§7.2 Circular Plates and Diaphragms 197 Substituting egns.(7.3)and (7.4)in egns.(7.1)and (7.2)yields E de ox=(1)"dx Eu [de ie. 0x= 1-吗a+vg (7.5) Eu 「d81 Similarly, =0-x (7.6) dx Thus we have equations for the stresses in terms of the slope and rate of change of slope de/dx.We shall now proceed to evaluate the bending moments in the two planes in similar form and hence to the procedure for determination of 0 and de/dx from a knowledge of the applied loading. 7.2.Bending moments Consider the small section of plate shown in Fig.7.3,which is of unit length.Defining the moments M as moments per unit length and applying the simple bending theory, Unit length Fig.7.3. Substituting eqns.(7.5)and (7.6). Et3 8 MxY= 121-2)dc (7.7) Et3 Now 12(1-y2) =D is a constant and termed the flexural stiffness 「d81 so that Mxy =D (7.8) dx x 「6 de and,similarly, Myz =D +V (7.9) d$7.2 Circular Plates and Diaphragms 197 Substituting eqns. (7.3) and (7.4) in eqns. (7.1) and (7.2) yields E d6 u6 a, = ~ i.e. Similarly, Eu Eu de u, = ~ + v- (1-9) [: dx] (7.5) (7.6) Thus we have equations for the stresses in terms of the slope 6 and rate of change of slope d6/dx. We shall now proceed to evaluate the bending moments in the two planes in similar form and hence to the procedure for determination of 6 and d@/dx from a knowledge of the applied loading. 7.2. Bending moments Consider the small section of plate shown in Fig. 7.3, which is of unit length. Defining the moments M as moments per unit length and applying the simple bending theory, az c 1 x t3 ct3 M=-=- - -- y u [ 12 1 - 12u m Fig. 7.3. Substituting eqns. (7.5) and (7.6), Et3 [ 9 + 21 12(1- 9) dx Mxr = Et3 Now = D is a constant and termed the j-lexural stiffness 12(1 - I?) so that and, similarly, (7.7)