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slickdeals (Structural) (OP)
11 May 11 11:38
I am sure this has been beaten to death already......but thought I should ask anyways.

Assume you have a 2' high concrete pedestal spaced on a grid of 30' x 20'. A W24 steel beam spans between the pedestals in the 30' direction. There are end stiffeners welded to the W24 when it bears over the column to prevent rotation @ support. In the other direction, steel joists spaced at 5' o.c. span into the top flange of the W24.

For gravity loading only, is the unbraced length of W24 :
1. 5' ?
2. 30' ?
3. Something in between?

RFreund (Structural)
11 May 11 11:58
If the joist and joist connection is stiff enough (see appendix 6) to prevent movement than I would say 5'

Attached is some notes (not mine) that I have found helpful.

EIT

slickdeals (Structural) (OP)
11 May 11 12:02
RF:
IT will prevent movement between the flange and the joist, but nothing is stopping the lateral movement of whole system. There is nothing providing lateral bracing. I am inclined to think 30', most definitely not 5'.

If one compression flange wants to move, then it will take the other compression flange with it.

Lion06 (Structural)
11 May 11 12:03
I'm also of the mind that it's 5'.  Assuming of course that the strength/stiffness requirements check out, as RF noted.  I'd be surprised if it didn't check out, though.

I think the floor construction plays a part in this, too, though.  Is this metal roof deck?  Slab on composite deck?  Is the W24 composite with the slab?   
Lion06 (Structural)
11 May 11 12:04
Oh, you're assuming this isn't decked at all?
slickdeals (Structural) (OP)
11 May 11 12:10
This is an academic question, not a real project. But I am sure the concepts would apply in any real building.

It is decked, just bare metal deck. But what prevents the whole system from laterally displacing? The only stiffness is from the weak axis bending capacity of the W24 web.

Make sense?

Lion06 (Structural)
11 May 11 12:18
I think if it is decked (even with bare metal deck), and that deck (diaphragm) is positively attached to the joists, that when the joists want to move to brace the W24 that the diaphragm will restrain it.  

I'm assuming that there are W24's orthogonal to the ones you're talking directly about (which would be parallel to the joists) that are anchored to the piers in a similar fashion that would essentially act as the lateral system.
BAretired (Structural)
11 May 11 12:34
The unbraced length is 5' with deck...30' without.

BA

RFreund (Structural)
11 May 11 13:14
I will try to search for a recent post very similar to this and I had the very same question as you and it never really got answered but here are my thoughts:
If the compression flange wants to move laterally due to LTB then the joist will restrain this movement and the force on the joist would be transfered into the deck, the deck then distributes this force to the lateral load resisting system.
However I have never seen a check for this or this load added to a LFRS design.

EIT

RFreund (Structural)
11 May 11 13:19
Here is the thread I was thinking of:

Truss / Joist Girder Stability Bracing
thread507-287322: Truss / Joist Girder Stability Bracing
 

EIT

JAE (Structural)
11 May 11 13:39
I agree with BAretired:  The unbraced length is 5' with deck...30' without.

 
2Hats (Structural)
11 May 11 14:00
I'm pretty sure what you're describing is a lean-on bracing system (in the absence of deck). Galambos (Guide to stability design criteria for metal strucures) discusses these systems.
The answer depends on the number of W24 being braced agains each other. As the number gets large, your unbraced length should approach 5ft.
ash060 (Structural)
11 May 11 14:10
You could use some cross bracing to prevent the section from twisting, using the joists as the system, but you would have to brace both flanges.  

I did something very similar to this, but made a truss with the top flanges using angles.  It seems to work.

What you bring up is bridging.  Joist bridging is used for exactly the situation you mention.  before the deck is on the joist chord it has to be braced for construction loads hence bridging.  You can use horizontal or diagonal bridging with diagonal being the better option.

There are some good notes by Larry Griffis called "Steel Design After College" on AISC's website.
delagina (Structural)
11 May 11 14:15
based on the salmon and johnson book it should be 30' for global lateral buckling
Lion06 (Structural)
11 May 11 14:59
delagina, where do you see that?
slickdeals (Structural) (OP)
11 May 11 15:11
I don't think it is lean-on. There is nothing to "lean" against.
There are a total of 2 W24. IT represents one bay only.

msquared48 (Structural)
11 May 11 15:16
I also would say 5 feet, assuming there is no fixity of the beam at the columns, and that the joists bear on top of the steel beam with decking attached to the joists.

