LTB of a Vierendeel Truss
LTB of a Vierendeel Truss
(OP)
Greeting fellow eng'ers
I have a engineering problem that comes up time and time again in our industry, but as far as I know, very few people have proposed a reasonable solution. I need to be able to calculate when a vierendeel truss will buckle out-of-plane.
Context: We manufacture 2-D vierendeel trusses for the entertainment industry (these are NOT box trusses). They have no lateral bracing and are hung from the roof or gridiron by cables (tension only members). They quite often have point loads between the supports, (having typically four to six cables as supports they are suspended from). Spans between supports are anywhere from 8' to 15'. Quite often the ends are cantilevered up to 6' past the final support point.
Elastic analysis will give me vertical deflections and stresses but not buckling. The way we analyze this now is by calculating the axial compression of the bottom chord and use the outside support points as lateral bracing to calculate the Euler buckling load. Then recalculate the allowable point (or distributed) loads based on Euler.
I have this in Inventor, hoping to do a buckling analysis, but Inventor only does modal analysis, and I have no idea if the eigenvalues are the same as buckling or how to access the modal eigenvalues in this program (new to Inventor Pro).
None of the AISC LTB equations work since they are based on lateral bracing. Any ideas on how to rationally approach this?
Many thanks
Cleagl
I have a engineering problem that comes up time and time again in our industry, but as far as I know, very few people have proposed a reasonable solution. I need to be able to calculate when a vierendeel truss will buckle out-of-plane.
Context: We manufacture 2-D vierendeel trusses for the entertainment industry (these are NOT box trusses). They have no lateral bracing and are hung from the roof or gridiron by cables (tension only members). They quite often have point loads between the supports, (having typically four to six cables as supports they are suspended from). Spans between supports are anywhere from 8' to 15'. Quite often the ends are cantilevered up to 6' past the final support point.
Elastic analysis will give me vertical deflections and stresses but not buckling. The way we analyze this now is by calculating the axial compression of the bottom chord and use the outside support points as lateral bracing to calculate the Euler buckling load. Then recalculate the allowable point (or distributed) loads based on Euler.
I have this in Inventor, hoping to do a buckling analysis, but Inventor only does modal analysis, and I have no idea if the eigenvalues are the same as buckling or how to access the modal eigenvalues in this program (new to Inventor Pro).
None of the AISC LTB equations work since they are based on lateral bracing. Any ideas on how to rationally approach this?
Many thanks
Cleagl






RE: LTB of a Vierendeel Truss
I have used it in a variety of situations and find it very helpful.
BA
RE: LTB of a Vierendeel Truss
RE: LTB of a Vierendeel Truss
The entertainment rigging industry was pretty loose as I recall, they can do some amazingly bad (dangerous) things with your products, and then ask you to stand behind and/or below them. That's scary. Although, maybe OSHA and city inspectors are starting to bring some control and regulation. You say: 4 to 6 cables as supports; with spacings of 8' to 15' btwn. the cables; hung from the roof structure or, or worse yet, a grid work of cables. Vertical cables stretch quite a bit, and cable nets or grid works deflect in even more indeterminate ways. Do you have any real idea what your real reactions and truss stresses are, are some assumed reactions almost zero due to cable extension or movement? This question should figure into your very first "explicit imperfections" per ishvaaag's comments.
I've used the methods suggested by BA, although it's been a long time and I didn't dig out my text books to refresh my memory. What ishvaaag suggests sounds right to me, although he knows far more about which programs and the exact details for the use of each program.
I assume you really didn't mean 90' long trusses, (6 spans)(15'). But, one way to make your problems easier to deal with would be to limit your truss length to 15 or 20', a few more trusses and reaction points needed, but much easier to handle in the field. And, limit the trusses to two reaction or support points, a determinate structure from this standpoint now; with restrictions on cantilever lengths and loadings and load points. Otherwise, I don't know how you determine your reactions and their defected positions and the potential for transverse reaction components. Didn't your industry go to triangular and box trusses in part because they were more stable and a bit more rugged?
