Name: rigid body force balance in equilibrium
Uploaded: 2023-09-22T11:49:22.000Z
Duration: 1 min 28 s
Channel: JoVE

Sert bir cisim, dış kuvvetlerin etkisi altında herhangi bir deformasyona uğramaz.
O noktası etrafında bir kuvvet momenti ile sonuçlanan, dik bir radyal mesafe r'de bir dış kuvvet F'ye maruz kalan bir atlıkarıncayı düşünün.
Atlıkarıncaya birden fazla kuvvet etki ederse, denge koşulu, üzerine etki eden tüm dış kuvvetlerin toplamı sıfır olduğunda elde edilir.
Dengenin diğer koşulu, O noktası etrafındaki tüm momentlerin toplamının sıfıra eşit olması gerektiğini belirtir.
Moment A noktasında ölçüldüğünde, O noktasındaki momentin toplamı ile dik mesafe ve uygulanan kuvvetin çapraz çarpımı olarak ifade edilebilir.
Bu koşullar, cismin statik dengede herhangi bir öteleme veya dönme hareketine maruz kalmamasını sağlar.
Katı cisim içindeki iç kuvvetler aynı büyüklüğe sahip olduğundan ve zıt yönlerde hareket ederek Newton'un üçüncü hareket yasası nedeniyle birbirini iptal ettiğinden, burada sadece dış kuvvetler dikkate alınır.

<ol>
	<li>Bira, F.P.; Johnston, E.R.; Mazurek, D.F; Cromwell, P.J. ve Öz, B.P. (2019). Mühendisler için Vektör Mekaniği \u2012 Statik ve Dinamik. New York: McGraw-Tepesi. sayfa 170</li>
</ol>

denge koşulları

Conditions of Equilibrium

Denge, bir rijit cismin herhangi bir çevrimsel veya translasyonel harekete tabi olmadığı bir durumu ifade eder. Bu durum, bir rijit cisim üzerinde etkili olan kuvvet ve çiftin sıfır olduğunda gerçekleşir. Harici kuvvetlerin birleşik etkisi sıfır olduğunda, rijit cisim denge durumunda kabul edilir.

Denge koşulları için iç kuvvetler dikkate alınmaz çünkü bunlar cisim içerisinde eşit ve zıt çiftler halinde meydana gelir ve birbirini etkisiz hale getirir. Bu sebeple bu iç kuvvetler, rijit cismin genel hareketine veya hareket değişimine katkıda bulunmaz. Denge, cisim üzerinde etkili olan harici kuvvetlerin ve momentlerin dengesine bağlı olarak belirlenir çünkü bunlar çevrimsel veya translasyonel harekete sebep olurlar.
Denge için gerekli ve yeterli koşullar, sonuç kuvvetinin ve momentin sıfıra eşitlendiği durumla belirlenebilir. Ayrıca, vektör denklemleri her bir kuvvet ve momenti dikdörtgen bileşenlerine ayrılarak altı skalara dönüştürülebilir. Bu, harici kuvvet bileşenlerinin x, y ve z yönlerinde dengeli olduğu ve harici kuvvetlerin x, y ve z eksenleri etrafındaki momentlerinin de dengeli olduğu anlamına gelir. Eğer rijit cisim denge durumunda ise, harici kuvvet sistemi cisime translasyonel veya çevrimsel hareket kazandırmaz.

Rijit bir cismin denge denklemlerini yazmak için öncelikle cisim üzerine etkili olan tüm kuvvetleri belirleyin ve ardından buna uygun bir serbest cisim diyagramı çizin. Yapıya uygulanan kuvvetlerin yanı sıra yapı tarafından destekler tarafından oluşturulan tepkimeleri de dikkate alın. Her tepkimeyi doğru bir şekilde belirlemek, bilinmeyen kuvvetleri ve tepkimeleri çözmede yardımcı olabilir.

Denge koşullarının bilinmesi, rijit cisimlerle ilgili problemleri analiz etmek için kritik öneme sahiptir. Bilinmeyen kuvvetleri ve tepkimeleri belirleyerek ve denge için gerekli ve yeterli koşulları kullanarak, rijit cisimlerin davranışını öngörmek mümkündür.