 

Mike McCann
MMC Engineering
Motto:  KISS
Motivation:  Don't ask

slickdeals (Structural) (OP)
11 May 11 15:40
See attached.

slickdeals (Structural) (OP)
11 May 11 16:03
If I had 5 columns carrying compression loads spaced 5' apart. If I had a mid-height brace, connecting the columns, but not really connected to anything else, the column unbraced length is the full height, right?

The columns would buckle globally because the mid-height beam even though present is not bracing it.

BAretired (Structural)
11 May 11 16:06
The end stiffeners and the deck.

BA

Lion06 (Structural)
11 May 11 16:09
I think the case that you show in the sketch is slightly different than the previous discussion (at least based on some of the assumptions I made).  

Some of this will come down to detailing and whether the connection between the stacked beams can transfer moment to brace the W24.  Let's assume for a second that it can't.  

If the connection between the stacked beams can't transfer moment AND there is no beam parallel to the high beams that can take a diaphragm force into the piers, then I agree that the unbraced length of the W24's would be 30'.

Although, just to talk about it.  The last stacked beam at each end (that stacks directly on top of the end plate of the W24.......... I think that end plate and connection detail would be stiff enough to give the diaphragm a "lateral system" such that it would still be bracing the S24's.

 
RFreund (Structural)
11 May 11 16:10
I see now, this is a 1 bay system.  Then I would say that your Lb is still 5' (I think) but you may need to check overall lateral torsional buckling.

I don't have the book with me but I believe on page 231 of
Guide to Stability Design Criteria for Metal Structures By Ronald D. Ziemian

Try this link:

http://books.google.com/books?id=DDYw9UUFHkUC&pg=PA231&lpg=PA231&dq=twin+girder+lateral+stability+global+buckling&source=bl&ots=fr5CIHOMMO&sig=aAcjObxeVECb9LUZuomazyB4YkU&hl=en&ei=AOzKTYa8CurL0QHw5entCA&sa=X&;oi=book_result&ct=result&resnum=5&ved=0CEgQ6AEwBA#v=onepage&q&f=false

EIT

slickdeals (Structural) (OP)
11 May 11 16:11
@BA:
Interesting....I had not thought of that. I do apologize if this is rudimentary question, but I am having trouble visualizing it all.

The deck then spans as a deep beam between the 4 stiffeners? The deck is not attached to the beam, but to the joists. Do you mind explaining further?

BAretired (Structural)
11 May 11 16:12
slickdeals,

In your sketch, you asked "what is stopping the lateral displacement?"  The answer is the end stiffeners and the steel deck.

In your last post, you are correct.  Five columns, braced only with a mid-height brace are not really braced because all columns can buckle in the same direction.

BA

delagina (Structural)
11 May 11 16:12
fig 9.2.2
RFreund (Structural)
11 May 11 16:13
Actually for my case to apply you would need cross frames or moment resistance from the top beams that Lion is alluding to.

EIT

BAretired (Structural)
11 May 11 16:25
slickdeals,

The end stiffeners prevent the ends of the beams from rotating.  

The steel deck acts as a diaphragm or deep girder.  It prevents the joists from translating relative to each other.  If the joist ends are held in a straight line, the top flange of the beam cannot buckle over its full 30' length but it can buckle over the 5' spacing of the joists.

BA

Lion06 (Structural)
11 May 11 16:26
BA-
I think that's totally awesome that we posted so close to each other (yours must have come up when I was typing mine, because I didn't see it before-hand) on such a theoretical topic and reached the exact same conclusion.

There, that makes up for the last time my gut was so off with that wood capacity!
azcats (Structural)
11 May 11 18:11
I'll quote the commentary of appendix 6, Sec 6.3:

"Beam bracing must prevent the twist of the section, not lateral displacement.  Both lateral bracing (for example, joists attached to the compression flange of a simply supported beam) and torsional bracing (for example, a cross frame or diaphragm between adjacent girders) can effectively control twist."

IMO, your situation (with or without deck) is braced against lateral-torsional buckling at 5' provided there is some sort of reasonable connection between the joists and that the joists meet the bracing requirements of Appendix 6.

