Name: resultant forces in force and couple systems
Uploaded: 2023-09-22T11:49:22.000Z
Duration: 1 min 18 s
Channel: JoVE

等価合力と垂直な作用線を持つ合力カップルモーメントを持つシステムは、新しい作用線に沿って作用する等価な単一の合力に減らすことができます。
コンカレントフォースシステムは、共通のポイントで交差するすべてのフォースの作用線を持つため、このポイントではモーメントは発生せず、単一の合力で表すことができます。
コプラナーフォースシステムでは、すべてのフォースの作用線と結果力は同じ平面上にあります。したがって、結果として生じるカップルモーメントは、結果力に対して垂直になります。
合力モーメントは、合力を垂直な距離だけ移動させて同じモーメントを生成することで置き換えることができます。
同様に、平行力システムでは、すべての力と合力は同じ軸に平行です。
そして、結果として生じるカップルモーメントは、結果力に対して垂直にあります。
したがって、システムは、垂直軸上にある点に作用する同等の単一の合力に縮小できます。

<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。177-179ページ。</li>
</ol>

力とカップルシステムの簡略化 i

剛体の解析を簡素化するため、力とカップルモーメントのシステムを等価なシステムに簡略化する概念は重要です。この簡略化によって、システムによって生じる外部効果をより簡単に計算し理解することができます。特に、等価な結果力と結果カップルモーメントが直交する作用線を持つシステムは、新しい作用線に沿って作用する単一の等価な結果力にさらに簡略化できます。この方法で簡略化できる主な力システムには、共通、共面、平行力システムの3つの主要なタイプがあります。

共通の力システムは、作用線が1つの点で交差する力から成り立ちます。この交差により、その点でモーメントは生じず、システムは交差点で作用する単一の結果力によって表現できます。この簡略化によって、力システムの複雑さが大幅に減少し、より簡単な解析が可能になります。

共面力システムでは、すべての力と結果力の作用線が同じ平面にあります。このシステムの結果カップルモーメントは、結果力に対して垂直であり、さらなる簡略化が可能です。結果力を垂直な距離で移動することで、元のシステムと同じモーメントを生じさせることができます。

平行力システムは、同じ軸に平行な力から成り立ち、結果力もその軸に平行です。この場合、結果カップルモーメントは結果力に対して垂直であり、簡略化が可能です。システムは、垂直な軸上にある点に作用する単一の等価な結果力に簡略化できます。

これらの力システムのそれぞれにおいて、力とカップルモーメントを等価な単一の結果力に簡略化するプロセスは、剛体に対する外部効果の解析と理解を簡素化します。この簡略化は、設計と安全性の目的で複雑な力システムを解析する必要があるエンジニアリングの応用において有益です。

共通、共面、平行力システムの基本的な原則を理解することで、エンジニアや他の専門家は、様々な力にさらされる構造物、機械、その他のシステムをより効果的に解析し設計することができます。複雑な力システムを単一の等価な結果力に簡略化することで、計算が容易になり、より効率的かつ実用的な設計が可能となります。

力とカップルシステムの簡略化 I

力と結合モーメントのシステムを等価なシステムに縮小するという概念は、剛体の解析を簡略化する上で不可欠です。これ。。。

simplification-of-a-force-and-couple-system-i

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Force System Resultants

力の系の合力

KEY TERMS AND CONCEPTS

主要用語と概念

Simplification of a Force and Couple System I

resultant forces in force and couple systems

Force and couple systems can be reduced to a simpler equivalent system. This makes rigid body analysis easier because the external effect of the forces is captured with fewer elements. When the resultant force and resultant couple moment have perpendicular lines of action, the system may be reduced further to a single resultant force along a new line of action.

Three common force systems can be simplified this way: concurrent, coplanar, and parallel. A concurrent force system has lines of action that meet at one point. Because the forces pass through the same point, no moment is produced there, and the system can be replaced by one resultant force acting at that intersection.

A coplanar force system has all force lines of action in the same plane. In this case, the resultant couple moment is perpendicular to the resultant force. That allows the force to be shifted by a perpendicular distance while keeping the same moment as the original system.

