CE Statics Chapter 5 Lectures 2 and 3 EQUATIONS OF EQUILIBRIUM The body is subjected to a system of forces which lies in the x-y plane. From equilibrium equations: Fx =0 Fy =0 M =0 Alternatively, F a =0 M A =0 M B =0 F1 F2 F3 F4 A B C a a If the system of forces is replaced by a single resultant force F R = F (acting at point A) and a resultant couple moment M R = M A If M A =0, then, M RA = 0 FRFR A B C a a M RA For F R to satisfy ( Fa = 0), then F R has no component along the a-a axis, so the line of action of F R is perpendicular to the a-axis. For M B = 0 to be satisfied, then F R must be equal to zero since F R does not pass through point B. FRFR A B C a a A second alternative equations of equilibrium: MA =0 MB =0 MC =0 where A, B, and C do not lie on the same line. FRFR A B C a a M RA If M A to be zero, then M RA = 0 M B =0 if F R passes through B If M C =0 is to be satisfied, then F R = 0 So the body is in equilibrium. FRFR A B C a a M RA Procedure for Analysis DRAW FREE-BODY DIAGRAM APPLY EQUILIBRIUM EQUATIONS TWO AND THREE FORCE MEMBERS Two Force Members Members subjected to forces only (no moments) at two points. FAFA FBFB For the member to be in equilibrium, F A and F B must be of the same magnitude and opposite direction ( F = 0). For M = 0 to be satisfied, F A and F B must be co-linear with each other. Three-Force Members Members subjected to three forces are called three-force members For these members to be in equilibrium, forces are required to be either concurrent or parallel. If F1 and F2 intersect at point (A) to satisfy M = 0, then F3 must pass through point (A). F1 F2 F3 A If F1 and F2 are parallel, then they intersect at infinity. For the body to be in equilibrium ( M = 0), then F3 must pass that point of intersection. Therfore, F3 is also parallel to F1 and F2. F1 F2 F3