## Circular Plates And Diaphragms

Summary

The slope and deflection of circular plates under various loading and support conditions are given by the fundamental deflection equation where y is the deflection at radius r\ dy/dr is the slope 0 at radius r; Q is the applied load or shear force per unit length, usually given as a function of r\ D is a constant termed the "flexural stiffness" or "flexural rigidity" = Ep/[ 12(1 — v2)] and t is the plate thickness. For applied uniformly distributed load (i.e. pressure q) the equation becomes

For central concentrated load F

Q =- and the right-hand-side becomes--

2nr 6 2nrD

For axisymmetric non-uniform pressure (e.g. impacting gas or water jet)

q = K/r and the right-hand-side becomes — K/2D The bending moments per unit length at any point in the plate are:

Similarly, the radial and tangential stresses at any radius r are given by:

radial stress ar =

tangential stress az —

Alternatively,

For a circular plate, radius R, freely supported at its edge and subjected to a load F distributed around a circle radius R\

y max and

8 nD

3 F 4m2

R Ri

 Loading condition Maximum deflection (>max) Maximum stresses
0 0