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Effects of Intermediate bracing on effective length of large cantilever
2

Effects of Intermediate bracing on effective length of large cantilever

Effects of Intermediate bracing on effective length of large cantilever

(OP)
Hi,

I'm working on a temporary beam that will cantilever 20 meters, I'm looking for information regarding the effective length to use. Most publication only discuss the restraint condition at the tip and the root, but what effects do adding intermediate bracing have on the effective length. Its a built up beam 2500mm deep. I've read Galambos guide to stability design criteria for metal structures but there is no discussion regarding the effect of intermediate stiffeners.

Any guidance or information is appreciated.

RE: Effects of Intermediate bracing on effective length of large cantilever

for me, the post is not quite clear since you first say that you are looking for the influence of intermediate bracings (i.e. discrete restraints which prevent LTB) but then refer to the the influence of intermediate stiffeners. which one is it? as far as i know, the presence of (full depth web) stiffeners does little to influence the critical length, although I am thinking of an I beam...not sure how applicable this is for your case. i may be wrong but i think there is a post around here which tackled the influence of stiffeners and went quite in depth into it.

in general, the critical length, directly related to the elastic critical moment of the member is not that straight forward...cantilever results in increased complexity. built up section 2500mm deep even more complexity...add discrete lateral restraints and I imagine it would be difficult to find guidance or similar examples. 20m is also a very large span.

i suggest you post a sketch and additional info in which you detail overall dimensions, load type and magnitude and your built up cross-section geometry. it would definitely help with getting more precise opinions.

overall i would suggest that the most straightforward way to analyze your problem would be to do a linear buckling analysis, probably based on a shell model of your actual cross section. you can then directly use the critical moment calculated, or use it to back calculate the critical length.

RE: Effects of Intermediate bracing on effective length of large cantilever

A linear buckling analysis would miss inelastic buckling, but that may not be a concern with these spans.

RE: Effects of Intermediate bracing on effective length of large cantilever

I agree with the fact that putting a stiffener in does not constitute a restraint.

Depending on your code, for a valid restraint for flexural loads you either need to laterally restrain the critical compression flange (prevent sideways/lateral movement), or prevent twist of the cross section (or both). A stiffener by itself does nothing to achieve either of these.

Your code should apply directly to this situation. There is nothing special required.

Is it an isolated beam, or are there a series of beams running parallel?

RE: Effects of Intermediate bracing on effective length of large cantilever

(OP)
Sorry, I meant to write intermediate bracing. I plan on making a FEM and running a bucking analysis but was wondering if there were methods to check the models by hand. I'll try to post a sketch shortly.

RE: Effects of Intermediate bracing on effective length of large cantilever

(OP)
There are two beams 9.5 meters apart, and will be braced together at both the top and bottom flange

RE: Effects of Intermediate bracing on effective length of large cantilever

Treat each section of the beam between restraints as a separate segment for evaluating the strength. Its no different to say a simply supported beam with a restrain to midspan. Your code should be letting you treat this as two discrete lengths with a factor based on the moment shape within half the beam and using half the beam length for the effective length x some multipliers based on type of restraint afforded.

If you post the code you are working to people can provide further specific examples?

RE: Effects of Intermediate bracing on effective length of large cantilever

(OP)
Canadian building code. I understand using discrete length with a factor but I can't seem to find what factors to use for braced segments on a cantilever.

RE: Effects of Intermediate bracing on effective length of large cantilever

I imagine the fact that it's a cantilever doesn't matter unless you have an unrestrained end which probably is only applicable for the last segment at the tip. Put it this way, the first segment into the cantilever with multiple braced segments doesn't know its part of a cantilever. So same rules apply, I'm not familiar with the Canadian code, but every other code I've had experience with deals with it in a similar (this) manner.

RE: Effects of Intermediate bracing on effective length of large cantilever

Quote (Agent666)

Depending on your code, for a valid restraint for flexural loads you either need to laterally restrain the critical compression flange (prevent sideways/lateral movement), or prevent twist of the cross section (or both). A stiffener by itself does nothing to achieve either of these.

Huh? Unless I'm missing something the critical flange here is the top, tension flange.

RE: Effects of Intermediate bracing on effective length of large cantilever

Why would the top flange be critical if its in tension? The tension flange won’t buckle

RE: Effects of Intermediate bracing on effective length of large cantilever

I don't think I said it was either flange, but the compression flange is usually the critical flange, whether its the top or bottom flange depends on the direction of the loading.

For a cantilever tip though you need to restrain both flanges, only doing the compression flange isn't sufficient for the restraint to be effective, as the tension flange is still unstable.

RE: Effects of Intermediate bracing on effective length of large cantilever

Agreed Agent, sorry for clarity my response was to human909

RE: Effects of Intermediate bracing on effective length of large cantilever

As I understand it there is only one critical flange. Hence the name. My understanding and what the definition that is commonly found is that the critical flange is the flange that will deflect/[move laterally] the furthest if restraint is removed. For a cantilever this is normally top flange.

Quote (MIStructE_IRE)

Why would the top flange be critical if its in tension? The tension flange won’t buckle
The beam buckles the tension flange deflects. Either way the critical flange is the top tension flange.

Quote (Agent666)

I don't think I said it was either flange, but the compression flange is usually the critical flange, whether its the top or bottom flange depends on the direction of the loading.
One common exception is cantilevers where the top flange is critical. Which is the tension flange.

Quote (Agent666)

For a cantilever tip though you need to restrain both flanges, only doing the compression flange isn't sufficient for the restraint to be effective, as the tension flange is still unstable
The critical flange is the top flange. So if you are wanting to increase the buckling load that is where you should be restraining first.


I welcome views that contrast with the notion that the critical flange is the top flange. But it isn't exactly something I've made up. It is codified, can be recognise by buckling analysis or playing at home with a ruler.

RE: Effects of Intermediate bracing on effective length of large cantilever

human909, once you restrain the tension flange, then the compression flange then becomes the critical flange, hence the need to restrain both flanges at the tip of a cantilever as I noted for a valid/effective restraint. Both are critical in a sense. Otherwise I totally agree with what you are saying apart from this subtlety.

