Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_51

⚡ Mecademy AIENG정역학 · ch4  Problem Statement The base of an automobile jackstand forms an equilateral triangle of side length 10 in. and is centered under the collar A. Model the structure as one with a ball and socket at each joint and determine the forces in members BC, BD, and CD. Neglect any horizontal reaction components under the feet B, C, and D. Problem 4/51 (a) Force in members BC, BD, and CD 1. Formula: First, we determine the geometry of the jackstand. Let the origin be the centroid of the equilateral triangle base . The vertical height is and the side length is . The distance from the centroid to each vertex (radius of the circumscribed circle) is: The length of the slanted members () is: From vertical equilibrium at joint , the vertical component of the force in each slanted member () is: The horizontal radial component of the force pushing outward at each base joint is: At base joint , the force is balanced by members and : 2. Substitution: Substitute , , and : O BCDh=16 in. s=10 in. R= 3 s AB,AC,AD L= h+R 22 A F s F = s,z (where P = 3 P 800 lb) F= H F tanθ= s,z F s,z ( h R ) BF H BCBD F = H 2F cos30⇒ base ∘ F = base 3 F H s=10 in.h=16 in.P=800 lb R= ≈ 3 10 5.7735 in. 3. Calculation: Calculate : Calculate : 4. Result: ● Final Conclusion: By symmetry, the forces in all three base members are equal. Since the slanted members are in compression and push the joints outward, the base members must be in tension to maintain equilibrium. The force in each base member i