Name: finding the resultant of distributed loads
Uploaded: 2023-09-22T11:49:32.000Z
Duration: 1 min 13 s
Channel: JoVE

Dans les applications d’ingénierie, il est important de tenir compte de la répartition des charges le long de la ligne.
La force nette appliquée en raison de la charge répartie est représentée par un vecteur unique, appelé force résultante.
Considérons une plaque plate de forme arbitraire soumise à une charge uniforme.
La force agissant sur une aire infinitésimale de la plaque a une amplitude équivalente à l’élément de volume différentiel.
La force résultante agissant sur la plaque est calculée en additionnant toutes les forces différentielles agissant sur toute la surface de la plaque.
L'intégration sur l'aire de la plaque nous donne une expression pour calculer l'intensité de la force résultante, qui est également égale au volume total sous le diagramme de charge répartie.
L’emplacement de la force résultante est déterminé en comparant les moments de la force résultante avec ceux de toutes les forces différentielles autour de leurs axes respectifs.
Les expressions obtenues impliquent que la ligne d'action de la force passe par le centre géométrique ou le centroïde du volume sous le diagramme de charge distribuée.

<ol>
	<li>Hibbeler, R.C. (2016). Mécanique du génie : Statique. Quatorzième édition, New Jersey : Pearson. Section 9.4, p. 511.</li>
	<li>Beer, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. et Self, B.P. (2016). Mécanique vectorielle pour les ingénieurs. Onzième édition, New York : McGraw-Hill Education. Section 5.3, p. 262.</li>
</ol>

résultante d'une charge distribuée générale

Resultant of a General Distributed Loading

Lors de la conception de structures exposées à des charges non uniformes, il est crucial de prendre en compte la force résultante et son emplacement. Cette force résultante est un seul vecteur représentant la force nette appliquée en raison de la charge distribuée. Des exemples tels que la distribution de charge due au vent et la distribution de charge sur un pont illustrent comment ce concept est utilisé pour analyser et concevoir des structures sûres et fiables dans des conditions de charge variables. La plupart des structures, comme les bâtiments résidentiels, les ponts et les tours, sont conçues pour résister à des charges de vent non uniformes, qui varient avec la vitesse et la direction du vent. De même, les ponts sont conçus pour supporter le poids des véhicules qui les traversent. Cependant, la répartition du poids des véhicules n'est pas uniforme et certaines parties du pont peuvent subir plus de contraintes et de déformations que d'autres. Il est nécessaire de calculer la force résultante agissant sur les bâtiments ou les ponts, ce qui constitue un problème de distribution de charge non uniforme. Pour déterminer cette force, il faut additionner et intégrer la magnitude de chaque force différentielle agissant sur des zones infinitésimales sur la surface portante. La magnitude de cette force résultante est égale au volume total sous le diagramme de chargement distribué. L'emplacement de cette force résultante peut être déterminé en comparant ses moments avec les moments de toutes les forces différentielles par rapport à leurs axes respectifs. Cela implique que la ligne d'action de cette force passera par le centre géométrique ou le centre de gravité du volume considéré. Savoir où et combien de forces sont appliquées sur une structure permet aux ingénieurs de garantir une résistance et une rigidité suffisantes pour que la structure soit adaptée à l'usage prévu. Ces valeurs peuvent également changer en fonction des conditions de charge variables, il est donc essentiel de prendre en compte ces changements potentiels afin de concevoir une structure sûre et sécurisée.

Résultante d'une charge distribuée générale

Lors de la conception de structures exposées à des charges non uniformes, il est crucial de prendre en compte la force résultante et son emplacement. Cette force résultante est une seule ...

resultant-of-a-general-distributed-loading

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finding the resultant of distributed loads

Distributed loads create a force that is spread over a surface instead of acting at one point. To analyze this kind of loading, engineers use a single resultant force. That force represents the net effect of the entire load.

This idea is important in structures that face non-uniform loads. Wind can push on buildings and towers with changing speed and direction, so the load is not evenly spread. Bridges also experience non-uniform loading from vehicles, and some parts of the bridge can feel more stress and strain than others.

To find the resultant force, the small forces acting on tiny areas are added together with integration over the load-bearing surface. The size of the resultant force equals the total area under the distributed-loading diagram. Its location is found by comparing moments, which means the turning effects of the force about an axis.

The line of action of the resultant passes through the geometric center, or centroid, of the volume under the load diagram. Knowing both the size and location of the force helps engineers judge whether a structure has enough strength and rigidity. Because loading can change, these calculations help support safe and reliable design for buildings, bridges, and other structures.

Finding the Resultant of Distributed Loads

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resultant of a general distributed loading

Distributed loads create a force that is spread over a surface instead of acting at one point. To analyze this kind of loading, engineers use a single resultant force. That force represents the net effect of the entire load. This idea is important in structures that face non-uniform loads. Wind can push on buildings and towers with changing speed and direction, so the load is not evenly spread. Bridges also experience non-uniform loading from vehicles, and some parts of the bridge can feel...

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key terms and concepts

Learn how engineers combine non-uniform loads into one resultant force, find its location with moments, and apply the idea to bridges and buildings.

Finding the Resultant of Distributed Loads | JoVE K12

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Finding the Resultant of Distributed Loads

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