A parallel force system has forces that are parallel to the same axis. The resultant force is also parallel to that axis. Here, the resultant couple moment is perpendicular to the resultant force, so the system can be reduced to one equivalent force acting at a point on the perpendicular axis.

These reductions are useful in engineering because complex force systems often need to be checked for design and safety. By using concurrent, coplanar, and parallel force systems, engineers can analyze structures, machines, and other rigid bodies more efficiently. Turning several forces and couple moments into one resultant force also makes the calculations simpler and the design process more practical.

Resultant Forces in Force and Couple Systems

resultant-forces-in-force-and-couple-systems

moment of a force: scalar formulation

Torque on a Flywheel: Direction and Size

Torque, or the moment of a force, describes how a force can make an object turn about an axis. It is a vector quantity, so it has both size and direction. This idea is important in physics, mechanics, and engineering. A simple flywheel example shows how torque works. The flywheel rotates about point O when a force is applied to it. The moment arm is the perpendicular distance from point O to the line of action of the force. The moment, in newton-meter (N-m), is found by multiplying the force...

moment of a force: problem solving

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resultant moment: scalar formulation

Net Moment Sign Convention in 2D Forces

Net moment in two-dimensional force systems shows how multiple forces can cause rotation about a fixed point. The scalar formulation helps analyze equilibrium in structures that are acted on by several forces. It focuses on the x-y plane and uses a simple sign rule to describe the direction of rotation. To find the resultant moment, the moments from all forces in the system are considered about a chosen point A. Each moment is assigned a sign based on its sense of rotation. Positive moments...

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cartesian form for vector formulation

Calculating Moment with Cartesian Vectors

Calculating moment with Cartesian vectors shows how position and force vectors work together. The moment of force is the cross product of these vectors, so it is a vector quantity. In Cartesian form, unit vectors help write the vectors in component form. The cross product can be arranged in determinant form. That determinant is then expanded to find the Cartesian vector form of the moment of force. This method gives a clear way to work through the calculation step by step. A revolving door...

resultant moment: vector formulation

Calculating Torque from Multiple Forces

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principle of moments

Resolving Forces in Moment Calculations

The principle of moments, also called Varignon's theorem, explains how a force creates rotation about a point. It is a key idea in physics and engineering. It also helps describe when a rigid body stays in equilibrium under external forces. The moment of a force is found by multiplying the force by the perpendicular distance from the point of application to the point being studied. A larger force or a larger distance gives a larger moment. This makes the idea useful for checking how strongly a...

principle of moments: problem solving

Torque About an Axis in 3D Systems

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moment of a force about an axis: scalar

Bicycle Torque and Moment About an Axis

The moment of a force about an axis describes how a force can make an object turn around a fixed line. In scalar analysis, the moment is found from the perpendicular distance between the axis of rotation and the line of action of the force. That distance is called the moment arm. A bicycle gives a clear example of this idea. When the cyclist pushes on the pedal, the chain applies a force to the wheel’s axle and makes it rotate. The axis of rotation passes through the axle, and the moment arm...

moment of a force about an axis: vector

Torque on a Bicycle Wheel: Vector Method

Torque, or the moment of a force, explains how a force can make an object rotate about an axis. A bicycle is a clear example. When a cyclist presses on the pedal, the crankshaft turns and helps drive the wheel. To analyze this motion, a coordinate system is set up first. The x-axis is tangential to the wheel, the y-axis is perpendicular to the x-axis and points upward, and the z-axis points outward from the wheel. In this setup, the force on the wheel axle lies along the x-axis. The axle...

couple

Couple Moment in Force Systems

A couple is a pair of parallel forces that are equal in magnitude and opposite in direction. The two forces are separated by a perpendicular distance called the couple arm. Together, they create a turning effect on a body instead of a net push. This turning effect is called the couple moment. It rotates the body about an axis that is perpendicular to the plane of the forces. The SI unit for a couple moment is the Newton-meter (N-m). A common example is tightening a bolt with a lug wrench. In...

