Equilibrium of Non-Concurrent Force System

There are three equilibrium conditions that can be used for non-concurrent, non-parallel force system.

The sum of all forces in the x-direction or horizontal is zero.

$\Sigma F_x = 0$   or   $\Sigma F_H = 0$


The sum of all forces in the y-direction or vertical is zero.

$\Sigma F_y = 0$   or   $\Sigma F_V = 0$


The sum of moment at any point O is zero.

$\Sigma M_O = 0$


The three equilibrium conditions can solved up to three unknowns in the system. If the system involves more than three unknowns, it is called indeterminate. Indeterminate structures are beyond the scope of Engineering Mechanics, it is one of the topics in Strength of Materials and Theory of Structures.