# Force couple simplification

How is it possible to add all the force components to find resultant when forces are acting at different points on the body?

• this is where centre of mass comes in. All external forces acting on different points of the same system, creates the same effect as if they were all acting on the centre of mass of the system. – Jim Haddocc Oct 17 '16 at 6:59

If the body is subjected to a force or forces that do not act on its CG then there will be torque which has to be countered by reaction forces acting as a couple at the supports with equal magnitude and opposite direction which equate to to torque create by the forces acting on the body.

By definition a static body means it is not accelerating or rotating:
$\sum F_x=0, \sum F_y=0, \sum F_z=0 \ and \sum M=0$.
However if the forces are acting through CG of the body then we can just go ahead and add them up as vectors.