HomeWork6 - H.W.#6 y a x q ( x) The above simply supported...

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H.W.#6 The above simply supported plate at 0 and x x a = = and of infinite length in the y-direction is subjected to the following loadings which vary in the x direction only: Develop the general deflection equations for the loadings ( a ), ( b ), and ( c ) using integration method and Fourier series. Evaluate x Q at 0 and x x a = = and x M at / 2 x a = . Compare both methods using 1 n = in Fourier series. Discuss the problem. ( 29 q x a y x 0 q ( 29 0 sin x q x q a π = x x x 0 q c b ( 29 a ( 29 b ( 29 c 1
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Solution Case (a) linearly decreasing load Classical method ( 29 0 1 x q x q a = - ( 29 4 0 0 4 iv q x d w x Dw q q dx D a = = - 2 0 0 1 2 3 0 0 1 2 3 4 2 0 0 1 2 3 4 5 3 2 0 0 1 2 3 4 2 2 6 6 24 2 24 120 6 2 q Dw q x x c a q q Dw x x c x c a q q c Dw x x x c x c a q q c c Dw x x x x c x c a ′′′ = - + ′′ = - + + ′ = - + + + = - + + + + 4 2 0 at 0 0, 0 t 0 0 w x c w x c ′′ = = = = = = 2 2 0 0 1 1 0 1 0 at 0 2 6 3 q q w x a a a c a c q a ′′ = = = - + = - 4 4 4 3 0 0 0 0 3 3 0 at
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This note was uploaded on 09/24/2011 for the course CIVL 7690 taught by Professor Staff during the Summer '10 term at Auburn University.

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HomeWork6 - H.W.#6 y a x q ( x) The above simply supported...

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