Equations of static equilibrium:
In particular, if the forces are parallel and we take z-axis parallel to them, then the first, second and last equations are identically satisfied (no force exist along x and y axes). Therefore, the equations of static equilibrium are reduced to three, viz.
∑ Fz = 0, ∑ M x = 0, ∑ M y = 0
If the forces are concurrent and if we select the point of concurrence as the origin then the last three equations shall always be satisfied and only three equations shall be required to solve the problems. These are
∑ Fx = 0, ∑ Fy = 0, ∑ Fz = 0
Likewise, in the case of concurrent forces in a plane there shall be only two equations of static equilibrium:
∑ Fx = 0, and ∑ Fy = 0
In case of parallel forces in a plane, these equations shall be
∑ Fz = 0, and ∑ Fy = 0
Where, O is the moment centre in the plane containing the parallel forces. O can be any point in the plane. The z-axis shall be parallel to the direction of forces.