Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_33

⚡ Mecademy AIENG정역학 · ch6  Problem Statement The homogeneous square body is positioned as shown. If the coefficient of static friction at B is 0.40, determine the critical value of the angle below which slipping will occur. Neglect friction at A. Problem 6/33 (a) Critical angle for slipping ● Calculation Process 1. Free Body Diagram and Force Analysis: Let be the weight of the square and its side length. The square is in equilibrium under the following forces: Weight acting vertically downwards at the center . Normal force at corner . Since friction is neglected at , is perpendicular to the wall. The wall makes an angle of with the horizontal to the left, which means its angle with the positive x-axis is . The normal force is thus directed at above the horizontal (pointing right): . Normal force and friction force at corner . is directed upwards, and is directed to the left to resist the horizontal component of . At the verge of slipping, . 2. Equilibrium Equations: From : From : Substitute these into the slipping condition : θ θ Ws WG N A AAN A 60 ∘ 60 ∘ 120 ∘ N A 30 ∘ N = A N (cos30i+ A ∘ sin30j) ∘ N B F B BN B F B N A F = B μ N = sB 0.40N B F =∑ x 0 N cos30− A ∘ F = B 0⟹F = B N A 2 3 F =∑ y 0 N + B N sin30− A ∘ W=0⟹N = B W− 2 N A F = B 0.40N B 3. Moment Equilibrium about B: We set the origin at corner . Based on the geometry, the coordinates of corner and center are: Sum of moments (taking counter-clockwise as positive): 4. Final Calculation: Substitute : ● Final Conclusi