Name: virtual work for finding unknown forces
Uploaded: 2023-09-22T11:49:20.000Z
Duration: 1 min 13 s
Channel: JoVE

Considera un sistema di collegamento a forbice collegato a una molla, che non è tesa con una certa angolazione.
In presenza di una forza esterna, la molla si allunga e il sistema subisce uno spostamento virtuale. In questa condizione, solo la forza della molla e la forza esterna contribuiscono al lavoro.
Per determinare l'angolo di deflessione per mantenere l'equilibrio del sistema, vengono determinate le coordinate di posizione delle due forze rispetto a un punto fisso.
Quindi, vengono valutate la quantità di compressione della molla e la forza della molla corrispondente.
Differenziando le coordinate di posizione si ottengono gli spostamenti virtuali corrispondenti alle due forze.
La forza esterna agisce nella direzione dello spostamento virtuale, quindi svolge un lavoro positivo. Nel frattempo, la forza della molla agisce in modo opposto allo spostamento virtuale e svolge un lavoro negativo.
Successivamente, il principio del lavoro virtuale viene utilizzato per scrivere l'equazione del lavoro virtuale per il sistema.
Risolvendo l'equazione del lavoro virtuale per la forza data, è possibile ottenere l'angolo necessario per mantenere l'equilibrio del sistema di collegamento a forbice.

<ol>
	<li>Hibbeler, R.C. (2016). Ingegneria Meccanica: Statica. Quattordicesima edizione, New Jersey: Pearson. Sezione 11.3, pp. 587-588.</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 582.</li>
</ol>

principio del lavoro virtuale: risoluzione dei problemi

Il principio del lavoro virtuale è un concetto essenziale nel campo della meccanica e dell'ingegneria. Viene utilizzato per risolvere problemi legati all'equilibrio di una struttura o di un sistema. Si basa sull'assunzione che se un sistema è in equilibrio, il lavoro svolto da tutte le forze durante uno spostamento virtuale è zero. Questo principio viene applicato considerando gli spostamenti virtuali del sistema e il lavoro corrispondente svolto dalle forze interne ed esterne.

Per applicare il principio del lavoro virtuale, è necessario esprimere le coordinate di posizione delle forze interne ed esterne in termini di un parametro di coordinate comune. Questo parametro è tipicamente un angolo, una distanza o uno spostamento che è rilevante per il problema in questione.

Una volta che le coordinate sono state espresse, gli spostamenti virtuali corrispondenti a ciascuna delle forze vengono trovati differenziando le espressioni delle coordinate. Gli spostamenti virtuali rappresentano spostamenti ipotetici che il sistema potrebbe subire e ci permettono di calcolare il lavoro virtuale svolto da ciascuna forza che agisce sul sistema.

La forza esterna che agisce sul sistema svolge un lavoro positivo quando si muove nella direzione del suo spostamento virtuale, mentre le forze interne svolgono un lavoro negativo quando si oppongono ai loro spostamenti virtuali.

Per risolvere un problema utilizzando il principio del lavoro virtuale, si identificano prima le forze e i momenti sconosciuti che sussistono all'interno del sistema. Quindi si valuta il lavoro svolto da forze e momenti durante uno spostamento virtuale ipotetico del sistema. Lo spostamento virtuale è molto piccolo e rappresenta uno spostamento ipotetico che il sistema subisce. Ciò consente di determinare ogni forza e momento che agisce sul sistema e il lavoro svolto da essi durante questo spostamento virtuale.

Successivamente, si scrive l'equazione del lavoro virtuale per il sistema, utilizzando il principio del lavoro virtuale. Questa equazione considera gli spostamenti virtuali e il lavoro corrispondente svolto da ciascuna forza e ciascun momento che agisce sul sistema. Infine, si risolve l'equazione del lavoro virtuale che fornisce i valori delle forze e dei momenti sconosciuti nel sistema.

Il principio del lavoro virtuale è utile per risolvere problemi legati a sistemi complessi che coinvolgono molte parti interconnesse. È ampiamente utilizzato nell'ingegneria e nella meccanica per calcolare le forze e i momenti sconosciuti di una struttura o di un sistema.

