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Given: A painter weighing Wman = 180 lb stands on a ladder. The uniform ladder has weight Wladder = 40 lb. The center of gravity (C.G.) of the painter is located at a = 2.5 ft and b = 6.0 ft. Let L = 6 ft and H = 12 ft. Req'd: Determine the magnitude of the reaction force at B. Assume that Point A acts as a roller and Point B acts as a pinned support. |
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Sol'n: Draw a FBD of the man-ladder system. Since Point A acts as a roller, its only reaction force is in the x-direction RAx. Point B (a pin) has reaction forces in both x- and y-directions, RBx and RBy. The weight of the man Wman acts at the C.G. of the man while that of the ladder acts at its mid-point (C.G.), L/2 and H/2. Applying equilibrium:
= RBx = 47.5 lb Magnitude of reaction at B: RB = (RBx2 + RBy2)1/2 RB = 225 lb |
 FBD of Ladder |
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