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I literally just have a thin steel wall that stands vertically with a load on top. The thin edges of the wall are oriented vertically with the load applied on top of the top thin edge, with the large planar faces of the wall facing horizontally to the sides. I thought there would be an easy calculation based on height, length, thickness (width) and a material parameter for the steel I’m using, but internet searches have yielded me no useful information as to the specific scenario I’m looking for. Is it not that simple to calculate wall strength based on a top loaded compressive force oriented vertically downward onto the height of the wall? Someone please help!

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  • $\begingroup$ The key word you are looking for is buckling. Note that if your thin wall isn't supported on the vertical edges than the section on plate buckling won't help, because your boundary conditions are totally different. Your wall will probably buckle pretty much like a 2-D column. $\endgroup$ – TimWescott Sep 9 '19 at 16:55
  • $\begingroup$ The thing is, the wall shouldn't be designed so the thin panel carries any compressive load at all, except its own weight. There should be a frame round it to carry the loads. $\endgroup$ – alephzero Sep 9 '19 at 19:27
  • $\begingroup$ The Wallis supported at the bottom, and it is not an actual wall of a building. Think of a piece of sheet metal standing on its edge. Imagine the bottom is completely fixed and can’t move. I need to know how much force can be applied to the top of it before it would buckle or start to irreversibly compress. $\endgroup$ – SuperYoughe Sep 9 '19 at 19:40
  • $\begingroup$ It will buckle , the compressive strength has nothing to do with it. $\endgroup$ – blacksmith37 Oct 10 '19 at 0:27
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The analysis of your wall depends on many factors, is it supported at all sides or just the top and bottom or may be it is acting as a cantilever.

Also whether the supports are clamped or pinned.

As a very conservative start you can use $$ P_{Critical}= \frac{\pi^2EI}{(KL)^2} $$

K is the effective length factor and ranges from 2 for cantilever to 0.5 for fixed/fixed ends.

Roark’s Formulas for Stress and Strain by WARREN C. YOUNG RICHARD G. BUDYNAS 7th edition has formulas on plate buckling on chapter 15, pp 715 to 730.

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    $\begingroup$ The slightest amount of geometrical imperfection, or loads that are not perfectly vertical, makes this not "conservative" at all. If I was going to spend any time near it, I would apply a safety factor of at least 100. $\endgroup$ – alephzero Sep 9 '19 at 19:29
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    $\begingroup$ @alephzero, I am not sure! the formula I used is the Euler's buckling load for columns, a plate has much more stability, so much so that engineers even don't use Euler's for flat or curved plates. However it gives a lower limit estimate. if the OP clarifies his configuration of the wall we can compare the results between plate formulas ad Euler's. $\endgroup$ – kamran Sep 9 '19 at 19:45

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