Principle of virtual work

Virtual Work

Principle of virtual work 

If a particle, rigid body, or system of rigid bodies which is in equilibrium under various forces is given an arbitrary virtual displacement, the net work done by the external forces during that displacement is zero.

The principle of virtual work is particularly useful when applied to the solution of problems involving the equilibrium of machines or mechanisms consisting of several connected members.

Imagine the small virtual displacement of particle which is acted upon by several forces. The corresponding virtual work is:

𝛿𝑈 = 𝐹1 ⋅ 𝛿𝑟 + 𝐹2 ⋅ 𝛿𝑟+ 𝐹3 ⋅ 𝛿𝑟

      = (𝐹1 + 𝐹2 + 𝐹3) ⋅ 𝛿𝑟 

       = 𝑅 ⋅ 𝛿r

• If a particle is in equilibrium, the total virtual work of forces acting on the particle is zero for any virtual displacement. 

• If a rigid body is in equilibrium, the total virtual work of external forces acting on the body is zero for any virtual displacement of the body. 

• If a system of connected rigid bodies remains connected during the virtual displacement, only the work of the external forces need be considered.