By Maan H Jawad
This booklet is written basically for pro engineers drawn to designing plate and shell buildings. It covers easy points of theories and offers examples for the layout of parts as a result of inner and exterior a lot in addition to different a lot, equivalent to wind and useless so much. a number of derivations are saved quite easy and the ensuing equations are simplified to a degree the place the engineer can follow them on to layout difficulties. extra difficult derivations and extra common equations are available within the literature for these attracted to a closer wisdom of the theories of plates and shells. The examples given all through this booklet are meant to teach the engineer the extent of study had to in achieving a secure layout in keeping with a given required measure of accuracy. This publication is additionally acceptable for complex engineering classes
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Uniformly loaded plate. Solution (a) Let the coordinate system be as shown in Fig. 1-14. Equation (1-40) can be solved by letting f (x, y) equal a constant po because the load is uniform over the entire plate. Hence, pmn ¼ 4po ab Z bZ a sin 0 0 mkx nky 4po 16po sin dxdy ¼ 2 ðcos mk À 1Þðcos nk À 1Þ ¼ 2 k mn k mn a b where m = 1, 3, 5,. . n = 1, 3, 5,. . From Eq. (1-39), p¼ l l X 16po X mkx nky sin sin : k 2 mn m ¼ 1;3;... n ¼ 1;3;... a b Substituting this equation and Eq. (1-41) into Eq. (1-26) gives wmn ¼ m ¼ 1; 3; 5; .
All other quantities are assumed positive as shown in Fig. 1-8. Problems 1-6 Find Mx, My, Mxy, Qx, and Qy of a rectangular plate whose deflection is given by w ¼ k sin mkx nky sin a b where k, a, b, n, and m are constants. 1-7 Derive Eqs. (1-25), (1-27), and (1-28). 1-6 Boundary Conditions The most frequently encountered boundary conditions for rectangular plates are essentially the same as those for beams. They are either fixed, simply supported, free, or partially fixed as shown in Fig. 1-9. org/about-a Boundary Conditions 17 Figure 1-9.
Org/about-a Plates with Various Boundary Conditions 39 Figure 2-1. F-15 Fighter. ) and the total deflection is given by w¼ l X Am sinh m ¼ 1;2;... þ Dm y cosh mky mky mky þ B m cosh þ Cm y sinh a a a mky a sin l X mkx 4po a 4 mkx sin þ : 5k 5D m a a m ¼ 1;3;... Figure 2-2. Rectangular plate with various boundary conditions. org/about-a 40 Bending of Various Rectangular Plates Since the deflection is symmetric with respect to x = a/2, m must be odd and the deflection expression becomes w¼ l X mky mky mky þ Bm cosh þ Cm y sinh a a a m ¼ 1;3;...