Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_62

⚡ Mecademy AIENG정역학 · ch6  Problem Statement The design of a joint to connect two shafts by a flat 5° tapered cotter is shown by the two views in the figure. If the shafts are under a constant tension T of 200 lb, find the force P required to move the cotter and take up any slack in the joint. The coefficient of friction between the cotter and the sides of the slots is 0.20. Neglect any horizontal friction between the shafts. Problem 6/62 (a) Force P required to move the cotter ● Calculation Process 1. Identify Given Values and Constants: Tension in shafts: Taper angle: Coefficient of static friction: Friction angle: 2. Establish Equilibrium for the Cotter: The cotter is a wedge subjected to a horizontal squeezing force from the tension in the shafts. To move the cotter downwards (to take up slack), the applied force must overcome the vertical components of the contact forces (normal force and friction) on both faces. On the vertical face: The normal force is . The friction force opposing downward motion is . On the tapered face: The horizontal component of the resultant contact force must balance the shaft tension . The vertical force required to drive this side of the wedge is . 3. Present Final Formula: Summing the vertical forces required to move the cotter downwards: T=200lb α=5 ∘ μ = s 0.20 φ=tan(μ )= −1 s tan(0.20)≈ −1 11.31 ∘ T P N = 1 T F = 1 μ N = s1 Ttanφ T Ttan(φ+α) P=Ttanφ+Ttan(φ+α) P=T[tanφ+tan(φ+α)] 4. Substitute Values and Calculate: ● Final Conclusion: The f