Name: cable tension under uniform loading
Uploaded: 2025-05-22T09:06:04.000Z
Duration: 1 min 29 s
Channel: JoVE

Consider a cable fixed at two supports subjected to uniform loading. Determine the maximum tension in the cable.
For analysis, consider the origin at the cable&#39;s center due to its symmetry.
Recall the cable&#39;s shape equation for distributed load and substitute the known constant loading value.
Next, integrate the equation, and by applying the boundary conditions at the origin, the constant C2 is determined.
By taking the first derivative of the cable&#39;s shape equation, the slope can be determined. Applying the boundary conditions for the slope at the origin, C1 is obtained.
By substituting the integration constants and position coordinates of the support and rearranging the equation, the horizontal tensile force is obtained.
Recall the slope equation, and substitute the x-coordinate value at the support where the angle is maximum.
Cabel&#39;s tension changes with the angle, which is the maximum near support.
Applying the trigonometric relation and rearranging the terms, the maximum tension equation is obtained.
Finally, by substituting the horizontal tension equation and known values, the maximum tension in the cable is obtained.&#160;

kabel: probleemoplossing

Wanneer u te maken heeft met een kabel die bevestigd is aan twee ondersteuningen en onderworpen is aan uniforme belasting, is het cruciaal om de maximale spanning in de kabel te bepalen. Dit proces kan worden opgesplitst in verschillende belangrijke stappen, zoals hieronder beschreven: <img alt="Figure 1" src="/files/ftp_upload/14310/14310_Figure_1v3.svg" style="text-align: center; height: 300px;"> Analyseer het probleem: Begin met het begrijpen van het gegeven scenario en de omstandigheden van de kabel. Identificeer de ondersteuningen, het type belasting en alle andere relevante informatie. Bepaal de vormvergelijking van de kabel: Gebruik de principes van evenwicht en de eigenschappen van de kabel om de vormvergelijking vast te stellen die de curve van de kabel beschrijft. Deze vergelijking relateert de vorm van de kabel aan de aangebrachte belasting. <img alt="Equation 1" src="/files/ftp_upload/14310/14310_Equation_1v2.svg" style="text-align: center; height: 35px;"> Integreer de vergelijking: Integreer de vormvergelijking om een functie te verkrijgen die de vorm van de kabel representeert. Dit integratieproces stelt u in staat om de constanten in de vergelijking te bepalen. Door de randvoorwaarden bij de oorsprong toe te passen, kan de waarde van één van de integratieconstanten worden bepaald. <img alt="Equation 2" src="/files/ftp_upload/14310/14310_Equation_2v2.svg" style="text-align: center; height: 35px;"> Bereken de helling: Neem de eerste afgeleide van de vormvergelijking van de kabel om de helling van de kabel op elk gegeven punt te bepalen. Pas de randvoorwaarden voor de helling bij de oorsprong toe om de waarde van een andere integratieconstante te verkrijgen. Bereken de horizontale trekkracht: Door de integratieconstanten en de positiecoördinaten van de ondersteuning in de vormvergelijking in te voeren. Herschik de termen om de horizontale trekkracht op de kabel te vinden. <img alt="Equation 3" src="/files/ftp_upload/14310/14310_Equation_3v2.svg" style="text-align: center; height: 35px;"> Bepaal de hoek: Gebruik de helling vergelijking om de hoek van de kabel op verschillende punten te berekenen. Vind de locatie langs de kabel waar de hoek maximaal is, meestal in de buurt van de ondersteuningen. Maak gebruik van de goniometrische relaties om de maximale spanning uit te drukken in termen van de horizontale trekkracht en de hoek van de kabel. <img alt="Equation 4" src="/files/ftp_upload/14310/14310_Equation_4v2.svg" style="text-align: center; height: 35px;"> Bereken de maximale spanning: Voer de vergelijking voor horizontale spanning en de bekende waarden in in de vergelijking voor maximale spanning. Dit stelt u in staat om de maximale spanning in de kabel te berekenen. <img alt="Equation 5" src="/files/ftp_upload/14310/14310_Equation_5v2.svg" style="text-align: center; height: 40px;">

Kabel: Probleemoplossing

When dealing with a cable that is fixed to two supports and subjected to uniform loading, it is crucial to determine the maximum tension in the cable. ...

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Cable: Problem Solving

cable tension under uniform loading

Cable tension under uniform loading is found by analyzing a cable fixed between two supports. The problem starts with the support conditions and the load on the cable. From there, the cable’s shape must be described with an equation that matches the curve formed by the load.

The next step is to integrate the shape equation to get the cable’s shape function. This makes it possible to solve for constants in the equation. The boundary condition at the origin gives one constant. The slope, which is the first derivative of the shape equation, gives the cable’s tilt at any point. A second boundary condition at the origin is used to find another constant.

After the constants are set, the horizontal tensile force can be calculated from the support coordinates and the shape equation. The slope equation is then used to find the cable angle at different points. The angle is usually largest near the supports, so that location is used to determine the maximum tension.

Trigonometric relationships connect the maximum tension to the horizontal tensile force and the cable angle. Once the horizontal tension equation and the given values are substituted into the tension formula, the maximum tension in the cable can be found.

Cable Tension Under Uniform Loading

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cable: problem solving

Cable tension under uniform loading is found by analyzing a cable fixed between two supports. The problem starts with the support conditions and the load on the cable. From there, the cable’s shape must be described with an equation that matches the curve formed by the load. The next step is to integrate the shape equation to get the cable’s shape function. This makes it possible to solve for constants in the equation. The boundary condition at the origin gives one constant. The slope, which...

key terms and concepts

Follow the steps to find maximum cable tension under uniform loading using the cable shape equation, slope, boundary conditions, and trigonometry.

Cable Tension Under Uniform Loading | JoVE K12

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Cable Tension Under Uniform Loading

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