## F

Fig. 1.52 Four boundary conditions in the cylindrical bending of a long plate. The uniform load q is negative in the four cases

Taking the origin of the z, y frame at the middle of the neutral surface and since the load is symmetrical, the ordinate and slope are null at the origin. So the constants Ci=C2 =0 and the flexure is w q x4 +(Mo _ x2

If the plate is with simply supported edges free to move in x, the bending moment at the edge is null (cf. Fig. 1.52). Setting M0 = 0 entails w = 4ID (2x2 - 3^2)x2, w{±t/2} = -5q(A/384D,

If the plate is with built-in edges free to move in x, the slope is null at the edge (cf. Fig. 1.52). Setting dw/dx\±t/2 = 0 entails Mo = q^/12 and w

• Loaded plate with opposite edge forces F, -F, in x-direction: Other load configurations of interest are similar to the two previous cases with the load q, moments M0, —M0, but now including opposite forces F, —F, applied to the long edges at x = ±t/2 and in the x-direction (cf. Fig. 1.52). Set F > 0 at x = lj2 and denote ^ a dimensionless quantity defined by

0 0