RE: Effects of Intermediate bracing on effective length of large cantilever

Your first statement seem to go against the underlying definition of a critical flange. Could you please elaborate on your definition of the critical flange? Oh and as far I can tell restraining the critical flange. The top tensile flange in a cantilever, will vastly increase the buckling limit of the beam and will in most cases be sufficient.

Again I'll happily be proven wrong if we want to got further than semantics. But from my reading of the AS code and buckling analysis does support my contention.

That said I've seen plenty of good posts from you in these forums so I am more than happy to admit that I'm incorrect. If you can show why. Codes don't hold the answers to everything but they are a strong pointer in the right direction.

RE: Effects of Intermediate bracing on effective length of large cantilever

Its noted in the commentary from memory (of NZS3404 at least), and our codes are basically the same except we have the seismic stuff and better slenderness limits, and you guys have the block shear stuff which our code doesn't codify. Otherwise its 99% the same. I'll see if I can find it and post back the clause.

I don't think you are wrong with your definition of the flange that wants to move the furthest necessarily. It's a good way to think of it, its just once you grab hold of the tension flange, the compression flange still wants to do its buckling thing like it would in a non-cantilever. Its not fundamentally different in that respect just because its a cantilever.

RE: Effects of Intermediate bracing on effective length of large cantilever

Here you go, from NZS3404



This is taught to everyone in University here as a fundamental concept. I note in AS4100 however, it doesn't say this last bit about both flanges which is surprising. But its a real effect backed by research and needs to be considered. You Aussies are usually stealing our stuff, surprised you have not stolen this yet glasses.

If you think of it like this, if you put a 'L' restraint to the tension flange of a simply supported beam, then it does nothing for the compression flange (see figure below from the AS4100 code) I hope you would agree? i.e. a 'U' restraint (EDIT - as far as the critical flange is concerned)!

This is the exact condition at the end of the cantilever isn't it if you only laterally restrain the tension flange? So I believe it covers the requirement in AS4100, its just not spelt out clearly/specifically like it is in NZS3404 so perhaps people don't pick up on it over the ditch in Aussie? Does that satisfy you?



RE: Effects of Intermediate bracing on effective length of large cantilever

Thanks Agent666. smile
You mostly have highlighted the differences in our understanding. From what I can see there are differences in our codes and the NZ code is more conservative here.

Quote (Agent666)

This is taught to everyone in University here as a fundamental concept. I note in AS4100 however, it doesn't say this last bit about both flanges which is surprising. But its a real effect backed by research and needs to be considered. You Aussies are usually stealing our stuff, surprised you have not stolen this yet
Cheeky. rednose But I won't dispute it. (I do find it interesting that the NZ code redefines what is a critical flange (aka both) but that is semantics rather flawed engineering.)

Quote (Agent666)

If you think of it like this, if you put a 'L' restraint to the tension flange of a simply supported beam, then it does nothing for the compression flange (see figure below from the AS4100 code) I hope you would agree? i.e. a 'U' restraint (EDIT - as far as the critical flange is concerned)!
Agreed.

Quote (Agent666)

This is the exact condition at the end of the cantilever isn't it if you only laterally restrain the tension flange?
No. I don't believe so because the tension flange is the critical flange. Aka, the flange that will deflect the most. Aka, the flange that will require the stiffest restraint.

Quote (Agent666)

So I believe it covers the requirement in AS4100, its just not spelt out clearly/specifically like it is in NZS3404 so perhaps people don't pick up on it over the ditch in Aussie?
The thing is that it IS spelt out clearly. But just contrasts to NZS3404.
AS4100
"5.5.3 Segments with one end unrestrained
When gravity loads are dominant, the critical flange of a segment with one end unrestrained
shall be the top flange."


Regarding what is actually good engineering. Well the NZ approach is no doubt more conservative. Whether the AS approach fails to properly consider compression flange buckling is the next question. My 'gut' feeling the compression flange in an normal cantilever isn't going to buckle readily with the tension flange restrained and twist restraint at the point of maximum compression.

But 'gut' feelings don't cut it. And I'll need to do some proper calculations or resort to other people's to try to answer it.


Again thanks Agent666. I'm still curious about this and happy to delve deep to prove myself 'wrong' or 'right'.


(I certainly have seen many cantilevered steel members without bottom flange restraints. I have designed such cantilevers myself in the past. I'd be happy delve more into this, and I am currently doing so.)

RE: Effects of Intermediate bracing on effective length of large cantilever

Quote (human)

No. I don't believe so because the tension flange is the critical flange. Aka, the flange that will deflect the most. Aka, the flange that will require the stiffest restraint.

Once you restrain the tension flange (say an 'L' restraint), then the tension flange cannot move laterally. Then the compression flange becomes the flange that will move the most (you seem to imply its not going to move, but it is still subject to instability. I really don't know how to explain it any clearer. You're getting hung up on the critical flange forever being the tension flange, and its not the case in the view of our code at least and my understanding of how things fail.

Apply your critical flange criteria once again after restraining the tension flange, by AS4100's definition your cantilever then becomes restrained at both ends and the criteria is its the flange that then moves the most which is the compression flange. If I get time in the next day I'll do a mastan2 model to prove the impact of restraints one way or the other, I'm not disputing the fact that the tension restraint might do something, but the figure with the unrestrained section is pretty clear in interpreting what is going to occur when thinking about it from a "first principles" approach. Other codes round the world treat it in a similar manner, whether this reflects the true behaviour or is conservative I'll leave to the code writers.







RE: Effects of Intermediate bracing on effective length of large cantilever

Quote (Agent666)

You're getting hung up on the critical flange forever being the tension flange
I'm not hung up on it. Simply by some definitions it is. (aka AS4100 as quoted)

Quote (Agent666)

Once you restrain the tension flange (say an 'L' restraint), then the tension flange cannot move laterally. Then the compression flange becomes the flange that will move the most (you seem to imply its not going to move, but it is still subject to instability. I really don't know how to explain it any clearer
You've explained that quite clearly. But the thing is, by the definitions previously referred to the critical flange is "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." Restraining the critical flange doesn't make the other flange the critical flange under this definition!

Quote (Agent666)

Apply your critical flange criteria once again after restraining the tension flange, by AS4100's definition your cantilever then becomes restrained at both ends and the criteria is its the flange that then moves the most which is the compression flange.
No see above. And it isn't my definition. It is AS4100.

