Virtual Work

Consider a body in static equilibrium undergoing an infinitesimal small virtual displacement or a rotation.

The virtual work done is the product of the virtual force and displacement. Similarly for a virtual rotation, the work done is the product of the moment and virtual angular displacement.

The principle of virtual work states that the algebraic sum of the virtual work done by all the forces and moments is zero for any virtual displacement or rotation.

When a ball undergoes a virtual downward displacement, its weight does positive virtual work, while the normal force does negative virtual work.

For equilibrium conditions, the sum of all the virtual work done must be zero.

Similarly, when a supported beam undergoes a virtual rotation, only two forces do the work.

The components of the reaction force at the support do not contribute to virtual work.

By considering the virtual displacements along the y-direction, and applying the principle of virtual work, the virtual work equation is derived.

The term in the parentheses indicates the state of rotational equilibrium.