Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_70

⚡ Mecademy AIENG정역학 · ch4  Problem Statement Determine the magnitude of the pin force at . The frame consists of a curved member of radius and an L-shaped member . A clockwise couple of is applied to member . The horizontal distance from the vertical line through to the vertical segment is . The vertical dimensions of member are as shown, with from the top corner to the moment and another from the moment to pin . Problem 4/70 (a) Magnitude of the pin force at ● Calculation Process 1. Identify Member Properties and Geometry: Member is pinned at and with no intermediate loads, making it a two- force member. The force it exerts on member at pin acts along the straight line . Assuming the curved member is a quarter-circle of radius , and placing the origin at , pin is located at . Member is an L-shaped rigid body. Pin is located horizontally from . Since the top corner is at height and pin is below it, the coordinates of are . For member , the equilibrium of forces implies . Thus, the magnitude of the force at is equal to the magnitude of the force at . 2. Moment Equilibrium Equation: Summing moments about point for member : Where (clockwise). The moment of (acting along line ) about can be found using the perpendicular distance from to line . The equation of line is or . The perpendicular distance from BOA 0.4 mAB200 N⋅ m ABO BC0.6 mAB0.4 m 0.4 mB B OAOA ABA OA R=0.4 m O(0,0)A(0.4 m,0.4 m) ABB0.6 m O0.4 mB0.4+0.4= 0.8 mB(0.6 m,−0.4 m) ABF=∑0F = B −F A BA B AB M = ∑ B 0⇒M+ coupl