Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_112

⚡ Mecademy AIENG정역학 · ch5  Problem Statement Determine the shear force and bending moment in the beam at a section 2 ft to the right of end . Problem 5/112 (a) Determination of Shear Force at 1. Formula: First, find the reaction at support using moment equilibrium of the entire beam. Then, use the vertical force equilibrium for a section of the beam from to : 2. Substitution: Total length . Total triangular load . Resultant distance from , . Reaction at : . Load intensity at (by similar triangles): . Load on segment: . 3. Calculation: 4. Result: VM A Vx=2 ft A x=0x=2 ft M = ∑ B 0⇒R ⋅ A L−W ⋅ total =xˉ B 0 F = ∑ y 0⇒V=R − A W segment L=6 ft W = total ⋅ 2 1 6 ft⋅400 lb/ft=1200 lb B =xˉ B ⋅ 3 1 6 ft=2 ft AR ⋅ A 6−1200⋅2=0⇒R = A 400 lb x=2 ftw = 2 ⋅ 6 2 400= lb/ft 3 400 W = segment ⋅ 2 1 2 ft⋅ lb/ft= 3 400 lb 3 400 V=400− 3 400 V= = 3 1200−400 3 800 V=266.666...≈267 lb 267 lb ● Final Conclusion: The shear force at a section 2 ft to the right of end is . (b) Determination of Bending Moment at 1. Formula: Apply moment equilibrium about the cut at : where is the distance from the cut to the centroid of the triangular load segment. 2. Substitution: , . . Centroid of the segment load from the cut: . 3. Calculation: 4. Result: ● Final Conclusion: The bending moment at a section 2 ft to the right of end is . ✨ Final Answer Summary (a) (b) Mecademy AI Solution · ENGProblem 5/112 VA267 lb Mx=2 ft x=2 ft M = ∑ cut 0⇒M=R ⋅ A x−W ⋅ segment d d R = A 400 lbx=2 ft W = segment lb 3 400 d= ⋅ 3