Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_109

⚡ Mecademy AIENG정역학 · ch5  Problem Statement Draw the shear and moment diagrams for the loaded beam. What are the values of the shear force and bending moment at the middle of the beam? Problem 5/109 (a) Support Reactions ● Calculation Process 1. Present Final Formula: To find the reaction at support , we apply the moment equilibrium equation about point . Then, we use the force equilibrium equation in the vertical direction to find the reaction at support . 2. Substitute Values: Assuming upward forces and counter-clockwise moments as positive for the equilibrium equations: 3. Partial Operations: Solving for : Solving for : 4. Final Calculation: B A A M = ∑ A 0, F = ∑ y 0 M = ∑ A (1000 lb)(3 ft)+2100 lb-ft−B (9 ft)= y 0 F = ∑ y A − y 1000 lb+B = y 0 B y 3000+2100=9B y 5100=9B y B = y ≈ 9 5100 566.67 lb A y A = y 1000−566.67=433.33 lb A = y 433.3 lb(↑) B = y 566.7 lb(↑) ● Final Conclusion: The vertical reactions at the supports are and . (b) Shear Force and Bending Moment at the Middle ● Calculation Process 1. Present Final Formula: The middle of the beam is at from point . We cut the beam at this point and consider the equilibrium of the left portion. 2. Substitute Values: The cut is between the load and the concentrated couple. 3. Partial Operations: Calculate : Calculate : 4. Final Calculation: ● Final Conclusion: At the middle of the beam (), the shear force is and the bending moment is . (c) Shear and Bending Moment Diagrams ● Calculation Process 1. Present Final Formula