Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_85

⚡ Mecademy AIENG정역학 · ch5  Problem Statement Calculate the supporting force and moment at for the loaded cantilever beam. Problem 5/85 (a) Supporting force at the fixed support 1. Formula: The supporting vertical force must balance the total equivalent concentrated force of the distributed load. 2. Substitution: The load is uniform with acting over the length from to . 3. Calculation: Determine the length of the loaded section: Calculate the magnitude: Convert to kilonewtons: 4. Result: ● Final Conclusion: The supporting vertical force at point is acting upward. (b) Supporting moment at the fixed support 1. Formula: The reaction moment must balance the moment produced by the distributed load about point . where is the distance from point to the centroid of the distributed load. R A M A A R A A R A F F = ∑ y 0⟹R − A F=0⟹R = A w (x)dx ∫ x 1 x 2 w=600N/m x=4mx=8m R = A 600N/m×(8m−4m) L = load 8−4=4m R = A 600×4=2400N R = A 2.4kN 2.4kN AR = A 2.4kN M A A M A A M = ∑ A 0⟹M − A F⋅=xˉ0⟹M = A F⋅xˉ xˉA 2. Substitution: Equivalent force Distance to centroid 3. Calculation: Compute product: Convert to kilonewton-meters: 4. Result: ● Final Conclusion: The supporting moment at point is acting in the counter-clockwise direction. ✨ Final Answer Summary (a) (b) Mecademy AI Solution · ENGProblem 5/85 F=2400N =xˉ4m+ = 2 4m 6m M = A 2400N×6m M = A 14400N⋅m M = A 14.4kN⋅m 14.4kN⋅m AM = A 14.4kN⋅m R = A 2.4kN M = A 14.4kN⋅m