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

En los puentes colgantes, los cables principales experimentan cargas distribuidas, que pueden transferirse a las torres de soporte y anclajes. Determina la forma y la tensión del cable.
Se supone que el cable es flexible, inextensible y con un peso insignificante para el análisis.
Considere un pequeño segmento del cable y dibuje el diagrama de cuerpo libre del segmento que muestra la carga distribuida y los cambios en la fuerza de tracción.
A continuación, se aplican las ecuaciones de equilibrio y sustituyendo las fuerzas y momentos horizontales y verticales que actúan sobre el segmento, se obtiene un conjunto de ecuaciones.
Dividiendo cada ecuación por Δx y tomando cada límite tendiendo a cero, se obtiene un nuevo conjunto de tres ecuaciones.
La integración de la primera ecuación produce la componente horizontal de la fuerza de tracción en cualquier punto a lo largo del cable.
A continuación, integra la segunda ecuación. Dividiéndolo por el componente de la fuerza de tracción y sustituyendo el valor de tanθ, se obtiene la expresión de la pendiente del cable.
Finalmente, al realizar una segunda integración en la ecuación derivada se determina la curva del cable.

<ol>
	<li>Hibbeler, R.C. (2016). Ingeniería Mecánica \u2012 Estática y Dinámica. Hoboken, Nueva Jersey: Pearson Prentice Hall. págs. 384-386.</li>
</ol>

cable sometido a una carga distribuida

El análisis de los puentes colgantes es un proceso complejo y crítico que involucra múltiples factores, incluyendo la forma y tensión de los cables principales. Los cables principales de los puentes colgantes están sujetos a cargas distribuidas, lo cual resulta en cambios en las fuerzas de tensión y la deformación del cable. Estas cargas deben ser cuidadosamente consideradas para asegurar que el puente sea seguro y capaz de soportar el peso de diferentes cargas. <img alt="Figura 1" src="/files/ftp_upload/14308/14308_Figure_1v2.svg" style="text-align: center; height: 350px;"> Para analizar un cable sometido a cargas distribuidas, se considera un pequeño segmento del cable y se dibuja un diagrama de cuerpo libre que muestra la carga distribuida y los cambios en la fuerza de tensión. Se obtiene un conjunto de ecuaciones aplicando las ecuaciones de equilibrio y sustituyendo las fuerzas horizontales y verticales y los momentos que actúan sobre el segmento. Dividir cada ecuación por delta Δx y tomar el límite cuando tiende a cero produce un nuevo conjunto de tres ecuaciones. La primera ecuación obtenida a partir de este análisis ayuda a determinar la componente horizontal de la fuerza de tensión en cualquier punto a lo largo del cable. <img alt="Ecuación 1" src="/files/ftp_upload/14308/14308_Equation_1v2.svg" style="text-align: center; height: 13px;"> También permite calcular la tensión del cable en cualquier punto a lo largo de su longitud. La expresión para la pendiente del cable se obtiene dividiendo la segunda ecuación, que es la componente vertical de la fuerza de tensión, con la componente de la fuerza de tensión horizontal y sustituyendo el valor de tan θ. <img alt="Ecuación 2" src="/files/ftp_upload/14308/14308_Equation_2v2.svg" style="text-align: center; height: 35px;"> Finalmente, realizando una segunda integración en la ecuación derivada se determina la curva del cable. <img alt="Ecuación 3" src="/files/ftp_upload/14308/14308_Equation_3v2.svg" style="text-align: center; height: 35px;"> De esta manera, el proceso nos ayuda a entender el comportamiento del cable cuando está sometido a cargas distribuidas. También es útil en el diseño del sistema de soporte del puente y asegurarse de que los cables puedan soportar el peso del tráfico y otras tensiones.

Cable sometido a una carga distribuida

El análisis de puentes colgantes es un proceso complejo y crítico que involucra múltiples factores, incluida la forma y la tensión de los cables principales. ...

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Mechanical Engineering

Ingeniería Mecánica

Unit 1

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Internal Forces

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KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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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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...

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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.

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Finding Cable Shape Under Distributed Load

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