Name: finding resultant loads on a beam
Uploaded: 2023-09-22T11:49:22.000Z
Duration: 1 min 29 s
Channel: JoVE

Una viga de longitud L sometida a una carga variable, que es una combinación de distribución de carga parabólica y trapezoidal a lo largo del eje x.
En la carga parabólica, considere un elemento diferencial de fuerza dR sobre la longitud dx. La carga resultante se obtiene integrando el elemento diferencial a lo largo de la longitud de la carga. Se encuentra en el centroide del área parabólica y la coordenada x del centroide se determina mediante el principio del momento.
El área trapezoidal se puede dividir en áreas rectangulares y triangulares, con la carga resultante actuando en sus centroides. Estos centroides se colocan a la mitad de la longitud del rectángulo y a un tercio de la longitud de la base desde el lado vertical del triángulo.
La carga resultante para el área trapezoidal se obtiene sumando las cargas individuales resultantes y pasa a través del centroide del área, determinada por el principio del momento.
La carga distribuida total es la suma de las cargas resultantes de las áreas trapezoidal y parabólica, que pasan por el centroide del área combinada, determinada por el principio del momento.

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	<li>Cerveza, F.P.; Johnston, E.R.; Mazurek, D.F.; Cromwell, P.J. y Self, B.P. (2019). Mecánica vectorial para ingenieros: estática y dinámica. Nueva York: McGraw-Hill. págs. 264</li>
	<li>Meriam, J.L.; Kraige, L.G. y Bolton, J.N. (2020). Ingeniería Mecánica \u2012 Estática. Hoboken, Nueva Jersey: John Wiley. págs. 273</li>
	<li>Hibbeler, R.C. (2016). Ingeniería Mecánica \u2012 Estática y Dinámica. Hoboken, Nueva Jersey: Pearson Prentice Hall. págs. EM-2</li>
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carga a lo largo de un solo eje

En ingeniería estructural, el análisis de vigas sujetas a cargas variables es un aspecto crítico para comprender el comportamiento y rendimiento de estos elementos estructurales. Un escenario común implica una viga sometida a una combinación de diferentes distribuciones de carga. Considere una viga de longitud L sometida a una carga variable, que es una combinación de distribución de carga parabólica y trapezoidal a lo largo del eje x. En este caso, es esencial determinar las cargas resultantes, sus ubicaciones y el centroide del área combinada para predecir la respuesta de la viga bajo estas condiciones de carga. En primer lugar, examine la distribución de carga parabólica. Considere un elemento diferencial de fuerza dR actuando sobre una pequeña longitud dx. Para determinar la carga resultante para el área parabólica, el elemento diferencial dR se integra sobre toda la longitud de la carga. La ubicación de esta carga resultante está en el centroide del área parabólica. El principio del momento se aplica para encontrar la coordenada x del centroide, que establece que el primer momento del área respecto a un eje es igual al producto del área y la distancia de su centroide desde el eje. A continuación, se analiza la distribución de carga trapezoidal dividiéndola en dos regiones rectangular y triangular. Las cargas resultantes para estas regiones individuales actúan en sus respectivos centroides. Para el área rectangular, el centroide se encuentra a la mitad de la longitud del rectángulo. Para el área triangular, el centroide se encuentra a un tercio de la longitud de la base desde el lado vertical del triángulo. Al agregar las cargas resultantes individuales para las áreas rectangular y triangular, se puede determinar la carga resultante para todo el área trapezoidal. La ubicación de la carga resultante pasa a través del centroide del área trapezoidal, que también se puede determinar utilizando el principio del momento. De manera similar, al agregar las cargas resultantes tanto de las áreas parabólicas como trapezoidales, se puede determinar la carga resultante total actuando sobre la viga. La ubicación de la carga resultante total pasa a través del centroide del área combinada, que se puede determinar aún más utilizando el principio del momento.

Carga a lo largo de un solo eje

En ingeniería estructural, el análisis de vigas sometidas a cargas variables es un aspecto crítico para comprender el comportamiento y el rendimiento de estas ...

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Force System Resultants

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Load along a Single Axis

finding resultant loads on a beam

Structural engineering often requires finding the resultant load on a beam with changing force patterns. Here, a beam of length L carries a varying load made from parabolic and trapezoidal load distributions along the x-axis. The goal is to find the total load, where it acts, and the centroid of the combined area so the beam’s response can be predicted.

The parabolic load is handled first. A small force element, dR, acts over a short distance, dx, and these elements are integrated across the full length of the load. The resultant load for the parabolic area acts at the centroid of that area. The x-coordinate of the centroid is found with the moment principle, which says the first moment of an area about an axis equals the area times the distance to its centroid.

The trapezoidal load is then split into two simpler shapes. One part is rectangular, and the other is triangular. Their resultant loads act at their own centroids. For the rectangle, the centroid lies halfway along its length. For the triangle, the centroid is one-third of the base length from the vertical side.

After those parts are found, their loads are added to get the resultant load of the full trapezoidal area. That load passes through the centroid of the trapezoid, which can also be found with the moment principle. Finally, the resultant loads from the parabolic and trapezoidal areas are combined. Their sum gives the total load on the beam, and its location passes through the centroid of the combined area.

Finding Resultant Loads on a Beam

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Structural engineering often requires finding the resultant load on a beam with changing force patterns. Here, a beam of length L carries a varying load made from parabolic and trapezoidal load distributions along the x-axis. The goal is to find the total load, where it acts, and the centroid of the combined area so the beam’s response can be predicted. The parabolic load is handled first. A small force element, dR, acts over a short distance, dx, and these elements are integrated across the...

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key terms and concepts

Learn how parabolic and trapezoidal loads on a beam are broken into simpler areas, then combined to find the resultant force and centroid.

Finding Resultant Loads on a Beam | JoVE K12

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Finding Resultant Loads on a Beam

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