Name: shearing stress pattern in a narrow beam
Uploaded: 2024-05-23T12:59:49.000Z
Duration: 1 min 11 s
Channel: JoVE

Une section élémentaire d’une poutre est considérée pour analyser la distribution des contraintes. L’amplitude de la force de cisaillement exercée sur la face horizontale de l’élément est obtenue à partir de l’expression de cisaillement horizontal.
La contrainte de cisaillement moyenne sur cette face est déterminée en divisant le cisaillement horizontal par la surface de la face.
Les contraintes de cisaillement sur les plans transversal et horizontal de la section de la poutre sont égales, représentant la contrainte moyenne le long de la ligne sur la partie supérieure de la poutre. Les contraintes de cisaillement sont nulles sur les faces supérieure et inférieure car aucune force n’est exercée.
Dans une poutre rectangulaire étroite, la contrainte de cisaillement sur la largeur de la section de la poutre varie moins de 0,8 % de la contrainte de cisaillement moyenne car la largeur est inférieure à un quart de sa profondeur.
Ainsi, l’équation de contrainte de cisaillement moyenne est utilisée pour déterminer la contrainte de cisaillement en tout point de sa section transversale.
Dans la section transversale de la poutre rectangulaire, les contraintes de cisaillement sont réparties de manière parabolique, avec une contrainte nulle en haut et en bas.

répartition des contraintes dans une poutre rectangulaire étroite

Distribution of Stresses in a Narrow Rectangular Beam

Lors de l'étude de la répartition des contraintes des poutres, l'examen d'une section élémentaire est essentiel. Pour déterminer la contrainte de cisaillement moyenne sur cette face, le cisaillement calculé est divisé par la surface. Il est important de noter que les contraintes de cisaillement sur les plans transversal et horizontal de la poutre se reflètent, indiquant une répartition cohérente des contraintes le long de la région supérieure de la poutre. Notamment, les contraintes de cisaillement sont absentes au niveau des surfaces supérieure et inférieure de la poutre en raison de l'absence de forces appliquées dans ces zones.

Pour les poutres à section rectangulaire étroite, la variation de la contrainte de cisaillement sur la largeur est minime, inférieure à 0,8 % de la contrainte moyenne. Cette variation mineure est attribuée au fait que la largeur de la poutre est nettement inférieure à sa profondeur, ce qui fait de l'équation de contrainte de cisaillement moyenne une méthode fiable pour évaluer la contrainte en tout point de la section-transversale de la poutre. Dans la section transversale de la poutre rectangulaire, les contraintes de cisaillement sont réparties de manière parabolique. Cette distribution présente une contrainte nulle sur les bords supérieur et inférieur de la poutre, avec une augmentation de la contrainte vers le centre. Ce profil de contrainte parabolique est essentiel pour comprendre comment les poutres gèrent les contraintes, garantissant ainsi leur intégrité structurelle et leur capacité à supporter des charges sans compromettre la stabilité.

Répartition des contraintes dans une poutre rectangulaire étroite

Une section élémentaire d’une poutre est considérée pour analyser la distribution des contraintes. L’amplitude de la force de cisaillement exercée sur l’horizontale ...

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

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

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 bottom surfaces, because no applied forces act there.

For a narrow rectangular cross-section, the change in shearing stress across the width is very small. It is less than 0.8% of the average stress. Because the beam is much wider in depth than in width, the average shearing stress equation works well at any point in the cross-section.

Across the rectangular beam&amp;#39;s transverse section, the shearing stress follows a parabolic shape. A parabolic distribution curves upward from the edges to the center. Stress is zero at the top and bottom edges and rises toward the middle. This pattern helps explain how beams carry load while staying structurally stable.

Shearing Stress Pattern in a Narrow Beam

shear on the horizontal face of a beam element

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

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...

distribution of stresses in a narrow rectangular 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

Explore how shearing stress changes across a narrow rectangular beam, including zero stress at the edges and a parabolic distribution toward the center.

Shearing Stress Pattern in a Narrow Beam | 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.

Shearing Stress Pattern in a Narrow Beam

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