Meriam, Kraige & Bolton — Statics of Particles: Problem 2_72

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/72 Determine the equivalent force–couple system at the center O for each of the three cases of forces being applied along the edges of a square plate of side d. Problem 2/72 To determine the equivalent force–couple system at the center , we must calculate the resultant force vector and the resultant moment for each case. We use a coordinate system with the origin at the center , the positive -axis directed to the right, and the positive -axis directed upwards. Counter-clockwise (CCW) moments are considered positive. (a) Case (a) ● Calculation Process 1. Identify Forces and Their Positions: Force 1: Along the left edge, magnitude , directed downwards. In vector form: . Its line of action is at . Force 2: Along the bottom edge, magnitude , directed to the right. In vector form: . Its line of action is at . 2. Calculate Resultant Force : 3. Calculate Resultant Moment : The moment of a force about a point is given by . Moment from : (CCW) Moment from : (CCW) ● Final Conclusion: The equivalent system at consists of a resultant force and a counter-clockwise moment . O RM O Oxy F F = 1 −Fjx=−d/2 F F = 2 Fiy=−d/2 R R= F= ∑F + 1 F= 2 Fi−Fj M O M=xF − y yF x F 1 M = 1 (−d/2)(−F)−(0)(0)= Fd 2 1 F 2 M = 2 (0)(0)−(−d/2)(F)= Fd 2 1 M = O M + 1 M = 2 F d+ 2 1 F d= 2 1 Fd (CCW) OR=Fi− FjM= O Fd (CCW) (b) Case (b) ● Calculation Process 1. Identify Forces and Their Positions: Force 1: Along the top edge, magnitude , directed to the right. In vect