Name: beam shear flow from bending moments
Uploaded: 2024-05-23T12:59:49.000Z
Duration: 1 min 16 s
Channel: JoVE

Le petit élément d'une poutre prismatique sous l'effet des forces de cisaillement verticales et horizontales, ainsi que des forces normales, est pris en compte pour l'analyse du cisaillement sur une face horizontale.
À l’aide de l’équation d’équilibre, l’équilibre des forces agissant sur cet élément est examiné pour déterminer la force de cisaillement horizontale. Cette force est alors assimilée aux moments de flexion et au premier moment de la section transversale.
L’analyse de l’élément inférieur ou de l’élément supérieur donne le même résultat, car les forces de cisaillement exercées l’une sur l’autre sont égales en amplitude mais opposées en direction.
On observe également que le premier moment de la partie au-dessous d'une certaine ligne dans le faisceau est égal en amplitude mais de signe opposé au premier moment de la partie au-dessus.
Le premier moment atteint son maximum lorsque la distance par rapport à l’axe neutre est égale à zéro, car les éléments au-dessus de l’axe neutre contribuent positivement à la partie intégration de l’équation des forces de cisaillement horizontales, tandis que ceux en dessous contribuent négativement.
Lorsque le cisaillement horizontal est divisé par la longueur de l’élément, l’écoulement de cisaillement est obtenu.

cisaillement sur la face horizontale d'un élément de poutre

Shear on the Horizontal Face of a Beam Element

Pour comprendre le cisaillement sur le côté plat d'un élément de poutre prismatique, considérez les forces de cisaillement verticales et horizontales, ainsi que les forces normales, agissant sur l'élément. Les sections supérieure (U) et inférieure (L) de l'élément, divisées par l'axe neutre de la poutre, sont examinées. L'équilibre de ces forces est déterminé en appliquant l'équation d'équilibre, qui permet d'identifier la force de cisaillement horizontale. Cette force est directement liée aux moments de flexion et au premier moment d'inertie de la section. L'analyse donne des résultats cohérents, que ce soit en examinant la partie supérieure ou inférieure de la poutre, car les forces de cisaillement sont égales en ampleur mais opposées en direction.

Il est important de noter que le premier moment de la section de la poutre en dessous d'une ligne spécifique est le même que le premier moment de la section au-dessus, à la fois en amplitude et en direction. Ce premier moment atteint son maximum au niveau de l'axe neutre de la poutre. Ici, les sections au-dessus de l'axe neutre contribuent positivement au calcul des forces de cisaillement horizontales, tandis que celles en dessous contribuent négativement. Le calcul de l’écoulement de cisaillement consiste à diviser le cisaillement horizontal par la longueur de l'élément de poutre. Comprendre ce processus est essentiel pour obtenir une vue complète de la manière dont le cisaillement fonctionne sur un plan horizontal au sein de la poutre, ce qui est crucial pour évaluer l'intégrité structurelle et les exigences de conception des éléments de poutre dans les projets d'ingénierie.

Cisaillement sur la face horizontale d'un élément de poutre

Le petit élément d'une poutre prismatique sous l'effet des forces de cisaillement verticales et horizontales, ainsi que des forces normales, est pris en compte pour l'analyse du cisaillement sur ...

shear-on-the-horizontal-face-of-a-beam-element

Education

Enseignement

JoVE Core

Mechanical Engineering

Génie mécanique

Unit 1

Unité 1

Shearing Stresses in Beams and Thin-Walled Members

Contraintes de cisaillement dans les poutres et les éléments à parois minces

shearing-stresses-in-beams-and-thin-walled-members

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

beam shear flow from bending moments

Beam shear flow comes from the horizontal shear that acts on a prismatic beam element. The element is also acted on by vertical shear forces and normal forces. To study this behavior, the beam is divided into upper and lower sections by the neutral axis.

