# Resultant of Non-Concurrent Force System

The resultant of non-concurrent force system is defined according to magnitude, inclination, and position.

The magnitude of the resultant can be found as follows

$R_y = \Sigma F_y$

$R = \sqrt{{R_x}^2 + {R_y}^2}$

The inclination from the horizontal is defined by

The position of the resultant can be determined according to the principle of moments.

$Rd = M_R$

$R_yi_x = M_R$

$R_xi_y = M_R$

Where,

F_{x} = component of forces in the x-direction

F_{y} = component of forces in the y-direction

R_{x} = component of thew resultant in x-direction

R_{y} = component of thew resultant in y-direction

R = magnitude of the resultant

θ_{x} = angle made by a force from the x-axis

M_{O} = moment of forces about any point O

d = moment arm

M_{R} = moment at a point due to resultant force

i_{x} = x-intercept of the resultant R

i_{y} = y-intercept of the resultant R