Name: locating the beam’s highest deflection
Uploaded: 2024-05-23T13:00:03.000Z
Duration: 1 min 13 s
Channel: JoVE

Considere um trem se movendo em uma ponte. Aqui, uma carga assimétrica é aplicada a uma viga apoiada onde a deflexão máxima geralmente não ocorre no meio.
A deflexão máxima da viga é calculada identificando o ponto O na curva, onde a tangente da viga é horizontal.
A inclinação da tangente no ponto X é determinada calculando o desvio tangencial entre os apoios e dividindo-o por sua distância.
Como a inclinação no ponto O é zero, a inclinação entre O e X é igual à inclinação negativa em X.
O primeiro teorema momento-área é usado para localizar o ponto O medindo uma área sob o diagrama M / EI igual à inclinação negativa no suporte X.
A deflexão máxima é igual ao desvio tangencial do apoio X em relação ao ponto O. Este valor pode ser obtido calculando-se o primeiro momento relativo ao eixo vertical através de X da área entre X e O.

deflexão máxima

Ao analisar vigas sob a ação de cargas assimétricas, como um trem movendo-se em uma ponte, é crucial determinar com precisão os pontos de tensão e deflexão máximas. O processo envolve a identificação da deflexão máxima da viga, o que nem sempre pode ocorrer no seu ponto médio devido à distribuição desigual da carga.

A deflexão máxima ocorre em um ponto específico, conhecido como ponto O, onde a tangente à curva de deflexão é horizontal. Para encontrar o ponto O, a inclinação da tangente em qualquer ponto X ao longo da viga é examinada. A inclinação no ponto X pode ser calculada considerando o desvio tangencial entre os apoios e dividindo-o pela sua distância. Esta inclinação é zero no ponto O, indicando o local de deflexão máxima.

O primeiro método de área de momento desempenha um papel fundamental na localização do ponto O. De acordo com este método, a área sob o diagrama de momento fletor entre quaisquer dois pontos ao longo da viga corresponde à mudança na inclinação entre esses pontos. O ponto O pode ser identificado calculando esta área até a inclinação negativa no apoio X.

Uma vez determinado o ponto O, a deflexão máxima é calculada analisando o desvio tangencial do apoio X em relação ao ponto O. Esta abordagem fornece um método sistemático para avaliar o comportamento estrutural de vigas sob carregamento assimétrico, garantindo a segurança e estabilidade de estruturas como pontes ferroviárias.

Deflexão Máxima

Considere um trem se movendo em uma ponte. Aqui, uma carga assimétrica é aplicada a uma viga apoiada onde a deflexão máxima geralmente não ocorre em ...

Education

JoVE Core

Mechanical Engineering

Engenharia Mecânica

Unit 1

Unidade 1

Deflection of Beams

Deflexão de Vigas

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

Maximum Deflection

locating the beam’s highest deflection

Maximum deflection in a supported beam depends on where the load is placed. With an unsymmetrical load, such as a train moving across a bridge, the beam may bend most at a point that is not the midpoint. Finding that point is important for judging stress and deflection in the structure.

The point of maximum deflection is called point O. At point O, the tangent to the deflection curve is horizontal. That means the slope is zero there. To locate point O, the slope at any point X along the beam is examined.

The slope at point X can be found from the tangential deviation between the supports divided by the distance between them. When this slope becomes zero, point O has been reached. The First Moment-Area Theorem helps with this step. This theorem says the area under the bending moment diagram between two points equals the change in slope between those points.

Point O is identified by using that area up to the negative slope at support X. After point O is found, the maximum deflection is calculated by studying the tangential deviation of support X about point O. This method gives a clear way to analyze beams under unsymmetrical loading and helps support the safety and stability of structures like railway bridges.

Locating the Beam’s Highest Deflection

deformation of a beam under transverse loading

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Beam Slope and Deflection by Singularity

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Beam Deflection Under Combined Loads

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Beam Deflection Using Moment-Area Rules

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Moment-Area Method for Cantilever Deflection

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Beam Deflection and Level Points

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maximum deflection

Maximum deflection in a supported beam depends on where the load is placed. With an unsymmetrical load, such as a train moving across a bridge, the beam may bend most at a point that is not the midpoint. Finding that point is important for judging stress and deflection in the structure. The point of maximum deflection is called point O. At point O, the tangent to the deflection curve is horizontal. That means the slope is zero there. To locate point O, the slope at any point X along the beam...

key terms and concepts

Learn how unsymmetrical loads shift the point of maximum deflection in a supported beam and how the First Moment-Area Theorem helps locate it.

Locating the Beam’s Highest Deflection | JoVE K12

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mechanical engineering

Locating the Beam’s Highest Deflection

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