Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_25

⚡ Mecademy AIENG정역학 · ch4  Problem Statement The rectangular frame is composed of four perimeter two-force members and two cables and which are incapable of supporting compression. Determine the forces in all members due to the load in position (a) and then in position (b). Problem 4/25 (a) Force in members due to load in position (a) at joint 1. Formula: First, we determine which cable is active. A downward load at the right side of the frame ( or ) tends to elongate the diagonal and shorten the diagonal . Since cables cannot support compression, diagonal is slack: Next, we apply equilibrium equations at the joints. Let be the angle of the diagonal with the horizontal: 2. Substitution: Analyze Joint (load acts downward at ): Analyze Joint : 3. Calculation: From Joint with : From Joint : AC BD L LB BCAC BDBD F = BD 0 θ AC tanθ= = 3d 4d ⇒ 3 4 sinθ= ,cos θ = 5 4 5 3 BLB F = ∑ y 0⇒−L−F − BC F sinθ= BD 0 F = ∑ x 0⇒F − AB F cosθ= BD 0 C F = ∑ y 0⇒F + BC F sinθ= AC 0 F = ∑ x 0⇒−F − CD F cosθ= AC 0 BF = BD 0 −L−F − BC 0=0⇒F = BC −L=L (Compression) F − AB 0=0⇒F = AB 0 C −L+F (4/5)= AC 0⇒F = AC L= 4 5 1.25L (Tension) For member , since joints and are fixed pin supports on a rigid wall, the member does not carry any force required for the equilibrium of joints and : 4. Result: , , , , , ● Final Conclusion: Under load position (a), the diagonal cable is in tension with a force of , while cable is slack. The vertical member and horizontal member are in compression with magnitudes and re