Like I said it seems the discussion has devolved into semantics about the definition of the 'critical flange' and variations in codes. I think we are both interested in the true behaviour rather than simply comparing differences in codes.

RE: Effects of Intermediate bracing on effective length of large cantilever

I may have lost track in the back and forth about exactly what the discussion is about, but the AU code doesn't permit subdivision of FU or PU segments due to intermediate lateral (only) restraints. There must also be full or partial twist restraint so that both flanges are at least elastically-restrained. Or you design for the full FU/PU length.

If the cantilever tip has F or P restraint, it will be an FF/PP/FP segment for buckling design. See the last two rows of AS4100 Table 5.6.1. The critical flange will then be the compression flange.

Edit: so you essentially have to know the restraint conditions before deciding which is the critical flange.

RE: Effects of Intermediate bracing on effective length of large cantilever

If this does end up in mastan, can it be the case of:

- cantilever (for vertical loading)
- point load applied at the tip: bending moment = P*L
- lateral-rotational restraints at both ends (ie loaded point is restrained as well as the rigid support)

RE: Effects of Intermediate bracing on effective length of large cantilever

@canwesteng good point. i dont know what code op is using but in eurocode the inelastic part is accounted for through the imperfection factors in the chosen buckling curves...
@op remember to brace the beams by taking the restraining forces to a bracing system or similar. in other words, remember not to just brace the two beams between themselves, as theoretically they can both buckle in the same way at the same time.

RE: Effects of Intermediate bracing on effective length of large cantilever

Regarding the two parallel beams case. If providing twist restraint, then its my understanding that you can link the two beams with members perpendicular to the span with end conditions the achieve the cross section twist restraint then this still achieves restraint (it's not dependant on preventing lateral deflection of the critical flange. You need to either prevent twist or lateral deflection, not necessarily both. Though many practical arrangements obviously achieve both.

If you simply link the two beams say with a pin ended strut but don't prevent the lateral deflection of the critical flange (by say adding some plan bracing) then this doesn't meet the fundamental requirements for a restraint. A common example of this that people always seem to incorrectly take is considering each and every purlin as providing restraint when those purlin have no load path for the accumulation of the restraint force (for example beam is free to deflect about minor axis unless the purlin connect the something that isn't moving (like a stiff wall or something similar)).

RE: Effects of Intermediate bracing on effective length of large cantilever

Quote (human909)

I think we are both interested in the true behaviour rather than simply comparing differences in codes.

I believe that I may have something to offer on this front. I believe that thinking about which flange moves the most is definitely to head in the right direction. However, I think that it's even better to be thinking about the related concept of where the point of LTB rotation lies vertically. It's also useful to keep in mind that LTB is not really about compression flange buckling per se but, rather, the flopping over of the entire cross section to a position that would exacerbate deflection and move the applied loads closer to the ground (potential energy reduction which governs most natural things). Thinking about LTB in terms of compression flange buckling is a useful concept that will steer one in the right direction the vast majority of the time. But not all of the time.

Consider the two most common examples:

1) Free cantilever with no effective lateral or torsional bracing at the tip. The point of LTB rotation is below the bottom flange and LTB is the flopping over of the cantilever tip. Therefore, the most effective location for LTB bracing is at the top/tension flange which allows your bracing to act at the greatest lever arm.

2) Cantilever with both lateral and torsional bracing at the tip which is, coincidentally, is the best kind of cantilever by far. Now the cantilever tip can't flop over so it's very different. Instead, it would be a location between brace points where the cross section would have to flop over. Here the point of LTB rotation is above the top flange of the beam owing to the compression flange's tendency to kick out laterally. Therefore, the most effective location for the LTB bracing is the bottom/compression flange which allows your bracing to act at the greatest lever arm relative to the point of rotation. As others have pointed out, there's really nothing particularly "cantilevery" about this case. It's pretty much just an upside down gravity beam with some moment at one end.

Quote (Agent666)

For a cantilever tip though you need to restrain both flanges, only doing the compression flange isn't sufficient for the restraint to be effective, as the tension flange is still unstable.

3) The interesting case of lateral restraint to the top/tension flange only and no rotational restraint. I would describe it like this:

a) This is, in fact, acceptable so long as it's evaluated properly. One would want a pretty compelling reason to go down this path, of course, given it's inferiority compared to other options.

b) I'd expect that the critical mode of buckling for this case would be the cantilever tip rolling over but constrained to roll about the intersection of the web and top flange. This would have greater buckling capacity than the free cantilever case but less capacity than the case where the cantilever tip is rotationally restrained. There's a method for evaluating this that I've heard termed "constrained axis buckling".

RE: Effects of Intermediate bracing on effective length of large cantilever

Quote (Agent666)

If providing twist restraint, then its my understanding that you can link the two beams with members perpendicular to the span with end conditions the achieve the cross section twist restraint then this still achieves restraint (it's not dependant on preventing lateral deflection of the critical flange.

This I agree with. If the cantilever tips can't flop over into weak axis bending, then that ceases to be a valid buckling mode regardless of the presence or absence of lateral restraint.

Quote (Agent666)

You need to either prevent twist or lateral deflection, not necessarily both.

This I do not strictly agree with. I believe that:

1) You always need to prevent twist.

2) Preventing lateral deflection, alone, is never sufficient to prevent LTB.

A simple span beam with the compression flange continuously braced laterally and rotational end restraint can actually LTB buckle. We pay no heed to this mode simply because the buckling load is so ridiculously high that it merits no practical attention. You'd have section yielding etc long before you got there.

RE: Effects of Intermediate bracing on effective length of large cantilever

Well phrased. Kootk. And had a similar understanding though not the confidence in my understanding to properly expressive it.

Incidentally, the cantilever I recently design and went back to review. Partly to test my knowledge and partly as a secondary check fits you description of the best kind of cantilever. Tip lateral restraint and rotational restrain on the top flange.

It becomes pretty clear that with these restraints the compression flange is going to move first. Whether restraint on this flange is necessary, I'm going to re-check when I have time.

RE: Effects of Intermediate bracing on effective length of large cantilever

Quote (human909)

Tip lateral restraint and rotational restrain on the top flange.

Is your rotational restraint:

1) rotational restraint of the top flange (as stated) or;

2) effective rotational restraint of the entire cross section?

It would need to be #2 to fit my definition of "the best kind of cantilever".

