Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_107

⚡ Mecademy AIENG정역학 · ch5  Problem Statement Draw the shear and moment diagrams for the beam subjected to the end couple. What is the bending moment at a section 0.5 m to the right of ? Problem 5/107 (a) Determination of Support Reactions ● Calculation Process 1. Present Final Formula: We apply the equations of static equilibrium for the entire beam. Let be the pin support at the left end () and be the roller support at distance from . The clockwise couple is applied at the free end of the overhang, to the right of . 2. Substitute Values: Taking moments about support (counter-clockwise as positive): Summing vertical forces: 3. Partial Operations: Solving for : Solving for : 4. Final Calculation: The reactions are: MB Ax=0B 2 mAM = 0 120 N⋅m 2 mB M = ∑ B 0, F = ∑ y 0 B M = ∑ B −A (2)+ y 120=0 F = ∑ y A + y B = y 0 A y 2A = y 120⟹A = y 60 N (upward) B y 60+B = y 0⟹B = y −60 N (downward) A = y 60 N↑,B = y 60 N↓ ● Final Conclusion: The support reactions are acting upwards and acting downwards. (b) Shear and Moment Diagrams ● Calculation Process 1. Present Final Formula: Define the shear force and bending moment as functions of distance from the left end . For : For : 2. Substitute Values: For the first segment (): For the second segment (): 3. Partial Operations: Simplifying the moment expression for the second segment: Key values for the diagrams: At : , At : , At : , At : , (balanced by the external CW couple) 4. Final Calculation: The shear diagram consists of a rectangle of