Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_30

⚡ Mecademy AIENG정역학 · ch4  Problem Statement Determine the forces in members and of the symmetrically loaded truss. Problem 4/30 (a) Force in member 1. Formula: Based on the symmetry of the truss and loading, we first determine the support reactions. The total downward load is the sum of the loads applied at the joints: Due to symmetry, the vertical reaction at each support ( and ) is half the total load: To find the force in member , we apply the Method of Sections. We pass a vertical section through members , , and and consider the equilibrium of the left portion. For vertical equilibrium of the left portion: 2. Substitution: Substitute the known values of the reaction and external loads into the equilibrium equation: 3. Calculation: Simplify the expression to find : Sum of external vertical forces: The equation becomes: Since member is a diagonal (its angle is not zero), the only solution is for its force to be zero. 4. Result: CGGH CG P = total + 2 L L+L+ = 2 L 3L AF R = A R = F = 2 3L 1.5L CG CDCGGH F = ∑ y R − A P − A P + H F sinθ = CGCG 0 1.5L−0.5L−1.0L+F sinθ = CGCG 0 F CG 1.5L−0.5L−1.0L=0 0+F sinθ = CGCG 0 CGθ CG F = CG 0 ● Final Conclusion: The force in member is , making it a zero-force member under this specific symmetric loading condition. (b) Force in member 1. Formula: We use the same left portion from the section cut through , , and . To find the force in member directly, we sum the moments about joint , where members and intersect, eliminating them from the