If it's #1, you could initiate a buckling mode that starts of as web sidesway buckling at the cantilever tip.

This is probably just semantics but, then, semantics are a big deal in these discussions. It may well be that your top flange rotational restraint is also whole section rotational restraint (stiffeners etc).

RE: Effects of Intermediate bracing on effective length of large cantilever

Quote (KootK)

This I do not strictly agree with. I believe that:

1) You always need to prevent twist.

2) Preventing lateral deflection, alone, is never sufficient to prevent LTB.

Swinging the pendulum the other way a bit, I would say that:

3) There are many practical situations in which providing lateral, translational restraint of the compressed flange takes LTB off of the functional table but;

4) Where #3 is the case, the lateral restraint is really provided as a means of restraining one particular mode of twist.

5) Interestingly, it would seem that rotation restraint is always the stronger form of bracing. This, given that translational restraint will generally eliminate one mode of twist while leaving others in play (usually of no practical consequence). Rotational restraint, by comparison, takes LTB completely off of the table for a particular unbraced length.

RE: Effects of Intermediate bracing on effective length of large cantilever

As usual, if you want the TRVTH you need to go to Australia.

https://espace.library.uq.edu.au/view/UQ:278979

None of that 'bth flenges a crutical, eh bro' nonsense either. You can't handle the truth! wink

RE: Effects of Intermediate bracing on effective length of large cantilever

2
Ok for what its worth, I found the results of doing a simple case in mastan2 quite interesting to quantify relative effects. It showed a rotational restraint at the tip wasn't a hell of a lot better than the unrestrained case, and by far the best benefit gained is by preventing the lateral deflection of both flanges (which also prevents twist).

Considered effects of warping, analysis based on elastic critical buckling load (i.e. doesn't require any modelling of initial imperfections, file size blows out to Gigabytes if you do this for some reason). Geometry is setup so elastic buckling occurs, i.e. no inelastic buckling occurs.

Obviously you would still need to apply the code 'curves' to get a real code capacity which is the codes way of dealing with initial imperfections, residual stresses (all 2nd order effects basically). For example in AISC, you would work out the stress due to the buckling moment, and then run it through the normal flexural torsional buckling equations using this value.

Similarly for AS4100/NZS3404 (Which I'm more familiar with) you'd run it through the procedure in clause 5.6.4, the value coming out of your mastan2 analysis is M_ob. To work out alpha_m you need another model that is setup to give you the reference buckling moment (the constant moment case which is equivalent to use of an alpha_m of 1.0). Work out M_oa once you have alpha_m, then proceed to work out alpha_s like you normally would. M_bx = alpha_m*alpha_s*M_sx. Job done.

File attached, just play with the fixities on the cantilever tip to see the relative effects. Note that the I-section shapes are just there as a visual aid to visualise the deflection/rotation behaviour in the buckled shape and to provide approx modelling of restraint location.

All cases have arbitrary vertical point load at tip. Exact value of buckling capacity isn't important, the relative ratios is the point I'm reviewing here. i.e. if you do xxxx restraint then elastic buckling capacity increases by a factor of yyyy relative to the unrestrained case!

Keep in mind this is all relative to the actual section and geometry being used and isn't a hard rule to be applied to all situations.

Following cases were looked at:-
CASE - (BUCKLING LOAD FACTOR) RATIO - SCENARIO

Case 1 - (874) 1.000 - unrestrained tip (no restraints)
Case 2 - (1329) 1.521 - top flange lateral restraint only at tip
Case 3 - (1810) 2.071 - top and bottom flange lateral restraint at tip (note also prevents twist)
Case 4 - (1190) 1.362 - bottom flange lateral restraint only at tip
Case 5 - (1216) 1.391 - Twist restraint only at tip
Case 6 - (1777) 2.033 - Twist restraint and lateral restraint to top flange at tip (Basically effectively similar to Case 3 restraints)

CASE 1

CASE 2

CASE 3

CASE 4

CASE 5

CASE 6


Hopefully that highlights the relative importance/differences in the application of different types of restraints and adds some credence to the restraining the tension flange only argument, and slightly higher capacity if restraining both flanges laterally.

I think it effectively shows that using either lateral restraint, or twist restraint achieves the same result (1.4-1.5 times in this demonstration), and that adding both twist and lateral restraint improves things further.

Finally if you are interested in mastan2 they have free stability fun modules self teaching material on their website that I highly recommend working through at your own pace as it's very useful for teaching the basics of what does and doesn't affect stability and the basis of how the code curves are derived. It's based on AISC, but can easily be worked through using any other code for comparison.

RE: Effects of Intermediate bracing on effective length of large cantilever

KootK, Australian & NZ codes are setup on the basis of either requiring lateral or twist restraint. You don't always need lateral restraint as you noted.

Hopefully the outputs above demonstrate they are relatively similar in their effect. Most practical scenarios you usually have both though, and I got a reasonable increase in the buckling load by applying both, relative to only one type.

NZ/AU codes deal with the whole section twist restraint vs flange only twist restraint through the use of a Fixed and Partial type of restraint that can involve slightly different scaling for the effective length used. For most cases they are considered the same though.

From our code for example, makes it pretty simple to classify requirements, some types have classifications on what you can consider a moment connection/pin or stiff/flexible member, etc so you can apply it to practical arrangements:-

RE: Effects of Intermediate bracing on effective length of large cantilever

Quote (Agent666)

KootK, Australian & NZ codes are setup on the basis of either requiring lateral or twist restraint. You don't always need lateral restraint as you noted.

I'm not sure that you've properly digested the point that I've attempted to make Agent666.

I wasn't saying that you sometimes don't need lateral restraint; I was saying that youalways need twist restraint. Lateral restraint can certainly be effective but my point is really that the root cause of it's effectiveness is that it prevents twist.

In the most pedantic and semantic of ways, my beef was really with the emphasized part of the statement below which, in my mind, implies that twist restraint is optional. And, of course, it's not optional. The only question is how you obtain twist restraint. Roll beam vs lateral brace etc.

Quote (Agent666)

You need to either prevent twist or lateral deflection, not necessarily both.]

