Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_106

⚡ Mecademy AIENG정역학 · ch5  Problem Statement Draw the shear and moment diagrams for the loaded cantilever beam. State the value of the bending moment at midbeam. Problem 5/106 (a) Support Reactions at the Fixed End ● Calculation Process 1. Present Final Formula: We apply the equations of static equilibrium for a rigid body. 2. Substitute Values: Let be the vertical reaction force at (upward) and be the reaction moment (counter-clockwise). Sum of vertical forces: Sum of moments about : 3. Partial Operations: For force: For moment: 4. Final Calculation: The reactions are: ● Final Conclusion: The support reactions at the fixed end consist of an upward force of and a counter-clockwise bending moment of . (b) Shear and Bending Moment Diagrams ● Calculation Process F = ∑ y 0, M = ∑ A 0 R A AM A R− A P−P=0 AM − A P − ( 2 l )P(l)=0 R = A P+P=2P M = A + 2 Pl Pl= Pl 2 3 R = A 2P↑,M = A 1.5Pl↺ A 2P1.5Pl 1. Present Final Formula: Define sections at and . 2. Substitute Values: Segment 1 (): Segment 2 (): 3. Partial Operations: Simplifying the moment equations: Diagram Key Points: Shear (): Starts at , stays constant until , then drops to , stays constant until , then drops to . Moment (): Starts at at , increases linearly to at , then increases linearly with a smaller slope to at . 4. Final Calculation: The diagrams are composed of constant shear segments and linear moment segments. ● Final Conclusion: The shear force is for the first half and for the second half. The bending moment incr