Name: cable tension under uniform loading
Uploaded: 2025-05-22T09:06:04.000Z
Duration: 1 min 29 s
Channel: JoVE

Considere un cable fijado a dos soportes sometidos a una carga uniforme. Determine la tensión máxima en el cable.
Para el análisis, considere el origen en el centro del cable debido a su simetría.
Recuerde la ecuación de forma del cable para la carga distribuida y sustituya el valor de carga constante conocido.
A continuación, se integra la ecuación, y aplicando las condiciones de contorno en el origen, se determina la constante C2.
Tomando la primera derivada de la ecuación de la forma del cable, se puede determinar la pendiente. Aplicando las condiciones de contorno para el talud en el origen, se obtiene C1.
Sustituyendo las constantes de integración y las coordenadas de posición del soporte y reorganizando la ecuación, se obtiene la fuerza de tracción horizontal.
Recuerde la ecuación de la pendiente y sustituya el valor de la coordenada x en el soporte donde el ángulo es máximo.
La tensión de Cabel cambia con el ángulo, que es el máximo cerca del soporte.
Aplicando la relación trigonométrica y reordenando los términos, se obtiene la ecuación de máxima tensión.
Finalmente, sustituyendo la ecuación de tensión horizontal y los valores conocidos, se obtiene la tensión máxima en el cable.

<ol>
	<li>Hibbeler, R.C. (2016). Ingeniería Mecánica \u2012 Estática y Dinámica. Hoboken, Nueva Jersey: Pearson Prentice Hall. págs. 384-385, 393.</li>
</ol>

cable: resolución de problemas

Cuando se trata de un cable que está fijo a dos soportes y se somete a una carga uniforme, es crucial determinar la máxima tensión en el cable. Este proceso se puede descomponer en varios pasos clave, como se indica a continuación: <img alt="Figure 1" src="/files/ftp_upload/14310/14310_Figure_1v3.svg" style="text-align: center; height: 300px;"> Analizar el problema: Comience por comprender el escenario dado y las condiciones del cable. Identifique los soportes, el tipo de carga y cualquier otra información relevante. Determinar la ecuación de forma del cable: Utilice los principios de equilibrio y las propiedades del cable para establecer la ecuación de forma que describe la curva del cable. Esta ecuación relaciona la forma del cable con la carga aplicada. <img alt="Equation 1" src="/files/ftp_upload/14310/14310_Equation_1v2.svg" style="text-align: center; height: 35px;"> Integrar la ecuación: Integre la ecuación de forma para obtener una función que represente la forma del cable. Este proceso de integración le permite determinar las constantes en la ecuación. Al aplicar las condiciones de contorno en el origen, se puede determinar el valor de una de las constantes de integración. <img alt="Equation 2" src="/files/ftp_upload/14310/14310_Equation_2v2.svg" style="text-align: center; height: 35px;"> Encontrar la pendiente: Tome la primera derivada de la ecuación de forma del cable para determinar la pendiente del cable en cualquier punto dado. Aplique las condiciones de contorno para la pendiente en el origen para obtener el valor de otra constante de integración. Calcular la fuerza de tensión horizontal: Sustituya las constantes de integración y las coordenadas de posición del soporte en la ecuación de forma. Reorganice los términos para encontrar la fuerza de tensión horizontal que actúa sobre el cable. <img alt="Equation 3" src="/files/ftp_upload/14310/14310_Equation_3v2.svg" style="text-align: center; height: 35px;"> Determinar el ángulo: Utilice la ecuación de pendiente para calcular el ángulo del cable en varios puntos. Encuentre la ubicación a lo largo del cable donde el ángulo es máximo, generalmente cerca de los soportes. Utilice relaciones trigonométricas para expresar la tensión máxima en términos de la fuerza de tensión horizontal y el ángulo del cable. <img alt="Equation 4" src="/files/ftp_upload/14310/14310_Equation_4v2.svg" style="text-align: center; height: 35px;"> Encontrar la tensión máxima: Sustituya la ecuación de tensión horizontal y los valores conocidos en la ecuación de tensión máxima. Esto le permitirá calcular la tensión máxima en el cable. <img alt="Equation 5" src="/files/ftp_upload/14310/14310_Equation_5v2.svg" style="text-align: center; height: 40px;">

Cable: Resolución de problemas

Cuando se trata de un cable que está fijado a dos soportes y sometido a una carga uniforme, es crucial determinar la tensión máxima en el cable. ...

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KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

Cable: Problem Solving

cable tension under uniform loading

Cable tension under uniform loading is found by analyzing a cable fixed between two supports. The problem starts with the support conditions and the load on the cable. From there, the cable’s shape must be described with an equation that matches the curve formed by the load.

The next step is to integrate the shape equation to get the cable’s shape function. This makes it possible to solve for constants in the equation. The boundary condition at the origin gives one constant. The slope, which is the first derivative of the shape equation, gives the cable’s tilt at any point. A second boundary condition at the origin is used to find another constant.

After the constants are set, the horizontal tensile force can be calculated from the support coordinates and the shape equation. The slope equation is then used to find the cable angle at different points. The angle is usually largest near the supports, so that location is used to determine the maximum tension.

Trigonometric relationships connect the maximum tension to the horizontal tensile force and the cable angle. Once the horizontal tension equation and the given values are substituted into the tension formula, the maximum tension in the cable can be found.

Cable Tension Under Uniform Loading

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cable: problem solving

Cable tension under uniform loading is found by analyzing a cable fixed between two supports. The problem starts with the support conditions and the load on the cable. From there, the cable’s shape must be described with an equation that matches the curve formed by the load. The next step is to integrate the shape equation to get the cable’s shape function. This makes it possible to solve for constants in the equation. The boundary condition at the origin gives one constant. The slope, which...

key terms and concepts

Follow the steps to find maximum cable tension under uniform loading using the cable shape equation, slope, boundary conditions, and trigonometry.

Cable Tension Under Uniform Loading | JoVE K12

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Cable Tension Under Uniform Loading

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