Also, I'm not sure I like the sketch on how you envision the buckling.  The flanges don't stay parallel in LTB.

http://www.adina.com/newsgH49.shtml

You can see how a member of reasonable stiffness would restrain the buckling in the animation linked above.

But, I could be wrong...
Lion06 (Structural)
11 May 11 18:27
Az-  I don't think I agree for joists with no deck.  The deck takes the brace forces to the lateral system.  Without deck, the joist is just pushing in the other beam.  I don't thing that constitutes bracing.  I would analogies that to bottom chord bracing for OWSJ.  The bottom chord bracing isn't effective unless it actually connects back to something capable of taking out the brace force..
azcats (Structural)
11 May 11 19:09
IMO, if that beam top flange can't rotate, it can't buckle.  The joist (again, if it meets appendix 6 requirements) restrains the twisting.  

Are there really push/pull forces to resolve in LTB bracing or do the braces themselves just need to be strong enough not to buckle while doing bracing work?

Fun (for us - my wife would just be looking at me weird) discussion here.
JAE (Structural)
12 May 11 0:03
The braces need to be BOTH strong enough and stiff enough.

Appendix 6 outlines this for a nodal brace (joists with deck) and relative braces (joists without deck).

 
RFreund (Structural)
12 May 11 7:08
Damn.

After reading Lion and BA I should have stuck with my original post regarding the load path.

However, if you have no deck then I believe not only do your braces need to be strong and stiff enough to prevent twist (Lb then = 5') but also you must consider overall lateral torsional buckling which is what I posted about earlier. See the the link above or search for twin girder stability / buckling.

Or at least I think...

Or you could check to see one of the W24's is sufficiently strong and stiff enough to resist the force that is applied from the brace (joist in this case) in weak axis bending and deflection.  However you would need to check bending strength in both directions.

Or at least I think...

EIT

csd72 (Structural)
12 May 11 7:48
In practice I would do as others have said and use 5' with deck and 30' without, though as the load applied by the joists is technically destabilising then you could potentially get more than 30'.

If the joists were connected to the web of the beam with a full height fin plate and two well spaced bolts then I would think that you could treat them as a torsional restraint and reduce down the 30' but in this case you would rely on the thin web to transfer torsion which would be inadequate.  
SAIL3 (Structural)
12 May 11 8:50
I have always believed that if you prevent the compression flange of a beam from lateral displacement then it eliminates LTB.
For LTB to occur, the compression fla must first displace laterally as the rotation occurs....it can not rotate "in-place" without lateral displacement of the compression fla.
So in essence, I disagree with the reg'd stiffeness of bracing members in the AISC 13th edition..
csd72 (Structural)
12 May 11 9:01
there has to be some sort of stiffness, otherwise people could weld a half inrod to the top and call it a bracing strut.
Lion06 (Structural)
12 May 11 9:49
The only reason the brace prevents movement is because of the stiffness.  The brace isn't a hard point that is unyielding.  It is itself a spring with a stiffness of it's axial stiffness.  If you tried bracing the top flange of the beam with a spring shock absorber from a car, I think we can agree that it can be positively attached to the beam's top flange, but not prevent lateral movement that would occur when the beam wants to buckle.
csd72 (Structural)
12 May 11 10:13
lion06, thats what i was trying to say. should have said half inch rod.
SAIL3 (Structural)
12 May 11 12:58
Sorry, I should have said rotational stiffeness....axial was covered by designing the brace for the old 2to4% of the axial load in the fla of the bm....and I am not aware of any problems that arose from that method...going through the extra time and effort of checking rotational stiffeness to me is another example of the the recent shotgun approach of the AISC code of checking every nit-picking possibility wheather it applies or is actually meaningful or not
csd72 (Structural)
12 May 11 13:10
Yes it seems to be the way codes are going these days virtually forces you to use a computer package to cover all these idiosyncrasies.
slickdeals (Structural) (OP)
12 May 11 13:10
Thanks for this discussion.
Please see revised sketch and provide your comments.

ToadJones (Structural)
12 May 11 13:29
I am going to hi-jack this thread.

