Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_11

⚡ Mecademy AIENG정역학 · ch4  Problem Statement Determine the forces in members AB, BC, and BD of the loaded truss. Problem 4/11 (a) Force in member AB 1. Formula: First, determine the support reactions using global equilibrium equations for the entire truss. Let be the radius of the semicircle and be the applied horizontal load. 2. Substitution: Taking moments about joint : Summing vertical forces: Summing horizontal forces: Now, analyze Joint . The member acts as a straight two-force member at a angle. 3. Calculation: From the vertical equilibrium at joint : RL M = ∑ A 0, F = ∑ x 0, F = ∑ y 0 A M = ∑ A C (2R)− y L(R)=0⟹C = y (upward) 2 L F = ∑ y A + y C = y 0⟹A = y − (downward) 2 L F = ∑ x A + x L=0⟹A = x −L (to the left) AAD45 ∘ F = ∑ y A + y F sin(45)= AD ∘ 0 F = ∑ x A + x F + AB F cos(45)= AD ∘ 0 A − + 2 L F = AD ( 2 1 )0⟹F = AD 2 L 2 Substitute into the horizontal equilibrium: 4. Result: (Tension) ● Final Conclusion: The force in member is in tension. (b) Force in member BC 1. Formula: Apply the method of joints at joint or joint . At joint , summing forces in the horizontal direction: 2. Substitution: Substitute the value of found in part (a). 3. Calculation: Alternatively, at joint , summing vertical forces to find where chord is at : Summing horizontal forces at joint : 4. Result: (Tension) ● Final Conclusion: The force in member is in tension. F AD −L+F + AB = ( 2 L 2 )( 2 1 )0 −L+F + AB = 2 L 0 F = AB L− = 2 L 2 L F = AB 2 L AB 2 L BCB F = ∑ x 0⟹F − BC F = AB 0 F AB