Name: beam stress patterns under transverse load
Uploaded: 2024-05-23T12:59:58.000Z
Duration: 1 min 11 s
Channel: JoVE

Une poutre prismatique exposée à des charges transversales arbitraires entraîne des moments de cisaillement et de flexion.
La contrainte sur un élément de surface de la poutre est une contrainte normale, tandis que sur une surface neutre, il s’agit d’une contrainte de cisaillement.
La contrainte normale maximale à l’intérieur de la section transversale peut dépasser la contrainte normale à la surface de la poutre.
La distribution principale des contraintes dans une poutre rectangulaire étroite en porte-à-faux sous une charge concentrée est étudiée pour analyser la contrainte normale maximale.
Les résultats du calcul indiquent que la contrainte normale maximale ne dépasse pas la contrainte normale dans l'une ou l'autre des deux sections de poutre.
Si c'est le cas, c'est généralement dans les zones proches de la charge où la contrainte normale est inférieure à la contrainte de cisaillement.
L’équation de contrainte normale maximale calculée pour les sections rectangulaires peut être appliquée à de nombreuses poutres de section non rectangulaire.
Cependant, lorsque de grandes contraintes de cisaillement coexistent avec des contraintes normales substantielles près de la surface de la poutre, la contrainte normale maximale peut dépasser la contrainte normale.

contraintes principales dans une poutre

Principal Stresses in a Beam

Dans les poutres prismatiques soumises à des charges transversales arbitraires, il est essentiel d'analyser l'interaction entre les forces de cisaillement et les moments de flexion afin de comprendre la répartition des contraintes et de garantir l'intégrité structurelle. La contrainte normale ou de flexion la plus élevée se produit au niveau des fibres externes de la poutre, diminuant linéairement jusqu'à zéro sur l'axe neutre. En revanche, la contrainte de cisaillement culmine au niveau de l’axe neutre et diminue vers les surfaces extérieures.

L'analyse des contraintes principales est primordiale, en particulier dans le cas de poutres en porte-à-faux rectangulaires étroites soumises à des charges concentrées. Les contraintes principales, c'est-à-dire les contraintes normales maximales et minimales en tout point, se produisent sur des plans exempts de contraintes de cisaillement. Ces contraintes sont essentielles pour identifier les points de défaillance potentiels. Les études informatiques montrent généralement que la contrainte normale maximale au sein de ces poutres ne dépasse généralement pas les contraintes de surface, sauf à proximité des points d'application de la charge, où la contrainte de cisaillement peut dépasser la contrainte normale.

La méthode de calcul de la contrainte normale maximale est généralement efficace pour les sections rectangulaires et peut être adaptée aux formes non rectangulaires grâce à des calculs ou une modélisation informatique plus avancés. Il est important de considérer les situations dans lesquelles des contraintes de cisaillement importantes coexistent avec des contraintes normales importantes près de la surface de la poutre. Ces conditions peuvent conduire à des modes de défaillance inattendus, tels que des fissures induites par le cisaillement, mettant en évidence la complexité de la conception de structures réelles.

Contraintes principales dans une poutre

Une poutre prismatique exposée à des charges transversales arbitraires entraîne des moments de cisaillement et de flexion.
La contrainte sur un élément de surface de la poutre est normale ...

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JoVE Core

Mechanical Engineering

Unit 1

Principal Stresses under a Given Loading

KEY TERMS AND CONCEPTS

beam stress patterns under transverse load

Beam stress patterns under transverse load depend on both bending and shear. In a prismatic beam, these two effects work together to shape how stress is distributed across the cross-section and to help engineers judge structural integrity.

The largest normal, or bending, stress appears at the outer fibers of the beam. It drops in a straight line to zero at the neutral axis, which is the line in the cross-section where bending stress changes direction. Shear stress behaves differently. It is highest at the neutral axis and fades toward the outer surfaces.

Principal stresses are also important, especially in narrow rectangular cantilever beams with a concentrated load. Principal stresses are the maximum and minimum normal stresses at a point. They act on planes where shear stress is zero, which makes them useful for locating possible failure points.

Computational studies show that the maximum normal stress inside these beams usually does not exceed the surface stress. A common exception is near the load application point, where shear stress can become larger than normal stress. For rectangular cross-sections, the usual maximum-normal-stress method works well, while non-rectangular shapes may need more advanced calculations or computational models.

The video also highlights cases where strong shear stress and significant normal stress occur near the beam surface at the same time. These conditions can cause unexpected failure modes, including shear-induced cracking. That is why real-world beam design must consider both bending and shear, not just one stress type alone.

Beam Stress Patterns Under Transverse Load

beam-stress-patterns-under-transverse-load

principal stresses in a beam

Beam stress patterns under transverse load depend on both bending and shear. In a prismatic beam, these two effects work together to shape how stress is distributed across the cross-section and to help engineers judge structural integrity. The largest normal, or bending, stress appears at the outer fibers of the beam. It drops in a straight line to zero at the neutral axis, which is the line in the cross-section where bending stress changes direction. Shear stress behaves differently. It is...

design of transmission shafts - stress analysis

design-of-transmission-shafts-stress-analysis

Transmission Shaft Bending and Torsion

Transmission shafts carry power while facing both bending and torsion. In gear systems, these loads create force-couple systems at the center of the shaft cross-section. That means the shaft must be checked for transverse loading and twisting at the same time. The transverse loads create shearing stress, but it is usually smaller than the stress from torque and is often ignored. Even so, the normal stress from these loads can add to the maximum shearing stress in the shaft. To find that normal...

transmission shafts: problem solving

Sizing a Solid Power Transmission Shaft

A solid power transmission shaft must be sized so it can carry both torque and bending loads. In this problem, the shaft connects a motor to a machine tool through a gear, so the design must resist the stress created by rotation and force transfer. The first step is to calculate the torque on the gear. This uses the power carried by the shaft and its rotational speed. The tangential force on the gear is then found from the torque and the gear radius. Next, bending moment diagrams are used for...

stresses under combined loadings

Principal and Shear Stresses in a Bent Tube

A bent tube with a circular cross-section can experience normal stress, shear stress, principal stress, and maximum shearing stress when several loads act on it. To analyze these stresses, the tube is sliced at key points and the internal forces at each section are examined at the centroid. This helps show how the material responds under combined loading. Normal stress comes from axial forces and bending moments. It can be tensile or compressive, and it changes across the cross-section from...

key terms and concepts

Explore how bending stress, shear stress, and principal stresses act in a beam under transverse loading, including neutral axis behavior and failure risks.

Beam Stress Patterns Under Transverse Load | 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 Stress Patterns Under Transverse Load

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