RE: LTB of a Vierendeel Truss
RE: LTB of a Vierendeel Truss
Thanks to BA for the Newmark suggestion. A little intimidating, but it might be good to have a couple of methods to compare.
It is true that our industry has a wide variety of people both with and without good judgment, but the good news is we use very conservative approaches. We use FS of 8 against rupture and a FS of 5 against yielding. Thanks again for all the help. I'll post results when I have them.
RE: LTB of a Vierendeel Truss
1) What is the span/depth ratio of your typical truss?
2) How is lateral support provided to your compression chords at the supports?
If your truss is supported at the top chord and loaded at the bottom chord, is it really possible for the whole truss to glogally LTB? It seems unlikely unless your span to depth ratios are pretty large. You've got too much going for you by way of restoring forces.
If you have effective lateral support for your compression chord at the supports, you should be able to make a reasonable approximation by simply calculating regular compression buckling loads in the chord.
RE: LTB of a Vierendeel Truss
BA
RE: LTB of a Vierendeel Truss
I think that I may be learning something here..
RE: LTB of a Vierendeel Truss
RE: LTB of a Vierendeel Truss
BA
RE: LTB of a Vierendeel Truss
RE: LTB of a Vierendeel Truss
BA
RE: LTB of a Vierendeel Truss
Suspended by (4), 1/4" dia 7x19 cable. The ends cantilever 7.5' past the last support points. There really is no lateral bracing at all. Top and bottom chords 1.5" sched 40 (or sched 80) pipe. verticals 1/4" x 3" flat. Typical loads would be 15-50 lbs plf
For this particular case we have 2 load cases, a) a UDL of about 17 lbs /lf for the entire length, and b) 60 lbs /lf on just the two cantilevers. In real life what happens to these is in load case b) is that the ends sag, the two center lines go slack and the center of the beam flexes out-of-plane. But at what value is difficult to predict.
As above what we do now is Euler buckling on the lower chord using the outside two support points as the unbraced length (in this case Lb=40'-0").
RE: LTB of a Vierendeel Truss
With your truss, as well as with lifting beams, I believe that it is the restoring forces generated by the load / support conditions that prevents LTB. However, I think that only works with fairly low L/d ratios.
With your situation, I suspect that LTB is a legitimate concern, particularly at the cantilevers. Loading the compression flange will increase stability but not eliminate the possibility of LTB altogether.
Could you generate faux solid beam properties for your truss and use those to calculate LTB as you would for an I beam? Ix, Iy, Cw etc would be based on the chords only.
I do suspect that you can assume rotational support -- at least some -- at the locations that you mentioned. I'm having a hard time rationalizing why however...
RE: LTB of a Vierendeel Truss
In this case, the unbraced length of the bottom chord is 54', not 40'. But it is not loaded at the ends. The load increases gradually from each end to the end suspension points. It can be solved using Newmark's procedures.
BA
RE: LTB of a Vierendeel Truss
If our concern is simply the buckling of the compression chord alone then yes, the unbraced length is 54'.
However, simply preventing column style buckling of the compression chord does not preclude LTB of the composite section (the same holds true for the lower WT portion of I-beams). This is because the section can still become unstable by the tension chord rotating around the un-buckled bottom chord.
Since structures like lifting beams and Cleagl's truss are able to sustain some load without LTB, some form of rotational restraint must be present by virture of the loading / support conditions.
As a thought experiment, consider the reverse of this problem. Same truss but with the support cables attached to the bottom chord and the loads applied to the top chord? What's the capacity of that system? Zero, right? Zero, even though you could still do that buckling check on the bottom chord and determine a capcity.
It may be that I'm missing something here. I've got an older version of Timoshenko's book at my desk (pre gere). Which section is Newmark's method found?
RE: LTB of a Vierendeel Truss
The unbraced length is 54' because there are no lateral braces anywhere and 54' is the extent of compressive stress in the chord. The location of the support cables affects the bending moment in the truss and hence the magnitude of compression in the bottom chord, but has no bearing on unbraced length. The buckled shape of the chord must be a continuous curve over the full length.
