Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_122

⚡ Mecademy AIENG정역학 · ch5  Problem Statement Draw the shear and moment diagrams for the beam loaded by the force applied to the strut welded to the beam as shown. Specify the bending moment at point . Problem 5/122 (a) Determination of Support Reactions 1. Formula: Apply the equilibrium equations for the entire beam assembly. 2. Substitution: Let the beam be oriented along the -axis with at , at , and the end of the beam at . The force applied at height creates a clockwise couple at the end of the beam. 3. Calculation: From the moment equation: (directed upwards) From the force equation: (directed downwards) 4. Result: ● Final Conclusion: The reaction at support is acting downwards, and the reaction at support is acting upwards. (b) Shear and Bending Moment Diagrams 1. Formula: Use the relations and for each segment of the beam. F B M = ∑ A 0, F = ∑ y 0 xAx=0B x=bx=2bFh M = C Fh M = ∑ A B (b)− y F(h)=0 F = ∑ y A + y B = y 0 B = y b Fh A = y −B = y − b Fh A = y − , B = b Fh y b Fh A b Fh B b Fh V=F ∑ vertical M=M ∑ cut 2. Substitution: For segment : ; For segment : ; 3. Calculation: Shear Diagram: Constant value of from to , then jumps to and remains from to . Moment Diagram: Linear decrease from at to at . It then remains constant at until the end of the beam at . At the very end, the applied clockwise couple closes the diagram to zero. 4. Result: ● Final Conclusion: The shear is constant negative in the first half and zero in the second. The bending moment is linearly negat