hw4-2008sol

hw4-2008sol - 1. Set the center of Z-shaped beam cross...

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Unformatted text preview: 1. Set the center of Z-shaped beam cross section as origin of coordinate. The moment of inertia I yy = integraldisplay A y 2 dA = 2 3 ( h- 2 t ) ( t 2 ) 3 + 2 3 t parenleftbigg ( t 2 ) 3 + ( b- t 2 ) 3 parenrightbigg I zz = integraldisplay A z 2 dA = 2 3 t ( h 2- t ) 3 + 2 3 b parenleftbigg ( h 2 ) 3- ( h 2- t ) 3 parenrightbigg I yz = integraldisplay A yzdA = 1 2 ( bt- b 2 )( t 2- ht ) plug in numbers, t = 3 4 in, b = 8 in, h = 20 in, we have I yy = 222 . 3379 in 4 I zz = 1508 in 4 I yz = 418 . 6875 in 4 Youngs Modulus is E = 200 GPa, L = 12 in. (a) Generalized flexure method, coordinates of point A is ( y, z ) = (- 10 ,- 7 . 625) , M z =- 15000 in-lbs, M y = 0 in-lbs, use transformation formulas for the moments of inertia = 1 2 tan 1 parenleftbigg- 2 I yz I yy- I zz parenrightbigg = 16 . 54 o Iy 1 y 1 = I yy + I zz 2 + I yy- I zz 2 cos 2 - I yz sin 2 = 98 in 4 Iz 1 z 1 = I yy + I zz 2- I yy- I zz 2 cos 2 + I yz sin 2 = 1632 . 31 in 4 Iy 1 z 1 = I yy- I zz 2 sin 2...
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This note was uploaded on 05/19/2008 for the course MAE 314 taught by Professor Rabiei,heeter during the Spring '08 term at N.C. State.

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hw4-2008sol - 1. Set the center of Z-shaped beam cross...

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