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

Nei ponti sospesi, i cavi principali sono sottoposti a carichi distribuiti, che possono essere trasferiti alle torri di supporto e agli ancoraggi. Determinare la forma e la tensione del cavo.
Si presume che il cavo sia flessibile, inestensibile e con un peso trascurabile per l'analisi.
Si consideri un piccolo segmento del cavo e si disegni il diagramma a corpo libero del segmento che mostra il carico distribuito e le variazioni della forza di trazione.
Successivamente, applicare le equazioni di equilibrio e sostituendo le forze e i momenti orizzontali e verticali che agiscono sul segmento, si ottiene un insieme di equazioni.
Dividendo ogni equazione per Δx e prendendo ogni limite tendente a zero, si ottiene un nuovo insieme di tre equazioni.
L'integrazione della prima equazione produce la componente orizzontale della forza di trazione in qualsiasi punto lungo il cavo.
Quindi, integra la seconda equazione. Dividendolo per la componente della forza di trazione e sostituendo il valore di tanθ, si ottiene l'espressione per la pendenza del cavo.
Infine, l'esecuzione di una seconda integrazione sull'equazione derivata determina la curva del cavo.

<ol>
	<li>Hibbeler, R.C. (2016). Ingegneria Meccanica \u2012 Statica e Dinamica. Hoboken, New Jersey: Pearson Prentice Hall. pagine 384-386.</li>
</ol>

cavo soggetto a un carico distribuito

L'analisi dei ponti sospesi è un processo complesso e critico che coinvolge vari fattori, tra cui la forma e la tensione dei cavi principali. I cavi principali dei ponti sospesi sono soggetti a carichi distribuiti, che comportano variazioni delle forze di trazione e deformazioni del cavo. Questi carichi devono essere attentamente considerati per garantire che il ponte sia sicuro e in grado di sostenere il peso di diversi carichi.

<img alt="Figure 1" src="/files/ftp_upload/14308/14308_Figure_1v2.svg" style="text-align: center; height: 350px;" />

Per analizzare un cavo soggetto a carichi distribuiti, si consideri un piccolo segmento del cavo e si disegni un diagramma di corpo libero che mostri il carico distribuito e le variazioni della forza di trazione. Applicando le equazioni di equilibrio e sostituendo le forze e i momenti orizzontali e verticali che agiscono sul segmento, si ottiene un insieme di equazioni. Dividendo ciascuna equazione per delta Δx e prendendo il limite che tende a zero, si ottiene un nuovo set di tre equazioni. La prima equazione ottenuta da questa analisi aiuta a determinare la componente orizzontale della forza di trazione in qualsiasi punto lungo il cavo.

<img alt="Equation 1" src="/files/ftp_upload/14308/14308_Equation_1v2.svg" style="text-align: center; height: 13px;" />

Inoltre, consente di calcolare la tensione del cavo in qualsiasi punto lungo la sua lunghezza. L'espressione per la pendenza del cavo si ottiene dividendo la seconda equazione, che è la componente verticale della forza di trazione, con la componente della forza di trazione orizzontale e sostituendo il valore di tan θ.

<img alt="Equation 2" src="/files/ftp_upload/14308/14308_Equation_2v2.svg" style="text-align: center; height: 35px;" />

Infine, eseguendo una seconda integrazione sull'equazione derivata, si determina la curva del cavo.

<img alt="Equation 3" src="/files/ftp_upload/14308/14308_Equation_3v2.svg" style="text-align: center; height: 35px;" />

Pertanto, il processo ci aiuta a comprendere il comportamento del cavo quando è soggetto a carichi distribuiti. È anche utile nella progettazione del sistema di supporto del ponte e nell'assicurarsi che i cavi possano sopportare il peso del traffico e di altre sollecitazioni.

Cavo Soggetto a un Carico Distribuito

L'analisi dei ponti sospesi è un processo complesso e critico che coinvolge molteplici fattori, tra cui la forma e la tensione dei cavi principali. ...

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Internal Forces

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KEY TERMS AND CONCEPTS

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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

finding-cable-shape-under-distributed-load

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relation between the distributed load and shear

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cable subjected to a 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...

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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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