Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_100

⚡ Mecademy AIENG정역학 · ch6  Problem Statement For the design of the band brake shown, find the couple required to turn the pipe in the V- block against the action of the flexible band. A force is applied to the lever, which is pivoted about . The coefficient of friction between the band and the pipe is , and that between the pipe and the block is . The weights of the parts are negligible. Problem 6/100 (a) Analysis of the lever and tension To find the tension in the flexible band at its attachment point , we analyze the equilibrium of the lever . We assume the lever is horizontal and the force is applied vertically. The band at is at an angle of to the vertical, as indicated by the radius to the tangency point. 1. Formula: 2. Substitution: From the diagram, the horizontal distance from the pivot to the line of action of is , and the horizontal distance to point is . Only the vertical component of the tension creates a moment about . 3. Calculation: 4. Result: ● Final Conclusion: The tension in the band at point is . (b) Analysis of the band friction and tension M P=25 lb O0.30 0.40 T A A OAPP A45 ∘ M = ∑ O 0 O P15 ′′ A4 ′′ T A O (P⋅15)−(T cos45⋅ A ∘ 4)=0 375−T ⋅ A 0.7071⋅4=0 375−2.8284T = A 0 T = A ≈ 2.8284 375 132.58 lb T = A 132.58 lb A132.58 lb T B The band wraps around the pipe from a vertical segment at the fixed support to the tangent point at from the vertical. We determine the tension at the fixed support when rotation of the pipe is impending. 1. Formula: Where is th