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

$R_x = \Sigma F_x$

$R_y = \Sigma F_y$

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

 

The inclination from the horizontal is defined by

$\tan \theta_x = \dfrac{R_y}{R_x}$

 

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

$M_R = \Sigma M_O$

$Rd = M_R$

$R_yi_x = M_R$

$R_xi_y = M_R$

 

Where,
Fx = component of forces in the x-direction
Fy = component of forces in the y-direction
Rx = component of thew resultant in x-direction
Ry = component of thew resultant in y-direction
R = magnitude of the resultant
θx = angle made by a force from the x-axis
MO = moment of forces about any point O
d = moment arm
MR = moment at a point due to resultant force
ix = x-intercept of the resultant R
iy = y-intercept of the resultant R
 

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