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

Los cables flexibles se utilizan para el soporte y la transmisión de carga en diversas aplicaciones.
Considere un cable AB fijado en dos puntos, que experimenta múltiples cargas concentradas verticales.
Determine la forma del cable y la tensión en cada porción del cable, conociendo las distancias horizontales entre las cargas y el soporte.
Para el análisis, se supone que el cable es flexible, inextensible y tiene un peso insignificante.
El cable consta de varios segmentos en línea recta, cada uno sometido a una fuerza de tracción constante.
Dibuje un diagrama de cuerpo libre del cable para determinar las fuerzas de reacción en los soportes. Aquí, el número de componentes de reacción desconocidos excede las ecuaciones de equilibrio.
Considere el punto D en el cable a una distancia conocida y dibuje un diagrama de cuerpo libre del segmento AD. Al usar la ecuación de equilibrio de momento en el punto D, se obtiene una ecuación adicional.
Recordando las ecuaciones de equilibrio y utilizando las fuerzas de reacción, se obtiene la distancia vertical entre el apoyo A y cada carga concentrada.
Del mismo modo, se puede obtener la tensión en cada segmento, que es máxima cuando el segmento tiene el ángulo de inclinación más grande.

<ol>
	<li>Cerveza, F.P.; Johnston, E.R.; Mazurek, D.F.; Cromwell, P.J. y Self, B.P. (2019). Mecánica vectorial para ingenieros: estática y dinámica. Nueva York: McGraw-Hill. Págs. 403-404.</li>
	<li>Hibbeler, R.C. (2016). Ingeniería Mecánica \u2012 Estática y Dinámica. Hoboken, Nueva Jersey: Pearson Prentice Hall. págs. 381.</li>
</ol>

cable sometido a cargas concentradas

Los cables flexibles son comúnmente utilizados en diversas aplicaciones para soporte y transmisión de carga. Considere un cable fijo en dos puntos y sometido a múltiples cargas concentradas verticalmente. Determine la forma del cable y la tensión en cada parte del cable, dadas las distancias horizontales entre las cargas y los soportes. 

<img alt="Figure 1" src="/files/ftp_upload/14307/14307_Figure_1v2.svg" style="text-align: center; height: 350px;">

Para el análisis, se asume que el cable tiene las siguientes propiedades:

<ol style="list-style-type: lower-alpha;"> 

	<li>Flexible, lo que le permite cambiar de forma bajo la influencia de las cargas aplicadas.</li> 

	<li>Infinitamente extensible, es decir, su longitud no cambia bajo tensión.</li> 

	<li>Un peso despreciable, lo que implica que el peso propio del cable no afecta significativamente su comportamiento.</li>
</ol> 

El cable consiste en varios segmentos de línea recta, siendo cada segmento sometido a una fuerza de tensión constante. Para determinar las fuerzas de reacción en los soportes, se puede trazar un diagrama de cuerpo libre del cable. Sin embargo, en el caso dado, el número de componentes de reacción desconocidos generalmente excede el número de ecuaciones de equilibrio disponibles. Se requiere una ecuación adicional. Considere el punto D en el cable a una distancia conocida de los soportes para obtener una ecuación adicional. Tras trazar un diagrama de cuerpo libre del segmento AD y utilizar la ecuación de equilibrio de momentos en el punto D, se puede derivar otra ecuación que ayuda a resolver el sistema. 

<img alt="Equation 1" src="/files/ftp_upload/14307/14307_Equation_1v2.svg" style="text-align: center; height: 13px;">

La distancia vertical desde el soporte A hasta cada carga concentrada se puede determinar con las fuerzas de reacción conocidas. Esto se puede lograr recordando la ecuación de equilibrio, la cual establece que la suma de las fuerzas verticales que actúan sobre el cable debe ser igual a cero. Una vez que se hayan determinado las distancias verticales, se puede calcular la tensión en cada segmento del cable. La tensión alcanza su máximo cuando el segmento tiene el mayor ángulo de inclinación. 

<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;">

Cable Sometido a Cargas Concentradas

Los cables flexibles se utilizan comúnmente en diversas aplicaciones para el soporte y la transmisión de carga. Considere un cable fijado en dos puntos y sometido a ...

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

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Finding Tension in a Loaded Cable

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