, in all likelihood, well above the beam to;

2) Rotation about the point in space where the web intersects the top flanges, sometimes termed constrained axis buckling.

With this in mind, the key difference between my method and Agent's would be:

3) I feel that the unbraced length should be the beam span between supports.

4) Agent feels that the unbraced length should be, roughly, the distance from the supports to the inflection points (my interpretation of his position). It's easier to talk about this if we just assume that top flange restraint is effectively continuous. I'm not accusing Agent of doing IP bracing here.

Obviously, one would think that these two different interpretations would lead to a large discrepancy in capacity. One of my hopes with this thread is that I'll be able to parse out just why that isn't the case (assuming that it isn't). Viewing AS4100 from my North American perspective, I find it odd that one seems to be able to evaluate a flange buckling mode using unbraced compression flange buckling lengths that wind up being less than the distance between points of compression flange lateral restraint. My guess is that it's "baked into the cake" of the method someplace but I just haven't discovered where yet.

Interestingly, the wording of AS4100 implies the conversion of segment length into "effective length" via some factors. One idea I've been exploring is whether or not that effective length ends up being something close to what I would consider the "real" unbraced length when all is said and done. Unfortunately, in playing with it, I've so far been unable to demonstrate that equivalency to myself.

RE: Rafter without fly brace?

Quote (kootk)

Interestingly, the wording of AS4100 implies the conversion of segment length into "effective length" via some factors. One idea I've been exploring is whether or not that effective length ends up being something close to what I would consider the "real" unbraced length when all is said and done. Unfortunately, in playing with it, I've so far been unable to demonstrate that equivalency to myself.

In most cases where the load is laterally restrained, constrained to be acting through the shear center (k_t=1.0), then the length will either be slightly higher through the k_l factor, or quite a bit lower using the k_r factor.

If one segment in a member achieves full lateral restraint (this is basically meaning it has enough restraint to achieve the plastic moment capacity), then the adjacent segment can take one end being restrained against minor axis rotation in plan (can take k_r =0.85 for adjacent segment for example). If segments on both ends of segment have FLR, then you can take k_r=0.7 for that segments design. You can achieve the same effect through rigidly connecting to intersection members if they are stiff enough.

If you took k_r=0.7, which requires an F or P restraint at each end. Then the curve I posted comparing to AISC, results in much less difference between the two standards. This may suggests AISC maybe assumes this inherently, whereas we have to prove it. But as I noted previously the American curve is more of an average through experimental results, whereas the NZ/AU one is definitely more of a lower bound as I understand it.

RE: Rafter without fly brace?

Quote (kootk)

I find it odd that one seems to be able to evaluate a flange buckling mode using unbraced compression flange buckling lengths that wind up being less than the distance between points of compression flange lateral restraint

If you have L restraints, you cannot get the effective length lower than the physical length between L restraints. It's either going to be the same length or higher through the k_l or k_t factors. k_r = 1.0 as soon as an L restraint is present.

RE: Rafter without fly brace?

Quote (kootk)

If you have L restraints, you cannot get the effective length lower than the physical length between L restraints. It's either going to be the same length or higher through the k_l or k_t factors. k_r = 1.0 as soon as an L restraint is present.

I understand and have been interpreting it the same. But I still observe the same oddity. In my world, and Yura's, the buckling length is between points of F-restraint only. If K_this and K_that get it back to the same place, then peachy, concern alleviated. I'm not yet convinced that's the case.

RE: Rafter without fly brace?

Quote (Agent666)

Choose your poison via an appropriate sketch (beam geometry, loading scenario, restraint locations, etc so it demonstrates whatever differences you are looking for with regard to the reversal of moment/inflection point)

Yesss... now where getting somewhere.

I chose the example shown below. I'd like you to arrange the span, load, and beam size to make the example as meaningful as possible. My thoughts in that regard:

A) A slender-ish beam rather than a stocky one to exacerbate LTB issues.

B) Loads producing something in the range of 125% over load for checking bottom flange buckling LTB in segment 1-3.

I'm also going to add some rules to the game:

Quote (KootK)

1) Before I start, I'd like to agree on the best example. I'm thinking either OP's original one or the manual example that I posted.

2) I'd like someone to run the example via software first and then provide me with a meaningful beam size and loading to check.

3) It's quite likely that I wont get to this until Xmas break. From now until Dec 31, I'm stuck in PDH Armageddon.

4) I expect somebody to pony up with an FEM investigation when the time is right. Part of my reasoning in choosing this example is that I feel it will FEM better in the absence of true continuity.

5) I'm going to probe AS4100 theory more deeply here before I dive in. I expect some real cooperation with that rather than defensive xenophobia.

RE: Rafter without fly brace?

Hold off on the example. I can do better

RE: Rafter without fly brace?

Quote (KootK)

For this, I submit that you're using incorrect assumptions. The "next in line" buckling mode for the beam under consideration is section rotation about the intersection of the web and top flange. So there should be no lateral movement of the top flange to consider. And yes, the lateral restraints to the top flange do improve capacity. That's what changes the buckling mode from:

1) Rotation about a point in space above the shear center and, in all likelihood, well above the beam to;

2) Rotation about the point in space where the web intersects the top flanges, sometimes termed constrained axis buckling.

Just an FYI. I looked at multimodes and still didn't see the buckling mode you described. I ran a large variety of gravitational load cases with different restrains, different load heights and included some continuous beams. The only time I ever got significant movement of the bottom flange was bottom supported unrestrained at the support. (Which isn't surprising if you view the support as an upwards load.) I haven't posted all this because nothing I found was particularly noteworthy.

Quote (KootK)

Hold off on the example. I can do better
Great. I'll run it both with buckling analysis and to AS4100 as implimented by SpaceGass.

Oh and Kootk. Good to have you back, I hope the inlaws was fun! You contribution is helpful, anything that makes people think about things is good. Your understanding of LTB is no doubt better than mine. Bit I too will debate and question stuff that doesn't quite look right. As far as AS4100 goes, it does seem a little screwy in its binary determination of 'the critical flange' which leads to perverse results as I noted earlier. So far I haven't seen anything unconservative in it's treatment of LTB but the simplifications do make it excessively conservative in some scenarios.

RE: Rafter without fly brace?

Quote (Steve)

13 Nov 19 11:27
Does anyone have time to run a beam through Microstran/Space Gass code check.

Microstran counts lateral restraint on compression flange as an L restraint, which it uses to define effective length. It does it according to code.

RE: Rafter without fly brace?

Quote (Agent)

There is no scenario that I'm aware of where the bottom flange buckles that reduces the potential energy.

Thank you for doing the laterally unrestrained case.

I’m sure I’ve seen buckling cases where bottom flange buckles more. The bottom flange of a continuous beam carries a lot of compressive strain energy, which can be shed via a lateral buckle (a point KootK is emphasising).Maybe they’re just obscure cases that don’t matter..

In any case, you results confirm the point of the critical flange not necessarily being the compression flange, as you show top flange buckling the most, even when it’s in tension.

RE: Rafter without fly brace?

It will be the Cb vs alpha,m difference that saves the day. Yura's Cb numbers for beams with inflection points are much larger than alpha,m from the A/NZ codes, moreso if you shorten the segment with intermediate lateral restraints.

I'm not sure about the potential energy definition. Isn't that equivalent to requiring the centre of rotation be below the beam, otherwise rotation will lift the beam? What about beams in space?

RE: Rafter without fly brace?

Quote (Tomfh)

I’m sure I’ve seen buckling cases where bottom flange buckles more. The bottom flange of a continuous beam carries a lot of compressive strain energy, which can be shed via a lateral buckle (a point KootK is emphasising).Maybe they’re just obscure cases that don’t matter.
You are correct my statement is not completely accurate. There are some cases where you see exactly what you describe. But at least for my chosen example and combinations this occurs well beyond yield points and well beyond other less obscure buckling cases.

Previously I was focussing on unrestrained flange cases as that is what we were discussing. KootK mention "constrained axis buckling" so that is what I modelled just now.

But bear in mind that occurs at ~10x the load of the unconstrained case and about ~10x beyond the yield point.

RE: Rafter without fly brace?

Quote (Human909)

Just an FYI. I looked at multimodes and still didn't see the buckling mode you described.

I'm not surprised. As I mentioned somewhere above, I think that it would take a pretty contrived example to make OP's real world situation go south. But I'm going to do my darnedest to contrive just such an example. We. Shall. See.

There's something about my world view here on Eng-Tips that I've been hesitant to share because it's difficult to articulate without my sounding like a raging egomaniac. I have something important in common with Albert Einstein. I know, right? Sadly, that thing is neither intelligence nor creativity. Rather, what we have in common is that we both consider the mental experiment to be the source of all understanding.

Almost everything that Einstein came up with was the byproduct of a a handful of mental experiments that required no laboratory work to develop. Yes, experiments were later done by others for verification and that was in important step. But Einstein didn't let the eventual need for such verification hold him back from dreaming the big dreams.

When I come at something hard here on Eng-Tips, I go straight for the root, physical theory of it and pursue that like a dog with a bone in a way that, frankly, some find off putting. I run my own mental experiments until I feel that I've gotten the model perfected in my head. For me, this is the way that I learn and discover. The flip side of this coin is that:

1) While I respect that FEM results have value, that's never sufficient for me.

2) While I respect that code interpretations have value, that's never sufficient for me.

3) While I respect that empirical testing has value, that's never sufficient for me.

4) While I respect that gobs of analytical data have value, that's never sufficient for me.

5) I tend scoff at homework assignments asking me to provide code interpretations, empirical data, analytical date, or FEM results. I just don't care all that much about these things compared to the root, physical model in my head.

So I guess that's my roundabout way of saying that I'm not overly concerned about whether or not your FEM model predicts the buckling mode that I described. If it can be predicted on paper, and in the model in my head, that's what interests me. I would actually argue thatt he buckling mode that I described is the only logical "next in line" mode regardless of whether it's "far off" or not. And I've got a hunch that this far-off-ness might be used to resolve the apparent discrepancy between "compression flange" and "flange that moves most". More on that later.

Quote (KootK)

Oh and Kootk. Good to have you back, I hope the inlaws was fun!

Thanks, it's good to be back. I actually had to put this down not because of time constraints (doesn't take much) but because I was getting too distracted thinking about this to be "present" with my family. Found myself zoning out on conversations with people that I haven't seen in three years. Not good.

RE: Rafter without fly brace?

Quote (Steve49)

I'm not sure about the potential energy definition. Isn't that equivalent to requiring the centre of rotation be below the beam, otherwise rotation will lift the beam? What about beams in space?

I don't think so. All roads lead back to the load making it's way closer to the earth. What it does mean, however, is:

1) It gets really, really hard to make something buckle via the constrained axis buckling model where the bottom flange swings upwards.

2) Sometimes you'll get a secondary peak/trough in the stability graph. While one might argue that intermediate point might not be reliably stable, it sure does make it a lot less likely that you'll see real failures in the real world. And interesting, and quite related example of this is tension chord buckling in trusses.

RE: Rafter without fly brace?

Quote (KootK)

Rather, what we have in common is that we both consider the mental experiment to be the source of all understanding.
I hear you. Mental models and asking the right questions can take you an extremely long way.

Quote (KootK)

So I guess that's my roundabout way of saying that I'm not overly concerned about whether or not your FEM model predicts the buckling mode that I described. If it can be predicted on paper, and in the model in my head, that's what interests me.
I totally get that.

The FEM analysis is a tool. It could readily be wrong or just not have the right inputs. As I showed above I did force the buckling mode out of the closet with the restraints you mentioned and plenty of load.

Quote (Steve49)

I'm not sure about the potential energy definition. Isn't that equivalent to requiring the centre of rotation be below the beam, otherwise rotation will lift the beam? What about beams in space?
Beams in space still have a potential energy given by the load direction. Gravity on a mass is just the convenient and most common supplier of the force. An alternative could be a pnematic cyclinder where the potential energy is the compressed gas, any movement in the cylinder deflecting/buckling a beam is a reduction in that potential energy. Plenty of structural analysis can be done in terms energy conservation. In basic deflection the load supplies work and the beam strain energy in the beam is equal to that work.

RE: Rafter without fly brace?

Quote (Human)

Previously I was focussing on unrestrained flange cases as that is what we were discussing.

Agree. The unrestrained case is the relevant one for this discussion, as that defines the critical flange for a new lateral restraint, e.g. a midspan restraint.

When I said bottom flange can buckle I meant in the unrestrained case. Not higher order buckling modes. If it only happens in higher order buckling modes then it can be ignored.

Quote (HUman)

As I showed above I did force the buckling mode out of the closet with the restraints you mentioned and plenty of load.

Did you restrain only top flange? I would have thought you'd see a half wave buckle of the bottom flange. That's what kootk is concerned about.

RE: Rafter without fly brace?

think that 24 ft in your diagram should be 32 ft

Edit:
I know you all are focused on the AS4100 and I'm interested to see the various results after reading all of the above.

As some one that was taught AISC's method this is how I learned to check KootK's above example:
Lb for postive moment = 4 ft < Lp = 7.31 ft determined via equation F2-5 -> Lp = 1.76 ry sqrt(E/Fy)
LTB not applicable for this case
Mp = Zx Fy = 1016.67 ft-kips equation F2-1

Lb for negative moment = 32 ft > than both Lp and Lr -> LTB must be checked
Calculation for Cb:

Calculation of Yielding, LTB, and Compression Flange Local Buckling:

Open Source Structural Applications: https://github.com/buddyd16/Structural-Engineering

RE: Rafter without fly brace?

Quote (Tomfh)

That's what kootk is concerned about.

It should be what everybody is concerned about.

As I see it, the buckling mode shown below is the only practical LTB buckling mode worthy of consideration here. OP didn't tell us the joist spacing but I presume it's close enough that the top flange can be thought to be continuously braced.

Does anybody disagree that the LTB buckling mode shown below is "the thing" as far as this discussion goes? We're wasting our time on the rest if we don't all first agree on this.

RE: Rafter without fly brace?

Quote (Tomfh)

Did you restrain only top flange?
Yes.

Quote (Tomfh)

I would have thought you'd see a half wave buckle of the bottom flange. That's what kootk is concerned about.
I've never seen this in my modelling and I've tried hard to make it happen. (short of imposing loads upwards) It also doesn't make sense to me as a possibility because a full wave would mean an increase in height of the loaded points on the beam. Which goes against energy conservation. (If the beam buckles you must have a weighted net movement of the load on the beam in the direction of the load, otherwise conservation of energy is violated!)

Quote (Celt83)

I know you all are focused on the AS4100 and I'm interested to see the various results after reading all of the above.
Other codes for comparison are just as important. Thanks.

Quote (Kootk)

It should be what everybody is concerned about.

As I see it, the buckling mode shown below is the only practical LTB buckling mode worthy of consideration here. OP didn't tell us the joist spacing but I presume it's close enough that the top flange can be thought to be continuously braced.

Does anybody disagree that the LTB buckling mode shown below is "the thing" as far as this discussion goes? We're wasting our time on the rest if we don't all first agree on this.
From my perspective the conversation long moved away from the example you posted because we spent a while discussing and analysing the UNRESTRAINED case. If we are talking about continually restrained top flanges then that is an entirely different scenario. The effective length according to AS4100 is heavily reduced as previously discussed. To reiterate we get 3 segments with their effective length the distance from the restraint to the inflection point, inflectio to inflection and inflection to restraint.

The inflection point isn't a restraint, but it is where the restrainst become effective if you follow AS4100.
SpaceGass and Microstran implement it this way.

RE: Rafter without fly brace?

Quote (celt83)

think that 24 ft in your diagram should be 32 ft

Correct. Gratitude.

Quote (celt83)

I know you all are focused on the AS4100 and I'm interested to see the various results after reading all of the above.

1) I was intending to do this anyhow so you've saved me some effort.

2) This serves as a nice check that the example makes sense and produces the result that I was intending.

3) Acknowledging that I'm surely bypassing a lot of nuance, it seems to me that the AS4100 effective length would need to be about 400% of the segment length for equivalency.

4) I would have calculated this as you have. That said, it's prudent to acknowledge that this method is not the constrained axis method which would yield a higher capacity. This is what I was alluding to in the statement below from long, long ago. This is yet another thing that I'm starting to wonder about. Perhaps the AS4100 method does actually account for the contrained axis effect in a way that the stock AISC procedure does not.

Quote (KootK)

6) As shown in sketch D below, our real world expectation is actually constrained axis buckling about the top of the beam. This usually has a higher capacity than sketch C but is a serious pain the the butt to calculate so we just go with sketch C and call that good enough.

RE: Rafter without fly brace?

Quote (Human909)

Which goes against energy conservation. (If the beam buckles you must have a weighted net movement of the load on the beam in the direction of the load, otherwise conservation of energy is violated!)

I disagree. Anything that rolls the beam on its side and results in deflection tend towards the Iy value rather than the Ix satisfies the energy conservation. That said, these points are germane to this. The effect of the top flange rotating and initially raising the joists would be an example of the secondary peak/trough business.

Quote (KootK)

1) It gets really, really hard to make something buckle via the constrained axis buckling model where the bottom flange swings upwards.

2) Sometimes you'll get a secondary peak/trough in the stability graph. While one might argue that intermediate point might not be reliably stable, it sure does make it a lot less likely that you'll see real failures in the real world. And interesting, and quite related example of this is tension chord buckling in trusses.

RE: Rafter without fly brace?

Yes.

Ok, fair enough.

Quote (Human)

It also doesn't make sense to me as a possibility because a full wave would mean an increase in height of the loaded points on the beam. Which goes against energy conservation. (If the beam buckles you must have a weighted net movement of the load on the beam in the direction of the load, otherwise conservation of energy is violated!)

Yeah, you may be right that the load helps stabilise the bottom flange. I need to think more about that...

RE: Rafter without fly brace?

Quote (Human909)

From my perspective the conversation long moved away from the example you posted because we spent a while discussing and analysing the UNRESTRAINED case.

I disagree. I thought that we were only studying the unrestrained case as a means of dealing with the critical flange definition business en-route to evaluating the real restraint condition.

Quote (Human909)

If we are talking about continually restrained top flanges then that is an entirely different scenario.

Not so much continuously restrained as, rather, restrained as such a short interval that the only meaningful LTB mode becomes constrained axis buckling about the web to top flange intersection.

And I don't see this as being any kind of theoretical deal breaker. The idea is simply to brace the top flange well enough that the only LTB mode of consequence is the bottom flange kicking out.

Quote (KootK)

The inflection point isn't a restraint, but it is where the restrainst become effective if you follow AS4100.

Agreed. This is partly why I selected the example that I did. For this one, the IP and the first effective restraint point should be coincident.

RE: Rafter without fly brace?

Quote (KootK)

I disagree. I thought that we were only studying the unrestrained case as a means of dealing with the critical flange definition business en-route to evaluating the real restraint condition.
Yes it seems that we were talking at somewhat cross purposes. I think we are slowly getting to be on the same page. So we'll move on... I'll get to you example now.

Quote (KootK)

I disagree. Anything that rolls the beam on its side and results in deflection tend towards the Iy value rather than the Ix satisfies the energy conservation.
Fair point. It depends where you place the load. On the top flange or central. (I've been modelling doing both.)

Anyway I'll post my results both theoretical buckling and AS4100 calcs soon.

RE: Rafter without fly brace?

I'd also like for all parties to agree on the interpretation of the clause below.

THE CLAUSE IMPLIES THIS

When studying brace point #7, it is prudent to consider the absence of brace point #7 concurrently with the presence of brace points 1,2,3,4,5,6,8. It is this mental experiment that guides us to our determination with respect to which flange is critical and which flange moves the most in the absence of restraint.

THE CLAUSE DOES NOT IMPLY THIS

When studying brace point #7, it is prudent to consider the absence of brace points 2,3,4,5,6,7,8 (no restraint other than at the member ends).

THE POLL

Anybody disagree on this point?

RE: Rafter without fly brace?

Quote (Human909)

Anyway I'll post my results both theoretical buckling and AS4100 calcs soon.

Do any of you Aussies have the calc set up as an easily modifiable spreadsheet, similar to what Celt83 has for AISC? If so, maybe we could tweak a few things quickly to figure out what the AS4100 method would look like if done KootK style. Beats waiting for Xmas if it's me doing it from scratch.

RE: Rafter without fly brace?

Quote (KootK)

When studying brace point #7, it is prudent to consider the absence of brace point #7 concurrently with the presence of brace points 1,2,3,4,5,6,8. It is this mental experiment that guides us to our determination with respect to which flange is critical and which flange moves the most in the absence of restraint.

Rewrite

When studying brace point #7, it is prudent to consider the absence of brace point #7 concurrently with the presence of any brace points 1,2,3,4,5,6,8 located where the braced flange would be in compression. It is this mental experiment that guides us to our determination with respect to which flange is critical and which flange moves the most in the absence of restraint.

This sure does get complex. I was reading the doc below and, based on that, it sounds as though Trahair would have actually have preferred several methods even more complex that the current AS4100 one. I pitty the fool who finds himself a structural engineer in AU with English as a second language.

RE: Rafter without fly brace?

Hey. KootK. I feel like I might be making a high school level mistake here but I'm getting your beam well into yielding without even considering buckling. My input. 9.75m long, 1112kN load, 1355kNm moment on end. Result ~387mPa peak stress...

Quote (KootK)

I'd also like for all parties to agree on the interpretation of the clause below.
I think we all disagree with this clause as far as applying AS4100 is concerned. It isn't in line with how it is use or the spirit 5.5.2 and 5.5.3. That said logically your clause could be superior but it is impractical and is also potentially self referential. ie restrain 1 depends on restraint 2 and restraint 2 thus depends on restrain 1.

Here is the output:

AS4100 1998 CALCULATIONS FOR GROUP 1 (*=Failure)
------------------------------------

Critical load case is 1, out of 1

Section: *W27x84 (I or H section, Rolled/SR)

Failure Crit Start Finish Axial Major Minor Major Minor Load
Mode Case Pos'n Pos'n Force Shear Shear Moment Moment Factor

Section 1 0.000 0.00 0.00 556.03 -1355.82 0.00 0.66*
Member 1 0.000 2.438 0.00 -1355.82 0.00 0.66*
Shear 1 0.000 0.00 0.00 556.03 -1355.82 0.00 0.74*
(1.00)

Grade= 36 Fy = 248.2 MPa
Fyw = 248.2 MPa Fu = 399.9 MPa
Ltot = 9.754 m Lseg = 2.438 m (FL Bot-Top)
kt = 1.00 (5.6.3) kl = 1.00 (5.6.3)
kr = 1.00 (5.6.3) Le = 2.438 m (Bending) (5.6.3)
Lx = 9.754 m (Compression) Ly = 9.754 m (Compression)
Lz = 9.754 m (Torsion)
Ly/ry= 185.4 (Compression) Le/ry= 46.3 (Bending)

Arf = 0.0 mm^2 Arw = 0.0 mm^2
An = 15935.5 mm^2 Ae = 0.0 mm^2 (6.2.2)
Kf = 0.00 (6.2.2) Kt = 1.00 (7.3)
αm = 1.82 (5.6.1.1) αs = 0.93 (5.6.1.1)
αcx = 0.00 (6.3.3) αcy = 0.00 (6.3.3)
αb = 0.00 (6.3.3) βme = 0.00 (8.4.4.1)
βmx = 0.50 (8.4.2.2) βmy = 0.00 (8.4.2.2)
γ = 0.00 (8.3.4) ϕ = 0.90 (3.4)

N* = 0.00 kN
Vx* = 0.00 kN (not considered) Vy* = 556.03 kN
Mx* = -1355.82 kNm (Compact) My* = 0.00 kNm (Compact)

ϕNt = 0.00 kN (7.2) ϕNs = 0.00 kN (6.2)
ϕNcx = 0.00 kN (6.3.3) ϕNcy = 0.00 kN (6.3.3)
ϕNoz = 0.00 kN (8.4.4.1) ϕMo = 4476.96 kNm (5.6.1)
ϕVvm = 631.26 kN (5.12) ϕMf = 610.55 kNm (5.12.2)
ϕMsx = 893.21 kNm (5.2) ϕMsy = 116.41 kNm (5.2)
ϕMbx = 893.21 kNm (5.6) ϕMox = 0.00 kNm (8.4.4)
ϕMrx = 0.00 kNm (8.3.2) ϕMry = 0.00 kNm (8.3.3)
ϕMix = 0.00 kNm (8.4.2.2) ϕMiy = 0.00 kNm (8.4.2.2)
ϕMtx = 0.00 kNm (8.4.5.2) ϕMcx = 0.00 kNm (8.4.5.1)

Mx*
---- = 1.52 > 1.00* (Fail) Flexural-torsional buckling (5.6)
ϕMbx

RE: Rafter without fly brace?

Quote (Human909)

I feel like I might be making a high school level mistake here but I'm getting your beam well into yielding without even considering buckling.

That was by design (see my mathcad work in the problem statement). For modelling, I'd recommend either:

1) Jack up fy so it doesn't yield and accept a purely elastic buckling analysis or;

2) Keep the inelastic analysis and just report an ALR (applied load ratio) on a dummy applied load.

Quote (human909)

I think we all disagree with this clause as far as applying AS4100 is concerned.

Yeah, I was worried that might be the case.

Quote (Human909)

It isn't in line with how it is use or the spirit 5.5.2 and 5.5.3.

I'm not so sure. This might be yet another case where the wording is actually perfect in the literal sense. It's also partly why I was harping on the one stage vs two stage procedure previously. Done as separate checks for bottom chord and top chord buckling as we do in North America, it would go:

1) Study top chord buckling and cycle through each brace considering it removed with it's neighbors at compression location present.
2) Study bottom chord buckling and cycle through each brace considering it removed with it's neighbors at compression locations present.

Like anything else, judgement would eliminate 3/4 of the cases and it would go quickly. This would also be easy to program because it's methodical.

Quote (Human909)

but it is impractical and is also potentially self referential. ie restrain 1 depends on restraint 2 and restraint 2 thus depends on restrain 1.

I know, that's precisely why it concerns me.

Quote (Human909)

ϕMsx = 893.21 kNm (5.2) ϕMsy = 116.41 kNm (5.2)

So about 50% more capacity than AISC.

Quote (Human909)

kr = 1.00 (5.6.3) Le = 2.438 m (Bending) (5.6.3)

So 8' or 1/4 the the 32' that would be used via AISC.

Thanks for this. So much fun.

RE: Rafter without fly brace?

Kookt,
That was by design
Good to know I'm not going crazy.

So about 50% more capacity than AISC.
I get section capacity of 656 ft.kip vs 530ft.kip from Celt83. So 23% more capacity.

RE: Rafter without fly brace?

Quote (human909)

I get section capacity of 656 ft.kip vs 530ft.kip from Celt83. So 23% more capacity.

Ah yes.. I forgot to switch yours to kip-foot. Better. Thanks for the correction.

RE: Rafter without fly brace?

@Human909: Can you force your tool to run it at Le = 32' somehow? This would be how I would have done it if left to my own devices, pre-thread.

RE: Rafter without fly brace?

I gotta dissapear for a bit but here you go Kootk:
Le=32ft

AS4100 1998 CALCULATIONS FOR GROUP 1 (*=Failure)
------------------------------------

Critical load case is 1, out of 1

Section: *W27x84 (I or H section, Rolled/SR)

Failure Crit Start Finish Axial Major Minor Major Minor Load
Mode Case Pos'n Pos'n Force Shear Shear Moment Moment Factor

Section 1 0.000 0.00 0.00 556.03 -1355.82 0.00 0.66*
Member 1 0.000 9.754 0.00 -1355.82 0.00 0.38*
Shear 1 0.000 0.00 0.00 556.03 -1355.82 0.00 0.74*
(1.00)

Grade= 36 Fy = 248.2 MPa
Fyw = 248.2 MPa Fu = 399.9 MPa
Ltot = 9.754 m Lseg = 9.754 m (FF Bot-Bot)
kt = 1.00 (5.6.3) kl = 1.40 (5.6.3)
kr = 1.00 (5.6.3) Le = 9.754 m (Bending) (5.6.3)
Lx = 9.754 m (Compression) Ly = 9.754 m (Compression)
Lz = 9.754 m (Torsion)
Ly/ry= 185.4 (Compression) Le/ry= 185.4 (Bending)

Arf = 0.0 mm^2 Arw = 0.0 mm^2
An = 15935.5 mm^2 Ae = 0.0 mm^2 (6.2.2)
Kf = 0.00 (6.2.2) Kt = 1.00 (7.3)
αm = 1.70 (5.6.1.1) αs = 0.34 (5.6.1.1)
αcx = 0.00 (6.3.3) αcy = 0.00 (6.3.3)
αb = 0.00 (6.3.3) βme = -1.00 (8.4.4.1)
βmx = 0.50 (8.4.2.2) βmy = 0.00 (8.4.2.2)
γ = 0.00 (8.3.4) ϕ = 0.90 (3.4)

N* = 0.00 kN
Vx* = 0.00 kN (not considered) Vy* = 556.03 kN
Mx* = -1355.82 kNm (Compact) My* = 0.00 kNm (Compact)

ϕNt = 0.00 kN (7.2) ϕNs = 0.00 kN (6.2)
ϕNcx = 0.00 kN (6.3.3) ϕNcy = 0.00 kN (6.3.3)
ϕNoz = 0.00 kN (8.4.4.1) ϕMo = 378.60 kNm (5.6.1)
ϕVvm = 631.26 kN (5.12) ϕMf = 610.55 kNm (5.12.2)
ϕMsx = 893.21 kNm (5.2) ϕMsy = 116.41 kNm (5.2)
ϕMbx = 517.07 kNm (5.6) ϕMox = 0.00 kNm (8.4.4)
ϕMrx = 0.00 kNm (8.3.2) ϕMry = 0.00 kNm (8.3.3)
ϕMix = 0.00 kNm (8.4.2.2) ϕMiy = 0.00 kNm (8.4.2.2)
ϕMtx = 0.00 kNm (8.4.5.2) ϕMcx = 0.00 kNm (8.4.5.1)

Mx*
---- = 2.62 > 1.00* (Fail) Flexural-torsional buckling (5.6)
ϕMbx

RE: Rafter without fly brace?

Quote (Steveh49)

Is the AISC code routinely applied by checking different top and bottom flange unbraced lengths, eg full length of span for bottom flange as discussed in this topic?

I believe so, per Celt83's analysis.

Quote (Steveh49)

I wouldn't have read that from the Lb definition in F2.2. Seems pretty similar to AS/NZS: "braced against lateral displacement of the compression flange"
.

I see what you mean. Still, viewed from the perspective that I've been espousing, the bottom flange of any segment with an IP does qualify as a compression flange. And I believe that this is the North american dogma just as doing otherwise appears to be the AU dogma. A somewhat analogous situation is shown below. Would we call that something other than a compression column because the top half feels no compression? KL for that column is less than 1.0L but also greater than 0.5L.

RE: Rafter without fly brace?

You could have at least chosen a Australian section and grade of steel if you wanted some software comparisons....

RE: Rafter without fly brace?

Quote (kootk)

Rewrite

This is only important for your way of doing things, so how you apply it is up to you. Wasn't that the whole point of this exercise to see how you have interpreted the requirements? Trying to get us to agree is pointless as it's not how it's intended to be done.

RE: Rafter without fly brace?

Quote (Agent666)

You could have at least chosen a Australian section and grade of steel if you wanted some software comparisons....

What, I gotta post all the sketches, dig up all the articles, find the published examples, and craft the demo problems to suit other people's preferences? Fire up the ovaries and adapt something similar. We'll sort it out.

RE: Rafter without fly brace?

Quote (Agent666)

Wasn't that the whole point of this exercise to see how you have interpreted the requirements?

This is a somewhat separate aspect of the discussion that I'm hoping will yield interesting, additional discussion and possibly insight into the confusion over the critical flange definition. That said, it does of course tie into my general intent to try to understand the AS4100 LTB provisions.

Quote (Agent666)

This is only important for your way of doing things, so how you apply it is up to you.

Well yes, I do realize that I've got big boy pants on and can apply things as I like. I'm not seeking permission for that. Moreover, I don't do any real world AS4100 design. This is all just sport for me. Baby step by baby step, I'm trying to get us to consensus on the basics of the AS4100 provisions as a means to sussing out the root causes of our differences. This is one of those baby steps which is why it's important to me.

Quote (Agent666)

Trying to get us to agree is pointless as it's not how it's intended to be done.

Where can I sign up to be the arbiter of what is and is not worthwhile discussion? Seems like a good gig.

My impression here is that many of us, myself included, lack a cogent theoretical understanding of just how the AS4100 provisions work their magic. If we had such an understanding, I don't think that we'd be 160+ posts into trying to reconcile our differences on what should be entry level stuff. Instead, we'd just point to our cogent theoretical model and agree that "yup, it must be like this otherwise it wouldn't agree with the theory".

So I'm trying to construct such a cogent theoretical model and I was hoping that you and others would join me for that adventure. That said, it's not as though you're chained to this conversation like Prometheus to the stone. If you don't see any value in playing my reindeer games then don't play. Like a sack of bricks, you can just chose to put it down if you wish.

RE: Rafter without fly brace?

Well can I confirm a couple of things to get underway:-

The A36 material, is it actually 248.2MPa for both web and flange like human909's example implies (i.e. not different yield stresses for flange and web like many AU/NZ sections), only important for shear capacity I guess if there was shear and bending interaction.

Whats up with the section dimensions of the W27x84? Me no understand given my ignorance with american sections?

RE: Rafter without fly brace?

Quote (Human909)

The bottom flange buckling isn't in play, the beam will yield before it is in play.

I believe this to be a logical error in your thinking on this. Just because a bottom flange buckling mode passes the LTB check, or another failure mode occurs first, that doesn't mean that bottom flange buckling wasn't the critical buckling mode to be checked in the first place.

Quote (Human909)

But like is insisted upon time and time again. AS4100 is a broad check.

Yes, this is has been insisted upon time and time again and proven theoretically exactly zero times. So I cling to my right to ask.

Quote (Human909)

Why check for scenarios that aren't feasible?

Because your only practical choices here are:

1) Check bottom flange buckling OR;
2) Check nothing at all.

If you would please respond to this challenge, I'm fairly certain that I can convince you of the correctness of my reasoning in this. Please. This is one aspect that should be very easy to resolve.

Quote (KootK)

A challenge for you Human909: sketch me a single bucking mode that would be further up the list in terms of its eigenvalue and could possibly occur in the presence of the lateral restraints. Just one.

RE: Rafter without fly brace?

Human 909 & KootK - In the case of top flange lateral restraint, the bottom flange buckling (lateral and vertical translation) is resisted by the web. For the bottom flange to buckle, the web must fail. So which is the easier way for the beam, yielding in the bottom flange or bottom flange folding by bending the web? This will depend on the dimensions. Perhaps in reality yielding happens first 100% of the time, but I doubt it.

PS: I have watched this discussion intently and am very thankful to all contributors.

RE: Rafter without fly brace?

Quote (Human909)

.. In occasions where it comes into play for example at a moment reversal ...
I believe this is excatly the condition that KootK posted is it not?

Quote (Human909)

..AS4100 would require restraints on the bottom flange to the effective length or alternatively the design capacity is reduced.
so for the above beam are you indicating that AS4100 would treat this similarly to AISC and say that the unbraced length is 32'?

Open Source Structural Applications: https://github.com/buddyd16/Structural-Engineering

RE: Rafter without fly brace?

Quote (HS_PA_EIT)

For the bottom flange to buckle, the web must fail

I disagree.

One way for the flange to buckle would certainly be for the web to fail in transverse flexure. And this sort of resembles a reaction / concentrated load phenomenon that we call web sidesway buckling in the North American parlance (first sketch below). Back in the spring of 2018, WARose and I hammered out what I suspect still stands as the definitive Rumble in the Jungle on that topic if you're curious to learn more: Link. In my opinion, it's next to impossible to generate this failure mode away from concentrated loads and reactions however.

