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

Uma viga de comprimento L sujeita a uma carga variável, que é uma combinação de distribuição de carga parabólica e trapezoidal ao longo do eixo x.
Na carga parabólica, considere um elemento diferencial de força dR sobre o comprimento dx. A carga resultante é obtida integrando o elemento diferencial ao longo do comprimento da carga. Ele está localizado no centróide da área parabólica, e a coordenada x do centróide é determinada usando o princípio do momento.
A área trapezoidal pode ser dividida em áreas retangulares e triangulares, com a carga resultante atuando em seus centróides. Esses centróides são posicionados na metade do comprimento do retângulo e a um terço do comprimento da base do lado vertical do triângulo.
A carga resultante para a área trapezoidal é obtida pela soma das cargas resultantes individuais e passa pelo centróide da área, determinado pelo princípio do momento.
A carga total distribuída é a soma das cargas resultantes das áreas trapezoidal e parabólica, passando pelo centróide da área combinada, determinada pelo princípio do momento.

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	<li>Cerveja, F.P.; Johnston, E.R.; Mazurek, D.F; Cromwell, PJ e Self, BP (2019). Mecânica vetorial para engenheiros \u2012 estática e dinâmica. Nova Iorque: McGraw-Hill. pág. 264</li>
	<li>Oliveira, J.L.; Kraige, L.G. e Bolton, J.N. (2020). Engenharia Mecânica \u2012 Estática. Hoboken, Nova Jersey: John Wiley. pág. 273</li>
	<li>Hibbeler, R.C. (2016). Engenharia Mecânica \u2012 Estática e Dinâmica. Hoboken, Nova Jersey: Pearson Prentice Hall. pp EM-2</li>
</ol>

carga ao longo de um único eixo

Na engenharia estrutural, a análise de vigas sujeitas a cargas variáveis é um aspecto crítico para entender o comportamento e desempenho desses elementos estruturais. Um cenário comum envolve uma viga sujeita a uma combinação de diferentes distribuições de carga.

Considere uma viga de comprimento L sujeita a uma carga variável, que é uma combinação de distribuição de carga parabólica e trapezoidal ao longo do eixo x. Nesse caso, é essencial determinar as cargas resultantes, suas posições e o centroide da área combinada para prever a resposta da viga nessas condições da carga.

Primeiramente, examine a distribuição de carga parabólica. Considere um elemento diferencial de força dR atuando sobre um pequeno comprimento dx. Para determinar a carga resultante para a área parabólica, o elemento diferencial dR é integrado ao longo de todo o comprimento da carga. A localização dessa carga resultante está no centroide da área parabólica. O princípio do momento é aplicado para encontrar a coordenada x do centroide, que afirma que o primeiro momento da área em relação a um eixo é igual ao produto da área pelo distância do seu centroide em relação ao eixo.

Em seguida, a distribuição de carga trapezoidal é analisada dividindo-a em duas regiões retangulares e triangulares. As cargas resultantes para essas regiões individuais atuam em seus respectivos centroides. Para a área retangular, o centroide está posicionado na metade do comprimento do retângulo. Para a área triangular, o centroide está localizado a um terço do comprimento da base afastado do lado vertical do triângulo.

Ao somar as cargas resultantes individuais das áreas retangulares e triangulares, é possível determinar a carga resultante para toda a área trapezoidal. A localização da carga resultante passa pelo centroide da área trapezoidal, que também pode ser determinada usando o princípio do momento.

Da mesma forma, ao adicionar as cargas resultantes das áreas parabólica e trapezoidal, é possível determinar a carga resultante total atuando na viga. A localização da carga resultante total passa pelo centroide da área combinada, que pode ser determinada ainda mais usando o princípio do momento.

Carga ao longo de um único eixo

Na engenharia estrutural, a análise de vigas submetidas a cargas variáveis é um aspecto crítico para entender o comportamento e o desempenho dessas ...

Education

JoVE Core

Mechanical Engineering

Engenharia Mecânica

Unit 1

Unidade 1

Force System Resultants

Resultantes de Sistemas de Forças

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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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load along a single axis

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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mechanical engineering

Finding Resultant Loads on a Beam

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