Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_115

⚡ Mecademy AIENG정역학 · ch6  Problem Statement The bar clamp is being used to clamp two boards together while the glue between them cures. What torque must be applied to the handle of the screw in order to produce an 80-lb compression between the boards? The -in.-diameter single-thread screw has 12 square threads per inch, and the effective coefficient of friction is 0.20. Neglect any friction in the pivot contact at . What torque is required to loosen the clamp? Problem 6/115 (a) Torque to produce an 80-lb compression 1. Formula: The torque required to tighten a square-thread screw (raise a load or increase compression) is given by: where: is the axial load (clamping force) is the mean radius of the screw is the friction angle, is the lead angle, 2. Substitution: Clamping force Mean diameter Mean radius Threads per inch , so pitch Single-thread screw implies lead Coefficient of friction Calculate angles: M 8 3 CM ′ M M M=Wrtan(φ+α) W r φφ=tan(μ) −1 αα=tan −1 ( πd L ) W=80 lb d= in= 8 3 0.375 in r= = 2 d 0.1875 in n=12p= in 12 1 L=p= in 12 1 μ=0.20 φ=tan(0.20)≈ −1 11.310 ∘ α= tan = −1 ( π⋅0.375 1/12 )tan ≈ −1 ( 4.5π 1 )4.047 ∘ Substitute into torque formula: 3. Calculation: 4. Result: ● Final Conclusion: The torque required to produce the 80-lb compression is . (b) Torque required to loosen the clamp 1. Formula: The torque required to loosen a square-thread screw is given by: 2. Substitution: Using the values from part (a): 3. Calculation: 4. Result: ● Final Conclusion: The to