Another, more likely, failure mode is shown in the second sketch below and taken from early on in this discussion. And it does not involve the failure of the web. About the same time that I first posted that sketch, I was describing LTB as:

Quote (KootK paraphrase)

..rotation about a point in space above, below, or at the elevation of the shear center an horizontally in line with the shear center

I made a point of using that particular phrasing because I believe that it is the only, wholly accurate what to describe the physical phenomenon of lateral torsional buckling. That said, one can only repeat such a mouthful of jargon so many times before wanting to claw out their own larynx. So now I'm just using the more colloquial "bottom/top flange buckling" which seems to do a much better job of speaking to people's intuitions. It is important to recognize that there is a difference however.

In my next post, I'm going to do something nifty and related as it pertains to some of steveh49's previous work. It will also bear some similarity to celt83's previous work on flange buckling which has since been retracted. Stay tuned.

Quote (HS_PA_EIT)

PS: I have watched this discussion intently and am very thankful to all contributors.

Welcome to the discussion; I very much look forward to your contributions.

RE: Rafter without fly brace?

Quote (HU)

For the bottom flange to buckle, the web must fail.

No, distortional buckling does not need to occur. The entire cross section can simply twist/warp (albeit with greater difficulty due to top flange being restrained horizontally).

RE: Rafter without fly brace?

KootK - I understand, I think my language was weak on that one. I can now see how a top flange lateral restrain could provide little to no resistance to twist, thereby allowing the beam to rotate as in your sketch D constrained axis negative LTB. Your concept of the center of rotation for LTB has been useful for me in thinking about this.

That looks like a good thread, I'll have to give it a read. Thank you.

I am questioning the following:

Quote (kootk)

This is the part that strikes me as being hugely in error. Of course I'm focused on the bottom flange bucking mode. Given that the top flange is effectively continuously braced, there is no possibility of top flange buckling. So, in practical terms, is bottom flange buckling not the only mode of buckling in play here?
For determining the critical flange, don't you have to consider the "section" in the absence of any restraint for AS4100? I would think that because of this definition, either flange is in play. In this case perhaps there is some reasoning as to why the critical flange for a segment restrained at both ends is always the compression flange. I have a feeling that understanding what influences the center of rotation location (at centroid, above or bellow) for an unrestrained segment might hold the key.

RE: Rafter without fly brace?

Tomfh - I see that now. That was an error in my thinking/language (got to be careful with the word "must"). Thank you

RE: Rafter without fly brace?

Quote (HS_PA_EIT)

You couldn't imagine how good it makes me feel to hear that it's been useful to at least one person.

Quote (KootK)

This is the part that strikes me as being hugely in error. Of course I'm focused on the bottom flange bucking mode. Given that the top flange is effectively continuously braced, there is no possibility of top flange buckling. So, in practical terms, is bottom flange buckling not the only mode of buckling in play here?

Quote (HS_PA_EIT)

For determining the critical flange, don't you have to consider the "section" in the absence of any restraint for AS4100?

As you ponder my statement, it is absolutely crucial that you think only in terms of what you feel will actually happen, physically, in real life. No code talk. Once you start putting it into the context of AS4100 (or AISC), everything gets irrevocably muddied by:

Those two things probably are correct. However, using them as a crutch form of theoretical evidence to prevents us from discussing the theory in a meaningful way. I've been battling exactly this effect for the better part of a month now.

Quote (HS_PA_EIT)

I would think that because of this definition, either flange is in play

For physical, real world buckling, the top flange is out of play by definition as it is laterally restrained at such close intervals as to be continuously restrained. Ask yourself this: could the LTB buckling mode shown below physically occur with the top flange prevented from displacing laterally? If it can't, then top flange buckling has to be off of the table and the constrained axis LTB buckling would become critical.

A big part of what I'm striving to understand myself is how it can possibly make sense to make all of your LTB design decisions assuming an unrestrained system when, in fact, the actual, critical buckling mode will be anything but unrestrained. It would appear to be related to Human909's assertion that the AS4100 LTB checks actually preclude all relevant buckling modes as apposed to a particular mode.

RE: Rafter without fly brace?

OK found a copy of AS4100:
From the KootK example W27x84 using a segment with the bottom compression flange as the critical flange.

Effective length 5.6.3:

l = 4 ft or 48" = distance between points of partial restraint, assume we meet 2nd figure in figure 5.4.2.2

Kt = 1 + 2 (di/l) (tf/2 tw)^2 / nw (table 5.6.3(1) - PP restraint)
di = 23.625 in
l = 48 in
tf = 0.64 in
tw = 0.46 in
nw = 1 (1 web)

Kt = 3.651

Kl = 1.4 (Table 5.6.3(2) - PP Restraint and Load at top flange)

Kr = 0.70 (Table 5.6.3(3) - PP Restraint at both ends)

le = Kt Kl Kr l = 171.74 in

Member Capacity using Section 5.6.1.1 Open Sections with equal flanges

The moment profile yields:
alpha,m = 1.71 (table 5.6.1 (1.35 + beta,m * 0.36, where in this case beta,m = 1.0))

Ms = Zx Fy = 244 in3 x 50 ksi x 1 ft/12 in = 1016.67 ft-k

Mo:

where Iw = Cw in AISC = Warping Constant
E = 29000 ksi
G = 11200 ksi
Iy = 106 in4
le = 171.74 in
J = 2.81 in4
Iw = Cw = 17900 in6

Mo = 14527.68 in-k * 1 ft/12 in = 1210.64 ft-k

Ms/Mo = 0.84

alpha,s:

alpha,s = 1.085

Mb = alpha,m alpha,s Ms <= Ms (eq. 5.6.1.1(1))
Mb = 1.71*1.085*1016.67 = 1886.3 ft-k <= Ms = 1016.67 ft-k, Ms controls.

So considerably more capacity than my AISC approach.

Question I am left with on this is the detail for partial restraint shows a fixed connection to the tension flange, would standard composite construction satisfy the fixity requirement? If not then I'd say you'd fall into an unrestrained condition and land back at an unbraced length of 32 ft which from quick numbers following the same procedure in AS4100 yields only 443.31 ft-kips, or less than that of my current AISC approach.

Open Source Structural Applications: https://github.com/buddyd16/Structural-Engineering

RE: Rafter without fly brace?

Quote (steveh49)

I think there might be a quick and easy first test we can apply. Taking the W27x84 and the same bi-linear shape of the moment diagram from the test case, I reduced the maximum bending moment to 1240 kNm which is the design section capacity phi.Ms. I then increased the sub-segment length until the AS4100 LTB capacity phi.Mb = phi.Ms. The sub-segment length was 5.065m (ie from end of beam to the inflection point) giving overall beam length of 20.26m before LTB governs according to AS4100.

If I may be so presumptuous, I believe KootK will have an opinion on whether this is realistic or not. If that opinion is that it is not, he may never 'drop his bone' and accept AS4100. That doesn't need to end the discussion but people may at least continue knowing that.

Firstly, please recognize that my only beef with AS4100 at this time is that:

a) I don't understand it on a theoretical basis and;
b) A room full of smart, AS4100 practitioners seem incapable of explaining it to me on a theoretical basis.

I presently have no concerns regarding AS4100's level of conservatism for LTB checking.

So on to the fun stuff. Your example was clever. Me likey. As I understand it, the crux of the example was to exaggerate the length of the original problem until constrained LTB did in fact occur; and, in doing so, suggesting that it would take a rather ridiculous span to make that happen (66.5 ft).

You have rightly presumed that that I would question whether or not your example was realistic. LTB is an abstract mathematical concept and, obviously, I don't have a "feel" for it as I have a feel for how far I can hit my seven iron into the wind. Moreover, whatever "feel" I do have for LTB is irrevocably tainted by my long history with the AISC provision. So I'll not claim that I can challenge the reasonableness of your hyperbolic example on the basis of intuition alone.

So what can I do to challenge the reasonableness of your example?

1) I could run it in Mastan. I may do this eventually but I wouldn't hold your breath.

2) I could transmogrify your example into one of my own that I feel does an excellent job of teasing out the salient issues and placing them into a context in which "reasonableness" may more easily be judged via intuition. Truly, you'll have to just download the sketch and read the damn thing start to finish. Brief summary:

START

a) I assumed that bottom flange buckling is restrained by two, torsional stiffness components: the St. Venant and the Warping.

b) In the context of constrained axis buckling, the warping stiffness "is" the flange buckling laterally. So that's baked into the cake.

c) I replaced the St. Venant stiffness of the entire wide flange with a CHS member having nearly the same St. Venant stiffness. Everything is drawn to scale.

d) To make the thing tractable, I neglected some things such as the fact that the axial force in flange varies spatially. Still, it is a strut with 406K axial load applied to its ends.

e) The example considers the compression flange of the beam as a 66.5' flange-column having a slenderness ratio of 276. The flange-column would have axial compression loads to the tune of 406,000 lbs applied to the ends. This is actually more than the {As x Fy = 312k] of the flange. That's immaterial really though. 312k or 406k, it's a crap ton of of axial on a 66.5' column with a 276 slenderness ratio.

f) Naturally, we must consider that the flange-column is actually braced along it's 66.5' length. That bracing:

a) comes from the St.Venant torsional stiffness of the section;
b) varies linearly in it's effectiveness;
c) is at a maximum at near the supports and;
d) is at a minumum at the center of the beam.

This is what I have represented with the CHS section in the faux representation.

FINISH

So, assuming that I haven't screwed something up in my rush to pull this together, the question becomes:

How reasonable is it for us to expect that the 66.5' flange-column of my faux model will not buckle under a 406,000 lb load?

Seriously, what do you think?

EDIT: here's a dropbox link to the sketches in PDF format: Link. The file upload feature here is no longer working for me either.

RE: Rafter without fly brace?

Quote (Kootk)

For physical, real world buckling, the top flange is out of play by definition as it is laterally restrained at such close intervals as to be continuously restrained. Ask yourself this: could the LTB buckling mode shown below physically occur with the top flange prevented from displacing laterally? If it can't, then top flange buckling has to be off of the table and the constrained axis LTB buckling would become critical.
Except constrained axis LTB buckling doesn't become critical. Beam yielding becomes critical because the load required for the buckling mode you are suggesting is off the charts.

By your logic you need to keep checking every critical buckling mode ad-infinitem.

RE: Rafter without fly brace?

Celt, the restraint you're assuming isn't classified as an L restraint. That's a P restraint. An L restraint is just preventing lateral deflection of the critical flange, not preventing twist. So only the restraint at 8' is effective, I've argued I'd only take the one at 12' being effective due to the proximity of the inflection point.

Alpha_s is less than or equal to one, if greater than one, set it to 1. Noted it doesn't expressly say this but it is implied based on what the factor represents.

Alpha_m is also only evaluated based on the segment length, not the entire member length. This will typically mean for shorter segments with little change in moment alpha_m being lower.

RE: Rafter without fly brace?

Quote (Human909)

Except constrained axis LTB buckling doesn't become critical. Beam yielding becomes critical because the load required for the buckling mode you are suggesting is off the charts.

Except that you are comparing apples and oranges. Beam yielding and LTB buckling are separate failure modes. Just because you hit yielding prior to constrained axis LTB, that does not mean that constrained axis isn't the critical LTB buckling mode. It just means that LTB doesn't govern the failure of the particular situation that you're considering.

Quote (Human909)

By your logic you need to keep checking every critical buckling mode ad-infinitem.

Yes, and this is precisely what we do using AISC. You know, if we replace ad-infnitem with "just stop someplace reasonable". A reasonable place to stop, for example, would be any buckling mode indicating a capacity higher than yield.

For the third time now, would you answer the challenge below:

Quote (Human909)

If you would please respond to this challenge, I'm fairly certain that I can convince you of the correctness of my reasoning in this. Please. This is one aspect that should be very easy to resolve.

Quote (KootK)

A challenge for you Human909: sketch me a single bucking mode that would be further up the list in terms of its eigenvalue and could possibly occur in the presence of the lateral restraints. Just one.

RE: Rafter without fly brace?

Quote (Agent666)

Celt, the restraint you're assuming isn't classified as an L restraint. That's a P restraint. An L restraint is just preventing lateral deflection of the critical flange, not preventing twist. So only the restraint at 8' is effective, I've argued I'd only take the one at 12' being effective due to the proximity of the inflection point.
Probably should have said I looked at the segment from 4' to 8' which looks to only classify as P restraint on either end, which is why I chose that segment.
All the definitions for L restraint seem to contain a "and act at the critical flange" clause, so seems I'd agree with you that the first x in KootK's sketch that could count as L bracing would be at 12', so my take on the lateral bracing classification across the beam would be:
F P P L L L P P F

Quote (Agent666)

Alpha_s is less than or equal to one, if greater than one, set it to 1. Noted it doesn't expressly say this but it is implied based on what the factor represents.
Rereading that makes total sense that this should be limited to 1

Quote (Agent666)

Alpha_m is also only evaluated based on the segment length, not the entire member length. This will typically mean for shorter segments with little change in moment alpha_m being lower
yep solid catch I ran the calc over the full length first and whiffed on this the second time thru.

Open Source Structural Applications: https://github.com/buddyd16/Structural-Engineering

RE: Rafter without fly brace?

Quote (steveh49)

Regarding the discussion of Kl=1.0 for top flange loading from 14 Nov 16:40 to 19:30, I thought the lateral restraint at the load location removes the tendency of the additional ('p-delta') torque to exacerbate the twist and promote instability. By being sufficiently stiff to qualify as a lateral restraint, it provides sufficient horizontal force above the shear centre to counteract the destabilising torque. Possible alternative view: the lateral restraint moves the point of rotation very close to the top flange and the vertical load has ~zero lever arm about the point of rotation despite the shear centre kicking sideways relative to the top flange.

Would you say that the lateral brace at [2] makes this truss immune to LTB? Of course you wouldn't. But wait, isn't this different because it lacks rotational restraint at the ends?. Nah, not fundamentally. The rotational restraint at the ends increases the resistance offered to LTB but does not eliminate the fundamental tendency towards LTB. We could do something similar with a flat truss having end rotational restraint but it would take me all night to do a decent job of the buckled shape.

RE: Rafter without fly brace?

I had more errors so made a quick spreedsheet to avoid some calculator mistakes:

For Segment 0 to 4 ft - Bottom flange critical:

CODE -->

Mm = 	1000	x1.7	1700
M2	872	XM2	760384
M3	750	XM3	562500
M4	625	xM4	390625

alpha,m	1.298690688

segment L	4	ft	48	in

Segment End Bracing
0	F
L	P
FP	1

5.6.3 Effective Length

Kt = 	1.166	Table 5.6.3(1)
di = 	23.625	in
l = 	48	in
tf = 	0.64	in
tw = 	0.46	in
nw = 	1

Kl = 	1.4	Table 5.6.3(2)	assumes end reaction as segment load applied at bottom flange

Kr = 	1	Table 5.6.3(3)

Le = 	78.335	in

5.6.1.1 - Open Section with equal flanges

alpha,m = 	1.298	[calculated above]

E = 	29000	ksi
G = 	11200	ksi
Iy = 	106	in4
J = 	2.81	in4
Iw = Cw = 	17900	in6

Mo = 	65449.2	in-k	5454.10	ft-k	eq. 5.6.1.1(3)

Zx = 	244	in4
Fy = 	50	ksi

Ms = 	12200	in-k	1016.67	ft-k	5.2.1

Ms/Mo = 	0.186

alpha,s = 	0.933	eq. 5.6.1.1(2)

Mb = 	1231.73	ft-k	<=	Ms = 	1016.67	ft-k
Mb,use = 	1016.67	ft-k 

Segment 4 ft to 8 ft - Bottom flange critical:

CODE -->

segment L	4	ft	48	in

Segment End Bracing
0	P
L	P
PP	2

5.6.3 Effective Length

Kt = 	1.331	Table 5.6.3(1)
di = 	23.625	in
l = 	48	in
tf = 	0.64	in
tw = 	0.46	in
nw = 	1

Kl = 	1	Table 5.6.3(2)	assumed 1 as no load applied in segment

Kr = 	1	Table 5.6.3(3)

Le = 	63.907	in

5.6.1.1 - Open Section with equal flanges

alpha,m = 	1.75	table 5.6.1

E = 	29000	ksi
G = 	11200	ksi
Iy = 	106	in4
J = 	2.81	in4
Iw = Cw = 	17900	in6

Mo = 	97738.5	in-k	8144.88	ft-k	eq. 5.6.1.1(3)

Zx = 	244	in4
Fy = 	50	ksi

Ms = 	12200	in-k	1016.67	ft-k	5.2.1

Ms/Mo = 	0.125

alpha,s = 	0.967	eq. 5.6.1.1(2)

Mb = 	1720.51	ft-k	<=	Ms = 	1016.67	ft-k
Mb,use = 	1016.67	ft-k 

Equivalent AISC check of entire span as L for bottom flange:

CODE -->

segment L	32	ft	384	in

Segment End Bracing
0	F
L	F
FF	0

5.6.3 Effective Length

Kt = 	1.000	Table 5.6.3(1)
di = 	23.625	in
l = 	384	in
tf = 	0.64	in
tw = 	0.46	in
nw = 	1

Kl = 	1.4	Table 5.6.3(2)

Kr = 	0.7	Table 5.6.3(3)

Le = 	376.320	in

5.6.1.1 - Open Section with equal flanges

alpha,m = 	1.71	table 5.6.1

E = 	29000	ksi
G = 	11200	ksi
Iy = 	106	in4
J = 	2.81	in4
Iw = Cw = 	17900	in6

Mo = 	3806.9	in-k	317.25	ft-k	eq. 5.6.1.1(3)

Zx = 	244	in4
Fy = 	50	ksi

Ms = 	12200	in-k	1016.67	ft-k	5.2.1

Ms/Mo = 	3.205

alpha,s = 	0.263	eq. 5.6.1.1(2)

Mb = 	457.00	ft-k	<=	Ms = 	1016.67	ft-k
Mb,use = 	457.00	ft-k 

Open Source Structural Applications: https://github.com/buddyd16/Structural-Engineering

RE: Rafter without fly brace?

I think this is the check you mention Agent
segment = 0 ft to 12 ft or from support to first brace point that could be considered an L brace.

CODE -->

segment L	12	ft	144	in

Segment End Bracing
0	F
L	L
FL	0

5.6.3 Effective Length

Kt = 	1.000	Table 5.6.3(1)
di = 	23.625	in
l = 	144	in
tf = 	0.64	in
tw = 	0.46	in
nw = 	1

Kl = 	1	Table 5.6.3(2)

Kr = 	1	Table 5.6.3(3)

Le = 	144.000	in

5.6.1.1 - Open Section with equal flanges

alpha,m = 	1.3	table 5.6.1 first figure in table with beta,m = -0.5 - M0= -1000 M12 = 500

E = 	29000	ksi
G = 	11200	ksi
Iy = 	106	in4
J = 	2.81	in4
Iw = Cw = 	17900	in6

Mo = 	20187.7	in-k	1682.31	ft-k	eq. 5.6.1.1(3)

Zx = 	244	in4
Fy = 	50	ksi

Ms = 	12200	in-k	1016.67	ft-k	5.2.1

Ms/Mo = 	0.604

alpha,s = 	0.738	eq. 5.6.1.1(2)

Mb = 	975.49	ft-k	<=	Ms = 	1016.67	ft-k
Mb,use = 	975.49	ft-k 

Open Source Structural Applications: https://github.com/buddyd16/Structural-Engineering

RE: Rafter without fly brace?

Hey KootK. I think I might make this my last post because I don't think I'm my contribution is being constructive anymore. I appreciate your intrigue and knowledge and your persistance on this issue.

Quote (Kootk)

Except that you are comparing apples and oranges. Beam yielding and LTB buckling are separate failure modes.
Correct.

Quote (Kootk)

Just because you hit yielding prior to constrained axis LTB, that does not mean that constrained axis isn't the critical LTB buckling mode. It just means that LTB doesn't govern the failure of the particular situation that you're considering.
Precisely. But section 5.6 doesn't claim checking LTB it is a calculation for "nominal member moment capacity". The upper bound is by definition limitted by the section capacity.

Quote (Kootk)

Yes, and this is precisely what we do using AISC. You know, if we replace ad-infnitem with "just stop someplace reasonable". A reasonable place to stop, for example, would be any buckling mode indicating a capacity higher than yield.
AS4100 stops at the section capacity. AKA when the beam starts yielding. This is also a pretty damn reasonable place to stop.

Quote (Kootk)

For the third time now, would you answer the challenge below:
A challenge for you Human909: sketch me a single bucking mode that would be further up the list in terms of its eigenvalue and could possibly occur in the presence of the lateral restraints. Just one.
I thought I've answered that. There has never been any disagreement that if the top flange is FULLY restrained then the next up on the list is bottom flange buckling as you have illustrated. Christ I even posted a picture of it myself several dozen posts ago.

RE: Rafter without fly brace?

Quote (Human909)

I think I might make this my last post because I don't think I'm my contribution is being constructive anymore.

Stay. Your contributions could potentially be extremely constructive for me if you would only just indulge me and provide me with what I've been asking for:

Quote (KootK)

Ideally, I would have you each post a sketch similar to mine showing the expected movements of both flanges in plan.

How hard is it to just draw two colored lines and send that over to me? Surely, after all the effort that I've poured into assisting you here, you could do that much for me before your withdraw?

Quote (Human909)

There has never been any disagreement that if the top flange is FULLY restrained then the next up on the list is bottom flange buckling as you have illustrated.

This statement is basically saying that constrained axis lateral buckling IS the critical buckling mode. And that's in complete opposition to what you've been telling me for some time. What gives? If this means that your sketched, critical buckling mode would be identical to mine then please just say so. In that case, no sketch from you required.

Quote (Human909)

Christ I even posted a picture of it myself several dozen posts ago.

You've posted a ton of pictures. How on earth am I supposed to know which one you meant to answer my question with? Regardless, wouldn't reposting that picture -- or just giving me the two lines that I seek -- be far less effort that fighting me on this post after post?

Lastly, note that any buckling mode should have the beam pinned with respect to weak axis bending and the supports. Otherwise, it's not an apples to apples comparison with the base code methods. Your models seem to consistently show weak axis rotational fixity at the supports.

RE: Rafter without fly brace?

I didn't see Kootk's bottom flange buckling mode in Human909's images, but Agent666 mastan2 results seem to show it.

RE: Rafter without fly brace?

Quote (celt83)

I think this is the check you mention Agent
segment = 0 ft to 12 ft or from support to first brace point that could be considered an L brace.

Yes, except there's a strength reduction factor of 0.9 to add in at the end that you've missed

Beta_m is also positive when bent in double curvature, so alpha_m = 1.75+1.05*0.5+0.3*(0.5)^2=2.35.

So basically you have FLR as phiMbx = phiMsx (I.E. alpha_m * alpha_s >= 1.0.

Regarding your other checks, with AS4100/NZS3404 and the L restraints to the top flange, when the bottom flange is in compression, it's deemed the critical flange. Therefore the L restraint to the top flange is basically nothing and has no consideration. Therefore the first restraint to the critical compression flange is at 8' or 12' depending on your view.

So saying there is a P restraint at 4' isn't a correct approach.

Best way to think of it is as follows, just determine if a flange is in compression at the point of restraint and pickup the appropriate restraint. Noting an F restraint to the tension flange can be a P restraint in terms of the compression flange. But other than the designation changing an F & P are the same analytically for determine the effective length.

CODE

Top flange restraints
FLLLLLLLF
F-------F
Bottom flange restraints 

- = no restraint if the flange is in compression at this station.

RE: Rafter without fly brace?

When do people use P restraints? I can’t recall ever bothering with them.

RE: Rafter without fly brace?

KootK -
1.) Code stuff completely out the window, I have no problem thinking of the beam prior to being laterally restrained. Or rather, in the condition before I have provided anything but end restraint. I think of this as the first iteration. In this state I need to compare three numbers: moment at yield, moment at the critical (first) LTB mode, and the applied moment. If LTB is the critical failure mode, I add restraints to rule out that particular LTB mode. Can I stop here and say that yield is now the critical failure mode? No, because I need to know that the new critical LTB mode occurs at a higher moment than yield. Because of the added lateral restraint, LTB is changed, now the critical (first ) LTB mode is your constrained axis negative moment LTB. But is that the critical failure mode? I agree that it should be checked. For yield capacity to be claimed, LTB checking should be iterated (adding restraint and rechecking) until the critical LTB mode is shown to occur after yield.
Supposing constrained axis negative moment LTB occurs before yield, I might decide to add more restraint and check again. Something like this might be next:

I think you are dead on with this:

Quote (KootK)

Yes, and this is precisely what we do using AISC. You know, if we replace ad-infnitem with "just stop someplace reasonable". A reasonable place to stop, for example, would be any buckling mode indicating a capacity higher than yield.

So when can we add restraint and call it a day?

RE: Rafter without fly brace?

Quote (Agent666)

Beta_m is also positive when bent in double curvature, so alpha_m = 1.75+1.05*0.5+0.3*(0.5)^2=2.35.
This is how I calculated it on my first pass but the diagram and range presented in table 5.6.1 seemed to suggest that the negative value should be used? Now looking at it again a value of -1 results in alpha,m of 1 which would align with the constant M diagram so seems the intent for moment reversal is positive beta,m and negative for just a change in end moment value but not sign.

Quote (Agent666)

So saying there is a P restraint at 4' isn't a correct approach.
so is it then a fair assumption to say that standard construction doesn't satisfy the P restraint condition indicated in figure 5.4.2.2, otherwise this would seem to be at odds with your statement?

This all is turning out to be moot for the example KootK posed as everything is checking out above the yield moment.

Expanding to AISC where the definition of Lb is length between points that are either braced against lateral displacement of compression flange or braced against twist of the cross section, I think there is a rational argument to take the same 12' segment as Lb.

Cb:
x2.5 2500
Mmax 1000 x12.5 12500
Ma 625 x3 1875
Mb 250 x4 1000
Mc 125 x3 375

Rm 1

Cb 2.173913043

which has the same result of yielding being the controlling failure mode.

Open Source Structural Applications: https://github.com/buddyd16/Structural-Engineering

RE: Rafter without fly brace?

Quote (Celt83)

This all is turning out to be moot for the example KootK posed as everything is checking out above the yield moment.

Firstly, thank you for all of the effort that you've put forth in checking out my example, both in AS4100 and AISC. You did all of the work originally assigned to me and did it much thoroughly and more quickly than I would have. It's eased my burden substantially.

Secondly, once I get myself right with AS4100, I intend to never, ever again bother checking LTB on joist loaded floor girders unless they're cantilevered. This is clearly where AS4100 takes us to in the end. And it will be a nice little, lucrative take-away for me from this exercise. I postulate that the same may well be true of roof girders although owing to the same constrained axis effect even if the bottom flange is everywhere in compression.

Quote (Celt83)

Expanding to AISC where the definition of Lb is length between points that are either braced against lateral displacement of compression flange or braced against twist of the cross section, I think there is a rational argument to take the same 12' segment as Lb.

This will require us to have words however. What, exactly, is that rational argument, articulated in your own words as best you can? Is it purely semantic? Is it because considering L-restraint / constrained axis buckling clearly improves capacity? Or is there a theoretical reason, as I would hope?

I can't dispute that Le=12' is appropriate for AS4100 because I don't understand AS4100 on a theoretical basis. No theoretical understanding = not qualified to poke. I do, however, understand the AISC procedure on a theoretical basis and feel confident in saying that it is built around Lb being the distance between points that would be, in Aussie parlance, the distance between F/P restraints. I couldn't hope to explain that any better than the Yura paper did.

RE: Rafter without fly brace?

Quote (Tomfh)

When do people use P restraints? I can’t recall ever bothering with them.

- I can't imagine that there are many practical opportunities

- My reading suggests that some folks may be attempting to do this in metal frame building by creating torsional connections between purlins and the rafters they would brace. I have no idea how much of this is happening out in the real world however.

- In temporary works, situations arise were you have somebody wanting to avoid stiffeners at the supports of a simply supported beam. This is a straight up no-no via AISC but, in the future, I'm hoping to use AS4100 P-restraints to make a go of it.

RE: Rafter without fly brace?

Quote (KootK)

This will require us to have words however. What, exactly, is that rational argument, articulated in your own words as best you can? Is it purely semantic? Is it because considering L-restraint / constrained axis buckling clearly improves capacity? Or is there a theoretical reason, as I would hope?

From a purely semantic view the definition of Lb very specifically says "..points that are either braced against lateral displacement of compression flange or.."
so at 0' the bottom flange is in compression and braced at the support
in the range 0' < x <= 8' the bottom flange is the compression flange and unbraced
at 8' neither flange is the compression flange as this is the inflection point
at 12' the top flange is now both the compression flange and braced
so by a literal interpretation of the definition of Lb the unbraced length could be taken as 12'.

Reviewing all of the FEM results presented by Agent666 and Human909 this would seem to align with the buckling results they are getting.

My use of the full length for the bottom flange check was really just an extension of what you would do for a roof beam controlled by wind uplift, or put another way a beam that experiences negative bending across the full span. In this case I think AS4100 would seem to treat the beam identical to AISC.

I need to do a lot more reading/research/re-learning on my end to bring an approach founded in first principles to this though.

To really get a definitive answer on this, for use in my area, I've reached out to AISC to get their input on this specific example case relative to the determination of Lb, will post when I hear back from them.

Open Source Structural Applications: https://github.com/buddyd16/Structural-Engineering

RE: Rafter without fly brace?

Quote (HS_PA_EIT)

I think you are dead on with this

Do you practice with AS4100 regularly?

Your agreement is a mixed bag for me. One the one hand, it feels great to have you agree with my position. On the other, this slows me down from possibly shifting my understanding to Human909's explanation of a single LTB procedure that deals with all buckling modes in one go.

The procedure that you described is exactly how I have seen things in the past. I would describe is as a hierarchical approach to LTB checking following this recipe:

1) Pick a beam such that all of your non-LTB failure modes pass (yield, shear, deflection...)
2) Start LTB with no bracing at all or, alternately, any bracing that will be present for free.
3) Identify and assess the single critical buckling mode associated with physical reality of #2,
4) If LTB governs over the other stuff and capacity is insufficient, add one brace. Otherwise STOP.

Quote (HS_PA_EIT)

So when can we add restraint and call it a day?

This would be step #4 in combination, of course, with step #1.

This procedure brings me back to my questioning of the interpretation of 5.5.1.1 and, in particular, the importance of the word "that" in that clause. Given a hierarchical procedure like that described above I would revise step #4 as follows:

4) If LTB governs over the other stuff and capacity is insufficient, add one brace to the critical flange at the proposed location of the the brace. The critical flange shall be that flange which would move the most under LTB buckling at the location of the proposed brace with the restraining effect of all previously added braces accounted for. Otherwise STOP.

For example, in checking constrained axis LTB, you'd come to that already assuming the presence of all the top flange restraints. As such the only flange capable of moving would be the bottom flange. So the bottom flange would be the critical one across the entire length of the beam for this particular LTB mode which is, of course, exactly as it would have to be if one were seeking to add a bottom flange brace in order to progress to the next possible LTB buckling mode.

What I find particularly interesting about 5.5.1.1 is that, in my opinion, a literal read of that clause should suggest exactly the interpretation that I've outlined. No "bending to my will" required. Were I a martian spending my first day on earth, my interpretation is how I would read 5.5.1.1 from the get go. I was surprised to learn that it is not, in fact, interpreted as I have outlined.

RE: Rafter without fly brace?

Quote (Celt83)

so by a literal interpretation of the definition of Lb the unbraced length could be taken as 12'.

One could find gobs of example problems done to AISC practice with a modicum of digging. And, as you know, you wont find a single one that interprets Lb as you have above. So, in terms of the dogma of how how things are interpreted in AISC markets, I don't feel that's in debate.

I certainly agree that we could add more capacity to our negative moment LTB checks by accounting for the constrained axis buckling effect. However, to stay in keeping with the existing AISC LTB theoretical framework, I think that would have to be in keeping with Yura's definition: the distance between points of beam torsional restraint. And it's important to recognize that we already have something for this. An "in the margins" procedure for checking constrained axis buckling exists. It's just not common practice to use us for routine design.

Yura's take on it is repeated below. I'll be waiting with baited breath to hear what AISC has to say about this but I'll also be utterly astonished if they break with Yura on this. It may we Yura providing the answer to your question, either directly or indirectly.

As a side anecdote, I actually started my career with an industry association similar to AISC. I thought that such an experience would be utterly amazing as far a tech development was concerned. I would be at the nexus of developing knowledge surrounded by the best minds in the game! It was one of the most disappointing experiences of my life and I was done with that in a year. The process of answering tech questions at the associations is like this:

1) Question lands on the desk or either an EIT or a PhD that's spent the last decade thinking about nothing other than compound buckling in unequal leg, FRP angles.

2) Question gets forwarded to some committee formed for the purpose. The committee will consist of more PhD's who specialize is something unrelated and some practitioners who probably aren't much more well versed in the issue than the person asking the question. Maybe less. And none of these busy folks really have time for this crap.

3) A shabby consensus is formed from the opinions of the three out of twenty committee members who bothered to respond. And that gets forwarded to the question asker, back through the guy at step #1.

So I don't have a ton of faith in the help desks to help with the truly deep questions. We've had quite a few issues arise here where we've attempted that with mixed results. Answers, even from Larry Muir, to the tune of:

4) The guy who wrote that clause died in 1965 and nobody really remembers how it was derived.

5) AISC considers this an area where designers are expected to apply their own engineering judgment.

RE: Rafter without fly brace?

Quote (kootk)

What I find particularly interesting about 5.5.1.1 is th

Kootk, yes that’s another reason why it’s easier to just use the compression flange check.

But for our discussion here you could focus on one single midspan lateral top restraint, which covers the fundamental question at hand, and which avoids those other complexities about adding more and more restraints.

RE: Rafter without fly brace?

Quote (KootK)

Kootk, yes that’s another reason why it’s easier to just use the compression flange check
.

It is definitely easier. But is it more correct? If the compression flange definition and the max movement definition ever find themselves in conflict, it is my opinion that it is the compression flange definition that should take a back seat. Or, better yet, get out of the car altogether.

In support of this, consider that:

1) The max movement definition should be applicable everywhere.

2) The compression flange definition flops at cantilevers.

Usually that which is more generally applicable winds up being more theoretically correct. Back to Einstein again.

Quote (Tomfh)

But for our discussion here you could focus on one single midspan lateral top restraint, which covers the fundamental question at hand, and which avoids those other complexities about adding more and more restraints.

That actually gets back to an issue that I'm going to revisit with Agent666 in my next post. That said, I really don't want to avoid the complexities. In my mind that is fitting the problem to match the desired solution. I seek a general purpose, applies all the time, kind of understanding.

RE: Rafter without fly brace?

Just some housekeeping on some old questions that I've not yet tended to. It's all in references to the sketches below and the posts that contained the. At long last, I think that I'm up to date on my correspondence.

Quote (Agent666)

I see what you did, it's a blowup of the middle span! Looking comprehension....

Yeah, I wanted to kick myself in the face as soon as I read your comment. I didn't know how to do the dashed box, blowup thing quickly in blue beam so I figured "it's obviously, nobody will get confused". Obviously not obvious.

Quote (Agent666.)

If I do a buckling analysis for a scenario like this, I get the top compression flange buckling the furthest at midspan where you proposed the L restraint. So I'm just never seeing this effect you are noting at that mid point of the middle span that the tension flange is buckling the furthest like you're stating/proposing?

My intent was to propose something almost like a calculus/limits scenario whereby the zone of compression in the top flange would effectively shrink to zero. Or, say, 6". In such a scenario, you'd have virtually all of the top flange in tension and virtually all of the bottom flange in compression. I had thought, with great confidence, that this would produce a situation in which:

1) The compression/critical flange for the first, central L-restraint would be the top flange but;

2) At the location of the central brace, it would be the bottom flange that moved the most.

But, then, your FEM says otherwise. I may have to fact check that with my own FEM, however, as I'm not sure that you modeled thing as I would have. Changes I would make include:

4) I'd shrink the zone of top flange compression a great deal.

5) I'd model the central span on it's own without weak axis end fixity.

If that still doesn't show the results that I expect, I'll just a have to accept that my instincts on this one led me astray. It won't be the first time.

Quote (Agent666)

But I am seeing in the negative moment region that the top flange in tension is moving further than the compression flange, which I assume is the point you're getting at?

Nope. That is interesting and meaningful but I did not anticipate that and was not looking for it.

RE: Rafter without fly brace?

Quote (KootK)

One could find gobs of example problems done to AISC practice with a modicum of digging. And, as you know, you wont find a single one that interprets Lb as you have above. So, in terms of the dogma of how how things are interpreted in AISC markets, I don't feel that's in debate.

yeah like I said need to do more reading/re-learning on my end spent a bit to long in the land of concrete, I thought the most appropriate example to find would be a moment frame beam but even AISC's official examples included bottom flange bracing. Got a copy of the Yura paper so plan to digest.

To borrow a term from Agent666's blog, I've been a bit of Sheep on this topic.

Open Source Structural Applications: https://github.com/buddyd16/Structural-Engineering

RE: Rafter without fly brace?

Celt, check out CL 5.4.2.4 (in AS4100) or CL5.4.2.3 (in NZS3404) for the definition of a lateral L restraint. Basically it's pinned to the flange, preventing lateral deflection, but not preventing twist, if attached to the non-critical flange then its considered to do nothing.

In NZS3404 commentary (unsure if its in AS4100 commentary as well), there are some conditions to meet regarding classifying restraints and the moment/pinned fixity. For a beam or purlin, if of sufficient depth with an appropriate connection, then most certainly it may be able to meet the P restraint condition you highlighted.

Beta_m in NZS3404 is defined as:-

I believe this is the correct interpretation, because you'll get quite a different answer if you used the eqn for alpha_m for comparison than what your calculation was in taking it negative.

I'll need to read over the AISC guidance, that compression flange criteria you've noted essentially seems like the same thing AU/NZ standards are considering to be honest, even if most people may not have picked up on it.

RE: Rafter without fly brace?

Since I checked and AS4100 does not have the same clarifying provisions, here is the NZS3404 provisions for classification of a restraint:-

RE: Rafter without fly brace?

Quote (Agent666)

I'll need to read over the AISC guidance, that compression flange criteria you've noted essentially seems like the same thing AU/NZ standards are considering to be honest, even if most people may not have picked up on it.

It isn't that nobody picked up on it. Rather, it's that we're immersed in examples, software routines, textbooks, and the advice of mentors that all point in the direction of a particular interpretation. Sound familiar?

This is basically the inverse of what I've been up against here with AS4100. Imagine my consternation coming to AS41000, reading nearly identical statements, and finding that they're applied very differently.

The one thing that AISC has going for is that it's very easy to track down the theoretical underpinnings of their LTB method and establish which interpretation is consistent with this. This is just a feature of big market. Derivations for Canadian stuff is often frustratingly hard to track down too.

RE: Rafter without fly brace?

Quote (Celt83)

yeah like I said need to do more reading/re-learning on my end..

Start with the Yura paper. And, if you want more, I highly recommend the book below. They derive much of the AISC stuff from first principles and show in enough intermediate steps on the math that you should have a pretty good shot at following along.

Quote (Celt83)

To borrow a term from Agent666's blog, I've been a bit of Sheep on this topic.

Meh... sometimes you're a sheep, sometimes a shepherd. There's too much out there to know for any individual to know it all. I do like the EngVsSheep business. It's perfect for the application sticks in the imagination. If Agent gets hit by a truck, I hope to steel it for my own web presence.

Quote (Celt83)

Check out Appendix A in TR14 from the American Wood Council

As an aside, I'm pretty sure that recent editions of the Breyer tome on NDS wood design still suggests inflection point bracing for glulam beams.

RE: Rafter without fly brace?

Quote (Agent666)

For a beam or purlin, if of sufficient depth with an appropriate connection, then most certainly it may be able to meet the P restraint condition you highlighted.

More common to count twist retrained purlins (eg fly braced) as F restraint, isn’t it?

RE: Rafter without fly brace?

I can't keep away. But I'll try to stay away from rehasing.

Quote (Kootk)

Secondly, once I get myself right with AS4100, I intend to never, ever again bother checking LTB on joist loaded floor girders unless they're cantilevered. This is clearly where AS4100 takes us to in the end. And it will be a nice little, lucrative take-away for me from this exercise. I postulate that the same may well be true of roof girders although owing to the same constrained axis effect even if the bottom flange is everywhere in compression.
I'm probably misundsterdanting you here; but a check is usuall necessary for roof girders due to bottom flange buckling under uplift. Hence the need for fly-braces.

Quote (Agent666)

Since I checked and AS4100 does not have the same clarifying provisions, here is the NZS3404 provisions for classification of a restraint
Some of those clarifications are helpful. Though the bit about purlins surprises me because I'm surprised that tour typical purlin will be stiff enough to count for a F restraint. I normally treat purlins as L restraints on the top flange except where there are fly braces in which case it is F top flange and F bottom flange.

Quote (Kootk)

It is definitely easier. But is it more correct? If the compression flange definition and the max movement definition ever find themselves in conflict, it is my opinion that it is the compression flange definition that should take a back seat. Or, better yet, get out of the car altogether.
All our codes take short cuts for the sake of simplicity and ease. As long as they don't lead to unconservative outcomes then there isn't an issue. (Choosing the compression flange definition might be LESS conservative sometimes, but not necessarily unconservative. If you get my distinction.)

Quote (Kootk)

2) The compression flange definition flops at cantilevers.
It does which is why it doesn't apply at cantilevers. (5.5.3)

RE: Rafter without fly brace?

Quote (Human909)

nts on the top flange except where there are fly braces in which case it is F top flange and F bottom flange.

F typically refers to the cross section as a whole. What do you mean by F top and F bottom?

RE: Rafter without fly brace?

Quote (Agent666)

Since I checked and AS4100 does not have the same clarifying provisions, here is the NZS3404 provisions for classification of a restraint:-

Interesting. I hadn't seen those purlin depth rules before for assessing whether a restraint is P vs F?. Are they commonly used in NZ when assessing P vs F?

Also, do you really consider a standard two bolt purlin cleat with 2mm oversize holes a moment connection?

RE: Rafter without fly brace?

Quote (human)

All our codes take short cuts for the sake of simplicity and ease. As long as they don't lead to unconservative outcomes then there isn't an issue. (Choosing the compression flange definition might be LESS conservative sometimes, but not necessarily unconservative. If you get my distinction.)

I view it exactly the same way. Sometimes the compression flange is a worse place to brace, but if it works it works.

It is a bit sad though that the simplified rules have led so many engineers into believing that the compression flange is always the best place to brace, and that bracing the tension flange is automatically inneffective.

RE: Rafter without fly brace?

Quote (Tomfh)

F typically refers to the cross section as a whole. What do you mean by F top and F bottom?
Good question. You are correct F refers to a cross section as a whole. Just like all the restraint provisions. But the determination of whether a particular cross section is F, P, or even unconstrained is dependent on the load conditions. You have multiple load conditions so the normal approach that I use and is used by computer programs like Space Gass is specify the F,P,L etc restraints PER flange. They will then control the effective length calculation depending on the load condition being considered.

RE: Rafter without fly brace?

Ok fair enough. I didn't realise the F and P terms were used with specific reference to flange restraints. I use microstran which uses E (ELASTIC), N (NONE), L (LATERAL) for each flange.

RE: Rafter without fly brace?

Quote (Human909)

But I'll try to stay away from rehasing.

Wow... you're still not going to answer my challenge. I was really hoping that you'd once-hash that. Oh well, clearly there's something preventing you from cooperating that I'm not privy to so I'll just let that go.

Quote (Human909)

I'm probably misundsterdanting you here; but a check is usuall necessary for roof girders due to bottom flange buckling under uplift. Hence the need for fly-braces.

Nope, you heard right. The main take away for me here has been that constrained axis LTB kicks ass. And that effect should be significantly in play regardless of which flange gets the constraining. What's more, with wind uplift, you also get the benefit of the load being "below" the shear center.

Quote (Human909)

It does which is why it doesn't apply at cantilevers. (5.5.3)

I know, that's precisely why I said that it flops at cantilevers.

Quote (Human909)

All our codes take short cuts for the sake of simplicity and ease. As long as they don't lead to unconservative outcomes then there isn't an issue.

I guess that this is just a philosophical difference. Sure, everything in engineering involves simplification and approximation. I don't, however, see that as justification for failing to understand the theoretical foundations of the simplifications and approximations that we use. Quite the opposite in fact. I think that shortcuts can be dangerous in the hands of those who don't understand the theory behind them.

RE: Rafter without fly brace?

Quote (Kootk)

Nope, you heard right. The main take away for me here has been that constrained axis LTB kicks ass. And that effect should be significantly in play regardless of which flange gets the constraining. What's more, with wind uplift, you also get the benefit of the load being "below" the shear center.

You don't get to count the lateral restraints for wind uplift unless rotationally restrained e.g. fly braces. AS4100 counts wind uplift with lateral restraints on the tension/non-critical flange as completely unrestrained.

RE: Rafter without fly brace?

Quote (Tomfh)

You don't get to count the lateral restraints for wind uplift unless rotationally restrained e.g. fly braces. AS4100 counts wind uplift with lateral restraints on the tension/non-critical flange as completely unrestrained.

I don't seek AS4100's permission to do this. I'll do it independently based on my theoretical understanding of constrained axis buckling. Or I won't, depending on the conclusions that I reach when I study it in detail. AS4100 will inform my decision but it will be me making the decision.

RE: Rafter without fly brace?

Quote (Tomfh)

You don't get to count the lateral restraints for wind uplift unless rotationally restrained e.g. fly braces. AS4100 counts wind uplift with lateral restraints on the tension/non-critical flange as completely unrestrained.
Agreed

Quote (KootK)

The main take away for me here has been that constrained axis LTB kicks ass. And that effect should be significantly in play regardless of which flange gets the constraining.
That is not comfirmed by code nor buckling analysis.

RE: Rafter without fly brace?

KootK - I'm in the US and have had little exposure to AS 4100, so I can't speak to the theoretical background or how it is regularly applied. I'm trying to gain understanding and hope that my ignorance is not taken as offensive to anyone. Here is a worked example from "Steel Structures Design Manual To AS 4100" First Edition by Brian Kirke, Senior Lecturer in Civil Engineering Griffith University and Iyad Hassan Al-Jamel, Managing Director ADG Engineers Jordan.

Maybe there is effectively zero possibility within the practical limits of real world construction of an LTB mode (constrained axis LTB) occurring before yielding with the compression flange fully restrained.

RE: Rafter without fly brace?

Quote (KootK)

The main take away for me here has been that constrained axis LTB kicks ass. And that effect should be significantly in play regardless of which flange gets the constraining.

Quote (Human909)

That is not confirmed by code...

1) You'll have to forgive me if I don't feel constrained on this by the lack of explicit code approval from a code section that no one can tell me the theoretical basis for.

2) Things like this are precisely why I seek to understand the theory behind code clauses. It gives me the ability to, and the ethical justification for, extending code provisions. That, rather than being a slave to their literal interpretation like an unthinking robot.

Quote (Human909)

That is not confirmed by...buckling analysis.

3) Fantastic. I love being proven wrong in the present so that I can be more often right in the future. Please post the details of that buckling analysis.

RE: Rafter without fly brace?

Quote (HS_PA_EIT)

KootK - I'm in the US and have had little exposure to AS 4100, so I can't speak to the theoretical background or how it is regularly applied.

No problem at all. For something like this, it's just important to know the background of the person behind the ideas. In your statements, I was hearing a lot of echoes of my own thinking which led me to suspect that we may have similar backgrounds when it comes to steel design. While I values your opinion very much, I'm sure that it will come as no surprise to hear that, on this topic, I'd value it even more if you were an Aussie practitioner. That whole "horse's mouth" thing, you know?

Quote (HS_PA_EIT)

Here is a worked example from "Steel Structures Design Manual To AS 4100" First Edition by Brian Kirke, Senior Lecturer in Civil Engineering Griffith University and Iyad Hassan Al-Jamel, Managing Director ADG Engineers Jordan.

Thanks for the example. It's definitely more cut and dry with simple span beams and continuous compression flange bracing. I'm fairly certain that all codes give you a pass on LTB in that situation. That said, I agree with your base point that I would reiterate in my own words as follows:

1) The number of possible modes of instability is theoretically infinite.

2) The number of modes of instability of real practical concern is quite limited.

3) It is the purview of both design standards and design engineers to intelligently navigate the juxtaposition of #1 & #2.

Quote (HA_PA_EIT)

Maybe there is effectively zero possibility within the practical limits of real world construction of an LTB mode (constrained axis LTB) occurring before yielding with the compression flange fully restrained.

That is most definitely the case and is why I've been describing the LTB checking of the examples as effectively:

4) Check LTB of the constrained axis buckling mode as I've described it OR;

5) Trust that #4 is bloody awesome and check nothing at all.

The key feature there is simply to recognize that, if you are going to bother checking any LTB mode, then recognize that the only meaningful check is the constrained axis LTB mode. That, at least as far as it pertains to North American practice where we tackle instability phenomena in a hierarchical fashion as we've already discussed.

The infinite nature of instability is something that seems to factor heavily into the confusion that often surrounds free cantilever design. In that case, you're dealing with a couple of separate LTB buckling modes that occur in unusual close proximity to one another from a potential/strain energy perspective. The top flange is your most effective first brace point but, then, push things a little further and you'll have the bottom flange flopping out to the side. These are really two separate LTB modes rather than a single one. I suspect this is why some codes conclude that you should just be bracing both flanges if your really want to tax a cantilever.

Because no one else will do it for me, I've been trying to generate some high level theoretical explanations of AS4100 of my own. It's still a work in progress but one candidate for "how does it work" is something like this:

1) Only actually give explicit consideration to one buckling mode: the completely unrestrained mode. If capacity is insufficient, add your first brace.

2) Effectively "over-brace" the unrestrained LTB mode by adding more restraints to that LTB mode even though that LTB mode ceased to be a physical possibility, or the critical LTB mode, once the first brace was added.

3) Make the argument that the over-bracing of the unrestrained LTB mode from step #2 effectively eliminates the possibility of any subsequent LTB modes from coming to pass.

I think that this would be consistent with what you're suggesting (and I agree with). There are some big logical gaps to fill in that explanation but, at the least, it would resolve these issues that I have with understanding the AS4100 procedure:

A) How does it address all LTB modes by explicitly considering only one LTB mode (or no actual buckling mode, I'm not sure)? You know, if Human909 is right about that being the case.

B) How can it be that the effective length used is something other than the actual buckling length of the thing doing the bucking? That this is true is clear now from the Yura paper, the FEM models, the design example, and reasonable expectations of physical behavior.

RE: Rafter without fly brace?

I'm a bit busy to think about the deeper and more meaningful questions posed in the past few days but here's some quick input.

Quote (human909)

Sorry. What? How do you figure this?
The hand check numbers are from your Space Gass output and the capacity according to the elastic buckling method is taken from Agent666's Cases 2 & 3. Cases 2 & 3 are the same according the the AS4100 hand method (they differ only by a lateral restraint to the tension flange) and Agent got similar results for the two. Case 3 just made it to the section capacity while case 2 fell about 3% short. Hitting section capacity is what keeps the final result similar between hand calc and elastic buckling but I think there would be other cases where the difference is larger and I think that would be unconservatism on the part of the hand calculations.

Quote (KootK)

My impression here is that many of us, myself included, lack a cogent theoretical understanding of just how the AS4100 provisions work their magic

What are the major differences to AISC? It looks to me that, aside from L restraints on segments with moment reversal, they're pretty similar. Our L_e calculation may have a bit more to it. Is there more?

I'm at the point of wondering whether L restraints with moment reversal are something not handled well by AS4100. Perhaps the rule was derived from considering simply-supported beams but applied generally. See graph at the end.

Quote (KootK)

I could run it in Mastan. I may do this eventually but I wouldn't hold your breath.

I don't know how to run it in Mastan (on the to-learn list). That's why we prevail upon the generosity of Agent666 (please). I'd like to run the W27x84 in the following cases:
- The 32-foot span with just one L restraint to top flange at midspan; and
- The 22 metre span with top flange L restraints at 1.1m.

Quote (KootK)

Would you say that the lateral brace at [2] makes this truss immune to LTB?
I don't like the look of node 4. That aside, K_l=1.0 doesn't mean immune from LTB, it means no more exposed to LTB than for shear centre loading. But I now agree that top flange loading at a top flange L restraint should use K_l>1.0 if the bottom flange is going to move sideways.

Quote (Tomfh)

When do people use P restraints? I can’t recall ever bothering with them.
They might be free or geometrically preferable to F restraint whilst almost doing the same job. I've attached some guidance on what is F/P from an article in the Australian Steel Institute Journal from 1993 (by Trahair, Hogan & Syam).

https://files.engineering.com/getfile.aspx?folder=...

Quote (KootK)

AISC procedure on a theoretical basis and feel confident in saying that it is built around Lb being the distance between points that would be, in Aussie parlance, the distance between F/P restraints

AISC 360-16 Section F2.2 says "Lb = length between points that are either braced against lateral displacement of the compression flange or braced against twist of the cross section." That's AS/NZS F, P or L restraint, isn't it? At least for beams without moment reversal. And the difference for moment reversal is the unwritten law that "the" compression flange is both flanges.

Quote (KootK)

ere I a martian spending my first day on earth, my interpretation is how I would read 5.5.1.1 from the get go. I was surprised to learn that it is not, in fact, interpreted as I have outlined.
AS1250, the allowable stress predecessor to AS4100, said: "The critical flange of a member is that part which would deflect the furthest during buckling in the absence of the restraint being designed." I agree with that. I think it's also what you're saying.

Quote (KootK)

It is definitely easier. But is it more correct? If the compression flange definition and the max movement definition ever find themselves in conflict, it is my opinion that it is the compression flange definition that should take a back seat.
My opinion is that moving furthest is more correct hence mentioned first, while compression flange is the simplification for ease of routine design. Compression flange is self-reliant and easy to determine whereas moving flange depends on the other restraints and is less easy to determine. Quoting again from AS1250, the compression rule of thumb is filed under 'if an exact analysis is not available'.

Quote (KootK)

The main take away for me here has been that constrained axis LTB kicks ass. And that effect should be significantly in play regardless of which flange gets the constraining
Bottom flange L restraint in a simply supported beam under gravity loading does nothing for capacity. I can't find much else regarding tests or analysis of L restraints, which is why I wonder whether simply-supported results were just extrapolated to applying universally. The graph below shows results of elastic buckling analysis. Note also Agent666's case #1 rotated about the bottom flange anyway so bottom flange restraints wouldn't be stressed.

Quote (KootK)

A) How does it address all LTB modes by explicitly considering only one LTB mode (or no actual buckling mode, I'm not sure)? You know, if Human909 is right about that being the case.

B) How can it be that the effective length used is something other than the actual buckling length of the thing doing the bucking? That this is true is clear now from the Yura paper, the FEM models, the design example, and reasonable expectations of physical behavior.

A) I'm not sure it is just one mode. We have to check all segments but often it's obvious which will govern. I think in the W27x84 case they represent different modes as different flanges are critical.

B) The effective length combined with the alpha_m factor is meant to relate to the capacity of a beam under uniform moment. I can imagine that the length would get a bit abstract when the moment is nothing like uniform.

RE: Rafter without fly brace?

Quote (steveh49)

I don't know how to run it in Mastan (on the to-learn list). That's why we prevail upon the generosity of Agent666 (please). I'd like to run the W27x84 in the following cases:
- The 32-foot span with just one L restraint to top flange at midspan; and
- The 22 metre span with top flange L restraints at 1.1m.

I agree, Agent666 & Human909 have been carrying more than their share of the load on the modelling front. To help rectify that, and to to have some fun of my own, I'm going to take a swing at both of your proposed models. I'm also going to include links to my Mastan files for the benefit of anyone who would like to critique them or use them or as convenient starting points for their own exploratory modeling. The slowest part of getting started is figuring out how to do build a functional model that delivers what you need. And drawing those stupid faux cross sections so that you can see the twist.

For your 32 ft example, see the plot below and this Mastan file: Link. Quick notes:

- Elastic critical analysis.
- No imperfections modeled so a high side estimate.
- Fy inflated to ensure an elastic buckling failure mode.
- No weak axis rotational restraint at the ends.
- Applied Load Ration = 0.59
- Fails at 0.59 x 250k = 147k
- Clearly a version of the constrained axis buckling mode that I've been droning on about.

RE: Rafter without fly brace?

Quote (steveh49)

I'd like to run the W27x84 in the following cases...the 22 metre span with top flange L restraints at 1.1m.

To clarify and update others on the situation that I believe we are testing, my understanding is that we're querying this:

Quote (steveh49)

I think there might be a quick and easy first test we can apply. Taking the W27x84 and the same bi-linear shape of the moment diagram from the test case, I reduced the maximum bending moment to 1240 kNm which is the design section capacity phi.Ms. I then increased the sub-segment length until the AS4100 LTB capacity phi.Mb = phi.Ms. The sub-segment length was 5.065m (ie from end of beam to the inflection point) giving overall beam length of 20.26m before LTB governs according to AS4100.

Quote (KootK)

Your example was clever. Me likey. As I understand it, the crux of the example was to exaggerate the length of the original problem until constrained LTB did in fact occur; and, in doing so, suggesting that it would take a rather ridiculous span to make that happen (66.5 ft).

So the exact numbers here have been drifting a bit. And, because of the way that Mastan is sort of unit-less and has canned AISC sections in inches, it's much easier for me to work with spans and segment lengths that are in even increments of inches. So I tweaked your numbers a bit but, I suspect, the analysis will still serve the purpose that you'd intended.

For this example, see the plot below and this Mastan file: Link. Quick notes:

- Span = 70 ft = 21.3m
- Sub-segment length = 7 ft = 2.13m (10th points. Probably doesn't matter much as long as it's close enough to force the constrained axis buckling mode.
- Elastic critical analysis.
- No imperfections modeled so a high side estimate.
- Fy inflated to ensure an elastic buckling failure mode.
- No weak axis rotational restraint at the ends.
- Applied Load Ratio = 0.1026
- Fails at 0.1026 x 250k = 26k point load
- Fails at 2768 kip*in end moment = 313 kN*m (25% of your phi.Ms. value of 1240 kNm)

CONCLUSION: if I've not screwed anything up, I believe that this would suggest that the beam length at which constrained axis LTB would occur can be expected to be significantly shorter than the value at which AS4100 would predict that LTB would govern over phi.Ms.

SURPRISE OBSERVATION: the moments at the ends are different from the moments in the middle. I should have anticipated this, in retrospect, but did not.

RE: Rafter without fly brace?

You don't need to model any imperfections with the elastic or inelastic critical load analyses. It is effectively an eigenvalue analysis solving the governing equations for the modes and hence reference buckling moment and alpha_m directly. The imperfections are dealt with afterwards in the AS4100 and NZS3404 methods as per the example I wrote up on the screenshot by applying the alpha_s factor. If you're doing any of the 1st/2nd order equations then you explicitly need to model the imperfections and set up the residual stress model, and of course include warping.

The only thing you need to ensure if doing the eigenvalue analysis is to enable warping (why it's not turned on by default....), but only on the main beam, not on all the bits to visualise the twist, because it changes the answer when it should have no effect.

I was also getting elastic buckling without jacking up f_y.

It's important to recognise that the moment at which buckling occurs in the analysis is not the design capacity. So don't compare these moments directly. edit... Bolded for super importance!

I mentioned as well that because you're dealing with a centerline model with restraints off the centerline, the stiffness of bits to visualise the web twist comes into play. How stiff to make it, really don't know but I found taking a member the same thickness as the web and making it as wide as the beam depth kind of cake up as a lower bound.

I didn't review your file, just generalising comment for anyone using mastan2.

I actually think in hindsight the case #2 I did I screwed up the calc because I think I still looked at the total length when I should have been looking at 8' or 12'. That's what I get for trying to do it on the calculator on my phone. So it will have FLR, no 3% shortfall.

RE: Rafter without fly brace?

Mastan2 has metric sections also. The unitless thing can get confusing. So best to stick to what you know and convert end answer.

If you've not got the same moment then I think you've applied the wrong moment to balance the load you put at the center?

RE: Rafter without fly brace?

I didn't actually apply any end moments. I just fixed the ends to produce the same result as I figured that would be simple and dummy proof. I suspect that its something to do with equilibrium being enforced on the buckled shape. The end moments would presumably rotate in space about the z-axis, just like the ends themselves.

RE: Rafter without fly brace?

KootK:
Does mastan2 consider shear deformation, that could be one factor for the different fixed end moments.

Agent666:
If I understand the value taken from the buckling analysis replaces the Fcritical value used in the LTB check, is that accurate?

RE: Rafter without fly brace?

Quote (Celt83)

KootK: Does mastan2 consider shear deformation, that could be one factor for the different fixed end moments.

I'm not really sure. It takes in [mu] and [E] so it could calculate [G]. And my guess is that the Ayy and Azz are shear areas that I currently have set to infinite. I speculate that Mastan can include shear deformation but, as I've been using it, has not been. Unfortunately, it's not the kind of program where you can just click in a box and push F1.

You should just get Mastan. It's free and you'd love it.

Quote (Celt83)

Agent666: If I understand the value taken from the buckling analysis replaces the Fcritical value used in the LTB check, is that accurate?

On a related note, I'd like to explore some things here that do take account of imperfections etc. And, if possible, I'd like us to agree to a common way of handling that, be it the AS4100 method or something else. So I'm in the market for recommendations if anyone has any. I'd like it to be simple, if possible, to limit the time investment. One option I'm considering is this:

1) Look up the AISC tolerance on beam sweep.

2) Apply a torsion to the beam at the load point equal to the vertical load multiplied by the sweep. So T = P * L/1000 or something like that. Essentially just a perturbation.

RE: Rafter without fly brace?

Quote (KootK)

Secondly, once I get myself right with AS4100, I intend to never, ever again bother checking LTB on joist loaded floor girders unless they're cantilevered. This is clearly where AS4100 takes us to in the end. And it will be a nice little, lucrative take-away for me from this exercise. I postulate that the same may well be true of roof girders although owing to the same constrained axis effect even if the bottom flange is everywhere in compression.

With Mastan set up on my virtual machine, it seemed easy enough to just test this and put it to bed.

All cases: W27x84; 32ft; 35 kip uplift loads at 1/8th points; total load = 245 kip; elastic critical run; no week axis rotational restraint at ends.

Case 1: simple span beam with no L-restraints. ALR = 0.44233; Total Load = 109 kip

Case 2: simple span beam with L-restraints. ALR = 0.59638; Total Load = 146 kip

Case 3: fixed end beam with no L-restraints. ALR = 2.882; Total Load = 706 kip

Case 4: fixed end beam with L-restraints. ALR = 7.001; Total Load = 1715 kip

CONCLUSIONS:

A) For the simple span case where the bottom flange is everywhere in compression, the improvement was not as much as I'd hoped at only about 34%. Looking at the deflected shapes, it seems that this is because the unrestrained center of LTB rotation is pretty much at the roof deck level anyhow so not much changes by adding the deck.

b) Once end moments are introduced, the improvements come fast and a constrained axis LTB failure seems improbable. This jives with the AS4100 method which would have counted several of the top flange restraints as L-bracing at the ends of the beam. And I think that I might see why now. Once your get both flanges trying to do some buckling, the LTB mode becomes skewed more towards the lateral than the torsional. This pushes the center of LTB rotation up further above the top flange and makes the the L-restraints that much more effective.

RE: Rafter without fly brace?

Quote (Celt)

If I understand the value taken from the buckling analysis replaces the Fcritical value used in the LTB check, is that accurate?

Not quite, in AISC I believe you replace F_e the elastic buckling stress, then evaluate F_critical normally from there! It's basically the same in AU/NZ standards, instead of working in stress which is fairly meaningless, we work in moment. Elastic buckling moment is equivalent to elastic buckling stress, Fcrit is equivalent to member moment capacity M_bx.

So in AISC there is a codified way of taking account of any restraint condition imaginable, backing up the assertion that any restraint to the compression flange can in fact be used as essentially AU/NZ standards have the exact same provisions, a buckling analysis quantifies the effect. I linked to an article earlier that suggested AISC doesn't account for initial imperfections so there are some differences in the underlying stuff though.

So in conclusion you can do a buckling analysis to work out the elastic buckling stress, clause E3 states this explicitly (see below). Once you have this from a buckling analysis then you carry on as per normal design.

So keeping this in mind, if you're ignoring any intermediate restraints that a buckling analysis might show are effective you're potentially being very conservative (obviously every scenario is different), even if that's the way the examples and hand checks show to AISC.

I hope my earlier case #1 demonstrated that the buckling analysis route gave exactly the same result as codes theoretical approach. Now as things get more complex, a buckling analysis is still going to give the theoretical buckling moment (and allow for calculation of the exact alpha_m instead of using a curve fit equation), the code provisions might for the sake of needing to cover 1001 cases give a (hopefully) conservative all encompassing answer.

What the buckling analysis does allow you to get into is say you have a rotational spring as a restraint, you can evaluate this directly as its neither pinned with no rotational restraint, nor is it fixed with no rotation. This is the beauty of using a buckling analysis, you're simply working out the theoretical buckling moment but directly for any restraint condition imaginable. The moment value coming out of the buckling analysis is exactly in the form expected by the code to then go on and apply your normal buckling curves modifications to account for the 2nd order effects (initial imperfections, out of plumbness, residual stresses, etc, in AU/NZ speak this is the alpha_s factor).

You can apply the imperfections directly in mastan2 using the update geometry tool (you'll find some videos by the author on youtube showing you how to do this).

But as I noted, it's not of importance if you are doing the code implied eigenvalue analysis, by this I mean get buckling moment, apply normal code reduction, get equivalent capacity.

If you go through the mastan2 stability fun modules, it takes you through each type of analysis and compares answers. The upshot is if you allow for all the second order effects and use the 2nd order elastic or inelastic analysis you'll get pretty close the code curve which indirectly allows for these things (these analyses are more your full on FEM type of thing that gives you the capacity directly because you've allowed for the 2nd order stuff and don't need to apply the code curve reductions (i.e. alpha_s in AS4100/NZS3404 terms).

Screenshot below of my attempt at this when I went through it a year or two ago with both AISC and NZS3404 results. Shows the importance of allowing for warping and imperfections. Note where the default AISC curve sits relative to the L/1000+ warpingresidual stress curve relative to the NZS3404 kr=1.0 curve. The Adina FEM results were provided by the author for comparison, you work out all the rest as part of the stability fun exercise if you want to go down that rabbithole! (I highly recommend it if you have hours to spare, and I mean hours (per module)....).

direct link to full size picture

RE: Rafter without fly brace?

Quote (Steve)

I've attached some guidance on what is F/P from an article in the Australian Steel Institute Journal from 1993 (by Trahair, Hogan & Syam).

Thanks for that. Most of those P connections I never use, but good to know.

Interesting that they count a fly brace on unlapped purlins as P. “Design of Portal Frames” says to not bother and take kt=1.0 at fly bracing.

Quote (Steve)

Perhaps the rule was derived from considering simply-supported beams but applied generally.

It needn’t just be simply supported cases. As noted by others above, for gravity loads the top flange is often the best place to buckle, period, even in continuous beams when the top flange has gone into tension. That is to say the top flange will often buckle the furthest, even in tension zone. Bracing it boosts buckling capacity more than the bottom compression flange, contrary to the “compression flange is critical” rule. (Vice versa for wind uplift). From memory the old code AS1250 reflected this. It specified critical flange for gravity as top flange, and bottom flange for wind.

Then they changed the simplified rule to “compression flange is critical”, which emphasises moment reversal - even through moment reversal isn’t actually that relevant to LTB - (buckling shapes do not mirror bending moment diagrams)

The current rule covers cases where bottom flange compression is really important (say a deep haunch), and still probably good enough even when the tension flange is the real critical flange - which is a lot of the time.

RE: Rafter without fly brace?

Quote (Kootk)

A) For the simple span case where the bottom flange is everywhere in compression, the improvement was not as much as I'd hoped at only about 34%. Looking at the deflected shapes, it seems that this is because the unrestrained center of LTB rotation is pretty much at the roof deck level anyhow so not much changes by adding the deck.

Yes, you’re grabbing it in a place it doesn’t move much, so grabbing it there doesnt do much.

This is what we were saying before, hence AS4100 saying no restraint for you if you grab it there.

RE: Rafter without fly brace?

Quote (Tomfh)

Yes, you’re grabbing it in a place it doesn’t move much, so grabbing it there doesnt do much. This is what we were saying before, hence AS4100 saying no restraint for you if you grab it there.

I'm afraid that was not what you said before Tomfh. What you said before was basically "AS4100 says no". What would have been more useful would have been "AS4100 says no and the thoeretical reasons for that are X, Y, and Z". You know, the "why" versus the "what". Instead, I had to chase down the why myself this morning.

Besides, it's not like a 34% improvement is nothing. Clearly, grabbing the tension flanges for the constrained axis LTB effect is doing a fair bit, even for simple span beams.

RE: Rafter without fly brace?

We weren’t saying AS4100 says it for no reason.

It’s obvious why laterally bracing a non critical flange (ie laterally bracing close to the centre of rotation) is generally considered ineffective. Because the beam can still fall over. You’re adding your pin at the pivot point, where it does far less. That’s exactly what happens in these situations. The beam can just flop over, pivoting about the restraint.

When you brace the part that wants to move (aka the critical flange) you inhibit that rotation from occurring at that section.

RE: Rafter without fly brace?

Quote (Tomfh)

We weren’t saying AS4100 says it for no reason.

I didn't say that you said it for no reason. I said that you didn't provide the reason. I don't read minds.

Quote (Tomfh)

It’s obvious why laterally bracing a non critical flange is generally considered ineffective

It wasn't obvious to me. Nor should it have been as a 34% improvement is still a fair amount of improvement, particularly for the most extreme of cases (100% bottom flange in compression)

And yes, I get the mechanism. I described it myself earlier.

Quote (KootK)

looking at the deflected shapes, it seems that this is because the unrestrained center of LTB rotation is pretty much at the roof deck level anyhow so not much changes by adding the deck.

These two statements of yours now seem to conflict. I'm basically just agreeing with the first one.

Quote (tomfh)

It is a bit sad though that the simplified rules have led so many engineers into believing that the compression flange is always the best place to brace, and that bracing the tension flange is automatically inneffective.

Quote (Tomfh)

It’s obvious why laterally bracing a non critical flange is generally considered ineffective

RE: Rafter without fly brace?

Quote (Kootk)

And yes, I get the mechanism

Ok good. Then you understand why AS4100 considers it ineffective. Not sure why you needed to fight over it.

Quote (Kootk)

These two statements of yours now seem to conflict.

They’re not in conflict.

The first statement refers to the AS4100 rule that “the compression flange is the critical flange”. This rule (and the background to it) is murky, and does lead to some confusion about the actual best place to brace. It incorrectly identifies some compression flanges as “critical” when they aren’t actually the critical flange. But as noted it is good enough to treat the compression flange as the critical flange, even when it isn’t really the critical flange.

The second statement refers to the rule that says it is ineffective to laterally brace a non critical flange. The “theory” behind the rule is obvious. We don’t seem to disagree on it.

RE: Rafter without fly brace?

Quote (Agent666)

If I do a buckling analysis for a scenario like this, I get the top compression flange buckling the furthest at midspan where you proposed the L restraint. So I'm just never seeing this effect you are noting at that mid point of the middle span that the tension flange is buckling the furthest like you're stating/proposing?

Back to this with Mastan using this file and the methodology described below: Link

Doing it this way, I was able to create a situation in which the following is true at the mid-span section where one might contemplate a brace;

1) The bottom flange is in tension.
2) The top flange is is in compression.
3) The bottom/tension flange would move the most (+1.00 for the bottom/tension flange; -0.68 for the top/compression flange).
4) One might rationally expect that the bottom/tension flange would be the best place for this brace.

And yes, this was very much a contrived example designed to produce this effect. As such, the example's practical significance is limited.

Quote (KootK)

My intent was to propose something almost like a calculus/limits scenario whereby the zone of compression in the top flange would effectively shrink to zero. Or, say, 6". In such a scenario, you'd have virtually all of the top flange in tension and virtually all of the bottom flange in compression. I had thought, with great confidence, that this would produce a situation in which:

1) The compression/critical flange for the first, central L-restraint would be the top flange but;

2) At the location of the central brace, it would be the bottom flange that moved the most.

