Principle of Virtual Work: What is Virtual Work? Explain it

By BYJU'S Exam Prep

Updated on: September 25th, 2023

Since the beginning of statics research, the concept of the Principle of Virtual Work has been applied to some degree. It was known as “the law of lever” and was employed by the Greeks, medieval Arabs, and Latins. The principle of virtual work and the associated calculus of variations were initially created to examine systems of rigid structures. Still, they were later expanded to include the study of the mechanics of deformable bodies.

The study of forces and movement in a mechanical system leads to virtual work when the concept of least action is applied. Because the Principle of virtual work could be taken alone as the basis for all of the mechanics, the virtual work concept was thought to be more basic than the present understanding that least action does not account for non-conservative forces.

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What is the Principle of Virtual Work?

According to the principle of virtual work, total virtual work done by all the forces acting on a system in static equilibrium is zero for a set of infinitesimal virtual displacements from equilibrium.” John Bernoulli devised this technique in 1717. We must be extremely clear about the definitions of work, virtual work, and virtual displacement to understand the “principle of virtual work.” When an object is moved over a distance by an external force, at least a portion of that force must be applied in the direction of the displacement. This is known as “work” in physics. If the force is constant, work is calculated by multiplying the length of the path by the component of the force acting along the path. Mathematically, the work can be given as; W= f.d

Any system of forces that is in equilibrium is a virtual force. A virtual displacement of a system can be defined as “an infinitesimal displacement of any mechanical system point that is compatible with the system’s constraints that may or may not happen.” so any displacement that is possible without violating any constraints is referred to as a virtual displacement. In continuation of this, virtual work is defined as, ”The work performed by a real force operating through a virtual displacement or a virtual force acting through a real displacement is known as virtual work”.

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Mathematical Relation of Principle of Virtual Work

A special type of problem in mechanics involves problems of systems in equilibrium. In these systems, the problem is finding the system’s configuration in equilibrium subjected to any type of constraint.

According to the virtual work principle, any infinitesimal virtual displacement in configuration space consistent with the constraints doesn’t require any work. Simply put, the total virtual work of forces operating on a particle in equilibrium is zero for any virtual displacement. Mathematically, it can be written as;

U = F.δx = M.δθ = 0

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Advantages of Principle of Virtual Work Method

  1. It is not essential to disassemble the systems to develop relationships between the active forces.
  2. Without considering the reactive forces, relationships between the active forces can be found directly.
  3. This method is particularly helpful in identifying the position of equilibrium of a system under known loads.
  4. One significant advantage of the virtual work principle is that it requires active forces when the system goes through a virtual displacement to identify its mechanics.
Important Topics for Gate Exam
Internal and External Forces Lami’s theorem
Psychrometry Composite Material
Types of Patterns Gear Design
Ceramics System of Forces
Admixtures Metal Casting
Sand Casting Heat Treatment Process


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