Name: two-force body equilibrium
Uploaded: 2025-05-22T09:06:02.000Z
Duration: 1 min 30 s
Channel: JoVE

위쪽 끝이 고정된 팔에 수직으로 매달려 있는 램프를 고려하십시오.
암 부재가 분리되어 있고 두 힘이 A와 B의 두 지점에서 중간에 하중이 가해지지 않고 작용하는 경우 이를 2력 부재라고 합니다. 여기서 힘의 성질은 인장 또는 압축입니다.
두 힘 구성원이 평형 상태에 있으려면 힘FA 와 FB 의 크기는 같아야 하지만 방향은 반대여야 합니다.
모멘트 평형에 대한 조건을 만족하려면 FA 와 FB 가 동일한 작용선을 가져야 합니다.
일반적으로 2-포스 멤버는 포인트 A와 B에 작용하는 여러 힘을 가질 수 있으며, 이는 포인트 A와 B에서 결과 힘으로 표시됩니다.
한쪽에 가해지는 힘의 크기와 방향을 알면 다른 쪽에 가해지는 힘을 계산할 수 있습니다. 이렇게 하면 평형 방정식에서 미지수의 수가 줄어듭니다.
2력 부재는 반드시 직선일 필요는 없습니다. 구부리거나 구부러질 수 있으며 트러스, 프레임 및 기계의 구조를 해석하는 데 사용됩니다.

<ol>
	<li>히벨러, R.C. (2016). Engineering Mechanics \u2012 정역학 및 동역학. 뉴저지 호보켄: 피어슨 프렌티스 홀. 230쪽.</li>
	<li>맥주, F.P.; 존스턴, ER; 마주렉, D.F; 크롬웰, PJ 및 셀프, BP (2019). 엔지니어를 위한 벡터 역학 \u2012 Statics and Dynamics. 뉴욕 : McGraw-Hill. 195쪽.</li>
</ol>

이력부재(두 개의 힘을 가진 물체)

Two Force Member

이력부재의 평형상태는 실제 응용에서 흔히 접할 수 있는 특별한 경우입니다. 이력부재는 오직 두 개의 외부 힘을 받는 강체입니다. 이러한 물체가 평형상태에 있기 위해서는 두 힘이 같은 크기, 같은 작용선, 그리고 반대 방향을 가져야 합니다.

<img alt="Figure 2" src="/files/ftp_upload/14273/14273_PT_Figure_1v2.svg" style="text-align: center; height: 350px;" />

표시된 플레이트 중 각각 A과 B에서 작용하는 두 가지 힘을 받는 것을 고려해 봅니다. 플레이트가 평형 상태에 있다면, 어떤 축에 대해서도 F1와 F2의 모멘트의 합은 0이어야 합니다. 점 A의 모멘트를 합하면 F2의 모멘트는 0이어야 합니다. 결과적으로, 점 A의 모멘트를 합하면, F2의 모멘트는 0이어야 한다는 것을 알 수 있습니다. 결과적으로, 점 A을 통과해야 합니다. 마찬가지로, 점 B의 모멘트를 합하면, F1의 작용선은 점 B을 통과해야 한다는 것을 알 수 있습니다. 이는 두 힘이 동일한 작용선을 갖는다는 것을 의미합니다. 즉, A과 B을 연결하는 선을 가짐을 의미합니다.

또한 두 힘은 크기가 같고 방향이 반대임을 알 수 있습니다. 이는 식 σ Fx = 0과 σFy = 0에서 알 수 있으며, 여기서 힘은 서로 상쇄됩니다.

여러 힘이 A과 B에 작용하면, A에 작용하는 힘은 그 결과인 F1로 대체될 수 있으며, 그 결과인 F2는 B에 작용하는 힘을 대체할 수 있습니다. 이력부재는 일반적으로 단지 두 지점에서 작용하는 힘을 받는 강체로 정의될 수 있습니다. 어떤 경우에도 결과인 F1와 F2는 물체의 평형을 보장하기 위해 동일한 작용선, 동일한 크기, 그리고 반대 방향을 가져야 합니다.

2-force body의 평형은 실제 응용 프로그램에서 자주 발생하는 특별한 경우입니다. two-force body는 다음과 같은 강체입니다.

Education

교육

JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Equilibrium of a Rigid Body

강체의 평형

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 works at point B. Summing the moments about point B shows that the line of action of F1 must pass through point B. So both forces lie on the line joining A and B.

The force balance also requires ΣFx = 0 and ΣFy = 0. These equations show that the two forces have the same magnitude and opposite directions, so they cancel each other out. When several forces act at A and B, each group can be replaced by a resultant force. Those resultants must still share the same line of action, the same magnitude, and opposite directions for the body to stay in equilibrium.

Two-Force Body Equilibrium

conditions of equilibrium

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...

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

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 a two-force body stays in equilibrium by using moment balance, force balance, and the rules for line of action, magnitude, and direction.

Two-Force Body Equilibrium | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Two-Force Body Equilibrium

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