Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_116

⚡ Mecademy AIENG정역학 · ch6  Problem Statement The cylinder weighs 80 lb and the attached uniform slender bar has an unknown weight . The unit remains in static equilibrium for values of the angle ranging up to but slips if exceeds . If the coefficient of static friction is known to be 0.30, determine . Problem 6/116 (a) Determination of weight ● Calculation Process 1. Analyze the geometry and forces: The system consists of a cylinder and a uniform bar acting as a single rigid body. Cylinder weight: acting at the center . Bar weight: acting at its center of mass, which is at a distance from center . At the impending slip angle , the friction forces and at the contact points reach their maximum values: and . The V-notch surfaces are at to the horizontal. This means the normal forces and are inclined at to the horizontal, or to the vertical. 2. Establish the Moment Equilibrium Equation about the center : To oppose the clockwise moment from the bar's weight, the friction forces must provide a counter- clockwise moment. Substitute and known values: 3. Establish Force Equilibrium Equations for the entire unit: Let be horizontal and be vertical. W θ45 ∘ θ 45 ∘ W W W = c 80 lbO Wd= = 2 L = 2 40 20 in.O θ=45 ∘ F A F B F = A μ N sA F = B μ N sB 60 ∘ N A N B 30 ∘ 60 ∘ O M = ∑ O 0:F R+ A F R− B Wdsinθ=0 F=μ N s μ R(N + sA N )= B W(20)sin45 ∘ 0.30(12)(N + A N )= B 20W(0.7071) 3.6(N + A N )= B 14.142W⟹(N + A N )= B 3.9284W x y 4. Combine equations to solve for : Substitute the expression f