Equation is given for the maximum stress and deflection for circular flat plates subject to concentrated (pressure) with the edge either clamped or supported. In practice, the edge conditions are usually uncertain and some compromise must be made. The equations are only valid if the deflection is small compared to the plate thickness.

Symbols used:
r = radius of circular plate, (m, in)
a = minor length of rectangular plate, (m, in)
b = major length of rectangular plate
P = concentrated load, (N, lbs)
v = Poisson’s ratio
E = Young’s modulus, (N/m², lbs/in²)
t = plate thickness, (m, in)
s _m = maximum stress, (N/m², lbs/in²)
y_m = maximum deflection, (m, in)

Circular plate, concentrated load, edges clamped equation and calculator.

Stress At Center Lower Surface

Deflection at center

D = flexural rigidity= (Et³/(12 ( 1 -v²)