The force balance on the small element is written with an equilibrium equation. That step reveals the horizontal shearing force. This force is tied to the bending moments and to the cross-section’s first moment of inertia.

The same result is obtained whether the upper section or the lower section is used. The shear forces are equal in magnitude but point in opposite directions. The first moment of the area below a chosen line matches the first moment of the area above it in magnitude and direction.

This first moment is largest at the neutral axis. Sections above the neutral axis add positively to the horizontal shear calculation. Sections below the neutral axis add negatively.

Shear flow is found by dividing the horizontal shear by the length of the beam element. This makes it easier to describe how shear acts on a horizontal plane inside the beam. Understanding this relationship helps with structural integrity checks and beam design in engineering projects.

Beam Shear Flow from Bending Moments

shear on the horizontal face of a beam element

Beam shear flow comes from the horizontal shear that acts on a prismatic beam element. The element is also acted on by vertical shear forces and normal forces. To study this behavior, the beam is divided into upper and lower sections by the neutral axis. The force balance on the small element is written with an equilibrium equation. That step reveals the horizontal shearing force. This force is tied to the bending moments and to the cross-section’s first moment of inertia. The same result is...

distribution of stresses in a narrow rectangular beam

distribution-of-stresses-in-a-narrow-rectangular-beam

Shearing Stress Pattern in a Narrow Beam

Shearing stress in a narrow rectangular beam is found by studying a small elemental section of the beam. The average shearing stress on that face is calculated by dividing the shear by the surface area. This gives a simple way to describe how the load is spread through the beam. The shearing stresses on the beam&amp;#39;s transverse and horizontal planes match each other. That means the stress pattern is consistent in the upper region of the beam. Shearing stress is also absent at the top and...

shearing stresses in a beam: problem solving

shearing-stresses-in-a-beam-problem-solving

Beam Shear Stress Analysis and Safety Check

Beam shear stress analysis shows how loads create internal stress in a cantilever beam with a rectangular cross-section. The beam in this problem carries both a distributed load and a point load. The goal is to find the shearing stress at key points and check whether the beam stays within a safe limit. The first step is to identify all loads acting on the beam. Next, the reactions at the fixed end are found using equilibrium equations. The vertical reaction combines the distributed load and...

plastic deformations

Cantilever Beam Yield and Failure

Cantilever beams show how a material bends, yields, and can eventually fail under load. A cantilever beam is fixed firmly at one end and loaded at the other end. When the load stays within the elastic range, the beam returns to its original shape after the load is removed. That reversible behavior is called elasticity. If the load goes beyond the elastic limit, the beam begins plastic deformation. Plastic deformation means the shape change is permanent. In a cantilever beam, this change starts...

unsymmetric loading of thin-walled members

unsymmetric-loading-of-thin-walled-members

Shear Center in Thin-Walled Members

Thin-walled members with non-symmetrical cross-sections are widely used in engineering structures because they save material while still providing strength. Their shape helps with structural integrity, but it also makes load analysis more complex. When these members are loaded in an unsymmetrical way, the stress is not spread evenly. Unsymmetrical loading can make a member bend and twist at the same time. That combined action can lead to deformation or even structural failure. Engineers must...

unsymmetric loading of thin-walled members: problem solving

unsymmetric-loading-of-thin-walled-members-problem-solving

Finding the Shear Center of a Channel Section

Finding the shear center of a channel section starts with the member’s shear force and moments of inertia. A shear center is the point where a load must act so the section bends without twisting. For a channel with uniform thickness, height, and width, the distance to this point can be calculated from the section geometry. The first step is to compute the shear flow at a set distance from the end of the flange. Shear flow is the force per unit length along the wall of the section. It is found...

key terms and concepts

Learn how horizontal shear, bending moments, and first moment of inertia work together in a prismatic beam element, and how shear flow is calculated.

Beam Shear Flow from Bending Moments | 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.

Beam Shear Flow from Bending Moments

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