The maximum deflection is at the centre and again equal to the deflection of the supports relative to the centre.

Substituting for the constants with r — R in eqn. (7.22),

maximum deflection = — —— + —— —-- -—

qR4 64 D

i.e. substituting for D,

3 qR4 16Et3

With v = 0.3 this value is approximately four times that for the clamped edge condition.

As before, the stresses are obtained from eqns. (7.14) and (7.15) by substituting for dO/dr and 6/r from eqn. (7.21),

qr2 qR2

This gives a maximum stress at the centre where r = 0

E t qR2


3 qR2 3 qR2

(3 + v) also at the centre i.e. for a uniformly loaded circular plate with edges freely supported,

3 qR2

^max ^Zmax

7.7. Circular plate with central concentrated load F and edges clamped

For a central concentrated load,

0 0

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