Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_52

⚡ Mecademy AIENG정역학 · ch6  Problem Statement The large turnbuckle supports a cable tension of . The screws have a mean diameter of and have five square threads per inch. The coefficient of friction for the greased threads does not exceed . Determine the moment applied to the body of the turnbuckle (a) to tighten it and (b) to loosen it. Both screws have single threads and are prevented from turning. Problem 6/52 (a) Moment to Tighten the Turnbuckle 1. Present Final Formula: The total moment required to tighten the turnbuckle is the sum of the moments required for the two screws (one right-hand and one left-hand). For each screw, the moment is . Thus, the total moment is: 2. Substitute Values: Cable tension, Mean diameter, Number of threads per inch, Pitch, For single threads, Lead Helix angle tangent, Coefficient of static friction, 3. Partial Operations: Helix angle Friction angle 10,000 lb1 -in. 4 1 1.150 in. 0.25M M M = 1 tan(φ+ 2 Td α) M=2× tan(φ+ 2 Td α)=T d ( 1−μtanα tanα+μ ) T=10,000 lb d=1.150 in. n=5⟹p= = 5 1 0.2 in. L=p=0.2 in. tanα= = πd L π(1.150) 0.2 μ=0.25 M= (10,000 lb)(1.150 in.) [ 1−0.25 ( 1.150π 0.2 ) +0.25 1.150π 0.2 ] tanα= ≈ 1.150π 0.2 0.05536 α=arctan(0.05536)≈3.169 ∘ φ=arctan(0.25)≈14.036 ∘ Tightening angle 4. Final Calculation: Converting to : ● Final Conclusion: The moment required to tighten the turnbuckle is approximately (or ). (b) Moment to Loosen the Turnbuckle 1. Present Final Formula: The total moment required to loosen the turnbuckle (to over