Name: beam internal force analysis at point a
Uploaded: 2023-09-22T11:49:26.000Z
Duration: 1 min 28 s
Channel: JoVE

5キロニュートンのビームOCがあり、斜めに傾斜し、両端で支持されているとします。点Aでの内部荷重を求めます。
ビームを支えるジョイントは反力を受けます。点Oの周りのモーメント方程式を使用し、値を代入することにより、点Cの反力を決定できます。
ビームの重量は中心に作用し、そのコンポーネントで分解できます。
ここで、点 A を通る架空の線がビームを 2 つのセクションに分割していると考えてみます。次に、未知の力が最小のセグメントの自由体図を描きます。
平衡方程式を思い出し、水平方向に沿った力の値を代入することにより、断面内の垂直力を決定できます。
負の符号は、断面に作用する垂直力の反対方向を示します。
同様に、平衡方程式を使用し、垂直方向の力の値を代入することにより、断面内のせん断力を決定できます。
最後に、モーメント方程式を使用して、点Aのモーメントの大きさを決定できます。

<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ホーボーケン、ニュージャージー州:ピアソンプレンティスホール、pp 345、355。</li>
</ol>

構造部材の内部負荷：問題解決

構造部材を設計または解析する際には、その部材内で発生する内部負荷を考慮することが重要です。これらの内部負荷には、法線力、せん断力、曲げモーメントが含まれます。エンジニアは、これらの内部負荷を計算することで、構造部材が適用された外部力をサポートできることを確認することができます。

これを説明するために、水平面と53.13°の角度で傾斜した線OC（5 kN）を考えてみましょう。両端で支持されています。点Aにおける内部負荷を決定してください。

<img alt="Equation 1" src="/files/ftp_upload/14299/14299_Figure_1v3.svg" style="text-align: center; height: 250px;" />

このためには、まず点Cにおける反力を計算する必要があります。これは、点Oを中心としたモーメント方程式を使用して値を代入することで求めることができます。

<img alt="Equation 1" src="/files/ftp_upload/14299/14299_Equation_1v2.svg" style="text-align: center; height: 13px;" />

次に、点Cにおける水平方向の反力を計算することができます。これは1.87 kNです。

次に、重さが中心で作用していると仮定される線の重さをその成分に分解します。点Cにおける反力を計算し、線の重さを分解したら、点Aにおける内部負荷を決定することができます。

これを行うために、点Aを通過する架空の線を考え、線を2つのセクションに分割します。次に、未知の力が最小のセグメントの自由体図を描きます。平衡方程式を思い出し、水平方向の力の値を代入することで、セクションの法線力を-5.12 kNで求めることができます。マイナスの符号は、仮定された方向とは逆の断面への法線力を示しています。

同様に、平衡方程式を使用して垂直方向の力の値を代入することで、セクションのせん断力を1.5 kNで決定することができます。最後に、モーメント方程式を使用して点Aでのモーメントの大きさを求めることができます。これは8.94 kN・mです。

これらの手順に従うことで、構造部材の点Aにおける内部負荷を求めることができます。この問題解決プロセスは、構造部材が設計された力に耐えることを保証するために重要です。

構造部材を設計または解析する際には、部材内で発生する内部荷重を考慮することが重要です。これらの内部負荷...

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

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

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 equation about point O and substituting the known values. From this step, the horizontal reaction force at C is 1.87 kN. The beam’s weight is also treated as acting at the center, and it is resolved into horizontal and vertical components.

Next, an imaginary cut is made through point A. This splits the beam into two sections. A free-body diagram is then drawn for the section with the fewest unknown forces. Using equilibrium equations, the normal force at the cut is found to be -5.12 kN. The negative sign means the force acts opposite to the assumed direction.

The same section is used to find the shear force and bending moment. From the vertical force equation, the shear force is 1.5 kN. From the moment equation, the bending moment at point A is 8.94 kN·m. This step-by-step method shows how internal loadings are determined in a structural member.

Beam Internal Force Analysis at Point A

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

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

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

Find the internal normal force, shear force, and bending moment at point A of an inclined beam using equilibrium, reaction force, and a free-body diagram.

Beam Internal Force Analysis at Point A | JoVE K12

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mechanical engineering

Beam Internal Force Analysis at Point A

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