MAE_101-Midterm-Solution - Midterm Solution 1 MAE 101...

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MAE 101. Statics and Strength of Materials © G. E. Orient 2006 1 Midterm - Solution
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MAE 101. Statics and Strength of Materials © G. E. Orient 2006 2 Problem 1 The horizontal bar of weight W is supported by a roller support at A and the cable BC . Apply rigorous analysis of equilibrium to determine the angle α , the tension in the cable, and the magnitude of the reaction at A . (The answer may be intuitively obvious, but prove it using basic principles) Free body diagram and equations of equilibrium From (*) either T=0 or cos α=0 If T=0 then (**) cannot be satisfied If cos α=0 then α=π/2 and T=W/2 A y W T 2 sin 0 sin 2 sin 0 cos 2 0 2 ) ( W T T W T W A F T F W A W L LA M y y x y y B = = + - = + - = = = = = + - = α α α α (*) (**)
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MAE 101. Statics and Strength of Materials © G. E. Orient 2006 3 Problem 2 The Pratt bridge truss supports loads at F , G , and H . Determine the axial forces in members BC , BG , and FG . l=4m, F 1 =60 kN, F 2 =80 kN, F 3 =20 kN Global FBD, Equilibrium Method of joints Joint A A x A y E y F 2 F 1 F 3 = = = = - + + = = + - - - = = + + = = + - - - = 0 0 90 0 70 4 3 2 0 4 3 2 3 2 1 3 2 1 3 2 1 3 2 1 ) ( x x x y y y y y y y A A A F kN E F F F A E F F F A F kN F F F E l E l F l F l F M P AF A y P AB kN A P P P P F kN A A P P A F y AB AF AF AB x y y AB AB y y 90 tan cos 0 cos 3 . 127 2 sin 0 sin = - = - = = + = - = - = - = = + = α α α α α F 2 F 1 F 3 l l l l l α=45 o
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MAE 101. Statics and Strength of Materials © G. E. Orient 2006 4 Problem 2 – cont’d Method of joints Joint F Joint B F 1 P AF P FG P FB kN F P F P F T kN P P P P F BF BF y AF FG FG AF x 60 0 ) ( 90 0 1 1 = = = - = = = = + - = P BA P BF P BG P BC ) ( 120 cot ) 2 ( cos ) ( 0 cos cos ) ( 43 . 42 2 ) ( sin sin 0 sin sin 1 1 1 C kN F A P P P P P P F T kN F A F A P
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