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Now let's assume that we put a divider in the middle of the hollow cube of a certain thickness. The property of the divider material has a yield strength of lets say 30ksi.

And now somehow one side of the cube is pressurized to 5ksi and the other side of the divider is 14psi (atmospheric).

So my question is, if the thickness of that divider is 1mm, by intuition even though the pressure is less than the yielding point the divider will break because it's so thin.

So than what is the governing point or equation that introduces the thickness of a divider as a variable?