Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_118

⚡ Mecademy AIENG정역학 · ch4  Problem Statement Determine the forces in members , , and of the loaded truss. Problem 4/118 (a) Determination of Support Reactions 1. Formula: Due to the symmetry of both the truss geometry and the applied loading about the vertical center line through node , the vertical reactions at the supports and are equal. 2. Substitution: The total downward load is the sum of all individual loads at the top joints: 3. Calculation: Since the loading and geometry are symmetric: 4. Result: , . ● Final Conclusion: The reaction at support is acting vertically upward. (b) Analysis of Joint B and Member Force AH 1. Formula: We first analyze joint to identify any zero-force members. At joint , only vertical member and diagonal member meet. Since the load at is vertical, the horizontal component of member force must be zero. Then, for the vertical section containing nodes , , and , we take the moment CHAHCD=BC=CD =DEEF DA G F = ∑ y 0⟹R + A R − G P = ∑ i 0 P = ∑ i 1.5+3+3+3+1.5=12 kN R = A R = G = 2 12 kN 6 kN↑ R = A 6 kNR = G 6 kN A6 kN BB ABBCB BC F = ∑ x 0⟹F cosθ = BCBC 0⟹F = BC 0 ABC about node to find . 2. Substitution: Let be the origin . Based on the dimensions, is at , is at , and is at . 3. Calculation: 4. Result: (Tension). ● Final Conclusion: The force in member is in tension. (c) Determination of Forces in Members CD and CH 1. Formula: Using a vertical section through members , , and , we apply equilibrium to the left portion of the truss. Let be the angl