Theory of Elastic Stability by Timoshenko and Gere - Article 2.15. This book can be downloaded for free.
BA
RE: LTB of a Vierendeel Truss
Are you of the opinion then that your compression chord check IS the LTB check? That's the crux of my objection.
RE: LTB of a Vierendeel Truss
Why aren't your end supports at a panel points 7'± from the ends, instead of just near them? Seems you have enough problems without secondary stresses in the top chord. For this load configuration adding some of your own dead load in the middle of the truss would allow you to adjust the stresses in the t&b chords, maybe to your advantage or disadvantage.
And, better yet, at the two panel points 7'± from the ends, weld a 3' piece of pipe to the top chord, pointing up, in the plane of the truss, and attach support cable to the top of this 3' piece of pipe. Also, maybe the vert. chord member should be pipe too, not 1/4" x 3" bar. You want to develop some moment cap'y. Do this same thing in the middle of the truss, but hanging below the bottom chord, and affix your own dead loads, you pick the weights. Voila! You have some rotational resistance, which increases as the truss starts to rotate. Ask ishvaaag how to introduce these as variable rate torsional spring restraints to your computer model. These 3' pipes, or some such, with a 1'+ back span, to engage the opposite parallel chord, could just be clamped over (around) a standard truss.
Add these to your idea pile: If you had a triangular pick-up frame above the top chord, with the cable attached at its high point, 3' above the top chord and centered over my 7' panel point, and this frame slopes down to grasp the top chord 4' from the truss end and 10' from the truss end. This frame may have some moment cap'y. across the t&b chords too. This would certainly change the stresses in you standard truss. I think, for the better, although I haven't analyzed that as I type this. I think you would learn a great deal testing one of these trusses and determining what loads, at different locations, start to cause some amount of lateral rotation of each chord.
RE: LTB of a Vierendeel Truss
I googled the name of the book and authors. Several sites were selling the book at reasonable rates, but one site offered free download. I can't seem to find it now.
Yes.
cleagl,
Can you add a cable at each end? That would remove the large bending moment which is causing the buckling problem.
Alternatively, move the end cables to the middle of the uniform load to reduce moment.
BA
RE: LTB of a Vierendeel Truss
Here are the relevant pages of the reference we discussed earlier.
BA
RE: LTB of a Vierendeel Truss
RE: LTB of a Vierendeel Truss
The attached sketch may be a better alternative.
BA
RE: LTB of a Vierendeel Truss
Dhengr: those are some great practical tips. I'd considered the extension pieces too. I didn't bring it up though because I was unsure of how long the posts would have to be in order to get the job done.
Having spent most of the weekend thinking about it, here's my idea for checking the LTB of the truss. I'm just making this up for others to comment on though . Take it with a grain of salt.
Things in general become unstable when they find a way to deform into a lower energy configuration than that generated by the preferred non-buckled configuration. Could you:
1) Approximate all of your uniform loads as point loads to simplify the modeling.
2) Analyze the truss in its unbuckled configuration and measure the displacement of all of loads.
3) Multiply the loads in #2 by their respective displacement to get a measure of potential energy change for that deflected configuration.
4) Analyze the truss again in a configuration that mimics LTB. I'm thinking that you rotate the thing 90 degrees and suspend it from Dhengr's extensions. You'd apply the loads in their original orientation and allow torsion et. to work it's magic. Again, record the displacements of the loads.
5) Multiply the loads in #4 by their respective displacement to get a measure of potential energy change for that deflected configuration.
6) Compare the results of #3 & #5. If the potential energy lost from the buckled configuration is less than the potential energy lost in the non-buckled configuration, you're good to go for LTB. Otherwise, your in trouble.
Any thoughts? Like I said, this is just an idea. Don't anybody run off and try this at home...
RE: LTB of a Vierendeel Truss
These loads are trivial and do not warrant a fancy analysis. The load appears to be that of a stage curtain. Place the hangers in a more sensible location.
BA
RE: LTB of a Vierendeel Truss
RE: LTB of a Vierendeel Truss
I agree that it is valid if he maintains 7' cantilevers, but why would he want to do that?