But, then, your FEM says otherwise. I may have to fact check that with my own FEM, however, as I'm not sure that you modeled thing as I would have. Changes I would make include:

4) I'd shrink the zone of top flange compression a great deal.

5) I'd model the central span on it's own without weak axis end fixity.

If that still doesn't show the results that I expect, I'll just a have to accept that my instincts on this one led me astray. It won't be the first time.

RE: Rafter without fly brace?

I'm hoping someone will take mercy on me as this is a long thread and I'm having a hard time establishing what the argument is. A couple questions might help those who later find this:

Can you define and L-brace and a P-brace?

My understanding of the argument:
If you have a continuous beam or in the example above a fixed end beam, what is the unbraced length for buckling assuming:
• The top flange is restrained against lateral translation
• At the ends of the beam the Top flange is restrained against lateral translation and the bottom flange cannot rotate/translate relative to the top flange.
It seems like everyone has agreed that it should be defined as the length between "columns"
Then it seems we discovered there is some benefit to having the top of the beam braced against lateral translation even when checking the end (negative) moments. This benefit is or is not codified?

I'm I close?

RE: Rafter without fly brace?

Quote (Tomfh)

Ok good. Then you understand why AS4100 considers it ineffective. Not sure why you needed to fight over it

Firstly, I don't "fight". I debate like a civilized person. If you see this as fighting, that says more about your mindset than mine.

Secondly, I continued to debate this because:

1) You neglected to offer any theoretical explanation for your statements and;

2) I wasn't really wrong (34% improvement). Rather, I just wasn't as right as I'd suspected.

I came at this today by:

a) Doing all the research legwork myself.

b) Sharing my research results with others rather than just laying down unsubstantiated claims.

c) Making a point of reporting back to the group that things did not work out as well as I had anticipated.

I consider this to be a gentlemanly and adequate response on my part. To the extent that a mea nulpa was warranted, it's been issued. What more would you ask of me?

If we're "fighting", it's because you couldn't resist diving back in to poke the bear a little more, even though there was really no reason to do so. Frankly, this particular bear doesn't mind all that much so poke away. Just don't lose your composure when I continue to poke back.

RE: Rafter without fly brace?

Quote (kootk)

If we're "fighting", it's because you couldn't resist diving back in to poke the bear a little more

I’m going to respond if you dispute key concepts like the ineffectiveness of lateral braces on non critical flanges.

You started out in this thread saying it is fundamentally wrong to count lateral braces at critical flanges (leading a few people astray in the process), and now here we are and you’re arguing we should be counting not only lateral braces of critical flanges, but lateral braces of non critical flanges.

RE: Rafter without fly brace?

Quote (L-Brace)

Can you define and L-brace and a P-brace?

L-brace: Aussie for just straight up lateral (L) support without providing any torsional restraint to the beam. Usually this is how own would conservatively treat a steel joist tying in.

P-brace: Aussie for a full fixity brace (lateral + torsion) that only does a partial (P) job of being a full fixity brace. An example would be a top side purlin moment connected to the beam supported to it without a stiffener pair on the beam. In reality, all open webbed steel joist connections are somewhat a version of this.

Quote (RFreund)

It seems like everyone has agreed that it should be defined as the length between "columns"

Oh no, not at all. Me, Yura (read that attached paper), and most AISC practitioners see it that way. The Aussie code seems not to and treats the effective buckling length as the length between L-braces. This was the initial source of contention. At this point, we've established that the AISC and AS4100 methods are practiced quite differently. My current bones of contention are these:

1) I don't understand the underlying theory that justifies AS4100 treating the unbraced LTB length as something much shorter than it obviously is in the real world (distance between points of twist restraint) and;

2) The AS4100 method seems to operate on a single, unrestrained LTB buckling mode rather tackling the multiple, possible modes in a hierarchical fashion as we do with AISC. Again, this is a theoretcial understanding issue for me. I just don't undertand how AS4100 works the magic that it seems to. I want a look at the wizard behind the curtain.

Quote (RFreund)

Then it seems we discovered there is some benefit to having the top of the beam braced against lateral translation even when checking the end (negative) moments. This benefit is or is not codified?

I wouldn't say that it was discovered here. I've been mentioning the constrained axis buckling check since the very beginning and extolling its virtues in improving capacity. This is the effect that you've described. As for codification:

1) The base method in the AISC SCM does not account for this.

2) The are AISC documents, such as the Seismic Design Manual, that do provide guidance for constrained axis LTB checking.

3) Frankly, it's hard to say if AS4100 explicitly checks constrained axis buckling or not as nobody seems to really be able to explain how AS4100 actually works. Certainly, the outcomes are much closer to #2 above than they are to #1. And that makes me suspect that, one way or another, AS4100 is dealing with constrained axis buckling.

RE: Rafter without fly brace?

Quote (Rfreund)

Then it seems we discovered there is some benefit to having the top of the beam braced against lateral translation even when checking the end (negative) moments. This benefit is or is not codified?

I'm I close?

Laterally bracing a beam (anywhere) provides some benefit. Some places are especially good to brace. Some are average. Some are very poor. The codes critical flange provisions - in particular the rule to treat the compression flange as the critical flange - are an attempt to formulate this into simple rules.

If you use the simple AS4100 rule (compression flange is critical) you cannot count top restraints in the negative bending moment zone in the way you could under AS1250. You can use a buckling analysis to show the top flange is genuinely critical, but you leave yourself open to criticism because people are squeamish about bracing the tension flange.

RE: Rafter without fly brace?

Quote (Tomfh)

You started out in this thread saying it is fundamentally wrong to count lateral braces at critical flanges (leading a few people astray in the process)

Nope. I suggested that it was incorrect to consider the unbraced LTB buckling length as anything other than the distance between points of twist restraint. And can you really blame me given that:

1) That's what Yura says,
2) That's how AISC, my home code, is applied,
3) That fits the theory that underlies AISC,
4) Nobody seems to be able to explain, theoretically, how AS4100 gets away with doing it differently.

And even if I'm 100% wrong about every damn thing that I've said and done here, so what? I don't just come here to teach others and have my ego stroked; I come here to learn when the occasion presents its self. As such, I'm allowed to be wrong. I'm even allowed to be wrong and then continue speaking after having been wrong. I know, it's craaazy right?

This thread has clearly created a great deal of value for a number of people, me included. Do you really think that would have been the case if I hadn't poked my head in, asked a few questions, and challenged some things? At the end of the day, debate is really the domain of those who actually like to debate. Other folks should consider golf.

RE: Rafter without fly brace?

Quote (Kootk)

Frankly, it's hard to say if AS4100 explicitly checks constrained axis buckling

It doesn’t check it explicitly. AS4100 capacity equations are an envelope and provided you laterally brace according to the codes “critical flange” rules then you keep your actual
buckling modes within the calculated envelope. AS4100 is just a curve drawn outside all the points. You don’t actually check the points directly.

RE: Rafter without fly brace?

Quote (Tomfh)

It doesn’t check it explicitly. AS4100 capacity equations are an envelope and provided you laterally brace according to the codes “critical flange” rules then you keep your actual buckling modes within the calculated envelope. AS4100 is just a curve drawn outside all the points. You don’t actually check the points directly.

1) Yeah, I've been starting to wonder if that's how it works. That is your understanding, Human909's understanding, but not steveh49's understanding. I'm not sure where Agent666 stands on this.

2) What I'm most interested in now is understanding the basis for, or development of, that envelope of which you speak. I consider such an envelope, that would consider all possible buckling modes, to be an impressive achievement. We in North America should adopt this technology. And so I'd like to understand how it has been developed.

3) Above, you described this envelope as a calculated envelope. I take it that your understanding is that this envelope was arrived at through running computational trials rather than, say, testing or experience?

4) Do you know of anything in print, anywhere, that mentions this envelope? I've not stumbled across a single thing. Given the importance of the envelope, I'd have expected it to be described, at least in passing, in a commentary, textbook, or something like that. How did you come to know of its existence?

5) The 70' case that I ran for steveh49 suggested that the AS4100 provisions did a poor, and very unconservative job of estimating the beam length at which LTB would begin to govern. Perhaps that example is so extreme as to be outside the realm of practical application.

6) Even if AS4100 is partly empirical, it cannot be entirely empirical. Many of the equations are the usual looking suspects that are consistent with stability theory. At best, it must be an empirical curve indexed to theoretical work, similar to how punching shear is related to the Timoshenko derivation but not exactly that (goal posts moved to suit test results).

RE: Rafter without fly brace?

Quote (Kootm)

2) What I'm most interested in now is understanding the basis for, or development of, that envelope of which you speak.

I don’t know the details, but it is certainly based on theory and experiment.

Quote (Kootk)

he 70' case that I ran for steveh49 suggested that the AS4100 provisions did a poor, and very unconservative job of estimating the beam length

Sorry, are you saying you have found an example where AS4100 is unconservatice and overstates actual beam capacity?

RE: Rafter without fly brace?

Quote (kootk)

Do you know of anything in print, anywhere, that mentions this envelope? I've not stumbled across a single thing. Given the importance of the envelope, I'd have expected it to be described, at least in passing, in a commentary, textbook, or something like that. How did you come to know of its existence?

This is what the alpha_s factor does. I've mentioned previously on two occasions now in this thread that I can remember that it savagely scales back the theoretical capacity until every test (159 I believe) which they compared results to was above the line. Whereas AISC goes somewhere through the middle of the test data, and isn't a lower bound approach, more of an average. This can easily be seen in the graph I posted a few posts back. NZS3404 capacity is way lower than AISC for example. I posted a specific comparison much earlier in the thread without all the other cases included. Edit: this was the 'The YELLOW section' graph posted right at the beginning that you commented on.

I'll dig out the references to this aspect. The alpha_s was a curve fitting exercise basically, empirically derived. To match the theory results to what was observed in real world tests.

RE: Rafter without fly brace?

Quote (Tomfh)

Sorry, are you saying you have found an example where AS4100 is unconservatice and overstates actual beam capacity?

Sort of, if one has faith in:

1) steveh49's calculations and;

2) my Mastan modelling and;

3) the validity of a 70' beam example.

Do a "find" in your browser for this phrase: "SURPRISE OBSERVATION". That will take you to the latest post on that. Alternately, it was the second thing that I posted today.

Summary:

1) Running my W27x84 test case through AS4100 indicated that my constrained axis LTB mode was highly improbable.

2) To emphasize #1, Steve calculated the length of beam that would be needed for my test case before LTB would govern per AS4100. This ended up being 65'+ compared to the original length of 32'.

3) I set up a Mastan model that suggested that, at Steve's calculated beam length, you'd be at 400% of the available LTB capacity rather than 100% of the LTB capacity per AS4100.

This is no great smoking gun but it is a discrepancy.

RE: Rafter without fly brace?

Ok, so Steve is saying that according to AS4100 it buckling as it hits section capacity, and you’re saying it buckling at only 25% of section capacity?

RE: Rafter without fly brace?

Quote (Agent666)

This is what the alpha_s factor does. I've mentioned previously on two occasions now in this thread that I can remember that it savagely scales back the theoretical capacity until every test (159 I believe) which they compared results to was above the line. Whereas AISC goes somewhere through the middle of the test data, and isn't a lower bound approach, more of an average. This can easily be seen in the graph I posted a few posts back. NZS3404 capacity is way lower than AISC for example. I posted a specific comparison much earlier in the thread without all the other cases included. Edit: this was the 'The YELLOW section' graph posted right at the beginning that you commented on.

I've reviewed and considered the graphs that you posted repeatedly. In doing so, however, they appeared to me to be:

1) Graphs comparing single buckling modes over a range of unbraced lengths and not;

2) Graphs comparing envelopes of multiple buckling modes over a range of unbraced lengths per Tomfh's explanation.

If the graphs are #2, then that's great to know. I don't see how I could have been expected to know that, however, unless someone mentioned it. The shape of these graphs look like every other buckling curve fit that I've seen that were all in reference to a single buckling mode rather than envelopes of several buckling modes.

Quote (Agent666)

The Adina FEM results were provided by the The Adina FEM results were provided by the author for comparisonfor comparison

If there was an author, does that mean that the graphs are part of a document that you could either share with me or refer me to so that I might review it myself?

@Agent666: as long as I have your attention, can you confirm that your understanding of how AS4100 LTB works matches Tomfh's and Human909's, repeated below? The salient features there being that:

1) The AS4100 procedure checks no particular LTB buckling mode and, rather;

2) Checks all buckling modes at once by ensuring that parameters lie within a set of enveloping curves that encompass numerous intividual LTB buckling modes.?

Quote (Agent666)

It doesn’t check it explicitly. AS4100 capacity equations are an envelope and provided you laterally brace according to the codes “critical flange” rules then you keep your actual buckling modes within the calculated envelope. AS4100 is just a curve drawn outside all the points. You don’t actually check the points directly.

Quote (Human909)

As above you seem fixated on the notion that a codified buckling check needs to focus on ONE buckling mode. That is a bit useless really. You need a check (or many checks) that covers ALL buckling modes.

RE: Rafter without fly brace?

Quote (Tomfh)

Ok, so Steve is saying that according to AS4100 it buckling as it hits section capacity, and you’re saying it buckling at only 25% of section capacity?

Exactly right in so much as we trust Mastan to work that out and me to use Mastan properly.

RE: Rafter without fly brace?

Quote (Kookt)

- Fails at 2768 kip*in end moment = 313 kN*m (25% of your phi.Ms. value of 1240 kNm)

CONCLUSION: if I've not screwed anything up, I believe that this would suggest that the beam length at which constrained axis LTB would occur can be expected to be significantly shorter than the value at which AS4100 would predict that LTB would govern over phi.Ms.

SURPRISE OBSERVATION: the moments at the ends are different from the moments in the middle. I should have anticipated this, in retrospect, but did not.
I am getting the first positive buckling mode failure at 2844kN. Well past the beams capacity.

And for good measure 410kN according to AS4100

Quote (Space Gass)

AS4100 1998 CALCULATIONS FOR GROUP 1 (*=Failure)
------------------------------------

Critical load case is 1, out of 1

Section: W27x84 (I or H section, Rolled/SR)

Failure Crit Start Finish Axial Major Minor Major Minor Load
Mode Case Pos'n Pos'n Force Shear Shear Moment Moment Factor

Section 1 0.000 0.00 0.00 215.00 -1144.88 0.00 1.08
Member 1 0.000 6.390 0.00 -1144.88 0.00 1.01
Shear 1 0.000 0.00 0.00 215.00 -1144.88 0.00 1.35
(1.00)

Grade= 50 Fy = 344.7 MPa
Fyw = 344.7 MPa Fu = 448.2 MPa
Ltot = 21.300 m Lseg = 6.390 m (FL Bot-Top)
kt = 1.00 (5.6.3) kl = 1.00 (5.6.3)
kr = 1.00 (5.6.3) Le = 6.390 m (Bending) (5.6.3)
Lx = 21.300 m (Compression) Ly = 21.300 m (Compression)
Lz = 21.300 m (Torsion)
Ly/ry= 404.8 (Compression) Le/ry= 121.4 (Bending)

Arf = 0.0 mm^2 Arw = 0.0 mm^2
An = 15935.5 mm^2 Ae = 0.0 mm^2 (6.2.2)
Kf = 0.00 (6.2.2) Kt = 1.00 (7.3)
αm = 2.09 (5.6.1.1) αs = 0.44 (5.6.1.1)
αcx = 0.00 (6.3.3) αcy = 0.00 (6.3.3)
αb = 0.00 (6.3.3) βme = 0.20 (8.4.4.1)
βmx = 0.50 (8.4.2.2) βmy = 0.00 (8.4.2.2)
γ = 0.00 (8.3.4) ϕ = 0.90 (3.4)

N* = 0.00 kN
Vx* = 0.00 kN (not considered) Vy* = 215.00 kN
Mx* = -1144.88 kNm (Compact) My* = 0.00 kNm (Compact)

ϕNt = 0.00 kN (7.2) ϕNs = 0.00 kN (6.2)
ϕNcx = 0.00 kN (6.3.3) ϕNcy = 0.00 kN (6.3.3)
ϕNoz = 0.00 kN (8.4.4.1) ϕMo = 750.41 kNm (5.6.1)
ϕVvm = 1057.10 kN (5.12) ϕMf = 847.98 kNm (5.12.2)
ϕMsx = 1240.57 kNm (5.2) ϕMsy = 161.68 kNm (5.2)
ϕMbx = 1154.45 kNm (5.6) ϕMox = 0.00 kNm (8.4.4)
ϕMrx = 0.00 kNm (8.3.2) ϕMry = 0.00 kNm (8.3.3)
ϕMix = 0.00 kNm (8.4.2.2) ϕMiy = 0.00 kNm (8.4.2.2)
ϕMtx = 0.00 kNm (8.4.5.2) ϕMcx = 0.00 kNm (8.4.5.1)

Mx*
---- = 0.99 < 1.00 (Pass) Flexural-torsional buckling (5.6)
ϕMbx

RE: Rafter without fly brace?

Human909, what are your end restraints? Are they restrained against minor axis bending? I think others are releasing this. And are both ends restrained longitudunally, so pinned-pinned rather than pinned-roller?

Buckling length looks like ~30% of total length as used by AS4100. Is that the case?

RE: Rafter without fly brace?

What are you and kootk doing different in your buckling analyses?

RE: Rafter without fly brace?

Quote (Human909)

Well past the beams capacity.

Can you elaborate upon the point that you intended to make with that statement? For as long as we're discusding elastic buckling capacity, other failure modes are not germane to the discussion. They'll govern over elastic stability... or they won't. Either way, they'll be checks separate, and uncoupled, from LTB.

RE: Rafter without fly brace?

Kootk, he’s saying the beam is yielding well
before it buckles.

RE: Rafter without fly brace?

Oh, I know. And I'm saying that's irrelevant with respect to the discussion of elastic stability. I believe that it serves as a persistent and unecesary distraction in a discussion already nearly too complex for mortal minds to readily decipher.

RE: Rafter without fly brace?

Exactly Tomfh. I believe it is completely necessray. As has already been acknowledged, we have no desire to consider ALL buckling modes as part of AS4100 member capacity check, just those that lie within the section capacity.

Quote (Steveh49)

Human909, what are your end restraints? Are they restrained against minor axis bending? I think others are releasing this. And are both ends restrained longitudunally, so pinned-pinned rather than pinned-roller?
Thanks for clarifying.
My end restraints on the previous model was on the two edges of the web which did give some degree of stiffness in the minor plane. I re-ran the model with no stiffness in the minor plane and got 1845kN Picture below.
(Though having completely restrained in the major axis and completely pinned in the minor axis is a unusual connection!)

Beam restraint viewed from below.
-Full translational restaint Rotationally restrained in the major axis, rotationally unrestrained in the minor axis.
-Lateral restrains on top falnge as described by Kootk

RE: Rafter without fly brace?

Quote (kootk)

If there was an author, does that mean that the graphs are part of a document that you could either share with me or refer me to so that I might review it myself?

The author of mastan2 was what I meant. The results are part of the stability fun modules, module 4 I believe. The graphs are generated when you undertaking the stability fun module.

Quote (kootk)

@Agent666: as long as I have your attention, can you confirm that your understanding of how AS4100 LTB works matches Tomfh's and Human909's, repeated below? The salient features there being that:

1) The AS4100 procedure checks no particular LTB buckling mode and, rather;

2) Checks all buckling modes at once by ensuring that parameters lie within a set of enveloping curves that encompass numerous individual LTB buckling modes.?

Disagree with 1 & 2, as you are checking the only critical buckling mode. Really this is the mode with the lowest reference buckling moment. That's the whole point, to find the lowest buckling moment, and work this through to a capacity.

When doing it by hand, you are checking the critical buckling mode, it doesn't matter what it is really is the point the others are making (which I agree with). Provided the effective length is correct then it theoretically buckles at the reference buckling moment (Moa) (edit - this is Mo x alpha_m essentially), you could have 101 different beams with all sorts of restraint conditions with the same effective length, and the reference buckling moment (Mo) would be the same. This is what the theory says. Then knowing the theoretical buckling moment you apply code reductions (alpha_s/phi, etc). The factors on effective length have been calibrated against tests, etc.

The point is you don't need to know the buckling mode, or how it fails, it is irrelevant really. The only variable in the reference buckling moment formula is the length that can change.

When you do it by buckling analysis you are solving the fundamental governing equation of LTB for the system and getting to the critical mode of buckling failure directly, if you want you can back calculate out the effective length to understand whats going on you can do so from the fundamental equation. But the actual mechanism of buckling is really irrelevant or redundant as you are essentially skipping over it determining the only (most) critical reference buckling moment which you need for determining the design capacity.

You all need to stop quoting the reference buckling moment directly as a capacity, it isn't! See my post above. If you're quoting capacities based on a buckling analysis then at least work it through using the AS4100/NZS3404/AISC360 provisions for doing so so everyone is comparing apples with apples.

RE: Rafter without fly brace?

I don't understand what this envelope check would look like. Isn't it game over after the beam fails when the lowest buckling mode/load is reached? Should I care if there are two more modes < yield and another at 107% of yield after finding a substantially lower LTB load? Is the envelope just the check of the various segments?

I agree with Agent's preceding post but I think that AS4100 is considering a buckling mode when the various factors are determined, at least comparatively to the reference mode. It's built in (but simplified/approximated to the same degree as the method overall) because the factors have come from tests/analyses which did have specific modes.

RE: Rafter without fly brace?

Not sure if I've had an epiphany about what KootK wants to understand about AS4100 or whether he'll turn around and say this is obvious and everyone already knows, but here goes.

Yura defined the segment length based on twist restraints. AS4100 places a greater emphasis on lateral restraint. AS4100 technically defines a twist restraint with no lateral restraint as unrestrained, knowing this may be conservative. Not sure how our bridge engineers handle this in long-span bridges but I see that the latest bridge code has added some motherhood statements without providing a design procedure. AU/NZ engineers probably do a buckling analysis or use Yura's 'Fundamentals' article for designing torsional restraints.

For AS4100, an L restraint is as good as an F restraint except that you can't use k_r < 1.0 with L restraints. See the graph I posted 23 Nov 14:27 which shows a case where the L restraint does the job of an F restraint and is better than a twist restraint. I find human909's latest buckling shape image interesting as it appears to match the AS4100 assumption: the bottom flange is only moving near the beam ends where it is in compression and the top flange restraints are ineffective at restraining the bottom flange. It looks straight and along its original alignment in the middle of the beam where it is in tension. The top flange L restraints are acting as F restraints. But this is very different to the Mastan buckled shapes and key to the AS4100 'magic' being correct for moment reversal within segment.

It would be interesting to see whether human909's method (and Mastan) handles reference cases well. Eg take away all the top flange lateral braces and subject the beam to a uniform moment. Does the buckling load match the M_o formula? Then change the loading to midspan point load with end moments equal to midspan moment. Is the buckling load 1.71*M_o?

RE: Rafter without fly brace?

Quote (steveh49)

AS4100 technically defines a twist restraint with no lateral restraint as unrestrained, knowing this may be conservative. Not sure how our bridge engineers handle this in long-span bridges but I see that the latest bridge code has added some motherhood statements without providing a design procedure.
I was going to disagree with you on this one but rereading 4100, seems to concur with what you have said.

I went through this more than 12 months ago digging through resources. I've been building plent of long span 15-20m gantries. I treat tortional restrains as partial restraints. Though maybe this is quite debatable as far as AS4100 goes. This is from the Steel Designers Handbbook. (GORENC, TINYOU, SYAM)

I typically use plan bracing OR full web stiffeners with deep channel between them. I should run the system through elastic buckling analysis and have a look.

RE: Rafter without fly brace?

Quote (Steve)

See the graph I posted 23 Nov 14:27 which shows a case where the L restraint does the job of an F restraint and is better than a twist restraint.

What is that graph based on?

It doesn’t agree with Mastan analyses above, and isn’t very intuitive. I’m not sure how an L can really be as good as F in reality, or how L on non critical flange can do literally nothing...

RE: Rafter without fly brace?

Thanks Kootk and Tomfh for the recap.

I would concur that the unbraced length should be handled as the distance between columns and Kootk has done an admiral job defending this point.

I would like to define the braces again becasue I think that is important:

F-brace: Lateral deflection and twist are prevented.
P-brace: Lateral deflection of the tension flange is prevented. Twist can occur (i.e. the compression flange can move relative to the top flange)
L-brace: Lateral deflection of the compression flange is prevented
U - Unrestrained: No restraint.

To prevent lateral-torsional buckling you either need to prevent deflection of the compression flange or prevent the rotation of the flanges (i.e. both flanges can translate laterally but cannot rotate).

Now that Human909 removed the weak-axis restraint does the Mastan Model results match?
Curious to how this compares to the nominal capacity allowed by AS4100.

Also curious to find out more about the P-brace. This would apply to buildings with roofs that have continuous/drop beam system (Gerber system) where the beams are continuous but they don't use a stiffener. I know (in the US) this is a fairly big no-no and there are known failures because of this.

RE: Rafter without fly brace?

Last time I looked I thought NZS3404 allowed just rotational restraints, but re-reading the definition of an 'F' & 'P' restraints it it seems it doesn't as there needs to be some effective/partial lateral restraint of the critical flange. However in reality just rotational restraining the section without lateral restraint is a valid means of increasing it's resistance to LTB. The classic examples is parallel bridge girders constrained to the same rotation with no plan bracing. I.e. all of those examples from the steel designers handbook, except for the last one with the bracing would qualify for this enhancement. I'm not sure if this is the intent of NZS3404 to prevent this type of rotational restraint being used in isolation, I certainly recall some literature showing it being used in a NZ context.

Quote (steveh49)

Eg take away all the top flange lateral braces and subject the beam to a uniform moment. Does the buckling load match the M_o formula? Then change the loading to midspan point load with end moments equal to midspan moment. Is the buckling load 1.71*M_o?

Yes it does. I showed this in case#1. This is how clause 5.6.4 requires you to work out alpha_m, and was how I checked alpha_m was actually comparable to the eqn in the table in a following post. If you setup the same uniform conditions for any span L, it should give you Mo. This is in mastan2, I can't say human909s analysis will show this because I'm not familiar with the software he's using and if it's even doing the same type of analysis because it seems FEM based, made from plates, and it raises many questions for me. To the best of my knowledge human just quotes reference buckling moments and not design capacities so it makes it hard to compare results directly.

It would be quite easy to show, for example use one of the cases where alpha_m is given explicitly. Then the reference elastic buckling moment from a buckling analysis should be alpha_m x Mo (derived from Mo eqn).

RE: Rafter without fly brace?

RFreund, your definitions are off a little, especially in the restraint of twist department for F/P types. Bang on for L/U types though.

Best to see below regarding F/P restraints rather than me trying to re-hash it in my own words.

RE: Rafter without fly brace?

Quote (FReund)

I would concur that the unbraced length should be handled as the distance between columns and Kootk has done an admiral job defending this point.

Curious how you would defend that position knowing that AISC allows you to use a elastic buckling analysis which accounts for any degree of restraint imaginable.

Does AISC live in a world where if you use the hand method, it's strictly consider LTB between supports (Blue pill).

But if you use a buckling analysis you can consider any imaginable degree of restraint (Red pill).

That just seems a little crazy to me.

This is a serious question, just facilitating your opinion?

RE: Rafter without fly brace?

RFreund will have his own take on things here but I'm going to throw in my own responses for good measure as these questions really do speak to the depth of misunderstanding at play.

Quote (Agent666)

Curious how you would defend that position knowing that AISC allows you to use a elastic buckling analysis which accounts for any degree of restraint imaginable.

1) Distance between columns = distance between points of cross section twist restraint.

2) Distance between points of twist restraint makes sense as the LTB buckling length because that is the physical length over which the phenomenon that is LTB occurs. This shows up in:

a) Physical testing.

b) All of our FEM models.

c) Yura's work.

d) Trahair's work.

AISC's allowing you to consider all lateral restraints available doesn't conflict with this definition of Lb when viewed in this way. For the case at hand, the critical buckling mode is as shown below and is what has been referred to as constrained axis buckling. The salient feature being that:

3) It accounts for the beneficial effects of the L-restraints and;

4) It is still an LTB buckling mode that involves the entire length of the beam between supports.

Quote (Agent666)

That just seems a little crazy to me.

If there is something that is unintuitive, I would argue that it is AS4100 using something other than the distance between points of twist restraint as the LTB buckling length. That, because using the distance between L-restraints would appear to be the examination of buckling lengths not actually reflective of the physical buckling length. I get that you see all of this differently and that's fine. To cross the divide here however, we're all going to have to find a way to parse out and understand the perspective of the other side.

RE: Rafter without fly brace?

Quote (steveh49)

Not sure if I've had an epiphany about what KootK wants to understand about AS4100 or whether he'll turn around and say this is obvious and everyone already knows, but here goes.

I would think that the silver bullet here would almost have to be something that is obvious to some parties and opaque to others.

Quote (steveh49)

For AS4100, an L restraint is as good as an F restraint except that you can't use k_r < 1.0 with L restraints.

Yes, if L-restraints are as good or nearly as good as F restraints then this would be a epiphany from my end. It would explain the anomaly, from my perspective, that is AS4100 treating the buckling length as something near to the subsegement lengths (8' here) when the actual, physical length of the LTB phenomenon is the entire beam length (32' here). This will have two dimensions for me:

1) Verifying that this is how AS4100 works and;

2) Justifying that this approach is theoretically appropriate.

Phase two can wait. For now, just having phase one settled would be a massive win for me in the understanding department. Massive. And I see your point, the graph below would suggest that, at least in some situations, An L-brace might be considered effectively an F-brace.

Quote (steveh49)

I find human909's latest buckling shape image interesting as it appears to match the AS4100 assumption: the bottom flange is only moving near the beam ends where it is in compression and the top flange restraints are ineffective at restraining the bottom flange. It looks straight and along its original alignment in the middle of the beam where it is in tension. The top flange L restraints are acting as F restraints. But this is very different to the Mastan buckled shapes and key to the AS4100 'magic' being correct for moment reversal within segment.

Mastan and Human909's stuff are both just FEM models. One way or another, they have to be made to agree. In my mind, the differences between software models cannot stand as the "key" to explaining the AS4100 magic. Three things about Human909's model catch my eye and, hopefully, he can speak to them:

1) If I understand the symbology correctly, there is still some degree of weak axis rotational restraint at the beam ends.

2) The bottom flanges buckle in opposite directions. That S-shape suggests that this is something other than first mode behavior. This may be related to my next point.

3) Graphically, it appears that the load may have been applied at a point lower on the cross section than the top flange.

RE: Rafter without fly brace?

Quote (RFreund)

P-brace: Lateral deflection of the tension flange is prevented. Twist can occur (i.e. the compression flange can move relative to the top flange)

I think that needs some tightening.

P-brace:

1) lateral deflection of the tension flange is prevented.

2) rotation of the tension flange is prevented by some kind of moment/torsion connection between the brace and the tension flange.

3) rotational restraint of the tensions flange ---> rotational restraint of the entire cross section --> indirect lateral restraint of the compression flange.

4) If the indirect lateral restraint of the compression flange is relatively flexible, then you're talking P-restraint instead of F-restraints. Sometimes the difference will be the absence of a web stiffener which will make the compression flange lateral restraint more flexible by way of something that looks a bit like web sidesway buckling.

Quote (Rfreund)

Also curious to find out more about the P-brace. This would apply to buildings with roofs that have continuous/drop beam system (Gerber system) where the beams are continuous but they don't use a stiffener.

Normally, with steel joists, the joist connections would not be considered P-braces because the connections between the joist seats and the girders would lack #2 above.

RE: Rafter without fly brace?

Quote (Agent666)

You all need to stop quoting the reference buckling moment directly as a capacity, it isn't!

"You all" is a pretty big bucket. Does it include my work? It shouldn't. Two perfectly valid things can be done with the reference buckling moments from FEM:

1) Compare one reference buckling moment to another so suss out the impacts of various changes to the situation.

2) Use a reference buckling moment as an upper bound capacity.

I believe that I carefully placed all of my stuff into one of those two buckets with statements like the one below that I included along with my modelling results.

Quote (KootK)

No imperfections modeled so a high side estimate

In the interest of full disclosure, I would like to trade in adjusted capacities but have not been because:

3) I don't yet know how to do that in a way consistent with what others expect here and;

4) I don't yet know if doing this would represent more of a time expenditure than I can spare.

I invested my Friday evening and my Saturday morning into learning Mastan so that I could help share the modelling load here that I felt was being unfairly shouldered by a small group. As much as I would prefer to deal in "true" capacities, holding off my FEM participation another month until I got that aspect sorted didn't strike me as prudent. You go to war with the army you have, not the army you wish you had.

RE: Rafter without fly brace?

Quote (steveh49)

But I now agree that top flange loading at a top flange L restraint should use K_l>1.0 if the bottom flange is going to move sideways.

That's too bad because I've since changed my mind and rescind my concern. This is neat... and cleaner than most things here. Start with a full read of the attached sketch.

Yesterday, you asked for the W27x84 with a single L-restraint at mid-span to be modeled. I did that and thought to myself "Great, I'll run this same model with the load at the shear center and the load at the top flange. The top flange loaded model will buckle earlier and this will support my position that k_l should be greater than unity for that." I did this exercise and the results were just as I expected: capacity is less with the load at the top flange than it is with the load at the shear center. Unfortunately, this was never the right question to ask so the answer was meaningless.

The right question to ask is really this: of the various vertical positions available for the load, which one represents neutral stability? That, because the LTB capacities are calibrated to the neutral stability condition. And the neutral stability position is not, strictly speaking, the beam shear center. Rather, it is the center of rotation for the critical LTB buckling mode. Once the mid-span L-brace is added, that center of rotation becomes the top flange and, therefore, the top flange becomes the neutral load position. Everything shifts up as shown below. As a way to "feel" this, imagine the load applied at point [D} in the sketch below, with the top flange L-restraint in play. Obviously, in this position, the load is actually stabilizing rather than just neutral.

Neat huh? In a way, this dovetails into your hypothesis that, in many cases, L-restraints are effectively F-restraints. It is, after-all, acknowledged by all that the destabilizing effect of a load in a destabilizing position ends at the nearest F-restraint where it gets absorbed into the bracing.

RE: Rafter without fly brace?

Quote (Agent666)

Last time I looked I thought NZS3404 allowed just rotational restraints, but re-reading the definition of an 'F' & 'P' restraints it it seems it doesn't as there needs to be some effective/partial lateral restraint of the critical flange. However in reality just rotational restraining the section without lateral restraint is a valid means of increasing it's resistance to LTB. The classic examples is parallel bridge girders constrained to the same rotation with no plan bracing. I.e. all of those examples from the steel designers handbook, except for the last one with the bracing would qualify for this enhancement. I'm not sure if this is the intent of NZS3404 to prevent this type of rotational restraint being used in isolation, I certainly recall some literature showing it being used in a NZ context.
Yep. I don't think it is the intent of AS4100 or NZS3404 to prevent this. In fact AS4100 and I would presume NZ3404 has a clause on diaphrams made to restrict rotation. But but rereading things that clause doesn't undo the previous devinitions of P restrains requiring lateral restraint.

This ia something else I'll modelling. And see how it compares to L restraints.

Kootk
1) If I understand the symbology correctly, there is still some degree of weak axis rotational restraint at the beam ends.
No. In the last picture showed there is none.

The bottom flanges buckle in opposite directions. That S-shape suggests that this is something other than first mode behavior. This may be related to my next point.
That was the first mode with the seecond buckling in the opposite S shape. Full mode buckling doesn't have to be full lenght. I'll go back an grab pictures of a bunch of modes if that will help.

3) Graphically, it appears that the load may have been applied at a point lower on the cross section than the top flange.
Loaded on the top flange directly above the web.

RE: Rafter without fly brace?

Quote (Kootk)

In a way, this dovetails into your hypothesis that, in many cases, L-restraints are effectively F-restraints

I don’t believe it. I’m perplexed by the suggestion (and the graph) that L restraints are as good as F restraint.

It’s one thing to treat L as the same for design purposes, but really and truly just as good?

When a beam buckles the cross sections move and rotate. So how can a pin do the same thing as full restraint?

RE: Rafter without fly brace?

Question for everyone: Why do the Mastan models predict Kootk's bottom flange buckle, but human's FEM model (and the graphs) predict localised buckling between lateral restraints?

