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

캔틸레버 빔은 자유 단부에서 하중을 받을 때 고정 단부에서 최대 굽힘 모멘트를 발생시킵니다.
굽힘 모멘트가 빔의 탄성 한계를 초과할 때까지 수직 응력은 항복 강도 이하로 유지됩니다. 이 시점을 넘어서면 고정된 끝에서 양보가 시작됩니다.
탄성 영역과 소성 영역 사이의 경계는 탄성 코어의 절반 두께를 측정하여 얻을 수 있습니다.
하중이 특정 임계값에 도달하면 고정 끝 근처의 섹션이 완전히 플라스틱이 되어 플라스틱 힌지를 형성합니다. 이 힌지는 빔이 지원할 수 있는 최대 하중을 나타냅니다.
부분적으로 소성 단면에서는 면에 가해지는 수직 응력이 균일하게 분포되고 항복 강도와 같습니다.
아래쪽 면의 전단력은 0이므로 전단 응력의 평균 값이 0이 됩니다. 수직 전단은 단면의 탄성 부분에 완전히 분포됩니다.
탄성부의 면적이 감소함에 따라 최대 전단 응력이 증가하고 결국 항복 강도에 도달하여 빔의 궁극적인 파괴에 기여합니다.

소성 변형

Plastic Deformations

소성 변형은 재료 과학의 기본 개념을 나타내며, 이는 재료가 탄성 능력 이상의 응력을 받을 때 재료 모양의 되돌릴 수 없는 변화를 설명합니다. 이 현상은 구조 엔지니어링, 특히 한쪽 끝이 단단히 고정되고 반대쪽 끝에서 하중을 견디는 구조인 캔틸레버 빔을 설계하고 분석하는 데 중요합니다. 이러한 빔은 탄성 범위 내에서 하중을 받게 되면 하중을 제거하면 원래의 모양으로 돌아가는 탄성 특성을 나타냅니다. 그러나 이 탄성 경계를 초과하면 최대 굽힘 모멘트로 인해 고정 끝에서 시작되어 '소성 힌지'로 알려진 영구 굽힘으로 나타나는 소성 변형이 발생합니다.

하중이 증가함에 따라 플라스틱 힌지는 빔의 자유 끝쪽으로 점진적으로 확장되어 가역적 변형에서 비가역적 변형으로 전환됩니다. 이러한 변화는 또한 적용된 하중에 정비례하는 균일한 패턴에서 재료의 항복점을 정의하는 보다 복잡한 배열로 빔 내의 응력 분포를 변경합니다. 계속해서 하중을 가하면 빔이 파손됩니다.

안전하고 경제적으로 실행 가능해야 하는 구조물을 설계할 때 소성 변형의 개념을 이해하는 것이 중요합니다. 이러한 구조물이 예상 하중을 견딜 수 있는지 확인하는 것이 중요합니다.

캔틸레버 빔은 자유 단부에서 하중을 받을 때 고정 단부에서 최대 굽힘 모멘트를 발생시킵니다.
굽힘 모멘트가 능가할 때까지 ...

Education

교육

JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Shearing Stresses in Beams and Thin-Walled Members

보 및 박판 부재의 전단 응력

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

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

Cantilever Beam Yield and Failure

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