Unbraced length of column encased in masonry?  
slickdeals (Structural) (OP)
12 May 11 13:30
Toad,
Don't muddy the water...........start a new thread. POR FAVOR!!! smile

ToadJones (Structural)
12 May 11 13:38
will do,
Sorry.
I will title it "yet ANOTHER unbraced length question"
Lion06 (Structural)
12 May 11 13:40
Slick-
The answer to the last question in the sketch is yes.  That provides rotational restraint with or without the presence of the deck.
BAretired (Structural)
12 May 11 16:57
Sorry Lion, I am going to have to disagree with your last post.

The question on the sketch was "If a kicker is provided as shown and the deck is removed, is the unbraced length 5'?"

If a kicker is provided at both ends of the joist, I agree that rotational restraint has been provided to both beams.  I do not agree that lateral restraint has been provided to the top flange of either beam and I do not agree that the unbraced length is 5'.  

The top flange of both beams will behave as a column with variable axial load.  The unbraced length is 30' and it will buckle over a 30' length.  Failure will not be by flexural torsional buckling, but elastic column buckling, modified slightly by the tension in the bottom flange trying to hold it in line (something I would ignore in design).

BA

hokie66 (Structural)
12 May 11 17:12
...And modified by tension in the top flange trying to hold it in line?
Lion06 (Structural)
12 May 11 17:22
BA-
Fair enough.  I looked at the one end and assumed that detail would be typical at both ends.  

As far as the lateral restraint of the top flange, AISC doesn't require lateral restraint of the top flange to brace the beam for LTB.  It can be accomplished through rotationally restraining the beam section.

Once the one end is restrained rotationally, I think the entire section (in weak-axis bending) is effective in restraining the top flange of the other beam.  

I would analogize this to a moment frame where one beam/column connection is a moment connection and the other is a shear connection.  Both columns are stable even though only one is rotationally restrained.
Lion06 (Structural)
12 May 11 17:38
I'm going to call the W24 with the stiffeners and kickers BEAM 1, the opposite W24 without the stiffeners and kickers BEAM 2, and the infill beams that stack BEAM3.

I think that the stiffeners and kickers on BEAM 1 constitute rotational restraint and will act as a brace.  Beam bracing doesn't have to be lateral restraint of the top flange, it can be accomplished through rotational restraint alone.  Additionally, the bracing accomplished via rotational restraint is not affected by what's going on at the other end of BEAM 3.  The only way for BEAM 1 to buckle (LTB) is by overwhelming BEAM3 in strong axis bending.

For BEAM 2, that's not quite as clear.  It would depend on the weak axis bending stiffness of BEAM 1.  If BEAM 2 is to buckle (LTB), then BEAM 1 would have inadequate stiffness in weak axis bending to brace BEAM 2.  I see BEAM 3 acting as the brace back to BEAM 1, which has the entire section engaged in weak axis bending via the kickers and stiffeners.
hokie66 (Structural)
12 May 11 17:50
For BEAMs3 to restrain rotation of BEAM 1 between the supports, the connections have to be stiff, and in the sketch, it doesn't look like that is the case.
Lion06 (Structural)
12 May 11 18:35
I think any positive connection between the bottom flange of BEAM 2/top flange of BEAM 1, kicker to BEAM 3, and kicker to the stiffener on BEAM 1 would restrain rotation of BEAM 1.

He just sketched something there.  Obviously, if there's no positive connection between the parts then everything is a moot point, but almost any positive between those different pieces would restrain BEAM 1 rotationally.
BAretired (Structural)
12 May 11 18:51
The main point of contention seems to be that the spacing of torsional restraints alone defines the unbraced length of a simple span beam.  AISC appears to say that but CSA S16 does not.  

I consider the unbraced length to be the spacing of lateral bracing members.  Rotational restraints are required at supports.

BA

hokie66 (Structural)
12 May 11 20:00
Check out the photos in this thread for some beam buckling.
thread607-269140: Interesting Integral abutment behaviour
JennyNakamura (Structural)
13 May 11 1:21
I'm coming into this kind of late and haven't read through all the responses, but I believe the answer to the original question is 5' without the deck and 0'(continous lateral support) with the deck.

Lateral torsional buckling is a strong-axis bending phenomenon. When you brace the compression flange against "torsion" the "lateral" movement will not follow.

