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Previously, I was told by someone I trust well that a column can avoid buckling at the first critical load by applying the load "instantaneously" with a magnitude between the first and second critical loads. Of course nothing is instantaneous, so an idealization would be applying the load as a step function. I am an undergraduate mechanical engineer with no practical background with buckling failures and was hoping someone can shed some light on this problem.

I'm sorry I have few details or sources backing this question up, I have been trying to confirm it and have been unable to find it online.

Is this true? Can buckling be avoided at the first critical load by instantaneously applying a load between the first and second critical loads?

Thank you!

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  • $\begingroup$ pulse step loads resist more buckling than static loads. Reminds me when 5 MPH bumpers were invented in the early 70's, an ME student friend of mine design a precrushed array of coke cans and drove his car at 5MPH into a brick wall, backed by concrete and soil. The car chassis survived and the cans crushed the prescribed amount but the g levels were significant . My Rule of Thumb is the g shock level in a linear spring is the ratio of free fall height/stop height =g so since 5MPH = free fall from 255mm and the can was precrushed to yield 100mm deflection, it should have only been 2.5 g shock $\endgroup$ – Tony Stewart Sunnyskyguy EE75 May 18 '17 at 22:23
  • $\begingroup$ but it was a much higher jerk than he expected since the buckling force was dynamic and not constant. $\endgroup$ – Tony Stewart Sunnyskyguy EE75 May 18 '17 at 22:24
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This is just wrong.

The notion of a "critical load" in Euler buckling is a very simplified mathematical idealization of the situation. In the real world, buckling behaviour always involved nonlinear dynamics, and if you apply a big enough load, the structure will always buckle - though if you apply the load fast enough, it may buckle into a different shape from what would happen with a smaller load.

The only situation I can think of where this idea is "sort of correct" is shaft whirling in rotordynamics, which vaguely analogous to buckling. In that case, if you accelerate or decelerate the rotor fast enough through a critical speed, there isn't enough time for the displacement to get big enough to cause failure, and continuous operation at speeds above the critical speed is stable. This idea is used in the design of some types of rotating machines.

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Euler's buckling is the behavior of static loads and not time-dependent loads. You would need to look at nonstatic beam deflections but I doubt that instantaneous loading will prevent buckling. In contrast, it is more likely that a step function loading will excite some critical frequency of the system which might lead to instability and hence buckling.

In general, it might be useful to you to understand what buckling means. Buckling is an instability of an equation. Differential equations permit many solutions. Sometimes these solutions are stable and sometimes they are unstable (like in buckling). When a solution is unstable then little perturbations of the actual state will lead to divergent behavior of the state and you might get a totally different behavior (like buckling).

So actually it is possible to observe no buckling (which is always a possible solution for the bar under compression) of your system even for very large loads. But small perturbations from this state will lead to deviations from this solution, hence it is unlikely that you will observe this case in real life.

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