RE: Effects of Intermediate bracing on effective length of large cantilever

Quote (Steve)

As usual, if you want the TRVTH you need to go to Australia

Any chance you'd want to direct a bro' to the parts of that doc that you consider salient? It's rather long and, apparently, printed on a Gutenberg press. I read the conclusions and there were no surprises there other than the interesting tidbit below. And I guess that's to be expected. Kinda like how the best place for a horizontal stiffener on a plate girder is NOT the center of the web.

RE: Effects of Intermediate bracing on effective length of large cantilever

I understand in your code you might need both twist and lateral restraint. But in reality having just a lateral restraint still affords some increased resistance to buckling.

In terms of our NZ/AU code twist restraint is actually optional (I'm sure others will back me up here unless I've been taught to do it wrong for 20 years!?). We have a third Lateral restraint category that is quantified, provided its applied to the critical flange. That is the point I am making, lateral restraint in the absence of twist restraint does something (in practice and in some codes), but naturally there are some penalties involved. If you don't like the approach take it up with the code writers (I am not one). The 'L' isn't as effective, but it is still better than nothing, if I understand you correct you are implying its good for nothing in your code, but it isn't in practice is my point, and our code takes advantage of this fact.

I mean if you like, go and prove otherwise in a rational buckling analysis and post back to prove the point one way or another. I'm happy to consider alternative views if there is some evidence.

I've demonstrated that having either one on its own has effectively the same effect on buckling using the mastan2 model. Increases of 1.4-1.5, of a similar magnitude, and a definate difference between only having twist restraint and twist and lateral restraints together.

From our code, perhaps this confirms our definition, maybe its considered semantics though.

RE: Effects of Intermediate bracing on effective length of large cantilever

You're still not hearing me Agent666. I'm not arguing that translational restraint is ineffective. I'm arguing that, in reality, all translational restraint really IS rotational restraint. See the sketch below for one example. That's how translational restraint works for LTB: it restrains rotation about a point somewhere in space. There is no such thing as LTB restraint that is not rotational restraint because, fundamentally, the name of the game is to keep the member from flopping over and increasing it's deflection. Lateral LTB restraint, somehow in the absence of twist restraint, simply isn't a thing.

Quote (Agent66)

If you don't like the approach take it up with the code writers (I am not one)

I have little interest in what anybody's codes say, including my own. Blind monkey code following is for lesser mortals. I play in the fundamental principles sandbox or not at all.



RE: Effects of Intermediate bracing on effective length of large cantilever

Yeah I get your point (now apparently), its potentially decreasing the rotation rather than completely preventing it for a cantilever (hence requirement in NZ at least to restrain both flanges).

I was incorrectly interpreting what you were saying that you required physical twist restraint (as part of your physical restraint) in addition to lateral restraint requirement, but you're essentially saying its a by product of laterally restraining the section that twist is perhaps reduced or eliminated. See we got there in the end 2thumbsup.

I was working/interpreting in terms of the code or any definition "rotational restraint" prevents all twist. Its either rotational or lateral from a definition/classification point of view, but fundamentally the twist is but one part of the complex fundamentals in increasing the buckling capacity, warping and residual stresses all play a role as well as the torsional stiffness.

In case 2 I posted, the twist rotation is still there you will observe at the point where I restrained the tip, even though the critical tension flange is restrained laterally only. This goes back to the compression flange still being unstable in this state and wanting to kick out.

To play devil advocate I'm curious how the following observations sit with your theory regarding the reduction of twist?
If I observe the reported twist along the member at the tip it's actually 3+ times higher at the tip when you add the lateral restraint than with the unrestrained section:-
Case 1 with unrestrained end: x_twist = 0.0002218
Case 2 with top flange lateral restraint only: x_twist = 0.0007423

Twist is only one part of the complex web of elastic buckling, warping stiffness, torsional stiffness and residual stresses all play a role. To boil it down to just twist reduction is perhaps overly simplistic.

If I still don't get it we should move on! The poor OP's had his thread well and truly hijacked at this point!

RE: Effects of Intermediate bracing on effective length of large cantilever

Quote (KootK)

Any chance you'd want to direct a bro' to the parts of that doc that you consider salient?

It's all good stuff, but Figures 5-8 tell the story pretty quickly. Note that the wording in this document regarding translational-only restraint is as used by Agent666 (and I think most texts on the subject) rather than your own (ie lateral restraint is also rotational). I prefer to keep to the common language rather than redefining; it did take several posts for the two of you to get on the same page.

The bit I was really pointing out is that the translational-only restraint ('L' restraint in A/NZ terms) does increase the buckling capacity of the resulting FL cantilever but our codes don't permit this increase to be used. The segment would be classified as FU for design. The ignored increase in capacity is almost double in most plotted cases for tip restraint at the top flange.

The optimum full-restraint location plotted on Figures 3 & 4 (which you highlighted in the conclusion) wasn't any real surprise. If you're going to introduce an additional restraint, you should make it so you have two segments each with shorter effective length than the total length of the cantilever. For tip load, the restraint should be closer to the tip, while for distributed it should be closer to the support.

RE: Effects of Intermediate bracing on effective length of large cantilever

Hi Agent666,
Your results look somewhat like Figure 5 from the UQ paper I posted - shear centre load case. I believe this is for K=0.6 as stated at the top of the figure (rather than 0.1 as stated in the caption). What is the K-value from your model? I suspect K<0.6.

K = sqrt(pi^2*E*Iw/(G*J*L^2))

RE: Effects of Intermediate bracing on effective length of large cantilever

Its was 610UB101, cantilever length is L=5486mm. So K = 1.62?

RE: Effects of Intermediate bracing on effective length of large cantilever

I suspected wrong then. Figure 3 actually shows little dependence on K from 0.1 to 1.0 so maybe this extends to 1.6 also.

RE: Effects of Intermediate bracing on effective length of large cantilever

The relative ratios between shear ctr loading do look like a reasonable match for the overarching behaviour I noted (compared to figure 5 for example) in terms of both rotational restraint and translational restraint cases more or less being a similar number, full restraint case being approx 50-60% more.

RE: Effects of Intermediate bracing on effective length of large cantilever

Quote (KootK)

Is your rotational restraint:

1) rotational restraint of the top flange (as stated) or;

2) effective rotational restraint of the entire cross section?

It would need to be #2 to fit my definition of "the best kind of cantilever".

If it's #1, you could initiate a buckling mode that starts of as web sidesway buckling at the cantilever tip.

