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

Consideremos un cuerpo en equilibrio estático que experimenta un pequeño desplazamiento virtual infinitesimal o una rotación.
El trabajo virtual realizado es el producto de la fuerza y el desplazamiento virtual. Del mismo modo, para una rotación virtual, el trabajo realizado es el producto del momento y el desplazamiento angular virtual.
El principio del trabajo virtual establece que la suma algebraica del trabajo virtual realizado por todas las fuerzas y momentos es cero para cualquier desplazamiento o rotación virtual.
Cuando una pelota experimenta un desplazamiento virtual hacia abajo, su peso hace un trabajo virtual positivo, mientras que la fuerza normal hace un trabajo virtual negativo.
Para condiciones de equilibrio, la suma de todo el trabajo virtual realizado debe ser cero.
De manera similar, cuando una viga apoyada se somete a una rotación virtual, solo dos fuerzas hacen el trabajo.
Los componentes de la fuerza de reacción en el soporte no contribuyen al trabajo virtual.
Al considerar los desplazamientos virtuales a lo largo de la dirección y y aplicar el principio del trabajo virtual, se deriva la ecuación del trabajo virtual.
El término entre paréntesis indica el estado de equilibrio rotacional.

<ol>
	<li>Hibbeler, R.C. (2016). Ingeniería Mecánica: Estática. Decimocuarta edición, Nueva Jersey: Pearson. Sección 11.1, págs. 583 y 584.</li>
	<li>Meriam, J.L., Kraige, L.G. y Bolton, J.N. (2016). Ingeniería Mecánica: Estática y Dinámica. Octava edición, Singapur: John Wiley & Sons. Sección 7.2, págs. 394 y 395.</li>
	<li>Beer, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. y Self, B.P. (2016). Mecánica vectorial para ingenieros. Undécima Edición, Nueva York: McGraw-Hill Education. Págs. 577-578.</li>
</ol>

trabajo virtual

El principio del trabajo virtual establece que si un cuerpo está en equilibrio estático y dinámico, entonces la suma de todo el trabajo virtual realizado por todas las fuerzas externas y momentos del par para cualquier desplazamiento virtual dado debe ser cero. En el equilibrio estático, un cuerpo puede experimentar un movimiento imaginario o virtual, como el desplazamiento o la rotación. El trabajo virtual realizado por una fuerza es igual al producto escalar de la fuerza y el desplazamiento virtual en la dirección de la fuerza. Cuando se trata de rotar virtualmente un momento de par, se aplica el mismo principio. El trabajo de rotación virtual realizado se determina multiplicando el momento de pares por su respectiva rotación virtual. Para ilustrar este concepto utilizando un ejemplo, supongamos que hay una bola que está sobre una superficie plana. Dibujar su diagrama de cuerpo completo revelará que cuando hay un desplazamiento virtual hacia abajo, el peso realizará un trabajo virtual positivo, mientras que la fuerza normal realizará un trabajo virtual negativo. Para lograr el equilibrio, la suma de todas estas fuerzas debe ser cero, por lo que se puede formular una ecuación que represente esta condición. El concepto de trabajo virtual se utiliza para resolver problemas relacionados tanto con partículas como con cuerpos rígidos. Al tratar con cuerpos rígidos sujetos a fuerzas coplanares, se requieren tres ecuaciones separadas, ya que se relacionan con diferentes tipos de desplazamientos, es decir, traslaciones en las direcciones x e y y rotaciones alrededor de un eje perpendicular al plano xy. En conclusión, el trabajo virtual es un concepto fundamental en la mecánica que permite a los ingenieros y científicos predecir el comportamiento de estructuras y máquinas sin probarlas físicamente. Es una herramienta poderosa que se puede utilizar para analizar el comportamiento de sistemas estáticos y dinámicos, y tiene aplicaciones de amplio alcance en la ingeniería y la ciencia.

Trabajo virtual

El principio del trabajo virtual establece que si un cuerpo está en equilibrio estático y dinámico, entonces la suma de todo el trabajo virtual realizado por todas las fuerzas externas ...

Education

Educación

JoVE Core

Mechanical Engineering

Ingeniería Mecánica

Unit 1

Unidad 1

Virtual Work

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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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virtual work

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...

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Finding Forces with Virtual Work in Linked Bodies

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Virtual Work for Finding Unknown Forces

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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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