Buckling Load for Simply Supported Plate

The difference comes from the fact that the plate is considered as "free supported" (accepts rotations but not displacements) on all 4 sides even if load is applied only on 2 opposite sides.

In the case of a beam there are only end rotating "bearings".

If the plate is totally free (accepts rotations AND displacements) on the 2 unloaded sides you may use the equation for the beam. In this case the plate has in transverse direction all over the width same deformation there will be no rotations but only displacements.

Sorry nick name but I think you are wrong. The load I gave is not for the plate that is simply supported on all sides, but it is actuall free on the two sides where the load is not working. If the plate is simply supported on all sides, the buckling load is another then the one I gave.

You are describing my problem correct in your last sentence.

"If the plate is totally free (accepts rotations AND displacements) on the 2 unloaded sides you may use the equation for the beam. In this case the plate has in transverse direction all over the width same deformation there will be no rotations but only displacements."

But it is not as you say that you can use the equation for the beam here, all text-books I have looked in states that you have to use the expression with the platestifness. So the plate load becomes bigger by a factor of 1/(1-v*v) than the beam load. So there is no convergence according to the textbooks, and if I get to see the derivation of this plate-load I might understand why.

v=poisson ratio

Then I am NOT the only one to be wrong since I checked with other sources (3).

Any way if the Poisson coefficient appears it means that the transverse contraction / tension is taken into consideration. If the ratio is small then the side effect is small enough to be neglected.

If you find some thing more on the subject then I would appreciate to have the link or the information.

Try "Theory of Plates and Shells" by Timoshenko and Woinowsky-Krieger.

At one time I had a set of books from AISI (American Iron and Steel Institute) on the design of cold-formed steel members that included specifications for buckling of plates (more specifically, the web of cold formed sections). Included all possible edge conditions (including supported top and bottom only with loads applied at supported edge). If I recall, they included graphic solutions as well as calculations. I would try checking there.

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