Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_116

⚡ Mecademy AIENG정역학 · ch4  Problem Statement All two-force members of the loaded truss are of the same length. Member BCD is a rigid beam. Determine the forces in members BG and CG in terms of the load L. Problem 4/116 (a) External Reactions Analysis ● Calculation Process 1. Present Final Formula: Since all two-force members have the same length , the joints form equilateral triangles. The span of the truss is . Joint is at a distance from . Taking moments about and using force equilibrium: 2. Substitute Values: 3. Partial Operations: From the moment equation: From the vertical force balance: (Assuming as there are no horizontal external loads). 4. Final Calculation: The reactions are (upward) and (upward). ● Final Conclusion: The reaction at the pin support is and at the roller support is . (b) Forces in Members AB and ED s AE=3sG sAA M = ∑ A 0, F = ∑ y 0 R ⋅ E (3s)−L⋅s=0 R + Ay R − E L=0 R = E = 3s L⋅s 3 L R = Ay L− = 3 L 3 2L R = Ax 0 R = Ay 3 2L R = E 3 L A 3 2L E 3 L ● Calculation Process 1. Present Final Formula: Using the method of joints at and . Members and are at and to the horizontal respectively. 2. Substitute Values: 3. Partial Operations: (The negative signs indicate compression). 4. Final Calculation: , . ● Final Conclusion: Member has a compressive force of and member has a compressive force of . (c) Forces in Members BG and CG ● Calculation Process 1. Present Final Formula: Analyze joint . The members and make angles of with the horizontal bottom chord. Due