Short Notes: Virtual Work | Short Notes for Mechanical Engineering PDF Download

 Page 1


Virtual Work
Virtual displacement: Given a system in equilibrium, its virtual displacement is 
imagined as follows: Move the system slightly away from its equilibrium position 
arbitrarily but consistent with the constraints. This represents a virtual 
displacement of the system.
Virtual displacement is denoted by
Sr
to distinguish it from a real displacement
dr
Virtual work: The work done by any force
F
during a virtual displacement is called virtual work. It is denoted by 
6W 
. Thus
SW = F»6r
Work done by a constraint force is usually zero, implies that virtual work done by a 
constraint force is also zero. Also keep in mind that in calculating the work
F»6r
done by the force
F :6r
represents the displacement of the point where the force is being applied.
Page 2


Virtual Work
Virtual displacement: Given a system in equilibrium, its virtual displacement is 
imagined as follows: Move the system slightly away from its equilibrium position 
arbitrarily but consistent with the constraints. This represents a virtual 
displacement of the system.
Virtual displacement is denoted by
Sr
to distinguish it from a real displacement
dr
Virtual work: The work done by any force
F
during a virtual displacement is called virtual work. It is denoted by 
6W 
. Thus
SW = F»6r
Work done by a constraint force is usually zero, implies that virtual work done by a 
constraint force is also zero. Also keep in mind that in calculating the work
F»6r
done by the force
F :6r
represents the displacement of the point where the force is being applied.
Principle of virtual work: The necessary and sufficient condition for equilibrium of g 
mechanical system without friction is that the virtual work done by the externally 
applied forces is zero.
For a system in equilibrium, each particle in the system is in equilibrium under the 
influence of externally applied forces and the forces of constraints.
For the ith particle:
F ixunalj + F c o v m m ij — 0 (F ) ¦ 6^ — 0
For a system of composed of many subsystems:
y ] (FesUTKOl,! + F I )-Srj = 0
Net virtual work done by constraint forces is zero. This means that the total virtual 
work done by the external forces vanishes.