Name: beam types and support conditions
Uploaded: 2023-09-22T11:49:26.000Z
Duration: 1 min 30 s
Channel: JoVE

ビームは、部材に沿ったさまざまな点に適用される荷重を支えるように設計された、まっすぐで長い構造部材です。
ビームは、形状、断面、サポートタイプ、および平衡状態に基づいて分類できます。
ジオメトリに基づいて、ビームは直線、テーパー、またはカーブにすることができます。
Iビーム、Tビーム、Lビーム、Cビーム、長方形ビームなど、さまざまな断面形状を持つことができます。
支持体に応じて、ビームは単純支持、張り出し、連続、片持ち、または固定に分類できます。そのサポート間の距離は、ビームのスパンと呼ばれます。
単純に支持されたビームは両端で支持され、張り出したビームはその支持の1つを超えて伸びています。
片持ち梁は一端で固定されており、固定端から伸びています。
連続ビームは2点以上で支持されますが、固定ビームは両端で固定することも、一端で支持することもできます。
ビームサポートでの反応は、サポートが3つの未知数のみを含む場合、静的に決定できます。追加の未知数がある場合、ビームは静的に不確定です。

<ol>
	<li>ビール、FP;ジョンストン、ER;マズレック、D.F;クロムウェル、PJおよびセルフ、BP(2019)。エンジニアのためのベクトル力学 \u2012 静力学と動力学。ニューヨーク:マグロウヒル。378-379ページ</li>
</ol>

梁（はり）は構造工学や建設の重要な要素で、その長さの間にさまざまな点でかかる荷重を支えるために設計されています。これらの長くて直線的な部材は、幾何学、断面形状、支持形式、および平衡条件に基づいて分類することができます。

幾何学に基づくと、梁は直線、細い、または曲がったものに分類されます。直線の梁は最も一般的なタイプで、その全長を通じて断面形状が一定です。一方、細い梁はその長さにわたって断面形状が変化します。曲がった梁は曲線の形状をしています。

また、梁にはI形梁、T形梁、L形梁、C形梁、または長方形梁のようなさまざまな断面形状があります。各形状は、応用や梁が支える荷重に応じて独特の耐荷能力を提供するように特別に設計されています。

支持形式は梁の設計と性能に重要な役割を果たします。支持に基づいて、梁は単純支持、はり出し、連続、カンチレバー、または固定のように分類することができます。支持部の間の距離は梁の距離（スパン）として知られています。

単純支持梁は両端に支持部がありますが、はり出し梁はそのうちの一方の支持部を超えて伸びています。カンチレバー梁は一方の端で固定され、固定点から伸びています。連続梁は長さの中で2つ以上の点で支持を持ち、固定梁は両端に固定されるか、片方の端で支持されて他方の端で固定されます。

梁の支持部での反力は、支持が3つの未知数のみを含む場合に静的に決定可能です。しかし、もし追加の未知数があれば、梁は静的に不定です。

梁は、構造エンジニアリングと建設に不可欠なコンポーネントであり、その長さに沿ってさまざまなポイントで加えられる荷重を支えるように設計されています。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

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 include I-beams, T-beams, L-beams, C-beams, and rectangular beams. Each shape is designed to handle load-bearing needs in a different way, depending on where and how the beam is used.

Supports create another major way to classify beams. A simply supported beam has supports at both ends. An overhanging beam extends beyond one of its supports, while a cantilever beam is fixed at one end and extends outward from that fixed point.

Some beams have more than two supports. A continuous beam has support at more than two points along its length. A fixed beam may be fixed at both ends, or supported at one end and fixed at the other end. The span of a beam is the distance between its supports.

Beam reactions can also be described by equilibrium. A beam is statically determinate if its supports create only three unknowns. If there are more unknowns, the beam is statically indeterminate. This difference is important when analyzing how the beam carries load.

Beam Types and Support Conditions

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

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

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 beams are classified by shape, cross-section, supports, span, and equilibrium. Explore simply supported, cantilever, continuous, and fixed beams.

Beam Types and Support Conditions | 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

Beam Types and Support Conditions

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