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

Considera i cavi nelle linee aeree di trasmissione dell'energia. Determinare la forma o l'abbassamento e la tensione del cavo per garantire la stabilità delle linee di trasmissione dell'energia.
Per l'analisi del cavo sottoposto al proprio peso, viene utilizzata una funzione di carico generalizzata che agisce lungo la lunghezza dell'arco del cavo anziché la lunghezza proiettata.
Quindi, considera un piccolo segmento del cavo e disegna un diagramma a corpo libero del segmento.
Applicando le equazioni di equilibrio, si può ottenere un insieme di tre equazioni. Qui, la prima e la seconda equazione rappresentano rispettivamente la componente orizzontale e verticale della forza di trazione.
Utilizzando il teorema di Pitagora, è possibile stabilire una relazione tra la variazione della distanza verticale, dy e la lunghezza dell'arco del cavo, ds. Questa relazione è sostituita nella terza equazione.
Infine, riorganizzando i termini e integrando l'equazione, è possibile determinare l'espressione della forma del cavo.

<ol>
	<li>Hibbeler, R.C. (2016). Ingegneria Meccanica \u2012 Statica e Dinamica. Hoboken, New Jersey: Pearson Prentice Hall. pagine 388-390.</li>
</ol>

cavo soggetto al proprio peso

Le linee di trasmissione dell'energia elettrica aeree si affidano ai cavi per trasportare l'elettricità su lunghe distanze. Per garantire la stabilità e la funzionalità di queste linee, è cruciale comprendere la forma e la tensione sperimentata dai cavi sotto l'influenza del proprio peso.

Per analizzare un cavo soggetto al proprio peso, viene utilizzata una funzione di carico generalizzata. Questa funzione considera la forza che agisce lungo la lunghezza dell'arco del cavo, anziché la sua lunghezza proiettata, fornendo una rappresentazione più accurata del comportamento del cavo. Per analizzare ulteriormente il cavo, viene preso in considerazione un piccolo segmento del cavo e viene disegnato un diagramma delle forze libere. Il diagramma aiuta a visualizzare le forze che agiscono sul segmento del cavo e serve come base per l'applicazione delle equazioni di equilibrio.

<img alt="Figure 1" src="/files/ftp_upload/14309/14309_Figure_1v2.svg" style="text-align: center; height: 350px;" />

Un insieme di tre equazioni può essere ottenuto applicando le equazioni di equilibrio al segmento del cavo. La prima e la seconda equazione rappresentano rispettivamente le componenti orizzontali e verticali della forza di trazione che agisce sul cavo.

<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;" />

Utilizzando il teorema di Pitagora, può essere stabilita una relazione tra la variazione della distanza verticale (dy) e la lunghezza dell'arco del cavo (ds). La relazione viene quindi sostituita nella terza equazione ottenuta dalle equazioni di equilibrio. Infine, riordinando i termini dell'equazione e integrando l'equazione ottenuta, è possibile determinare un'espressione per la forma del cavo.

<img alt="Equation 4" src="/files/ftp_upload/14309/14309_Equation_4v3.svg" style="text-align: center; height: 70px;" />

Questa espressione consente agli ingegneri di calcolare la pendenza e la tensione nel cavo, garantendo la stabilità e l'efficienza delle linee aeree di trasmissione dell'energia elettrica.

Cavo soggetto al proprio peso

Le linee aeree di trasmissione dell'energia si basano su cavi per trasportare l'elettricità su grandi distanze. Per garantire la stabilità e la funzionalità di queste linee, ...

Education

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JoVE Core

Mechanical Engineering

Ingegneria Meccanica

Unit 1

Unità 1

Internal Forces

Forze interne

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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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bending and torsional moments

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internal loadings in structural members: problem solving

internal-loadings-in-structural-members-problem-solving

Beam Internal Force Analysis at Point A

Beam internal force analysis shows how normal force, shear force, and bending moment act inside a structural member. These internal loadings help engineers check whether a beam can support the external forces applied to it. The example uses a beam OC that weighs 5 kN and is inclined at 53.13° with the horizontal. The beam is supported at both ends. The goal is to find the internal loadings at point A. The first step is to find the reaction force at point C. This is done by taking the moment...

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shear diagram

Beam Shear Force Diagram

Beam shear force diagrams show how shear changes along the length of a supported beam. In beam mechanics, they help students track the internal shear force caused by perpendicular loads. The beam AB in this example is supported at both ends, so the first step is to draw a free-body diagram that shows the external forces and internal reactions. The reaction forces at supports A and B are found with equilibrium equations for force and moment. For the beam shown, the vertical reaction at A is 24...

bending moment diagram

Beam Load Analysis with Moment Diagrams

Beam load analysis uses a bending moment diagram to show how bending changes along the length of a beam. This diagram helps engineers and designers check whether a structure can handle applied forces. It is also useful for parts such as shelving arms, which must resist forces and moments from a load. To build the diagram, start by finding the reactive forces and any couple moments on the beam. In some cases, especially when a beam is inclined, these forces must be resolved into components that...

relation between the distributed load and shear

relation-between-the-distributed-load-and-shear

Shear Change Under Distributed Loading

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relation between the shear and bending moment

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Shear and Moment Diagrams in Beam Loads

Shear and moment diagrams help show how a beam responds to loads. A beam can carry a distributed load, concentrated loads, and a couple moment. These loads create internal shear forces and bending moments. The beam is examined by isolating a small elemental section and drawing a free-body diagram. For that section to stay in equilibrium, the moment on the right side must be slightly larger than the moment on the left side. The distributed load also has a resultant force that acts at a...

shear and bending moment diagram: problem solving

shear-and-bending-moment-diagram-problem-solving

Beam Load Analysis with Shear Diagrams

Beam load analysis uses shear and bending moment diagrams to track the internal forces in a beam. These diagrams are important when a beam carries concentrated loads and a distributed load. They help show how the beam responds so structures can be designed safely and efficiently. The first step is to draw a free-body diagram of the whole beam. A free-body diagram shows the concentrated loads, the distributed load, and the reaction forces at the supports. Use the equilibrium equations, where...

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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...

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cable subjected to 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.

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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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