Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_120

⚡ Mecademy AIENG정역학 · ch5  Problem Statement Draw the shear and moment diagrams for the cantilever beam subjected to the combination of distributed and point loads. State the distance to the left of where the bending moment is zero. Problem 5/120 (a) Determination of Reactions at Support A 1. Present Final Formula: From equilibrium of the entire beam, we sum vertical forces and moments about support . Let be measured from the left free end (). 2. Substitute Values: The downward distributed load is , acting at its centroid (which is from ). The upward point load is at ( from ). The applied moment at the left end is (Counter-clockwise). 3. Partial Operations: Vertical reaction: (The reaction is downward). Moment reaction: (The reaction is clockwise). 4. Result: (downward), (clockwise). ● Final Conclusion: The reaction at support consists of a downward vertical force of and a clockwise moment of . (b) Shear Force and Bending Moment Diagrams bA AxL=13 m F = ∑ y 0, M = ∑ A 0 W=2 kN/m×6 m= 12 kNx=3+3=6 m13−6=7 mA P=35 kNx=11 m2 mA M = 0 15 kN⋅m F = ∑ y −12+35+R = A 0 M = ∑ A 15−12(7)+35(2)+M = A_react 0 R = A 12−35=−23 kN23 kN 15−84+70+M = A_react 0⇒1+M = A_react 0⇒M = A_react −1 kN⋅m1 kN⋅m R = A 23 kNM = A 1 kN⋅m A 23 kN1 kN⋅m 1. Formula: The shear and bending moment are determined by integrating the load and shear functions respectively, starting from the left free end where and (using the convention where CCW applied moment at left end is positive). 2. Substitution: : , : ; : ;