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

I cavi flessibili sono utilizzati per il supporto e la trasmissione del carico in varie applicazioni.
Si consideri un cavo AB fissato in due punti, che subisce più carichi concentrati verticali.
Determinare la forma del cavo e la tensione in ogni parte del cavo, conoscendo le distanze orizzontali tra i carichi e il supporto.
Per l'analisi, si presume che il cavo sia flessibile, inestensibile e abbia un peso trascurabile.
Il cavo è costituito da diversi segmenti rettilinei, ciascuno sottoposto a una forza di trazione costante.
Disegna un diagramma a corpo libero del cavo per determinare le forze di reazione ai supporti. Qui, il numero di componenti di reazione sconosciute supera le equazioni di equilibrio.
Considerare il punto D sul cavo a una distanza nota e disegnare un diagramma a corpo libero del segmento AD. Utilizzando l'equazione di equilibrio del momento nel punto D, si ottiene un'equazione aggiuntiva.
Richiamando le equazioni di equilibrio e utilizzando le forze di reazione, si ottiene la distanza verticale tra il supporto A e ciascun carico concentrato.
Allo stesso modo, è possibile ottenere la tensione in ciascun segmento, che è massima quando il segmento ha l'angolo di inclinazione maggiore.

<ol>
	<li>Birra, F.P.; Johnston, E.R.; Mazurek, D.F; Cromwell, P.J. e Self, B.P.(2019). Meccanica vettoriale per ingegneri \u2012 Statica e dinamica. New York: McGraw-Hill. Pagine 403-404.</li>
	<li>Hibbeler, R.C. (2016). Ingegneria Meccanica \u2012 Statica e Dinamica. Hoboken, New Jersey: Pearson Prentice Hall. pagine 381.</li>
</ol>

cavo sottoposto a carichi concentrati

I cavi flessibili sono comunemente utilizzati in varie applicazioni per il supporto e la trasmissione del carico. Si consideri un cavo fissato ai due punti e sottoposto a carichi concentrati multipli in verticale. Determinare la forma del cavo e la tensione in ogni porzione del cavo, date le distanze orizzontali tra i carichi e i punti di supporto.

<img alt="Figure 1" src="/files/ftp_upload/14307/14307_Figure_1v2.svg" style="text-align: center; height: 350px;" />

Per l'analisi, si assume che il cavo abbia le seguenti proprietà:

<ol style="display: flex; flex-direction: column; gap: 10px; list-style-type: lower-alpha;">
 <li>Flessibile, il che gli consente di cambiare forma sotto l'influenza dei carichi applicati.</li>
 <li>Inestensibile, il che significa che la sua lunghezza non cambia sotto tensione.</li>
 <li>Peso trascurabile, il che implica che il peso del cavo non influisce significativamente sul suo comportamento.</li>
</ol>

Il cavo è composto da diversi segmenti rettilinei, con ciascun segmento sottoposto a una forza di trazione costante. Per determinare le reazioni nei punti di supporto, è possibile disegnare un diagramma di corpo libero del cavo. Tuttavia, nel caso dato, il numero di componenti di reazione sconosciute superi tipicamente il numero di equazioni di equilibrio disponibili, è necessaria un'equazione aggiuntiva. Per ottenerla si consideri il punto D sul cavo a una distanza nota dai punti di supporto. Tracciando un diagramma del corpo libero del segmento AD e utilizzando l'equazione di equilibrio dei momenti nel punto D, è possibile derivare un'altra equazione che aiuta a risolvere il sistema.

<img alt="Equation 1" src="/files/ftp_upload/14307/14307_Equation_1v2.svg" style="text-align: center; height: 13px;" />

La distanza verticale dal supporto A a ciascun carico concentrato può essere determinata con le forze di reazione conosciute. Ciò può essere ottenuto richiamando l'equazione di equilibrio, che afferma che la somma delle forze verticali che agiscono sul cavo deve essere uguale a zero. Una volta determinate le distanze verticali, è possibile calcolare la tensione in ciascun segmento del cavo. La tensione è massima quando il segmento ha l'angolo di inclinazione più grande.

<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;" />

Cavo sottoposto a carichi concentrati

I cavi flessibili sono comunemente utilizzati in varie applicazioni per il supporto e la trasmissione del carico. Considera un cavo fissato in due punti e sottoposto a...

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Mechanical Engineering

Ingegneria Meccanica

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Internal Forces

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TERMINI E CONCETTI CHIAVE

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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key terms and concepts

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

Finding Tension in a Loaded Cable | JoVE K12

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Finding Tension in a Loaded Cable

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