Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_13

⚡ Mecademy AIENG정역학 · ch4  Problem Statement Determine the forces in members , and of the loaded truss. All triangles are . Problem 4/13 (a) Force in member 1. Formula: Joint is a simple connection of three members , , and . Equilibrium in the vertical direction: . 2. Substitution: Since and are horizontal and collinear, and there is no external load at joint , the force in the vertical member must be zero. 3. Calculation: No further calculation needed as it is a zero-force member. 4. Result: ● Final Conclusion: The force in member is . (b) Force in member 1. Formula: First, find the external reactions. Total span . Taking moments about : At joint , equilibrium of forces: . At joint , . 2. Substitution: From joint : . At joint , the vertical components of , , and must sum to zero: BJ,BI,CI,CH,DG,DHEG 45− ∘ 45− ∘ 90 ∘ BJ JAJJIBJ F =∑ y 0 AJJI JBJ F = ∑ y F = BJ 0 F = BJ 0 BJ0 BI L=18+ ′ 12= ′ 30 ′ A M = ∑ A 0⇒R (30)− F 7(18)=0⇒R = F 4.2 kips↑ F = ∑ y 0⇒R + A 4.2−7=0⇒R = A 2.8 kips↑ AF sin45+ AB ∘ R = A 0BF =∑ y 0 AF (1/ )+ AB 22.8=0⇒F = AB −2.8 kips (C) 2BF AB F BI F BJ (F sin45) − AB ∘ vertical push F sin45− BI ∘ F = BJ 0 3. Calculation: 4. Result: ● Final Conclusion: The force in member is . (c) Force in member 1. Formula: Analyze joint . Sum of vertical forces: . 2. Substitution: Member is in tension, so at joint , it pulls up and to the left. Its vertical component is . 3. Calculation: 4. Result: ● Final Conclusion: The force in member is . (d) Force in member 1. Formula: