Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_111

⚡ Mecademy AIENG정역학 · ch5  Problem Statement Draw the shear and moment diagrams for the loaded beam. Determine the values of the shear force and bending moment at midbeam. Problem 5/111 (a) Calculation of Support Reactions ● Calculation Process 1. Present Final Formula: To find the reactions at support and , we apply the equilibrium equations: 2. Substitute Values: Taking counter-clockwise (CCW) moments as positive: 3. Partial Operations: From the moment equation about : Substitute into the force equilibrium equation: 4. Final Calculation: The vertical reaction forces are: ● Final Conclusion: The reaction at support is upward, and the reaction at support is upward. (b) Shear Force Diagram and Value at Midbeam AB M = ∑ A 0, F = ∑ y 0 M = ∑ A 12B − y 4(2)−6(5)+7−5(10)=0 F = ∑ y A + y B − y 4−6−5=0 A 12B − y 8−30+7−50=0 12B − y 81=0⟹B = y = 12 81 6.75 kN B y A + y 6.75−15=0⟹A = y 8.25 kN A = y 8.25 kN,B = y 6.75 kN A8.25 kN B6.75 kN ● Calculation Process 1. Present Final Formula: The shear force at any section is calculated by summing the vertical forces to the left of the section: 2. Substitute Values: The total length of the beam is . Midbeam is at . For the interval : 3. Partial Operations: The shear force diagram values are: : : : : 4. Final Calculation: At (midbeam): ● Final Conclusion: The shear force at midbeam is . (c) Bending Moment Diagram and Value at Midbeam ● Calculation Process 1. Present Final Formula: The bending moment is obtained by integrating the shear force