7.9. Circular plate subjected to a load F distributed round a circle

Consider the circular plate of Fig. 7.5 subjected to a total load F distributed round a circle of radius R\. A solution is obtained to this problem by considering the plate as consisting of two parts r < R\ and r > R\, bearing in mind that the values of 6, y and Mr must be the same for both parts at the common radius r = R\.

Fig. 7.5. Solid circular plate subjected to total load F distributed around a circle of radius R\.

Thus, for r < R\, we have a plate with zero distributed load and zero central concentrated load, i.e.

For non-infinite slope at the centre, C2 = 0 and with the axis for deflections at the centre of the plate, y = 0 when r = 0, C3 = 0. Therefore for the inner portion of the plate

For the outer portion of the plate r > R] and eqn. (22.20) reduces to

0 0

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