RE: Rafter without fly brace?

I had to go back an re-read some stuff, but Celt should have received more stars, just saying. It seems like there is a large discrepancy between the two codes for this case. I'm still unclear what the AS4100 says the unbraced length for the negative moment (bottom flange) should be.

Quote (Agent666)

Curious how you would defend that position knowing that AISC allows you to use a elastic buckling analysis which accounts for any degree of restraint imaginable.
Does AISC live in a world where if you use the hand method, it's strictly consider LTB between supports (Blue pill).
But if you use a buckling analysis you can consider any imaginable degree of restraint (Red pill).

I should start by saying that it seems like we are both considering the unbraced length correctly in terms of the code. Meaning that the length between column (i.e. 32' in the example) is correct for AISC. For AS4100 it is not that length, it is shorter. However, I still think it has more to do with the definitions of the braced locations.
As far as the Red/Blue pill - the simple response is... kinda, yeah. Meaning if you're doing it by hand you basically assume LTB even though it is constrained axis buckling in this case. If you want to go through a more rigorous approach, nothing is stopping you.
Also thanks for clarifying the definitions.

Quote (Kootk)

Normally, with steel joists, the joist connections would not be considered P-braces because the connections between the joist seats and the girders would lack #2 above.
That's a good point. There are actually some tests out there that show there is some, but that is a different discussion for a different day.

Quote (Agent666)

Best way to think of it is as follows, just determine if a flange is in compression at the point of restraint and pickup the appropriate restraint. Noting an F restraint to the tension flange can be a P restraint in terms of the compression flange. But other than the designation changing an F & P are the same analytically for determine the effective length.

Quote (Agent666)

Top flange restraints
FLLLLLLLF
F-------F
Bottom flange restraints

So this could be:
FLLLLLLLF
FPP---PPF

I have yet to go through the Mastan results, but it sounds like:
Mastan gives you something above AISC equation because AISC is assuming LTB vs Constrained axis buckling.
Mastan gives you elastic buckling lower than what AS4100 gives you.
I might have this wrong...

RE: Rafter without fly brace?

Quote (Tomfh)

Question for everyone: Why do the Mastan models predict Kootk's bottom flange buckle, but human's FEM model (and the graphs) predict localised buckling between lateral restraints?
Excellent question.

I hope to look into my model deeper today, but this depends time constraints.... I'll recheck my results and check other buckling modes. There is a good chance that somewhere along the line I'll see the full wave bottom flange buckling. (In many of the cases I have seen this as the first buckling mode. A complete constrained axis buckling does normally result in this. But the model isn't truly fully restrained, it only has restraints every 2.1m)

His results also seem to occur at a MUCH lower load and below AS4100 code so I suspect something is amiss. If anybody could replicate or check Kootk's mastran results that will be great.

RE: Rafter without fly brace?

Quote (Tomfh)

It’s one thing to treat L as the same for design purposes, but really and truly just as good?

To the extent that [as good = as efficient at preventing sectional rotation], the L-brace certainly is not just as good. But, with stability bracing, what really matters is whether or not the bracing is good enough to force a higher mode of buckling.

I stumbled across an interesting case of the weird stuff that can happen when exploring the uplift situation. The combination of a few L-braces, and a load applied in a high stability vertical position. created the effect of a an F-brace at mid-span. There is much that makes this example only weakly analogous but, again, weird stuff happens in the land of stability.

In order, below, you're seeing:

1) No L-brace.

2) L-brace at mid-span only.

3) L-brace at mid-span and each 1/4 point immediately to the side.

My best explanation for this is that, once the top flange L-bracing is effectively continuous, the load being applied in a stabilizing position overpowers the tendency towards a single curvature buckling mode.

RE: Rafter without fly brace?

Quote (RFreund)

That's a good point. There are actually some tests out there that show there is some, but that is a different discussion for a different day.

You'll find a good chunk of that information here: Link. It's super old though. Like, inflection point bracing old. I agree though, adding this effect to an already complex discussion wouldn't be likely to help anything.

RE: Rafter without fly brace?

Quote (kootk)

To the extent that [as good = as efficient at preventing sectional rotation], the L-brace certainly is not just as good. But, with stability bracing, what really matters is whether or not the bracing is good enough to force a higher mode of buckling.

Agree. My confusion is because Agent's graph says an L restraint on critical flange provides identical performance as an F restraint, and that an L restraint on non critical flange is identical to no restraint. The graph refers to simply supported beam, but the same logic applies to our scenario.

Likewise human's buckling examples show the Laterally restrained beam acting as though it's Fully restrainted. It is confining the bottom flange buckles to very short wavelengths, of (approximately) same length as the top flange restraints spacing. That again would suggest L is as good as F. But I can't understand why the beam would bother doing this, as opposed to a gentler wavelength similar to the mastan buckled shapes, and your original paint sketches.

RE: Rafter without fly brace?

Ok here are some picures of the different modes for Kootk's 70ft beam:
First 3 modes in order including the calculated buckling forces in kN. (You'll notice the first one is about 5% less than I previously reported this is due to me refining the restraint points to a smaller point on the mesh.)

The bottom mode is essentially Kookt's full wave buckling mode. It comes in much later. Not suprising really because it takes a fair bit more energy to buckle a 21m beam than a 2.1m sub section.

RE: Rafter without fly brace?

Human, Are those restraints pin? The top flange doesn't seem to be rotating, and the web appears to be bending? I could be wrong. It's a bit hard to see...

RE: Rafter without fly brace?

Quote (Tomfh)

But I can't understand why the beam would bother doing this, as opposed to a gentler wavelength similar to the mastan buckled shapes, and your original paint sketches

Yesir. I'll make the identical argument below.

Quote (Human909)

Full mode buckling doesn't have to be full lenght.

I agree and posted an interesting example of this myself two posts back, complete with a proposed explanation for the unexpected shape. That said, these are complex software algorithms that we're using and stability can get crazy complex at times. When like something strikes me as spurious, I feel compelled to find an explanation for it before moving on. In this case, this is what I find spurious.

1) My software and yours disagree. Obviously they can't both be right. If your software showed my buckling mode, or my software showed your buckling mode, I'd feel a lot more confident.

2) As Tom mentioned above, your buckled mode shapes would seem non-optimum from an energy perspective with respect to the shape that the bottom flange takes on. That doesn't necessarily mean that shape is wrong but I would like to find an explanation for it before collectively agreeing that it's right. Are you able to offer any explanation for the double curvature mode shape at this time?

RE: Rafter without fly brace?

Quote (Human909)

Not suprising really because it takes a fair bit more energy to buckle a 21m beam than a 2.1m sub section.

I believe that it's the reverse actually. The longer unbranded length should require less strain energy to initiate buckling. That's what makes it go first.

RE: Rafter without fly brace?

@Human909 - is your beam fixed at the support against major axis bending and released in the minor axis?
Sorry this might have been asked before, but it looks like there is no major axis restraint.

@Kootk regarding your analysis/conclusions in the 23 Nov 19 19:37 post:
You wanted to put to bed the W27x84; 32ft;....
Your conclusions seem to indicate that the AISC LTB check using braced length of 32' would be fairly conservative in this case, correct? You were checking the results that Celt83 originally ran?

RE: Rafter without fly brace?

Quote (Kootk)

1) My software and yours disagree. Obviously they can't both be right. If your software showed my buckling mode, or my software showed your buckling mode, I'd feel a lot more confident.
I'm looking at mine carefully. I don't have the confidence to say mine is right over yours.... For simple Euler buckling the results from NASTRAN FEA match up with theory extremely well and it isn't particularly sensitive to mesh size. I've been having a close look at mesh size effect in the last 20 minutes and it still seems sentive to mesh size so I should refine the mesh until it isn't. (Obviously bigger meshes mean significantly longer run times expecially with a 21m beam!

Quote (Kootk)

I believe that it's the reverse actually. The longer unbranded length should require less strain energy to initiate buckling. That's what makes it go first.
I can see both sides of the argument. The shorter length means less beam involved AND only involves on 2.1m segment unlike you drawing which shows two 2.1m segments. It also is occuring where the compression in the bottom flange is the greatest.

BTW refining my mesh is converging on lower values of buckling force ~1000kN. Which would imply that AS4100 is unconservative here. (Which is what Kootk has previously claimed)

Though I'm still seeing single segment buckling as the first buckling mode. Full beam buckling doesn't come into play until ~2.5x the force.

RE: Rafter without fly brace?

Quote (Human)

The shorter length means less beam involved AND only involves on 2.1m segment unlike you drawing which shows two 2.1m segments.

Symmetry means you should have both though. Your two modes show them both happening at almost the same load. Because the meshing will be a bit assymetric, I think the software is splitting it into two modes, when really they are one and the same. Your earlier example shows it doing what kootk has drawn, with both appearing in one mode.

Can you confirm what the top restraints are? See my question 25 Nov 19 01:19. I'm trying to understand why your images appear to show web distortion.

RE: Rafter without fly brace?

Quote (Tomfh)

Symmetry means you should have both though. Your two modes show them both happening at almost the same load. Because the meshing will be a bit assymetric, I think the software is splitting it into two modes, when really they are one and the same. Your earlier example shows it doing what kootk has drawn, with both appearing in one mode.
True.

Quote (Tomfh)

Can you confirm what the top restraints are? See my question 25 Nov 19 01:19. I'm trying to understand why your images appear to show web distortion.
Top restraints are lateral only every at 10% spacing. They are currently area restrains so some rotational restrain might come into play. I can try line restraints and see if there is a significant change.....

Okay.... Thanks for pressing me on this Tom. With single point vertex restraints my model starts to look alot like Kookt's model. And does imply massive unconservatism from AS4100 in this circumstance. In fact I'm now down to 159kN with non linear elastic analysis! (compared to 1154kN member capacity from AS4100) Whether this unconservatism manifests in reality is a good question. The lack of ANY stiffness given at the restraints is not realistic and as we have seen the theoretical buckling analysis is very sensitive to even minor rotational stiffness at points.

-My modelling has used small face restraints that has implicit rotational stiffness even if the restraint is translational only
-These implicit rotational stiffnesses in the restrains have had significant affects from a TRUE point restraint
-With tighter meshing and better use of point restrains I'm seeing similar behaviour too kootk's modelling

Result:
Kootk (1)
Human909 (0)

RE: Rafter without fly brace?

So AS4100 is actually relying on some rotational restraint at L-restraints?, even though the premise of L restraints is no rotational restraint?

RE: Rafter without fly brace?

Quote (RFeund)

So this could be:
FLLLLLLLF
FPP---PPF

No because an L restraint to the top flange tension is an unrestrained section for the bottom flange. The code explicitly states this.

Quote:

Mastan gives you something above AISC equation because AISC is assuming LTB vs Constrained axis buckling

Mastan is simply solving for the critical buckling mode, whatever that happens to be, it's not really important.

Quote:

Mastan gives you elastic buckling lower than what AS4100 gives you.

No, it gives exactly the same, in so far as as long as alpha_m estimation is similar the numbers will be the same. An elastic buckling analysis is code agnostic if you like. What you do with the elastic buckling moment is of course where the codes differ, but they differ in the same way that the hand methods differ.

RE: Rafter without fly brace?

Quote (Tomfh)

So AS4100 is actually relying on some rotational restraint at L-restraints?, even though the premise of L restraints is no rotational restraint?
I would suggest not.

If what these models Kootk's and now mine are showing is correct then it is a case of AS4100 just not looking for and therefore not finding the buckling modes in the bottom flange. Which would imply what Kootk has been saying all along is correct. On the other hand if what Kootk is correct and AS4100 completely misses all this then the next question is how does AS4100 get away with this?

One very big unrealistic part of this model is the lack of ANY restraint in the minor axis of the beam but complete restraint in the major axis. You have to try pretty hard to do that.

RE: Rafter without fly brace?

Quote (Human)

then the next question is how does AS4100 get away with this?

If your buckling numbers are correct then yes indeed...

I always assumed that lateral restraints, whilst not actually producing a buckling mode with half wave length X, nonetheless produced a mode that was less critical than a reference case with half wave length X.

If in fact it doesn’t and L restraints can result on a lower buckling load than AS4100 assumes, then I have no idea how L restraints work.

Quote (Human)

One very big unrealistic part of this model is the lack of ANY restraint in the minor axis of the beam but complete restraint in the major axis

Are you talking about lateral rotational restraint? I.e. kr factor? You’re saying that even though we may assume say kt=1.0, that it’s not really 1.0?

Hopefully there is just something wrong with the analyses, or someone’s forgotten to carry the 1 somewhere along the way....

RE: Rafter without fly brace?

Quote (Tomfh)

Are you talking about lateral rotational restraint? I.e. kr factor? You’re saying that even though we may assume say kt=1.0, that it’s not really 1.0
I'm talking about the end restrains of the beam. I've tried to replicate Kootk's model which from what I understand has end restraints that are rotationally fixed in the major bending axis but totally without rotational restraint (pinned) in the minor bending axis.

Quote (Tomfh)

Hopefully there is just something wrong with the analyses, or someone’s forgotten to carry the 1 somewhere along the way....
There have been a few misses with analysis as variations in assumptions make a big deal. But I'm not sure what kookt has presented and I have now come close to replicating is wrong. It is just that you'll struggle to find such perfect pinned lateral restraints and perfectly pinned minor axis restraints. But it does call into question the shortcut that AS4100 is taken which is what kootk has been pushing at for a while.

RE: Rafter without fly brace?

Quote (Human)

I understand has end restraints that are rotationally fixed in the major bending axis but totally without rotational restraint (pinned) in the minor bending axis.

I may be misinterpreting you, but isn’t fixed major axis merely beam continuity (a perfectly feasible scenario), and isn’t the lack of minor axis restraint merely the absence of what the code refers to as lateral rotational restraint?

RE: Rafter without fly brace?

3

Quote (KootK)

Verifying that this is how AS4100 works

A situation where appeal to authority is the only option. You must be in uncomfortable territory! I've attached a paper by Trahair et al explaining AS4100's lateral buckling method. For those who don't know, Trahair was the co-chairman of the committee that developed AS4100 and was probably 'the guy' on the lateral buckling provisions. Yura might be the US equivalent (?)

https://files.engineering.com/getfile.aspx?folder=...

Some sections that are relevant to the various directions this discussion is taking are:

- 4.1.4: "Despite this lack of restraint against twist rotation, laterally-restrained intermediate cross-sections... act effectively as if fully restrained." But for just the equivalence of L restraints to F restraints in AS4100 I don't think we need this article. You would only need to look at one page of the code I think - the tables for the factors that contribute to effective length L_e. Anywhere there's an option for L restraint, substitute F restraint and the factor is the same. FF = FL = LL and FP = PL. (Except k_r as noted before.)

- 4.1.5: "Cross-sections that are not effectively prevented from deflecting laterally are treated as unrestrained in AS4100, no matter how effective the restraint against twisting may be", then suggesting that design by lateral buckling can be used if this is considered too conservative.

- 4.3.3: Load height factor at point of lateral restraint. See the 5th paragraph. This seems to imply that a bottom non-critical flange won't move sideways at all when the top flange is L-restrained. Perhaps the case without moment reversal, see below.

Quote (KootK)

Justifying that this approach is theoretically appropriate.

I haven't done an exhaustive literature review and am not capable of doing so, but when I do read about LTB it seems that simply-supported beams without moment reversal are very commonly the case that is considered unless moment distribution is specifically being investigated. Then the simply-supported case is assumed to apply generally without any rigorous proof. Since first coming to this topic, I have wondered if that is the case with L restraints. That graph I posted that shows critical flange L restraint exactly equalling F restraint (like in AS4100) and non-critical flange L restraint doing exactly nothing (like in AS4100) was for the simply supported case - no moment reversal. The paper it comes from only covers simply-supported and cantilever beams: top flange always critical. The paper is Australian, from 1986 (a few years before AS4100 was first published in 1990) and you can see how the AS4100 rules would be a conservative simplification for the cases covered. My suspicion is firming that the AS4100 L-restraint rules were written without any consideration of moment reversal.

Quote (Tomfh)

I’m not sure how an L can really be as good as F in reality, or how L on non critical flange can do literally nothing...

It's complicated. Here's a fuller picture. Note for beams where St Venant torsion dominates over warping torsion (K=0.1), the restraint location on the cross section doesn't matter at all. 2*b_bar/h = -1 is the bottom flange (b_bar is the brace distance above the shear centre/centroid).

RE: Rafter without fly brace?

Quote (Steve)

It's complicated.

That’s for sure.

What paper are these graphs from?

RE: Rafter without fly brace?

Holy crap steveh49!! Epiphany confirmed. Thank you so much. I'm actually getting closure on this which, after all this time, I'd all but given up on. I regret that I have but one star to give for your efforts.

RE: Rafter without fly brace?

But in general how can L restraint be said to act as if fully restrained when Often see rotation at L restraints during buckling?

And likewise how can a lateral brace on non critical flange be said to act as if unrestrained when we see movement of the non critical flange in the unrestrained case? You see this even in a simple beam.

RE: Rafter without fly brace?

Well if you modelled an F (or P) restraint with a realistic rotational stiffness sufficient to restrain the section I'd bet you'd still see the same rotation.

Then the question applies to all restraints. The increase in capacity (but really buckling critical load) is linear with stiffness increase of the restraining system. Once you get over the theoretical stiffness you force a higher mode of buckling.

You can see this here to some degree in the example I came up with for axial loading. If I was to vary the stiffness of the left UC column and plot the buckling load it would hopefully follow the classic linear increase in buckling load up to a point where your higher mode buckling is fully developed. I haven't done this yet for a bending case, but it's on my list of things to do.

I also went through and did some comparisons to tabulated alpha_m values to highlight the fact that the elastic critical load analysis is outputting the theoretical alpha_m x M_o. Here

RE: Rafter without fly brace?

Quote (Tomfh)

I may be misinterpreting you, but isn’t fixed major axis merely beam continuity (a perfectly feasible scenario), and isn’t the lack of minor axis restraint merely the absence of what the code refers to as lateral rotational restraint?
No you aren't misinterpreting me. I'll have to look into this. This connection doesn't seem in the spirit of a P restraint...

Quote (Tomfh)

But in general how can L restraint be said to act as if fully restrained when we see often see rotation at L restraints during buckling?
I agree, it cannot be identical. In certain circumstances it's ability to prevent the first mode of buckling occuring could be identical which could be the basis for the claim that they act "effectively as if fully restrained"

Quote (Kootk)

Holy crap steveh49!! Epiphany confirmed. Thank you so much. I'm actually getting closure on this which, after all this time, I'd all but given up on. I regret that I have but one star to give for your efforts.

RE: Rafter without fly brace?

Quote (human909)

Ditto. I've been grinning at your feisty posts for a while now. As you'll recall, a zillion posts back, I encouraged you to jump off of the fence and dive into the pool even if you weren't 100% confident in your opinions. And wow did you ever translate that recommendation into action. You went from guppy to great white almost overnight. And I feel that much good came of that. In particular:

Quote (Human909)

Result:
Kootk (1)
Human909 (0)

It was uncommonly gracious of you to concede the point to me once you'd realized that it had been lost. That said, the FEM work that you did wasn't the least bit in vain in my opinion. Having a surprising result confirmed by two independent modelers, using two different software packages, and coming from two different fundamental perspectives was invaluable with respect to establishing credibility for the results. Part of the reason that I wanted to jump into the FEM game here is that I don't think that it's ever ideal to put all of our eggs in any one persons's FEM basket for complex stuff like this.

Quote (Human909)

If what these models Kootk's and now mine are showing is correct then it is a case of AS4100 just not looking for and therefore not finding the buckling modes in the bottom flange.

For an AS4100 audience, I consider that to be a better articulation of my fundamental concern than anything that I was able to conjure up myself. And I think that you were able to do that precisely because you are something of a "converted opponent" so to speak. I really struggled to express this in a way that an AS4100 crowd would "hear", probably because I was unable to fully separate myself from my own perspective.

In short, even though we've had some contentious moments, know that there are no hard feelings on my end and, rather, plenty of newfound respect. We cool.

We cool... but we're not quite done. I'm going to lay down some serious brain candy two posts from now. I'd love it if you'd stick around long enough to check that out and, if appropriate, critique it for me.

RE: Rafter without fly brace?

Quote (Tomfh)

But in general how can L restraint be said to act as if fully restrained when Often see rotation at L restraints during buckling?

I agree, it's a bit of a conundrum in light of the information that's been presented in this thread so far. We'll definitely have to acquire that paper of Steve's and seen what we might glean from that.

Quote (Tomfh)

And likewise how can a lateral brace on non critical flange be said to act as if unrestrained when we see movement of the non critical flange in the unrestrained case?

This, I actually feel that I can answer now. Please check out my next post which will be lengthy but, I suspect, well worth the while.

RE: Rafter without fly brace?

Quote (Human)

In certain circumstances it's ability to prevent the first mode of buckling occuring could be identical which could be the basis for the claim that they act "effectively as if fully restrained"

Agree. It can be identical (eg simple supported case?). But I don’t understand how they extrapolate to the general position that an L is as effective as an F in all circumstances.

I always assumed that an L wasn’t as good, but that it boosted buckling performance enough for AS4100 to accept it.

RE: Rafter without fly brace?

Quote (Kootk)

You went from guppy to great white almost overnight.

Quote (Kootk)

It was uncommonly gracious of you to concede the point to me once you'd realized that it had been lost.
Lol. Thanks (I think) for the backhanded compliments. :-p But I can't help but to be slightly less gracious now and defend myself! I was never a guppy, I was just biding my time. Regarding being gracious, well I try not to find myself in that position. But would happily recognise mistakes or other peoples correct contributions.

Most of our disagreement has been over interpretations and semantics rather than actual engineering. I still do believe that you have a better grasp of the topic that I do. But that won't stop my from trying to contribute or disputing claims you may make.

Quote (Kootk)

We cool... but we're not quite done.
Yeah. I need to win back a few points! :-p (Or just collaboratively reach common ground and answers.)

And one more thing. Going back to rotational restrains being used for mulitple adjacent beams. It seems that plenty of Australians may be doing it wrong, that includes myself:
4.1.5: "Cross-sections that are not effectively prevented from deflecting laterally are treated as unrestrained in AS4100, no matter how effective the restraint against twisting may be", then suggesting that design by lateral buckling can be used if this is considered too conservative.

This contradicts what I posted earlier which is from one of the more prominent texts of AS4100.

RE: Rafter without fly brace?

KOOTK'S ALL ENCOMPASSING THEORY OF AS4100 LTB

For the sake of readability, I'm going to present everything that follows as fact even though it is really just my opinion. Just imagine all statements preceded by an "in my opinion".

When Steveh49 provided me with the revelation that AS4100 is treating L-restraints as Faux-F-Restraints, that gave me the missing puzzle piece that I needed really pull together a cohesive theory that I've been ruminating on for a few weeks.

A) WHAT THE THEORY WILL EXPLAIN

A1) Why we see the apparent discrepancy between the "compression flange" and "flange that moves furthest" definitions of the critical flange.

A2) Why, in the context of the AS4100 LTB method, a brace point must restrain lateral translation and cannot simply restrain rotation (roll beam concept considered valid in AISC methodology).

A3) Why, in the context of the AS4100 LTB method, the tension flange must not be treated as though it provides effective LTB bracing even if, in many real world situations, it may indeed provide effective LTB bracing.

B) WHY MY ANTIPODEAN FRENEMIES SHOULD LOVE THIS THEORY

B1) The theory explains all of the stuff listed above as a coherent, inter-related story. The truth tends to do this.

B2) The theory results in pretty much the most literal read of AS4100 possible. I know that it gets your guys' blood up when I try to reinterpret your codes. I would only alter 5.5.2 like this to avoid the confusion that we've seen in this thread:

Quote (AS4100 Modified)

5.5.2 Segments with both ends restrained. The critical flange at any section of a segment restrained at both ends shall be the compression flange regardless of whether or not the compression flange would deflect the farther during buckling in the absence of restraint.

C) BACKGROUND

I've been debating LTB with folks on Eng-Tips for years now. And I always describe the phenomenon using the pedantic phrase twist about a point in space located at, directly above, or directly below she shear center. I describe it like that because I feel that's the most precise description and the only one that keeps you out of trouble at free cantilevers and the like.

Invariably, somebody chimes in with "I disagree, LTB is really caused by the compression flange acting like a column and trying to buckle laterally while the tension flange attempts to straighten itself out". This is the argument shown below. I defend my position vigorously but, really, I sympathize. Most of the time, I think that compression flange buckling really is the bulk of the LTB story and that LTB can pretty accurately be envisioned as the superposition of two separate effects:

C1) The [L] in LTB. A nearly pure lateral sway about a point of rotation in space above or below the shear center.

C2) The [T] in LTB. A nearly pure torsional roll over about the shear center or a point close to it.

Different situations have different proportions of [L] relative to [T]. For a free cantilever, for example, the center or rotation is somewhere down in the earth's mantle and [L] dominates. In this case, the flange that is furthest from the center of LTB rotation, and would deflect the most, is the most efficient to brace. That flange may or may not be in compression as the free cantilever example demonstrates.

For any beam constrained to buckle about a point of rotation at or between its flanges, however, [T] will tend to dominate. In this case, the story of LTB that is "the compression flange buckles as a column" is pretty near to being the complete truth. As such, in this instance, the best (and really only) way to eliminate this source of instability is to brace that column (compression flange).

D) THE THEORY

Quote (AS4100)

5.5.2 Segments with both ends restrained. The critical flange at any section of a segment restrained at both ends shall be the compression flange.

So what's special about an end restrained beam segment that allows it to be put into this convenient bucket where the compression flange is always the critical flange? I contend that the special feature of such a beam is that, once a meaningful, lateral brace is added along its length, it becomes a member in which twist ([T]/C2) dominates and lateral sway ([L]/C1) is effectively off of the table without further designer attention. And this is why braces must prevent lateral movement and not just twist for the AS4100 method (A2). A brace can't be imagined to rule out the lateral component of LTB if it doesn't, you know, restrain the lateral component.

Once the source of instability associated with lateral sway ([L]/C1) has been stripped away by the lateral brace, the only remaining source of instability is that associated with pure-ish twist ([T]/C2). And since that is instigated by something resembling pure "column buckling", the only rational way to deal with that is to laterally brace the compression flange. This is why tension flange bracing is deemed useless when applying this portion of AS4100 (A3). Tension flange bracing would improve twist ([T]/C2) resistance but it wouldn't come close to eliminating it because the compression flange could still "column buckle" and force rotation about the axis of the tension flange.

E) THE CONCLUSION

5.5.2 Should be read literally, as the compression flange being the critical no matter what (A1). It isn't actually the case that 5.5.2 is a subset of 5.1.1. They are separate and one need not imply the other as shown below.

RE: Rafter without fly brace?

Quote (Human909)

Going back to rotational restrains being used for mulitple adjacent beams. It seems that plenty of Australians may be doing it wrong, that includes myself:4.1.5: "Cross-sections that are not effectively prevented from deflecting laterally are treated as unrestrained in AS4100, no matter how effective the restraint against twisting may be", then suggesting that design by lateral buckling can be used if this is considered too conservative.

1) I don't think that rotational only bracing is for real wrong; it's just not consistent with the AS4100 procedure for the reason that I suggested in my All-encompassing Theory post. Presumably, if you use a different method to assess stability, or a buckling analysis as you've suggested, you'd be fine. I think that this may have been what steveh49 was suggesting with his reference to the bridge design world. In that space, situations routinely come up where rotation only bracing is necessary/convenient.

2) From an energy perspective, a beam that doesn't rotate doesn't buckle. A beam can sway laterally until hell freezes over but lateral motion alone doesn't bring the load any closer to the earth and, therefore, doesn't represent buckling instability.

3) For the scenarios shown below, one could make the argument that the thing that we're calling the "beam" is really a single, composite member represented by each pair of members connected together torsionally. In that way, each two member "beam" could be designed in compliance with AS4100 as a torsionally awesome beam having no intermediate bracing. Just sayin'.

RE: Rafter without fly brace?

Quote (Kootk)

5.5.2 Should be read literally, as the compression flange being the critical no matter what (A1). It isn't actually the case that 5.5.2 is a subset of 5.1.1. They are separate and one need not imply the other as shown below.

Yes we discussed this previously. Most of us seemed to agree that 5.5.2 is separate (though overlapping) with 5.5.1.

In my opinion it's still very murky.

L restraints only laterally restrain the point they're attached to. They don't laterally restrain the entire cross section. As it rolls the entire cross section except the point of support continue to move laterally.

RE: Rafter without fly brace?

Quote (Tomfh)

Yes we discussed this previously. Most of us seemed to agree that 5.5.2 is separate (though overlapping) with 5.5.1.

Yup, but as far a I know, my latest theory is the only rational explanation for "why" so far proposed.

Quote (Tomfh)

L restraints only laterally restrain the point they're attached to. They don't laterally restrain the entire cross section. As it rolls the entire cross section except the point of support continue to move laterally.

I offered a complete explanation for that in my theory, centered around the diagram below.

RE: Rafter without fly brace?

Quote (Kootk)

I offered a complete explanation for that in my theory, centered around the diagram below.

But what about the bottom flange moving laterally?

I don't draw the distinction between torsion and lateral movement you do. It's a global translation. I don't think it's right to say the beam isn't moving laterally and is merely twisting. When the top flange is pinned and the beam rolls the beam centroid still translates and rotates. Certainly it rotates a lot less than with no lateral restraint, but it's still not pure rotation/torsion.

RE: Rafter without fly brace?

Quote (Tomfh)

I don't draw the distinction between torsion and lateral movement you do.

If you're not willing to entertain thinking in those terms then, truly, my theory is not for you as it's very much predicated upon that. However, as shown below, I am far from the first to think of LTB in terms of largely separated twist and lateral sway components. And I contend that the writers of AS4100 may have been thinking in this way too.

Quote (Tomfh)

But what about the bottom flange moving laterally?

The bottom flange moving laterally only contributes to the instability associated with the lateral sway of the cross section. For the component of instability associated with twist alone, the bottom flange is actually improving the stability of the situation. As such, once the lateral motion is removed from the system by a new brace, so is the instability associated with tension flange lateral movement.

Quote (Tomfh)

Certainly it rotates a lot less than with no lateral restraint, but it's still not pure rotation/torsion.

You'll notice in my work that I took care to always describe it in terms like nearly pure rotation rather than just pure rotation. My supposition is that there's a world of difference between LTB where the center of rotation is in the earths mantle and LTB where the center of rotation is within the depth of the cross section.

Quote (KootK)

C1) The [L] in LTB. A nearly pure lateral sway about a point of rotation in space above or below the shear center.

C2) The [T] in LTB. A nearly pure torsional roll over about the shear center or a point close to it.

Quote (KootK)

For any beam constrained to buckle about a point of rotation at or between its flanges, however, [T] will tend to dominate.

These are all statements that I chose to phrase as I did specifically to acknowledge that the separation between church and state is imperfect.

RE: Rafter without fly brace?

Yes there is such a thing as pure (or nearly pure etc) lateral movement, and yes such a thing as pure torsional movement, and yes AS4100 and Trahair are well aware of that.

What I'm saying is that in reality it's not nearly such a neat distinction in a buckled beam. A lateral brace doesn't eliminate lateral movement and leave (near)pure torsion as you seem to be suggesting. The beam is swinging about the lateral restraint, which involves lateral and torsional motion. A buckled laterally restrained beam doesn't look like your "1.2 Torsional effect" diagram. The beam has moved laterally, as well as twisted. It's simply not a "near pure twist".

RE: Rafter without fly brace?

KootK -> Your theory seems to offer a good explanation of what the code writers may have been implying, but then I'm lead to beleive that we (maybe not we) are interpreting the braced points incorrectly. Going back to the 70' long fixed-end beam problem that you and human909 worked out and found that the buckling load is much lower than the AS4100 would predict... I just can't imagine they would overlook a situation like this. In which case the unbraced length should be interpreted differently. I'm not familiar enough with AS4100 to address this though. Also in the same breath though, I'm reminded of the number of structures that I've seen with continuous beams and no stiffeners/braces at columns and have not had issues (yet?).

RE: Rafter without fly brace?

Quote (Rfreund)

Going back to the 70' long fixed-end beam problem that you and human909 worked out and found that the buckling load is much lower than the AS4100 would predict... I just can't imagine they would overlook a situation like this.

I think that is the most productive area we should keep looking at.

It would be odd for the code writers to overlook such a major discrepancy, and AS4100 seems to work.

And yet we are showing plausible buckling modes that clash with the spirit of L restraints being as good as F restraints.
I don’t believe we have got to the bottom of how L restraints can be just as effective as F restraints, when we are seeing rotation at the restraint points in the models.

Are we just missing something? Or is AS4100 possibly unconservatively, and works because of additional restraints you get in real structures, e.g. some rotational fixity at "pinned" purlin and joist connections.

RE: Rafter without fly brace?

Quote (RFreund)

@Kootk regarding your analysis/conclusions in the 23 Nov 19 19:37 post:
You wanted to put to bed the W27x84; 32ft;....
Your conclusions seem to indicate that the AISC LTB check using braced length of 32' would be fairly conservative in this case, correct? You were checking the results that Celt83 originally ran?

I actually only ran that because steveh49 asked for it. That said, that one would be pretty close to the "put it to bed" number. I'd been meaning to do that exercise anyhow so here it is, cleaned up with the full set of braces and no accounting for imperfections.

Mp = 1016 k-ft = AISC plastic = AS4100 plastic

Mn = 589 k-ft = AISC LTB number done the usual way assuming a member with no intermediate restraint.

Mb = 1171 k-ft = AS4100 LTB number assuming a segment length of 8'. This exceeds Mp of course.

Mastan = 690 k-ft = 250k x L/8 x ALR = 250k x L/8 x 0.69.

So you're getting a 17% bump by going from regular AISC LTB to constrained axis AISC LTB. This actually seems pretty modest considering you're going from no intermediate restraint to, basically, a continuously braced top flange.

Mastan elastic critical buckling, sans imperfections comes in at 50% AS4100 LTB. Shutout to Celt's spreadsheet for running the AS4100 for me. It takes a village.

Mastan file can be found here for review & tinkering: Link

RE: Rafter without fly brace?

Kootk, aren't you actually comparing the As4100 capacity to AISC capacity to a elastic critical buckling moment though? They are two different things and not comparable in any way. I've said it a few times now in the thread but if I'm reading it right people don't understand me or something? The mastan2 buckling moment is not the design capacity.

Mastan2 is giving you alpha_m times M_o. You can back calculate out alpha_m using the equation for M_o, or by working out M_o by setting up the alpha_m = 1.0 case in mastan2. (see here if you didn't already look at it when I posted earlier)

Edit, just to clarify for multiple segments you need to follow 5.6.4 procedure, and evaluate on a segment by segment basis still for critical limiting segment

Then work out alpha_s using M_o, then capacity = alpha_m x alpha_s x Msx x phi.

Can you confirm you are doing this please when comparing these numbers?

Quote (kootk )

Mastan elastic critical buckling, sans imperfections
I'll say it again, you don't need imperfections modeled when doing the eigenvalue analysis (elastic critical load analysis in mastan2).

RE: Rafter without fly brace?

Quote (kootk)

For this example, see the plot below and this Mastan file: Link. Quick notes:

- Span = 70 ft = 21.3m
- Sub-segment length = 7 ft = 2.13m (10th points. Probably doesn't matter much as long as it's close enough to force the constrained axis buckling mode.
- Elastic critical analysis.
- No imperfections modeled so a high side estimate.
- Fy inflated to ensure an elastic buckling failure mode.
- No weak axis rotational restraint at the ends.
- Applied Load Ratio = 0.1026
- Fails at 0.1026 x 250k = 26k point load
- Fails at 2768 kip*in end moment = 313 kN*m (25% of your phi.Ms. value of 1240 kNm)

CONCLUSION: if I've not screwed anything up, I believe that this would suggest that the beam length at which constrained axis LTB would occur can be expected to be significantly shorter than the value at which AS4100 would predict that LTB would govern over phi.Ms.

When I check your file to see what everyone is going on about regarding the apparent unconservatism (because I haven't really been following along with tht line of the conversation), I note the model doesn't have warping set to continuous. So results are not quite valid as you get a reasonable benefit from this.

