Bending Forces¶

This page shows the way to calculate the bending force and displacement on a circular plate that is simply supported and loaded uniformly. This is a useful calculation to perform for end platens on internal pressure vessels.

Plate Rigidity¶

\(D = \frac{E t^3}{12(1-\nu^2)}\)

Displacement¶

\(y_c = \frac{-qa^4}{64D} \frac{5+\nu}{1+\nu}\)

Stress¶

\(M_\text{max} = \frac{qa^2}{16}(3+\nu)\)

\(\sigma_\text{max} = M_\text{max} \frac{6}{t^2}\)

Nomenclature¶

\(D\) = Plate rigidity
\(q\) = Load/area
\(a\) = Radius of plate
\(t\) = Thickness
\(E\) = Young’s modulus
\(\nu\) = Poisson’s ratio
\(y\) = Displacement
\(M\) = Moment
\(\sigma\) = Stress