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

플렉시블 케이블은 다양한 응용 분야에서 지원 및 부하 전달에 사용됩니다.
두 지점에 고정된 케이블 AB에서 여러 수직 집중 부하가 발생한다고 가정해 보십시오.
케이블의 모양과 케이블의 각 부분의 장력을 결정하고 하중과 지지대 사이의 수평 거리를 파악하십시오.
분석을 위해 케이블은 유연하고 확장할 수 없으며 무게가 무시할 수 있는 것으로 가정합니다.
케이블은 여러 직선 세그먼트로 구성되며 각 세그먼트는 일정한 인장력을 받습니다.
케이블의 자유물체 다이어그램을 그려 지지부에서의 반력을 결정합니다. 여기서, 알려지지 않은 반응 성분의 수는 평형 방정식을 초과합니다.
알려진 거리 에서 케이블의 D 지점을 고려하고 세그먼트 AD의 자유체 다이어그램을 그립니다. 점 D에서 모멘트 평형 방정식을 사용하면 추가 방정식을 얻을 수 있습니다.
평형 방정식을 상기하고 반력을 사용함으로써 각 집중 하중에 대한 지지 A 사이의 수직 거리를 얻습니다.
유사하게, 각 세그먼트의 장력을 얻을 수 있으며, 이는 세그먼트가 가장 큰 경사각을 가질 때 최대입니다.

<ol>
	<li>맥주, F.P.; 존스턴, ER; 마주렉, D.F; 크롬웰, PJ 및 Self, BP(2019). 엔지니어를 위한 벡터 역학 \u2012 Statics and Dynamics. 뉴욕 : McGraw-Hill. 403-404쪽.</li>
	<li>히벨러, R.C. (2016). Engineering Mechanics \u2012 정역학 및 동역학. 뉴저지 호보켄: 피어슨 프렌티스 홀. 381쪽.</li>
</ol>

집중하중을 받는 케이블

유연한 케이블은 지지 및 하중 전달을 위해 다양한 응용 분야에서 일반적으로 사용됩니다. 두 지점에 고정되어 있고 수직으로 집중된 여러 하중을 받는 케이블을 생각해 보세요. 하중과 지지대 사이의 수평 거리를 고려하여 케이블의 모양과 케이블 각 부분의 장력을 결정합니다.

<img alt="그림 1" src="/files/ftp_upload/14307/14307_Figure_1v2.svg" style="text-align: center; height: 350px;" />

분석을 위해 케이블은 다음과 같은 속성을 갖는 것으로 가정됩니다.

<ol style="list-style-type:lower-alpha;">
<li>유연성이 있어 적용된 하중의 영향으로 모양이 바뀔 수 있습니다.</li>
<li>확장 불가능, 즉 장력이 가해져도 길이가 변하지 않음을 의미합니다.</li>
<li>케이블의 자체 무게가 케이블 동작에 큰 영향을 미치지 않음을 의미하는 무시할 수 있는 무게입니다.</li>
</ol>

케이블은 여러 개의 직선 세그먼트로 구성되며, 각 세그먼트는 일정한 인장력을 받습니다. 지지점에서의 반력을 결정하기 위해 케이블의 자유물체 다이어그램을 그릴 수 있습니다. 그러나 주어진 경우에는 알려지지 않은 반응 성분의 수가 일반적으로 사용 가능한 평형 방정식의 수를 초과합니다. 추가 방정식이 필요합니다. 추가 방정식을 얻으려면 지지대로부터 알려진 거리에 있는 케이블의 점 D를 고려해 보세요. 세그먼트 AD의 자유물체도를 그리고 D 지점의 모멘트 평형 방정식을 사용하여 시스템을 해결하는 데 도움이 되는 또 다른 방정식을 유도할 수 있습니다.

<img alt="Equation 1" src="/files/ftp_upload/14307/14307_Equation_1v2.svg" style="text-align: center; height: 13px;" />

지점 A에서 각 집중 하중까지의 수직 거리는 알려진 반력을 사용하여 결정할 수 있습니다. 이는 케이블에 작용하는 수직 힘의 합이 0과 같아야 한다는 평형 방정식을 통해 달성할 수 있습니다. 수직 거리가 결정되면 각 케이블 세그먼트의 장력을 계산할 수 있습니다. 세그먼트의 경사각이 가장 클 때 장력이 최대가 됩니다.

<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;" />

플렉시블 케이블은 일반적으로 지원 및 부하 전달을 위한 다양한 응용 분야에 사용됩니다. 두 지점에 고정된 케이블을 고려하십시오.

Education

교육

JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Internal Forces

내력

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

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

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

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

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

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

Finding Tension in a Loaded Cable

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