Good day,
Today I experimented a bit with nonlinear stability analysis on pure beam models.
First, I asked myself what the essential purpose of nonlinear stability analysis for beams could be. Ultimately, in steel design, I verify using the results of the static analysis according to second-order theory + imperfections (general method) considering the partial safety factor gamma 1 = 1.1. Thus, I have already provided the stability proof within the framework of a cross-sectional verification, and the stability analysis would have little added value or additional benefit. A practical example of how this analysis would be useful to me would be great. Furthermore, I had the theory that the actual use of nonlinear stability analysis for beam models serves a numerical load-bearing capacity calculation (method P-P), provided that nonlinear material is combined with nonlinear stability analysis. In my attempt with a system where plastic hinges form and the load-bearing capacity increases as a result of the plastic hinge chain formation, I unfortunately had to find that the moment at the fixed end continues to increase and no plastic hinge is formed. I tried to model the following system numerically:
Accordingly, a plastic hinge should form at a moment of 189 kNm, and the moment at the fixed end should not be able to increase further. Unfortunately, I was not able to model this:
Now I have 2 questions:
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What exactly does the plastic material represent in bars
since it obviously cannot model plastic hinges?
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What is the purpose of nonlinear stability analysis regardless of whether GNA, GNIA, or GMNIA in pure beam models?
I would be very grateful for your feedback.
Best regards,
Nick Böttcher
. The nonlinear stability analysis only makes sense if there is any nonlinearity in the model. It can be used for structures with nonlinear hinges, supports or members like tension members which are failing. A linear analysis cannot find the correct critical load factor in these cases.