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MAE 101 homework 5 sol

# MAE 101 homework 5 sol - MAE 101 Homework 3 Solution...

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MAE 101: Homework 3 Solution October 13, 2011 Problem 6.8 The Howe and Pratt bridge trusses are subjected to identical loads. 1. In which truss does the largest tensile force occur? In what member(s) does it occur, and what is its value? 2. In which truss does the largest compressive force occur? In what member(s) does it occur, and what is its value? B C D L F F F E A Howe G H I L L L L Solution: (a) Howe Bridge: The moment about A is M A = - 6 F + 4 E = 0, from which E = 3 2 F . Denote the axial force in the member I , K by IK . (1) Joint E : DE = - E sin 45 = - 3 2 2 F ( C ) EI = DE cos 45 = 3 2 F ( T ) (2) Joint D : CD = DE cos 45 = - 3 2 F ( C ), DI = - DE sin 45 = 3 2 F ( T ) (3) Joint I : CI = F -| DI | sin 45 = - 2 2 F ( C ), HI = EI - CI sin 45 = 2 F ( T ) (4) Joint H : CH = F ( T ) , GH = HI = 2 F ( T ). By symmetry (the reaction at A has no x -component) the axial forces in the other members are HG = HI , CG = CI , BG = DI , CD = BC , AG = EI , and AB = DE . In the Howe truss, the members HI and GH have the highest tensile force GH = HI = 2 F ( T ) and the members DE and AB have the highest compressive force AB = DE = - 3 2 2 F ( C ) (b) Pratt Bridge: The moment about A is M A = - 6 F + 4 E = 0, from which E = 3 2 F . 1

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L F F E A Pratt B C D G H I F L L L L F E F A B C D L F F F E A B C D G H G H I F L L L L L L L L L I A X A Y F DE CD DE DI EI E F F E L L L L L 45 ° 45 ° 45 ° 45 ° 45 ° 45 ° 45 ° 45 ° HI CI DI EI F GH HI CH F (1) Joint E (2) Joint D (5) Joint H (3) Joint I (4) Joint H (1) Joint E (2) Joint I (3) Joint D (4) Joint C EI DE E F DI EI HI DC DH DI DE BC DC CH F BH HI GH Howe Bridge Pratt Bridge (1) Joint E: DE = - 3 2 2 F ( C ), EI = - DE 2 = 3 2 F ( T ) (2) Joint I : DI = F ( T ), HI = EI = 3 2 F ( T ) (3) Joint D : DH = - 2 DI - DE = 2 2 F ( T ), DC = DE 2 - DH 2 = - 2 F ( C ) (4) Joint C : BC = DC = - 2 F ( C ), CH = 0 (5) Joint H : GH = HI = 3 2 F ( T ). The axial forces in the remaining members are determined from symmetry. In the Pratt Bridge, the highest tensile force occurs in members EI , HI , GH , and AG = 3 2 F ( T ) , and the highest compressive force occurs in members DE and AB = - 3 2 2 F ( C ) . Thus (a) the Howe bridge has the highest tensile force in a member, and (b) the value of the compressive force is the same in members DE and AB = 3 2 2 F ( C ) for both bridges.
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MAE 101 homework 5 sol - MAE 101 Homework 3 Solution...

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