Equilibrium of force system | Formulas

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The body is said to be in equilibrium if the resultant of all the force acting on a body is zero. There are mainly two types of equilibrium. One is translational and another one rotational equilibrium. Let us check out the equilibrium formulas for each type of force system following below. 

Formulas of equilibrium of force system: 


Concurrent force system: 

∑Fx = 0
∑Fy = 0

Parallel force system:

∑F = 0 
∑Mo = 0 

Nonconcurrent nonparallel force system: 

∑Fx = 0
∑Fy = 0
∑Mo = 0 

Where ∑Fx is the sum of all forces in the x-direction
∑Fy is the sum of all forces in the y-direction
∑F is the sum of all forces
∑Mo is the sum of the moment at any point O

Important points on equilibrium force:

  • Two forces are in equilibrium if they are equal and opposite direction. 
  • Three coplanar forces in equilibrium are called concurrent forces. 
  • Three or more concurrent forces in equilibrium form a close polygon when joint in head to tail manner. 

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