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

ランプがアームから垂直にぶら下がっていて、その上端が固定されているとします。
アームメンバーが分離されており、2つの力がAとBの2点で作用し、その間に負荷がない場合、それは2つの力のメンバーと呼ばれます。ここで、力の性質は引張または圧縮のいずれかです。
2 つの力を持つメンバーが平衡状態にあるためには、力 F A と FB の大きさは等しく、方向は反対である必要があります。
モーメント平衡の条件を満たすには、F AとFBは同じ作用線を持つ必要があります。
一般に、2 つの力を持つメンバーは、点 A と B に作用する複数の力を持つことができ、それらは点 A と B の合力として表されます。
一方の側の力の大きさと方向がわかっている場合は、もう一方の側の力を計算できます。これにより、平衡方程式から未知数の数が減少します。
2 力部材は必ずしも直線ではなく、曲げたり曲げたりすることができ、トラス、フレーム、および機械の構造を解析するために使用されます。

<ol>
	<li>ヒベラー、RC(2016)。エンジニアリングメカニクス \u2012 静力学と力学。 ニュージャージー州ホーボーケン:ピアソンプレンティスホール。230ページ。</li>
	<li>ビール、FP;ジョンストン、ER;マズレック、D.F;クロムウェル、PJおよびセルフ、BP(2019)。エンジニアのためのベクトル力学 \u2012 静力学と動力学。ニューヨーク:マグロウヒル。195ページ。</li>
</ol>

二つの力

Two Force Member

二つの力体の平衡は、実用的な応用でよく遭遇する特定の場合です。二つの力体とは、外部から受ける力が二つだけの剛体のことを指します。このような体が平衡状態にあるためには、二つの力は同じ大きさで、同じ作用線上にあり、逆方向である必要があります。

<img alt="Figure 2" src="/files/ftp_upload/14273/14273_PT_Figure_1v2.svg" style="text-align: center; height: 350px;" />

示されたプレートのいずれかに、それぞれ点Aと点Bで作用するF1とF2の二つの力が加わっているとします。もしプレートが平衡しているならば、F1とF2のモーメントの合計はどの軸周りでもゼロでなければなりません。点A周りのモーメントを合計すると、F2のモーメントはゼロでなければならないことがわかります。結果として、その作用線は点Aを通過しなければなりません。同様に、点B周りのモーメントを合計すると、F1の作用線は点Bを通過しなければなりません。これは、両方の力が同じ作用線を持っていることを意味します-点Aと点Bを結ぶ直線です。

さらに、二つの力の大きさは同じであり、逆方向であることを示すことができます。これは、方程式ΣFx = 0 および ΣFy = 0 から明らかです。これらの力は互いに打ち消し合います。

点Aと点Bで複数の力が作用する場合、点Aで作用する力はそれらの合力F1に置き換えることができ、点Bで作用する力はそれらの合力F2に置き換えることができます。二つの力のメンバーとは、一般的には二つの点で作用する力によって受ける剛体と定義されます。いかなる場合でも、体の平衡を保証するために、合力F1とF2は同じ作用線、同じ大きさ、逆方向でなければなりません。

2つの力を持つ物体の平衡は、実際のアプリケーションでよく遭遇する特定のケースです。二力体は、...

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Equilibrium of a Rigid Body

剛体のつり合い

KEY TERMS AND CONCEPTS

主要用語と概念

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 機械工学は、平衡、力、トラス解析、構造力学などの重要なトピックをカバーする簡潔でわかりやすいアニメーション ビデオを提供します。実際のアプリケーションを探索し、科学者主導の実験を通じてこれらのコンセプトが実際に動作しているのを目撃してください。

mechanical engineering

Two-Force Body Equilibrium

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