Name: finding cable shape under distributed load
Uploaded: 2025-05-22T09:06:04.000Z
Duration: 1 min 24 s
Channel: JoVE

Dans les ponts suspendus, les câbles principaux subissent des charges réparties, qui peuvent être transférées vers les tours de support et les ancrages. Déterminez la forme et la tension du câble.
On suppose que le câble est flexible, inextensible et que son poids est négligeable pour l’analyse.
Considérez un petit segment du câble et dessinez le schéma du corps libre du segment montrant la charge répartie et les changements de force de traction.
Ensuite, appliquez les équations d’équilibre et en substituant les forces et les moments horizontaux et verticaux agissant sur le segment, on obtient un ensemble d’équations.
En divisant chaque équation par Δx et en prenant chaque limite tendant vers zéro, on obtient un nouvel ensemble de trois équations.
L’intégration de la première équation donne la composante horizontale de la force de traction en tout point le long du câble.
Ensuite, intégrez la deuxième équation. En la divisant par la composante de la force de traction et en substituant la valeur de tanθ, on obtient l’expression de la pente du câble.
Enfin, la réalisation d’une seconde intégration sur l’équation dérivée permet de déterminer la courbe du câble.

<ol>
	<li>Hibbeler, R.C. (2016). Génie mécanique \u2012 Statique et dynamique. Hoboken, New Jersey : Pearson Prentice Hall. p. 384 à 386.</li>
</ol>

câble soumis à une charge distribuée

L'analyse des ponts suspendus est un processus complexe et crucial qui implique plusieurs facteurs, notamment la forme et la tension des câbles principaux. Les câbles principaux des ponts suspendus sont soumis à des charges distribuées, ce qui entraîne des changements de forces de tension et de déformation du câble. Ces charges doivent être soigneusement prises en compte pour s'assurer que le pont est sûr et capable de supporter le poids de différentes charges. <img alt="Figure 1" src="/files/ftp_upload/14308/14308_Figure_1v2.svg" style="text-align: center; height: 350px;"> Pour analyser un câble soumis à des charges distribuées, considérez un petit segment du câble et dessinez un diagramme de corps libre montrant la charge distribuée et les changements de force de tension. Un ensemble d'équations est obtenu en appliquant les équations d'équilibre et en substituant les forces horizontales et verticales ainsi que les moments agissant sur le segment. En divisant chaque équation par delta Δx et en prenant chaque limite tendant vers zéro, on obtient un nouvel ensemble de trois équations. La première équation obtenue à partir de cette analyse permet de déterminer la composante horizontale de la force de tension à n'importe quel point le long du câble. <img alt="Equation 1" src="/files/ftp_upload/14308/14308_Equation_1v2.svg" style="text-align: center; height: 13px;"> Elle permet également de calculer la tension du câble à n'importe quel point de sa longueur. L'expression de la pente du câble est obtenue en divisant la deuxième équation, qui est la composante verticale de la force de tension, par la composante de la force de tension horizontale et en substituant la valeur de tan θ. <img alt="Equation 2" src="/files/ftp_upload/14308/14308_Equation_2v2.svg" style="text-align: center; height: 35px;"> Enfin, en effectuant une deuxième intégration sur l'équation dérivée, on détermine la courbe du câble. <img alt="Equation 3" src="/files/ftp_upload/14308/14308_Equation_3v2.svg" style="text-align: center; height: 35px;"> Ainsi, le processus nous aide à comprendre le comportement du câble lorsqu'il est soumis à des charges distribuées. Il est également utile dans la conception du système de support du pont et pour s'assurer que les câbles peuvent supporter le poids de la circulation et d'autres contraintes.

Câble soumis à une charge distribuée

L’analyse des ponts suspendus est un processus complexe et critique qui implique de multiples facteurs, notamment la forme et la tension des câbles principaux. ...

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Cable Subjected to a Distributed Load

finding cable shape under distributed load

Cable shape under a distributed load is found by analyzing the forces along a small piece of the cable. This method is important in suspension bridge design because the main cables must carry changing loads safely. The load causes the tensile force in the cable to change, and it also creates cable deformation.

The analysis starts with a free-body diagram of a short cable segment. The diagram shows the distributed load and the change in tensile force across that segment. Equilibrium equations are then applied to the horizontal force, vertical force, and moments acting on the cable piece.

Next, each equation is divided by delta x, and the limit is taken as delta x approaches zero. This gives a new set of three equations. The first equation helps determine the horizontal component of tensile force at any point along the cable, and it can also be used to find the cable tension along its length.

The second equation is used to find the slope of the cable. It relates the vertical component of tensile force to the horizontal component. By substituting tan theta, the cable angle can be linked to the shape of the cable. A second integration of the final equation gives the curve of the cable. This analysis helps engineers understand cable behavior under distributed loads and design bridge support systems that can handle traffic weight and other stresses.

Finding Cable Shape Under Distributed Load

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key terms and concepts

Analyze how a suspension bridge cable responds to distributed loads using free-body diagrams, equilibrium equations, slope, tension, and cable curve.

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Finding Cable Shape Under Distributed Load

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