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

Considere um sistema de ligação de tesoura conectado a uma mola, que não é esticada em um determinado ângulo.
Na presença de uma força externa, a mola se estica e o sistema sofre um deslocamento virtual. Nesta condição, apenas a força da mola e a força externa contribuem para o trabalho.
Para determinar o ângulo de deflexão para manter o equilíbrio do sistema, são determinadas as coordenadas de posição das duas forças em relação a um ponto fixo.
Em seguida, a quantidade pela qual a mola é comprimida e a força da mola correspondente são avaliadas.
A diferenciação das coordenadas de posição fornece os deslocamentos virtuais correspondentes às duas forças.
A força externa atua na direção do deslocamento virtual, por isso faz um trabalho positivo. Enquanto isso, a força da mola atua de forma oposta ao deslocamento virtual e faz um trabalho negativo.
Em seguida, o princípio do trabalho virtual é usado para escrever a equação do trabalho virtual para o sistema.
Resolvendo a equação de trabalho virtual para a força dada, pode-se obter o ângulo necessário para manter o equilíbrio do sistema de ligação tesoura.

<ol>
	<li>Hibbeler, R.C. (2016). Engenharia Mecânica: Estática. Décima quarta edição, Nova Jersey: Pearson. Seção 11.3, pp. 587-588.</li>
	<li>Cerveja, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. e Self, B.P. (2016). Mecânica vetorial para engenheiros. Décima primeira edição, Nova York: McGraw-Hill Education. Pág. 582.</li>
</ol>

princípio do trabalho virtual: resolução de problemas

O princípio do trabalho virtual é um conceito essencial no campo da mecânica e engenharia. Ele é usado para resolver problemas relacionados ao equilíbrio de uma estrutura ou sistema. Ele se baseia na suposição de que se um sistema está em equilíbrio, o trabalho realizado por todas as forças durante um deslocamento virtual é zero. Este princípio é aplicado considerando deslocamentos virtuais do sistema e o trabalho correspondente realizado pelas forças internas e externas.

Para aplicar o princípio do trabalho virtual, é necessário expressar as coordenadas de posição das forças internas e externas em termos de um parâmetro de coordenada comum. Este parâmetro é tipicamente um ângulo, distância ou deslocamento relevante para o problema em questão.

Uma vez que as coordenadas tenham sido expressas, os deslocamentos virtuais correspondentes a cada uma das forças são encontrados diferenciando as expressões de coordenadas. Os deslocamentos virtuais representam deslocamentos hipotéticos que o sistema poderia sofrer e nos permitem calcular o trabalho virtual realizado por cada força atuando no sistema.

A força externa atuando no sistema realiza trabalho positivo quando está se movendo na direção de seu deslocamento virtual, enquanto as forças internas realizam trabalho negativo quando estão se opondo aos seus deslocamentos virtuais.

Para resolver um problema usando o princípio do trabalho virtual, primeiro, identifique as forças e momentos desconhecidos que existem dentro do sistema. Em seguida, avalie o trabalho realizado por essas forças e momentos durante um deslocamento virtual hipotético do sistema. O deslocamento virtual é muito pequeno e representa um deslocamento hipotético que o sistema sofre. Isso permite a determinação de cada força e momento atuando no sistema e o trabalho realizado por eles durante esse deslocamento virtual.

Em seguida, escreva a equação do trabalho virtual para o sistema usando o princípio do trabalho virtual. Esta equação considera os deslocamentos virtuais e o trabalho correspondente realizado por cada força e momento atuando no sistema. Finalmente, resolver a equação do trabalho virtual fornece os valores das forças e momentos desconhecidos no sistema.

O princípio do trabalho virtual é benéfico para resolver problemas relacionados a sistemas complexos envolvendo muitas partes interconectadas. É amplamente utilizado na engenharia e mecânica para calcular as forças e momentos desconhecidos de uma estrutura ou sistema.

Princípio do Trabalho Virtual: Resolução de Problemas

O princípio do trabalho virtual é um conceito essencial no campo da mecânica e da engenharia. Isso é usado para resolver problemas relacionados ao equilíbrio ...

principle-of-virtual-work-problem-solving

Education

JoVE Core

Mechanical Engineering

Engenharia Mecânica

Unit 1

Unidade 1

Virtual Work

Trabalho Virtual

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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

O JoVE Core Mechanical Engineering oferece vídeos animados concisos e de fácil compreensão que abrangem tópicos-chave como equilíbrio, forças, análise de treliças e mecânica estrutural. Explore suas aplicações no mundo real e observe esses conceitos em ação por meio de experimentos conduzidos por cientistas.

mechanical engineering

Virtual Work for Finding Unknown Forces

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