BA
RE: LTB of a Vierendeel Truss
dhengr made some good suggestions regarding modifying the geometry/physical form to aid in the way the truss handles the moment. However,...
The geometry is fixed for several reasons.
1. This is a part of a standard product line. The form and layout are standardized for manufacturing and we usually create these from 20' lengths plus a custom center part to reach the customer's overall required length. This is partially why the lift lines are not (exactly) on the truss panel points. The roof steel that the lift line are supported from are not on 4' spacing (which is the spacing of the web members)
2. The additional components dhengr suggests to add to the top chord is a good idea and we have done before, however for this job the owner requires the truss to be raised as high as possible so the main curtain (good call BA) can be flown out of sight. These cables are part of a rigging counterweight system.
3. Unfortunately, the building is existing and there is no suitable structure above the area of the cantilever, hence the large overhang. There is a strong possibility, that if we can't come up with another alternative we will fabricate this from HSS4x2x1/4 with the strong axis oriented horizontally. That would be less expensive than creating structure at the underside of the roof. The objection from the owner would be that the equipment all attaches to the truss with standard hardware for 1.5" sched 40 pipe, so he would need to buy or make different attachment hardware.
4. KootenayKid, I like your energy idea and will probably pursue that and compare to BA's suggestion about Newmark. I was able to download Timoshenko's book as well and have read though that section and it seems pretty sensible.
Thanks again to all for the insights, they are much appreciated.
-cleagl
RE: LTB of a Vierendeel Truss
BA
RE: LTB of a Vierendeel Truss
I'm still not satified that checking the compression chord for column style buckling precludes LTB failure.
Looking at the Mcr equation for LTB of beams, it seems to me that you could use that equation with Cw conservatively -- and appropriatley -- taken as 1.0. Iy and J would be calculated including the combined TC/BC section. Of course, this only applies if you have legitimate rotational restraint somewhere in the system
Mcr = PI/(ky*L)*SQRT(E*Iy*G*J)
RE: LTB of a Vierendeel Truss
RE: LTB of a Vierendeel Truss
RE: LTB of a Vierendeel Truss
Sloping cables is a possibility. See attached.
BA
RE: LTB of a Vierendeel Truss
Yes. If the operation mechanics permits it, the supporting scheme shown by you reduces the negative moment and minimizes the stability concerns.
RE: LTB of a Vierendeel Truss
The cantilever moment, Mc = (D + 60)C2/2.
The span moment, M = D*L2/8 - Mc.
where D is the dead load of the truss, C us the cantilever length and L is the distance between the outer two cables, in our case, 40'.
This truss has no lateral support anywhere. Its unbraced length could be said to be infinite. Neglecting the dead load of the truss, the buckling length (not the unbraced length) is 54'.
The dead load, D may be adjusted until the central moment is zero. Does that mean the buckling length of the bottom chord is reduced by a factor of 2 to 27'?
D may be further adjusted until a point of inflection occurs at each of the inner cables, i.e. at L/3. Does that mean that the buckling length becomes (L/3 + C)?
If the dead load is sufficient to create a small positive moment at midspan, the length of chord in compression and hence the buckling length is reduced. There are some on this forum who would disagree.
BA
RE: LTB of a Vierendeel Truss
In order to get an inflection point at the third points of the 40' span, the negative moment at the exterior cables must be (w/8)*(402 - (40/3)2) = 177.8w. This assumes the two interior cables will be unstressed.
Equating these expressions, the truss must weigh 9.6 plf in order to produce an inflection point at each of the third points of the span. Then the buckling length is reduced to 7 + 40/3 = 20.3'.
An HSS 4x2x1/4 weighs 6.9 plf, so if the top chord plus web members weigh 2.7 plf, perhaps the problem is solved without doing anything further.
BA
RE: LTB of a Vierendeel Truss
You probably only need to do this once or twice with different trusses to start getting a "feel" for the problem.
Michael.
Timing has a lot to do with the outcome of a rain dance.
RE: LTB of a Vierendeel Truss
See the link:
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