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

Considérons un corps en équilibre statique subissant un petit déplacement virtuel infinitésimal ou une rotation.
Le travail virtuel effectué est le produit de la force virtuelle et du déplacement. De même pour une rotation virtuelle, le travail effectué est le produit du moment et du déplacement angulaire virtuel.
Le principe du travail virtuel stipule que la somme algébrique du travail virtuel effectué par toutes les forces et tous les moments est nulle pour tout déplacement ou rotation virtuel.
Lorsqu’une balle subit un déplacement virtuel vers le bas, son poids effectue un travail virtuel positif, tandis que la force normale effectue un travail virtuel négatif.
Pour les conditions d’équilibre, la somme de tout le travail virtuel effectué doit être nulle.
De même, lorsqu’une poutre supportée subit une rotation virtuelle, seules deux forces effectuent le travail.
Les composantes de la force de réaction au niveau du support ne contribuent pas au travail virtuel.
En considérant les déplacements virtuels le long de la direction y et en appliquant le principe du travail virtuel, l’équation du travail virtuel est dérivée.
Le terme entre parenthèses indique l’état d’équilibre rotationnel.

<ol>
	<li>Hibbeler, R.C. (2016). Mécanique du génie : Statique. Quatorzième édition, New Jersey : Pearson. Section 11.1, p. 583 et 584.</li>
	<li>Meriam, J.L., Kraige, L.G. et Bolton, J.N. (2016). Mécanique de l’ingénierie : statique et dynamique. Huitième édition, Singapour : John Wiley & Sons. Section 7.2, p. 394 et 395.</li>
	<li>Beer, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. et Self, B.P. (2016). Mécanique vectorielle pour les ingénieurs. Onzième édition, New York : McGraw-Hill Education. p. 577 et 578.</li>
</ol>

travail virtuel

Le principe du travail virtuel stipule que si un corps est en équilibre statique et dynamique, alors la somme de tous les travaux virtuels réalisés par toutes les forces externes et les moments de couple pour tout déplacement virtuel donné doit être nulle. En équilibre statique, un corps peut subir un mouvement imaginaire ou virtuel, tel qu'un déplacement ou une rotation. Le travail virtuel réalisé par une force est égal au produit scalaire de la force et du déplacement virtuel dans la direction de la force. Lorsqu'il s'agit de faire virtuellement tourner un moment de couple, le même principe s'applique. Le travail de rotation virtuel est déterminé en multipliant le moment de couple par sa rotation virtuelle respective. Pour illustrer ce concept à l'aide d'un exemple, supposons qu'il y ait une balle posée sur le dessus d'une surface plate. Le diagramme de son corps entier révélera que lorsqu'il y a un déplacement virtuel vers le bas, le poids effectuera un travail virtuel positif, tandis que la force normale effectuera un travail virtuel négatif. Pour atteindre l'équilibre, la somme de toutes ces forces doit être nulle, et donc une équation représentant cette condition peut être formulée en conséquence. Le concept de travail virtuel est utilisé pour résoudre des problèmes liés aux particules et aux corps rigides. Lorsqu'il s'agit de corps rigides soumis à des forces coplanaires, trois équations distinctes sont nécessaires, car elles sont liées à différents types de déplacements – translation dans les directions x et y et rotations autour d'un axe perpendiculaire au plan x–y. En conclusion, le travail virtuel est un concept fondamental en mécanique qui permet aux ingénieurs et aux scientifiques de prédire le comportement des structures et des machines sans les tester physiquement. C'est un outil puissant qui peut être utilisé pour analyser le comportement de systèmes statiques et dynamiques, et il a des applications variées en ingénierie et en science.

Travail virtuel

Le principe du travail virtuel stipule que si un corps est en équilibre statique et dynamique, alors la somme de tout le travail virtuel effectué par toutes les forces externes...

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JoVE Core

Mechanical Engineering

Génie mécanique

Unit 1

Unité 1

Virtual Work

KEY TERMS AND CONCEPTS

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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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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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