Name: shearing stress pattern in a narrow beam
Uploaded: 2024-05-23T12:59:49.000Z
Duration: 1 min 11 s
Channel: JoVE

ビームの要素セクションは、応力の分布を解析するために考慮されます。要素の水平面に加えられるせん断力の大きさは、水平せん断表現から得られます。
その面の平均せん断応力は、水平せん断を面の面積で割ることによって求められます。
ビーム断面の横面と水平面のせん断応力は等しく、ビーム上部のラインに沿った平均応力を表します。せん断応力は、力が加えられていないため、上面と下面でゼロです。
幅の狭い長方形の梁では、幅がその深さの 4 分の 1 未満であるため、梁セクションの幅に沿ったせん断応力の変化は平均せん断応力の 0.8% 未満です。
したがって、平均せん断応力方程式は、その断面積全体の任意の点でのせん断応力を決定するために使用されます。
矩形梁の横断面では、せん断応力は放物線状に分布し、上部と下部の応力はゼロです。

狭い長方形の梁における応力の分布

Distribution of Stresses in a Narrow Rectangular Beam

梁の応力分布を調べるには、要素断面を調べることが不可欠です。この面の平均せん断応力を決定するには、計算されたせん断を表面積で割ります。重要なのは、梁の横断面と水平面上のせん断応力が互いに反映されており、梁の上部領域に沿った一貫した応力分布を示していることです。特に、梁の上面と下面には力が加えられていないため、これらの領域にはせん断応力が存在しません。

狭い長方形の断面を持つ梁の場合、幅方向のせん断応力の変動は最小限で、平均応力の 0.8% 未満です。この小さな変動は、梁の幅がその深さよりもはるかに小さいため、平均せん断応力方程式は梁断面の任意の点にわたる応力を評価するための信頼できる方法となります。長方形の梁の横断面では、せん断応力が放物線状に分布します。この分布は、梁の上端と下端で応力がゼロであり、中心に向かって応力が増加していることを特徴としています。この放物線状の応力プロファイルは、梁が応力を管理し、安定性を損なうことなく構造の完全性と荷重に耐える能力を確保する方法を理解するために不可欠です。

ビームの要素セクションは、応力の分布を解析するために考慮されます。水平に及ぼされるせん断力の大きさ...

distribution-of-stresses-in-a-narrow-rectangular-beam

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Shearing Stresses in Beams and Thin-Walled Members

梁および薄肉部材におけるせん断応力

shearing-stresses-in-beams-and-thin-walled-members

KEY TERMS AND CONCEPTS

主要用語と概念

shearing stress pattern in a narrow beam

Shearing stress in a narrow rectangular beam is found by studying a small elemental section of the beam. The average shearing stress on that face is calculated by dividing the shear by the surface area. This gives a simple way to describe how the load is spread through the beam.

The shearing stresses on the beam&amp;#39;s transverse and horizontal planes match each other. That means the stress pattern is consistent in the upper region of the beam. Shearing stress is also absent at the top and bottom surfaces, because no applied forces act there.

For a narrow rectangular cross-section, the change in shearing stress across the width is very small. It is less than 0.8% of the average stress. Because the beam is much wider in depth than in width, the average shearing stress equation works well at any point in the cross-section.

Across the rectangular beam&amp;#39;s transverse section, the shearing stress follows a parabolic shape. A parabolic distribution curves upward from the edges to the center. Stress is zero at the top and bottom edges and rises toward the middle. This pattern helps explain how beams carry load while staying structurally stable.

Shearing Stress Pattern in a Narrow Beam

shear on the horizontal face of a beam element

shear-on-the-horizontal-face-of-a-beam-element

Beam Shear Flow from Bending Moments

Beam shear flow comes from the horizontal shear that acts on a prismatic beam element. The element is also acted on by vertical shear forces and normal forces. To study this behavior, the beam is divided into upper and lower sections by the neutral axis. The force balance on the small element is written with an equilibrium equation. That step reveals the horizontal shearing force. This force is tied to the bending moments and to the cross-section’s first moment of inertia. The same result is...

distribution of stresses in a narrow rectangular beam

Shearing stress in a narrow rectangular beam is found by studying a small elemental section of the beam. The average shearing stress on that face is calculated by dividing the shear by the surface area. This gives a simple way to describe how the load is spread through the beam. The shearing stresses on the beam&amp;#39;s transverse and horizontal planes match each other. That means the stress pattern is consistent in the upper region of the beam. Shearing stress is also absent at the top and...

shearing stresses in a beam: problem solving

shearing-stresses-in-a-beam-problem-solving

Beam Shear Stress Analysis and Safety Check

Beam shear stress analysis shows how loads create internal stress in a cantilever beam with a rectangular cross-section. The beam in this problem carries both a distributed load and a point load. The goal is to find the shearing stress at key points and check whether the beam stays within a safe limit. The first step is to identify all loads acting on the beam. Next, the reactions at the fixed end are found using equilibrium equations. The vertical reaction combines the distributed load and...

plastic deformations

Cantilever Beam Yield and Failure

Cantilever beams show how a material bends, yields, and can eventually fail under load. A cantilever beam is fixed firmly at one end and loaded at the other end. When the load stays within the elastic range, the beam returns to its original shape after the load is removed. That reversible behavior is called elasticity. If the load goes beyond the elastic limit, the beam begins plastic deformation. Plastic deformation means the shape change is permanent. In a cantilever beam, this change starts...

unsymmetric loading of thin-walled members

unsymmetric-loading-of-thin-walled-members

Shear Center in Thin-Walled Members

Thin-walled members with non-symmetrical cross-sections are widely used in engineering structures because they save material while still providing strength. Their shape helps with structural integrity, but it also makes load analysis more complex. When these members are loaded in an unsymmetrical way, the stress is not spread evenly. Unsymmetrical loading can make a member bend and twist at the same time. That combined action can lead to deformation or even structural failure. Engineers must...

unsymmetric loading of thin-walled members: problem solving

unsymmetric-loading-of-thin-walled-members-problem-solving

Finding the Shear Center of a Channel Section

Finding the shear center of a channel section starts with the member’s shear force and moments of inertia. A shear center is the point where a load must act so the section bends without twisting. For a channel with uniform thickness, height, and width, the distance to this point can be calculated from the section geometry. The first step is to compute the shear flow at a set distance from the end of the flange. Shear flow is the force per unit length along the wall of the section. It is found...

key terms and concepts

Explore how shearing stress changes across a narrow rectangular beam, including zero stress at the edges and a parabolic distribution toward the center.

Shearing Stress Pattern in a Narrow Beam | 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。

Shearing Stress Pattern in a Narrow Beam

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