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

균일한 하중을 받는 두 개의 지지대에 고정된 케이블을 고려하십시오. 케이블의 최대 장력을 결정합니다.
분석을 위해 대칭으로 인한 케이블 중심의 원점을 고려하십시오.
분산 부하에 대한 케이블의 형상 방정식을 상기하고 알려진 일정한 부하 값을 대체합니다.
다음으로 방정식을 적분하고 원점에 경계 조건을 적용하여 상수 C2 를 결정합니다.
케이블 형상 방정식의 1차 도함수를 취하여 기울기를 결정할 수 있습니다. 원점에서의 경사에 대한 경계 조건을 적용하면 C1이 얻어집니다.
지지부의 적분 상수와 위치 좌표를 대입하고 방정식을 재배열함으로써, 수평 인장력을 얻을 수 있다.
기울기 방정식을 떠올리고 각도가 최대인 지지부에서 x 좌표 값을 대체합니다.
Cabel의 장력은 최대 근거리 지지선인 각도에 따라 변합니다.
삼각법 관계를 적용하고 항을 재배열하면 최대 인장 방정식이 얻어집니다.
마지막으로, 수평 장력 방정식과 알려진 값을 대체하여 케이블의 최대 장력을 얻습니다.

<ol>
	<li>히벨러, R.C. (2016). Engineering Mechanics \u2012 정역학 및 동역학. 뉴저지 호보켄: 피어슨 프렌티스 홀. 384-385, 393쪽.</li>
</ol>

케이블: 문제 해결

두 개의 지지대에 고정되어 균일한 하중을 받는 케이블을 다룰 때 케이블의 최대 장력을 결정하는 것이 중요합니다. 이 과정은 다음과 같이 몇 가지 주요 단계로 나눌 수 있습니다:

<img alt="Figure 1" src="/files/ftp_upload/14310/14310_Figure_1v3.svg" style="text-align: center; height: 300px;">

문제 분석: 주어진 시나리오와 케이블의 상태를 이해하는 것으로 시작합니다. 지지대, 적재 유형 및 기타 관련 정보를 식별합니다.

케이블의 형상방정식 결정:케이블의 곡선을 나타내는 형상방정식을 설정하기 위해 평형원리와 케이블의 특성을 이용합니다. 이 방정식은 케이블의 형상과 가해진 하중을 연관시킵니다.

<img alt="Equation 1" src="/files/ftp_upload/14310/14310_Equation_1v2.svg" style="text-align: center; height: 35px;" />

방정식 적분:형상방정식을 적분하여 케이블의 형상을 나타내는 함수를 구합니다. 이 적분과정을 통해 식의 상수를 구할 수 있습니다. 원점에서 경계조건을 적용하여 적분상수 중 하나의 값을 구할 수 있습니다.

<img alt="Equation 2" src="/files/ftp_upload/14310/14310_Equation_2v2.svg" style="text-align: center; height: 35px;" />

기울기 찾기: 케이블의 형상방정식의 1차 도함수를 취하여 임의의 지점에서 케이블의 기울기를 구합니다. 원점에서 기울기의 경계조건을 적용하여 다른 적분상수의 값을 구합니다.

수평 인장력 계산: 형상방정식에 적분상수와 지지대의 위치좌표를 대입하여 항을 재정렬하여 케이블에 작용하는 수평 인장력을 구합니다.

<img alt="Equation 3" src="/files/ftp_upload/14310/14310_Equation_3v2.svg" style="text-align: center; height: 35px;" />

각도 결정:각도를 구하려면 기울기 방정식을 이용하여 다양한 지점에서 케이블의 각도를 계산합니다. 케이블을 따라 각도가 최대가 되는 위치를 찾으십시오(보통 지지대 근처). 삼각관계를 이용하여 최대 장력을 수평 인장력과 케이블의 각도로 표현하십시오(

<img alt="Equation 4" src="/files/ftp_upload/14310/14310_Equation_4v2.svg" style="text-align: center; height: 35px;">

최대 장력을 구합니다: 수평 장력 방정식과 알려진 값을 최대 장력 방정식에 대입합니다.

<img alt="Equation 5" src="/files/ftp_upload/14310/14310_Equation_5v2.svg" style="text-align: center; height: 40px;">

두 개의 지지대에 고정되고 균일한 하중을 받는 케이블을 다룰 때는 케이블의 최대 장력을 결정하는 것이 중요합니다. ...

