If a body is in equilibrium under the action of a system of forces, the work done is zero since there are no displacements. But if we assume that a body in equilibrium undergoes small imaginary displacements (known as virtual displacements) consistent with the geometrical conditions, imaginary work is said to be done by the system of forces. This imaginary work done is called virtual work.
The body A shown below is in equilibrium under the action of forces. However it assumed that it undergoes an imaginary displacement in the direction of force F.
Displacement in direction of force = Δs cos α Virtual work done = F Δs cos α.
Principle of virtual work
If a system of forces acting on a body or a system of bodies is in equilibrium, the total virtual work done by the forces acting on the body or system of bodies is zero for any virtual displacement consistent with geometrical conditions.
For example, consider the free-body diagram of the particle (ball) that rests on the floor. If we “imagine” the ball to be displaced downwards a virtual amount δy
Total virtual work done
Since the system is in equilbrium
Since δy ≠ 0, then N = W
A. APPLICATION OF THE PRINCIPLE OF VIRTUAL WORK ON BEAMS