Mae_101-midterm-solution

MAE_101-Midterm-Solution
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Unformatted text preview: MAE 101. Statics and Strength of Materials © G. E. Orient 2006 1 Midterm - Solution 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 sin 2 sin cos 2 2 ) ( W T T W T W A F T F W A W L LA M y y x y y B = = +-= +-= = = = = +-= α (*) (**) 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 = = = =-+ + = = +---= = + + = = +---= 90 70 4 3 2 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 cos 3 . 127 2 sin sin =-=-= = + =-=-=-= = + = α F 2 F 1 F 3 l l l l l α=45 o MAE 101. Statics and Strength of Materials © G. E. Orient 2006 4 Problem 2 contd 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 ...
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