Name: beam shear flow from bending moments
Uploaded: 2024-05-23T12:59:49.000Z
Duration: 1 min 16 s
Channel: JoVE

수직 및 수평 전단력과 수직력에 의해 작용하는 프리즘 빔의 작은 요소는 수직면의 전단을 분석하기 위해 고려됩니다.
평형 방정식을 사용하여 이 요소에 작용하는 힘의 균형을 검사하여 수평 전단력을 결정합니다. 그런 다음 이 힘은 굽힘 모멘트와 단면의 첫 번째 모멘트와 동일시됩니다.
하부 요소 또는 상위 요소를 분석하면 서로에게 가해지는 전단력의 크기는 같지만 방향은 반대이기 때문에 동일한 결과를 얻을 수 있습니다.
또한 빔의 특정 선 아래 부분의 첫 번째 모멘트는 크기가 같지만 부호가 위 부분의 첫 번째 모멘트와 반대인 것으로 관찰됩니다.
첫 번째 모멘트는 중립 축으로부터의 거리가 0이 될 때 최대에 도달하며, 중립 축 위의 요소는 수평 전단력 방정식의 적분 부분에 긍정적으로 기여하고 그 아래의 요소는 음수로 기여합니다.
수평 전단을 요소의 길이로 나누면 전단 흐름이 얻어집니다.

빔 요소의 수평면 전단

Shear on the Horizontal Face of a Beam Element

프리즘형 보 요소의 평평한 면에 대한 전단력을 이해하려면 요소에 작용하는 수직 및 수평 전단력과 수직력에 대해 생각해 보세요. 빔의 중립 축으로 구분되는 요소의 상부(U) 및 하부(L) 섹션을 검사합니다. 이러한 힘의 평형은 수평 전단력을 식별하는 데 도움이 되는 평형 방정식을 적용하여 결정됩니다. 이 힘은 굽힘 모멘트 및 단면의 첫 번째 관성 모멘트와 직접적인 관련이 있습니다. 전단력의 크기는 동일하지만 방향이 반대이기 때문에 분석은 빔의 상부 또는 하부를 검사하든 일관된 결과를 산출합니다.

특정 선 아래의 빔 단면의 첫 번째 모멘트는 크기와 방향 모두에서 그 위의 단면의 첫 번째 모멘트와 동일하다는 점에 유의하는 것이 중요합니다. 이 첫 번째 모멘트는 빔의 중립 축에서 최대에 도달합니다. 여기서 중립축 위의 단면은 수평 전단력 계산에 긍정적으로 기여하는 반면, 아래의 단면은 부정적으로 기여합니다. 전단 흐름 계산에는 수평 전단을 보 요소의 길이로 나누는 작업이 포함됩니다. 이 과정을 이해하는 것은 엔지니어링 프로젝트에서 빔 요소의 구조적 무결성과 설계 요구 사항을 평가하는 데 중요한 빔 내의 수평면에서 전단이 어떻게 작동하는지에 대한 포괄적인 보기를 제공하는 데 필수적입니다.

수직 및 수평 전단력에 의해 작용하는 프리즘 빔의 작은 요소는 수직력과 함께 전단력을 분석하기 위해 고려됩니다.

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

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

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 obtained whether the upper section or the lower section is used. The shear forces are equal in magnitude but point in opposite directions. The first moment of the area below a chosen line matches the first moment of the area above it in magnitude and direction.

This first moment is largest at the neutral axis. Sections above the neutral axis add positively to the horizontal shear calculation. Sections below the neutral axis add negatively.

Shear flow is found by dividing the horizontal shear by the length of the beam element. This makes it easier to describe how shear acts on a horizontal plane inside the beam. Understanding this relationship helps with structural integrity checks and beam design in engineering projects.

Beam Shear Flow from Bending Moments

shear on the horizontal face of a beam element

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 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

Learn how horizontal shear, bending moments, and first moment of inertia work together in a prismatic beam element, and how shear flow is calculated.

Beam Shear Flow from Bending Moments | 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.

Beam Shear Flow from Bending Moments

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