194 Mechanics of Materials 2 For a circular plate,radius R.freely supported at its edge and subjected to a load F distributed around a circle radius R F R ymax [3v)(R2)-Ri log.R] 8πD2(1+y) 3F 2(+)logR -)R + (R2-R) and 三0zm Table 7.1.Summary of maximum deflections and stresses. Loading Maximum Maximum stresses condition deflection (ymax) Urmas Ozmux Uniformly loaded, 3gR4 1661-2) 3qR2 3gR2 edges clamped 4r2 82I+v) Uniformly loaded. edges freely 3qR 3qR2 3g supported 16E735+1-) 823+ 82(3+) Central load F, 3FR2 3F 3vF edges clamped 4πE1-2) 2πt2 2n2 Central load F, From 3FR2 From edges freely 4玩E3+(1- 3 R 3F 2721+)log (I+v)log +(1-v) supported 2πt2 For an annular ring,freely supported at its outside edge,with total load F applied around the inside radius Ri,the maximum stress is tangential at the inside radius, 3F(1+v) R2 R i.e. πt2 (R-R) loge Ri If the outside edge is clamped the maximum stress becomes 3F (R2-R) Omax= 2πt2 R2 For thin membranes subjected to uniform pressure g the maximum deflection is given by ymax =0.662 R 9R7'3 Et For rectangular plates subjected to uniform loads the maximum deflection and bending moments are given by equations of the form 9b4 ymax a- Et3 M=Bgb2194 Mechanics of Materials 2 .. Central load F, edges clamped Central load F, edges freely support e d For a circular plate, radius R, freely supported at its edge and subjected to a load F distributed around a circle radius RI 1 3FR2 3F 3uF 2nr2 2nr2 From From 3FR2 3F R 3F r 2nr2 4?rEt" (I - 2) ~ - 1 and Table 7.1. Summary of maximum deflections and stresses. I Loading I ~ condition I ~aflxri~~~ Maximum stresses I Uniformly loaded, edges freely supported 16Et" For an annular ring, freely supported at its outside edge, with total load F applied around the inside radius RI , the maximum stress is tangential at the inside radius, i.e. If the outside edge is clamped the maximum stress becomes 3F (R' - R:) = [ R2 ] For thin membranes subjected to uniform pressure q the maximum deflection is given by For rectangular plates subjected to uniform loads the maximum deflection and bending moments are given by equations of the form 9b4 ymax = a￾Et3 M = &h2