Chap 4 Equilibrium of Rigid Bodies ๏ฟฝ ๐น๐น๐ฆ๐ฆ = 0 ๏ฟฝ ๐น๐น๐ฅ๐ฅ = 0 ๏ฟฝ ๐๐0 = 0 Prof. Osama Ahmed Mohamed, Ph.D., P.E., M.ASCE Review • Components of force ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ (๐๐) ๐๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ (๐๐) • Moment F d R ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ (๐๐) ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ (๐๐) ๐๐ ๐๐ = ๐น๐น๐น๐น R Definition: 2-force member is the one that is pinned at both ends and there is no load on it between the pinned ends. I can write the three equations of equilibrium which allow me to calculate 3 unknowns The number of unknown reactions is more than three, therefore, the three equations of equilibrium will not solve this problem. One way to solve this problem is to write the tension forces in cables AB and AD in vector form Write the two forces in vector form so you can identify which component produces moment about point B. โ ๐๐ Recall: ๐น๐นโ = ๐น๐น ๐๐ Ropes, cables, wires, and rods are under tension. Notice that a 2Force member doesn’t need to be straight. ๐๐ = 450 ๐๐ ๐๐ Consider a Free Body Diagram consisting of BC only ๐๐ = 450 100 inches ๐๐ = 450 100 ๐๐