Summary - Friction of Rigid Bodies Mechanical Engineering Notes | EduRev

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Mechanical Engineering : Summary - Friction of Rigid Bodies Mechanical Engineering Notes | EduRev

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Virtual work

If a body is in equilibrium under the action of a system of forces, the work done is zero since there are no displacements. But if we assume that a body in equilibrium undergoes small imaginary displacements (known as virtual displacements) consistent with the geometrical conditions, imaginary work is said to be done by the system of forces. This imaginary work done is called virtual work.

The body A shown below is in equilibrium under the action of forces. However it assumed that it undergoes an imaginary displacement in the direction of force F.
Displacement in direction of force = Δs cos α Virtual work done = F Δs cos α.

Summary - Friction of Rigid Bodies Mechanical Engineering Notes | EduRev


Principle of virtual work 

If a system of forces acting on a body or a system of bodies is in equilibrium, the total virtual work done by the forces acting on the body or system of bodies is zero for any virtual displacement consistent with geometrical conditions.

Summary - Friction of Rigid Bodies Mechanical Engineering Notes | EduRev

For example, consider the free-body diagram of the particle (ball) that rests on the floor. If we “imagine” the ball to be displaced downwards a virtual amount δy

 

Summary - Friction of Rigid Bodies Mechanical Engineering Notes | EduRev

Total virtual work done  Summary - Friction of Rigid Bodies Mechanical Engineering Notes | EduRev

Since the system is in equilbrium

Summary - Friction of Rigid Bodies Mechanical Engineering Notes | EduRev

Since δy ≠ 0, then  N = W


A. APPLICATION OF THE PRINCIPLE OF VIRTUAL WORK ON BEAMS

Summary - Friction of Rigid Bodies Mechanical Engineering Notes | EduRev

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