Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_2

⚡ Mecademy AIENG정역학 · ch4  Problem Statement Determine the force in each member of the loaded truss. Problem 4/2 (a) Force in each member of the truss ● Calculation Process 1. Present Final Formula: First, convert the suspended mass to a gravitational force (weight) acting at joint : Next, apply equilibrium equations at joint . Assuming tension () is positive and compression () is negative: Finally, the force in the vertical member can be determined from equilibrium at joint : 2. Substitute Values: Using : From : Substitute into : B W=m⋅g BT C F = ∑ x −F sin30− AB ∘ F sin60= BC ∘ 0 F = ∑ y F cos30− AB ∘ F cos60− BC ∘ W=0 AC C F = ∑ y F + AC F cos60= BC ∘ 0 (considering equilibrium of joint C a g= 9.81 m/s 2 W=400 kg× 9.81 m/s= 2 3924 N F =∑ x 0 −F ⋅ AB (0.5)−F⋅ BC = ( 2 3 )0⟹F = AB − F 3 BC F =∑ y 0 (− F )⋅ 3 BC − ( 2 3 )F ⋅ BC (0.5)=3924 3. Partial Operations: Solve for : Solve for : Solve for at joint : 4. Final Calculation: Convert to kilonewtons and assign tension/compression: ● Final Conclusion: The forces in the members are (Tension), (Compression), and (Tension). ✨ Final Answer Summary (a) (T), (C), (T) Mecademy AI Solution · ENGProblem 4/2 F BC −1.5F − BC 0.5F = BC 3924 −2F= BC 3924⟹F = BC −1962 N F AB F = AB − ⋅ 3(−1962)=3398.3 N F AC C F + AC (−1962)⋅(0.5)=0⟹F = AC 981 N F = AB 3.398 kN≈3.40 kN (Tension) F = BC 1.962 kN (Compression) F = AC 0.981 kN (Tension) F = AB 3.40 kNF = BC 1.962 kNF = AC 0.981 kN F = AB 3.40 kNF = BC 1.962 kNF = AC 0.981 kN