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

Si consideri un corpo in equilibrio statico che subisce un piccolo spostamento virtuale infinitesimale o una rotazione.
Il lavoro virtuale svolto è il prodotto della forza virtuale e dello spostamento. Allo stesso modo per una rotazione virtuale, il lavoro svolto è il prodotto del momento e dello spostamento angolare virtuale.
Il principio del lavoro virtuale afferma che la somma algebrica del lavoro virtuale svolto da tutte le forze e i momenti è zero per qualsiasi spostamento o rotazione virtuale.
Quando una palla subisce uno spostamento virtuale verso il basso, il suo peso fa un lavoro virtuale positivo, mentre la forza normale fa un lavoro virtuale negativo.
Per le condizioni di equilibrio, la somma di tutto il lavoro virtuale svolto deve essere zero.
Allo stesso modo, quando una trave supportata subisce una rotazione virtuale, solo due forze fanno il lavoro.
I componenti della forza di reazione sul supporto non contribuiscono al lavoro virtuale.
Considerando gli spostamenti virtuali lungo la direzione y e applicando il principio del lavoro virtuale, si ricava l'equazione del lavoro virtuale.
Il termine tra parentesi indica lo stato di equilibrio rotazionale.

<ol>
	<li>Hibbeler, R.C. (2016). Ingegneria Meccanica: Statica. Quattordicesima edizione, New Jersey: Pearson. Sezione 11.1, pp. 583-584.</li>
	<li>Meriam, J.L., Kraige, L.G. e Bolton, J.N. (2016). Meccanica ingegneristica: statica e dinamica. Ottava edizione, Singapore: John Wiley & Sons. Sezione 7.2 pp. 394-395.</li>
	<li>Birra, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. e Self, B.P. (2016). Meccanica vettoriale per ingegneri. Undicesima edizione, New York: McGraw-Hill Education. Pagine 577-578.</li>
</ol>

lavoro virtuale

Il principio del lavoro virtuale stabilisce che se un corpo è in equilibrio statico e dinamico, la somma di tutto il lavoro virtuale svolto da tutte le forze esterne e i momenti di coppia per una qualsiasi data spostamento virtuale, deve essere zero.

In equilibrio statico, un corpo può sperimentare un movimento immaginario o virtuale, come un'alterazione o una rotazione. Il lavoro virtuale svolto da una forza, è uguale al prodotto scalare della forza e dello spostamento virtuale nella direzione della forza. Quando si tratta di ruotare virtualmente un momento di coppia, si applica lo stesso principio. Il lavoro di rotazione virtuale viene determinato moltiplicando il momento di coppia con la sua rotazione virtuale corrispondente.

Per illustrare questo concetto con un esempio, supponiamo che ci sia una palla poggiata su una superficie piana. Disegnare il diagramma del corpo completo rivelerà che quando c'è uno spostamento virtuale verso il basso, il peso svolgerà un lavoro virtuale positivo, mentre la forza normale svolgerà un lavoro virtuale negativo. Per raggiungere l'equilibrio, la somma di tutte queste forze deve essere zero e quindi può essere formulata un'equazione che rappresenta questa condizione.

Il concetto di lavoro virtuale viene utilizzato per risolvere problemi legati sia a particelle che a corpi rigidi. Quando si tratta di corpi rigidi soggetti a forze complanari, sono necessarie tre equazioni separate, poiché si riferiscono a diversi tipi di spostamenti - traslazione nelle direzioni x e y e rotazioni attorno a un asse perpendicolare al piano xy.

In conclusione, il lavoro virtuale è un concetto fondamentale nella meccanica, che consente agli ingegneri e agli scienziati di prevedere il comportamento di strutture e macchine senza testarle fisicamente. È uno strumento potente che può essere utilizzato per analizzare il comportamento di sistemi statici e dinamici e ha applicazioni molto ampie in ingegneria e altre scienze.

Lavoro virtuale

Il principio del lavoro virtuale afferma che se un corpo è in equilibrio statico e dinamico, allora la somma di tutto il lavoro virtuale svolto da tutte le forze esterne ...

Education

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JoVE Core

Mechanical Engineering

Ingegneria Meccanica

Unit 1

Unità 1

Virtual Work

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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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Work in Force and Motion

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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

Virtual work helps find forces in a system of connected rigid bodies. It is a useful method when several links move together and the system is in equilibrium. In that case, the total virtual work is zero. To analyze the system, start with a free-body diagram. Use one independent coordinate to describe the link configuration. Then mark the deflected position that comes from a positive virtual displacement. This makes the small change in position clear before any calculations begin. Next,...

principle of virtual work: problem solving

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Virtual Work for Finding Unknown Forces

The principle of virtual work helps find unknown forces and moments in equilibrium problems. It is an important idea in mechanics and engineering. The method uses a small, hypothetical motion called a virtual displacement. If the system is in equilibrium, the work done by the forces during that displacement is zero. To apply this principle, the positions of the internal and external forces must be written in terms of one common coordinate parameter. That parameter can be an angle, a distance,...

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Conservative Forces and Path-Independent Work

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Gravitational and elastic potential energy are forms of stored energy from conservative forces. A conservative force, such as gravity or an elastic force, gives a body the capacity to do work. This capacity is measured as potential energy and depends on the body’s position relative to a fixed reference point, or datum. For gravitational potential energy, the datum is the level where the energy is taken as zero. If a body is above this reference plane, its weight has positive gravitational...

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Equilibrium Stability Through Potential Energy

Stability of equilibrium in physics and engineering can be studied by using a system’s potential energy. An equilibrium configuration is a state where the system can remain at rest. Stability describes whether the system tends to return to that state after a small disturbance. Problem solving begins by finding the equilibrium points of the system. This is done by setting the derivative of the potential energy function equal to zero and solving for the independent variable values that satisfy...

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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