Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_127

⚡ Mecademy AIENG정역학 · ch6  Problem Statement The uniform bar and attached cable of Prob. 6/104 are repeated here. If the coefficient of static friction between the cable and the small fixed peg is , determine the maximum angle for which equilibrium is possible. [Referencing Prob. 6/104: A light cable of total length is connected to the ends of a uniform bar of length . In the initial horizontal position, the peg is at a height directly above the midpoint of the bar.] Problem 6/127 (a) Calculation of the maximum angle 1. Formula: Total cable length from the initial horizontal configuration (Prob. 6/104a): For equilibrium of the bar, its center of mass must lie directly below the support peg . Thus, the median of triangle must be vertical. From the geometry, the tilt angle is related to the side lengths , bar length , and median length by: where . The tension ratio for equilibrium is . Slipping is avoided if: where is the wrap angle. For a cable passing over a peg with interior angle , the wrap angle is . Impending slip occurs at the maximum angle when . 2. Substitution: μ = s 0.20 θ L c L=0.6 m CH=0.3 m θ L = c 2 H + 2 ( 2 L ) 2 G CCMABC θL ,L AB L m sinθ= 2Lm L−L A 2 B 2 m= − 2 L +L A 2 B 2 4 L 2 = T B T A L B L A ≤ T B T A e μ β s βC β=π−C = L B L A e μ (π−C) s , , . . Let . Then and . From the Law of Cosines, the relationship for angle is: 3. Calculation: Solve numerically for : Calculate the wrap angle and ratio : Determine cable lengths and : Calculate the median length