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

Statik dengede sonsuz küçük bir sanal yer değiştirme veya dönme geçiren bir cisim düşünün.
Yapılan sanal iş, sanal kuvvetin ve yer değiştirmenin ürünüdür. Benzer şekilde, sanal bir rotasyon için yapılan iş, anın ve sanal açısal yer değiştirmenin ürünüdür.
Sanal iş ilkesi, tüm kuvvetler ve momentler tarafından yapılan sanal işin cebirsel toplamının, herhangi bir sanal yer değiştirme veya dönme için sıfır olduğunu belirtir.
Bir top sanal olarak aşağı doğru yer değiştirdiğinde, ağırlığı pozitif sanal iş yaparken, normal kuvvet negatif sanal iş yapar.
Denge koşulları için, yapılan tüm sanal işlerin toplamı sıfır olmalıdır.
Benzer şekilde, desteklenen bir ışın sanal bir dönüşe maruz kaldığında, işi yalnızca iki kuvvet yapar.
Destekteki reaksiyon kuvvetinin bileşenleri sanal çalışmaya katkıda bulunmaz.
Y yönü boyunca sanal yer değiştirmeler göz önünde bulundurularak ve sanal iş ilkesi uygulanarak, sanal iş denklemi türetilir.
Parantez içindeki terim, dönme dengesinin durumunu gösterir.

<ol>
	<li>Hibbeler, R.C. (2016). Mühendislik Mekaniği: Statik. On Dördüncü Baskı, New Jersey: Pearson. Bölüm 11.1, sayfa 583-584.</li>
	<li>Meriam, J.L., Kraige, L.G. ve Bolton, J.N. (2016). Mühendislik Mekaniği: Statik ve Dinamik. Sekizinci Baskı, Singapur: John Wiley & Sons. Bölüm 7.2, sayfa 394-395.</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 577-578.</li>
</ol>

sanal İş

Sanal iş ilkesi, bir cismi statik ve dinamik denge durumunda ise, dış kuvvetlerin ve çift momentlerin herhangi bir sanal yer değiştirmesi için yaptığı tüm sanal işin toplamının sıfır olması gerektiğini belirtir.

Statik denge durumunda, bir cisim hayali veya sanal bir hareket geçirebilir, örneğin yer değiştirme veya dönme. Bir kuvvetin yaptığı sanal iş, kuvvetin ve sanal yer değiştirmenin kuvvet yönünde olan iç çarpımına eşittir. Bir çift momentin sanal olarak döndürülmesi durumunda ise aynı ilke geçerlidir. Sanal dönme işi, çift momentin ilgili sanal dönme ile çarpılarak belirlenir.

Bu kavramı bir örnek üzerinden açıklamak için, bir topun düz bir yüzeyin üstünde durduğunu varsayalım. Tüm cisim diyagramını çizmek, aşağı doğru sanal bir yer değiştirmesi olduğunda ağırlığın pozitif sanal iş yapacağını, normal kuvvetin ise negatif sanal iş yapacağını ortaya çıkarır. Dengeyi sağlamak için, tüm bu kuvvetlerin toplamı sıfır olmalı ve buna göre bir denklem formüle edilebilir.

Sanal iş kavramı, hem tanecikler hem de rijit cisimlerle ilgili sorunları çözmek için kullanılır. Çift düzlem kuvvetlere maruz kalan rijit cisimlerle uğraşırken, farklı türdeki yer değiştirmelere ilişkin olduğundan üç ayrı denklem gereklidir - x ve y yönde çevrimsel olarak dönme için.

Sonuç olarak, sanal iş, yapıların ve makinelerin davranışını fiziksel olarak test etmeden öngörebilmek için mühendislerin ve bilim insanlarının kullanabileceği temel bir kavramdır. Bu, statik ve dinamik sistemlerin davranışını analiz etmek için kullanılabilecek güçlü bir araç olup, mühendislik ve bilim alanında geniş uygulamalara sahiptir.

Sanal İş

Sanal çalışma ilkesi, eğer bir cisim statik ve dinamik dengedeyse, o zaman tüm dış kuvvetler tarafından yapılan tüm sanal işlerin toplamı ...

Education

JoVE Core

Mechanical Engineering

Makine Mühendisliği

Unit 1

Ünite 1

Virtual Work

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

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

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

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Conservative Forces and Path-Independent Work

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Gravitational and Elastic Energy Stored

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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 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 in Force Equilibrium

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