Buckling Analysis - Case 01

I'm writing just as a simple possibility that might have occured: Some older FEA codes didn't use to account for beam offsets. If there are those beams with offsets in the model (somehow - but it looks like just a simple pressure vessel from the hand calculation parameters), that might have been taken into account in the hand calculation. In the FEA model, due to offsets not showing up in the linear buckling analysis, the structure would undergo "lower" stresses at the plane of buckling - compared to the actual offset beams' model. Just another angle of view if that would be the case. If not, everything ?ukasz Skotny mentioned are more likely. I'm not that as much of an expert as him about buckling, but his explanations make sense.

Carlos, There might be several reasons. I think those should be divided into 2 categories: 1. Even threw I'm not familiar with AWWA code the name "allowable stress" suggest this is according to some codified capacity. This means that such value already contains imperfections, perhaps even a safety factor. Also the equation seems pretty simple (I mean only t and R is required, even Young Modulus is not taken). Usually shell stability uses Timoshenko equation (ideal critical stress = 0.605E t /R) and then calculates slenderness according to it and then take imperfections into account and you get the result. Here, since it is a greatly simplified rule, it is most likely far on the safe side (simply to make the simplification possible at all!). 2. On another hand the analysis you show is an LBA analysis (linear buckling). I wrote about it on my blog recently (https://enterfea.com/linear-buckling-explained/). While it is a really nice tool it lacks certain capacities like: nonlinear geometry (that would reduce the capacity), it's not very imperfection sensitive (if you introduce imperfections they will reduce the capacity, but no second order bending will happen). Usually nonlinear buckling is required to solve such a problem (and that with nonlinear material and explicitly introduced imperfections in several different forms). To sum this up: you compare 2 completely different values. The code one is the capacity including nonlinearities, imperfections and perhaps even safety factors (or at least I hope so, as I wrote I'm unfamiliar with the code). The second one is an ideally elastic capacity of ideal shell - it will be much higher. It's a bit like comparing critical bending moment on a beam to beams capacity to bending... both are moments, but it is not the same. Here the code value is bending capacity (how much shell can carry according to the code), while the LBA outcome would be a critical bending moment (how much ideal shell can carry without yielding, imperfections etc.). Hope that helps :) Have a great day ?ukasz