There are many methods for solving problems involving the equilibrium of a rigid body under the action of three -or sometimes more than three -coplanar forces.

 

If three forces are in equilibrium they must be concurrent. So if a rigid body is in equilibrium under the action of three forces, and the point of intersection of two of the forces is known, the third force must pass through the same point. In this way a force whose direction is not normally known ( e.g. the force at a hinge) can be located on a diagram.

 

This principle can be extended to cover some problems where more than three forces are involved initially but can be reduced in number.

 

At a point of rough contact, for example, when friction is limiting, the resultant reaction can be used instead of normal reaction plus frictional force, so reducing the number of forces acting.

 

 

 

 

 

 

 

Once it is established that three forces are keeping a body in equilibrium, the triangle of forces or Lami's theorem can be applied, providing some elegant solutions as well as variety of method.