Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_29

⚡ Mecademy AIENG정역학 · ch4  Problem Statement Determine the forces in members and of the loaded truss. Problem 4/29 (a) Force in member BC 1. Formula: We will use the Method of Sections. Cut the truss vertically through members and . Consider the equilibrium of the left portion of the truss (containing joints and ). To find the force in member , we sum the moments about joint to eliminate the unknown forces and : 2. Substitution: From the geometry, joint is to the left of , and joint is vertically above . Assuming is in tension: 3. Calculation: Divide the entire equation by : 4. Result: (Tension) ● Final Conclusion: The force in member is in tension. (b) Force in member CG 1. Formula: Using the same left section from part (a), we sum the forces in the vertical () direction. Since member is the diagonal of a square with side length , its angle with the horizontal is . BCCG BC,CG,GF A,B,GBC GF CG F GF M = ∑ G 0 A12 ftGB 12 ftGF BC +F ⋅ BC (12 ft)−(15 kips)⋅(12 ft)=0 12 ft F − BC 15 kips=0 F = BC 15 kips F = BC 15 kips BC15 kips yCG12 ft θ45 ∘ F = ∑ y 0 2. Substitution: Assuming is in tension (pulling up and to the right from joint ): 3. Calculation: 4. Result: (Tension) ● Final Conclusion: The force in member is in tension. ✨ Final Answer Summary (a) (b) Mecademy AI Solution · ENGProblem 4/29 F CG G F sin(45)− CG ∘ 15 kips=0 F ⋅ CG = 2 1 15 kips F = CG 15 kips 2 F ≈ CG 15×1.4142=21.213 kips F = CG 21.2 kips CG21.2 kips F = BC 15 kips (T) F = CG 21.2 kips (T)