static force analysis

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Similarly a three force member will be in equilibrium if the vector sum of all these forces equal to zero and to satisfy the vector sum of all the moments about any arbitrary point equal to zero, their line of action should meet at a point.

Figure 4(a) shows a body subjected to three forces Also the line of action of coincide at point O. Hence the resultant of must F1 and F2 must pass through point O and it should be equal and opposite to force F3 . Hence for equilibrium, line of action of F3 should pass through point O as shown in Figure 4(b). In figure 4(c) the forces are shown to form a close polygon (triangle) and one may use Lami’s theorem (sine rule of tringle) to find the unknown forces if atleast one force is known both in magnitude and direction and the line of action of one more force is known. According to this theorem 

where , and αβ γ are angle as shown in figure 4(c).

For more than three forces one may draw force vector polygon or resolve the forces and moments to get the required force components.