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

Considere una viga cónica OB fijada en un extremo y sometida a una carga distribuida.
Determine la fuerza resultante equivalente de la carga variable y ubique su posición en la viga.
Primero, divida la carga distribuida en dos regiones triangulares.
A continuación, la magnitud de la carga resultante equivalente de la región triangular izquierda y derecha es igual al área de cada triángulo.
Cada carga resultante actúa en centroides, ubicados a un tercio de la longitud de la base desde el lado vertical AD del triángulo.
La carga resultante equivalente se puede determinar sumando la carga resultante individual de cada región triangular.
El momento alrededor del punto O se puede determinar sumando el momento individual que actúa debido a cada carga resultante.
Recordemos el principio del momento, que establece que el momento de la carga resultante equivalente alrededor del punto O es igual al producto de la carga resultante equivalente y la distancia desde el punto O.
Al sustituir los valores de la ecuación, se puede determinar la ubicación de la carga resultante equivalente.

<ol>
	<li>Hibbeler, R.C. (2016). Ingeniería Mecánica \u2012 Estática y Dinámica. Hoboken, Nueva Jersey: Pearson Prentice Hall, pp. 194-195</li>
</ol>

cargas distribuidas: resolución de problemas

Las vigas son elementos estructurales comúnmente utilizados en aplicaciones de ingeniería que requieren diferentes capacidades de carga. El primer paso para analizar una viga bajo una carga distribuida es simplificar el problema dividiendo la carga en regiones más pequeñas, lo que permite considerar cada región por separado y calcular la magnitud de la carga resultante equivalente que actúa en cada parte de la viga. La magnitud de la carga resultante equivalente para cada región se puede determinar calculando el área de las respectivas regiones, que representa la fuerza ejercida por la carga en cada región. A continuación, localice la posición de cada carga resultante en la viga. Esto se puede hacer encontrando los centroides de las regiones, que son los puntos donde se puede considerar concentrada la masa de las regiones. Las cargas resultantes individuales actúan en estos centroides, ejerciendo su fuerza en puntos específicos a lo largo de la viga. La carga resultante equivalente para toda la viga se puede calcular con las magnitudes y posiciones de las cargas resultantes individuales determinadas. Esto implica sumar las cargas resultantes individuales de las diferentes regiones para obtener la carga resultante equivalente total que actúa en la viga. El siguiente paso es determinar el momento alrededor de un punto específico, generalmente el extremo fijo de la viga. El momento mide el efecto de rotación de la fuerza que actúa sobre la viga. El momento resultante se puede determinar sumando los momentos individuales que actúan debido a cada carga. El momento de cada carga es igual al producto de la fuerza y su distancia desde el punto especificado. <img alt="Equation 1" src="/files/ftp_upload/14280/14280_PT_Equation_1.svg" style="text-align: center; height: 11px;"> Al recordar el principio del momento, el momento de la carga resultante equivalente alrededor del punto especificado es igual al producto de la carga resultante equivalente y la distancia desde ese punto. <img alt="Equation 2" src="/files/ftp_upload/14280/14280_PT_Equation_2.svg" style="text-align: center; height: 13px;"> Al reorganizar la ecuación y sustituir los términos, se puede determinar la ubicación de la carga resultante equivalente a lo largo de la viga. <img alt="Equation 3" src="/files/ftp_upload/14280/14280_PT_Equation_3.svg" style="text-align: center; height: 35px;">

Cargas distribuidas: Resolución de problemas

Las vigas son elementos estructurales comúnmente empleados en aplicaciones de ingeniería que requieren diferentes capacidades de carga. El primer paso en el análisis de un ...

Education

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JoVE Core

Mechanical Engineering

Ingeniería Mecánica

Unit 1

Unidad 1

Force System Resultants

Resultantes de Sistemas de Fuerzas

KEY TERMS AND CONCEPTS

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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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