Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_117

⚡ Mecademy AIENG정역학 · ch5  Problem Statement Draw the shear and moment diagrams for the beam shown. Determine the distance , measured from the left end, to the point where the bending moment is zero between the supports. Problem 5/117 (a) Determination of Support Reactions 1. Formula: Apply equilibrium equations for the entire beam. Let the pin support at the left end be and the roller support be . 2. Substitution: The total length of the beam is . The total uniform load is , acting at the center of the beam . Sum of moments about : Sum of vertical forces: 3. Calculation: (upward) (upward) 4. Result: , . ● Final Conclusion: The reaction at the left pin support is and the reaction at the roller support is . (b) Shear and Bending Moment Diagrams 1. Formula: Derive expressions for shear and moment by sections. 2. Substitution: b AB M = ∑ A 0, F = ∑ y 0 L=6+ ′ 3= ′ 9 ′ W=wL=100 lb/ft×9= ′ 900 lb x=4.5 ′ AR (6)− B (900)(4.5)=0 R+ A R − B 900=0 6R = B 4050⇒R = B 675 lb R = A 900−675=225 lb R = A 225 lbR = B 675 lb 225 lb 675 lb V(x)M(x) V= − w dx, M = ∫V dx ∫ Segment 1 (): (assuming ) Segment 2 (): (to satisfy ) 3. Calculation: Identify critical values for plotting. Shear : starts at , crosses zero at , reaches at . Jumps to at , then decreases linearly to at . Moment : starts at , reaches maximum positive value at . Reaches at the roller, then returns to at the free end . 4. Result: The shear diagram consists of two linear segments with a jump at the roller. The moment diagram co