Denge koşulları

Denge, katı bir cismin herhangi bir öteleme veya dönme hareketine maruz kalmadığı bir durumu ifade eder. Bu durum, kuvvet ve ...

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

rigid body force balance in equilibrium

Rigid body equilibrium depends on a balance of external forces and moments. A rigid body is in equilibrium when it has no translational motion and no rotational motion. This happens when the net force and the net couple acting on the body are both zero.

Internal forces are not used when checking equilibrium. These forces act in equal and opposite pairs inside the body, so they cancel each other. Because of that, they do not affect the overall motion or change in motion of the rigid body.

The external forces and moments determine whether the body stays balanced. These are the forces that can cause translation or rotation. The necessary and sufficient conditions for equilibrium are found by setting the resultant force and the resultant moment equal to zero.

The vector equations for equilibrium can also be written as six scalar equations. Each force and moment is resolved into rectangular components. This means the external force components in the x, y, and z directions must balance, and the moments about the x, y, and z axes must also balance.

To write equilibrium equations for a rigid body, first identify all forces acting on it. Then draw a free-body diagram. The reactions from supports must also be included. Correctly identifying each reaction helps solve unknown forces and reactions in structures.

Rigid Body Force Balance in Equilibrium

conditions of equilibrium

Rigid body equilibrium depends on a balance of external forces and moments. A rigid body is in equilibrium when it has no translational motion and no rotational motion. This happens when the net force and the net couple acting on the body are both zero. Internal forces are not used when checking equilibrium. These forces act in equal and opposite pairs inside the body, so they cancel each other. Because of that, they do not affect the overall motion or change in motion of the rigid body. The...

support reactions

Types of Structural Supports

Types of structural supports control how a coplanar force system moves and reacts under load. A coplanar force system is a set of forces that all lie in the same plane. The supports create reactions at the point of contact. These reactions help keep a structure stable under external forces. Supports work by stopping translation with an equal and opposite force. They can also stop rotation by applying a couple moment in the opposite direction. In structural design, these reactions are important...

internal forces and center of gravity

Forces Inside a Body and Balance

Internal forces and the center of gravity help explain how objects stay in balance. These mechanics ideas matter for structures, machines, and vehicles that must remain stable under different loads and conditions. Internal forces are created inside a body when its particles interact. They can appear as tension, compression, or shear forces. These forces act in collinear pairs with equal magnitude and opposite direction. Between connected parts, they cancel each other and help keep the body in...

alternative sets of equilibrium equations

alternative-sets-of-equilibrium-equations

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...

two force member

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...

three force member

Solving a Three-Force Member Example

A three-force member is a rigid body acted on by three forces at three points. The forces must have concurrent lines of action. If the forces are parallel, their lines of action stay parallel instead. A dumpster provides the example used here. It is connected to a pin support at point A and to a pin on a hydraulic cylinder at point B. The hydraulic cylinder acts as a two-force member in equilibrium. The dumpster weight acts through the center of gravity, and the support reaction acts at point...

equations of equilibrium in three dimensions

equations-of-equilibrium-in-three-dimensions

Checking Force Balance in 3D Structures

Checking force balance in 3D structures is a key step when a system is at rest. The vector and scalar equations of equilibrium are used to test whether a body is stable and will not collapse or fall apart. These equations give a clear way to study the forces acting on a body. The vector equations of equilibrium require the vector sum of all external forces on a body to equal zero. They also require the vector sum of the couple moments and the moments of all forces about a point to equal zero.

support reactions in three dimensions

3D Support Types for Stability and Motion

Support reactions in three dimensions keep structures stable and in equilibrium. They stop unwanted translation and rotation, so a design can handle external forces safely and work as intended. These reactions are important in many structures and systems. A ball and socket joint is one support that allows free rotation about any axis. It does not provide a moment that resists turning. At the same time, it restricts motion in space with three reaction forces along the three dimensions. A...

constraints and statical determinacy

Constraints in Structural Equilibrium

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 rigid body equilibrium is determined by balanced external forces and moments, free-body diagrams, and support reactions in high school physics.

Rigid Body Force Balance in 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

Rigid Body Force Balance in Equilibrium

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