Name: equivalent resultant loads on beams
Uploaded: 2023-09-22T11:49:23.000Z
Duration: 1 min 21 s
Channel: JoVE

テーパービームOBが一端に固定され、分散荷重を受けるとします。
変動荷重の等価合力を決定し、ビーム上の位置を特定します。
まず、分散荷重を2つの三角形の領域に分割します。
次に、左右の三角形領域の等価合力荷重の大きさは、各三角形の面積と等しくなります。
結果として生じる各荷重は、三角形の垂直辺ADから底辺の長さの3分の1に位置する重心に作用します。
等価合力荷重は、各三角形領域の個々の合力荷重を加算することで決定できます。
点Oの周りのモーメントは、各結果荷重によって作用する個々のモーメントを加算することによって決定できます。
点Oの周りの等価合力荷重のモーメントは、等価合力荷重と点Oからの距離の積に等しいというモーメント原理を思い出してください。
方程式の値を代入することにより、等価合力荷重の位置を決定できます。

<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: Pearson Prentice Hall, pp. 194-195</li>
</ol>

分布荷重：問題解決

ビームは様々な荷重を受ける工学的な応用で一般的に使用される構造要素です。分布荷重を受けるビームを解析するための最初のステップは、荷重をより小さな領域に分割して問題を単純化することです。これにより、各領域を個別に考慮し、ビームの各部分に作用する等価の結果力の大きさを計算することができます。各領域の等価の結果力の大きさは、各領域での荷重によって生じる力を表す領域の面積を計算することによって決定できます。

次に、ビーム上の各結果力の位置を特定します。これは、各領域の重心を見つけることによって行うことができます。各結果力は、これらの重心で作用し、ビーム上の特定の点で力を生じます。

全体のビームの等価な結果力は、決定された各結果力の大きさと位置を用いて計算することができます。これには、異なる領域の個々の結果力を合計して、ビームに作用する全体の等価な結果力を得ることが含まれます。

<img alt="Equation 1" src="/files/ftp_upload/14280/14280_PT_Equation_1.svg" style="text-align: center; height: 11px;" />

次のステップは、特定の点（通常はビームの固定端）周りのモーメントを決定することです。モーメントは、ビームに作用する力の回転効果を測定します。結果モーメントは、各荷重によって生じる個々のモーメントを追加することによって求めることができます。各荷重のモーメントは、力と指定された点からの距離の積と等しいです。

<img alt="Equation 2" src="/files/ftp_upload/14280/14280_PT_Equation_2.svg" style="text-align: center; height: 13px;" />

モーメントの原理を思い出すと、指定された点周りの等価な結果力のモーメントは、等価な結果力とその点からの距離の積と等しいです。

方程式を再配置し、用語を代入することにより、ビーム上の等価な結果力の位置を決定することができます。

<img alt="Equation 3" src="/files/ftp_upload/14280/14280_PT_Equation_3.svg" style="text-align: center; height: 35px;" />

ビームは、さまざまな耐荷重能力を必要とするエンジニアリングアプリケーションで一般的に使用される構造要素です。分析の最初のステップ...

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

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 must be located.

The position is found by using the centroid of each region. A centroid is the point where the region’s mass can be treated as concentrated. The individual resultant loads act at these centroids, so each force is placed at a specific point along the beam.

Once the separate forces and locations are known, they are combined to find the equivalent resultant load for the full beam. This is done by adding the individual resultant loads from the different regions. The result gives the overall force acting on the beam.

The next step is to determine the moment about a chosen point, usually the fixed end of the beam. A moment is the turning effect of a force. The total moment comes from adding the moments created by each load, and each moment equals force times distance from the chosen point.

By using the moment principle, the moment of the equivalent resultant load about that point must equal the force multiplied by its distance from the point. Rearranging that relationship makes it possible to find where the single equivalent load acts along the beam. This gives both the size and location of the load that replaces the distributed loading.

Equivalent Resultant Loads on Beams

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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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Calculating Moment with Cartesian Vectors

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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...

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Couple Moment in Force Systems

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Couple Moments and the Right-Hand Rule

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equivalent couples

Equivalent Couples in Mechanical Systems

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moment of a couple: problem solving

Torque from a Couple: Solving Forces

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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

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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...

simplification of a force and couple system: ii

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Resultant Force and Wrench Motion

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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 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 to replace a distributed load with one equivalent resultant force on a beam by using areas, centroids, and moments to find its location.

Equivalent Resultant Loads on Beams | 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

Equivalent Resultant Loads on Beams

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