Truss Lifting Analysis

[structcode666]

thread507-501119

There was a recent thread (about a year go) that went over some of the considerations behind the stability of a truss when it is being lifted. A method that was mentioned in the thread was a video by the AISC, linked below:

https://youtu.be/8lhyuhPtkZY?si=zO3XIVSu0OVMWEkC

My question is a simple one - why introduce the initial out-of-plane "deformed" truss shape and re-run the analysis? Why can't I just model the undeformed truss shape and run a standard buckling analysis?

Would love to know the background of the method, as well as ELI5 explanations of why we should go down this path.

A similar method was explained in Theory of Elastic stability by Timoshenko, however for a standard consultant trying to get an efficient and safe answer, I found that a bit too academic for my liking!

 

[Lomarandil]

I believe the answer depends on your finite element program of choice.

My understanding is that some programs can perform a buckling analysis without explicitly providing initial displacements (corresponding to real-world fabrication tolerances). But many programs will not account for initial imperfections and report erroneously high buckling loads.

It's also worth considering that the fabrication tolerances of your truss may be different from the default AISC building column tolerances.

 

[SWComposites]

The reason for including initial imperfections in a stability analysis is that a standard eigenvalue buckling analysis can greatly overestimate the buckling load. The imperfection "effect" is dependent on the type of loading and buckling mode. The extreme case is a cylinder under axial compression; think of standing on a Coke can and then putting a slight lateral deflection in the side wall. See also:

https://shellbuckling.com/imperfectionSensitivity.php

 

[structSU10]

The issue is that a linear buckling analysis on an ideal shape is very likely to give higher capacity than when an imperfection is introduced.

A brief description that may help is here:

https://enterfea.com/imperfections-in-buckling-design/

 

[glass99]

An eigenvalue analysis is technically unconservative in all instances, but for most architectural structures only by a little bit. Introducing initial out-of-straightness only affects most things I have looked at marginally. You can check that with a simple column say 10ft long with an out of straightness of 1/4" and a non-linear static analysis. The results will be within ~10%.

The part I find hardest in a truss structure is not the geometric imperfections, but whether the connections are moment connections in all directions. The bottom chords is effectively braced by the out of plane stiffness of the diagonals, but slip critical bolts are typically not used.

 

[Stress_Eng]

With beam column buckling, I’ve needed to include initial offset, be it sinusoidal or tolerance summation between parts, initial moments due to compression load offset and friction moments. The task is to incorporate all aspects of your boundary / loading conditions and geometry that can have any impact on your critical load. Supports will have rotational stiffness to some degree. Don’t forget plasticity and the use of Et (not relevant if slenderness ratio is high and you’re dealing with Euler buckling only, Et being tangent modulus).

 

[glass99]

@Stress_Eng: what do you mean by plasticity and Et? Generally in architectural structures we don't worry about the post yield buckling performance. The tension stiffening is taken into account somewhat in an eigenvalue analysis or a NL geometry static analysis.

My understanding is that initial displacements make a big difference in shell structures because they have these complex buckling modes where the initial displacement is a relatively large percentage of the "buckled length". You get an "oil canning" mode over a length of say 12", and a 1/4" initial displacement is a large percentage of that, setting up some unfortunate P-delta effects (membrane force times initial displacement).

Its a massive increment in effort to worry about those things, so it needs to be for a reason. In my office we frequently design wonky monocoques or super slender structures with kl/r > 300, in which case we worry about such things, but certainly not under all circumstances.

 

[montbIanc]

I think it's useful to compare various levels of analysis (levels of sophistication). I'll put them in this order:

1) Hand analysis (from the video).
2) Linear buckling analysis (mentioned in the initial question).
3) Direct analysis (from the video).
4) Advanced analysis.

I'll assume good information is (or can be) available so no garbage in-garbage out business. In that case we get more realistic output as we increase sophistication so it's practical reasons why anything other than advanced analysis is used. Could be time, budget, familiarity (I'm personally not experienced in advanced analysis), or the necessary information could be found but not easily.

So we trade off and lose realism. In the video, the direct analysis gave deflections and member forces including second order effects (with some loss of realism compared with advanced analysis; for example, using an approximate secant stiffness). An elastic buckling analysis doesn't give that information. A second-order analysis without initial imperfections (geometry and residual stresses) will underestimate them. In that case you need to do some post-processing if you want that information/increase in accuracy. Or assess whether the results are close enough, or known to be conservative - that is, validate the lack of realism for design purposes.

Overall, at each level of sophistication, you're doing some trade between realism, pre- vs post-processing, input data requirements, information produced, and volume of output data. Probably other factors I've forgotten. Even though I can't do advanced analysis it's still useful to know the general idea because it helps to assess the realism of the analysis methods I can and do use, and where I'm sitting on the curve of diminishing returns.

 

[JoshPlumSE]

My question is a simple one - why introduce the initial out-of-plane "deformed" truss shape and re-run the analysis? Why can't I just model the undeformed truss shape and run a standard buckling analysis?

I haven't reviewed the whole video, but watched enough to get the general idea. My thoughts:

1) The video was likely more concerned with AISC / Direct Analysis method than a general concept.
2) Usually (as others have mentioned already) "buckling analysis" is a linear elastic eigen value analysis and doesn't fully capture the "inelastic" buckling effects that could occur. For what it's worth, that's what the stiffness adjustments in the "direct analysis method" are meant to do... modify an elastic analysis in a way that can approximate the inelastic buckling that would likely occur.
3) Depending on the capabilities of the analysis program, it may be necessary to introduce an initial imperfection for the analysis to be capable of amplifying the non linear geometric effects during the analysis. For example if you have a cantilever column with only an axial load applied to it, many analysis programs will not show any moment in that column. So, no matter how high your axial load is, you won't see any buckling occur. But, if you introduce a slight imperfection (or out of straightness) into the column then your analysis program show how the column stability will be affected by axial forces that approach the buckling limit.

 

[CrabbyT]

The part I find hardest in a truss structure is not the geometric imperfections, but whether the connections are moment connections in all directions. The bottom chords is effectively braced by the out of plane stiffness of the diagonals, but slip critical bolts are typically not used.

Agreed. Personally, I'm a bit fan of sandwiching the bottom chord between a couple clip angles or shear tabs. The bottom chord doesn't get bolted or welded to the clips, you just sandwich it in between them so that it's free to move in the axial direction (the clips just prevent the bottom chord from deflecting out of plane).

 

[ThomasH]

The basis for my reasoning now is the Eurocode. But I know or assume there are similair methods available in other codes.

Step 1: Linear buckling analysis.
This will not give me load capacity that I can use for design. But it can give me a buckling length for a member or a buckling coefficient for a plated structure. Those parameters can be used to calculate either capacity for axial load or moment capacity (lateral buckling). If it is a plated structure a reduced stress can be calculated to be used as "allowed" stress.

The other option is to user the buckling shapes as basis for imperfections.

Step 2: Non-linear Analysis
Combine the relevant buckling shapes to an equivalent imperfection. Add non-linear material properties (plasticity etc) and run a non-linear analysis including large deformations.

If set up properly, and I haven't missed anything in this short description , the resulting capacity is the design load. Usually, when I run this type of analysis I plot load vs deformation as the load increases. The result is usually a significant increase in deformation for a certain load level. That is the failure.

I don't know how good structural software would be for this. But I have used app-purpose FEM-software several times.