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

Prenons l’exemple des câbles des lignes aériennes de transport d’électricité. Déterminez la forme ou l’affaissement et la tension du câble pour assurer la stabilité des lignes de transmission d’électricité.
Pour l'analyse du câble soumis à son propre poids, une fonction de charge généralisée est utilisée qui agit le long de la longueur de l'arc du câble au lieu de la longueur projetée.
Ensuite, considérez un petit segment du câble et dessinez un schéma de corps libre du segment.
En appliquant les équations d’équilibre, on peut obtenir un ensemble de trois équations. Ici, la première et la deuxième équation représentent respectivement la composante horizontale et verticale de la force de traction.
En utilisant le théorème de Pythagore, une relation peut être établie entre la variation de la distance verticale, dy et la longueur de l'arc du câble, ds. Cette relation est substituée dans la troisième équation.
Enfin, en réarrangeant les termes et en intégrant l’équation, l’expression de la forme du câble peut être déterminée.

<ol>
	<li>Hibbeler, R.C. (2016). Génie mécanique \u2012 Statique et dynamique. Hoboken, New Jersey : Pearson Prentice Hall. p. 388 à 390.</li>
</ol>

câble soumis à son propre poids

Les lignes de transmission d'électricité en hauteur utilisent des câbles pour transporter l'électricité sur de longues distances. Pour garantir la stabilité et le bon fonctionnement de ces lignes, il est crucial de comprendre la forme et la tension subies par les câbles sous l'influence de leur poids. Une fonction de charge généralisée est employée pour analyser un câble soumis à son propre poids. Cette fonction prend en compte la force agissant le long de la longueur de l'arc du câble plutôt que sa longueur projetée, ce qui permet une représentation plus précise du comportement du câble. Pour analyser davantage le câble, un petit segment du câble est considéré et un schéma corporel est dessiné. Ce schéma aide à visualiser les forces agissant sur le segment du câble et sert de base pour l'application des équations d'équilibre. <img alt="Figure 1" src="/files/ftp_upload/14309/14309_Figure_1v2.svg" style="text-align: center; height: 350px;"> Un ensemble de trois équations peut être obtenu en appliquant les équations d'équilibre au segment du câble. Les première et deuxième équation représentent les composantes horizontale et verticale de la force de tension agissant sur le câble, respectivement. <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;"> En utilisant le théorème de Pythagore, une relation peut être établie entre le changement de distance verticale (dy) et la longueur de l'arc du câble (ds). Cette relation est ensuite substituée dans la troisième équation obtenue à partir des équations d'équilibre. Enfin, en réarrangeant les termes de l'équation et en intégrant l'équation obtenue, une expression de la forme du câble peut être déterminée. <img alt="Equation 4" src="/files/ftp_upload/14309/14309_Equation_4v3.svg" style="text-align: center; height: 70px;"> Cette expression permet aux ingénieurs de calculer l'affaissement et la tension du câble, garantissant ainsi la stabilité et l'efficacité des lignes de transmission d'électricité en hauteur.

Câble soumis à son propre poids

Les lignes aériennes de transport d’électricité reposent sur des câbles pour transporter l’électricité sur de grandes distances. Pour assurer la stabilité et la fonctionnalité de ces lignes, il ...

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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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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

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Cable Sag Under Its Own Weight

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