Equilibrium means the body has no tendency to translate or to rotate:

 

1. No tendency for the body to translate means:

    The sum of all the External Force vector components along any axis equals zero. 

 

2. No tendency for the body to rotate means:

    The sum of all the moments (caused by the External Forces) about any point/axis equals zero.

 

The resultant of any general force system consists of resultant force (R) and a couple(C).

For equilibrium condition, R=0 and C=0;

ΣX is algebraic sum of all the forces acting along X-direction

ΣY is algebraic sum of all the forces acting along Y-direction

Also a couple acting at any point is sum of moment of all the forces at that particular point.

Hence ΣM=0;

Moment of a Force about a point is defined as product of magnitude of the force and perpendicular distance of its action line from the point.

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