Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_20

⚡ Mecademy AIENG정역학 · ch6  Problem Statement The right-angle body is to be withdrawn from the close-fitting slot by the force . Find the maximum distance from the horizontal centerline at which may be applied without binding. The body lies in a horizontal plane, and friction underneath the body is to be neglected. Take the coefficient of static friction along both sides of the slot to be . Problem 6/20 (a) Determination of the maximum distance ● Calculation Process 1. Present Final Formula: The condition for impending motion without binding (jamming) is found by setting the applied force equal to the total static friction force generated by the tilting moment. For a symmetric contact at the corners of a slot of length , the maximum distance is given by: 2. Substitute Values: To derive this, we establish the equilibrium of the body at the moment it is just about to slip (impending motion). Assume contact at the top-left corner (Point ) and bottom-right corner (Point ) of the slot. At point : Normal force acts downward, and friction acts to the left. At point : Normal force acts upward, and friction acts to the left. Force acts to the right at a distance above the centerline. Force equilibrium equations: P yP μ s y P by y = max 2μ s b A B A(0,c/2)N A F = A μN sA B(b,−c/2)N B F = B μN sB Py F = ∑ y 0⟹N − B N = A 0⟹N = A N = B N F = ∑ x 0⟹P−F − A F = B 0⟹P=μ N + sA μ N = sB 2μ N s 3. Partial Operations: Taking moments about the center of the slot : Notice that the friction momen