HomeWork7 - HW#7 1. a q0 x x a z qo a4 wmax = α , α =...

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Unformatted text preview: HW#7 1. a q0 x x a z qo a4 wmax = α , α = 0.0020932, at x = 0.55a, y = 0.5a D y 2. a 4 a 4 a 2 a 4 x a 4 x q0 x x a 2 x R y (a) Find the expression for R. 2 (b) If R = α qo a , find α . Take a minimum of 4 terms in the summation. α B0.1868, for 9 terms α B0.18538 , for 16 terms 1 R Solution for 2. From Eq. (4-39) amn = = 4q0 a2 a a 0 0 ∫∫ sin 4q a mπ x nπ y mπ x a a nπ y a sin dxdy = 20 cos cos a a a mπ a 0 nπ a 0 4q0 ( cos mπ − 1) ( cos nπ − 1) mnπ 2 From Eq. (4-37), w= a 1 ∞∞ mπ x nπ y ∑∑ 2 mn 2 2 sin a sin b . At x = a and y = a , the 4 π D m =1 n =1 m n 4 4 2 + 2 b a deflection is ∞ a4 ∞ wq0 = 4 ∑ ∑ amn π D m =1,3,5 n =1,3,5 mπ nπ sin 4 4 4 = 0.0021329 q0 a from Maple® for m=1,3,5 and n=1,3,5 2 D ( m2 + n2 ) sin From Eq. (4-42) amn = 4P mπξ nπη a a sin sin with ξ = and η = 2 a a a 4 4 wc1 = a a4 ∞ ∞ mπ x nπ y a a ∑∑ 2 mn 2 2 sin a sin a with x = 4 and y = 4 4 π D m =1 n =1 ( m + n ) wc 2 = a a4 ∞ ∞ mπ x nπ y a 3a ∑∑ 2 mn 2 2 sin a sin a with x = 4 and y = 4 4 π D m =1 n =1 ( m + n ) wc 3 = a a4 ∞ ∞ mπ x nπ y 3a a ∑∑ 2 mn 2 2 sin a sin a with x = 4 and y = 4 4 π D m =1 n =1 ( m + n ) wc 4 = a a4 ∞ ∞ mπ x nπ y 3a 3a ∑∑ 2 mn 2 2 sin a sin a with x = 4 and y = 4 4 π D m =1 n =1 ( m + n ) From Maple® for m=1,3,5 and n=1,3,5 2 a2 P D a2 P wc 2 = 0.002214 D a2 P wc1 = 0.002214 D 2 aP wc1 = 0.00156 D wc1 = 0.00543 0.0021329q0 a 4 / D P = R = wd / ∑ wci = = 0.1868q0 a 2 2 0.011418a / D If one extends the sum for m,n=1,2,3,4,5,6,7, the reaction becomes wd = 0.002131819 q0 a 4 D a2 P D 2 aP wc 2 = 0.002174 D a2 P wc1 = 0.002174 D a2 P wc1 = 0.00155977 D wc1 = 0.0055917 P = R = wd / ∑ wci = 0.002131819q0 a 4 / D = 0.18538q0 a 2 0.01149947 a 2 / D 3 ...
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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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HomeWork7 - HW#7 1. a q0 x x a z qo a4 wmax = α , α =...

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