0In general, it can be said that resulting of any number of concurrent forces in a plane is given by the closing side of the polygon of forces obtained by successive geometric addition of their free vectors.
In a particular case where the end of the last vector coincides with beginning of first vector, the resultant vanishes and the system is in equilibrium.
"This states that, whenever a system of coplanar concurrent forces are in equilibrium, the force polygon formed by their free vectors result in a closed polygon."
Three methods exist to find the unkown force or its direction in a given system of coplanar concurrent concurrent forces that is in equilibrium:
1. Lami's Theorem:
"If three concurrent forces acting on a body, kept in an equilibrium, then each force is proportional to the sine of the angle between the other two forces and the constant of proportionality is same.
A/sin(α)= B/sin(β) =C/sin(γ)....... (Sine rule)
Note: While applying this theorem, in FBD of the body, draw the directions of forces either directed towards or away from the point of concurrency.
2. Method of Projections:
Involves resolution of each force in to its rectangular components along X and Y axis.
Solve the following equations -
∑(Fx)i = 0 ; ∑(Fy)i = 0 ---
Sum of all X components of forces =0 and Sum of all Y components of forces = 0
3. Method od Moments:
Algebraic sum of moments of a system of concurrent forces in a plane become equal to zero abot two different points (moment centres) on the plane which are not on a straight line with the point of concurrency of the force system -
∑(Mb)i = 0 ; ∑(Mc)i = 0
