CONDITIONS OF EQUILIBRIUM

CONDITIONS OF EQUILIBRIUM

The structure is said to be in equilibrium if algebraic sum of all forces and moments are balanced.

It can also be explained as the magnitude of force acting on the structure is resisted by another force or set of forces of equal in magnitude and opposite in direction to the load acted.

Therefore, it can be stated that the net resultant force on the structure is equal to zero.

               Fig 1                                                                           Fig 2

                                                               Fig 3

·        Consider the figure 1 in which the body on the rigid support is subjected to the external forces of magnitude F₁, F2, F3 and F_4.

·   Further all forces are brought into a single force (Resultant –R); whose effect is same as that of combined effect of all the individual forces (shown in fig 2).

·    In order to maintain the body in the equilibrium state, the same magnitude of the force but opposite to the direction of the resultant will be acted on the body which is termed as equilibriant (E) (shown in fig 3).

 

Generally there are three conditions of equilibrium

1.     The algebraic sum of all the forces in horizontal direction or x direction acting on a structure is equal to zero.

∑F _x = 0

2.     The algebraic sum of all the forces in horizontal direction or x direction    acting on a structure is equal to zero.

∑F _y = 0

3.     The algebraic sum of all the moments acting on a structure is equal to zero.

      ∑M = 0

First two conditions are called as force equilibrium or translational equilibrium. The last condition is also called as torque equilibrium or rotational equilibrium.

Example for force equilibrium:

·        A book resting on the table.

·        A car moving with constant velocity

            

            Example for torque equilibrium

·        Children playing See saw

·        Driving Car steering