couples: scalar and vector formulation

Couple Moments and the Right-Hand Rule

Couple moments describe the turning effect of two parallel forces that are equal in magnitude and opposite in sense. This force pair creates rotation instead of straight-line motion. A common example is a ship’s steering wheel, where a small turn can guide the ship through the ocean. A couple moment can rotate clockwise or anticlockwise. The right-hand rule helps identify its direction. To use it, curl the fingers of your right hand in the direction of rotation. Your thumb points in the...

equivalent couples

Equivalent Couples in Mechanical Systems

Equivalent couples in mechanical systems describe pairs of forces that create the same rotational effect on a rigid body. Two couples are equivalent when they have the same moment magnitude and act in the same direction. They then cause the same angular displacement or angular acceleration in the body. A couple is made of equal and opposite forces separated by a perpendicular distance. The moment of the couple depends on both the force size and the spacing between the forces. For example, one...

moment of a couple: problem solving

Torque from a Couple: Solving Forces

The moment of a couple is a key physics and engineering idea for finding torque, or rotational force. A couple is made of two equal and opposite forces that act on an object. When those forces work together, they create a twisting effect that can rotate the object. The moment of a couple is calculated by multiplying the size of one force by the perpendicular distance between the two lines of action. That distance is the shortest straight-line distance between the force directions. This gives...

system of forces and couples

Equivalent Force and Moment Systems

Structural systems often experience several forces and couple moments at the same time. Engineers simplify these loading cases by replacing them with an equivalent force and moment system at a chosen point O. This makes the analysis easier while keeping the same external effects on the member. A key idea in this process is the principle of transmissibility. A force is a sliding vector, which means it can be moved anywhere along its line of action without changing how the body behaves...

simplification of a force and couple system i

Force and couple systems can be reduced to a simpler equivalent system. This makes rigid body analysis easier because the external effect of the forces is captured with fewer elements. When the resultant force and resultant couple moment have perpendicular lines of action, the system may be reduced further to a single resultant force along a new line of action. Three common force systems can be simplified this way: concurrent, coplanar, and parallel. A concurrent force system has lines of...

simplification of a force and couple system: ii

simplification-of-a-force-and-couple-system-ii

Resultant Force and Wrench Motion

Resultant force and resultant couple moment describe how several forces and moments act together on a rigid body in three dimensions. When many forces act on an object, they can be replaced by one equivalent force. The moments from those forces can also be combined into one equivalent couple moment. In some cases, the resultant force and the resultant couple moment are not mutually perpendicular. That means the angle between them is not 90 degrees. To study this situation, the couple moment is...

distributed loads

Load Distribution on Shelves and Dams

Load distribution helps engineers describe how force spreads across a surface or structure. A distributed load is a continuous force per unit area, rather than a single point force. It is a common idea in many practical situations. A bookshelf full of stacked books is one simple example. The weight of the books is spread along the shelf, so the pressure changes across the surface. This pressure is measured in Newtons per square meter, or Pascals. A hydroelectric dam gives another clear...

load along a single axis

Finding Resultant Loads on a Beam

Structural engineering often requires finding the resultant load on a beam with changing force patterns. Here, a beam of length L carries a varying load made from parabolic and trapezoidal load distributions along the x-axis. The goal is to find the total load, where it acts, and the centroid of the combined area so the beam’s response can be predicted. The parabolic load is handled first. A small force element, dR, acts over a short distance, dx, and these elements are integrated across the...

distributed loads: problem solving

Equivalent Resultant Loads on Beams

Equivalent resultant loads on beams can be found by breaking a distributed load into smaller regions. This makes the beam easier to analyze. Each region can then be handled on its own before the results are combined. The magnitude of the equivalent resultant load for each region comes from the area of that region. In this setting, area represents the force applied by the distributed load over that part of the beam. After finding the force for each region, the position of each resultant load...

key terms and concepts

Learn how concurrent, coplanar, and parallel force systems can be reduced to one equivalent resultant force and couple moment for simpler rigid body analysis.

Resultant Forces in Force and Couple Systems | 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

Resultant Forces in Force and Couple Systems

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