This is probably just semantics but, then, semantics are a big deal in these discussions. It may well be that your top flange rotational restraint is also whole section rotational restraint (stiffeners etc).

Thanks for asking. And yes it is 1) as stated, so it doesn't meet your definition of "the best kind of cantilever". (Sorry for misrepresenting your definition.) And you are absolutely right about the buckling mode possibility. And no it isn't just semantics in this case. (Despite a major in mathematics, my mathematical grasp on the expected buckling behaviour isn't as good as it could be. However my visual grasp on the expected behaviour is reasonably good.)

RE: Effects of Intermediate bracing on effective length of large cantilever

Quote (Agent666)

Ok for what its worth, I found the results of doing a simple case in mastan2 quite interesting to quantify relative effects. It showed a rotational restraint at the tip wasn't a hell of a lot better than the unrestrained case, and by far the best benefit gained is by preventing the lateral deflection of both flanges (which also prevents twist).
Thank you very much Agent666! 2thumbsup

I don't have access to mastan2 currently. If you can at all be bothered and do a 7 case:
Case 7 Twist restraint on top flange ONLY and lateral restraint to top flange ONLY at tip

I'd give you 1000 internet points! afro2

My reason. That is the cantilever I have hanging up at site currently and now I'm curious. (Curious not concerned.) Though I'll keep pulling on this thread myself regardless.


If people are interested I can even put up the design. It is a bit 'different' as it is cantilevered off a tension brace. Which given the position of the support and the points of lateral restraints it doesn't really fit nicely into the code requirements if taken at the letter. However given the restraints it has, the worst that could realistically occur is an elastic buckling sag. (Again, no calculations or modelling to go with that prior assessment, just visualisation.) I'll follow this up though because not I am curious!

RE: Effects of Intermediate bracing on effective length of large cantilever

That was case 6.

RE: Effects of Intermediate bracing on effective length of large cantilever

Quote (Agent 6)

That was case 6.
peace
Oh. Ok! smile

I interpreted Case 6 as full rotational restraint rather than just top flange rotation restraint. (I should have looked at your picture for case 6.)

Again thanks for following this through. It started as a dispute I initiated. I certainly have learnt from it. I hope you have found it productive too.

RE: Effects of Intermediate bracing on effective length of large cantilever

Quote (Agent666)

That was case 6.

I'm not convinced that it really was in a meaningful way. I suspect that human909 may have been effectively correct with this assessment:

Quote (human909)

I interpreted Case 6 as full rotational restraint rather than just top flange rotation restraint. (I should have looked at your picture for case 6.)

Two sources of my skepticism:

1) the deformed shape shows no apparent acknowledgement of web distortion (or it's just too small to see).

2) the applied load ration values for case 3 and case 6 are virtually identical which somewhat suggest that they are virtually equivalent in terms of modelling.

Quote (Agent666)

If I still don't get it we should move on! The poor OP's had his thread well and truly hijacked at this point!

For what it's worth, the "let's agree to disagree" business is -- and will always be -- a waste of words with me. I simply don't have that setting. And I consider it OP's prerogative to guide the discussion as he sees fit. In my opinion, he's already received all of the straight forward guidance here that he's likely to get and should consider the ensuing debate to be a valuable bonus.

RE: Effects of Intermediate bracing on effective length of large cantilever

Quote (Agent666)

It showed a rotational restraint at the tip wasn't a hell of a lot better than the unrestrained case

I've come to question the validity of this as well and offer the following up for consideration, none of which is definitive on its own:

1) Obviously, this isn't a good fit with long standing practice and assumptions. We've been believing in the whole "roll beam" thing for a while now.

2) The result isn't consistent with intuition or, at the least, not my intuition. True LTB instability requires that the load do work. In this case, that means the load moving vertically downwards. And all that I'm seeing appears to be lateral movement. I'll offer an explanation for this next.

3) For Mastan to do its thing, it requires some manner of "perturbation" to get the model moving. Whatever that perturbation is, I'm guessing that it encourages lateral movement and scales up with the applied load ratio just as the primary load does. So what we're seeing here may actually be:

a) Instability as represented by a loss of lateral stiffness rather than lateral torsional stiffness (LTB) and;

b) A lateral motion inducing perterbation that may be scaling up in a manner not consistent with real world conditions.

RE: Effects of Intermediate bracing on effective length of large cantilever

Quote (Agent666)

Twist is only one part of the complex web of elastic buckling, warping stiffness, torsional stiffness and residual stresses all play a role. To boil it down to just twist reduction is perhaps overly simplistic.

That statement strikes me as internally inconsistent. All of the complex web stuff that you listed as evidence that it's more than just twist in fact do point to twist in my opinion. Consider:

1) Warping stiffness. All about twist and the resistance to it.

2) Torsional stiffness. All about twist and the resistance to it.

3) Residual stresses. Residual stresses will mean a premature degradation of warping stiffness which circles back to #1.

Quote (Agent666)

To boil it down to just twist reduction is perhaps overly simplistic.

Truly, I believe that it is that simplistic even if the "twist" bucket contains, within it, many complex nuances. Do keep in mind that, when I reference "twist", I'm always speaking of rotation about a point coincident with the web but not necessarily within the depth of the cross section (usually above or below the cross section really). I'm starting to wonder if, when I say "twist", you might really be hearing "twist about the centroidal axis".

RE: Effects of Intermediate bracing on effective length of large cantilever

Quote (Agent666)

...but you're essentially saying its a by product of laterally restraining the section that twist is perhaps reduced or eliminated.

Yes! Take out the wishy washy "perhaps" and you've got my position down exactly. I believe that all LTB is twist and that all lateral bracing is an attempt to eliminate one or more modes of twist as instability mechanisms.

Quote (Agent666)

In case 2 I posted, the twist rotation is still there you will observe at the point where I restrained the tip, even though the critical tension flange is restrained laterally only. This goes back to the compression flange still being unstable in this state and wanting to kick out.

I see it but, in my opinion, this doesn't change the fact that it's still a failure of twisting. In adding the top flange lateral brace, you've simply exchanged twisting about a point far below the bottom flange for twisting about a point less far above the top flange. In making that trade we are, of course, moving to a higher energy state which implies a higher load capacity, just as your investigation indicates.