This global lateral movement that is being described can only be due to weak axis bending, with a load being applied horizontally. Lateral tosional bucking occurs in strong axis bending only and the uniform lateral displacement described in some of the posts will not occur due to a vertical load -- only if a horizontal force is applied.
csd72 (Structural)
13 May 11 3:40
Jenny, Sorry to be blunt but I disagree with your entire post.

I think you may have misread the post.
JennyNakamura (Structural)
13 May 11 4:58
csd72, Thanks for being polite. I think the thread kind of drifted.

The OP's 1st question was for "gravity loading only." For that scenario, the failure mode for strong-axis flexure would be LTB, for which I still stand by my answer -- section 6.3 of the AISC appendix clearly supports that as azcats pointed out earlier.

Later, the OP posted a sketch showing stacked framing with an applied lateral load. In that case, the unbraced length would be 30' with the stiffeners at the supports being the only thing resisting "lateral deflection," as others have pointed out. With the deck, there would be no reduction in weak axis bending capacity, as the deck would act as a diaphragm (assuming the deck had sufficient shear capacity and was fastened to the steel properly).

In reality, the deflection shown in the sketch would never happen, because the designer would probably have web stiffeners on the main beams under the joists which would minimize the rotation effect depicted on the sketch and the beam would bow outward, rather than tilt linearly.
csd72 (Structural)
13 May 11 5:38
Jenny,

I would suggest you have another look at it.

You say the effective lenth is 5' without any decking, what is to stop the top flange of both beams translating together?

You say that it is continuously restrained if there is deck but there is still only restraint at 5' centres and not continuous as you have stated (the joists are continuously restrained but not the main beams).

RE"Lateral torsional buckling is a strong-axis bending phenomenon. When you brace the compression flange against "torsion" the "lateral" movement will not follow." I agree to a certain extent though I am not sure where the torsional restraint is that you are referring to. Unless the stiffeners are piut in which you assume every designer would - good steel designers only put stiffeners in when they are required (thus the original post).

RE"This global lateral movement that is being described can only be due to weak axis bending, with a load being applied horizontally. Lateral tosional bucking occurs in strong axis bending only and the uniform lateral displacement described in some of the posts will not occur due to a vertical load -- only if a horizontal force is applied. "

If the beam was perfectly straight and vertical you would be correct, but as soon as there is any twisting then a component of the applied force becomes a lateral one. The reason why rotational restraint is not because there is not possibility of lateral translation but rather because the tension in the bottom flange acts to help keep it in place.

I have worked wuth unrestrained beams quite a lot and find that most engineers do not understand buckling as well as they think they do.
I believe it is important for all of us to occasionally question our own knowledge.
slickdeals (Structural) (OP)
13 May 11 8:09
Folks,
I must clarify a point. The arrow that I put in the sketch was not a lateral load, but the direction the system might move under gravity loading once the LTB kicks in.

I apologize for the confusion.

Lion06 (Structural)
13 May 11 8:28
Jenny,

I agree with csd.  I think you should re-think it.  My take on the sketch was that the arrow was merely pointing in the direction that the assumed buckling was taking place.  The horizontal load isn't gravity (as mentioned in the OP) and wouldn't cause LTB (at least not in the manner we typically think about it, through strong axis bending).

Regarding the 0' unbraced length comment - can you explain how you arrived at that conclusion?  I would have never come to an answer of 0' unbraced length, and, frankly, don't see how it's possible.  See my attached sketch.  I don't see how the unbraced length could ever = 0'.


Where was anyone describing a uniform lateral displacement?  



CSD-
I agree with you that most engineers don't understand buckling and stability issues as well as they think they do.  Elastic stability has always sort of fascinated me.  That's why I bought several decent books on the topic (including Timoshenko's Theory of Elastic Stability and Golambos' Stability of Structural Steel).  I fall into a different camp.  I don't understand it quite as well as I would like, but I think I have a pretty good grasp of my actual level of understanding on the topic (i.e. I know that I don't understand it as thoroughly as I would like).  The last Grad class I took was Advanced Structural Analysis.  I asked the professor there if they have a class dedicated to stability, but unfortunately the answer was NO.
I wouldn't mind getting my hands on Yura's notes from his stability seminars.
ble31980 (Structural)
13 May 11 9:04
I'll be the first to admit that I'm no where close to being an expert on beam stability.  That said, here's my opinion.

