7. F8 l.1378xlOlO P C all= 5.337xlo15 D + 4.1610xl015 EI l.1378xl0lO P ---~~0-~~-[x4 -4ox 3 +400x 2 J [y 4 -40y 3 +400y 2 J 5.337xl0 15 D + 4.1610xl0 15 EI In order to test the accuracy of this approximation refer to (7.F2) page 202 and note the tabulated values of center deflection and edge moments listed for rectangular clamped plates. From Table 35, the center deflection of a square clamped plate is given by the expression: P (a) 4 P w = 0.00126 ~ = 201.6 rl-- The Rayleigh-Ritz Solution provides a value for the center deflection in the following form (neglecting the stiffeners): l.1378xlOlO P 2 ----~~~0 r10 4 - 40(10 3 ) + 400(10 2 )} 5 .337xl0 15 D l .1378xl0 18 P P ------- 0 = 213. 19 - 0° 5.337xl0 15 D The difference between the one term Rayleigh-Ritz Solution and Timoshenko's Solution is approximately 6%. Similarly, check the edge moment predicted by the Rayleigh-Ritz approximation against the solution tabulated in (7.F2). M X @ y 10 X = 0 l.1378xlOlO P V = 0.3; EI= 0 5. 337xl015 Do [800] [10000] p 17.055 rl-- Mv -17.055 P,.,
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