Name: finding tension in a loaded cable
Uploaded: 2023-09-22T11:49:27.000Z
Duration: 1 min 28 s
Channel: JoVE

Cabos flexíveis são usados para suporte e transmissão de carga em várias aplicações.
Considere um cabo AB fixado em dois pontos, experimentando várias cargas concentradas verticais.
Determine a forma do cabo e a tensão em cada parte do cabo, conhecendo as distâncias horizontais entre as cargas e o suporte.
Para análise, o cabo é considerado flexível, inextensível e com peso insignificante.
O cabo consiste em vários segmentos em linha reta, cada um sujeito a força de tração constante.
Desenhe um diagrama de corpo livre do cabo para determinar as forças de reação nos suportes. Aqui, o número de componentes de reação desconhecidos excede as equações de equilíbrio.
Considere o ponto D no cabo a uma distância conhecida e desenhe um diagrama de corpo livre do segmento AD. Usando a equação de equilíbrio de momento no ponto D, uma equação adicional é obtida.
Recordando as equações de equilíbrio e usando as forças de reação, obtém-se a distância vertical entre o suporte A e cada carga concentrada.
Da mesma forma, a tensão em cada segmento pode ser obtida, que é máxima quando o segmento tem o maior ângulo de inclinação.

<ol>
	<li>Cerveja, F.P.; Johnston, E.R.; Mazurek, D.F; Cromwell, PJ e Self, BP (2019). Mecânica vetorial para engenheiros \u2012 estática e dinâmica. Nova Iorque: McGraw-Hill. Pág. 403-404.</li>
	<li>Hibbeler, R.C. (2016). Engenharia Mecânica \u2012 Estática e Dinâmica. Hoboken, Nova Jersey: Pearson Prentice Hall. pág. 381.</li>
</ol>

cabo sujeito a cargas concentradas

Cabo flexível é comumente utilizado em diversas aplicações para suporte e transmissão de carga. Considere um cabo fixado em dois pontos e sujeito a múltiplas cargas concentradas verticalmente. Determine a forma do cabo e a tensão em cada porção do cabo, dadas as distâncias horizontais entre as cargas e os suportes.



<img alt="Figure 1" src="/files/ftp_upload/14307/14307_Figure_1v2.svg" style="text-align: center; height: 350px;" />



Para a análise, assume-se que o cabo possui as seguintes propriedades:

<ol style="list-style-type:lower-alpha;">
	<li> Flexível, permitindo que ele mude de forma sob a influência de cargas aplicadas.</li>
	<li> Inextensível, significando que o seu comprimento não muda sob tensão.</li>
	<li>Peso negligenciável, o que implica que o peso próprio do cabo não impacta significativamente o seu comportamento.</li>
</ol>

O cabo é composto por vários segmentos em linha reta, com cada segmento sujeito a uma força de tração constante. Para determinar as forças de reação nos suportes, um diagrama de corpo livre do cabo pode ser desenhado. No entanto, no caso dado, o número de componentes de reação desconhecidos geralmente excede o número de equações de equilíbrio disponíveis. Uma equação adicional é necessária. Considere o ponto D no cabo em uma distância conhecida dos suportes para obter uma equação adicional. Ao desenhar um diagrama de corpo livre do segmento AD e usar a equação de equilíbrio de momento no ponto D, outra equação que ajuda a resolver o sistema pode ser derivada.



<img alt="Equation 1" src="/files/ftp_upload/14307/14307_Equation_1v2.svg" style="text-align: center; height: 13px;" />



A distância vertical entre o suporte A e cada carga concentrada pode ser determinada com as forças de reação conhecidas. Isso pode ser alcançado ao se recordar a equação de equilíbrio, que afirma que a soma das forças verticais atuantes sobre o cabo deve ser igual a zero. Uma vez que as distâncias verticais foram determinadas, a tensão em cada segmento do cabo pode ser calculada. A tensão é máxima quando o segmento tem o maior ângulo de inclinação.



<img alt="Equation 2" src="/files/ftp_upload/14307/14307_Equation_2v2.svg" style="text-align: center; height: 13px;" />





<img alt="Equation 3" src="/files/ftp_upload/14307/14307_Equation_3v2.svg" style="text-align: center; height: 13px;" />

Cabo sujeito a cargas concentradas

Os cabos flexíveis são comumente usados em várias aplicações para suporte e transmissão de carga. Considere um cabo fixado em dois pontos e submetido a ...

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 Concentrated Loads

finding tension in a loaded cable

Flexible cables can carry vertical point loads between two fixed supports. The cable is treated as flexible, inextensible, and nearly weightless. Under these conditions, it changes shape to form straight-line segments, and each segment carries a constant tensile force.

To analyze the cable, a free-body diagram is drawn for the whole cable. This helps identify the reaction forces at the supports. In many cases, the number of unknown reaction components is greater than the available equilibrium equations, so an extra equation is needed.

A point such as D, at a known distance from the supports, can provide that extra equation. By isolating segment AD and taking moments about point D, another equilibrium relation is obtained. The vertical distance from support A to each concentrated load can then be found from the reaction forces. Using the condition that the sum of the vertical forces on the cable equals zero, the remaining cable geometry can be determined.

Once the vertical distances are known, the tension in each cable segment can be calculated. The tension changes from segment to segment because the cable slope changes. The tension is largest in the segment with the greatest inclination angle.

Finding Tension in a Loaded Cable

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key terms and concepts

Learn how to analyze a flexible cable with vertical concentrated loads, use equilibrium and moments to find support reactions, cable shape, and segment tension.

Finding Tension in a Loaded Cable | JoVE K12

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Finding Tension in a Loaded Cable

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