Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_74

⚡ Mecademy AIENG정역학 · ch4  Problem Statement The clamp is adjusted so that it exerts a pair of 200-N compressive forces on the boards between its swivel grips. Determine the force in the threaded shaft and the magnitude of the pin reaction at . Problem 4/74 (a) Force in the threaded shaft ● Calculation Process 1. Formula: Considering the equilibrium of the upper jaw member , we take the sum of moments about the pivot pin to eliminate the unknown reaction forces at that point. where is the reaction force from the board on the jaw at , is the horizontal distance from to , is the force in the threaded shaft, and is the vertical distance from the horizontal line of to the shaft . 2. Substitution: From the geometric analysis of the diagram (assuming lies on the centerline of the boards): Clamping force (upward) Horizontal distance Vertical distance Substituting these values: 3. Calculation: BC D BC ABDE D M = ∑ D 0⇒F ⋅ E x − E F ⋅ BC ∣y ∣= B 0 F E Ex E DEF BC ∣y ∣ B DBC D F = E 200 N x = E 35 mm+40 mm=75 mm ∣y ∣= B 10 mm (centerline to F)+ 30 mm (F to BC)=40 mm 200 N⋅75 mm−F ⋅ BC 40 mm=0 15000 N⋅mm=40 mm⋅F BC F = BC = 40 15000 375 N Since the force at must create a clockwise moment to balance the counter-clockwise moment from the clamping force at , the shaft must push point to the left. This indicates the shaft is in compression. 4. Result: (Compression) ● Final Conclusion: The force in the threaded shaft is in compression. (b) Magnitude of the pin reaction at ● Calculation Proc