Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_118

⚡ Mecademy AIENG정역학 · ch5  Problem Statement Plot the shear and moment diagrams for the beam loaded as shown. What are the values of the shear force and bending moment at B? Determine the distance b to the right of A where the bending moment equals zero for the first time. Problem 5/118 (a) Support Reactions at A and B ● Calculation Process 1. Equilibrium Equations: To find the reactions and , we apply the moment equilibrium about point and the force equilibrium in the vertical direction. Let the left end of the beam be at . Point load is at . Support is at . Support is at . Triangular distributed load starts at and ends at . Its resultant is acting at its centroid . Counter-clockwise couple acts at . 2. Moment Equilibrium about A (): (Note: Distances are relative to . Forces to the left of or causing CCW rotation are positive in this sum). Self-Correction: Let's re-verify the moment arm for the triangular load. It is at , and is at . The arm is . Correct. Let's re-check the signs. Taking about : R A R B A x=0 7 kNx=2 m Ax=5 m Bx=10 m x=12 mx=15 m F = D × 2 1 3×4=6 kNx = D 12+ (3)= 3 2 14 m M = C 30 kN⋅mx=15 m M =∑ A 0 (7 kN)(3 m)−R (5 m)+ B (6 kN)(9 m)−30 kN⋅m=0 AA 21−5R + B 54−30=0 5R = B 45⟹R = B 9 kN x=14 Ax=514−5=9 m ↺+A at left: at right: (assuming up) at right: Couple at right end: (upwards). 3. Force Equilibrium (): ● Final Conclusion: The reaction at support is (upward) and at support is (upward). (b) Shear Force and Bending Moment at B ● Calculation Process 1. Shea