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

Il diagramma di taglio è una rappresentazione grafica della distribuzione delle forze di taglio lungo la lunghezza della trave.
Si consideri una trave AB supportata a due estremità e soggetta a carichi perpendicolari. Costruisci il suo diagramma di taglio.
Disegna il diagramma di corpo libero della trave. Utilizzando le equazioni di equilibrio di forza e momento, è possibile calcolare le forze di reazione su ciascun supporto.
Applicare il metodo della sezione alla trave.
Quindi, considera una distanza arbitraria dal punto A all'interno della regione AP. Disegna un diagramma di corpo libero della sezione. Nella condizione di equilibrio, la forza di taglio nella sezione è uguale alla forza di reazione al vincolo esterno.
Allo stesso modo, si consideri un punto arbitrario all'interno della regione PQ. Disegnando il diagramma di corpo libero e utilizzando l'equazione di equilibrio, è possibile determinare il taglio nella sezione.
Infine, il punto arbitrario è considerato all'interno della sezione QB. Disegnando il diagramma di corpo libero e richiamando l'equazione di equilibrio, è possibile determinare il taglio nella sezione, che rimane costante fino alla fine della trave e alla fine va a zero per mantenere l'equilibrio.

<ol>
	<li>Hibbeler, R.C. (2016). Ingegneria Meccanica \u2012 Statica e Dinamica. Hoboken, New Jersey: Pearson Prentice Hall. pagine 361.</li>
	<li>Birra, F.P.; Johnston, E.R.; Mazurek, D.F; Cromwell, P.J. e Self, B.P.(2019). Meccanica vettoriale per ingegneri \u2012 Statica e dinamica. New York: McGraw-Hill. Pagine 381.</li>
</ol>

diagramma di taglio

Nello studio della meccanica delle travi, i diagrammi di taglio svolgono un ruolo cruciale per comprendere la distribuzione delle forze di taglio lungo la lunghezza di una trave. Si consideri una trave AB supportata su entrambi i lati e soggetta a carichi perpendicolari.

Innanzitutto, si disegna un diagramma di corpo libero della trave, che rappresenta tutte le forze esterne e le reazioni interne che agiscono su di essa. È possibile calcolare le forze di reazione su ogni supporto utilizzando le equazioni di equilibrio delle forze e dei momenti. La componente verticale delle forze di reazione nei punti A e B, ottenuta per la trave data, è rispettivamente di 24 kN e 18 kN.

<img alt="Figure 1" src="/files/ftp_upload/14301/14301_PT_Figure_1v2.svg" style="text-align: center; height: 300px;" />

Un diagramma di taglio è una rappresentazione grafica che illustra la distribuzione delle forze di taglio lungo la lunghezza della trave. Per creare questo diagramma, si applica il metodo delle sezioni alla trave. Successivamente, si considera una distanza arbitraria dal punto A all'interno della regione AP. Si disegna un diagramma di corpo libero di questa sezione per analizzare le forze che agiscono su di essa. Nelle condizioni di equilibrio, la forza di taglio nella sezione è uguale alla forza di reazione sul supporto, che è V1=24 kN.

Allo stesso modo, si considera un punto arbitrario all'interno della regione PQ. Disegnando un diagramma di corpo libero di questa sezione e utilizzando l'equazione di equilibrio, si può determinare la forza di taglio, V2.

<img alt="Equation 1" src="/files/ftp_upload/14301/14301_Equation_1v2.svg" style="text-align: center; height: 13px;" />

Infine, si considera un punto arbitrario all'interno della sezione QB. Si disegna un diagramma di corpo libero per questa sezione e si richiama l'equazione di equilibrio per determinare la forza di taglio, V3, nella sezione.

<img alt="Equation 2" src="/files/ftp_upload/14301/14301_Equation_2v2.svg" style="text-align: center; height: 13px;" />

Questa forza di taglio rimane costante fino alla fine della trave, andando infine a zero per mantenere l'equilibrio.

Diagramma di taglio

Nello studio della meccanica delle travi, i diagrammi di taglio svolgono un ruolo cruciale nella comprensione della distribuzione delle forze di taglio lungo la lunghezza di una trave. Considerare...

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Mechanical Engineering

Ingegneria Meccanica

Unit 1

Unità 1

Internal Forces

Forze interne

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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 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

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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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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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cable: problem solving

Cable Tension Under Uniform Loading

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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

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Beam Shear Force Diagram

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