Name: finding tension in a loaded cable
Uploaded: 2023-09-22T11:49:27.000Z
Duration: 1 min 28 s
Channel: JoVE

Les câbles flexibles sont utilisés pour le support et la transmission de charge dans diverses applications.
Considérons un câble AB fixé en deux points, subissant plusieurs charges verticales concentrées.
Déterminez la forme du câble et la tension dans chaque partie du câble, en connaissant les distances horizontales entre les charges et le support.
Pour l’analyse, on suppose que le câble est flexible, inextensible et a un poids négligeable.
Le câble se compose de plusieurs segments en ligne droite, chacun soumis à une force de traction constante.
Dessinez un schéma du corps libre du câble pour déterminer les forces de réaction sur les supports. Ici, le nombre de composants de réaction inconnus dépasse les équations d’équilibre.
Considérons le point D sur le câble à une distance connue et dessinez un schéma du segment AD. En utilisant l’équation d’équilibre du moment au point D, on obtient une équation supplémentaire.
En rappelant les équations d’équilibre et en utilisant les forces de réaction, on obtient la distance verticale entre le support A et chaque charge concentrée.
De même, la tension dans chaque segment peut être obtenue, qui est maximale lorsque le segment a le plus grand angle d’inclinaison.

<ol>
	<li>Bière, F.P. ; Johnston, E.R. ; Mazurek, D.F ; Cromwell, P.J. et Self, B.P. (2019). Mécanique vectorielle pour les ingénieurs \u2012 Statique et dynamique. New York : McGraw-Hill. Pages 403 et 404.</li>
	<li>Hibbeler, R.C. (2016). Génie mécanique \u2012 Statique et dynamique. Hoboken, New Jersey : Pearson Prentice Hall. p. 381.</li>
</ol>

câble soumis à des charges concentrées

Les câbles flexibles sont couramment utilisés dans diverses applications pour le support et la transmission de charges. Considérez un câble fixé à deux points et soumis à plusieurs charges concentrées verticalement.

Déterminez la forme du câble et la tension dans chaque partie du câble, compte tenu des distances horizontales entre les charges et les supports. <img alt="Figure 1" src="/files/ftp_upload/14307/14307_Figure_1v2.svg" style="text-align: center; height: 350px;"> Pour l'analyse, on suppose que le câble a les propriétés suivantes : <ol style="list-style-type:lower-alpha;"> <li>Flexible, ce qui lui permet de changer de forme sous l'influence des charges appliquées.</li> <li>Inextensible, ce qui signifie que sa longueur ne change pas sous tension.</li> <li>Un poids négligeable, ce qui implique que le poids propre du câble n'a pas d'impact significatif sur son comportement.</li> </ol> Le câble est composé de plusieurs segments linéaires, chaque segment étant soumis à une force de tension constante. Pour déterminer les forces de réaction aux supports, un schéma du câble peut être dessiné. Cependant, dans le cas donné, le nombre de composantes de réaction inconnues dépasse généralement le nombre d'équations d'équilibre disponibles. Une équation supplémentaire est requise. Considérez le point D sur le câble à une distance connue des supports pour obtenir une équation supplémentaire. En dessinant un schéma du segment AD et en utilisant l'équation d'équilibre des moments au point D, une autre équation qui aide à résoudre le système peut être déduite. <img alt="Equation 1" src="/files/ftp_upload/14307/14307_Equation_1v2.svg" style="text-align: center; height: 13px;"> La distance verticale entre le support A et chaque charge concentrée peut être déterminée avec les forces de réaction connues. Cela peut être réalisé en rappelant l'équation d'équilibre, qui stipule que la somme des forces verticales agissant sur le câble doit être égale à zéro. Une fois les distances verticales déterminées, la tension dans chaque segment de câble peut être calculée. La tension est maximale lorsque le segment a l'angle d'inclinaison le plus grand. <img alt="Equation 2" src="/files/ftp_upload/14307/14307_Equation_2v2.svg" style="text-align: center; height: 13px;"> <img alt="Equation 3" src="/files/ftp_upload/14307/14307_Equation_3v2.svg" style="text-align: center; height: 13px;">

Câble soumis à des charges concentrées

Les câbles flexibles sont couramment utilisés dans diverses applications pour le support et la transmission de charge. Considérons un câble fixé en deux points et soumis à ...

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Cable Subjected to Concentrated Loads

finding tension in a loaded cable

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 equations, so an extra equation is needed.

A point such as D, at a known distance from the supports, can provide that extra equation. By isolating segment AD and taking moments about point D, another equilibrium relation is obtained. The vertical distance from support A to each concentrated load can then be found from the reaction forces. Using the condition that the sum of the vertical forces on the cable equals zero, the remaining cable geometry can be determined.

Once the vertical distances are known, the tension in each cable segment can be calculated. The tension changes from segment to segment because the cable slope changes. The tension is largest in the segment with the greatest inclination angle.

Finding Tension in a Loaded Cable

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Learn how to analyze a flexible cable with vertical concentrated loads, use equilibrium and moments to find support reactions, cable shape, and segment tension.

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Finding Tension in a Loaded Cable

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