Name: cantilever beam yield and failure
Uploaded: 2024-05-23T12:59:50.000Z
Duration: 1 min 19 s
Channel: JoVE

片持ち梁は、自由端で荷重を受けると、固定端で最大の曲げモーメントが発生します。
曲げモーメントが梁の弾性限界を超えるまで、垂直応力は降伏強度を下回ったままになります。このポイントを超えると、降伏は固定端から開始されます。
弾性ゾーンとプラスチックゾーンの境界は、弾性コアの半厚さを測定することで取得できます。
荷重が一定の閾値に達すると、固定端付近の部分が完全にプラスチックになり、プラスチックヒンジが形成されます。このヒンジは、ビームがサポートできる最大荷重を表します。
部分的に塑性な部分では、面の垂直応力は均一に分布し、降伏強度と等しくなります。
下面のせん断力はゼロであるため、せん断応力の平均値はゼロになります。垂直せん断は、断面の弾性部分全体に完全に分布しています。
弾性部分の面積が減少すると、最大せん断応力が増加し、最終的には降伏強度に達し、梁の最終的な破壊に寄与します。

塑性変形

Plastic Deformations

塑性変形は材料科学の基本概念であり、材料がその弾性限界を超える応力を受けたときの形状の不可逆的な変化を説明します。この現象は、構造工学、特に片持ち梁 (一方の端がしっかりと固定され、反対側の端で荷重に耐える構造) の設計と解析において重要です。この梁に弾性範囲内で荷重を加えると、荷重を取り除くと元の形状に戻り、弾性特性を発揮します。ただし、この弾性境界を超えると塑性変形が生じ、最大曲げモーメントにより固定端で開始され、「塑性ヒンジ」として知られる永久的な曲げとして現れます。

荷重が増加すると、塑性ヒンジが梁の自由端に向かって徐々に伸び、可逆変形から不可逆変形への移行を示します。この変化により、梁内の応力分布も、加えられた荷重に直接比例する均一なパターンから、材料の降伏点を定義するより複雑な配置へと変化します。継続的に荷重を加えると梁が破損します。

安全性と経済性の両方が求められる構造を設計する場合、塑性変形の概念を理解することが不可欠です。これらの構造が予想される荷重に耐えられることを確認することが重要です。

片持ち梁は、自由端で荷重を受けると、固定端で最大の曲げモーメントが発生します。
曲げモーメントがそれを超えるまで...

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

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 at the fixed end because the bending moment is greatest there. The bent region at that point is called a plastic hinge.

As the load increases, the plastic hinge spreads toward the free end of the beam. This marks the shift from reversible deformation to irreversible deformation. The stress pattern in the beam also changes. It no longer stays uniform and directly proportional to the applied load, and this change helps define the yield point of the material.

If loading continues, the beam will fracture. Knowing how cantilever beams behave under stress is important in structural engineering. It helps engineers design structures that are safe and still economical. These structures must be able to handle the loads they are expected to carry.

Cantilever Beam Yield and Failure

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

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

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...

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 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

Learn how a cantilever beam bends under load, forms a plastic hinge at the fixed end, reaches yield, and can fracture if loading continues.

Cantilever Beam Yield and Failure | 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。

Cantilever Beam Yield and Failure

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