Name: virtual work in force equilibrium
Uploaded: 2023-09-22T11:49:36.000Z
Duration: 1 min 20 s
Channel: JoVE

Consider a body in static equilibrium undergoing an infinitesimal small virtual displacement or a rotation.
The virtual work done is the product of the virtual force and displacement. Similarly for a virtual rotation, the work done is the product of the moment and virtual angular displacement.
The principle of virtual work states that the algebraic sum of the virtual work done by all the forces and moments is zero for any virtual displacement or rotation.
When a ball undergoes a virtual downward displacement, its weight does positive virtual work, while the normal force does negative virtual work.
For equilibrium conditions, the sum of all the virtual work done must be zero.
Similarly, when a supported beam undergoes a virtual rotation, only two forces do the work.
The components of the reaction force at the support do not contribute to virtual work.
By considering the virtual displacements along the y-direction, and applying the principle of virtual work, the virtual work equation is derived.
The term in the parentheses indicates the state of rotational equilibrium.

virtual work

The principle of virtual work states that if a body is in static and dynamic equilibrium, then the sum of all the virtual work done by all external forces and couple moments for any given virtual displacement must be zero.
In static equilibrium, a body can experience an imaginary or virtual movement, such as displacement or rotation. The virtual work done by a force is equal to the dot product of force and virtual displacement in the direction of the force. When it comes to virtually rotating a couple moment, the same principle applies. The virtual rotational work done is determined by multiplying the couple moment with its respective virtual rotation.
To illustrate this concept using an example, suppose there is a ball sitting on top of a flat surface. Drawing its full-body diagram will reveal that when there is a downward virtual displacement, the weight will do positive virtual work, while the normal force will do negative virtual work. To achieve equilibrium, the sum of all these forces must be zero, and so an equation representing this condition can be formulated accordingly.
The concept of virtual work is used to solve problems related to both particles and rigid bodies. When dealing with rigid bodies subjected to coplanar forces, three separate equations are required, since they relate to different types of displacements&#8212;translation in the x and y directions and rotations about an axis perpendicular to the x-y plane.
In conclusion, virtual work is a fundamental concept in mechanics that allows engineers and scientists to predict the behavior of structures and machines without physically testing them. It is a powerful tool that can be used to analyze the behavior of static and dynamic systems, and it has wide-ranging applications in engineering and science.

Virtual Work

The principle of virtual work states that if a body is in static and dynamic equilibrium, then the sum of all the virtual work done by all external forces ...

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virtual work in force equilibrium

Virtual work is a mechanics principle used to check equilibrium with imaginary motion. If a body is in static or dynamic equilibrium, the total virtual work from external forces and couple moments must be zero for any virtual displacement.

A virtual displacement is an imagined small movement. It can be a shift or a rotation. The virtual work done by a force equals the force dotted with the virtual displacement in the force’s direction. For a couple moment, virtual rotational work is found by multiplying the moment by the virtual rotation.

A simple example is a ball on a flat surface. If the ball has a downward virtual displacement, its weight does positive virtual work. The normal force does negative virtual work. The equilibrium condition then gives an equation in which the sum of these virtual works is zero.

Virtual work can be used for both particles and rigid bodies. For rigid bodies under coplanar forces, three equations are needed. They correspond to translation in the x direction, translation in the y direction, and rotation about an axis perpendicular to the x-y plane. Engineers and scientists use this method to study structures and machines without physically testing them.

Virtual Work in Force Equilibrium

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key terms and concepts

Learn how virtual work helps test equilibrium using imagined displacement, rotation, and force balance in particles and rigid bodies.

Virtual Work in Force Equilibrium | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Virtual Work in Force Equilibrium

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