# Pressure applied to flat plate

I have a question about the pressure placed on a plate of material X, how the force is distributed and what would be the material property that would determine its failure.

To simplify things "suppose" I wanted to build a vacuum chamber with a viewing window made of material X, that could handle a external pressure of 0.990Bar, and has a dimension of 500mm x 500mm x thickness. How could I calculate a for safety reasons the minimum thickness needed for the window so that it doesn't implode, ignoring safety factors for now. Also could this calculation be then used on a box of some arbitrary dimensions to calculate the minimum thickness of the material?

Thanks.

Thickness, $t$, for a window made of a brittle material (like most glasses) is: $$t=\sqrt{\frac{pr^2}{\sigma_{MOR}}}$$ Where $p$ is the pressure difference and $\sigma_{MOR}$ the Modulus of Rupture, which is roughly equal to the tensile strength, it's listed for most materials in data books or http://www.sgpinc.com/materials.htm Be careful that the pressure and modulus are in the same units .