Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_53

⚡ Mecademy AIENG정역학 · ch6  Problem Statement A compressive force of 600 N is to be applied to the two boards in the grip of the C-clamp. The threaded screw has a mean diameter of 10 mm and advances 2.5 mm per turn. The coefficient of static friction is 0.20. Determine the force which must be applied normal to the handle at in order to (a) tighten and (b) loosen the clamp. Neglect friction at point . Problem 6/53 (a) Force to tighten the clamp 1. Formula: For a square-threaded screw, the torque required to raise a load (tighten) is given by: The applied force is related to the torque by , where is the handle length. 2. Substitution: Axial load Mean diameter , so mean radius Lead Coefficient of static friction Handle length Helix angle : Substituting into the force equation: 3. Calculation: Numerator: F CA F M M=W⋅r⋅tan(α+φ)= s W⋅r⋅ 1−μ tanα s tanα+μ s FM=F⋅L h L h W=600 N d=10 mmr=5 mm L=2.5 mm μ = s 0.20 L = h 100 mm αtanα= = πd L 10π 2.5 F= = L h W⋅r ( 1−μ s πd L +μ πd L s ) 100 600⋅5 ( 1−0.20⋅ 10π 2.5 +0.20 10π 2.5 ) tanα= ≈ 10π 2.5 0.07958 0.07958+0.20=0.27958 Denominator: Bracket term: Final calculation: 4. Result: ● Final Conclusion: The force required at the handle to tighten the clamp and achieve a 600-N compressive force is . (b) Force to loosen the clamp 1. Formula: The torque required to lower a load (loosen) when the screw is self- locking () is: The required force is . 2. Substitution: 3. Calculation: Numerator: Denominator: Bracket term: Final calculation: 4. Re