Name: cable sag under its own weight
Uploaded: 2023-09-22T11:49:27.000Z
Duration: 1 min 13 s
Channel: JoVE

Consider the cables in overhead power transmission lines. Determine the shape or sag and tension in the cable to ensure stability in the power transmission lines.
For analysis of the cable subjected to its own weight, a generalized loading function is used that acts along the cable&#39;s arc length instead of the projected length.
Next, consider a small segment of the cable and draw a free-body diagram of the segment.
By applying the equations of equilibrium, a set of three equations can be obtained. Here, the first and second equation represents the horizontal and vertical component of the tensile force, respectively.
Using Pythagoras&#39; theorem, a relation can be established between the change in the vertical distance, dy and the arc length of the cable, ds. This relation is substituted in the third equation.
Finally, by rearranging the terms and integrating the equation, the expression for the shape of the cable can be determined.

cable subjected to its own weight

Overhead power transmission lines rely on cables to carry electricity across large distances. To ensure the stability and functionality of these lines, it is crucial to understand the shape and tension experienced by the cables under the influence of their weight.
A generalized loading function is employed to analyze a cable subjected to its own weight. This function considers the force acting along the cable's arc length rather than its projected length, providing a more accurate representation of the cable's behavior. To further analyze the cable, a small segment of the cable is considered, and a free-body diagram is drawn. The diagram helps to visualize the forces acting on the cable segment and serves as a basis for applying the equilibrium equations.
<img alt="Elastic beam bending diagram showing forces, displacement (dx, dy), and curvature (θ, Δθ)." src="/files/ftp_upload/14309/14309_Figure_1v2.svg" style="text-align: center; height: 350px;" data-altupdatedat="1761830439000" data-alt="Figure 1">
A set of three equations can be obtained by applying the equilibrium equations to the cable segment. The first and second equations represent the horizontal and vertical components of the tensile force acting on the cable, respectively.
<img alt="Static equilibrium equation: T cos θ = F_H, representing force balance concept." src="/files/ftp_upload/14309/14309_Equation_1v2.svg" style="text-align: center; height: 13px;" data-altupdatedat="1761830439000" data-alt="Equation 1">
<img alt="Truss analysis formula: \( T \sin \theta = \int w(s) \, ds \); structural equilibrium equation." src="/files/ftp_upload/14309/14309_Equation_2v2.svg" style="text-align: center; height: 28px;" data-altupdatedat="1761830439000" data-alt="Equation 2">
<img alt="Differential equation for beam deflection, dy/dx = 1/FH ∫w(s)ds, symbol analysis." src="/files/ftp_upload/14309/14309_Equation_3v2.svg" style="text-align: center; height: 32px;" data-altupdatedat="1761830439000" data-alt="Equation 3">
Using Pythagoras' theorem, a relationship can be established between the change in vertical distance (dy) and the arc length of the cable (ds). The relationship is then substituted into the third equation obtained from the equations of equilibrium. Finally, by rearranging the terms in the equation and integrating the obtained equation, an expression for the shape of the cable can be determined.
<img alt="Integral equation formula; mathematical expression for variable x; educational diagram." src="/files/ftp_upload/14309/14309_Equation_4v3.svg" style="text-align: center; height: 70px;" data-altupdatedat="1761830439000" data-alt="Equation 4">
This expression allows engineers to calculate the sag and tension in the cable, ensuring the stability and efficiency of overhead power transmission lines.

Cable Subjected to Its Own Weight

Overhead power transmission lines rely on cables to carry electricity across large distances. To ensure the stability and functionality of these lines, it ...

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cable sag under its own weight

Overhead power transmission cables sag under their own weight, and that shape affects how they carry electricity across long distances. To study this behavior, the cable is analyzed with a generalized loading function. This function treats the load along the cable's arc length instead of its projected length, which gives a more accurate picture of the cable's response.

The analysis then focuses on a small cable segment. A free-body diagram is drawn to show the forces acting on that segment. This diagram supports the equilibrium equations used to describe the horizontal and vertical components of the tensile force in the cable.

From these equilibrium equations, three relationships can be written. Two of them describe the horizontal and vertical tension components. The third uses Pythagoras' theorem to connect the change in vertical distance, dy, with the arc length, ds.

That relationship is substituted into the equilibrium equation for the segment. The equation is then rearranged and integrated. The result is an expression for the cable shape, which helps engineers calculate sag and tension and support stable, efficient overhead power transmission lines.

Cable Sag Under Its Own Weight

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Overhead power transmission cables sag under their own weight, and that shape affects how they carry electricity across long distances. To study this behavior, the cable is analyzed with a generalized loading function. This function treats the load along the cable's arc length instead of its projected length, which gives a more accurate picture of the cable's response. The analysis then focuses on a small cable segment. A free-body diagram is drawn to show the forces acting on that segment.

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key terms and concepts

Explore how a cable’s own weight creates sag, tension, and cable shape. See how equilibrium, a free-body diagram, and integration reveal the curve.

Cable Sag Under Its Own Weight | JoVE K12

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Cable Sag Under Its Own Weight

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