RE: Effects of Intermediate bracing on effective length of large cantilever

Quote (Agent666)

To play devil advocate I'm curious how the following observations sit with your theory regarding the reduction of twist?
If I observe the reported twist along the member at the tip it's actually 3+ times higher at the tip when you add the lateral restraint than with the unrestrained section:-
Case 1 with unrestrained end: x_twist = 0.0002218
Case 2 with top flange lateral restraint only: x_twist = 0.0007423

Fun. I shall be the devil then.

I would rationalize that observation as follows:

1) The two cases represent deformation states at two different load levels. I'd think that they would need to be at the same load levels for an apples to apples comparison.

2) The numbers that you're quoting represent twist about the centroidal axes rather than twist about the point in space about which LTB is occurring (usually well above or well below the cross section). As such, the lateral sway component of LTB is not being captured in the twist numbers. And that's important as lateral sway is an important part of the LTB mechanism and is, in fact, the very reason why cantilevers can go so wrong, so fast.

I should note that I don't much care for the common description of LTB where it's split into centroidal torsion + lateral sway as a means of making LTB intuitive for text book & code readers. When you look at the math it becomes clear that it really is not centroidal torsion + lateral sway as that would produce no downward movement on a centroidally applied load, no reduction in potential energy and, thus, no instability. I understand why Steve prefers to stick to the "common" language to avoid confusion but, for me, the common language is really imprecise language that leads to the kind of misunderstandings that we're having here. "Rotation about a point in space coincident with the web but often beyond it" is the precise way to define LTB motion.

3) In going from mastan case #1 to case #2, we're preventing the cantilever sway component of LTB and forcing the section to, instead, rotate a about a point in space that is both:

a) above rather than below the cross section and:
b) much closer to the centroidal axis of the cross section.

Intuitively, those suggest to me that:

c) The capacity of the member will be higher and;
b) Resistance will tend to be expressed, in larger proportion, via ceentroidal twist rather than lateral sway.

So the results are consistent with intuition and sit well with me in this respect.

RE: Effects of Intermediate bracing on effective length of large cantilever

Quote (steve)

The optimum full-restraint location plotted on Figures 3 & 4 (which you highlighted in the conclusion) wasn't any real surprise. If you're going to introduce an additional restraint, you should make it so you have two segments each with shorter effective length than the total length of the cantilever.

Well, if it wasn't any surprise for you then that speaks well of your grasp on the situation. My money says that nine out of ten north american engineers would have guessed that the best place to brace a cantilever was at the cantilever tip. That's invariably what you see in practice but, then, there are surely other reasons for that as well (diaphragm chords etc). I might be able to make use of this in practice. I've encountered a couple of instances where architects wanted to be able to "express" the cantilever rather than just seeing a rim piece.

RE: Effects of Intermediate bracing on effective length of large cantilever

I probably got the right answer for the wrong reason by oversimplifying. Just seemed that adding the restraint at the tip creates a single segment that's restrained at both ends with effective length equal to cantilever length - the base case. If the restraint is instead very slightly before the tip, there are two segments. I'm not concerned with the segment from restraint to tip because its very short length overcompensates being unrestrained at one end. The other segment from support to restraint is now shorter than the base case. The moment distribution is less favourable (no longer zero at one end) but you'd have to be unlucky to introduce a restraint that shortens the effective length and make things worse. Keep moving the restraint closer to the support until the tip segment becomes a problem and you've maximised the capacity.

I'm still digesting your other recent posts but my current thinking is the differing understanding/language may be between restraints that restrict twist vs restraints that completely prevent twist.

RE: Effects of Intermediate bracing on effective length of large cantilever

Quote (steve)

my current thinking is the differing understanding/language may be between restraints that restrict twist vs restraints that completely prevent twist.

I'm of a similar mind but would say it a little differently:

Quote (steve)

differing understanding/language may be between restraints that restrict one or more modes of twist about points in space coincident with the axis of the web but not necessarily coincident with the centroid vs restraints that completely prevent all modes of twist about all possible points in space.

I'm obviously bending over backwards to be precise here and realize that nobody speaks this way in real life.

RE: Effects of Intermediate bracing on effective length of large cantilever

I am not going to add to this in any meaningful way, but I would like to say:
Discussions like this are why I love frequenting eng-tips.
Thank you to all participants

RE: Effects of Intermediate bracing on effective length of large cantilever

Quote (KootK, regarding Mastan case 6)

Two sources of my skepticism:
1) the deformed shape shows no apparent acknowledgement of web distortion (or it's just too small to see).

2) the applied load ration values for case 3 and case 6 are virtually identical which somewhat suggest that they are virtually equivalent in terms of modelling.

1) Should we expect to see web distortion? If I've understood correctly, the actual model is just the line on the member centroid. Agent666 added the I-sections but they don't really contribute to the analysis. Although there may be a small contribution in this instance (because the restraints are applied to the I), won't the load's position below the restraint tend to restore the web towards vertical if it did try to kick sideways?

2) Agent666 did note that they are almost equivalent when he posted the mastan results. I know you're not fond of references to codes, but the A/NZ codes treat these two cases very similarly. Case 3 is Full restraint whereas case 6 is Partial (IMO*) resulting in a very small increase of effective length for case 6.

* - The code commentary acknowledges that the difference between F & P restraints is only defined qualitatively in the code, so it's always a matter of opinion.


Quote (KootK, regarding Mastan case 5)

True LTB instability requires that the load do work. In this case, that means the load moving vertically downwards. And all that I'm seeing appears to be lateral movement. I'll offer an explanation for this next.
The explanation could be as simple as the posted results have the vertical deflection component removed. It appears to me that none of the plots shows the tip deflecting vertically. Cases 3 & 6 show this clearly. The mastan result matches the analysis in the UQ paper. They didn't do any twist-restraint-only experiments though - probably quite hard to restrain twist without also some measure of lateral restraint.

Agent666 said the case 5 result was hardly better than case 1, but it's actually a 40% improvement. The best possible restraints only doubled the capacity (cases 3 & 6). Maybe the relative contributions of Iy and (Iw & J) are just similar for this particular geometry.

