Using a FBD of the beam, assuming members in tension, relate the force in the members and the applied force P by summing moments about the pin at A. Assume counterclockwise is positive in writing the equation.
Rigid bar ABCD is supported by a pin connection at A and by two axial bars (1) and (2). Bar (1) is a 30-in.-long bronze [E = 15700 ksi, α=α= 9.5 × 10−6/°F] bar with a cross-sectional area of 1.50 in.2. Bar (2) is a 40-in.-long aluminum alloy [E = 8000 ksi, α=α= 11.9 × 10−6/°F] bar with a cross-sectional area of 2.50 in.2. Both bars are unstressed before the load P is applied. Assume L1=30 in., L2=40 in., a=36 in., b=44 in., and c=14 in. If a concentrated load of P = 31 kips is applied to the rigid bar at D and the temperature is decreased by 80°F.
(A) Using a FBD of the beam, assuming members in tension, relate the force in the members and the applied force P by summing moments about the pin at A. Assume counterclockwise is positive in writing the equation.
Answer: (___ in.) F1 + (___ in.) F2 + (___ in.) (31 kips) = 0.
(B) Assume the rigid bar ABCD rotates clockwise around point A. Using a deflection sketch, relate the deflections of points B and C. Assume positive deflections are down. ANSWER IN vC
(C) Relate the deformations of member (1) and member (2). ANSWER IN δ2
(D) Determine the deflection of the rigid bar ABCD at point D. A positive deflection is down. IN INCH
(E) Determine the deflection of the rigid bar ABCD at point C. A positive deflection is down. IN INCH
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