Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_9

⚡ Mecademy AIENG정역학 · ch4  Problem Statement Determine the force in each member of the loaded truss. Make use of the symmetry of the truss and of the loading. Given Data: Loads: downward at joint , downward at joint , and downward at joint . Horizontal dimensions: . Vertical dimensions: . Supports: Pin at , roller at . Problem 4/9 (a) Support Reactions and Symmetry Analysis 1. Formula: Due to the vertical symmetry of the truss geometry and loading about the central axis passing through members , the vertical reactions at the supports must be equal. Total vertical force balance: . 2. Substitution: Total vertical load: . By symmetry: . 3. Calculation: (upward) (upward) Horizontal reaction at pin : . 4. Result: , , . ● Final Conclusion: The support reactions are upward at both and . Due to symmetry, member forces will satisfy: , , , 30 kNH60 kNG30 kN F AH=HG=GF=FE=5 m BH=CG=DF=4 m AE CG F =∑ y 0⟹R + A R = E P ∑ i P = total 30+60+30=120 kN R = A R = E 2 120 kN R = A 60 kN R = E 60 kN AF =∑ x 0⟹A = x 0 R = A 60 kNR = E 60 kNA = x 0 60 kNAE F = AB F ED F = AH F EF F = BH F DF , , and . (b) Analysis of Joint A and Joint H 1. Formula: Apply equilibrium equations at joint and then joint . Let be the angle of member with the horizontal: . 2. Substitution: Joint : ; . Joint : ; . 3. Calculation: . . From Joint : (Tension). From Joint : (Tension). 4. Result: , , , . ● Final Conclusion: Member forces are: is in compression, and are in tension, and is in tension. (c) Analysis of Joint B a