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

Stellen Sie sich ein Kabel vor, das an zwei Stützen befestigt ist, die gleichmäßig belastet werden. Bestimmen Sie die maximale Spannung im Kabel.
Berücksichtigen Sie für die Analyse den Ursprung in der Mitte des Kabels aufgrund seiner Symmetrie.
Rufen Sie die Formgleichung des Kabels für die verteilte Last auf, und ersetzen Sie sie durch den bekannten konstanten Lastwert.
Als nächstes integrieren Sie die Gleichung, und durch Anwenden der Randbedingungen am Ursprung wird die Konstante C2 bestimmt.
Durch die erste Ableitung der Formgleichung des Kabels kann die Steigung bestimmt werden. Wendet man die Randbedingungen für die Steigung am Ursprung an, erhält man C1.
Durch Ersetzen der Integrationskonstanten und Positionskoordinaten des Lagers und Neuanordnen der Gleichung erhält man die horizontale Zugkraft.
Rufen Sie die Neigungsgleichung auf, und ersetzen Sie den X-Koordinatenwert an der Stelle, an der der Winkel maximal ist.
Die Spannung des Kabels ändert sich mit dem Winkel, der die maximale Nahabstützung darstellt.
Wenn man die trigonometrische Beziehung anwendet und die Terme neu anordnet, erhält man die Gleichung für die maximale Spannung.
Schließlich wird durch Ersetzen der horizontalen Spannungsgleichung und bekannter Werte die maximale Spannung im Kabel erhalten.

<ol>
	<li>Hibbeler, R.C. (2016). Technische Mechanik \u2012 Statik und Dynamik. Hoboken, New Jersey: Pearson Prentice Hall. S. 384-385, 393.</li>
</ol>

kabel: problemlösung

Wenn man es mit einem Kabel zu tun hat, das an zwei Stützen befestigt ist und einer gleichmäßigen Last ausgesetzt ist, ist es entscheidend, die maximale Spannung im Kabel zu bestimmen. Dieser Prozess kann in mehrere wesentliche Schritte unterteilt werden, wie nachstehend beschrieben: <img alt="Figure 1" src="/files/ftp_upload/14310/14310_Figure_1v3.svg" style="text-align: center; height: 300px;"> Analysieren Sie das Problem: Beginnen Sie damit, das gegebene Szenario und die Bedingungen des Kabels zu verstehen. Identifizieren Sie die Stützen, die Art der Belastung und alle anderen relevanten Informationen. Bestimmen Sie die Formel zur Beschreibung der Form des Kabels: Verwenden Sie die Prinzipien des Gleichgewichts und die Eigenschaften des Kabels, um die Formel zur Beschreibung der Kurve des Kabels festzulegen. Diese Formel stellt einen Zusammenhang zwischen der Form des Kabels und der aufgebrachten Last her. <img alt="Equation 1" src="/files/ftp_upload/14310/14310_Equation_1v2.svg" style="text-align: center; height: 35px;"> Integrieren Sie die Formel: Integrieren Sie die Formel zur Form des Kabels, um eine Funktion zu erhalten, die die Form des Kabels repräsentiert. Dieser Integrationsprozess ermöglicht es Ihnen, die Konstanten in der Formel zu bestimmen. Durch Anwendung der Randbedingungen am Ursprung kann der Wert einer der Integrationskonstanten ermittelt werden. <img alt="Equation 2" src="/files/ftp_upload/14310/14310_Equation_2v2.svg" style="text-align: center; height: 35px;"> Finden Sie die Steigung: Nehmen Sie die erste Ableitung der Formel zur Form des Kabels, um die Steigung des Kabels an einem beliebigen Punkt zu bestimmen. Wenden Sie die Randbedingungen für die Steigung am Ursprung an, um den Wert einer weiteren Integrationskonstante zu erhalten. Berechnen Sie die horizontale Zugkraft: Ersetzen Sie die Integrationskonstanten und die Positionskoordinaten der Stütze in die Formel zur Form des Kabels. Ordnen Sie die Begriffe um, um die horizontale Zugkraft zu finden, die auf das Kabel wirkt. <img alt="Equation 3" src="/files/ftp_upload/14310/14310_Equation_3v2.svg" style="text-align: center; height: 35px;"> Bestimmen Sie den Winkel: Verwenden Sie die Steigungsformel, um den Winkel des Kabels an verschiedenen Punkten zu berechnen. Finden Sie die Stelle entlang des Kabels, an der der Winkel am größten ist, normalerweise in der Nähe der Stützen. Nutzen Sie trigonometrische Beziehungen, um die maximale Spannung in Bezug auf die horizontale Zugkraft und den Winkel des Kabels auszudrücken. <img alt="Equation 4" src="/files/ftp_upload/14310/14310_Equation_4v2.svg" style="text-align: center; height: 35px;"> Finden Sie die maximale Spannung: Setzen Sie die Gleichung für die horizontale Zugkraft und die bekannten Werte in die Gleichung für die maximale Spannung ein. Dadurch können Sie die maximale Spannung im Kabel berechnen. <img alt="Equation 5" src="/files/ftp_upload/14310/14310_Equation_5v2.svg" style="text-align: center; height: 40px;">

Kabel: Problemlösung

Wenn es sich um ein Kabel handelt, das an zwei Stützen befestigt und gleichmäßig belastet wird, ist es entscheidend, die maximale Spannung im Kabel zu bestimmen. ...

Education

Lehre

JoVE Core

Mechanical Engineering

Maschinenbau

Unit 1

Einheit 1

Internal Forces

Innere Kräfte

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

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

Description

Transcript

Tags