Name: beam load analysis with moment diagrams
Uploaded: 2025-05-22T09:06:03.000Z
Duration: 1 min 30 s
Channel: JoVE

Considérons une poutre AC en porte-à-faux sous une charge répartie, soutenue par deux joints. Construisez son diagramme de moment de flexion.
Dessinez le schéma du corps libre du faisceau et, à l’aide des équations d’équilibre, les forces de réaction à chaque support peuvent être calculées.
Appliquez la méthode de section à la poutre.
Ensuite, considérons une distance arbitraire x dans la région AB. La force résultante agit au milieu de la section. En utilisant l’équation d’équilibre sur le schéma du corps libre et en substituant les valeurs, on obtient l’équation du moment.
De même, considérons un point arbitraire dans la région BC. En dessinant le diagramme du corps libre et en utilisant l’équation d’équilibre, l’équation du moment pour la section BC est déterminée.
En remplaçant les valeurs de position dans les équations de moment, les valeurs de moment de flexion sont calculées.
Le diagramme du moment de flexion montre la représentation graphique des valeurs du moment de flexion le long de la longueur de la poutre.
En rappelant l’équation du moment et en appliquant la méthode de dérivation, on obtient les maxima locaux de chaque section.
Le diagramme du moment de flexion est obtenu en joignant ces points par des courbes paraboliques.

<ol>
	<li>Hibbeler, R.C. (2016). Génie mécanique \u2012 Statique et dynamique. Hoboken, New Jersey : Pearson Prentice Hall. p. 362.</li>
</ol>

diagramme des moments fléchissants

Bending Moment Diagram

Un diagramme des moments fléchissants est une représentation graphique des moments fléchissants subis par une poutre sous charge le long de sa longueur. C'est un outil essentiel pour les ingénieurs et les concepteurs afin d'analyser les structures et s'assurer qu'elles peuvent résister aux forces appliquées. Les étapes pour créer le diagramme des moments fléchissants pour une poutre sont énumérées ci-dessous. Déterminer les forces réactives et les moments de couple : Calculer toutes les forces réactives et les moments de couple agissant sur la poutre. Dans certains cas, lorsque la poutre est inclinée à un angle, ces forces sont résolues en leurs composantes agissant perpendiculairement et parallèlement à l'axe de la poutre. Sectionner la poutre et dessiner le diagramme du corps libre : Considérer une distance arbitraire à partir de l'extrémité gauche de la poutre. Cette distance arbitraire peut être étendue dans différentes régions le long de la longueur de la poutre. À chaque distance supposée, sectionner la poutre et créer un diagramme du corps libre d'un des segments. S'assurer que le moment fléchissant (M) est indiqué agissant dans leur sens positif, selon la convention de signe établie. Calculer le moment fléchissant : Appliquer les équations d'équilibre des moments et obtenir le moment fléchissant (M) par rapport à l'extrémité sectionnée du segment. Tracer le diagramme des moments : Créer le diagramme des moments (M en fonction de x) à partir du moment fléchissant obtenu le long de la poutre. Si les valeurs calculées des fonctions décrivant M sont positives, tracer les valeurs au-dessus de l'axe des x. Inversement, si les valeurs sont négatives, les tracer en dessous de l'axe des x. En suivant cette procédure, vous pouvez construire des diagrammes précis de cisaillement et de moments fléchissants pour n'importe quelle poutre. Ces diagrammes sont cruciaux pour concevoir des éléments structurels, tels que des bras de rayonnage, qui résistent aux forces et aux moments induits par les charges appliquées.

Diagramme des moments fléchissants

Un diagramme de moment de flexion est une représentation graphique des moments de flexion subis par une poutre sous charge sur toute la longueur de la poutre. C’est un ...

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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 act perpendicular and parallel to the beam axis. That gives the values needed for the next step.

Next, section the beam at an arbitrary distance from the left end and draw a free-body diagram for one part of the beam. The chosen distance can be moved to different regions along the beam length. On the cut section, show the bending moment, M, in the positive sense according to the sign convention.

Then apply the moment equilibrium equations to calculate the bending moment about the sectioned end. Use the results to plot the moment diagram, or M versus x, along the beam length. Positive values are drawn above the x-axis, and negative values are drawn below it. Following this method gives accurate shear and bending moment diagrams for beam design.

Beam Load Analysis with Moment Diagrams

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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...

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key terms and concepts

Learn how to analyze beam loads by finding reaction forces, sectioning the beam, solving for bending moment, and plotting the moment diagram.

Beam Load Analysis with Moment Diagrams | JoVE K12

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Beam Load Analysis with Moment Diagrams

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