But I am seeing the same differences in capacity, in my checks on the 70 ft case with L restraints only in the 5/8, 4/8, 5/8 span locations as per code requirement for consideration. The end span is critical. The difference from the hand check over 8001mm segment gives ~phiMbx = 682kNm. But the capacity from a buckling analysis method is coming out at phiMbx = 269kNm. This is just using table 5.6.1 case 1 for calculating alpha_m (have not calculated alpha_m using 5.6.4(b) method to see if that would be different).

RE: Rafter without fly brace?

I'll add my thanks to everyone on this topic. I tried to catch up on stars that I definitely owe but have hit the limit and the forum is robbing Peter's posts to give a star to Paul at this stage. Odd.

I need to re-read the all-encompassing theory but what's the verdict with moment reversal and L restraints? On first reading, if it's about flange buckling like a column, it seems that both flanges need to be braced similar to AISC method. Have I got that right?

Here's the paper I was pulling graphs from. Light on theory as it was mainly meant to enable design by buckling analysis without doing a buckling analysis but may be of interest and perhaps even useful in real designs.

https://files.engineering.com/getfile.aspx?folder=...

Quote (KootK)

my antipodean frenemies
I notice no-one else lasted the distance. Are we really that obnoxious?

Thanks very much for doing those Mastan cases. I will get around to doing with them what I wanted to. In one case that's on the proviso that I remember what I was trying to prove. This thread has moved pretty fast.

RE: Rafter without fly brace?

Quote (Agent666)

Kootk, aren't you actually comparing the As4100 capacity to AISC capacity to a elastic critical buckling moment though? They are two different things and not comparable in any way. I've said it a few times now in the thread but if I'm reading it right people don't understand me or something? The mastan2 buckling moment is not the design capacity.

I see what you're saying and are mostly correct. However, let's clarify a few things:
For discussion sake I think of capacity as the final design including a reduction factor. I don't think any of us are talking about this. I think we should stick with "nominal" capacities or "nominal" strengths. So no reduction or factor of safeties.

Next. (speaking in terms of AISC here) The overall capacity of the member will depend on which limit state governs. So if (according to AISC) you are in the elastic LTB length you could check LTB with a hand equation and compare this to your Mastan2 model. You could use either of these results for your elastic buckling nominal capacity. (Hopefully I have this all correct).
What I don't know is how well of a job we have done comparing these to AS4100. Meaning that is the Mb number (see quote below) the nominal strength of the beam considering all limit states? Or Just a buckling limit state. If the procedure is more of an envelope procedure, than I'm curious to know what the final nominal capacity is (hoping that it is less than elastic buckling found in Mastan2).

Quote (Kootk)

Mb = 1171 k-ft = AS4100 LTB number assuming a segment length of 8'. This exceeds Mp of course.

Quote (Agent666)

But I am seeing the same differences in capacity, in my checks on the 70 ft case with L restraints only in the 5/8, 4/8, 5/8 span locations as per code requirement for consideration. The end span is critical. The difference from the hand check over 8001mm segment gives ~phiMbx = 682kNm. But the capacity from a buckling analysis method is coming out at phiMbx = 269kNm. This is just using table 5.6.1 case 1 for calculating alpha_m (have not calculated alpha_m using 5.6.4(b) method to see if that would be different).

Could you maybe expand on this from your side when you get a chance. I have a hard time following where these numbers come from.

So the end span hand check (this is done using AS4100) for unbraced length of 8001mm (26.25ft) gives nominal capacity of 682kNm (503kip*ft)
However your check of the elastic buckling gives a moment of 269kNm (198.4kip*ft)
- How did you check elastic buckling?

In your eyes do you see this as AS4100 being unconservative or are you saying that there might be other code provisions which would reduce your nominal strength?

Thanks for staying with this.

RE: Rafter without fly brace?

Those are the final design capacities, this the only thing that's important for comparing results. I'll put up a full calc in due course to illustrate my methodology though so it can be reviwed/critiqued. The problem is everyone's quoting numbers but I'm not even sure what they are half the time, capacities getting mixed up with buckling moments and so forth.

I'm not even sure people are using their analysis tools correctly, we've got mastan models with no warping turned on, FEM models that are/were giving rubbish results, etc. Then making conclusions based on these results.

Regarding design by buckling analysis, I'm just following the code requirements for this (CL 5.6.4). Taking reference buckling moment M_o from the buckling analysis instead of from the equation, and getting significant differences once you back calculate out the moment modification factor alpha_m. I don't think anyone else is doing this from what I can see, but are still comparing apples with oranges. Happy to be corrected on this, which is why I raised it for clarification to make sure we are all talking the same language.

I suspect if you use the buckling moment value from the buckling analysis for determining F_e in AISC, you'll see the same disagreement probably when compared to the hand method (I'll try compare this as well, but I'm no AISC expert). I haven't seen anyone that I recall, using the buckling analyses to follow through and compare both AISC method for another comparison point to see if that agrees better when AS4100 doesn't seem to.

All I'm saying is you do it by hand using the normal 'hand check' provisions by basically following the prescribed effective length method and get more than twice the design capacity you get by following the buckling analysis route through to a design capacity which is actually working out the theoretical effective length based on your scenario of member/support/restraint/loading. As others have noted, this should be something we should probably concentrate on.

RE: Rafter without fly brace?

RFreund, AS4100/NZS3404 do the elastic/inelastic thing all in one step/equation as a reduction/scaling factor. Comparison curves have been posted previously comparing the two methods for the exact same member conditions.

RE: Rafter without fly brace?

Quote (Agent666)

When I check your file to see what everyone is going on about regarding the apparent unconservatism (because I haven't really been following along with tht line of the conversation), I note the model doesn't have warping set to continuous. So results are not quite valid as you get a reasonable benefit from this.

You are right about the warping continuity issue in the second 70' example. Thanks for catching that.

I have verified that warping continuity was turned on in all of the 32' examples that I ran so those should stand as originally posted in that regard.

Here's how the 70' example changes with the warping continuity issue corrected.

- Applied Load Ratio = 0.1026 0.13034
- Fails at 0.1026 0.13034 x 250k = 26k 33k point load
- Fails at 2768 kip*in 3421 kip*in end moment = 313 kN*m 387 kN*m (25% 31% of your phi.Ms. value of 1240 kNm)

The updated Mastan file is attached.

RE: Rafter without fly brace?

Quote (Agent666)

The problem is everyone's quoting numbers but I'm not even sure what they are half the time, capacities getting mixed up with buckling moments and so forth.

If the no imperfections buckling moment is less than AS4100 standard method predicts then it’s already unconservative, isn’t it?

RE: Rafter without fly brace?

Quote (Agent666)

Can you confirm you are doing this please when comparing these numbers?

Not confirmed. I am most definitely not doing that.

Quote (KootK)

Mastan elastic critical buckling, sans imperfections

Quote (Agent666)

I'll say it again, you don't need imperfections modeled when doing the eigenvalue analysis (elastic critical load analysis in mastan2).

I realize that imperfections don't need to be modeled to run an eigenvalue analysis. However, the results of an eigenvalue will not reflect the decrease in capacity resulting from imperfections if those imperfections are not given explicit consideration in the buckling analysis model. It was this latter point that I meant to convey. I'm trying to ensure that anyone reading the results does't erroneously assume that some consideration has been given to imperfection in my Mastan runs when it has not.

Quote (Agent666)

Kootk, aren't you actually comparing the As4100 capacity to AISC capacity to a elastic critical buckling moment though?

Absolutely, and that is by design.

Quote (Agent666)

They are two different things and not comparable in any way. I've said it a few times now in the thread but if I'm reading it right people don't understand me or something? The mastan2 buckling moment is not the design capacity.

I thought that'd I'd already explained this...

Quote (Agent666)

You all need to stop quoting the reference buckling moment directly as a capacity, it isn't!

Quote (KootK)

"You all" is a pretty big bucket. Does it include my work? It shouldn't. Two perfectly valid things can be done with the reference buckling moments from FEM:

1) Compare one reference buckling moment to another so suss out the impacts of various changes to the situation.

2) Use a reference buckling moment as an upper bound capacity.

I believe that I carefully placed all of my stuff into one of those two buckets with statements like the one below that I included along with my modelling results.

I believe that valid comparisons can be made and I am confused by your assertions to the contrary. I think that one just has to understand the nature of what is being compared. So I'll just tell you what I had in mind in greater detail and you can let me know what parts you object to:

1) For both AISC and AS4100, I take the adjusted LTB values coming out of Mastan as upper bounds to the true capacity. As far as I know, any subsequent adjustment factor such as phi_b or alpha_s only serve to lower the capacities generated by Mastan.

2) I take both the AISC and AS4100 design capacities calculated the traditional way as lower bound capacities.

3) If I find that the upper bound capacities coming out of Mastan (#1) are lower than the lower bound capacities coming out of AISC/AS4100, then I conclude that there's a problem that needs sorting (tomfh's last point I think).

4) I don't worry about converting the raw Mastan values to code appropriate, buckling analysis design values because any such conversion is only going lower the Mastan capacities and exacerbate any problems discovered in step #3). What was a problem at #3 just becomes more of a problem.

Are these not valid comparisons to make?

For an AISC audience, things work out great as AISC doesn't consider imperfections for LTB and the Mastan values are effectively [Mn] as far as I know. This is perfect for comparison.

For an AS4100 audience, I believe that I'm effectively providing [Mb/alpha_s]. Clearly, further post-processing isn't required to identify the discrepancies that currently concern us but, if anyone would like to undertake such post-processing, they are welcome to.

RE: Rafter without fly brace?

Quote (RFreund)

If the procedure is more of an envelope procedure...

As far as I'm concerned, we have established that the procedure is most definitely not an envelope procedure in the sense that this has been proposed previously. With the arrival of the Trahair doc provided by steveh49, it became clear that:

1) AS4100 is assuming L-braced points to be effectively braced against cross-section rotation for certain situations.

2) AS4100 is in fact evaluating particular, individual buckling modes, one for each segment between the L-braces thought to be equivalent to F-braces.

3) The only curve fitting going on is the micro-kind similar to what we do with Cb in the AISC methodology.

We've seen the wizard behind the curtain now and the magic is not what what it was purported to be.

@RFreund: I'm not trying to beat you up on this. I just want all parties here to be clear that we've moved on from the enveloped family of curves business. That, or I'd like to hear about any lingering doubt that may exist on the matter.

RE: Rafter without fly brace?

Quote (Agent666)

Edit, just to clarify for multiple segments you need to follow 5.6.4 procedure, and evaluate on a segment by segment basis still for critical limiting segment

Hold the phone... are you saying that, using the buckling analysis option, you'd still do the AS4100 post-processing segmentally? Even though your FEM model would show you something completely different (sketch below)? I had not anticipated that and it strikes me as a terribly inconsistent mix-match of the stories being told. Consider the following as it would pertain to the 70' beam example:

1) Your FEM shows buckling as a single half sine wave. Your post processing assumes six half sine waves.

2) Your FEM has provided you with information about a single buckling mode and you are applying it to six different cases, none of which match the FEM.

3) I would think that your slenderness parameter would be badly overestimated by segmental treatment and would be much more appropriately calculated based on the 70' beam length.

How do you rationalize this?

RE: Rafter without fly brace?

Quote (RFreund)

Also in the same breath though, I'm reminded of the number of structures that I've seen with continuous beams and no stiffeners/braces at columns and have not had issues (yet?).

The failure shown below happened in my neck of the woods and was judged to be the result of missing beam/column joint stiffeners allowing web side sway buckling to take place: Link.

The graph below is largely responsible for why failures don't happen and has two important, negative consequences for us:

1) it makes it difficult for structural engineers to demonstrate their value to society and;

2) it makes it difficult to separate luck from skill / correctness over the horizon of any one man's life span.

RE: Rafter without fly brace?

Quote (steveh49)

I need to re-read the all-encompassing theory but what's the verdict with moment reversal and L restraints? On first reading, if it's about flange buckling like a column, it seems that both flanges need to be braced similar to AISC method. Have I got that right?

I've certainly not arrived at a hard verdict yet and will reserve judgment until I've had a few days to review the latest article that you've kindly provided. I do have an interesting observation regarding two flange bracing and AISC though.

As you know, I've oft been quoting Yura's thing where he appears to suggest that the unbraced LTB length be the length between points of zero twist. I thought of an example where this recommendation is not followed however: pretty much every simple span beam ever (sketch below/attached). What to do...

RE: Rafter without fly brace?

Quote (kootk)

Absolutely, and that is by design.

I don't see a problem with this. That's essentially what you do when using the elastic buckling method version (except you also factor down the buckling load slightly via alpha S because obviously you can't use the idealised buckling load for a real beam).

Quote (kootk)

Hold the phone... are you saying that, using the buckling analysis option, you'd still do the AS4100 post-processing segmentally?

My understanding of the buckling method is it sidesteps all that. You don't calculate segment lengths, effective lengths, etc. You are essentially just calculate the buckling load, factoring it via alphaS, and use that directly. The alphaM factor drops out.

Quote (Kootk)

We've seen the wizard behind the curtain now and the magic is not what what it was purported to be.

I'm not ready to conclude that just yet, but things are not looking as good as they did :(

Hopefully these buckling models are wrong somehow, and hopefully there's a deeper rationale for counting L's as F's generally.

RE: Rafter without fly brace?

Quote (Kootk)

pretty much every simple span beam ever (sketch below/attached). What to do...

I think in the simple span case the bottom flange doesn't move at the position of the L restraint, thus increasing restraint level to F by bracing the bottom flange is redundant in those instances, and thus you can treat them as equivalent. That seems to be a large part of the basis for AS4100 saying L's are F's are equivalent.

Maybe you could run some mastan analyses with simple span with top L restraints and see if you can get the bottom (non critical) flange moving?

RE: Rafter without fly brace?

Below is Plate 1 from the Station Square Report by Dan Closkey. It shows the configuration of the cantilevered beam after failure but before collapse. The joists would normally be considered lateral supports for the beam, but the dark rectangle at the underside of one joist shoe suggests to me that the welding of that joist may have been omitted.

BA

RE: Rafter without fly brace?

This is a photo of the drop-in span after failure of the cantilevered beam. The darkened rectangle under each joist shoe suggests that these two joists were not welded to the beam. If so, the lack of lateral bracing of the top flange of both the cantilever and supported beam could have been a contributing factor in the collapse.

BA

RE: Rafter without fly brace?

Quote (Tomfh)

Maybe you could run some mastan analyses with simple span with top L restraints and see if you can get the bottom (non critical) flange moving?

Right. I somehow already managed to forget that I have the power to explore this stuff on my own.

All three runs are the same W27x84, 32' beam with L-restraint at the first and third quarter points.

CASE 1. ALR = 0.65 which is actually less than the negative bending on our test case (0.69). Gobs of section rotation at the 1/4 point L-restraints. This case has a concentrated load at mid-span without lateral restraint at the point of loading. This would be a rare occurrence in practice but might be something to bear in mind at, say, a beam transferring a column from above. Makes the default practice of a stiffener pair under the column seem quite prudent.

CASE 2. Point load at top flange and accompanied by lateral restraint. A little section rotation at the 1/4 point L-restraints. ALR = 3. Not worth thinking about.

CASE 3. Point load at bottom flange accompanied by lateral restraint there. ALR = 1.5. Next to no section rotation at the 1/4 point bracing. Normal positive bending LTB check with the unbraced length equal to 0.5L would pick this up perfectly so not an issue.

CONCLUSION: tough to find a practical situation where cross section rotation at an L-brace would be in issue for a simple span beam.

RE: Rafter without fly brace?

Quote (Kootk)

CONCLUSION: tough to find a practical situation where cross section rotation at an L-brace would be in issue for a simple span beam.

Makes sense. Not a lot of strain energy to shed from the bottom flange.

I do hope AS4100 isn't extrapolating the simple case where L is effectively equivalent to F, and applying it to all cases.

RE: Rafter without fly brace?

I think that the biggest takeway from this thread is probably this: when time permits, everybody should download their free copy of Mastan and learn to tinker. It's just too much fun. Plus, in all future stability threads, we'll be able to pedantic, nearly unassailable egomaniacs at our leisure. That right there's worth the price of admission.

RE: Rafter without fly brace?

Quote (Kootk's Reference)

A design approach that is consistent with current design provisions is to define the unbraced length as the spacing between points of zero twist...
Is this in AISC? Or where is the this from?
I've always understood that you can either restrain the compression flange from lateral movement or prevent twist. Which in the fixed end beam the bottom flange is only braced against lateral movement at supports.

Also is there somewhere I can 'borrow' AS4100?

RE: Rafter without fly brace?

Quote (Kootk)

everybody should download their free copy of Mastan and learn to tinker

Definitely. I’m going to get it. I’m learning a lot seeing all these test cases.

What I’d love to see is some real buckling results of continuous beams, with real L restraints. That would help settle it.

I wonder if there’s published results easily available?

RE: Rafter without fly brace?

@Agent666 I was reviewing some of the curves that you posted. It looks like they compare moment capacity to unbraced length which I suspect the AS4100 will be more conservative due to the equation. However, I assume they are both using the same unbraced length in this comparison. In the current situation we are using different unbraced lengths as directed by the code. So referring back to those curves doesn't seem to help in this situation.

RE: Rafter without fly brace?

Quote (RFreund)

Is this in AISC? Or where is the this from?

It's from the Yura article that you've probably heard referenced repeatedly. I posted a copy a zillion posts ago but I'll save you the trouble of fishing for that and just post another copy here. It's definitely worth a front to back read when you've got the time. AISC specific although, as you'd expect, rooted in first principle stuff.

Quote (RFreund)

I've always understood that you can either restrain the compression flange from lateral movement or prevent twist.

Agreed with the understanding that preventing twist can, in many ways, just be envisioned as another, indirect way to restrain the compression flange laterally. The glorious reach around.

Quote (RFreund)

Which in the fixed end beam the bottom flange is only braced against lateral movement at supports.

Agreed. The fundamental difference between AISC and AS4100 seems to boil down to just this: AS4100 lets your brace a flange with a lateral only brace on the other flange so long as that other flange is in compression at the location of the brace. With AISC, a flange can only be braced by a lateral only brace if that brace is attached to the flange intended to be braced. Or, at the least, this seem to be how it's applied. All of this, of course, harkens back to the recent "epiphany" that AS4100 treats L-Restraints as, effectively, F-restraints in many situations.

RE: Rafter without fly brace?

Quote (Kootk)

We've seen the wizard behind the curtain now and the magic is not what what it was purported to be.
Well I'm thoroughly confused by this diagram from the 'wizard'.

Wait. What?

Is this diagram suggesting that the the rafter is unrestrained by a moment end plate connected to a column. In what way is that not a flange restraint of any nature?

RE: Rafter without fly brace?

Maybe it’s intended to cover flexible columns? Seems a bit harsh though.

RE: Rafter without fly brace?

I considered that. Though even with sway columns and a flexible web your still would get the beam flanges restrained for buckling purposes. I'd hope my columms can provide more lateral restraint to a beam than a random purlin!

RE: Rafter without fly brace?

Yeah, i don’t really get it either.

RE: Rafter without fly brace?

It's because it's wrong, see corrected version here:-

RE: Rafter without fly brace?

Quote (kootk)

Hold the phone... are you saying that, using the buckling analysis option, you'd still do the AS4100 post-processing segmentally? Even though your FEM model would show you something completely different (sketch below)? I had not anticipated that and it strikes me as a terribly inconsistent mix-match of the stories being told. Consider the following as it would pertain to the 70' beam example:

Yes. You need to determine alpha_m for critical segment, so you can divide it out from the maximum moment to determine M_oa for your scenario (this is the reflection of theoretical L_e). Then you use this to determine alpha_s. Read 5.6.4, you can either use the table 5.6.1 to determine alpha_m or determine M_os and use the equation noted to determine alpha_m (keeping in mind alpha_m from tables are typically curve fit).

How many times do I need to explain this... serious question? Getting the mastan2 result is half of the job. Comparing anything but the end design capacity is flawed in my view, the buckling moment x alpha_m from a buckling analysis is not an upper bound indicator of capacity. Coming at this from the other direction because I'm not terribly familiar with aisc, what exactly are people reporting when quoting aisc capacities, is it a moment based on F_e?

RE: Rafter without fly brace?

This document by SCNZ describes the general process.

RE: Rafter without fly brace?

I think the question is whether it's correct to use alpha_m from the tables/equation using the AS4100 segment lengths when the buckling analysis doesn't match the hand-determined segments.

More generally, what if the restraints being relied on aren't in accordance with AS4100 F, P or L? Eg torsion cross-frames in bridges or bottom flange L on a beam with low E*Iw (K=0.1 so bottom flange L is as good as top flange per earlier graph).

Is there some way to use buckling analysis without having to know the effective length beforehand?

RE: Rafter without fly brace?

Quote (Agent)

Getting the mastan2 result is half of the job.

Could you show how doing the other half leads to a greater capacity?

I agree with Kookt here. The idealised buckling load shouldn’t be less than the predicted capacity. That kootk hasn’t done every step in the design chain doesn’t matter, as the steps reduce idealised capacity.

If we’re missing something please explain.

RE: Rafter without fly brace?

Quote (Alpham)

I think the question is whether it's correct to use alpha_m from the tables/equation using the AS4100 segment lengths when the buckling analysis doesn't match the hand-determined segments.

AlphaM is just a kludge used to predict buckling load when it’s not the basic case of uniform moment. It’s of little relevance when you calculate buckling load directly. That’s why they get you divide by it if using the elastic buckling method - so it cancels out.

RE: Rafter without fly brace?

Edit, this was in reply to steveh49s post above (Tom snuck a couple of replies in there)

Not sure to be honest. The real world scenarios I've used it are when you aren't sure where you fit into the stiff or flexible realm for restraint stiffness and whether that has any real world effect on the buckling. But you still have a discrete restraint provided of questionable stiffness that is adequate for the 2.5% restraint forces. So you can at least apply the segmentalised way of applying 5.6.4 in this scenario based on exercising some judgement.

As for when you have some kooky way of restraining it in a way that isn't in the spirit of the discrete L/P/F type restraints to non compression flanges then you're on your own there.

RE: Rafter without fly brace?

I never said applying the provisions to determine the design capacity leads to a greater capacity than the buckling moment value, the design capacity is going to be different. But how much different is highly dependant on removing the alpha_m and getting M_oa, then evaluating alpha_s, etc, etc.

By using the elastic buckling moment everyone's throwing around these values and comparing it for example to the spacegass checks or hand checks of design capacity when they aren't even comparing the same things. Buckling moment vs design capacities. Irrelevant comparison isn't it?

RE: Rafter without fly brace?

Alpha_m doesn't cancel though. You divide by it, do the nonlinear alpha_s calculation, then multiply by it.

RE: Rafter without fly brace?

It doesn’t make much difference. It more or less cancels out. It’s not the big deal you guys are saying.

It’s besides the point anyway, as the net result of the alpha and phi factors is a further REDUCTION in buckling load. It just makes it even worse.

RE: Rafter without fly brace?

2

Quote (Agent)

Buckling moment vs design capacities. Irrelevant comparison isn't it?

Design capacity coming out higher than the unfactored buckling moment is not an irrelevant comparison.

It’d be like if your pinned column capacity is coming out higher than its Euler buckling load.

RE: Rafter without fly brace?

I'm going to walk through this to make sure I have this right. Thanks Agent666 for posting that Portal Frame design tips.

Design procedure:

Quote (Portal Frame Design Tips Seminar Proceedings aka GEN7001)

Rafters
Nominal Bending Capacity Mbx in Rafters
Simplified Procedure
NZS 3404 uses a semi-empirical equation to relate the nominal bending capacity Mbx to the elastic buckling
moment Mo and the section strength Msx, which for Universal and Welded Beams and Columns can be taken as
Zexfy. This philosophy uses a set of semi-empirical equations to relate the member strength to the plastic
moment and the elastic flexural torsional buckling moment

Mbx = alpha_m * alpha_s * M_sx < M_sx

M_sx = Section strength, Z_x * F_y

alpha_m = Moment modification factor (similar to C.b) this will increase your nominal moment capacity due to the moment distribution.
alpha_s = Slenderness reduction factor. This is a reduction factor which basically reduces your section moment strength based on the ratio of the elastic buckling strength to the section strength

M_oa:GEN7001

So M_o:

This is the elastic buckling moment which gives almost the exact same result as AISC (calculate elastic buckling stress in AISC then multiply by the section modulus) when using the same unbraced length

So M_o = M_oa.
This is only used to get alpha_s

Case 1: Unbraced length is full beam as it would be in AISC.
Assuming the unbraced length is long enough that LTB governs. AS4100 will give you a lower beam capacity than AISC because M.o is reduced by alpha_s. However, it seems like AS4100 says that the unbraced length is not the full length. But this gets wierder...

Case 2: Unbraced length at inflection point.
The unbraced length for AS4100 will be on the order of L/4. This will give you a much higher M_o and M.b even when multipled by alpha_s than the AISC fully unbraced beam length.

What should the unbraced length be according to AS4100?

Quote (GEN7001)

With Fly Bracing under Downward Load
The effect of the bottom flange near the columns being in compression due to gravity loads or other loading
should be considered even though most of the bottom flange of the rafter is in tension. A fly brace is
recommended near each knee and near the ridge to restrain the inside corners of the frame at kinks. A stiffener
between column flanges as indicated in Figure 4 effectively extends the bottom flange of the haunch to the
outside column flange which is restrained by girts. This effectively provides some restraint to the inside of the
knee. However, a fly brace near the knee is still recommended. With fly braces at least at the knees and the
ridge, the effective length will be 0.85 times the spacing between fly braces.

An alternative approach is to consider the rafter segment between the column and point of contraflexure if
accurately known, or nearest purlin beyond the inflection point. The inflection point is considered to be
unrestrained in determining the effective length. This approach is described in an example by Clifton,
Goodfellow and Carson (1989)

I can't seem to find this reference:
Clifton, G. C., Goodfellow, B., Carson, W., Notes Prepared for a Seminar on Economical Single Storey Design and
Construction, HERA Report R4-52, New Zealand Heavy Engineering Research Association, Manukau City, 1989

However, when looking at the bottom flange it sounds like you would take a L.e as the segment from column to the first purlin beyond the inflection point (worst case). And the end conditions of this segment are FU which gives KL = 1.0 (I think?)

Example:
Using KootK's W27x84 70' (21.3m) long beam example. Which has lateral braces on the top flange every 7' (2.1m). Fixed in the strong axis at both ends. Point load at center causes an inflection point between the 2nd and 3rd lateral brace (on the top flange). So at about 17.5' (5.33m).

So unbraced length choices:

Unbraced Length: 70' with C.b and alpha_m = 1.0
• AISC M_nLTB (nominal lateral torsional buckling strength): 107 kip*ft (145kNm)
• AS4100 Mo: 107.5 kip*ft, alpha_s*M_s = 95.3 kip*ft
• Elastic buckling strength per Mastan2: 285kip*ft (386.5 kNm). This really isn't fair to compare to the above values as I haven't factored in C.b (alpha_m),b ut this is the highest value of moment capacity that can be achieved
*Note - Anything above 285kip*ft (386.5kN*m) can't be achieved. The beam will buckle prior to this moment
Updated with Cb and Alpha_m
C.b = 1.92
alpha_m: 1.7
ul]
• AISC M_nLTB: 206 kip*ft (280 kNm)
• AS4100 M_b = 162 kip*ft (220 kNm)

• [/ul]

AS4100_A: 17.5'
• AISC: Not allowed
• AS4100 Mo: 839.9 kip*ft (1138.7 kN*m), alpha_s*M_s = 468.8 kip*ft (635.6 kN*m)
AS4100_B: 21' (brace after inflection point)
• AISC: Not allowed
• AS4100 Mo: 610 kip*ft (827 kN*m), alpha_s*M_s = 398.4 kip*ft (540 kN*m)
Calc Numbers:

What is the equation for alpha_m? I can update these to include alpha_m and c.b factors.
- I will update these shortly
Side Comment: It would be great if we produced moment in Joules. Not sure why I find that so appealing. The whole energy thing I guess.

Hopefully I can get someone to double check this.

Takeaway
It seems like using the segment lengths (and please someone check these unbraced lengths for AS4100 cases) results in a beam capacity which cannot be achieved.

Edit 1: Formatting
Edit 2: Update alpha_s. This should multiply M_s not M_oa.

EIT
www.HowToEngineer.com

RE: Rafter without fly brace?

Hi RFreund, you're mixing a whole lot of ideas here that's going completely off target.

You're not multiplying alpha_s by Moa. You multiply the full plastic moment capacity (M_sx) by alpha_s x alpha_m x strength reduction factor. Moa is only required to calculate alpha_s. Otherwise it has no bearing on the capacity value or buckling values.

The moment coming out of the mastan2 buckling analysis is M_ob. This is M_oa x alpha_m. So to calculate alpha_s you need to determine alpha_m for the critical segment. Divide M_ob by alpha_m to get M_oa. Then work out alpha_s. Then work out M_bx the member moment capacity = phi x M_sx x alpha_m x alpha_s. If product of alpha_m and alpha_s is greater than 1 you have full lateral restraint, this means you can achieve the full plastic capacity of the beam. Phi is the strength reduction factor typically 0.9. M_sx is equal to plastic section modulus x yield strength.

Generalised alpha_m equation is as follows and is worked out on a segment by segment basis (I'm sure it was posted earlier but is list in the 400 plus posts above, but good luck finding it!) :-

There's also these equations for specific cases.

Alternatively you work it out from the process in CL5.6.4 which reads (this was the process being described in the SCNZ document I linked to):-

Hope that clears up the process for you?

RE: Rafter without fly brace?

Quote (Tom)

Design capacity coming out higher than the unfactored buckling moment is not an irrelevant comparison.

The point is just getting people to compare apples with apples, not oranges with apples. If you are comparing a design capacity to a buckling moment they are two very different things and that comparison is irrelevant. If others find it relevant, then carry on.

As engineers, the final product is design capacity, comparing this is the measure of how one standard or method is gauged relative to another. The buckling moment is a theoretical buckling value, and as RFruend has noted its essentially the same formulation for all standards, because well its based on the solving of the underlying principles with whatever boundary conditions you impose.

Quote (me)

Coming at this from the other direction because I'm not terribly familiar with aisc, what exactly are people reporting when quoting aisc capacities, is it a moment based on F_e?

Can someone please answer this for my own benefit in interpreting the apples from the oranges so I know what the AISC chaps are comparing to.

RE: Rafter without fly brace?

Quote (Agent666)

How many times do I need to explain this... serious question?

It was indeed a serious question. Persuasion is really a game of quality rather than quantity.
Regurgitating a previously unconvincing argument repeatedly, and unchanged, doesn't gradually make it more persuasive. So, unless you can find a way to add a little more meat to your persuasion sandwich, you can bank on having to repeat your explanation indefinitely.

Tomfh, on the other hand, was killing it in persuasion department while I was fast asleep. Persuasion by way of a much simplified, yet highly analogous, example. Socrates himself would have been proud. I couldn't have done it any better myself so I won't bother to try. Are you truly not persuaded by the logic in the argument below?

Quote (Tomfh)

Design capacity coming out higher than the unfactored buckling moment is not an irrelevant comparison.It’d be like if your pinned column capacity is coming out higher than its Euler buckling load.

Quote (Agent666)

Coming at this from the other direction because I'm not terribly familiar with aisc, what exactly are people reporting when quoting aisc capacities, is it a moment based on F_e?

My understanding is that the Mastan values would be straight up replacements for Fcr as it is defined below. That, because AISC gives no accounting of the impact of initial imperfections for LTB as AS4100 does via [alpha_s]. Note that [Cb] would then be based on a the entire member being the design segment rather than the sub-segments between L-braces as they are defined in AS4100. This is very much related to RFreund's comment below which I hope has not been glossed over as I suspect that it may hold one of the keys to sorting out our differences here. As I see it, the crux of things here is not what happens within a particular unbraced length but, rather, what the unbraced length should be to begin with.

I myself an a noob when it comes to doing LTB design via buckling analysis. So, if any AISC practitioners disagree with me on how such a design should be executed, I encourage them to come forward and show us how it's done for real. I'm happy to retract the claws for this part of the discussion.

Quote (RFreund)

@Agent666 I was reviewing some of the curves that you posted. It looks like they compare moment capacity to unbraced length which I suspect the AS4100 will be more conservative due to the equation. However, I assume they are both using the same unbraced length in this comparison. In the current situation we are using different unbraced lengths as directed by the code. So referring back to those curves doesn't seem to help in this situation.

RE: Rafter without fly brace?

Quote (Agent666)

Hi RFreund, you're mixing a whole lot of ideas here that's going completely off target.

You're not multiplying alpha_s by Moa. You multiply the full plastic moment capacity (M_sx) by alpha_s x alpha_m x strength reduction factor. Moa is only required to calculate alpha_s. Otherwise it has no bearing on the capacity value or buckling values.

Damn, good catch. I will update my calcs. Updated, let me know.

Quote (Kootk)

I myself an a noob when it comes to doing LTB design via buckling analysis. So, if any AISC practitioners disagree with me on how such an analysis should be executed, I encourage them to come forward and show us how it's done for real. I'm happy to retract the claws for this part of the discussion.
Fairly certain you're on the right track here.

Quote (Kootk)

As I see it, the crux of things here is not what happens within a particular unbraced length but, rather, what the unbraced length should be to begin with.
Yes, I think things are coming full circle back to this. I will try to post more on this later.

Back to the GEN7001 Document:
This entire document is discussing portal frames and when it looks at a case for uplift with no fly braces it recommends using the entire length as unbraced acknowledging that a portion of the bottom flange will be in tension. So in this case they ignore the inflection point. Not sure how much weight I can put into this contradiction, just mentioning it.

EIT
www.HowToEngineer.com

RE: Rafter without fly brace?

Quote (Agent)

The point is just getting people to compare apples with apples, not oranges with apples

It’s not an apples vs oranges comparison.

It’s a whole apple (predicted design capacity) vs half an apple (Mastan predicted buckling load).

The AS4100 elastic buckling design process reduces the size of the half apple even further. (The step you’re complaining isn’t being done).

We appear to be missing some of our apple. If you can point out where it is that’d be very helpful!

RE: Rafter without fly brace?

Nice work with the Fruit.

I have reached a definitive answer on this. The unbraced length is the entire beam length even using the AS4100.
I went back and looked in the 6th Edition to the Stability Design Criteria for Metal Structures. The formula used in AS4100 for M_o is the closed formed solution for the critical buckling moment for beams subject to a uniform moment. They specifically discuss our example case and specify the use of entire bottom flange if any portion of the bottom flange is in compression. They also give a special "C.b" or "alpha_m" factor that can be used which recognizes the benefit of the lateral restraint of the top flange. Below are some snippets.

Here is the closed form (same as AS4100):

Braced Points Are Not Inflection (I know this was already posted, but this is part of the same document that derives the LTB equation)

Influence of Cont Bracing on One Flange

Modified Cb

Where do we go from here?
1.) Speculate why AS4100 seems to indicate you can use a shorter segment? Kootk I think has this covered with his theory. I think he's been miles ahead of me on this the entire time.
Or figure out if the code is really telling you to take the entire length.

2.) Try to back calculate C.b using Mastan2. If I use the modified C.b factor I get 3.667. That means that the nominal capacity would be 393 kip*ft or 532.2 kNm. This is higher than the elastic buckling we found with mastan2. So let's scrutinize both.

EIT
www.HowToEngineer.com

RE: Rafter without fly brace?

So I'd like to get agreement on the hand equation results with the Mastan2 results (without having to contact Dr. Z).

Questions in mastan:
Kootk - How'd you know to add nodes and apply to the load to the top of the "fake beam" and also apply restraints to the top of the "fake beam"? Just using line elements and placing everything at the centroid seems wrong, but I didn't even realize that you could take in account load height an restraint location in Mastan2. Did you see an example of this somewhere? I'm just trying to understand the program better.

Problems with Cb:
The modified equation seems to be specific to a uniform load not a point load. Maybe this is giving the error. Maybe we try to model a uniform load in Mastan2?

Hand equation: 107 kip*ft x 3.667 = 392.6 kip*ft
Mastan2: 285 kip*ft

RE: Rafter without fly brace?

