Name: forces that bend and twist materials
Uploaded: 2025-05-22T09:06:03.000Z
Duration: 1 min 20 s
Channel: JoVE

曲げモーメントは、外力を受けたときに構造要素に発生する反力として定義され、要素が曲げられます。
構造要素が曲げを受けると、上部に圧縮法線力、下部に引張法線力が生成され、要素の曲げモーメントを決定するカップルが生成されます。
一方の端に固定された定規、飛び込み台、棒高跳びの曲げは、曲げモーメントの例です。
ねじりモーメントは、ねじれ力がその横軸に沿って物体に加えられ、断面がねじれるときに発生します。
衣服をねじる、ねじを打ち込む、ねじりばねは、ねじりの瞬間のいくつかの例です。
ビームの断面に作用する内力とカップルモーメントは、それらのx、y、z成分で表すことができます。
ねじりモーメント My は y 方向に沿って表され、Mx と Mz は x 方向と z 方向に沿った曲げモーメント成分を表します。

<ol>
	<li>Hibbeler、RC(2016)エンジニアリングメカニクス:静力学とダイナミクス 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、pp 344-345。</li>
	<li>メリアム、J.L.;Kraige、LG、およびBolton、JN(2020)。エンジニアリングメカニクス \u2012 静力学。ニュージャージー州ホーボーケン:ジョン・ワイリー。276ページ。</li>
</ol>

屈曲モーメントとねじれモーメント

Bending and Torsional Moments

屈曲モーメントとねじれモーメントは、構造工学における2つの基本的な概念です。それらは、異なる荷重条件下での材料や構造物の挙動を理解する上で重要な役割を果たします。

外部力が構造要素に作用した時に、その要素に反力が生じ、要素は曲げられます。構造要素が上方向に曲がると、上部に圧縮的な法線力が生じ、下部を引っ張る法線力が生じます。これにより、要素の屈曲モーメントが決まります。このモーメントは、興味のある点から力の作用線までの距離と力の大きさを考慮して計算されます。

一端で固定された定規の曲げは、屈曲モーメントの例です。サポートされていない端近くに垂直に力が加わると、定規は曲がります。加わる力により、固定端を中心としたモーメントが生じ、定規が曲がるまたは変形します。この状況では、定規は圧縮力と引張力の両方を経験します。加わる力から離れた定規の上側は引っ張られます。加わる力の方向を向いた定規の下側は圧縮されます。

ねじれモーメントは、体の横断面または長手方向に捻り力が加わり、断面が捻じれるときに生じます。この捻り力により、材料内部に内部抵抗が生じ、加えられた力に反対する力が生まれます。ねじれモーメントは、捻り力と興味のある点から力の作用線までの距離の積として計算されます。

ドライバーや電動ドリルを使用して材料にスクリューを取り付ける際、ねじれモーメントがスクリューに加わります。スクリュードライバーや電動ドリルによって生成される捻り力により、スクリューが回転し、材料からの抵抗が生じます。材料からの抵抗は、ねじれモーメントを生み出す反対力を生成します。

曲げモーメントとねじりモーメントは、構造工学における2つの基本的な概念です。彼らはの行動を理解する上で重要な役割を果たします...

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Internal Forces

内力

KEY TERMS AND CONCEPTS

主要用語と概念

forces that bend and twist materials

Bending and torsional moments describe how materials respond to force. These ideas are important in structural engineering because they help explain how beams, rulers, and screws change shape under load. A moment depends on both the size of the force and the distance from the point of interest to the force’s line of action.

A bending moment forms when an external force makes a structural element bend. If the element bends upward, the top side is in compression and the bottom side is in tension. These opposite forces create a couple that determines the bending moment. A ruler fixed at one end shows this effect when a downward force is applied near the free end.

In that ruler example, the force acts perpendicular to the ruler and causes it to deform around the fixed end. The side facing away from the applied force is in tension, and the side facing toward the force is in compression. This makes the bending moment easy to see in a simple everyday object.

A torsional moment happens when a twisting force is applied along a body’s transverse or longitudinal axis. The material resists that twist, so an internal force develops inside it. A screwdriver or power drill turning a screw shows torsion in action. As the screw rotates and meets resistance from the material, the twisting force and the opposing resistance create the torsional moment.

Forces That Bend and Twist Materials

sign convention

Beam Forces: Tension, Shear, and Bending

Beam analysis depends on the internal forces and moments inside a structure. These include normal force, shear force, and bending moment. Engineers use the method of sections to cut the beam and find these values. A sign convention helps show whether each result is positive or negative. Normal force acts perpendicular to the beam’s cross-section. It can pull the material in tension or push it in compression. Tension is taken as positive, while compression is taken as negative. This makes it...

normal and shear force

Beam Loads and Internal Forces

Beam loads create internal forces inside a structure. Weight, pressure, and other external forces can all act on a beam. These internal forces affect the beam’s stability and strength. Engineers study these forces to find their size and direction. A common approach is the method of sections. In this method, an imaginary cut is made at a chosen point on the beam, and the forces at that section are analyzed. One internal force is the normal force, also called the axial force. It acts...

bending and torsional moments

Bending and torsional moments describe how materials respond to force. These ideas are important in structural engineering because they help explain how beams, rulers, and screws change shape under load. A moment depends on both the size of the force and the distance from the point of interest to the force’s line of action. A bending moment forms when an external force makes a structural element bend. If the element bends upward, the top side is in compression and the bottom side is in tension.

