Name: beam shear force diagram
Uploaded: 2025-05-22T09:06:03.000Z
Duration: 1 min 27 s
Channel: JoVE

Das Schubdiagramm ist eine grafische Darstellung der Verteilung der Schubkräfte entlang der Länge des Trägers.
Stellen Sie sich einen Balken AB vor, der an zwei Enden abgestützt und senkrechten Lasten ausgesetzt ist. Konstruieren Sie das Scherdiagramm.
Zeichnen Sie das Freikörperdiagramm des Trägers. Mit Hilfe der Gleichgewichtsgleichungen von Kraft und Moment können die Reaktionskräfte an jedem Lager berechnet werden.
Wenden Sie die Schnittmethode auf den Balken an.
Betrachten Sie als Nächstes einen beliebigen Abstand von Punkt A innerhalb des Bereichs AP. Zeichnen Sie ein Freikörperdiagramm des Schnitts. Unter Gleichgewichtsbedingungen entspricht die Querkraft im Querschnitt der Reaktionskraft am Lager.
Betrachten Sie auf ähnliche Weise einen beliebigen Punkt innerhalb des Bereichs PQ. Durch Zeichnen des Freikörperdiagramms und unter Verwendung der Gleichgewichtsgleichung kann die Schubung im Schnitt bestimmt werden.
Schließlich wird der willkürliche Punkt innerhalb des Abschnitts QB betrachtet. Durch das Zeichnen des Freikörperdiagramms und das Abrufen der Gleichgewichtsgleichung kann die Schubung im Schnitt bestimmt werden, die bis zum Ende des Balkens konstant bleibt und schließlich gegen Null geht, um das Gleichgewicht aufrechtzuerhalten.

<ol>
	<li>Hibbeler, R.C. (2016). Technische Mechanik \u2012 Statik und Dynamik. Hoboken, New Jersey: Pearson Prentice Hall. Seite 361.</li>
	<li>Bier, F.P.; Johnston, E.R.; Mazurek, D.F.; Cromwell, P.J. und Self, B.P.(2019). Vektormechanik für Ingenieure \u2012 Statik und Dynamik. New York: McGraw-Hill. Seite 381.</li>
</ol>

scherendiagramm

Bei der Untersuchung der Balkenmechanik spielen Scherdiagramme eine entscheidende Rolle beim Verständnis der Verteilung der Scherkräfte entlang der Länge eines Balkens. Betrachten Sie einen Balken AB, der an beiden Enden unterstützt wird und senkrechten Lasten ausgesetzt ist. Zuerst wird ein Freikörperdiagramm des Balkens gezeichnet, das alle externen Kräfte und internen Reaktionen darstellt, die auf den Balken wirken. Die Reaktionskräfte an jeder Stütze können mit Hilfe der Gleichgewichtsgleichungen für Kraft und Moment berechnet werden. Die vertikale Komponente der Reaktionskräfte an den Punkten A und B für den gegebenen Balken beträgt jeweils 24 kN und 18 kN. <img alt="Figure 1" src="/files/ftp_upload/14301/14301_PT_Figure_1v2.svg" style="text-align: center; height: 300px;"> Ein Scherdiagramm ist eine grafische Darstellung, die die Verteilung der Scherkräfte entlang der Länge des Balkens illustriert. Um dieses Diagramm zu erstellen, wird die Methode der Schnitte auf den Balken angewendet. Als Nächstes wird ein beliebiger Abstand vom Punkt A innerhalb des Bereichs AP betrachtet. Ein Freikörperdiagramm dieses Abschnitts wird gezeichnet, um die darauf wirkenden Kräfte zu analysieren. Unter der Bedingung des Gleichgewichts entspricht die Scherkraft im Abschnitt der Reaktionskraft an der Stütze, also V1=24 kN. Ähnlich wird ein beliebiger Punkt innerhalb des Bereichs PQ betrachtet. Durch das Zeichnen eines Freikörperdiagramms dieses Abschnitts und die Verwendung der Gleichgewichtsgleichung kann die Scherkraft, V2, bestimmt werden. <img alt="Equation 1" src="/files/ftp_upload/14301/14301_Equation_1v2.svg" style="text-align: center; height: 13px;"> Schließlich wird ein beliebiger Punkt innerhalb des Abschnitts QB betrachtet. Ein Freikörperdiagramm wird für diesen Abschnitt gezeichnet, und die Gleichgewichtsgleichung wird herangezogen, um die Scherkraft, V3, im Abschnitt zu bestimmen. <img alt="Equation 2" src="/files/ftp_upload/14301/14301_Equation_2v2.svg" style="text-align: center; height: 13px;"> Diese Scherkraft bleibt bis zum Ende des Balkens konstant und geht letztendlich auf null zurück, um das Gleichgewicht zu halten.

Scherendiagramm

Bei der Erforschung der Balkenmechanik spielen Schubdiagramme eine entscheidende Rolle für das Verständnis der Verteilung der Schubkräfte über die Länge eines Trägers. Erwägen...

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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 kN and the vertical reaction at B is 18 kN. These values become the starting point for building the shear diagram.

To form the shear diagram, the method of sections is used. A point is chosen at an arbitrary distance from A in the region AP, and a free-body diagram of that section is drawn. From equilibrium, the shear force in that section is V1 = 24 kN.

The same process is repeated in the region PQ. An arbitrary point is selected, the section is isolated, and the equilibrium equation is applied to find V2. A third section is then taken in the region QB. Its free-body diagram gives V3, which stays constant until the end of the beam and then goes to zero so the beam remains in equilibrium.

Beam Shear Force Diagram

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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...

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internal loadings in structural members: problem solving

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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...

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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 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

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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

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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...

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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...

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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...

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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.

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 build a beam shear force diagram using free-body diagrams, reaction forces, and the method of sections for a supported beam.

Beam Shear Force Diagram | 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.

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Beam Shear Force Diagram

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