Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_34

⚡ Mecademy AIENG정역학 · ch6  Problem Statement The uniform rod with center of mass at G is supported by the pegs A and B, which are fixed in the wheel. If the coefficient of friction between the rod and pegs is , determine the angle through which the wheel may be slowly turned about its horizontal axis through O, starting from the position shown, before the rod begins to slip. Neglect the diameter of the rod compared with the other dimensions. Problem 6/34 (a) Determination of the slipping angle 1. Formula: We establish the equilibrium equations for the rod at the moment of impending slip. Let the -axis be directed along the rod and the -axis be perpendicular to it. Based on the diagram, peg is at distance to the left of the vertical centerline, and peg is at distance to the right. The center of mass is at a distance to the right of peg . Relative to the center of mass , the positions of the pegs are: Peg is above the rod, exerting a downward normal force . Peg is below the rod, exerting an upward normal force . The equilibrium equations are: At impending slip: 2. Substitution: From the moment equilibrium about : μθ θ xy Aa BaGb BG x = B −b,x = A −(2a+b) AN A B N B F = ∑ x 0:F + A F − B Wsinθ=0 F = ∑ y 0:N − B N − A Wcosθ=0 M = ∑ G 0:N (2a+ A b)−N (b)= B 0 F = A μN ,F = AB μN B G N = B N b 2a+b A Substitute this into the force equilibrium in the -direction: Now find : 3. Calculation: Calculate the total normal force: Substitute the friction relations into the -direction equili