Name: finding cable shape under distributed load
Uploaded: 2025-05-22T09:06:04.000Z
Duration: 1 min 24 s
Channel: JoVE

Nas pontes suspensas, os cabos principais sofrem cargas distribuídas, que podem ser transferidas para as torres de suporte e ancoragens. Determine a forma e a tensão do cabo.
O cabo é considerado flexível, inextensível e com peso insignificante para a análise.
Considere um pequeno segmento do cabo e desenhe o diagrama de corpo livre do segmento mostrando a carga distribuída e as mudanças na força de tração.
Em seguida, aplicamos as equações de equilíbrio e, substituindo as forças e momentos horizontais e verticais que atuam no segmento, obtém-se um conjunto de equações.
Dividindo cada equação por Δx e tomando cada limite tendendo a zero, obtém-se um novo conjunto de três equações.
A integração da primeira equação produz o componente horizontal da força de tração em qualquer ponto ao longo do cabo.
Em seguida, integre a segunda equação. Dividindo-o pelo componente da força de tração e substituindo o valor de tanθ, obtém-se a expressão da inclinação do cabo.
Finalmente, realizar uma segunda integração na equação derivada determina a curva do cabo.

<ol>
	<li>Hibbeler, R.C. (2016). Engenharia Mecânica \u2012 Estática e Dinâmica. Hoboken, Nova Jersey: Pearson Prentice Hall. pág. 384-386.</li>
</ol>

cabo sujeito a uma carga distribuída

A análise de pontes suspensas é um processo complexo e crítico que envolve múltiplos fatores, incluindo a forma e a tensão dos cabos principais. Os cabos principais de pontes suspensas estão sujeitos a cargas distribuídas, o que resulta em mudanças nas forças de tração e na deformação do cabo. Essas cargas devem ser cuidadosamente consideradas para garantir que a ponte seja segura e capaz de suportar o peso de diferentes cargas.

<img alt="Figure 1" src="/files/ftp_upload/14308/14308_Figure_1v2.svg" style="text-align: center; height: 350px;" />

Para analisar um cabo sujeito a cargas distribuídas, considere um pequeno segmento do cabo e desenhe um diagrama de corpo livre mostrando a carga distribuída e as mudanças na força de tração. Um conjunto de equações é obtido aplicando as equações de equilíbrio e substituindo as forças e momentos horizontais e verticais que atuam no segmento. Dividir cada equação por delta Δ x e tomar cada limite tendendo a zero gera um novo conjunto de três equações. A primeira equação obtida dessa análise ajuda a determinar a componente horizontal da força de tração em qualquer ponto ao longo do cabo.

<img alt="Equation 1" src="/files/ftp_upload/14308/14308_Equation_1v2.svg" style="text-align: center; height: 13px;" />

Também permite calcular a tensão do cabo em qualquer ponto ao longo de seu comprimento. A expressão para a inclinação do cabo é obtida dividindo a segunda equação, que é a componente vertical da força de tração, pela componente horizontal da força de tração e substituindo o valor de tan θ.

<img alt="Equation 2" src="/files/ftp_upload/14308/14308_Equation_2v2.svg" style="text-align: center; height: 35px;" />

Por fim, realizando uma segunda integração na equação derivada determina a curva do cabo.

<img alt="Equation 3" src="/files/ftp_upload/14308/14308_Equation_3v2.svg" style="text-align: center; height: 35px;" />

Dessa forma, o processo nos ajuda a entender o comportamento do cabo quando sujeito a cargas distribuídas. Também é útil no projeto do sistema de suporte da ponte e garantir que os cabos possam suportar o peso do tráfego e outras tensões.

Cabo sujeito a uma carga distribuída

A análise de pontes suspensas é um processo complexo e crítico que envolve vários fatores, incluindo a forma e a tensão dos cabos principais. ...

Education

JoVE Core

Mechanical Engineering

Engenharia Mecânica

Unit 1

Unidade 1

Internal Forces

Forças Internas

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

Cable Subjected to a Distributed Load

finding cable shape under distributed load

Cable shape under a distributed load is found by analyzing the forces along a small piece of the cable. This method is important in suspension bridge design because the main cables must carry changing loads safely. The load causes the tensile force in the cable to change, and it also creates cable deformation.

The analysis starts with a free-body diagram of a short cable segment. The diagram shows the distributed load and the change in tensile force across that segment. Equilibrium equations are then applied to the horizontal force, vertical force, and moments acting on the cable piece.

Next, each equation is divided by delta x, and the limit is taken as delta x approaches zero. This gives a new set of three equations. The first equation helps determine the horizontal component of tensile force at any point along the cable, and it can also be used to find the cable tension along its length.

The second equation is used to find the slope of the cable. It relates the vertical component of tensile force to the horizontal component. By substituting tan theta, the cable angle can be linked to the shape of the cable. A second integration of the final equation gives the curve of the cable. This analysis helps engineers understand cable behavior under distributed loads and design bridge support systems that can handle traffic weight and other stresses.

Finding Cable Shape Under Distributed Load

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key terms and concepts

Analyze how a suspension bridge cable responds to distributed loads using free-body diagrams, equilibrium equations, slope, tension, and cable curve.

Finding Cable Shape Under Distributed Load | JoVE K12

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Finding Cable Shape Under Distributed Load

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