Quote (KootK)

I should note that I don't much care for the common description of LTB where it's split into centroidal torsion + lateral sway as a means of making LTB intuitive for text book & code readers. When you look at the math it becomes clear that it really is not centroidal torsion + lateral sway as that would produce no downward movement on a centroidally applied load, no reduction in potential energy and, thus, no instability.
I'm going to request some of your precise/bent over backwards/twisted jester2 into a pretzel language. How does this tally with loads applied at restraint points like cases 3 & 6?

PS: While the common definition of twist restraint being fully-effective twist restraint (eg web that starts vertical must remain vertical) probably does come from the textbook definition of the mathematical boundary condition (phi = zero), I personally wouldn't call differential equations, that run to four differentiations deep, 'intuitive'.

I guess I also wouldn't say centroidal twist is the common definition. Figure 5.4.1 posted by Agent in the 18th post shows two unrestrained sections. Neither is twisting about the centroid.

RE: Effects of Intermediate bracing on effective length of large cantilever

Quote (dauwerda)

Discussions like this are why I love frequenting eng-tips. Thank you to all participants

Thanks for this. I feel the same and it's good to know that the conversation is of value to more than just the active participants.

Quote (Steve)

Should we expect to see web distortion? If I've understood correctly, the actual model is just the line on the member centroid.

We should certainly expect it if sidesway buckling is being accounted for which was human909's concern with case 6. If you're correct that it's a line member, as was the case a decade ago when I used tinker with Mastan then, without doubt, sidesway buckling is not being accounted for as it would be quite impossible with a line member.

Quote (steve)

Although there may be a small contribution in this instance (because the restraints are applied to the I), won't the load's position below the restraint tend to restore the web towards vertical if it did try to kick sideways?

No. That would be the case if the restraint were a vertical restraint but it's not. I see no reason why load applied below a rotational restraint would tend to straighten out the web.

Quote (steve)

The explanation could be as simple as the posted results have the vertical deflection component removed.

That explanation would be simple. And implausible in my opinion. I don't see why Mastan or Agent666 would bother to do this. I'll leave this one alone unless Agent666, or someone else, can supply some evidence to indicate that this is actually the case an worth discussing further.

Quote (steve)

It appears to me that none of the plots shows the tip deflecting vertically.

In my opinion, case 1 clearly shows rotation about a point below the cross section which, by definition, implies
vertical movement.

Quote (steve)

It appears to me that none of the plots shows the tip deflecting vertically. Cases 3 & 6 show this clearly.

I'm fairly certain that what is happening is that the vertical deformations included in all the plots are simply dwarfed by the lateral movements that represent the buckling. The buckling, after all, is movement without bound, right? So this dwarfing should not come as a surprise.

Quote (KootK)

I should note that I don't much care for the common description of LTB where it's split into centroidal torsion + lateral sway as a means of making LTB intuitive for text book & code readers. When you look at the math it becomes clear that it really is not centroidal torsion + lateral sway as that would produce no downward movement on a centroidally applied load, no reduction in potential energy and, thus, no instability.

Quote (steve)

I'm going to request some of your precise/bent over backwards/twisted jester2 into a pretzel language. How does this tally with loads applied at restraint points like cases 3 & 6?

Quite naturally. The cross section clearly flips over towards weak axis over a portion of the member over which internal moments are present. The result of will obviously be that vertical deflections are increased, whether or not they are too small to see compared to the gross, lateral movements.

RE: Effects of Intermediate bracing on effective length of large cantilever

Quote (steve)

Agent666 said the case 5 result was hardly better than case 1, but it's actually a 40% improvement. The best possible restraints only doubled the capacity (cases 3 & 6).

My real concern with this is not about how much improvement is there but, rather, that the buckling shape does not seem to have switched to a higher energy mode as it has with some of the other models and as I would expect it to here. It still very much looks like the first mode, lateral sway pattern that we've come to know and love about free cantilevers. And if there's no vertical movement associated with that, I question it's validity.

Anyone who's dabbled in the coding of these things will know that what the bot will register as "instability" in a non-linear analysis like this is really instances of stiffness diminishing to zero. In the context of case 5, it seems to me that this could occur via:

1) Loss of vertical stiffness at the point of load application as we would hope or;

2) Loss of lateral stiffness at the point of application of the perturbation mechanism which the model doesn't show us.

So, unless we fully understand the perturbation mechanism and how its being applied and scaled, I think that it is sensible to put a question mark on this particular result. Certainly, that is the case for me personally since I struggle to reconcile the Mastan result with my own intuition and the model that I that I carry around in my head.

Additionally, with case 5, what are we saying the final result is that would bring the load to ground? Lateral motion alone won't get the job done. Or are we saying that the thing bends around like a U-bolt until torsional flexibility becomes it's undoing?

I'll add that I do not dispute that perturbations represent real world imperfections. The most definitely do. But, as with many things, I think that the question becomes one of how the perturbations are applied and scaled and whether or not those things are adequate reflections of real world perturbations. Accurate modelling of the real world has turned out to be quite a challenge. Mastan is a great leap forward relative to our day to day FEM tools but, still, it's not a god program and our own intuition and understanding should not take a back seat to it.

This probably deserves it's own thread at some point but I consider the hierarchy of information quality in our field to be as follows, working from lowest quality to highest.

1) What is gleaned from our computer modelling tools "teaching" us things.

2) What we forensically piece together from what code writers choose to tell us.

3) What is gleaned from laboratory testing and real world failures.

4) What our own intuition and understanding of the physical universe is.

I assign value to all four sources and I'm sure that everyone's list is a little different. I sometimes flip flop on the order of #3 & #4. Ultimately, though, I see it as Einstein and Sheldon Cooper did. The ultimate laboratory is the laboratory of the mind and most of our best innovations will always come from there.


RE: Effects of Intermediate bracing on effective length of large cantilever

Quote (dauwerda)

II am not going to add to this in any meaningful way, but I would like to say:
Discussions like this are why I love frequenting eng-tips.
Thank you to all participants

I agree. I've looking to get back to playing around with this model at some stage soon. I've downloaded NASTRAN to do so but I couldn't get it working how I wanted.

I've now since been using it for another work related issue for buckling on a very non standard compression shape. (incidentally it seems to fail by eccentric yielding rather than buckling, but it needed to be checked.)

Either way I wan't to flesh out some better designs as check out the results that is spits out. It has the advantage of having plenty of nice options and plenty of pretty pictures.

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