Name: solving a three-force member example
Uploaded: 2023-09-22T11:49:22.000Z
Duration: 1 min 27 s
Channel: JoVE

3つの異なる点で作用する3つの力を受ける剛体は、3つの力のメンバーと呼ばれます。
これらの力の作用線は、作用線が平行である平行な力を除き、同時でなければなりません。
ポイントAでピンサポートに接続されたダンプスターと、ポイントBで油圧シリンダーに取り付けられたピンを考えてみましょう。
油圧シリンダーは、平衡状態にある2つの力のメンバーです。重量による力は重心を通じて作用し、支持体による反力は点Aで作用します。
最初のステップでは、ダンプスターに作用するすべての力を含むシステムのフリーボディ図を描画します。
力とモーメントの平衡方程式を使用して、未知の力F A と FCB を決定できます。
次に、点Aのモーメント平衡条件により、力FCBが計算されます。
垂直方向に沿った力平衡条件により、垂直方向の反力が得られます。
同様に、水平方向に沿って力の平衡条件を適用すると、水平方向の反力が得られます。

<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。196ページ</li>
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三力部材（three force members）

Three Force Member

三つの力が三つのポイントで作用する剛体は、三力部材として知られています。これらの力は、並行な力を除いて、共通の作用線を持たなければなりません。

例えば、ポイントAにピン支持に接続されたダンプスターと、ポイントBにハイドロリックシリンダに取り付けられたピンを考えてみましょう。

<img alt="Figure 1" src="/files/ftp_upload/14274/14274_Figure_1v3.jpg" style="text-align: center; height: 300px;" />

この場合、ハイドロリックシリンダは平衡状態である二力部材です。重量による力は重心を介して作用し、支持による反力はポイントAで作用します。

未知の力FAとFCBを解くために、最初のステップはダンプスターに作用するすべての力を含む全体の自由体図を作成することです。

<img alt="Figure 2" src="/files/ftp_upload/14274/14274_Figure_2v2.png" style="text-align: center; height: 250px;" />

次に、力とモーメントの平衡方程式を使用して未知の力の値を求めることができます。

<img alt="Equation 1" src="/files/ftp_upload/14274/14274_PT_Equation_1v2.svg" style="text-align: center; height: 13px;" />

<img alt="Equation 2" src="/files/ftp_upload/14274/14274_PT_Equation_2v2.svg" style="text-align: center; height: 13px;" />

<img alt="Equation 3" p="" src="/files/ftp_upload/14274/14274_PT_Equation_3v2.svg" style="text-align: center; height: 13px;" />

ポイントAにおけるモーメントの平衡条件により、力FCBの値が24.08 kNとなります。一方、垂直方向の力の平衡条件により、垂直反力FAy の値が9.74 kNとなります。同様に、水平方向の力の平衡条件を適用することで、水平反力FAxの値が25.74 kNとなります。

三力部材（Three Force Members）

3点に作用する3つの力を受ける剛体は、3つの力のメンバーとして知られています。これらの部隊は、...

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

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 A.

The solution starts with a free-body diagram of the entire system. That diagram includes every force acting on the dumpster. Then the force and moment equilibrium equations are used to solve for the unknown forces.

Taking moments about point A gives the cylinder force F CB as 24.08 kN. The vertical force equilibrium condition gives the vertical reaction F Ay as 9.74 kN. The horizontal force equilibrium condition gives the horizontal reaction F Ax as 25.74 kN.

Solving a Three-Force Member Example

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

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

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 to analyze a three-force member with a free-body diagram, equilibrium equations, and a dumpster example to find unknown reaction forces.

Solving a Three-Force Member Example | JoVE K12

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mechanical engineering

Solving a Three-Force Member Example

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