206 Mechanics of Materials 2 s7.9 3F R ()log (7.36) Thus the radial stress o,will be zero at the edge and will rise to a maximum value(theoret- ically infinite)at the centre.However,in practice,load cannot be applied strictly at a point but must contact over a finite area.Provided this area is known the maximum stress can be calculated. Similarly,from eqn.(7.15) Eu 022 (1-v2) and,again substituting for de/dr and 0/r, 3F 2r2 a+igg+a- (7.37) 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 R1.A solution is obtained to this problem by considering the plate as consisting of two parts r<Ri and r>Ri,bearing in mind that the values of e,y and M,must be the same for both parts at the common radius r =RI. Fig.7.5.Solid circular plate subjected to total load F distributed around a circle of radius R. Thus,for r<R1,we have a plate with zero distributed load and zero central concen- trated load, i.e. 9=F=0 Therefore from eqn.(7.20), y=Cir2 +Ca logr+C3 and from eqn.(7.19) 0=dy=Cur C2 dr 2 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 C12 y=- 4 ande=y。Cr dr 2206 Mechanics of Materials 2 97.9 R r 3F 2nt2 = --(I + v)log, - (7.36) Thus the radial stress a, will be zero at the edge and will rise to a maximum value (theoret￾ically infinite) at the centre. However, in practice, load cannot be applied strictly at a point but must contact over a finite area. Provided this area is known the maximum stress can be calculated. Similarly, from eqn. (7.15) ELI d8 6 a, = ____ (1 - v2) [vdr + ;] and, again substituting for d6/dr and 8/r, R 2d r a, = - 3F [(I + u)log, - + (1 - (7.37) 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 R1. A solution is obtained to this problem by considering the plate as consisting of two parts r < Rl and r > RI , bearing in mind that the values of 8, y and M, must be the same for both parts at the common radius r = Rl . Fig. 7.5. Solid circular plate subjected to total load F distributed around a circle of radius RI . Thus, for r < Rl, we have a plate with zero distributed load and zero central concen￾trated load, i.e. q=F=O Therefore from eqn . (7.20), and from eqn. (7.19) $=-==+2 dy Clr C dr 2 r 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