Name: beam forces: tension, shear, and bending
Uploaded: 2025-05-22T09:06:03.000Z
Duration: 1 min 30 s
Channel: JoVE

Quando una trave è soggetta a un carico, subisce forze interne che possono essere classificate come momenti normali, di taglio e flettenti.
Le forze interne possono essere determinate utilizzando il metodo delle sezioni. Una speciale convenzione dei segni viene applicata quando si verificano in coppia e la loro direzione dipende da quale lato della sezione deve essere analizzato.
Si presume che la forza normale sia positiva se crea tensione, mentre è considerata negativa se genera compressione nell'oggetto.
Supponiamo che le forze che agiscono tangenzialmente alla sezione trasversale siano dirette verso il basso e verso l'alto rispettivamente sui lati sinistro e destro della sezione. In tal caso, la forza di taglio è considerata positiva, risultando in una rotazione in senso orario.
Allo stesso modo, se la direzione delle forze su ciascun lato è invertita, si produce un taglio negativo, con conseguente rotazione in senso antiorario.
Quando una forza esterna agisce sulla trave, subisce un momento flettente, formando una curvatura concava verso l'alto o verso il basso. Il momento flettente è positivo per la curvatura verso l'alto e negativo per la curvatura verso il basso.

<ol>
	<li>Ferdinand Beer, E. Johnston, David Mazurek, Phillip Cornwell e Brian Self (2019). Meccanica vettoriale per ingegneri: statica e dinamicas. McGraw Hill. Pagine 380-391.</li>
	<li>Russell C. Hibbeler. (2016). Ingegneria meccanica: statica e dinamica. Pearson. pagine 343-345.</li>
</ol>

convenzione di segno

Quando si analizza una trave soggetta a varie sollecitazioni, è fondamentale comprendere le forze interne e i momenti generati all'interno della struttura. Queste forze interne possono essere ampiamente classificate in forze normali, forze taglianti e momenti flettenti. Per determinare queste forze e momenti, utilizziamo il metodo delle sezioni e applichiamo una specifica convenzione di segno basata sulla loro direzione e sul lato della sezione che viene analizzato.

La forza normale agisce perpendicolarmente alla sezione trasversale della trave e può causare tensione o compressione all'interno dell'oggetto. Quando la forza normale crea tensione, si assume che sia positiva, mentre quando genera compressione, viene considerata negativa.

La forza tagliante si riferisce alle forze che agiscono tangenzialmente alla sezione trasversale della trave. Queste forze si verificano tipicamente a coppie, con una forza che agisce sul lato sinistro della sezione e l'altra sul lato destro. Se la forza sul lato sinistro è diretta verso il basso e la forza sul lato destro è diretta verso l'alto, la forza tagliante è considerata positiva, con una rotazione in senso orario. Al contrario, se la direzione delle forze su ciascun lato viene invertita, si genera una forza tagliante negativa, con una rotazione in senso antiorario.

Il momento flettente è l'effetto rotazionale causato da una forza esterna che agisce sulla trave. Quando viene sottoposta a tale forza, la trave subisce una curvatura, che può essere o verso l'alto (concava) o verso il basso (convessa). La convenzione di segno per i momenti flettenti stabilisce che un momento flettente positivo corrisponda ad una curvatura verso l'alto (concava), mentre un momento flettente negativo corrisponda ad una curvatura verso il basso (convessa). Questa convenzione svolge un ruolo vitale nella comprensione del modello di deformazione della trave e nella progettazione di elementi strutturali adeguati per resistere alla flessione.

In sintesi, le convenzioni di segno per la forza normale, la forza tagliante e il momento flettente sono strumenti essenziali nella analisi strutturale. Aiutano gli ingegneri e i progettisti a comprendere il comportamento delle strutture sotto varie sollecitazioni, a prevedere possibili modalità di rottura e a progettare elementi strutturali robusti ed efficienti.

Convenzione di segno

Quando si analizza una trave sottoposta a vari carichi, è fondamentale comprendere le forze interne e i momenti generati all'interno della struttura. Questi...

Education

Didattica

JoVE Core

Mechanical Engineering

Ingegneria Meccanica

Unit 1

Unità 1

Internal Forces

Forze interne

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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 easier to read and compare force results during structural analysis.

Shear force acts tangentially along the cross-section of the beam. It often appears as a pair of forces, with one side of the cut carrying the left-side force and the other side carrying the right-side force. A downward force on the left side and an upward force on the right side represent positive shear and a clockwise rotation. If the directions are reversed, the shear force is negative and the rotation is counterclockwise.

Bending moment describes the turning effect created by an external force on a beam. It changes the beam’s shape into either an upward, concave curve or a downward, convex curve. A positive bending moment gives upward, concave curvature. A negative bending moment gives downward, convex curvature. These conventions help predict how beams deform under load and support better structural design.

Beam Forces: Tension, Shear, and Bending

sign convention

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...

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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.

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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

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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 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...

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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...

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...

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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.

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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 normal force, shear force, and bending moment use sign conventions in beam analysis, and how tension, compression, and curvature are labeled.

Beam Forces: Tension, Shear, and Bending | 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

Beam Forces: Tension, Shear, and Bending

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