Alright, consider me your Mastan support staff if you need that. Or are you planning to do the Mastan yourself?

Quote (RFreund)

Kootk - How'd you know to add nodes and apply to the load to the top of the "fake beam" and also apply restraints to the top of the "fake beam"? Just using line elements and placing everything at the centroid seems wrong, but I didn't even realize that you could take in account load height an restraint location in Mastan2

I took an experimental, evening graduate class in nonlinear structural analysis at Marquette back in 2005 with a professor who runs in the same circles as Dr. White and Dr. Ziemian. The course was awesome but would have been more aptly titled "Nifty Stuff from Dr.Z's Textook". We did a lot of Matlab etc but also spent a lot time with Mastan and worked through a lot of the precursors to what eventually became the Stability Fun series. Of course, that was fifteen years ago now and my long term memory is crap for anything other than first principles stuff.

Using line elements placed at the centroids is just what you do, for better or worse. Some notes on the fake beams in my models:

1) All of the fake beam line elements were the same cross section as the beam itself. This was really just a matter of convenience. Mastan is not super user friendly and it's a boon just to be able to click "All Members" and apply the same cross section to everything.

2) All connections between all member segments, including the fake beam elements, were rigidly connected for both flexure and warping torsion. Again with the "All Members" business.

3) For the most part, the fake beam elements are nothing more than visual aids to allow the user to visually perceive the rotation of the beam in addition to the centroidal displacement. The one important job that they do, as you surmised, is allow you to introduce loads and restraints at locations in space other than the beam centroid.

4) If you look closely as some of the Mastan output, you'll see that the presence of the fake beam elements does actually impact the results a bit. Those impacts are very small however and, for most intents and purposes, the fake beam elements can be considered purely "ride along", as we intend. For some of the models that I ran where the applied load ratio was in excess of 1.0, the first mode of buckling was actually the center tee stub of the fake beam twisting around ninety degrees like a goofy corkscrew. So there's that. I just put a fake x-dir restraint on the fake top flange and forced the real first mode to bubble back up to its rightful place at the surface.

5) I entertained the notion of trying to strategically chose the cross sections for the fake beams. One the one hand, you want something relatively flexible and inconsequential to minimize the impact on the overall beam behavior. On the other hand, you kind of want something stiff so that the applied loads move around with the beam rotation as you'd expect them to without any bonus flexibilities coming into play. In the end I concluded that, either way, the impact was going to be so negligible that it wasn't worth extra effort of trying to get fancy(er).

Quote (RFreund)

The modified equation seems to be specific to a uniform load not a point load. Maybe this is giving the error. Maybe we try to model a uniform load in Mastan2?

Sure. Do you want me to do this? Would you mind if we dropped the 70' beam example and migrated to back to the 32' test case? With the 70' case, I fear that our results will forever be tainted by "sure, but at 70' it's not a realistic example and, therefore, not wholly valid for comparison with code provisions". I actually feel that waay myself. The 70' example did it's job admirably as the hyperbolic example that it was intended to be but I think that it's time to put that one out to pasture in favor of something more representative of practical designs. Even at 32', Mastan's coming in at only 50% of the AS4100 capacity so there's still plenty of discrepancy to fret over.

- W27x84
- 1/8 th point top flange lateral bracing.
- Uniform load producing a peak moment near the plastic moment as before.
- 32' span
- Fixed beam ends.
- Weak axis rotation unrestrained at beam ends.

If you agree to this, I'll run it as listed above and modified as follows for Cb calculation:

- Remove all intermediate restraints.
- Move all load down to the shear center.

RE: Rafter without fly brace?

As a kid when I dreamt of becoming an engineer I never once thought I'd be sitting here looking at an analysis of fruit content titled "Cornucopia of beam failure modes"...

I'll never be able to look at an apple the same that's for sure

RE: Rafter without fly brace?

Quote (Kootk)

Even at 32', Mastan's coming in at only 50% of the AS4100 capacity

Can you please lock the bottom flange at the L restraints (ie turn the L's into F's) and see what it does to that 50%?

Regarding span lengths, I think 32' is too short for a W27 if we're talking about AS4100 steel rafters and want to have a "realistic" arrangement.

RE: Rafter without fly brace?

Sure. What do you like at 32'? 18x35? 16x26? I'd always intended for a low Iy/Ix to promote LTB. Where an L-brace is at the tension flange, you want it gone completely, right?

RE: Rafter without fly brace?

Quote (Kootk)

Sure. What do you like at 32'? 18x35? 16x26? I'd always intended for a low Iy/Ix to promote LTB

I was thinking more like Span to depth of 40+

Quote (Kootk)

Where an L-brace is at the tension flange, you want it gone completely, right?

No, I meant bracing all of the restraint points top and bottom, to make them all F restraints. To see how L restraints along the top compares to F restraints along the whole beam.

AS4100 is assuming L restraints are equivalent to F restraints. I'm curious as to what mastan says is the difference between the L restrained vs F restrained beam.

RE: Rafter without fly brace?

W10x12 coming up then, all braced up. I"ll put my money on it going past plastic section capacity.

RE: Rafter without fly brace?

Can you compare to the L case too, for that particular beam...

RE: Rafter without fly brace?

W10x12
Mid-span point load = 12 kip (full section yield at 11.7k)
Span = 36'

Run #1: ALR = 0.19055; L-braces everywhere.

Run #2: ALR = 0.68169; F-braces only at locations consistent with AS4100.

Run #3: ALR = 3.2025;F -braces everywhere.

RE: Rafter without fly brace?

What’s the unrestrained capacity of that beam?

RE: Rafter without fly brace?

Not much it seems. ALR = 0.069133. Unadjusted, elastic LTB "capaccity" as usual.

RE: Rafter without fly brace?

Why does the cross section stretch in those images?

RE: Rafter without fly brace?

As I described in my response to RFreund, the cross sections represent nothing at all in terms of reality. Just visual aids and a way to apply restraints and loads to locations other than the beam centroid. That said, they do draw a little load and, therefore, do deform a bit. For some of these buckling modes the deformation is incredibly small. So small that they are on par with the tiny cross section deformations which is why you see the stretching that you commented on. The reality is that these cross sectional deformations are present in all of the Mastan runs, they're just imperceptible relative to the other, much larger deformations in many cases. For comparison, in that last diagram in the bunch of three above, you're looking at a flange tip elongation measured in 10^-13 inches.

This is my best guess at least. It's difficult to parse out some of these effects.

RE: Rafter without fly brace?

I can only see two possibilities, unfortunately.

1. These buckling results are all wrong.

2. AS4100 simplified segment method can be unconservative when L restraints are used.

We could be missing something, but no ones coming up with much....

RE: Rafter without fly brace?

I messed up in a couple of spots when trying to explain the cross section distortions.

1) I shouldn't have given the impression that the nodal deformations were in inches. As mode shapes, they are entirely non-dimensional. When you look through the nodal displacements, you find that one of the nodes has a displacement of [1.0] and the rest of the nodes have absolute values less than [1.0]. And this is exactly as it should be given that the deflected shape is a normalized mode shape, not a real representation of displacement. A different kind of analysis, such as second order non-linear, would be required to estimate true displacements. For these Eigenvalue runs, the displacements are all just relative.

2) While it is true that the faux beam sections do draw some load and deform a bit, I believe that it was an error to suggest that those deformations were predominantly responsible for the sectional distortion that steveh49 commented on. Rather, I think that it works like this:

a) for some high energy mode shapes, the modal displacements of the buckled shapes are so small that they are of the same order as the displacements at the nodes of the faux cross sections.

b) All of the displacements get scaled twice: once for normalizing the mode shape and a second time to amplify the view for the operator. And this scaling applies to the distances between all nodes that have moved, including the nodes of the faux cross section.

c) Given [b & a], even a rigid body motion of the faux cross section may result in stretching of the distance between points, even when little to no stretching between points would be expected in the real, physical thing.

Applying this to the displaced shaped below, I would say that the points representing the top and bottom flange both moved in space, in opposing directions, as a result of mostly rigid body rotation. Then, when all of the distances between all of the displaced points were scaled, the proportions of the faux cross section got scaled too. This really is tough to explain but I'm fairly certain that we could tell a fairly similar -- and logical -- story about any of the other sectional distortions.

RE: Rafter without fly brace?

A happy post-Thanksgiving to all of my non-Canadian cohorts.

I prepared the attached PDF to answer some questions that I've been interested in since Celt83 conducted a similar exercise. And I thought that they might be of interest to the group. Basically, I wanted to study the flanges of our W27x84 test beam as isolated compression members to get a sense for how the behavior and capacity of such members would be affected by a compression distribution that varies over the length of the member and is substantially tension over segments of the member.

My observations:

1) In many important respects, a beam cannot be considered to be merely an assembly of independent axially loaded fanged. No surprise there. This representation completely ignores that fact that both flanges are continuously braced, to a degree, by the St.Venant torsional stiffness of the beam. That makes a big difference and must be remembered.

2) Relative to a classic, Euler column, a column loaded like a beam bottom flange would have about double the capacity.

3) A column loaded like a beam bottom flange still buckles over its entire length, as our LTB models have suggested.

4) Relative to a classic, Euler column, a column loaded like a beam top flange would have about fifteen times the capacity. Clearly, a flange with its compression field located at its ends (bottom flange) is much more unstable than a flange with it's compression field located at its middle (top flange).

5) I've come to view LTB, at least for our test case, as something like:

a) the bottom flange initiates some twist.

b) with some twist in play, some of the applied load becomes a weak axis load on the beam and initiates some sway.

Obviously, these are two actions occurring in tandem rather than sequentially.

RE: Rafter without fly brace?

Yep, and D shows the effect of fixing weak axis bending. It largely neuters the bottom flange compression near the supports.

RE: Rafter without fly brace?

Quote (Tomfh)

Yep, and D shows the effect of fixing weak axis bending.

Right. And that takes me back to some comments that Human909 made some time ago. I'd meant to comment on them then but things were moving fast and it got lost in the shuffle. I believe that his points were:

1) Human909 pointed out that, in many cases where you would have end moments develop, you would also naturally tend to have some degree of weak axis restraint. And that's true of course. I did my best to steer the conversation towards beams without weak axis end restraints for two reasons however:

a) AISC and most of the reference cases are built around members without the weak axis end restraint. So in the interest of comparing similar things, I thought it best to stick to beam ends that were pinned with respect to weak axis flexure.

b) In the literature, when they discuss interaction buckling, they're always careful to point out that the effect of considering weak axis behavior of adjacent spans isn't always your friend. Sometimes it does provide significant restraint to the span being studied and, naturally, will improve capacity in those cases. Other times, the adjacent span may actually be encouraging buckling in the span being studied rather than restraining. In that sense, even going with beam ends as weak axis pinned isn't always a conservative assumption. But, then, one has to put a pin in it someplace and move on. So we typically put the pin in the neutral, pinned ends assumption.

2) Human909 made note of the fact that, when beam ends were fixed about the weak axis, that made for a 100% increase in capacity. In examining the case below, that observation checks out. In going from pinned to fixed ends, you're basically going from k = 1.0 to k = 0.5 on the "flange as column" model. And while we don't see a 400% improvement in capacity, a large bump makes sense.

RE: Rafter without fly brace?

Quote (Kootk)

A happy post-Thanksgiving to all of my non-Canadian cohorts.
Thanks. And I'm thankful that the pace has slowed down here so it hasn't been too difficult to catch up.

Getting back to verifying the mastan results with the modified C.b factor...

Quote (Kootk)

W10x12
Mid-span point load = 12 kip (full section yield at 11.7k)
Span = 36'
AS4100 using inflection point and alpha_m: ALR = 0.547
AISC with normal cb: ALR = 0.1424
AISC with modified cb: ALR = 0.2715
Mastan (per Kootk) = 0.1906

What if we use a uniform load of 500 plf (give same end moment)
AS4100 using inflection point and alpha_m: ALR = 0.7276
AISC with normal cb: ALR = 0.1763
AISC with modified cb: ALR = 0.2222
Mastan (per Kootk) = ????

RE: Rafter without fly brace?

Please refer to the snips below and the attached PDF of the same.

I also wanted to explore a bit more the business of L-retraints (lateral only / one flange) being taken as equivalent to F-restraints (lateral restraint + cross section rotational restraint). A brief summary:

1) A while back, Steveh49 dropped on us the extinction level bombshell that AS4100 considers L-restraints equivalent to F-restraints in many cases. I don't think that I was alone in finding that shocking.

2) I came to a revelation of my own that, in fact, both AISC and AS4100 routinely assume that rotational restraint exists where only an L-brace is present. The ubiquitous case of that being simple span beams with intermediate, lateral braces on the top flange. So assuming rotational bracing at locations only having lateral bracing isn't an outlier thing, it's an all the time, everywhere thing. And it needs to be explained in that context.

3) In a post dated [27 Nov 19 01:59], tomfh and I explored how this applied to simple span beams and came to the conclusion that, indeed, it was appropriate to consider L-braces as F-braces for such cases.

Where I'm at now is that, if L-bracing is going to be effectively taken as F-bracing in some situations but not others, then I'd like to know the rules of the road. When is it okay and when is it not? To that end, I've studied the cases below. This is our usual W27x84 with the center point load. I've placed F-bracing at the inflection points and L-bracing in between. From the perspective of both AS4100 and AISC, the span between the IP F-bracings would be treated as an independent design segment within which the L-bracees could be assumed to prevent cross section rotation. So the point of the exercise, then, has been to assess the truthiness of that claim.

CASE 1

Here, at an ALR = 8.3991 and no bracing at the 1/4 points, it would appear that the L-braces are not effective rotational restraints. That said:

a) It appears to me that it is the buckling of the the spans to the left and right of the IP F-braces that is encouraging the bottom flange "kick out" between the IP F-braces.

b) To an extent I think that one can say that, if a buckling mode that would induce rotation at the L-braces occurs at a wildly high ALR, that's not really a repudiation of the notion that such L-braces are effectively F-braces.

CASE 2

At an ALR = 24.1222, this is the same as case one but with the addition of bottom flange bracing at the 1/8 th points. As can be seen by the snaking buckled shape between IP L-braces, and the relative absence of cross sectional rotation within that segment, this removes the tendency for twist between the IP F-braces entirely and restores that segment to a state where the assumption that the L-braces are effective F-braces would be appropriate. So a nice benefit of case two is that the end segments no longer buckle and encourage section rotation between IP F-braces. I would argue, however, that this benefit could be gained in two ways:

a) Provide actual bottom flange L-braces at the 1/8 th points as shown or;

b) Simply design the the segments left and right of the IP F-braces such that they don't buckle without the 1/8 th point bracing.

I feel that this is an important equivalency.

The Proposed Rules of the Road for L-braces Equivalent to F-braces

Speaking the parlance of AS4100, and being mindful of the AS4100 distinction between "segment" and "sub-segment", I tentatively propose that intermediate L-braces may be assumed to be equivalent to F-braces within a design segment, and therefore taken as forming sub-segments, when:

1) The design segment being studied is itself bounded on each end by F-braces (real, physical ones).

2) The design segments either side of the segment being studied, if present, have been properly designed to preclude buckling there.

3) A "compression flange" shall be defined as any flange experiencing compression anywhere within the design segment being studied, regardless of whether or not that flange would experience compression at the particular location of any given L-brace.

4) Any design segment may have as many as two compression flanges, as dictated by loading conditions. In such cases, both flanges must be independently stabilized laterally and independently evaluated for stability.

RE: Rafter without fly brace?

Quote (Kootk)

1) A while back, Steveh49 dropped on us the extinction level bombshell that AS4100 considers L-restraints equivalent to F-restraints in many cases. I don't think that I was alone in finding that shocking.

2) I came to a revelation of my own that, in fact, both AISC and AS4100 routinely assume that rotational restraint exists where only an L-brace is present.

I don’t quite agree with this. The codes (in particular AS4100) do not assume rotational restraint exists a L. AS4100 is quite explicit that no rotational restraint exists at L restraint. That’s the key feature of an L (as opposed to an F or P) - there is no rotational restraint. So the codes are not saying the rotational restraint is equivalent, they are saying it is equivalent level of buckling performance. They say you don’t need the full restraint to stabilise the cross section - and thus it is considered redundant to go from
L to F. They assume it won’t move if you stabilise the critical flange. Hence “equivalent” performance, even though they’re not actually equivalent.

These buckling runs you are doing suggest that is a a faulty assumption, in which case modified rules like you suggest are perhaps appropriate.

RE: Rafter without fly brace?

Quote (Tomfh)

I don’t quite agree with this.

Great. I would very much like for us to come to complete agreement on this aspect of things before moving on to other things. Moreover, I feel that's entirely possible given that I think we're saying identical things, just in different, and perhaps not perfectly precise, ways.

Quote (Tomfh)

..they are saying it is equivalent level of buckling performance. They say you don’t need the full restraint to stabilise the cross section...

I agree with that 100% and it is, in fact, what I had intended to say myself. Below, I'm going to elaborate at length on what I feel are the important similarities and differences between real, physical F-restraints and the equivalent, faux F-restraints that L-restraints are sometimes assumed to create. Please review it and let me know:

a) If you disagree with any of my assertions and/or;

b) If you feel that I've omitted anything important.

In this way, we can isolate the points of true disagreement, if any, and deal with them in a targeted fashion.

Comparing and Contrasting Real F-braces (RFB's) with Fuax-F-braces (FFB's)

1) An FFB is not as rotationally stiff as an RFB.

2) An FFB is not as rotationally strong as an RFB

3) Because of #1 and #2, an FFB cannot be assumed to define the end points of a design segment as an RFB can.

4) Within a range of applicability, an FFB can create a condition wherein a design segment may be subdivided into sub-segments for design purposes such that:

a) the end points of such sub-segments may be taken to be the locations of the FFB's and;

b) for the purpose of stability design, designers may assume that LTB buckling modes associated with cross sectional rotation at the ends of such sub-segments is precluded.

5) Where conditions are met such that an L-brace may be assumed to serve as an FFB, it is understood that no significant cross sectional rotation is expected to occur at the locations of the FFB's prior to the sub-segments between them reaching a point of LTB instability between the FFB's.

Now for the bar exam...

RE: Rafter without fly brace?

Quote (RFreund)

What if we use a uniform load of 500 plf (give same end moment)
AS4100 using inflection point and alpha_m: ALR = 0.7276
AISC with normal cb: ALR = 0.1763
AISC with modified cb: ALR = 0.2222
Mastan (per Kootk) = 0.19367

Done. A couple of things to note:

1) While Mastan does have a utility for uniform load, to my knowledge, there is no way to apply a uniform load to a member at any location other than the shear center. Rather than getting fancy with more faux members with difficult to predict behaviors, I just discretized the uniform load as serious of equivalent point loads at the 1/8th points. [500 plf * 36 ft / 7 = 2.571 k] each. Hopefully this is sufficient for your purposes.

2) I don't know about you but I'd expected the switch from a point load to a uniform load to have more impact than it seems to have. Having pondered this a bit, my explanation for this is:

a) LTB for this situation is mostly the story of the bottom flange kicking out laterally.

b) The tendency for the bottom flange to kick out laterally is most greatly affected by the compression force delivered to the ends of the bottom flange.

b) End moments, and therefore the compression force delivered to the ends of the bottom flange, are pretty much the same for both cases even though the lateral distribution of applied load is quite different.

Quote (RFreund)

And I'm thankful that the pace has slowed down here so it hasn't been too difficult to catch up.

Perhaps we should observe a self imposed limit of one post per person per day going forward. Except for me, I get five.

RE: Rafter without fly brace?

Kootk,

Yes I agree with your points 1-4

If the cross section doesn't move or rotate at the L restraint (i.e. forms buckling nodal point) then it should be equivalent in performance to an F restraint, e.g. what happens in the simply supported cases.

I would love if there was a deeper rationale than these isolated cases for AS4100's general advice to treat Ls as Fs, but it doesn't seem to be the case. :(

RE: Rafter without fly brace?

KootK,
What is the load level in those analyses? Does ALR=1.0 correspond to the bending moment at elastic buckling equalling plastic section capacity?

Your rules are how I had understood AISC 360 works based on discussion in this topic. Is that the case or are there differences?

RE: Rafter without fly brace?

Quote (steveh49)

Does ALR=1.0 correspond to the bending moment at elastic buckling equalling plastic section capacity?

Yes, roughly speaking, that is how the loads have been chosen in most cases. I always round a little one way or the other so that I've got sensible numbers to enter in to the models. That said, all that really matters is the load at which buckling occurs. I really only chose to input a load that would approximately produce plastic bending moments so that:

1) There would be some meaningful benchmark and;

2) We'd be dealing with numbers between 0.1 and 100 which feel better to humans than, say. 0.00000052147 which would be equally valid.

Quote (steveh49)

What is the load level in those analyses?

Always [Buckling Load = ALR x applied load]. I believe that I introduced the applied load level with the first instance of each geometrically different beam model. For all of the 32' W27x84 models, the load was 250k in the middle. For Tomfh's 36' W10x12 models, the load was 12k in the middle. If you're unable to decipher the load level for a particular run, let me know and I'll chace it down.

Quote (steveh49)

Your rules are how I had understood AISC 360 works based on discussion in this topic. Is that the case or are there differences?

That is the case. I was, however, intentionally avoiding that head to head comparison for the time being for fear that it would be somewhat inflammatory. Because I am a ridiculous glutton for punishment, I am eventually going to take another stab at rewriting/reinterpreting AS4100 in a way that I feel would resolve the discrepancies that now seem manifest. At this point, I feel that an error in the writing of AS4100 is at least as likely as:

3) All of he modelling work being wrong (certainly possible) or;

4) Trahair and the rest of genius kind actually botching the theory.

And likely or not, what does it hurt to run a mental, "what if" experiment of this sort for sport?

One of the outcomes of that hypothetical exercise will be that AS4100 would effectively collapse into being identical to AISC save for AS4100's more advanced consideration of imperfections. I'll in no way be insinuating that AS4100's only path to righteousness is to get in line behind AISC however. Rather, I'll make the argument that parity between the codes ought to be the default expectation given that:

5) This stuff is, at it's core, just Newtonian physics in a common gravitational field and;

6) Research is constantly shared across borders so cross pollination abounds.

RE: Rafter without fly brace?

Quote (Kootk)

At this point, I feel that an error in the writing of AS4100 is at least as likely as:

I consider that very unlikely. AS4100 surely intends for L to count as buckling node?

In my view the most likely option is there is a hole in the AS4100 theory, and that L restraints ought not be considered buckling nodal points, but in the real world L restraints actually function as P or F restraints, which significantly inhibits buckling, plus we rarely see ultimate design loads.

The modelling being wrong is also a real possibility. Maybe MASTAN can't do it properly. Human's NASTRAN models certainly seemed more inclined to produce buckle modes more in keeping with AS4100 assumptions.

RE: Rafter without fly brace?

Quote (steveh49)

Your rules are how I had understood AISC 360 works based on discussion in this topic. Is that the case or are there differences?

I'll also add that that is how AISC works only because that is, for reasons not known to me, how AISC is applied. As others have pointed out, based on syntax alone and in he absence of any ancillary documents, AISC reads as pretty much identical to AS4100.

AISC practitioner interpretation has broken in a more conservative direction which has led to AISC seeming to not have an issue with overestimating capacities. Still:

1) The AISC standard does not explicitly state the "rules" in the way that I have proposed and, more importantly;

2) The AISC standard certainly does not expound upon the reasoning for the rules.

In these respects, I feel that AISC could have done a much better job of fully conveying the nuances of its approach to LTB design.

RE: Rafter without fly brace?

Quote (Tomfh)

I consider that very unlikely.

Shocking.

Quote (Tomfh)

AS4100 surely intends for L to count as buckling node?

Agreed, under the right conditions. It is in the expression off those conditions that I speculate that an error might exist.

Quote (Human909Tomfh)

Human's NASTRAN models certainly seemed more inclined to produce buckle modes more in keeping with AS4100 assumptions

I disagree. My perception was that the NASTRAN models were plagued with modelling errors for much of the thread and, once those errors were resolved, the results began to align with the Mastan results and tell a similar story.

Quote (Tomfh)

Maybe MASTAN can't do it properly.

Maybe not. Or, more likely, maybe KootK can't do Mastan properly. Still, I think that the fact that the Mastan results and the AISC results are fairly well aligned adds some measure of credibility to the Mastan results.

RE: Rafter without fly brace?

Quote (Kootk)

I disagree. My perception was that the NASTRAN models were plagued with modelling errors for much of the thread and, once those errors were resolved, the results began to align with the Mastan results and tell a similar story.

I was referring to a few of the models showed short length bottom flange buckles between L restraints. Maybe these are due to modelling inconsistencies/errors like you suggest. Nonetheless I think it's worth keeping the NASTRAN short buckle results in mind. I don't believe it should be written off. Maybe NASTRAN is seeing something that MASTAN isn't.

Quote (Kootk)

Agreed, under the right conditions. It is in the expression off those conditions that I speculate that an error might exist.

AS4100 is pretty clear on it - a lateral restraint attached to the flange which buckles the furthest (5.5.1) or attached to a compression flange (5.5.2) counts as an L, which defines buckling length.

Quote (Kootk)

Maybe not. Or, more likely, maybe KootK can't do Mastan properly. Still, I think that the fact that the Mastan results and the AISC results are fairly well aligned adds some measure of credibility to the Mastan results.

The MASTAN results appear credible to me.

RE: Rafter without fly brace?

Quote (KootK)

My perception was that the NASTRAN models were plagued with modelling errors for much of the thread and, once those errors were resolved, the results began to align with the Mastan results and tell a similar story.

But you comments here are not really that accurate. This "plague" of "modelling errors" were models of imperfect pinned connections. They were removed to get alignment with the perfect pins being used to give the Mastan results. The reality is that REAL WORLD connections are not perfect pins. Real world connections almost always have a non negligible degree of stiffness and this stiffness is often enough to significantly change the buckling behaviour.

Also I wouldn't put the blame on NASTRAN, I'd put the blame on the user (myself) or the problem description (perfect pin connections).

I am currently of the opinion that AS4100 could be unconservative in some situations. The simple logical extension of a hypothetical infinitly long beam with L restrainst all along it having appropriate twist restraint is evidence of AS4100s failings. Whether this translates readily to realistic scenarios hasn't been adequately fleshed out.

RE: Rafter without fly brace?

Quote (Human)

The reality is that REAL WORLD connections are not perfect pins. Real world connections almost always have a non negligible degree of stiffness and this stiffness is often enough to significantly change the buckling behaviour.

That’s correct. But it is a problem if AS4100 is actually reliant upon rotational restraint occurring at L restraints. The whole premise of L restraint is no rotational restraint.

If I actually need some rotational stiffness at L restraints in order for AS4100 to work then I want to know about it.

And we don’t need infinite long beam for this to be a problem. These buckling results are perfectly ordinary span sizes.

RE: Rafter without fly brace?

Quote (human909)

How? It's not as though I misquote on purpose. I exert more quality control in my posts than most here on Eng-Tips but, in a 500 post thread, a couple are gonna slip past the goalie.

Quote (human909)

The reality is that REAL WORLD connections are not perfect pins.

I addressed that pretty thoroughly in my first post today. Things do move pretty fast here though so I'd not blame you if you'd missed that one.

Quote (KootK)

Right. And that takes me back to some comments that Human909 made some time ago. I'd meant to comment on them then but things were moving fast and it got lost in the shuffle. I believe that his points were:

1) Human909 pointed out that, in many cases where you would have end moments develop, you would also naturally tend to have some degree of weak axis restraint. And that's true of course. I did my best to steer the conversation towards beams without weak axis end restraints for two reasons however:

a) AISC and most of the reference cases are built around members without the weak axis end restraint. So in the interest of comparing similar things, I thought it best to stick to beam ends that were pinned with respect to weak axis flexure.

b) In the literature, when they discuss interaction buckling, they're always careful to point out that the effect of considering weak axis behavior of adjacent spans isn't always your friend. Sometimes it does provide significant restraint to the span being studied and, naturally, will improve capacity in those cases. Other times, the adjacent span may actually be encouraging buckling in the span being studied rather than restraining. In that sense, even going with beam ends as weak axis pinned isn't always a conservative assumption. But, then, one has to put a pin in it someplace and move on. So we typically put the pin in the neutral, pinned ends assumption.

Quote (human909)

Also I wouldn't put the blame on NASTRAN, I'd put the blame on the user (myself) or the problem description (perfect pin connections).

It was always my intent to assign any blame, if you want to call it that, as [100% Human909; 0% NASTRAN]. I intentionally didn't call you out by name when critiquing the NASTRAN models because I felt that it was unnecessary to do so and would be more tactful if I did not. I was trying to be polite and conciliatory within the limited range of my people skills.

RE: Rafter without fly brace?

Quote (Tomfh)

Nonetheless I think it's worth keeping the NASTRAN short buckle results in mind. I don't believe it should be written off. Maybe NASTRAN is seeing something that MASTAN isn't.

Abso-friggin-lutely the Nastran results should not be written off.

Quote (KootK)

Having a surprising result confirmed by two independent modelers, using two different software packages, and coming from two different fundamental perspectives was invaluable with respect to establishing credibility for the results.

The situation with the modelling, unfortunately, unfolded like this:

1) Human909 did a lot of modelling before I started.

2) I did a lot of modelling after Human909 stopped.

3) Due to the minimal overlap, Human909 and I only ever ran the same model once and the result, according to Human hisself, was:

Quote (Human909)

Kootk (1)
Human909 (0)

Of course one data point is no trend. If there is any doubt that a NASTRAN model would fail to confirm the results of one of my MASTAN models, I propose this:

1) Let's identify the model to be challenged.

2) Let's have human909 replicate my MASTAN model in NASTRAN.

3) Human and I will compare deflected shapes, weak axis bending moments, shear diagrams... whatever, until we get our models to agree.

This is, I submit, the rational thing to do when you have access to two fancy software packages. Make 'em fight it out!

RE: Rafter without fly brace?

Quote (Tomfh)

AS4100 is pretty clear on it - a lateral restraint attached to the flange which buckles the furthest (5.5.1) or attached to a compression flange (5.5.2) counts as an L, which defines buckling length.

AS4100 is pretty clear on it. However, if there are errors in AS4100, then AS4100 may be pretty clear on something that is incorrect or was never intended. And that's kind of my point.

I think that you're jumping the gun on your critique of my stuff here given that I haven't actually made my proper pitch yet. Steveh49 kind of tricked me into showing my cards before I'd wanted to. So how about this:

a) Put a pin in your critique for the time being.

b) When I've said my piece, I'll invite you to critique what I've tabled in it's entirety.

I'll get it done by Sunday night.

RE: Rafter without fly brace?

Quote (Kootk)

However, if there are errors in AS4100, then AS4100 may be pretty clear on something that is incorrect or was never intended.

If AS4100 is mistaken I'm sure they didn't intend for it. What I am saying is that if there are mistakes in AS4100 then it's not because of poor wording etc (eg as you previously hypothesized), I am saying the errors are because they are genuine mistakes in the theory, which has thus ended up in AS4100.

My money is currently on them wrongly extrapolating to all cases that L is equivalent to F (when it only applies in some cases), but that this theoretical hole is concealed by real world stiffness bonuses (e.g. purlin cleat rotational restraint), and also the normal strength buffer (phi factors, load factors etc).

Quote (Kootk)

I think that you're jumping the gun on your critique of my stuff

Which critque of your stuff? Which stuff in particular?

RE: Rafter without fly brace?

PS. I've been not around partly because of thread weariness, partly just busy with work and partly IT troubles; NASTRAN broke and I can't get it running again.

RE: Rafter without fly brace?

Quote (Kootk)

Done. A couple of things to note:

1) While Mastan does have a utility for uniform load, to my knowledge, there is no way to apply a uniform load to a member at any location other than the shear center. Rather than getting fancy with more faux members with difficult to predict behaviors, I just discretized the uniform load as serious of equivalent point loads at the 1/8th points. [500 plf * 36 ft / 7 = 2.571 k] each. Hopefully this is sufficient for your purposes.

2) I don't know about you but I'd expected the switch from a point load to a uniform load to have more impact than it seems to have. Having pondered this a bit, my explanation for this is:

Interesting and thank you. I think I can put this to bed for now. Can you share the Mastan model for this? In general the take away seems to be that there is an increase in buckling strength capacity when the top flange is laterally restrained but not enough that would always get you back to your plastic strength.

I don't think I really understand the current argument between Kootk and Tomfh. I understand you are trying to see when a restraint that restrains lateral movement can be considered equivalent to one that restrains both lateral and rotational. But I'm missing why this is relevant or what the (specific) consequences are.

This might be related to the above question - What in AS4100 says that you can consider the unbraced length to be an inflection point or the brace past the inflection point? If I read through the definitions it seems like you could make an argument that you need to use the entire bottom flange as the segment length. Maybe someone can walk me through how you are able to reach a different conclusion?

RE: Rafter without fly brace?

Quote (Rfruend)

What in AS4100 says that you can consider the unbraced length to be an inflection point or the brace past the inflection point? If I read through the definitions it seems like you could make an argument that you need to use the entire bottom flange as the segment length.

AS4100 defines segment (and subsegment) length as the distance between F, P or L restraints, thus an L past the inflection point counts at an end of sub segment.

No one does it as you are proposing. It’s not the intention.

The issue now is whether that intention is wrong.

RE: Rafter without fly brace?

Quote (RFreund)

What in AS4100 says that you can consider the unbraced length to be an inflection point or the brace past the inflection point?

Best be careful... accusing someone's code of allowing inflection point bracing these days is fightin' words. AS4100 most definitely does not support inflection point bracing. As a good way to clarify this, consider the situation of our W27X84 but imagine that the intent is to call the 1/4 points braced and delineating design sub-segments. As I understand it, most AS4100 practitioners would go to one brace past the inflection point but, as afar as I know, going to the brace at the inflection point is also street legal.

It would break down like this:

1) Inflection point bracing = no lateral restraint to either flange but call it a brace point anyhow.

2) AISC = usually lateral restraint to both flanges and, obviously, call it a brace point.

3) AS4100 = lateral restraint to just the top flange and call it functionally equivalent to lateral restraint to both flanges for stability purposes.

I do understand how, at first glance, one might erroneously assume that AS4100 is allowing inflection point bracing however. As is evident from the list, it's 1/2 way there as viewed with AISC eyes. That is, in fact, part of what drew my attention to this thread in the first place.

RE: Rafter without fly brace?

Quote (Kootk)

Best be careful... accusing someone's code of allowing inflection point bracing these days is fightin' words. AS4100 most definitely does not support inflection point bracing.

Not inflection point Per se, but the lateral braces past the inflection point.

RE: Rafter without fly brace?

Quote (Tomfh)

Which critque of your stuff? Which stuff in particular?

I mentioned that I was going to take another stab at re-writing / reinterpreting AS4100 and that immediately set off another round of debate about how we feel AS4100 is to be interpreted. We'll have that debate, for sure, but I'd like to forestall that until after I've actually pitched my re-write/reinterpret. I haven't done that yet.

Quote (KootK)

Because I am a ridiculous glutton for punishment, I am eventually going to take another stab at rewriting/reinterpreting AS4100 in a way that I feel would resolve the discrepancies that now seem manifest. At this point, I feel that an error in the writing of AS4100 is at least as likely as:

Quote (tomfh)

If AS4100 is mistaken I'm sure they didn't intend for it.

I agree and certainly never meant to suggest otherwise. If there's an error, I see it coming about as shown below/attached: plausibly and devoid of malicious intent.

Quote (tomfh)

What I am saying is that if there are mistakes in AS4100 then it's not because of poor wording etc (eg as you previously hypothesized), I am saying the errors are because they are genuine mistakes in the theory, which has thus ended up in AS4100.

I understand, I think, but disagree and will again hypothesize that the issue may be poor phrasing. However, with the next round, note that:

1) Previously, I'd hypothesized that the AS4100 phrasing was mildly ambiguous and therefore fodder for minor misinterpretation by designers. With the next round, I'll be proposing that the problem is something more akin to an error of omission that no designer could realistically have been expected to sort out on their own (unless they'd been part of a 500 post thread on the subject).

