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

Considere uma viga cônica OB fixada em uma extremidade e submetida a uma carga distribuída.
Determine a força resultante equivalente da carga variável e localize sua posição na viga.
Primeiro, divida a carga distribuída em duas regiões triangulares.
Em seguida, a magnitude da carga resultante equivalente da região triangular esquerda e direita é igual à área de cada triângulo.
Cada carga resultante atua em centróides, localizados a um terço do comprimento da base a partir do lado vertical AD do triângulo.
A carga resultante equivalente pode ser determinada adicionando a carga resultante individual de cada região triangular.
O momento em torno do ponto O pode ser determinado adicionando o momento individual agindo devido a cada carga resultante.
Lembre-se do princípio do momento, que afirma que o momento da carga resultante equivalente em torno do ponto O é igual ao produto da carga resultante equivalente e à distância do ponto O.
Substituindo os valores na equação, a localização da carga resultante equivalente pode ser determinada.

<ol>
	<li>Hibbeler, R.C. (2016). Engenharia Mecânica \u2012 Estática e Dinâmica. Hoboken, Nova Jersey: Pearson Prentice Hall, pp. 194-195</li>
</ol>

cargas distribuídas: resolução de problemas

Vigas são elementos estruturais comumente utilizados em aplicações de engenharia que requerem diferentes capacidades de carga. O primeiro passo para analisar uma viga sob uma carga distribuída é simplificar o problema dividindo a carga em regiões menores, o que permite considerar cada região separadamente e calcular a magnitude da carga resultante equivalente atuando em cada parte da viga. A magnitude da carga resultante equivalente para cada região pode ser determinada calculando a área das respectivas regiões, o que representa a força exercida pela carga em cada região.

Em seguida, localize a posição de cada carga resultante na viga. Isso pode ser feito encontrando os centroides das regiões, que são os pontos onde a massa das regiões pode ser considerada concentrada. As cargas resultantes individuais atuam nesses centroides, exercendo sua força em pontos específicos ao longo da viga.

A carga resultante equivalente para toda a viga pode ser calculada com as magnitudes e posições das cargas resultantes individuais determinadas. Isso envolve a adição das cargas resultantes individuais das diferentes regiões para obter a carga resultante equivalente global atuando na viga.

O próximo passo é determinar o momento em relação a um ponto específico, geralmente a extremidade fixa da viga. O momento mede o efeito rotacional da força atuando na viga. O momento resultante pode ser determinado adicionando os momentos individuais atuando devido a cada carga. O momento de cada carga é igual ao produto da força e sua distância do ponto especificado.



<img alt="Equation 1" src="/files/ftp_upload/14280/14280_PT_Equation_1.svg" style="text-align: center; height: 11px;" />



Ao lembrar do princípio do momento, o momento da carga resultante equivalente sobre o ponto especificado é igual ao produto da carga resultante equivalente e a distância desse ponto.



<img alt="Equation 2" src="/files/ftp_upload/14280/14280_PT_Equation_2.svg" style="text-align: center; height: 13px;" />



Ao rearranjar a equação e substituir os termos, a localização da carga resultante equivalente ao longo da viga pode ser determinada.



<img alt="Equation 3" src="/files/ftp_upload/14280/14280_PT_Equation_3.svg" style="text-align: center; height: 35px;" />

Cargas Distribuídas: Resolução de Problemas

As vigas são elementos estruturais comumente empregados em aplicações de engenharia que requerem diferentes capacidades de carga. O primeiro passo na análise de um ...

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

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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distributed loads: problem solving

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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mechanical engineering

Equivalent Resultant Loads on Beams

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