Principle of Virtual Work

  • Apply principal of virtual work in statics by understanding virtual displacements and virtual work.

“If a system in equilibrium under the action of a set of forces is given a virtual displacement, the virtual work done by the forces will be zero.”

The terms used in this statement are defined as follows:

  • A virtual displacement \(\delta\)s is an imaginary infinitesimal variation of the coordinate given instantaneously. The virtual displacement must be compatible with the constraints of the system.

  • Virtual work \(\delta\)W is the work done by all the active forces in a virtual displacement. Since there is no significant change geometry associated with the virtual displacement, the force acting on the system are assumed to remain unchanged for the calculation of \(\delta\)W.

Solved Examples

Solved Example:

24-6-01

Using principle of virtual work, determine the force P which will keep the weightless bar AC in equilibrium. Take length AB as 2m and length AC as 8m. The bar makes an angle of 30$^\circ$ with horizontal. All the surfaces in contact are smooth. Refer figure.

24.6-01



Solution:

24.6-01

By using the principle of virtual work, \begin{align*} P\dfrac {d}{d\theta }\left( 8\cos \theta \right) +800\left( \dfrac {d}{d\theta }6\sin \theta \right) &=0\\ P\left( -8\sin\theta \right) +800\left( 6\cos \theta \right) &=0\\ 8P\sin \theta &=4800\cos \theta \\ P&=600\cot \theta \\ &=600 \cot 30\\ &=1038\ N \end{align*}

Correct Answer: B

Solved Example:

24-6-02

Virtual work refers to: (TNTRB ME 2017)



Correct Answer: B

Solved Example:

24-6-03

The principle of virtual work states that, for a body to be in equilibrium, the virtual work should be: (CIL MT Civil 2020)

Correct Answer: B

Solved Example:

24-6-04

In virtual work equation some forces are neglected. Select the most appropriate answer from the following: (UPPSC AE Mechanical 2013 Paper I)

Correct Answer: D