internal loadings in structural members: problem solving

internal-loadings-in-structural-members-problem-solving

Beam Internal Force Analysis at Point A

Beam internal force analysis shows how normal force, shear force, and bending moment act inside a structural member. These internal loadings help engineers check whether a beam can support the external forces applied to it. The example uses a beam OC that weighs 5 kN and is inclined at 53.13° with the horizontal. The beam is supported at both ends. The goal is to find the internal loadings at point A. The first step is to find the reaction force at point C. This is done by taking the moment...

beams

Beam Types and Support Conditions

Beams are key parts of structural engineering and construction. They support loads that act at different points along their length. Engineers use beam shape and support conditions to understand how a beam will perform. Beams can be classified by geometry. Straight beams are the most common and have a constant cross-section along their length. Tapered beams change in cross-section from one end to the other, while curved beams have a curved shape. Beam cross-section also matters. Common shapes...

shear diagram

Beam Shear Force Diagram

Beam shear force diagrams show how shear changes along the length of a supported beam. In beam mechanics, they help students track the internal shear force caused by perpendicular loads. The beam AB in this example is supported at both ends, so the first step is to draw a free-body diagram that shows the external forces and internal reactions. The reaction forces at supports A and B are found with equilibrium equations for force and moment. For the beam shown, the vertical reaction at A is 24...

bending moment diagram

Beam Load Analysis with Moment Diagrams

Beam load analysis uses a bending moment diagram to show how bending changes along the length of a beam. This diagram helps engineers and designers check whether a structure can handle applied forces. It is also useful for parts such as shelving arms, which must resist forces and moments from a load. To build the diagram, start by finding the reactive forces and any couple moments on the beam. In some cases, especially when a beam is inclined, these forces must be resolved into components that...

relation between the distributed load and shear

relation-between-the-distributed-load-and-shear

Shear Change Under Distributed Loading

Shear force changes along a beam under a distributed load. In structural analysis, this relationship helps explain how beams respond to loading conditions that also include concentrated loads and a couple moment. To study the link, consider a small beam section that has no concentrated load or couple moment on it. Draw a free-body diagram for that elemental section. It includes the distributed load along the beam, the shear force V(x) on the right-hand side of the cut, and a small added shear...

relation between the shear and bending moment

relation-between-the-shear-and-bending-moment

Shear and Moment Diagrams in Beam Loads

Shear and moment diagrams help show how a beam responds to loads. A beam can carry a distributed load, concentrated loads, and a couple moment. These loads create internal shear forces and bending moments. The beam is examined by isolating a small elemental section and drawing a free-body diagram. For that section to stay in equilibrium, the moment on the right side must be slightly larger than the moment on the left side. The distributed load also has a resultant force that acts at a...

shear and bending moment diagram: problem solving

shear-and-bending-moment-diagram-problem-solving

Beam Load Analysis with Shear Diagrams

Beam load analysis uses shear and bending moment diagrams to track the internal forces in a beam. These diagrams are important when a beam carries concentrated loads and a distributed load. They help show how the beam responds so structures can be designed safely and efficiently. The first step is to draw a free-body diagram of the whole beam. A free-body diagram shows the concentrated loads, the distributed load, and the reaction forces at the supports. Use the equilibrium equations, where...

cable subjected to concentrated loads

Finding Tension in a Loaded Cable

Flexible cables can carry vertical point loads between two fixed supports. The cable is treated as flexible, inextensible, and nearly weightless. Under these conditions, it changes shape to form straight-line segments, and each segment carries a constant tensile force. To analyze the cable, a free-body diagram is drawn for the whole cable. This helps identify the reaction forces at the supports. In many cases, the number of unknown reaction components is greater than the available equilibrium...

cable subjected to a distributed load

Finding Cable Shape Under Distributed Load

Cable shape under a distributed load is found by analyzing the forces along a small piece of the cable. This method is important in suspension bridge design because the main cables must carry changing loads safely. The load causes the tensile force in the cable to change, and it also creates cable deformation. The analysis starts with a free-body diagram of a short cable segment. The diagram shows the distributed load and the change in tensile force across that segment. Equilibrium equations...

cable subjected to its own weight

Cable Sag Under Its Own Weight

Overhead power transmission cables sag under their own weight, and that shape affects how they carry electricity across long distances. To study this behavior, the cable is analyzed with a generalized loading function. This function treats the load along the cable's arc length instead of its projected length, which gives a more accurate picture of the cable's response. The analysis then focuses on a small cable segment. A free-body diagram is drawn to show the forces acting on that segment.

cable: problem solving

Cable Tension Under Uniform Loading

Cable tension under uniform loading is found by analyzing a cable fixed between two supports. The problem starts with the support conditions and the load on the cable. From there, the cable’s shape must be described with an equation that matches the curve formed by the load. The next step is to integrate the shape equation to get the cable’s shape function. This makes it possible to solve for constants in the equation. The boundary condition at the origin gives one constant. The slope, which...

key terms and concepts

Explore how bending and torsional moments act on materials, from a ruler bending at one end to a screw twisting under a screwdriver.

Forces That Bend and Twist Materials | 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

Forces That Bend and Twist Materials

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