LTB of a Vierendeel Truss

[cleagl]

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

 

[BAretired]

KK,
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.

Are you of the opinion then that your compression chord check IS the LTB check? That's the crux of my objection.

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

 

[BAretired]

KK,

Here are the relevant pages of the reference we discussed earlier.

BA

 

[ishvaaag]

Only to add that to check automatically the models with explicit initial deformations, the program has not only to have P-Delta included, but also a code for the material. If the pipe material is aluminum, RISA-3D has not as of now aluminum checks; SAP 2000 has.

 

[BAretired]

A load of 60 pounds per foot doesn't seem much, but for a 7' cantilever, it results in a negative moment of about 1500'#. If the truss is 1'-0" deep, the compression is 1500# in the bottom chord between supports. This is difficult to resist over such a long span.

The attached sketch may be a better alternative.

BA

 

[KootK]

Thanks for the PDF BA. Good stuff. As it turns out, pretty much Timoshenko's entire library is available online. Our IT guy's probably gonna come get me any minute now...

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...

 

[BAretired]

I agree that all cables should be attached at panel points of the truss. I thought they were.

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

 

[KootK]

The truss sounds every bit as insignificant as loads. I think that the OP's LTB concern is valid.

 

[BAretired]

KK,
I agree that it is valid if he maintains 7' cantilevers, but why would he want to do that?

BA

 

[cleagl]

Some information....

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

 

[BAretired]

HSS 4x2x1/4 has a radius of gyration of 1.26" which, by code, has a maximum length of 22.7' as a compression strut. Maybe you should consider using a larger section.

BA

 

[KootK]

Cleagl: if you do end up trying the energy method, please pass along the results. I'm very curious to see if it will bear fruit.

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)

 

[tai99]

Does all the cables need to be vertical? Can it be tilted, and utilize pulley to control up/down movement, if so required?

 

[KootK]

I also wondered if you could have small perpendicular trusses located at the support points?

 

[BAretired]

tai99,

Sloping cables is a possibility. See attached.

BA

 

[tai99]

BA:

Yes. If the operation mechanics permits it, the supporting scheme shown by you reduces the negative moment and minimizes the stability concerns.

 

[BAretired]

So far, we have been considering only 60 plf on the two cantilevers. Suppose we consider the dead load of the truss as well.

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

 

[BAretired]

Let the weight of truss be w plf. The moment on each cantilever would be (60 + w)* 7.0²/2 = 24.5 w + 1470.

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

 

[paddingtongreen]

I would be tempted to displace the joints of the cantilevers, linearly, horizontally, by a very small amount, say the fabrication tolerance. That is, put a slight bend in the truss at each of the outer supports, run the analysis. Modify the model so that all of the joints are in the horizontal location resulting from the previous run. Repeat as many times as necessary till the truss either buckles or finds equilibrium.

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.

 

[ATSE]

KK mentioned an energy method that is similar to one that R. Shankar Nair has presented and refined. Not only is Dr. Nair a gentlemen, but presents relatively complex ideas simply.
See the link:

http://www.aisc.org/store/p-939-pra...methods-to-structural-stability-problems.aspx