Question

Determine the reactions at the supports for the structures shown.

Answer 1

Draw the free body diagram of the given structure 156.61 kN.G 0,156.61 kN 225 kN 135 kN Calculate the angle θ. tan θ θ tan-1 (0.3) 10 16.7° Apply the equilibrium equation in vertical dırection A, B-156.61cos(16.7°)-156.61cos(16.7°)- 0 А. Ч В 300 Apply the equilibrium equation in horizontal direction. A +B 225-135+156.61sin(16.7°)-156.61sin(16.7°)-0 A +B 360

Apply the equilibrium equation at hinge C. 4.5 25x Mi-4.5A_ + 253.125 0 Apply the equilibrium equation at hinge D 2 225x7.5-A x12+ Mi +A, x10-156.61x5.22-0 1687.5-12A +M1 +10A -817.5042-0 M4-124 +10A, +870 0 Apply the equilibrium equation at hinge E. 4 -A, x 4.5+M +A x 20-156.61cos(16.7°)x5 0 -156.61cos(16.7°)x15 M4-4.5A 20A, 3000 0 Solving equations (3), (4) and (5) M-1092.9375 kN -m 4, 299. 125 kN A 162.66 kN From equation (1). 162.66+ B 300 B 137.34 kN

From equation (2) 299.125B 360 B. 60.875 KN Apply the equilibrium equation at hinge E. ME=0 4.5 2 15x 151.875 +MB-60.875x 4.5-0 M,-122.0625 kN·m