Meriam, Kraige & Bolton — Statics of Particles: Problem 2_75

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/75 If the resultant of the loads shown passes through point B, determine the equivalent force– couple system at O. Given values from the diagram: - Force at O: downward. - Force at A: upward, located to the right of O. - Force at C: downward, located to the right of O (). - Couple at C: Shown acting clockwise. - Point B is located to the right of O (). Problem 2/75 ● Calculation Process To determine the equivalent force–couple system at point , we first find the resultant force of the given system. Then, we use the condition that the resultant passes through point to establish the final equivalent system. 1. Resultant Force Calculation: The resultant force is the vector sum of all external forces acting on the beam. Summing the forces in the vertical -direction (with upward as positive): Thus, the resultant force is acting downward. 2. Determine Unknown Couple : The problem states that the resultant passes through point . For a system of forces to be equivalent to a single resultant force passing through a specific point, the sum of moments of all original forces and couples about that point must be zero. Let counter- clockwise (CCW) be positive. Summing moments about point ( from ): 10 kips 4 kips4 ft12 kips 10 ft4+ ′ 3+ ′ 3 ′ M 7 ft4+ ′ 3 ′ O RB R y R = y F = ∑ y −10 kips+4 kips−12 kips R = y −18 kips 18 kips R=−18j kips M RB B7 ftO M = ∑ B 10(7)−4(3)−12(3)−M=0 70−12−36−M=0 22−M=0⟹M=22 kip-ft Since the sign is positive, the ma