200 Mechanics of Materials 2 $7.5 Substituting in eqn.(7.18) 品品（器-号- Integrating, ()=6∫+] D 4 Integrating, +C2 slope = qr3 Fr C2 dr -i6D -8mD [2l0g,r-11+C+ (7.19) Integrating again and simplifying, deflection y = qr4 Fr2 2 64D 8 Dlog。r-刂+Ci4+Calog,+C (7.20) The values of the constants of integration will be determined from known end conditions of the plate;slopes and deflections at any radius can then be evaluated.As an example of the procedure used it is now convenient to consider a number of standard loading cases and to determine the maximum deflections and stresses for each. 7.5.Uniformly loaded circular plate with edges clamped The relevant fundamental equation for this loading condition has been shown to be 品品()】 Integrating. 品() 9r2 4D +C1 品() 93 4D Integrating. 94 16D+C12+C slope =9r3 C2 dr -16D+C2+ (7.21)200 Mechanics of Materials 2 Substituting in eqn. (7.18) $7.5 Integrating, --(rg)=-;/[y+--$]dr Id r dr 1 .. - d (rg) =-- 1 [$+Qlog,r +Clr dr D 4 2n Integrating, (7.19) qr3 Fr r c2 slope B= - = -- - ---[2log, r - 11 + CI - + - dY .. Integrating again and simplifying, dr 160 8x0 2r qr4 Fr2 r2 deflection y = -~ - -[log, r - 11 + CI- + Czlog, r + C3 640 8nD 4 (7.20) The values of the constants of integration will be determined from known end conditions of the plate; slopes and deflections at any radius can then be evaluated. As an example of the procedure used it is now convenient to consider a number of standard loading cases and to determine the maximum deflections and stresses for each. 7.5. Uniformly loaded circular plate with edges clamped The relevant fundamental equation for this loading condition has been shown to be Integrating, Integrating, - d [-- Id (91 dr rdr r dr dr dy r- dr d 1’ slope 6’ = - dr (7.21)