Name: equilibrium conditions for a supported plate
Uploaded: 2025-05-22T09:06:02.000Z
Duration: 1 min 31 s
Channel: JoVE

A, B ve C noktalarında desteklenen ve dış kuvvetlere maruz kalan dikdörtgen bir plaka düşünün.
Plakaya etki eden kuvvetler ve çift momentler, A noktasında etki eden eşdeğer bileşke kuvvete ve bileşke çift momente indirgenebilir.
Burada A ve B noktalarından geçen çizgi y eksenine paralel değildir. Plakanın denge denklemleri, alternatif denklem seti kullanılarak tanımlanabilir.
İlk denklem, bileşke kuvvetin x bileşenine sahip olmaması ve y eksenine paralel olması durumunda sağlanır.
İkinci denklem, A noktasındaki bileşke moment sıfır ise sağlanır.
Üçüncü denklem, B noktasındaki momentin sıfır olduğunu belirtir, bu da sistem üzerindeki bileşke kuvvetin y bileşeninin sıfır olduğu anlamına gelir.
İkinci bir alternatif denge denklemleri seti, A, B ve C noktalarındaki momentlerin toplamının sıfır olduğunu belirtir. Bu denklemler, bu noktalar doğrusal olmadığında sağlanır.

<ol>
	<li>Hibbeler, R.C. (2016). Mühendislik Mekaniği \u2012 Statik ve Dinamik. Hoboken, New Jersey: Pearson Prentice Salonu. sayfa 220.</li>
</ol>

denge denklemleri alternatif setleri

Alternative Sets of Equilibrium Equations

Mühendisler, yapıların davranışını analiz ederken genellikle denge kavramına dayanır. Bu, bir sistemde etki eden tüm kuvvetlerin ve momentlerin birbirini dengelediği, net hareket veya dönme olmadığı durumu ifade eder. Birçok durumda denge, standart denklemler kümesiyle tanımlanabilir. Bununla birlikte, bazı durumlarda, sistemin davranışını doğru bir şekilde tanımlamak için alternatif denge denklemleri kullanılmalıdır.

Bu tür bir durumun bir örneği, noktalar A, B ve C'de desteklenen ve dış kuvvetlere maruz kalan bir dikdörtgen tabakada gözlemlenebilir, şekilde gösterildiği gibi.

Bu durumda, tabakada etkili olan kuvvet ve çift moment, nokta A'da etkili olan eşdeğer sonuç kuvveti ve sonuç çift momente indirgenebilir. Bununla birlikte, A ve B noktalarından geçen çizgi, y-eksenine paralel değildir. Bu, standart denge denklemlerinin tabakanın davranışını tanımlamak için yeterli olmayacağı anlamına gelir. Bunun yerine, alternatif denge denklemleri kullanılmalıdır.

<img alt="Figure 1" src="/files/ftp_upload/14272/14272_PT_Figure_1v2.svg" style="text-align: center; height: 200px;" />

İlk denklem, tabakada etkili olan sonuç kuvvetinin x bileşeninin olmaması ve y-eksenine paralel olması gerektiğini belirtir. Bu, tabakanın yatay hareketinin olmadığından emin olur. İkinci denklem, A noktasındaki sonuç momentinin sıfır olması gerektiğini belirtir. Bu, A noktası etrafında tabakanın dönmediğinden emin olur. Üçüncü denklem, B noktasındaki momentin sıfır olması gerektiğini belirtir. Bu, sistemdeki sonuç kuvvetin y-bileşeninin sıfır olması gerektiği anlamına gelir ve denge için gereklidir. Birlikte, bu üç denklem tabakanın davranışını doğru bir şekilde tanımlar ve dengede kalmasını sağlar.

<img alt="Equation 1" src="/files/ftp_upload/14272/14272_Equation_1v2.svg" style="text-align: center; height: 55px;" />

Bazı durumlarda kullanılabilecek başka bir alternatif denge denklem kümesi, A, B ve C noktalarındaki momentlerin toplamının sıfır olması gerektiğini belirten denklemlerdir.

<img alt="Equation 2" src="/files/ftp_upload/14272/14272_Equation_2v2.svg" style="text-align: center; height: 55px;" />

Bu denklem kümesi, bu noktaların bir doğrultuda hizalanmadığı, yani hepsinin aynı çizgide bulunmadığı durumlarda sağlanır. Noktaların doğrultulu olduğu durumlarda denklemler standart denge denklemlerine indirgenir.

Denge Denklemleri Alternatif Setleri

Yapıların davranışını analiz ederken, mühendisler genellikle denge kavramına güvenirler. Bu, tüm kuvvetlerin ve anların bulunduğu durumu ifade eder ...

alternative-sets-of-equilibrium-equations

Education

JoVE Core

Mechanical Engineering

Makine Mühendisliği

Unit 1

Ünite 1

Equilibrium of a Rigid Body

Katı Cismin Dengesi

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

equilibrium conditions for a supported plate

Equilibrium conditions for a supported plate are used to describe when forces and moments balance. In this state, the plate has no net movement and no rotation. Engineers use these equations to study how structures behave under external loads.

In many cases, the standard equilibrium equations are enough. But some systems need an alternative set of equations to match the geometry of the support points. A rectangular plate supported at points A, B, and C is one example.

For this plate, the applied force and couple moment can be reduced to an equivalent resultant force and resultant couple moment at point A. However, the line through points A and B is not parallel to the y-axis. Because of that, the standard equations do not fully describe the plate’s behavior.

The alternative set requires the resultant force on the plate to have no x-component. It must be parallel to the y-axis, which prevents horizontal motion. It also requires the resultant moment at point A to be zero, so the plate does not rotate around point A. A third equation sets the moment at point B to zero, which means the y-component of the resultant force must also be zero for equilibrium.

Another alternative set states that the sum of the moments at points A, B, and C must be zero. This works when the three points are not collinear, meaning they do not lie on the same line. If the points are collinear, these equations reduce to the standard equilibrium equations.

Equilibrium Conditions for a Supported Plate

equilibrium-conditions-for-a-supported-plate

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alternative sets of equilibrium equations

Equilibrium conditions for a supported plate are used to describe when forces and moments balance. In this state, the plate has no net movement and no rotation. Engineers use these equations to study how structures behave under external loads. In many cases, the standard equilibrium equations are enough. But some systems need an alternative set of equations to match the geometry of the support points. A rectangular plate supported at points A, B, and C is one example. For this plate, the...

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Two-Force Body Equilibrium

A two-force body is a rigid body acted on by only two external forces. In equilibrium, those two forces must have the same magnitude, the same line of action, and opposite directions. This balance is what keeps the body at rest. For a plate with forces F1 and F2 applied at points A and B, equilibrium means the sum of moments about any axis is zero. If moments are summed about point A, the moment from F2 must be zero. That means the line of action of F2 must pass through point A. The same idea...

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Solving a Three-Force Member Example

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Constraints in structural engineering control how a body can move and help keep it in mechanical equilibrium. A constraint is a restriction on motion. When the right number of constraints is used, the system can stay balanced with the fewest supports needed. A system with the proper number of supports is called statically determinate. In that case, the unknown reaction forces can be found from equations of equilibrium. These systems are the easiest to analyze and design because the forces can...

key terms and concepts

Learn how a supported plate can be analyzed with alternative equilibrium equations, including force balance and zero moments at points A, B, and C.

Equilibrium Conditions for a Supported Plate | 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

Equilibrium Conditions for a Supported Plate

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