2) I am not, and will not be, suggesting that I'm in any way certain that there is a content error in AS4100. Rather, I'll exploring this as one possibility among several that I feel is again worthy of consideration because:

a) at the start of this thread, I might have put to likelihood of an AS4100 content error around 0.5% but;

b) after all that has transpired, I might now put the likelihood of an AS4100 conten error closer to 15%.

RE: Rafter without fly brace?

Yeah but guys like Trahair and all the other gurus who wrote the codes and bibles and sample problems do it exactly the same way we do. How could that be the case if things just got lost in translation?

RE: Rafter without fly brace?

Quote (Tomfh)

Not inflection point Per se, but the lateral braces past the inflection point.

Did I not articulate that sufficiently in the statement below? With the W27x84 exmple, I intentionally set it up so that the IP would also be the first brace point. I feel that makes for the most extreme / salient version for comparing things. If anyone had objected to that, I'd just have moved the quarter point brace over 6" into the compression zone and continued in the same vein.

Quote (Tofmh)

As I understand it, most AS4100 practitioners would go to one brace past the inflection point but, as afar as I know, going to the brace at the inflection point is also street legal.

True inflection point bracing, in the naughty sense, assumes that a member is F-braced at inflection points when there is no bracing in play. Whether AS4100 L-bracing is at the IP, or one brace past the IP, it's still a massively different thing simply because it's still a real brace instead of no brace at all, even if it is only providing restraint to one flange.

RE: Rafter without fly brace?

Quote (Kootk)

True inflection point bracing, in the naughty sense, assumes that a member is F-braced at inflection points when there is no bracing in play. Whether AS4100 L-bracing is at the IP, or one brace past the IP, it's still a massively different thing simply because it's still a real brace instead of no brace at all, even if it is only providing restraint to one flange.

Yes, agree completely.

RE: Rafter without fly brace?

Quote (Tomfh)

Yeah but guys like Trahair and all the other gurus who wrote the codes and bibles and sample problems do it exactly the same way we do. How could that be the case if things just got jumbled in the code writing process?

a) I don't know who exactly wrote the LTB section of AS4100 and therefore do not know if there are textbook examples by those people to indicate how they interpret things. Do you?

b) Since you don't yet know what reinterpretations I'm going to propose, how can you possibly know whether or not any particular textbook examples contradict them?

I'm begging you Tomfh: can you please put a pin in your critique until I've actually put pen to paper on my proposal? That would have to be more time efficient for us both.

RE: Rafter without fly brace?

Quote (RFreund)

Can you share the Mastan model for this?

A zip file containing all of the models that I've been using is attached. Ridiculously in the modern era, all 17 only occupy 100 kb of hard disk space. The file naming is not that descriptive but:

a) that's partly Mastan's fault as its naming rules are bizarrely limiting and;

b) upon opening a model, it ought not take anyone long to figure out which it is.

Quote (RFreund)

In general the take away seems to be that there is an increase in buckling strength capacity when the top flange is laterally restrained but not enough that would always get you back to your plastic strength.

Yes, as it pertains to AISC procedures. That said, in our explorations, I've not found the bump to be that significant in many cases. It was as low as 17% for the W27x84 I think. I think it understandable that one might leave that on the table in favor of simplicity when not motivated by desperation for capacity in an existing build situation etc.

Quote (RFreund)

I understand you are trying to see when a restraint that restrains lateral movement can be considered equivalent to one that restrains both lateral and rotational. But I'm missing why this is relevant or what the (specific) consequences are.

I hope that you'll stay tuned long enough to review one more post of mine. I'm planning to put something together just for us AISC folks and it will elaborate on this aspect of things.

RE: Rafter without fly brace?

Quote (Kookt)

a) I don't know who exactly wrote the LTB section of AS4100 and therefore do not know if there are textbook examples by those people to indicate how they interpret things. Do you?

Good question as to who actually wrote AS4100. Anyone know the authors?

Steveh49 linked to the Trahair document, where L is deemed equivalent to F. That seems a fairly clear example of the gurus aligning with the practitioners.

RE: Rafter without fly brace?

Quote (Tomfh)

AS4100 defines segment (and subsegment) length as the distance between F, P or L restraints, thus an L past the inflection point counts at an end of sub segment.

No one does it as you are proposing. It’s not the intention.

The issue now is whether that intention is wrong.

I agree that no practitioner does it this way (or atleast I take your word for it) and also agree that the issue is weather or not that is correct (I think we have shown that there are cases where this is unconservative). But if we take AS4100 to court and say "look at this design using your code, you way over estimate the capacity of this W10" it seems like they could argue that you should have used the entire length. Meaning if you start with the bottom flange it is the critical flange, what in the code says the sub-segment length stops at the lateral restraint on the opposite flange once you get past the inflection point. I just don't see it that clearly. I will try to walk through this later. Basically making a case (if I can) that the code says you need to use the full bottom flange length. Again not referencing any guides, just the language in the code.

Quote (Kootk)

I hope that you'll stay tuned long enough to review one more post of mine. I'm planning to put something together just for us AISC folks and it will elaborate on this aspect of things.
Fair enough.

RE: Rafter without fly brace?

Quote (RFreund)

ut if we take AS4100 to court and say "look at this design using your code, you way over estimate the capacity of this W10" it seems like they could argue that you should have used the entire length.

Critical flange is assessed at the cross section location, not the start of the flange (e.g. support). That is how the background theory is stated, how the code is written (e.g. "The critical flange at any section shall be the compression flange"), how the textbooks and canonical examples are presented, and how practitioners do it.

How do you mean they could argue the contrary? What specific wording do you believe suggests you need to consider compression in all cross sections as opposed to the cross section under consideration?

RE: Rafter without fly brace?

I haven't been following this thread religiously, but may be able to contribute something.

Firstly - according to my colleagues back in Straya, the 2019 AS4100 draft code has been released for public comment. After you've posted another 500 times, maybe you can suggest, if any, amendments to be included in the new code.

In regards to the authors of the bending section of the code. The commentary provides some insight. T.J. Hogan also seems to feature heavily throughout the commentary.

Not sure if it helps, but the commentary defines the critical flange as the following:

RE: Rafter without fly brace?

Thanks for posting the above comment Trenno from the 4100 commentary. I was meaning to post it myself but I've been distracted and had a bit of topic exhaustion.
-The comment is quite clear that 5.5.2 annd 5.5.3 are more specific clarifications of 5.5.1 rather than simplified choices.

In the meantime:
-I've got Nastran up and running again. Kootk (or anybody else) if you want something specific run through its paces with an FEA approach I'm willing to do it if you point me in the right direction regarding specific scenarios.

-I've also spent a little time digging around academic literature on the topic. Though in general the academics focus on theoretical buckling equations rather than definitions of the effective bending length. AS4100 is apparently more conservative that other codes regarding buckling when when you are comparing apples with apples with beams of the same effective length.

-A slight aside but in the fine print in Space Gass there a small comment regarding L restraints. SpaceGass a very significant market share in Australia for steel design.
This isn't exactly relevant but it is another hint at how L restraints have confused and been abused by structural engineers. This quote is in the context of MINOR AXIS compression effective lengths so it isn't the same thing.
"there is some recent doubt as to whether lateral restraints on equal flanged I or W shapes can restrain the overall cross section laterally"
(AKA in the past L flange restraints have been used by some engineers as minor axis buckling restraints.)

RE: Rafter without fly brace?

Quote (Human)

The comment is quite clear that 5.5.2 annd 5.5.3 are more specific clarifications of 5.5.1 rather than simplified choices.

I find it a bit odd that they refer to them as “more specific” when in many situations they give different answers.

Quote (Human)

Though in general the academics focus on theoretical buckling equations rather than definitions of the effective bending length

I’ve been noticing the same thing. The effective lengths seem to be assumed.

RE: Rafter without fly brace?

Quote (Tomfh)

I’ve been noticing the same thing. The effective lengths seem to be assumed.
Call me a cynic but in the realm of publish or perish there is often plenty of papers published that behind the knees of giants rather than on their shoulders.

The effective length is a clear from a theoretical perspective. Once you start messing around with it with qualitive restraints then it all gets a bit murky. (And the definitions of F,L,P restraints are largely qualative!)

RE: Rafter without fly brace?

Quote (Human909)

Kootk (or anybody else) if you want something specific run through its paces with an FEA approach I'm willing to do it if you point me in the right direction regarding specific scenarios.

Hell yes. I vote for the W10x12 example that I created for tomfh recently.

- 36' span W10x12
- Top flange L-brace at 1/8th points.
- Top and bottom flange L-braces at beam ends.
- Ends fixed for strong axis rotation. Longitudinal pins at web to flange intersections?
- Ends free for weak axis rotation.
- No warping restraint to flanges at beam ends.
- 250kip 12 kip downward point load at midspan applied to top flange.
- Weightless beam.
- Fy jacked up to 500 ksi so that elastic bucking is the only failure mode.
- Shear deformation turned off by setting G = infinity.
- E = 29000 ksi

You've mentioned topic fatigue numerous times. Pace yourself with this stuff. Take a week off to refresh. We've got all the time in the world.

RE: Rafter without fly brace?

Quote (Human909)

"there is some recent doubt as to whether lateral restraints on equal flanged I or W shapes can restrain the overall cross section laterally"

1) That's interesting and, I think, highlights the need to always be thinking of buckling in terms of a hierarchical, many mode process.

2) Of course a single flange L-brace does in fact restraint weak axis buckling. The question is, with that restrained, what mode is next in the sequence?

3) The next mode for a purely axial member would likely be pure torsional buckling, in this case constrained about the axis of the braced flange.

4) In my experience, even unconstrained torsional column buckling almost never governs for two fanged sections. It's an easy enough check though.

5) We could model this easily enough but it's probably a topic best left for another thread in order to be sensitive to everybody's fatigue levels.

RE: Rafter without fly brace?

Quote (Kootk)

- No warping restraint to flanges at beam ends.
- 250kip downward point load at midspan applied to top flange.
- Weightless beam.

I think this should be:
- 250kip 12KIP downward point load at midspan applied to top flange.

RE: Rafter without fly brace?

Quote (Kootk)

2) Of course a single flange L-brace does in fact restraint weak axis buckling. The question is, with that restrained, what mode is next in the sequence?
In pure compression you are pretty close to Euler theory land and you really are only thinking about 1 mode of buckling in each axis. Add your restraints, get your effective lengths anway you go. The next mode I suspect would be restrained flange minor axis buckling which would involve twisting of the section.

I imagine some engineers were counting L restrains on flanges to act as minor axis compression restraints. Think purlins on a portal frame building. That isn't something I'd like do. I'd use a centrodal lateral brace or fly bracing.

I'm currently in the process of designing a clad structure and I'm generally ignoring the restraint effects of the purlins except for a fews the points of fly braces. Moment reversal means adding a bunch of Ls on one side doesn't particularly help things much anyway. I've also chosen to avoid fly braces in the roof by using and H-beam because they'd be a pain to install. The lower columns, well there is 1400tonnes sitting on the 10mx35m structure. I'm not leaving compression buckling restrains to the purlins!

I'll see what I can get done now on NASTRAN. I might even through in the pure compression scenario in for fun.

RE: Rafter without fly brace?

Quote (RFreund)

I think this should be:

Corrected, thank you.

Quote (human909)

I'd use a centrodal lateral brace or fly bracing.

And there's the rub. I believe that a centroidal lateral brace would be no better than a single flange lateral brace and may well be a bit worse. Both bracing schemes would eliminate full length weak axis buckling. To the extent torsional buckling would be the next mode in line, the flange brace would be better than the centroidal brace because the centroidal brace would do nothing at all to restrain the cross section twist which is the crux of torsional column buckling. It sounds as though we're heading for another model-off after all...

RE: Rafter without fly brace?

Quote (KootK)

I believe that a centroidal lateral brace would be no better than a single flange lateral brace and may well be a bit worse. Both bracing schemes would eliminate full length weak axis buckling. To the extent torsional buckling would be the next mode in line, the flange brace would be better than the centroidal brace because the centroidal brace would do nothing at all to restrain the cross section twist which is the crux of torsional column buckling. It sounds as though we're heading for another model-off after all...

I couldn't resist looking into this so I took our W12 example and modeled it as a column with 100 k axial. It seems that I was partially wrong in my statement above.

The clips below show:

- The first three buckling modes with a mid-span, weak axis restraint at the column centroid.

- The first three buckling modes with a mid-span, weak axis restraint at one of the column flanges.

Here's what I see for takeaways:

1) For an eigenvalue buckling analysis, the first mode capacity for both brace arrangements is identical. I had this part right.

2) A centroidal brace is better for subsequent, higher energy buckling. The first torsional mode for the centroidal bracing happens at twice the load of the flange bracing. I had this part wrong.

RE: Rafter without fly brace?

First up:

Quote (Kootk)

And there's the rub. I believe that a centroidal lateral brace would be no better than a single flange lateral brace and may well be a bit worse. Both bracing schemes would eliminate full length weak axis buckling. To the extent torsional buckling would be the next mode in line, the flange brace would be better than the centroidal brace because the centroidal brace would do nothing at all to restrain the cross section twist which is the crux of torsional column buckling. It sounds as though we're heading for another model-off after all...
I did a quick look.

SCENARIO: 31UB 10m, fully fixed ends, pure compression
No restraints: 196kN
Centeral restraint: 496kN
Central restraint at flange: 394kN (21% less)
Central restraint at purlin 130mm off flange: 287kN (42% less)

A 20% drop might be borderline significant, a 42% drop certainly is significant. I suspect this is where the caution is warranted when people are using purlins or similar as flange restrains when in reality they are restraining a cleat that can be a non negligible distance from the flange. (But again this is point lateral restraints of infinite stiffness laterally and zero rotational stiffness. In reality the restraint would have some rotational stiffness and non infinite lateral stiffness....) That said I'd hope the purlin spacing is close enough that it completely wipes out minor axis buckling... Either way I think that is another topic.

I'll follow up with the W10x12

RE: Rafter without fly brace?

This one's for the AISC crowd.

When knocking on the door of this thread, my hope was always that I'd walk away from it with a little candy in hand. And not just a sucker either but, rather, a full sized bag of chips or a three pack of peanut-butter cups. You know, some pearls of wisdom for use in my own, real work using the AISC standard. I believe that I have that now and I'd like to share it, both as an act of friendly dissemination and to provide others an opportunity to critique what I think I now know.

We AISC'ers don't seem to have an under-capacity LTB problem and, as such, do not need to change our ways just yet. That said, the LTB story that now plays in my head is a much richer and more nuanced thing than the one that played in my head prior to this thread. I feel that there's value in that. Without further adieu, here are my before and after LTB stories, with reference to the beam shown below.

KOOTK LTB STORY BEFORE LTB THRILLA IN MANILA 2019

1) Check design segment {A} as top flange buckling @ [Lb = 4']

2) Check design segment {B} as bottom flange buckling @ [Lb = 32']

3) Pat self on back for a job well done.

KOOTK LTB STORY AFTER LTB THRILLA IN MANILA 2019

1) Check design segment {A} as top flange buckling @ [Lb = 4']

2) Recognize that #1 implicitly assumed that cross sections 1 & 2, bounding design segment [A], did not rotate appreciably. Marvel at this given that neither cross section is endowed with any physical, rotational restraint in the form of external bracing.

3) Recognize that the two things providing rotational restraint to cross sections 1 & 2 are the St. Venant torsional stiffness of the beam and the warping torsional stiffness of the beam. Further recognize that the warping torsional stiffness will dominate for most wide flange beams.

4) Recognize that the warping torsional stiffness of a wide flange beam basically amounts to the flanges acting as girts spanning horizontally between the rotationally restrained ends of the design segment. For this beam in particular, it's all about the bottom flange performing the girt function. So this is how cross sections 1 & 2 are rotationally stabilized. It's the bottom flange as stabilizing girt.

5) Given that the bottom flange is doing this important girt thing, question whether or not some kind of check should be performed on the bottom flange to ensure that it is strong and stiff enough to do the job. For a simple span beam with no bottom flange compression, no such check is performed. It seems that we are comfortable assuming that an all-tension flange can do the girt job effectively. And that's probably alright given that it really doesn't take much to brace a thing.

6) Recognize that the bottom flange is in compression over much of its length and will have a tendency to buckle between the ends of the beam. Further recognize that, if the bottom flange is allowed to buckle, it will kick the bottom flange out at cross sections 1 & 2 and, thus, utterly violate the assumption of near zero cross sectional rotation at those locations. What to do?

7) Check design segment [B] as bottom flange buckling @ [Lb = 32']. In addition to checking for bottom flange buckling in its own right, this check rectifies #6 by allowing us to continue to assume that cross sections 1 & 2 remain rotation free because the bottom flange was not allowed to kick out.

8) Given that negative bending LTB will govern, consider taking advantage of constrained axis LTB which accounts for the benefit of the top flange restraints in the calculation for bottom flange LTB buckling. The trade off is additional calculation complexity. Reject this given that experience has shown that the capacity increase is only on the order of 20% because the center of LTB rotation tends to be pretty close to the top flange even in the absence of the top flange bracing. Deflection concerns probably govern the design anyhow.

9) Pat self on back for a job well done.

RE: Rafter without fly brace?

Can you run the next one with pinned ends and Fy = 500 ksi.

RE: Rafter without fly brace?

Quote (Human909)

I suspect this is where the caution is warranted when people are using purlins or similar as flange restrains when in reality they are restraining a cleat that can be a non negligible distance from the flange.

I see what you mean. First below is unbraced column. Second is a brace placed 12" off of the flange to hyperbolically simulate the cleat business. You're almost down to the unbraced braced value and it doesn't take much imagine to see why with the buckled shape staring back at you.

RE: Rafter without fly brace?

KootK:

I've read thru the Yura document a few times and if I've understood it correctly Yura recommends a modified Cb formula to capture beams with reverse curvature.

Plotted in Fig. 7 in the document:

for the 32' - W27x84 beam this would yield a Cb of 3.67
So redoing the check with Lb = 32' and the new Yura Cb, I'm getting that yielding is the controlling limit state not Lateral Torsional Buckling, however if I am understanding your Mastan runs correctly they seem to indicate a much lower LTB value?

Open Source Structural Applications: https://github.com/buddyd16/Structural-Engineering

RE: Rafter without fly brace?

Quote (Kootk)

1) For an eigenvalue buckling analysis, the first mode capacity for both brace arrangements is identical. I had this part right.
And this is where the Mastan models seem to fall over. That is not at all logically consistant for the buckling model to be identical. You would expect some change in the mode even if it is small.
Here is my buckled shape:

And here is my first mode for the W10x12. The load factor is 0.375

(This seems differnt from yours but maybe I've made a mistake. You can see my constraints in my picture. Load is 53.38kN.

RE: Rafter without fly brace?

Quote (Human)

(This seems differnt from yours but maybe I've made a mistake. You can see my constraints in my picture. Load is 53.38kN.

Nope, the mode shape looks identical to mine.

Quote (Human909)

And here is my first mode for the W10x12. The load factor is 0.375

Well below plastic yield moment, as my models indicated.

That's good enough for my purposes. Thanks for the run.

RE: Rafter without fly brace?

Quote (Human909)

And this is where the Mastan models seem to fall over.

Perhaps, but it strikes me as premature to be blaming Mastan already. To quote a friend from, like, hours ago:

Also I wouldn't put the blame on NASTRAN MASTAN, I'd put the blame on the user (myself)...

Additionally, I still don't know much about your model. Can you run the W12x10 with pinned ends and Fy = 500 psi and post something showing:

1) The first three buckled mode shapes and;

2) What your FEM mesh looks like.

Lastly, I disagree with this.

Quote (Human909)

That is not at all logically consistant for the buckling model to be identical. You would expect some change in the mode even if it is small.
Here is my buckled shape:

Like anything else in buckling restraint, I would suspect that there is some value of offset at which the first mode buckling shape switches from one involving twist to one involving only S-shape weak axis buckling. And I'd absolutely expect that value of offset to be greater than zero. In fact, if your model can't be made to show that, I'd question its validity. Can you put the restraint at, say, 2" from the column centroid?

RE: Rafter without fly brace?

Quote (Celt83)

So redoing the check with Lb = 32' and the new Yura Cb, I'm getting that yielding is the controlling limit state not Lateral Torsional Buckling, however if I am understanding your Mastan runs correctly they seem to indicate a much lower LTB value?

It's a fair bit more nuanced than that I think. You'll notice that Yura's chart was based on a uniform load distribution whereas my W27x84 example modeled a concentrated load. The distribution of the load impacts the stability of the beam with greater load concentration towards midspan producing lower capacities.

To provide a more meaningful comparison, I reran the beam as fixed ended with a uniform load.

M_LTB_Mastan_Concentrated = 690 k-ft

M_LTB_Mastan_Uniform = 854.2 k-ft

Cb_Yura = 3.00

854.2 k-ft / 919.4 k-ft = 93%. As approximate as this stuff is, that's a non-discrepancy in my book.

RE: Rafter without fly brace?

Quote (KootK)

Like anything else in buckling restraint, I would suspect that there is some value of offset at which the first mode buckling shape switches from one involving twist to one involving only S-shape weak axis buckling. And I'd absolutely expect that value of offset to be greater than zero.

In support of that, I found the bifurcation offset point for the W10x12 column by trial and error.

1) With the restraint 2" from the flange or less, it's pure S-shape weak axis buckling. First clip below.

2) With the restraint 3" from the flange or more, it's a full length lateral torsional thing. Second clip below.

3) So my transition point is somewhere between 7" and 8" from the column centroid and outside of the flange altogether.

4) I would expect any offset value less than 7" from the centroid to have the same ALR at 0.1338.

5) I would expect this to vary with varying column size. Sometimes the transition point is inside the flanges and sometimes it's not.

RE: Rafter without fly brace?

Quote (Human909)

And here is my first mode for the W10x12. The load factor is 0.375

Something seems off with the proportions here. Are you sure that your beam isn't 36 inches instead of 36 feet? I get that there'll be some perspective at work but this scales off by a factor of 16.

RE: Rafter without fly brace?

Length is correct. There is significant perspertive foreshortening. I generally rotate the models in a manner I believe best conveys the buckling shape.

Quote (Kootk)

Like anything else in buckling restraint, I would suspect that there is some value of offset at which the first mode buckling shape switches from one involving twist to one involving only S-shape weak axis buckling. And I'd absolutely expect that value of offset to be greater than zero. In fact, if your model can't be made to show that, I'd question its validity.

Except the change in the first mode of buckling isn't binary. Nor can you think of a buckling mode as pure torsional or pure minor axis once you start offsetting the minor axis restrain. It becomes a mix of both hence the reduction in the buckling threshold. Any program that is outputing identical results despite a shift in the minor axis restraint is doing not doing the job completely. I'm not sure what Mastran does but if it runs sepparate buckling analysis on orthogonal planes then this might explain the outcomes. As far as the buckling shape goes it pretty much starts off as an S shape and then a twisted S shape as restraint moves further out. Since this starts off as the first buckling mode and continues to reduce in its threshold value then there is never any sharp transition to a different mode.

FEA buckling analysis is agnostic when it comes to the various buckling behaviours.

Quote (KootK)

Can you put the restraint at, say, 2" from the column centroid?
I can put it 1mm from the centroid and you will still get a reduced result. The buckling threashold is a decreasing monotonic function with regard to the restraint distance from the centroid.

A simple test with a plastic ruler could readily show this minor axis buckling with rotation.

RE: Rafter without fly brace?

Quote (Human909)

Except the change in the first mode of buckling isn't binary.

Not binary, just discontinuous with a flat spot. Something like this.

Quote (Human909)

Nor can you think of a buckling mode as pure torsional or pure minor axis once you start offsetting the minor axis restrain.

You most certainly can if you're not modelling imperfections and using an eigenvalue analysis.

Quote (Human909)

The buckling threashold is a decreasing monotonic function with regard to the restraint distance from the centroid.

Can you offer some proof of that, as I did for my stance in my previous post?

Quote (Human909)

I'm not sure what Mastran does but if it runs sepparate buckling analysis on orthogonal planes then this might explain the outcomes.

Nope, it's just straight up eigenvalue in 3D.

Quote (Human909)

A simple test with a plastic ruler could readily show this minor axis buckling with rotation.

Only because the ruler would represent a real world problem replete with imperfections. Take out the imperfections and it's a different ball game.

RE: Rafter without fly brace?

I think you are misunderstanding the differences between these modelling approaches.

A lateral brace that is eccentric (aka non central) IS an imperfection in this context.

Yes I do have proof I can do 10mm, 75mm and 149mm. But currently not in front of the computer. (I was going to do 1mm but I'd need to massively refine the mesh for that behaviour.)

RE: Rafter without fly brace?

Quote (Human909)

I think you are misunderstanding the differences between these modelling approaches.

I know almost nothing about your modeling approach. Tell me about it if your think there's something that I need to know but don't.

Quote (Human909)

A lateral brace that is eccentric (aka non central) IS an imperfection in this context.

Are you telling me that the offset brace would affect behavior prior to the attainment of the weak axis Euler load in the absence of other imperfections?

Quote (Human909)

Yes I do have proof I can do 1mm, 10mm, 75mm and 149mm. But currently not in front of the computer.

It's not actually proof until after you run the models. I might be able to get my hands on an educational version of NASTRAN. Can you send me dropbox links to your W10x12 beam and column models so that I can tinker with them?

RE: Rafter without fly brace?

Quote (Kookt)

Are you telling me that the offset brace would affect behavior prior to the attainment of the weak axis Euler load in the absence of other imperfections?
That is EXACTLY what I am telling you. And that is exactly what you would expect in REAL world buckling even without imperfections. The change in the restraint position decreases the required energy to buckle the beam.

Quote (Kookt)

It's not actually proof until after you run the models.
Well yeah well had run models just not the full set. And my phone which my last post was from doesn't have NASTRAN. BTW I removed my claim of running a 1mm model as the mesh size would get stupid to do that, so would the decimal places of difference. Anway here are my results.

MODEL: 31UB 10m, fully fixed ends, pure compression (200mm nominal mesh size setting, with refinements around necessary features)
RESULTS:
-Minor axis lateral brace on web at 5m, offset from beam central axis. Brace is at a point.
0mm OFFSET: 494.146kN
10mm OFFSET: 493.801kN
50mm OFFSET: 484.698kN
100mm OFFSET: 452.135kN
149mm OFFSET: 400.194kN (ON FLANGE RATHER THAN WEB)
(Note the last value 1.5% different from the one give a couple of hours ago. Once you change the mesh you are always going to expect differences.)

All these buckling shapes are the lowest energy mode and are largely of an S shape. 0mm offset gives a perfect S shape with no twist the S rotates around the restraint at 0mm. The rest have a degree of twist as the S now rotates around an offset restraint.

Of course all the caveats apply regarding 'models' but the point is that you keep the same model and move the restraint out you are going to get decreasing buckling loads in a monotonic fashion. There is no way around this given this is the lowest buckling mode AND you are reducing the effectiveness of the restraint for each fraction of a mm you move it away from the centroid. If you buckling analysis doesn't give results that behave in this manner then it isn't going deep enough to andequately address the nuances brought up in this tangent topic and possibly the topic as a whole.

NASTRAN is FEA buckling analysis thus it deals with a real 3D body, aka the precise shape affects the behaviour. Whereas (correct me if I'm wrong) Mastran relies on section properties, which alone can never fully describe a member.

Quote (Kootk)

I might be able to get my hands on an educational version of NASTRAN. Can you send me dropbox links to your W10x12 beam and column models so that I can tinker with them?
https://www.autodesk.com/education/free-software/n...
You should be able to get 30days free.

Quote (Kootk)

I know almost nothing about your modeling approach. Tell me about it if your think there's something that I need to know but don't.
FEA has been the brave new world of computerised modeling for decades now in many fields. Others can explain it far better than I can.
https://enterfea.com/what-is-buckling-analysis/

Of course like many 'models' it is not the real world. It is dependent on sensible inputs and sensible interpretation of outputs. However GOOD FEA has a better chance of approaching the real world than a few equations and a few characteristic properties of a section. This is especially so when things get non symetric.

RE: Rafter without fly brace?

Thanks for the info Human909. With regard to the column investigation, it sounds as though the discrepancy simply arises because I'm doing a bifurcation analysis and you're doing something fancier that embodies some manner of system perterbation, even if that's just mesh asymmetry. With the full blown FEM software there's usually an "analysis options" menu screen with gobs of options to choose from. Can you post a screen capture of that input screen with the options selected as you have done for your models so far? I'm fairly well versed in FEM and this would go a long way towards my understanding the nature of the models that you're running.

Are you able to share some of your recent models with me?

Quote (KootK)

Can you send me dropbox links to your W10x12 beam and column models so that I can tinker with them?

I'll have a steep learning curve to deal with if I start tinkering with NASTRAN. Having your files as starters would be a great help. It would also help me to understand your modelling choices.

Quote (Human909)

Whereas (correct me if I'm wrong) Mastran relies on section properties, which alone can never fully describe a member.

I believe that is correct although, for the benefit of anyone interested in Mastan, I should mention that it can do a good deal more than we've been doing with it in this thread. We've just been doing linear elastic eigenvalue buckling models so far but the software also has the ability to study plasticity and run non-linear second order analyses. With regard to the column discussion, one could do a true second order analysis in Mastan, along with some manner of imperfection representation, and arrive at similar results to what you've been producing.

Quote (Human909)

If you buckling analysis doesn't give results that behave in this manner then it isn't going deep enough to andequately address the nuances brought up in this tangent topic and possibly the topic as a whole.

In my opinion, Mastan is actually a better tool than full blown FEM for what we've been trying to do in this thread. Full blown FEM surely is a more accurate representation of reality but, I would argue, reality isn't really what were trying to parse out here. Instead, it seems to me that we're mostly trying to reconcile code provisions with the underlying LTB theory that informed them. And that underlying theory was linear elastic bifurcation buckling, just what we've been doing with Mastan but with a slightly higher degree of sophistication. In this respect, I feel that full blown FEM kind of "overshoots" things in making direct comparisons to code provisions less meaningful. That said, it is of great value here to be able to use Nastran to corroborate the modes shapes and capacities predicted by Mastan. Were Nastran mode shapes wildy different that the Mastan modes shapes then I would definitely be concerned.

RE: Rafter without fly brace?

In this post, I'm going to pose, and attempt to answer, this hypothetical question: if there is an error in AS4100's LTB provisions, and I do not know with any certainty that there is, what would be the least invasive way to rectify it? I feel that the exercise has value for two reasons:

a) If there is an error in AS4100, this might help to point us to its root source.

b) If there is an error in AS4100, this might help to point us to how it might be corrected.

In my final anaylysis, I've come up with the only potential error in AS4100 being one of omission, as follows.

@tomfh: now it's time to offer your critique of this if you wish. Fire away.

Quote (KootK's Proposed Addition to AS4100)

Beam segments containing moment reversals shall be investigated for LTB stability as follows:

1) Perform an LTB investigation considering the top flange to be the critical flange for its entire length and;

2) Perform an LTB investigation considering the bottom flange to be the critical flange for its entire length.

Were this change to be made, I see the following items being resolved:

A) no more issue with AS4100 potentially overestimating LTB capacity at moment reversals.

B) no more issue with AS4100 seeming to assume buckled shapes vastly different from Mastan/Nastran.

C) no more issue with conflicting definitions of the critical flange.

D) AS4100 and AISC become philosophically identical which is appealing if extraneous.

E) No more issue with AS4100 seeming to assume rotational stability where buckling analysis predicts otherwise.

RE: Rafter without fly brace?

Quote (Kootk)

Thanks for the info Human909. With regard to the column investigation, it sounds as though the discrepancy simply arises because I'm doing a bifurcation analysis and you're doing something fancier that embodies some manner of system perterbation, even if that's just mesh asymmetry.
No it isn't just system pertebation, though you are correct mesh asymetry can introduce some imperfections but generally that is a long way from real imperfection. The restraint itself introduces asymetry in the buckling mode. As I have highlighted an offset restrain reduces the required energy for minor axis buckling in a decreasing monotonic fashion with regard to the offset. That is expected from theory, from models and you expect that to be true in real life though imperfection might it an imperfect "decreasing monotonic" relationship.

Quote (Kootk)

With the full blown FEM software there's usually an "analysis options" menu screen with gobs of options to choose from. Can you post a screen capture of that input screen with the options selected as you have done for your models so far? I'm fairly well versed in FEM and this would go a long way towards my understanding the nature of the models that you're running.
I think we should start buckling analysis thread to address this and other aspects being discussed in this tangent. Keep this thread to the AS4100 rather than indepth buckling modelling

Quote (Kootk)

Are you able to share some of your recent models with me?
Get it up and running and I should be able to.

Quote (Kootk)

With regard to the column discussion, one could do a true second order analysis in Mastan, along with some manner of imperfection representation, and arrive at similar results to what you've been producing.
You remain under the false impression that these results are caused by "imperfections". They are not. The effect of an off set lateral brace in minor axis buckling is a reduction in the critical buckling threshold with or without real world imperfections. Oh and I think you have just created the next challenge for yourself.

Quote (Kootk)

Mastan is actually a better tool than full blown FEM for what we've been trying to do in this thread.
Fair call I can see some merit to this depending on your approach. My understanding is Mastan is going to more likely mimic classic section buckling as is considered by the code(s). FEA buckling analysis can be used to more accurate model the affects of real work restraint stiffnesses if you go that far (which I haven't in this thread.)

Like I said feel free to start a new thread to discuss buckling modelling. In the meantime here are a few videos to cover the basics. (I've only watched the first short one.)

RE: Rafter without fly brace?

Human,

In your opinion do your NASTRAN beam models show lower capacity than AS4100’s basic method?

Is your basic elastic buckling load coming out lower than the AS4100 capacity using the normal method?

RE: Rafter without fly brace?

Quote (Human909)

Like I said feel free to start a new thread to discuss buckling modelling.

Nah, I like this part of the discussion right where it is as I feel that difference between our modelling efforts are an important part of the current discussion.

Quote (KootK)

Can you post a screen capture of that input screen with the options selected as you have done for your models so far? I'm fairly well versed in FEM and this would go a long way towards my understanding the nature of the models that you're running.

@Human: can you please provide that? You're using very sophisticated software with, I'm sure, oodles of option settings. It's difficult to know how to interpret your results without knowing much about the modelling choices that you've made.

Quote (Human909)

Are you able to share some of your recent models with me?

Quote (Human909)

Get it up and running and I should be able to.

Can you please send me a link to your models soon, before I get it up and running? As you can imagine, getting set up with a whole new software package is going to require a significant time investment on my part. I'd like to have some trial models in hand to work with before I invest that effort. What's the difference on your end between sharing the models now or sharing them later?

RE: Rafter without fly brace?

The settings are largely the default. Messing around with the setting doesn't and shouldn't changes things beyond going for further refinement. It is the constraints, loading and 3D model that are the main influence. You really don't need 100 screenshots of things.

This is the column model.

RE: Rafter without fly brace?

Quote (human909)

You really don't need 100 screenshots of things.

I didn't ask for 100 screenshots. I asked for one. How. Hard. Is that?

Quote (human909)

It is the constraints, loading and 3D model that are the main influence.

If you think that those are the only variables that significantly affect the output of your 3D, shell element, non-linear, finite element buckling analysis software, you might want to watch a few YouTube videos yourself. I dunno:

- Nonlinear buckling analysis vs linear buckling analysis
- Element mesh size and shape
- Element type / formulation.
- Convergence tolerance.

Quote (human909)

The settings are largely the default.

Scary.

Thanks for the model.

RE: Rafter without fly brace?

Quote (human909)

The restraint itself introduces asymetry in the buckling mode. As I have highlighted an offset restrain reduces the required energy for minor axis buckling in a decreasing monotonic fashion with regard to the offset. That is expected from theory, from models...

If you're saying that a bifurcation model should behave as you've described, then color me unconvinced. Are you able to prove your assertion in any way other than FEM runs? I was able to corroborate my stance almost perfectly using hand calcs based on a paper by Helwig & Yura on the subject. See the attached PDF which contains the calcs and clips from the paper (copyrighted or I'd share it all). As the Mastan model predicted, the increasing monotonic lateral torsional buckling curve never see its peak value because you hit the S-shaped, weak axis buckling failure load at about 1/3 that. Whether or not this is the case, and the extent to which this is the case, is a function of the ratios of Iy, Cw, and J for a give section.

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