Education

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JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Internal Forces

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KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

sign convention

Beam Forces: Tension, Shear, and Bending

Beam analysis depends on the internal forces and moments inside a structure. These include normal force, shear force, and bending moment. Engineers use the method of sections to cut the beam and find these values. A sign convention helps show whether each result is positive or negative. Normal force acts perpendicular to the beam’s cross-section. It can pull the material in tension or push it in compression. Tension is taken as positive, while compression is taken as negative. This makes it...

normal and shear force

Beam Loads and Internal Forces

Beam loads create internal forces inside a structure. Weight, pressure, and other external forces can all act on a beam. These internal forces affect the beam’s stability and strength. Engineers study these forces to find their size and direction. A common approach is the method of sections. In this method, an imaginary cut is made at a chosen point on the beam, and the forces at that section are analyzed. One internal force is the normal force, also called the axial force. It acts...

bending and torsional moments

Forces That Bend and Twist Materials

Bending and torsional moments describe how materials respond to force. These ideas are important in structural engineering because they help explain how beams, rulers, and screws change shape under load. A moment depends on both the size of the force and the distance from the point of interest to the force’s line of action. A bending moment forms when an external force makes a structural element bend. If the element bends upward, the top side is in compression and the bottom side is in tension.

internal loadings in structural members: problem solving

internal-loadings-in-structural-members-problem-solving

Beam Internal Force Analysis at Point A

Beam internal force analysis shows how normal force, shear force, and bending moment act inside a structural member. These internal loadings help engineers check whether a beam can support the external forces applied to it. The example uses a beam OC that weighs 5 kN and is inclined at 53.13° with the horizontal. The beam is supported at both ends. The goal is to find the internal loadings at point A. The first step is to find the reaction force at point C. This is done by taking the moment...

beams

Beam Types and Support Conditions

Beams are key parts of structural engineering and construction. They support loads that act at different points along their length. Engineers use beam shape and support conditions to understand how a beam will perform. Beams can be classified by geometry. Straight beams are the most common and have a constant cross-section along their length. Tapered beams change in cross-section from one end to the other, while curved beams have a curved shape. Beam cross-section also matters. Common shapes...

shear diagram

Beam Shear Force Diagram

Beam shear force diagrams show how shear changes along the length of a supported beam. In beam mechanics, they help students track the internal shear force caused by perpendicular loads. The beam AB in this example is supported at both ends, so the first step is to draw a free-body diagram that shows the external forces and internal reactions. The reaction forces at supports A and B are found with equilibrium equations for force and moment. For the beam shown, the vertical reaction at A is 24...

bending moment diagram

Beam Load Analysis with Moment Diagrams

Beam load analysis uses a bending moment diagram to show how bending changes along the length of a beam. This diagram helps engineers and designers check whether a structure can handle applied forces. It is also useful for parts such as shelving arms, which must resist forces and moments from a load. To build the diagram, start by finding the reactive forces and any couple moments on the beam. In some cases, especially when a beam is inclined, these forces must be resolved into components that...

relation between the distributed load and shear

relation-between-the-distributed-load-and-shear

Shear Change Under Distributed Loading

Shear force changes along a beam under a distributed load. In structural analysis, this relationship helps explain how beams respond to loading conditions that also include concentrated loads and a couple moment. To study the link, consider a small beam section that has no concentrated load or couple moment on it. Draw a free-body diagram for that elemental section. It includes the distributed load along the beam, the shear force V(x) on the right-hand side of the cut, and a small added shear...

relation between the shear and bending moment

relation-between-the-shear-and-bending-moment

Shear and Moment Diagrams in Beam Loads

Shear and moment diagrams help show how a beam responds to loads. A beam can carry a distributed load, concentrated loads, and a couple moment. These loads create internal shear forces and bending moments. The beam is examined by isolating a small elemental section and drawing a free-body diagram. For that section to stay in equilibrium, the moment on the right side must be slightly larger than the moment on the left side. The distributed load also has a resultant force that acts at a...

shear and bending moment diagram: problem solving

shear-and-bending-moment-diagram-problem-solving

Beam Load Analysis with Shear Diagrams

Beam load analysis uses shear and bending moment diagrams to track the internal forces in a beam. These diagrams are important when a beam carries concentrated loads and a distributed load. They help show how the beam responds so structures can be designed safely and efficiently. The first step is to draw a free-body diagram of the whole beam. A free-body diagram shows the concentrated loads, the distributed load, and the reaction forces at the supports. Use the equilibrium equations, where...

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...

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...

cable subjected to its own weight

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.

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

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 Tension Under Uniform Loading

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