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

Considere los cables en las líneas aéreas de transmisión de energía. Determine la forma o el pandeo y la tensión en el cable para garantizar la estabilidad en las líneas de transmisión de energía.
Para el análisis del cable sometido a su propio peso, se utiliza una función de carga generalizada que actúa a lo largo de la longitud del arco del cable en lugar de la longitud proyectada.
A continuación, considere un pequeño segmento del cable y dibuje un diagrama de cuerpo libre del segmento.
Aplicando las ecuaciones de equilibrio, se puede obtener un conjunto de tres ecuaciones. Aquí, la primera y la segunda ecuación representan la componente horizontal y vertical de la fuerza de tracción, respectivamente.
Usando el teorema de Pitágoras, se puede establecer una relación entre el cambio en la distancia vertical, dy y la longitud del arco del cable, ds. Esta relación se sustituye en la tercera ecuación.
Finalmente, reorganizando los términos e integrando la ecuación, se puede determinar la expresión de la forma del cable.

<ol>
	<li>Hibbeler, R.C. (2016). Ingeniería Mecánica \u2012 Estática y Dinámica. Hoboken, Nueva Jersey: Pearson Prentice Hall. págs. 388-390.</li>
</ol>

cable sometido a su propio peso

Las líneas de transmisión eléctrica aérea dependen de cables para transportar electricidad a largas distancias. Para asegurar la estabilidad y funcionalidad de estas líneas, es crucial entender la forma y tensión experimentadas por los cables bajo la influencia de su propio peso. Se emplea una función de carga generalizada para analizar un cable sometido a su propio peso. Esta función considera la fuerza que actúa a lo largo de la longitud del arco del cable en lugar de su longitud proyectada, lo que proporciona una representación más precisa del comportamiento del cable. Para analizar aún más el cable, se considera un pequeño segmento del mismo y se dibuja un diagrama de cuerpo libre. El diagrama ayuda a visualizar las fuerzas que actúan sobre el segmento del cable y sirve como base para aplicar las ecuaciones de equilibrio. <img alt="Figure 1" src="/files/ftp_upload/14309/14309_Figure_1v2.svg" style="text-align: center; height: 350px;"> Un conjunto de tres ecuaciones se puede obtener aplicando las ecuaciones de equilibrio al segmento del cable. Las primeras dos ecuaciones representan las componentes horizontal y vertical de la fuerza de tensión que actúa sobre el cable, 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;"> Utilizando el teorema de Pitágoras, se puede establecer una relación entre el cambio en la distancia vertical (dy) y la longitud del arco del cable (ds). Luego, esta relación se sustituye en la tercera ecuación obtenida a partir de las ecuaciones de equilibrio. Finalmente, reorganizando los términos en la ecuación e integrando la ecuación obtenida, se puede determinar una expresión para la forma del cable. <img alt="Equation 4" src="/files/ftp_upload/14309/14309_Equation_4v3.svg" style="text-align: center; height: 70px;"> Esta expresión permite a los ingenieros calcular el pandeo y la tensión en el cable, asegurando la estabilidad y eficiencia de las líneas de transmisión eléctrica aérea.

Cable Sometido a su Propio Peso

Las líneas aéreas de transmisión de energía dependen de cables para transportar electricidad a grandes distancias. Para garantizar la estabilidad y la funcionalidad de estas líneas, ...

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Mechanical Engineering

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Unit 1

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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

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Cable Sag Under Its Own Weight

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