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

가공 송전선로의 케이블을 고려하십시오. 송전선로의 안정성을 보장하기 위해 케이블의 모양이나 처짐 및 장력을 결정하십시오.
자체 무게에 영향을 받는 케이블을 분석하기 위해 투영 길이 대신 케이블의 아크 길이를 따라 작용하는 일반화된 하중 함수가 사용됩니다.
다음으로, 케이블의 작은 세그먼트를 고려하고 세그먼트의 자유물체 다이어그램을 그립니다.
평형 방정식을 적용하면 세 가지 방정식 집합을 얻을 수 있습니다. 여기서, 첫 번째 및 두 번째 방정식은 각각 인장력의 수평 및 수직 성분을 나타냅니다.
피타고라스의 정리를 사용하여 수직 거리의 변화 dy와 케이블의 호 길이 ds 사이에 관계를 설정할 수 있습니다. 이 관계는 세 번째 방정식에서 대체됩니다.
마지막으로, 항을 재배열하고 방정식을 적분함으로써, 케이블의 형상에 대한 표현을 결정할 수 있습니다.

<ol>
	<li>히벨러, R.C. (2016). Engineering Mechanics \u2012 정역학 및 동역학. 뉴저지 호보켄: 피어슨 프렌티스 홀. 388-390쪽.</li>
</ol>

자체 무게를 받는 케이블

Cable Subjected to Its Own Weight

가공 송전선로는 케이블을 이용하여 먼 거리까지 전기를 운반합니다. 이러한 전선로의 안정성과 기능성을 확보하기 위해서는 케이블의 무게에 따른 형태와 장력을 이해하는 것이 매우 중요합니다.
케이블 자체의 무게를 받는 케이블을 분석하기 위해 일반화된 하중 함수가 사용됩니다. 이 함수는 케이블의 예상 길이가 아닌 케이블의 호 길이를 따라 작용하는 힘을 고려하여 케이블의 동작을 보다 정확하게 표현합니다. 케이블을 더 자세히 분석하기 위해 케이블의 작은 부분을 고려하고 자유 물체 도표를 작성합니다. 도표는 케이블 부분에 작용하는 힘을 시각화하는 데 도움이 되며 평형 방정식을 적용하기 위한 기초 역할을 합니다.

<img alt="Figure 1" src="/files/ftp_upload/14309/14309_Figure_1v2.svg" style="text-align: center; height: 350px;">

케이블 세그먼트에 평형방정식을 적용하면 3개의 방정식 집합을 얻을 수 있습니다. 첫 번째 방정식과 두 번째 방정식은 각각 케이블에 작용하는 인장력의 수평 성분과 수직 성분을 나타냅니다.
<img alt="Equation 1" src="/files/ftp_upload/14309/14309_Equation_1v2.svg" style="text-align: center; height: 13px;" />
<img alt="Equation 2" src="/files/ftp_upload/14309/14309_Equation_2v2.svg" style="text-align: center; height: 28px;" />
<img alt="Equation 3" src="/files/ftp_upload/14309/14309_Equation_3v2.svg" style="text-align: center; height: 32px;" />
피타고라스의 정리를 이용하면 수직거리의 변화(dy)와 케이블의 호 길이(ds) 사이에 관계를 설정할 수 있습니다. 그런 다음 관계는 평형방정식에서 얻은 세 번째 방정식으로 대체됩니다. 마지막으로 방정식의 항을 재정렬하고 얻은 방정식을 적분하면 케이블의 모양에 대한 식을 결정할 수 있습니다.
<img alt="Equation 4" src="/files/ftp_upload/14309/14309_Equation_4v3.svg" style="text-align: center; height: 70px;" />
이 식을 통해 엔지니어는 케이블의 처짐과 장력을 계산할 수 있으며, 가공 송전선의 안정성과 효율성을 보장합니다.

가공 송전선은 케이블에 의존하여 전기를 먼 거리로 운반합니다. 이 라인의 안정성과 기능을 보장하기 위해 ...

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Mechanical Engineering

Unit 1

Internal Forces

KEY TERMS AND CONCEPTS

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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shear and bending moment diagram: problem solving

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cable subjected to 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.

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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

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Cable Sag Under Its Own Weight

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