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Virtual Work

The particle (Fig. 9.2) A is acted upon by several forces “f1 , F2 , F3 , . . . , Fn  We imagine that A is displaced through a small displacement to A’. This imagined displacement is called virtual displacement (or). The scalar product of the forces and the displacement is the virtual work (δu).

δu  = F1 .δr + f2 .δr +f3 .δr +… +fn .δr

=(F1 +F2 +F3 +….+FN) .δr

=R .δr

Where R is the resultant of the force system. Thus, sum of the virtual work of individual

force is equal to the virtual work of the resultant force.

If under the action of forces (external), the body is in equilibrium, then R = 0

The principle of virtual work states “If a particle is in equilibrium, the total virtual work of the forces acting on the particle is zero for any virtual displacement of the particle”.