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

Belirli bir açıda gerilmemiş bir yaya bağlı bir makas bağlantı sistemi düşünün.
Dış bir kuvvetin varlığında, yay gerilir ve sistem sanal bir yer değiştirmeye uğrar. Bu durumda, sadece yay kuvveti ve dış kuvvet çalışmaya katkıda bulunur.
Sistemin dengesini korumak için sapma açısını belirlemek için, iki kuvvetin sabit bir noktaya göre konum koordinatları belirlenir.
Daha sonra yayın sıkıştırılma miktarı ve buna karşılık gelen yay kuvveti değerlendirilir.
Farklılaşan konum koordinatları, iki kuvvete karşılık gelen sanal yer değiştirmeleri verir.
Dış kuvvet sanal yer değiştirme yönünde hareket eder, bu nedenle olumlu iş yapar. Bu arada, yay kuvveti sanal yer değiştirmeye zıt hareket eder ve negatif iş yapar.
Daha sonra, sistem için sanal iş denklemini yazmak için sanal çalışma ilkesi kullanılır.
Verilen kuvvet için sanal iş denklemi çözülerek, makas bağlantı sisteminin dengesini korumak için gereken açı elde edilebilir.

<ol>
	<li>Hibbeler, R.C. (2016). Mühendislik Mekaniği: Statik. On Dördüncü Baskı, New Jersey: Pearson. Bölüm 11.3, sayfa 587-588.</li>
	<li>Bira, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. ve Öz, B.P. (2016). Mühendisler için Vektör Mekaniği. On Birinci Baskı, New York: McGraw-Hill Eğitimi. Sayfa 582.</li>
</ol>

sanal İş İlkesi: problem Çözme

Sanal iş ilkesi, mekanik ve mühendislik alanında temel bir kavramdır. Bu kavram, bir yapı veya sistemde dengeyle ilgili sorunları çözmek için kullanılır. İlke, bir sistem denge halindeyse, sanal bir yer değiştirmede tüm kuvvetler tarafından yapılan işin sıfır olduğu varsayımına dayanır. Bu ilke, sistemdeki sanal yer değişikliklerini ve iç ve dış kuvvetler tarafından yapılan ilgili işleri dikkate alarak uygulanır.

Sanal iş ilkesini uygulamak için iç ve dış kuvvetlerin konum koordinatlarını ortak bir koordinat parametresi olarak ifade etmek gereklidir. Bu parametre genellikle sorunla ilgili olan bir açı, mesafe veya yer değiştirme olabilir.

Koordinatlar ifade edildikten sonra, her bir kuvvetin sanal yer değişikliklerine karşılık gelen sanal yer değişiklikleri, koordinat ifadelerini türeterek bulunur. Sanal yer değişiklikleri, sistem tarafından geçebileceği varsayılan hayali yer değişiklikleridir ve bize sistem üzerinde etki eden her bir kuvvetin sanal yapılan işi hesaplama imkanı sağlar.

Sistem üzerinde etki eden dış kuvvet, sanal yer değişiminin yönünde hareket ettiğinde pozitif iş yapar, iç kuvvetler ise sanal yer değişimlerine karşı direndiklerinde negatif iş yaparlar.

Sanal iş ilkesini kullanarak bir problemi çözmek için önce sistem içindeki bilinmeyen kuvvetleri ve momentleri belirlemek gereklidir. Daha sonra bu kuvvetlerin ve momentlerin sistem üzerindeki sanal yer değiştirme sırasında yaptığı işi değerlendirin. Sanal yer değişimi çok küçüktür ve sistem tarafından belirli bir yer değişimi varsayımını temsil eder. Bu, sistemde etki eden her bir kuvveti ve momenti ve bu sanal yer değişimi sırasında yapılan işi belirlemeyi mümkün kılar.

Son olarak, sanal iş ilkesini kullanarak sistem için sanal iş denklemi yazın. Bu denklem, sistem üzerinde etki eden her bir kuvvet ve moment için sanal yer değişimleri ve buna bağlı olarak yapılan işi dikkate alır. Son olarak, sanal iş denklemini çözerek sistemdeki bilinmeyen kuvvetlerin ve momentlerin değerlerini elde edersiniz.

Sanal iş ilkesi, birçok bağlantılı parçanın bulunduğu karmaşık sistemlerle ilgili sorunları çözmek için faydalıdır. Mühendislikte ve mekanikte yaygın olarak kullanılarak bir yapı veya sistemin bilinmeyen kuvvetlerini ve momentlerini hesaplamak için kullanılır.

Sanal İş İlkesi: Problem Çözme

Sanal çalışma ilkesi, mekanik ve mühendislik alanında önemli bir kavramdır. Bu, denge ile ilgili sorunları çözmek için kullanılır ...

principle-of-virtual-work-problem-solving

Education

JoVE Core

Mechanical Engineering

Makine Mühendisliği

Unit 1

Ünite 1

Virtual Work

Sanal İş

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

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 Makine Mühendisliği, denge, kuvvetler, kafes kiriş analizi ve yapısal mekanik gibi temel konuları kapsayan kısa, anlaşılması kolay animasyonlu videolar sunar. Gerçek dünyadaki uygulamalarını keşfedin ve bilim insanlarının önderlik ettiği deneylerle bu kavramların uygulanmasına tanık olun.

mechanical engineering

Virtual Work for Finding Unknown Forces

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