I agree with those that say the unbraced lengths are 5' with the deck and 30' without.  This is assuming that the end stiffeners are rigid enough to prevent end rotation.  The way that I visualize the problem is by comparing it to a textbook wood-framed diaphragm and shear wall example.  While it's true you might have lateral displacement of the beam, similar to the displacement of a diaphragm, the deck will keep the top of the beams from rotating.  If you don't have the deck, I don't see how you can prevent the top flanges from rotating without the deck.

  
JennyNakamura (Structural)
13 May 11 16:43
Lion/csd,

I am re-reading my last post and now I don't even understand what I am talking about! So I will just stick to CMU warehouses with CFS roof purlins for now...

Fascinating subject, wish I could spend more time studying up on it. You could probably spend 40 hrs/week for a couple of months doing nothing but researching this topic, but who has time for that when we're all working so much free overtime (just a joke on a different thread)!

Thanks for opening my eyes, guys.
csd72 (Structural)
13 May 11 19:45
Never stop learning
hammer      
slickdeals (Structural) (OP)
14 May 11 7:58
All:
Based on my OP and the responses, I am going to try to make a summary of the various conditions that can alter the behavior (with deck & without deck). To be continued........

slickdeals (Structural) (OP)
14 May 11 9:29
See attached sketch. I am keeping this as a work in progress. There are various scenarios with possible (??) explanations.

I think it might be a good idea to suggest what the unbraced length might be and have a narrative of why it is so. I think having a metal deck makes things easier. I have purposely omitted the deck in order to help understand behavior better.

I appreciate you guys taking the time to review and comment.

RFreund (Structural)
14 May 11 12:16
Slick- first off, nice work!

Thoughts based on rereading Guide to Stability Design Criteria (GSDC) for Metal Structures By Ronald D. Ziemian Chapter 12.9:

Case A:
Scenario 1: Agree
Scenario 2: I believe this would be a "lean-on" system.  In this case the beams are linked together and lateral buckling cannot occur at the links unless all the members buckle. In this case the beams in the system cannot buckle until the sum of the maximum moment in each beam exceeds the sum of the individual buckling capacities of each beam.  Also the buckling of an individual beam can occur only between the cross members in a lean on system. That is what the GSDC says however I need to do a little more research here because in the Yura notes that I have found the bracing ability of the lean on member depends on how heavily it is loaded. Basically one beam would need to have sufficient strength and stiffness in the weak-axis to brace the other beam. However I should mention that references to "Bracing for Stability" 2009, Yura and Helwig, short course notes, North American Steel Construction Conference, Phoenix, AZ and "Global Lateral Buckling of I-Shaped.

Case B:
This seems as though it would be classified as Torsional Bracing. The GSDC reads 'If two adjacent beams are interconnected by a properly designed cross frame or diaphragm at midspan, that point can be considered a braced point when evaluating the beam-buckling strength. Because the beams can move laterally at midspan, the effectiveness of such a bracing system is sometimes questioned.  As long as the two flanges move laterally by the same amount, there will be no twist. If twist is prevented, the beam can be treated as braced.'
I believe that overall stability would need to be considered see my above post 11 May 11 16:10

Case C:
I need to give this more thought.  But I would like to put kickers at the end for some reason and say 5'

Case D:
Torsional Brace so 5' same as case B.  Consider overall global buckling of the system.

I still may need to do a little research and might be able to improve these answers.


 

EIT

BAretired (Structural)
14 May 11 12:52
Slickdeals,

I'll take a shot at it.

Case A

Scenario 1.  I agree that unbraced length for lateral torsion buckling is 5'.

Scenario 2.  The beams are unstable.  Unbraced length is meaningless.

Cases B, C and D

Beam rotation is restrained to some degree in all of these cases.  If the bracing satisfies code requirements respecting strength and stiffness, the unbraced length for lateral torsional buckling is 5' but the unbraced length for lateral buckling is 20'.  

The section resisting lateral buckling is the weak axis section modulus of the two W24 members.  If the W24 members are highly stressed by gravity load, the flange tips will not be very effective in resisting lateral buckling.  

Personally, I would not use Cases B, C or D.  In the absence of steel deck, I would add bracing in the horizontal plane to form a truss.  In that case, the stiffeners and kickers at the intermediate beams could be eliminated.

BA

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