Principio del lavoro virtuale: Risoluzione dei problemi

Il principio del lavoro virtuale è un concetto essenziale nel campo della meccanica e dell'ingegneria. Questo viene utilizzato per risolvere problemi legati all'equilibrio ...

principle-of-virtual-work-problem-solving

Education

Didattica

JoVE Core

Mechanical Engineering

Ingegneria Meccanica

Unit 1

Unità 1

Virtual Work

Lavoro virtuale

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

Principle of Virtual Work: Problem Solving

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, or another displacement that fits the problem. After the coordinates are written this way, the virtual displacements are found by differentiating the coordinate expressions. These displacements are hypothetical, but they show how the system could move.

Virtual work is then found from the forces acting on the system. An external force does positive work when it moves in the same direction as its virtual displacement. Internal forces do negative work when they oppose their virtual displacements. This sign difference is part of the virtual-work equation.

To solve a problem, first identify the unknown forces and moments in the system. Next, evaluate the work done during a virtual displacement. Then write the virtual-work equation for the whole system. Solving that equation gives the values of the unknown forces and moments. This approach is useful for complex systems with many connected parts.

Virtual Work for Finding Unknown Forces

work

Work in Force and Motion

Work connects force, motion, and energy in mechanics. It happens when a force acts on an object and the object moves along the line of action of that force. Work can also be described as energy transfer caused by applying a force, which leads to a change in the object’s motion or position. Work is calculated as the force multiplied by the part of the displacement in the same direction as the force. It can also be written as the dot product of the applied force and the object’s displacement. In...

work of a couple moment

Couple Moment Work in Rotation

Mechanical engineering studies motion, energy, and force, and it uses the idea of a couple moment to describe how two equal and opposite forces act on a rigid body. A couple moment is created when those forces act at two points on the body that are separated by a distance. When a rigid body moves because of a couple, its displacement can be split into two parts. First, the two points move by the same amount to their final positions. Then the body rotates about one of those points. During the...

virtual work

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...

virtual work for a system of connected rigid bodies

virtual-work-for-a-system-of-connected-rigid-bodies

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

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,...

mechanical efficiency of real machines

Friction’s Role in Machine Efficiency

Mechanical efficiency shows how well a machine turns input work into output work. It is calculated as the ratio of output work to input work. An ideal machine has an efficiency of one, which means the input work equals the output work. Real machines are never perfectly ideal because some energy is lost. Friction is one of the main causes of that loss. In a toggle vise used to compress wooden blocks, the sliding block rubs against the horizontal plane and creates friction. To find the...

conservative forces

Conservative Forces and Path-Independent Work

Conservative forces are forces whose work depends only on an object’s starting and ending positions. The path between those positions does not change the amount of work done. This idea is important in mechanical engineering because it helps describe how energy moves through a system. A conservative force also conserves energy in the sense that its work is path independent. Gravity is one example. Electrostatic forces and springs modeled by Hooke’s law are also examples. A ball rolling down a...

potential energy

Gravitational and Elastic Energy Stored

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...

potential-energy criterion for equilibrium

potential-energy-criterion-for-equilibrium

Stable Equilibrium Through Potential Energy

Potential energy helps determine when a mechanical system is stable at equilibrium. When a system is acted on by gravitational and elastic forces, its total potential function is the algebraic sum of gravitational potential energy and elastic potential energy. If the system is already in equilibrium and is given a small displacement, the work done on the system equals the negative of the change in potential energy between the starting and ending positions. For a virtual displacement, which is...

stability of equilibrium configuration

Types of Equilibrium in Mechanical Systems

Types of equilibrium in mechanical systems are stable, neutral, and unstable. These three cases help explain how a structure or object responds when it is pushed slightly away from balance. They are important for predicting whether a system will return to its original position, stay where it is, or move farther away. Stable equilibrium occurs when a system returns toward its original position after a small displacement. In this case, the potential energy is at a minimum. A cantilever beam...

one-degree-of-freedom system

Spring-Mass Motion and Energy Stability

A one-degree-of-freedom system uses a single independent variable to describe its state and behavior. In mechanical engineering, this kind of model helps explain how parts in a larger system respond to force. It also gives engineers a way to predict motion before a design is built in real life. A simple harmonic oscillator is one example of a one-degree-of-freedom system. A mass attached to a spring moves along one axis, and that position determines the system’s state. The spring force makes...

stability of equilibrium configuration: problem solving

stability-of-equilibrium-configuration-problem-solving

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 the principle of virtual work uses a small virtual displacement to find unknown forces and moments in equilibrium problems with connected systems.

Virtual Work for Finding Unknown Forces | 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 for Finding Unknown Forces

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