Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_62

⚡ Mecademy AIENG정역학 · ch4  Problem Statement A space truss is constructed in the form of a cube with six diagonal members shown. Verify that the truss is internally stable. If the truss is subjected to the compressive forces applied at and along the diagonal , determine the forces in members and . Problem 4/62 (a) Internal Stability Verification 1. Formula for Determinacy: For a space truss to be internally stable and statically determinate, it must satisfy the relation , where is the number of members and is the number of joints. 2. Substitution: Number of joints, (the vertices of the cube). Number of members, . 3. Calculation: Since , the condition is satisfied. 4. Result: Furthermore, the arrangement of diagonals (one per face) makes each of the six faces a rigid planar structure. A closed box composed of rigid faces is itself a rigid structure. ● Final Conclusion: The truss satisfies the necessary condition for static determinacy and is internally stable because its arrangement of diagonals provides rigidity to all faces of the cube. (b) Calculation of Member Forces and 1. Formula: Apply equilibrium equations , , and at the joints. The compressive force at acts towards : . The force at acts towards : . PF DFDEFEG m=3j−6m j j=8 m=12 edges+6 diagonals=18 3j−6=3(8)−6=24−6=18 m=18 EFEG F =∑ x 0F =∑ y 0F =∑ z 0 PFDP = F (−1,1,−1) 3 P DFP = D (1,−1,1) 3 P 2. Substitution and Joint Analysis: At joint : At joint : By symmetry and sequential joint equilibrium (): From joint : Fro