Name: equivalent resultant loads on beams
Uploaded: 2023-09-22T11:49:23.000Z
Duration: 1 min 21 s
Channel: JoVE

Considérons un OB à poutre conique fixé à une extrémité et soumis à une charge répartie.
Déterminez la force résultante équivalente de la charge variable et localisez sa position sur la poutre.
Tout d’abord, divisez la charge distribuée en deux régions triangulaires.
Ensuite, l’intensité de la charge résultante équivalente des régions triangulaires gauche et droite est égale à l’aire de chaque triangle.
Chaque charge résultante agit au niveau des centroïdes, situés à un tiers de la longueur de la base à partir du côté vertical AD du triangle.
La charge résultante équivalente peut être déterminée en additionnant la charge résultante individuelle de chaque région triangulaire.
Le moment autour du point O peut être déterminé en additionnant le moment individuel agissant en raison de chaque charge résultante.
Rappelez-vous le principe du moment, qui stipule que le moment de la charge résultante équivalente autour du point O est égal au produit de la charge résultante équivalente et de la distance du point O.
En substituant les valeurs de l’équation, l’emplacement de la charge résultante équivalente peut être déterminé.

<ol>
	<li>Hibbeler, R.C. (2016). Génie mécanique \u2012 Statique et dynamique. Hoboken, New Jersey : Pearson Prentice Hall, p. 194-195</li>
</ol>

charges distribuées : résolution de problème

Les poutres sont des éléments structurels couramment utilisés dans les applications d'ingénierie nécessitant différentes capacités de charge. La première étape de l'analyse d'une poutre sous une charge distribuée consiste à simplifier le problème en divisant la charge en régions plus petites, ce qui permet de considérer chaque région séparément et de calculer la magnitude de la charge résultante équivalente agissant sur chaque partie de la poutre. La magnitude de la charge résultante équivalente pour chaque région peut être déterminée en calculant la surface des régions respectives, ce qui représente la force exercée par la charge dans chaque région. Ensuite, localisez la position de chaque charge résultante sur la poutre. Cela peut être fait en trouvant les centres de gravité des régions, qui sont les points où la masse des régions peut être considérée comme concentrée. Les charges résultantes individuelles agissent à ces centres de gravité, exerçant leur force à des points spécifiques le long de la poutre. La charge résultante équivalente pour l'ensemble de la poutre peut être calculée avec les magnitudes et les positions des charges résultantes individuelles déterminées. Cela implique l'addition des charges résultantes individuelles des différentes régions pour obtenir la charge résultante équivalente globale agissant sur la poutre. L'étape suivante consiste à déterminer le moment par rapport à un point spécifique, généralement l'extrémité fixe de la poutre. Le moment mesure l'effet de rotation de la force agissant sur la poutre. Le moment résultant peut être déterminé en additionnant les moments individuels dus à chaque charge. Le moment de chaque charge est égal au produit de la force et de sa distance par rapport au point spécifié. <img alt="Equation 1" src="/files/ftp_upload/14280/14280_PT_Equation_1.svg" style="text-align: center; height: 11px;"> En rappelant le principe du moment, le moment de la charge résultante équivalente par rapport au point spécifié est égal au produit de la charge résultante équivalente et de la distance à partir de ce point. <img alt="Equation 2" src="/files/ftp_upload/14280/14280_PT_Equation_2.svg" style="text-align: center; height: 13px;"> En réarrangeant l'équation et en remplaçant les termes, on peut déterminer la position de la charge résultante équivalente le long de la poutre. <img alt="Equation 3" src="/files/ftp_upload/14280/14280_PT_Equation_3.svg" style="text-align: center; height: 35px;">

Charges distribuées : Résolution de problème

Les poutres sont des éléments structurels couramment utilisés dans les applications d’ingénierie nécessitant différentes capacités de charge. La première étape de l’analyse d’un ...

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Distributed Loads: Problem Solving

equivalent resultant loads on beams

Equivalent resultant loads on beams can be found by breaking a distributed load into smaller regions. This makes the beam easier to analyze. Each region can then be handled on its own before the results are combined.

The magnitude of the equivalent resultant load for each region comes from the area of that region. In this setting, area represents the force applied by the distributed load over that part of the beam. After finding the force for each region, the position of each resultant load must be located.

The position is found by using the centroid of each region. A centroid is the point where the region’s mass can be treated as concentrated. The individual resultant loads act at these centroids, so each force is placed at a specific point along the beam.

Once the separate forces and locations are known, they are combined to find the equivalent resultant load for the full beam. This is done by adding the individual resultant loads from the different regions. The result gives the overall force acting on the beam.

The next step is to determine the moment about a chosen point, usually the fixed end of the beam. A moment is the turning effect of a force. The total moment comes from adding the moments created by each load, and each moment equals force times distance from the chosen point.

By using the moment principle, the moment of the equivalent resultant load about that point must equal the force multiplied by its distance from the point. Rearranging that relationship makes it possible to find where the single equivalent load acts along the beam. This gives both the size and location of the load that replaces the distributed loading.

Equivalent Resultant Loads on Beams

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Equivalent resultant loads on beams can be found by breaking a distributed load into smaller regions. This makes the beam easier to analyze. Each region can then be handled on its own before the results are combined. The magnitude of the equivalent resultant load for each region comes from the area of that region. In this setting, area represents the force applied by the distributed load over that part of the beam. After finding the force for each region, the position of each resultant load...

key terms and concepts

Learn how to replace a distributed load with one equivalent resultant force on a beam by using areas, centroids, and moments to find its location.

Equivalent Resultant Loads on Beams | JoVE K12

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Equivalent Resultant Loads on Beams

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