Question

100 lb 3" Question #2 (4 pts.): The bracket at left has a uniform thickness of 2 inches, and unit weight of 1.75 lb/in3. The support of 0.35 with the floor, while the roller support at point B is frictionless. Determine the reactions in its supports at points A and B and whether the support at A will slip. at point A has a coefficient of friction

Answer 1

Draw the free body diagram of the bracket. 100 lb Cr 1.5 13.46 6,93 , , Calculate the horizontal position of center of gravity of the given shape from point A.

7-44-4X2-443 A+A2-4 (0.5x3.46 x6)| ocos 30% 3.46 sin 30° 6x8)(6.93-1xcos30°)-(π×(1.5)*)(6.93) (0.5x3.46x6)+(6x8)-x(1.5) 5.418 in 5.42 in Calculate the weight of the bracket. (1.75) (0.5x3.46x6)+(6x8)-(rxi3)(2)(981) 1761.78 lb Take the net moment about point B. Nx6.93-Wx (6.93-5.42)0 yWx(6.93-5.42) 6.93 (1761.78)x(6.93-5.42) 6.93 383.8811b Write the balanced force equation in vertical direction.

N4+N 1761.78+100x cos 30° 383.88+NB-1848.41b N 1464.521b Calculate the net force in horizontal direction at point A. FPsin 30 100x sin 30 501b Calculate the maximum friction force that can act at point A. -(0.35) (383.88) -134.361b Since, limiting value of friction force is much greater than the net force in horizontal direction(f,) n>(Z)H. Therefore, mction is sufficient to oppose the sliding motion at point A. Therefore, the support at A will NOT slip.