Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_126

⚡ Mecademy AIENG정역학 · ch6  Problem Statement The band wrench is useful for loosening and tightening such items as the whole-house water filter E shown. Assume that the teeth of the wrench do not slip on the band at point C and that the band is slack from C to its end D. Determine the minimum coefficient of static friction for which the band will not slip relative to the fixed filter. Problem 6/126 (a) Analysis of Band and Handle Equilibrium 1. Formula: To determine the minimum coefficient of static friction , we apply the belt friction formula for impending slip: where and are the tensions at the ends of the band wrap, and is the wrap angle in radians. Based on the geometry of the strap wrench, we also use the moment equilibrium of the handle about the contact point : 2. Substitution and Geometric Identification: Filter radius . Lever arm of force from the center is . The contact point is at the 3 o'clock position, so the horizontal distance from to is . The band is attached to the handle at and gripped at . From the diagram, the band wraps almost completely around the filter. We assume a full wrap, so radians. From the handle's head geometry, the tension acts at an offset from . Let the vertical distance from the handle centerline (point ) to point be . From the μ μ = T 2 T 1 e μβ T 1 T 2 β A M = ∑ A 0 r=55 mm POL=250 mm A AP250 mm−55 mm=195 mm BC β≈2π T B A ABh drawing's proportions and labels, we can assume for the head's functional width. 3. Calculation: For the handle i