Post Buckling Deflected Shape

[RFreund]

Is there an approximate way to find the deflection or deflected shape of the a member which has buckled elastically? Or is this something that requires full on Non-linear FEA. Seams like if it has buckled elastically there should be some sort approximation, may be if the load is within a few percent of buckling perhaps?

Thanks!

EIT

http://www.HowToEngineer.com

 

[KootK]

That is interesting. Could we start to call that justification for the mysterious 2%-ish bracing rules?

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[BAretired]

I do not have the Gaylord book, but how can there be a deflection associated with a load above P_E? After the column reaches buckling load, deflection rises without limit and the column fails.

BA

 

[Hokie93]

To quote from Gaylord & Gaylord (p. 191):
"The value of P at which a straight column becomes unstable is called the critical load. When the column bends at the critical load, it is said to have buckled. Therefore, the critical load is also called the buckling load. At the critical load the column is extremely sensitive to increase in load, in the sense that a very slight increase is accompanied by a large lateral deflection. Thus, if the critical load P = 4K/L for the column of Fig. 4-1a by only 2/3 percent, delta is 10 percent of the column length L (Fig. 4-1c)". Figure 4-1a is two rigid bars of length L/2 connected together by a rotational spring with a spring constant K.

The equation provided previously is an approximate solution that provides very similar results for lateral deflection to the two-bar with rotational spring model.

 

[racookpe1978]

I know the theory of the post-buckled, final column shape. And I know how and why that theoretical shape is theoretically going to be produced.

But, respectfully submitted, that "ain't gonna happen" UNLESS the buckling reaction is distributed evenly through the column mid-section AND the column cross-section through the mid-section of the curve starts off uniform and even, AND stays uniform and evenly misshapen during the entire period of movement.

Instead, the column will be uniformly deflected until the buckling collapse begins. At that point in time, and at that point along the column the where a weakness or flaw has happened, the column will "kink" and yield suddenly. The rest of the column - once the kink has started will restraighten slightly back from its ultimate yield (plastic - >2% yield) position.

You will end up two slightly curved ends and a sharp bend in the middle where the coulmn cross-section is flattened completely.