Meriam, Kraige & Bolton — Statics of Particles: Problem 2_145

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/145 Replace the two forces and one couple acting on the rigid pipe frame by their equivalent resultant force R acting at point O and a couple . Problem 2/145 1. Analysis of Forces and Couples First, we identify all the external forces and couples acting on the rigid pipe frame and express them in vector form using the standard right-handed Cartesian coordinate system shown in the diagram. We also determine the position vectors () for each force relative to the origin . Force 1 (): A force acting at the first joint. Based on the diagram, this joint is located along the positive -axis. The force is parallel to the -axis, pointing in the positive direction. Position vector: Force vector: Force 2 (): A force acting at the end of the tilted segment. The horizontal segment has a length of along the -axis. The final segment has a length of at an angle of below the horizontal, in the -plane. Position vector: Force vector: (directed vertically downward) Applied Couple (): A couple of magnitude is applied to the horizontal pipe segment. The curved arrow indicates a clockwise rotation when viewed from the positive -direction. Couple vector: 2. Determination of the Resultant Force M O (x,y,z)r O(0,0,0) F 1 60 lb 12 in.zx r = 1 12k in. F = 1 60i lb F 2 50 lb 15 in.y 10 in.30 ∘ yz r = 2 0i+(15+10cos30)j+ ∘ (12−10sin30)k ∘ r = 2 (15+8.660)j+(12−5)k=23.66j+7k in. F = 2 −50k lb M C 40 lb-ft y M = C −40j lb-ft=−480j lb-in. R The resultant force i