Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_108

⚡ Mecademy AIENG정역학 · ch5  Problem Statement Draw the shear and moment diagrams for the diving board, which supports the 175-lb man poised to dive. Specify the bending moment with the maximum magnitude. Problem 5/108 (a) Calculation of Support Reactions 1. Formula: We apply the equations of static equilibrium for a rigid body: Let be the reaction at support A (assumed downward) and be the reaction at support B (assumed upward). The distance from A to B is . The total length from A to the man is . The distance from B to the man is . 2. Substitution: Taking moments about support B (counter-clockwise positive): Summing vertical forces (upward positive): 3. Calculation: From the moment equation: From the force equation: 4. Result: (acting downward), (acting upward). ● Final Conclusion: The reaction at support A is downward, and the reaction at support B is upward. (b) Shear-Force and Bending-Moment Diagrams 1. Formula: Using the method of sections, the internal shear force and bending moment are functions of position (where at A). M = ∑ B 0, F = ∑ y 0 R A R B d = AB 42 in. L=12 ft=144 in. d = B−man 144 in.−42 in.=102 in. R (42 in.)− A (175 lb)(102 in.)=0 −R + A R − B 175 lb=0 R = A = 42 175×102 = 42 17850 425 lb R = B R + A 175=425+175=600 lb R = A 425 lbR = B 600 lb 425 lb 600 lb V Mxx=0 2. Substitution: For : For : 3. Calculation: Key values for plotting: At : , At : , At : , At : , 4. Result: The shear diagram consists of two constant regions: for the first and for the remain