Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_50

⚡ Mecademy AIENG정역학 · ch4  Problem Statement Determine the force in member DG of the compound truss. The joints all lie on radial lines subtending angles of 15° as indicated, and the curved members act as two-force members. Distance . Problem 4/50 (a) Force in member DG 1. Formula: First, determine the reactions at the supports. Due to the symmetry of the truss geometry and the central vertical load at joint , the vertical reactions at and are equal. Assuming a horizontal support surface, the horizontal reaction at (pin) is zero because the roller at cannot support horizontal force and there are no other external horizontal loads: . 2. Substitution: Establish a coordinate system with the center at the origin and the -axis oriented vertically along . Based on the 15° intervals between radial lines, the coordinates of the joints on the left side are: Joint : Joint : Joint : Joint : Joint : The reactions at joint are and (upwards). 3. Calculation: We solve the truss using the method of joints, starting from support . Joint A: Two unknown members and . Their direction vectors from are and . OC=OA=OB=R LCA B F = ∑ y 0⟹A + y B − y L=0⟹A = y B = y 2 L A B A = x 0 O(0,0) yOC C(0,R) G(−0.9Rsin15,0.9Rcos15)≈ ∘∘ (−0.2329R,0.8693R) D(−1.1Rsin30,1.1Rcos30)≈ ∘∘ (−0.5500R,0.9526R) H(−0.9Rsin45,0.9Rcos45)≈ ∘∘ (−0.6364R,0.6364R) A(−Rsin60,Rcos60)≈ ∘∘ (−0.8660R,0.5000R) AA = x 0A = y 0.5L A AHADA =u AH (0.8600,0.5103) =u AD (0.5726,0.8199) Solving this system gives (Compression) and (Tension)