qR2 8D

The maximum deflection of the plate will be at the centre, but since this has been used as the origin the deflection equation will yield y = 0 at r = 0; indeed, this was one of the conditions used to evaluate the constants. We must therefore determine the equivalent amount by which the end supports are assumed to move up relative to the "fixed" centre.

Substituting r — R in the deflection eqn. (7.22) yields maximum deflection =

The positive value indicates, as usual, upwards deflection of the ends relative to the centre, i.e. along the positive y direction. The central deflection of the plate is thus, as expected, in the same direction as the loading, along the negative y direction (downwards). Substituting for D,


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