Name: beam loads and internal forces
Uploaded: 2025-05-22T09:06:03.000Z
Duration: 1 min 14 s
Channel: JoVE

ビームに異なる荷重がかかると、内力が発生します。これらの力は、ビーム上の仮想点を考慮し、断面の方法を使用して決定できます。
ビームの断面に対して垂直に作用する内力は垂直抗力または軸力と呼ばれ、断面に接して作用する力はせん断力と呼ばれます。
これらの力は、各セグメントに反対方向に作用し、平衡方程式を適用することで決定できます。
荷重が変化する片持ち梁OBを考えてみましょう。ビームの中心に作用する法線力とせん断力を決定します。
これらの力は、断面法を使用し、ビームのセグメントABにかかる力を分析することによって決定できます。
類似の三角形の概念を使用して、中心の力を決定できます。
自由体図を描き、平衡方程式を使用することで、法線力とせん断力を決定できます。

<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:ピアソンプレンティスホール。343-344ページ。</li>
</ol>

通常力とせん断力

様々な荷重、例えば重さ、圧力、その他の外力が梁に作用すると、梁内部に内力が生じます。これらの力は、構造の全体的な安定性と強度に重要な影響を与えます。エンジニアは、これらの内力の大きさと方向を分析し決定するために、様々な手法を使用します。梁内部の内力を決定するために使われる一つの一般的な手法は、断面法と呼ばれます。この方法では、梁上の架空の点または断面を考慮し、その特定の点に作用する力を分析します。

通常力、または軸力とも呼ばれる力は、梁の断面に垂直に作用する内力です。この力は、梁に作用する荷重の性質によって圧縮力または引張力のいずれかとなります。一方、せん断力は、梁の断面に接線方向に作用する内力です。せん断力は、梁の各部分において逆方向に作用します。通常力とせん断力は、対象となる梁について平衡方程式を適用することで決定することができます。

通常力とせん断力の理解は、構造工学において重要です。これらの力は、梁や他の構造要素の安定性、強度、総合的な性能を決定する上で重要な役割を果たします。断面法や平衡方程式を使用することで、エンジニアは梁内部の内力を正確に決定し、運用寿命中に遭遇する荷重や応力に耐えることができる構造物を設計することができます。

ビームに重量、圧力、その他の外力など、さまざまな荷重がかかると、ビーム内に内部力が発生します。これら。。。

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

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 perpendicular to the beam’s cross-section. Depending on the load, this force can be compressive or tensile.

The other main internal force is the shear force. It acts tangentially, or along the cross-section. Shear forces act in opposite directions on each segment of the beam.

Normal and shear forces can be found by using equilibrium equations on the beam. This analysis is important in structural engineering. It helps engineers judge the stability, strength, and performance of beams and other structural elements.

Beam Loads and Internal Forces

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 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

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.

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

Learn how beam loads create internal normal and shear forces, and how engineers use the method of sections and equilibrium equations to analyze them.

Beam Loads and Internal Forces | JoVE K12

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mechanical engineering

Beam Loads and Internal Forces

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