Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_114

⚡ Mecademy AIENG정역학 · ch5  Problem Statement Draw the shear and moment diagrams for the linearly loaded cantilever beam and specify the bending moment at the support . Problem 5/114 (a) Support Reactions and the Bending Moment 1. Present Final Formula: The resultant force of the triangular distributed load and the reaction moment are found by equilibrium: where is the load intensity at distance from the fixed support . 2. Substitute Values: 3. Partial Operations: Calculate resultant : Calculate reaction moment : 4. Final Calculation: The vertical reaction at is (upward). The reaction moment at the support is (counter-clockwise). ● Final Conclusion: The bending moment reaction at the support is in the counter-clockwise direction. M A A M A R M A R= w (x)dx ∫ 0 l M = A x⋅ ∫ 0 l w(x)dx w(x)= x l w 0 xA R= x dx ∫ 0 l ( l w 0 ) M = A x x dx ∫ 0 l ( l w 0 ) RR= = l w 0 [ 2 x 2 ] 0 l 2 w l 0 M A M = A = l w 0 [ 3 x 3 ] 0 l 3 w l 0 2 AA = y R= w l 2 1 0 M = A w l 3 1 0 2 AM = A w l 3 1 0 2 (b) Shear-Force and Shear-Force Diagram 1. Present Final Formula: The shear force at any section is given by the vertical reaction at minus the accumulated load to the left of the section: 2. Substitute Values: 3. Partial Operations: 4. Result: The shear force diagram is a downward parabola: At , At , ● Final Conclusion: The shear-force distribution is , representing a parabolic curve starting at and dropping to zero at the free end. (c) Bending Moment and Bending-Moment Diagram 1. Present Final F