7.11
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 s…
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.
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Q1: What assumptions are made when analyzing a cable subjected to concentrated loads?
Cables are assumed to be flexible, allowing them to change shape under applied loads, and inextensible, meaning their length does not change under tension. Additionally, the cable's weight is assumed negligible, so it does not significantly impact the cable's behavior during analysis of concentrated loads.
Q2: Why is a free-body diagram of a cable segment necessary for solving concentrated load problems?
A free-body diagram of the entire cable often yields more unknown reaction components than available equilibrium equations. By isolating a segment at a known distance and applying the moment equilibrium equation at that point, an additional equation is obtained, allowing the system to be solved for reaction forces and tensions.
Q3: How does the shape of a cable change when subjected to multiple concentrated loads?
A cable subjected to concentrated loads forms several straight-line segments between load points and supports. Each segment maintains constant tensile force and connects at the load application points, creating a polygonal shape that reflects the distribution and magnitude of the applied vertical loads.
Q4: What is the relationship between cable segment inclination and tension magnitude?
Tension in a cable segment is maximum when the segment has the largest inclination angle relative to the horizontal. Segments with steeper angles experience greater tensile forces because they must support larger vertical load components while maintaining static equilibrium across the cable system.
Q5: How are vertical distances from support to load points determined in cable analysis?
Once reaction forces are known from equilibrium equations, vertical distances from support A to each concentrated load are determined by recalling the equilibrium equation that states the sum of vertical forces acting on the cable must equal zero. This allows calculation of the cable's vertical geometry.
Q6: What information is needed to determine tension in each cable segment?
To calculate tension in each cable segment, you need the reaction forces at supports, the horizontal distances between loads, and the vertical distances from support to each load point. With these values, the tension in each segment can be computed, with maximum tension occurring in segments with the largest inclination angle.
Q7: How does the moment equilibrium equation help solve indeterminate cable systems?
When the number of unknown reaction components exceeds available equilibrium equations, applying the moment equilibrium equation at a point on the cable segment provides an additional independent equation. This transforms the indeterminate system into a determinate one, enabling complete solution for all reaction forces and segment tensions.