Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_119

⚡ Mecademy AIENG정역학 · ch5  Problem Statement Construct the shear and moment diagrams for the beam subjected to the concentrated force and couple and the triangular load. State the maximum magnitude of the bending moment within the beam. Problem 5/119 (a) Calculation of Support Reactions ● Calculation Process 1. Present Final Formula: We model the beam with coordinates starting from the left end at . The beam has a total length of . The supports are located at () and (). The triangular distributed load starts at with intensity and ends at point ( ) where the intensity is zero. The resultant of the triangular load is: It acts at the centroid of the triangle, which is of the base from the left end: Other loads include a concentrated clockwise couple at and a concentrated downward force at the right end . 2. Substitute Values into Equilibrium Equations: Summing moments about support (): Summing moments about support (): 3. Partial Operations: From : x=0L=2+16+4+6=28 ft Ax=2 ftCx=18 ft x=0w = 0 300 lb/ftCx=18 ft F = tri w L = 2 1 0tri (300 lb/ft)(18 ft)= 2 1 2700 lb 3 1 =xˉ tri = 3 18 ft 6 ft M = 0 1500 lb-ftx= 22 ftP=1200 lbx=28 ft Cx=18 ft M = ∑ C 0⇒−R (16)+ A 2700(18−6)−1500−1200(10)=0 Ax=2 ft M = ∑ A 0⇒R (16)− C 2700(6−2)−1500−1200(28−2)=0 M =∑ C 0 −16R + A 32400−1500−12000=0⇒16R = A 18900⇒R = A 1181 From : 4. Verification: ● Final Conclusion: The reactions at the supports are (upward) and (upward). (b) Shear-Force and Bending-Moment Diagrams ● Calculation Process 1. Present