Name: beam shear stress analysis and safety check
Uploaded: 2024-05-23T12:59:49.000Z
Duration: 1 min 14 s
Channel: JoVE

Uma viga em balanço com uma secção retangular está sujeita a cargas distribuídas e pontuais.
Para calcular a tensão de cisalhamento na viga, as cargas que atuam sobre ela são primeiro identificadas. As reações na extremidade fixa são então calculadas usando equações de equilíbrio.
A reação vertical é a soma das cargas distribuídas e pontuais, e a reação de momento é a soma de seus momentos.
A distribuição da força de cisalhamento ao longo da viga devido às cargas é determinada desenhando um diagrama de força de cisalhamento a partir das forças de reação na extremidade fixa, incluindo a carga distribuída e a carga pontual.
A tensão de corte é calculada utilizando uma fórmula que considera a força de corte nesse ponto, o primeiro momento da área da secção em torno do eixo neutro e o momento de inércia da secção.
A tensão de cisalhamento é calculada em vários pontos críticos ao longo da viga, normalmente perto dos suportes e no local de carga pontual.
A tensão de cisalhamento máxima deve ser comparada com a tensão de cisalhamento permitida do material para determinar se a viga é segura.

tensões de cisalhamento em uma viga: resolução de problemas

Shearing Stresses in a Beam: Problem Solving

Uma viga cantilever com seção transversal retangular sob cargas distribuídas e pontuais sofre tensões de cisalhamento. A análise começa pela identificação das cargas que atuam na viga. Então, as reações na extremidade fixa da viga são calculadas usando equações de equilíbrio. A reação vertical é uma combinação das cargas distribuídas e pontuais, enquanto a reação de momento é a soma de seus momentos. A distribuição da força de cisalhamento ao longo da viga, resultante dessas cargas, é estabelecida criando um diagrama de forças de cisalhamento, começando na extremidade fixa e incorporando os efeitos das cargas distribuídas e pontuais.

A tensão de cisalhamento é determinada usando uma fórmula específica que considera a força de cisalhamento no ponto de interesse, o primeiro momento da área da seção transversal em relação à linha neutra Q, o momento de inércia da seção transversal I e ​​a largura da viga b:


<img alt="Equation 1" src="/files/ftp_upload/15648/15648_Equation_1.svg" style="height: 36px;">

Este cálculo é realizado em vários pontos críticos ao longo da viga, especialmente perto de apoios e onde são aplicadas cargas pontuais. A tensão de cisalhamento mais alta encontrada é então comparada com a tensão de cisalhamento admissível do material, para avaliar a segurança da viga sob as cargas dadas. Isto garante a integridade estrutural da viga, confirmando que os níveis de tensão não excedem os limites do material.

Tensões de cisalhamento em uma viga: Resolução de Problemas

Uma viga em balanço com uma secção retangular está sujeita a cargas distribuídas e pontuais.
Para calcular a tensão de cisalhamento na viga, as cargas atuantes ...

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

Education

JoVE Core

Mechanical Engineering

Engenharia Mecânica

Unit 1

Unidade 1

Shearing Stresses in Beams and Thin-Walled Members

Tensões Cisalhantes em Vigas e Elementos de Parede Fina

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

KEY TERMS AND CONCEPTS

TERMOS E CONCEITOS-CHAVE

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 the point load, and the moment reaction comes from the moments of both loads.

After the reactions are known, the shear force distribution is built with a shear force diagram. The diagram starts at the fixed end and shows how the distributed load and point load change the shear force along the beam. This makes it easier to locate the points where shear stress may be highest.

Shearing stress is then calculated with a formula that uses the shear force at the point of interest, the first moment of area Q about the neutral axis, the moment of inertia I, and the beam width b. The stress is evaluated at several critical locations, especially near the support and near the point load. The largest shearing stress is compared with the material's allowable shear stress to judge whether the beam is safe under the given loads.

Beam Shear Stress Analysis and Safety Check

beam-shear-stress-analysis-and-safety-check

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

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

Find shear reactions, draw the shear force diagram, and calculate beam shearing stress at critical points. Compare the result with allowable stress to check safety.

Beam Shear Stress Analysis and Safety Check | JoVE K12

O JoVE Core Mechanical Engineering oferece vídeos animados concisos e de fácil compreensão que abrangem tópicos-chave como equilíbrio, forças, análise de treliças e mecânica estrutural. Explore suas aplicações no mundo real e observe esses conceitos em ação por meio de experimentos conduzidos por cientistas.

Beam Shear Stress Analysis and Safety Check

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