Name: cable sag under its own weight
Uploaded: 2023-09-22T11:49:27.000Z
Duration: 1 min 13 s
Channel: JoVE

Considere os cabos em linhas aéreas de transmissão de energia. Determine a forma ou curvatura e tensão no cabo para garantir a estabilidade nas linhas de transmissão de energia.
Para análise do cabo submetido ao seu próprio peso, é utilizada uma função de carregamento generalizada que atua ao longo do comprimento do arco do cabo em vez do comprimento projetado.
Em seguida, considere um pequeno segmento do cabo e desenhe um diagrama de corpo livre do segmento.
Aplicando as equações de equilíbrio, um conjunto de três equações pode ser obtido. Aqui, a primeira e a segunda equação representam o componente horizontal e vertical da força de tração, respectivamente.
Usando o teorema de Pitágoras, uma relação pode ser estabelecida entre a mudança na distância vertical, dy e o comprimento do arco do cabo, ds. Essa relação é substituída na terceira equação.
Finalmente, reorganizando os termos e integrando a equação, a expressão para a forma do cabo pode ser determinada.

<ol>
	<li>Hibbeler, R.C. (2016). Engenharia Mecânica \u2012 Estática e Dinâmica. Hoboken, Nova Jersey: Pearson Prentice Hall. pág. 388-390.</li>
</ol>

cabo sujeito ao seu próprio peso

Linhas de transmissão de energia aéreas dependem de cabos para transportar eletricidade por grandes distâncias. Para garantir a estabilidade e funcionalidade dessas linhas, é crucial entender a forma e a tensão experimentada pelos cabos sob a influência de seu próprio peso.

Uma função de carga generalizada é empregada para analisar um cabo sujeito ao seu próprio peso. Essa função considera a força atuando ao longo do comprimento do arco do cabo em vez de seu comprimento projetado, fornecendo uma representação mais precisa do comportamento do cabo. Para analisar ainda mais o cabo, um pequeno segmento do cabo é considerado e um diagrama de corpo livre é desenhado. O diagrama ajuda a visualizar as forças atuando no segmento do cabo e serve como base para aplicar as equações de equilíbrio.

<img alt="Figure 1" src="/files/ftp_upload/14309/14309_Figure_1v2.svg" style="text-align: center; height: 350px;" />

Um conjunto de três equações pode ser obtido aplicando as equações de equilíbrio ao segmento do cabo. A primeira e a segunda equações representam as componentes horizontal e vertical da força de tração atuando no cabo, respectivamente.

<img alt="Equation 1" src="/files/ftp_upload/14309/14309_Equation_1v2.svg" style="text-align: center; height: 13px;" />

<img alt="Equation 2" src="/files/ftp_upload/14309/14309_Equation_2v2.svg" style="text-align: center; height: 28px;" />

<img alt="Equation 3" src="/files/ftp_upload/14309/14309_Equation_3v2.svg" style="text-align: center; height: 32px;" />

Usando o teorema de Pitágoras, uma relação pode ser estabelecida entre a variação na distância vertical (dy) e o comprimento do arco do cabo (ds). A relação é então substituída na terceira equação obtida das equações de equilíbrio. Por fim, rearranjando os termos na equação e integrando a equação obtida, uma expressão para a forma do cabo pode ser determinada.

<img alt="Equation 4" src="/files/ftp_upload/14309/14309_Equation_4v3.svg" style="text-align: center; height: 70px;" />

Essa expressão permite que os engenheiros calculem a flecha e a tensão no cabo, garantindo a estabilidade e eficiência das linhas de transmissão de energia aéreas.

Cabo sujeito ao seu próprio peso

As linhas aéreas de transmissão de energia dependem de cabos para transportar eletricidade por grandes distâncias. Para garantir a estabilidade e funcionalidade dessas linhas, ...

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 Its Own Weight

cable sag under its own weight

Overhead power transmission cables sag under their own weight, and that shape affects how they carry electricity across long distances. To study this behavior, the cable is analyzed with a generalized loading function. This function treats the load along the cable's arc length instead of its projected length, which gives a more accurate picture of the cable's response.

The analysis then focuses on a small cable segment. A free-body diagram is drawn to show the forces acting on that segment. This diagram supports the equilibrium equations used to describe the horizontal and vertical components of the tensile force in the cable.

From these equilibrium equations, three relationships can be written. Two of them describe the horizontal and vertical tension components. The third uses Pythagoras' theorem to connect the change in vertical distance, dy, with the arc length, ds.

That relationship is substituted into the equilibrium equation for the segment. The equation is then rearranged and integrated. The result is an expression for the cable shape, which helps engineers calculate sag and tension and support stable, efficient overhead power transmission lines.

Cable Sag Under Its Own Weight

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Overhead power transmission cables sag under their own weight, and that shape affects how they carry electricity across long distances. To study this behavior, the cable is analyzed with a generalized loading function. This function treats the load along the cable's arc length instead of its projected length, which gives a more accurate picture of the cable's response. The analysis then focuses on a small cable segment. A free-body diagram is drawn to show the forces acting on that segment.

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key terms and concepts

Explore how a cable’s own weight creates sag, tension, and cable shape. See how equilibrium, a free-body diagram, and integration reveal the curve.

Cable Sag Under Its Own Weight | 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.

mechanical engineering

Cable Sag Under Its Own Weight

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