Name: truss member force analysis by sections
Uploaded: 2025-05-22T09:06:03.000Z
Duration: 1 min 30 s
Channel: JoVE

Considere uma estrutura de treliça. As forças F1 e F2 estão atuando nos pontos B e D.
O método das seções é usado para determinar as forças que atuam em alguns membros de uma treliça. Baseia-se no princípio de que uma treliça em equilíbrio tem cada um de seus segmentos em equilíbrio.
Um diagrama de corpo livre da treliça é considerado para calcular as forças que atuam no membro EF, DC e DF.
A equação de equilíbrio para momentos em torno do ponto A pode ser usada para calcular a reação de suporte no ponto E.
Agora, um corte é feito ao longo de um plano seccional que cruza no máximo três membros.
Um diagrama de corpo livre da seção, assumindo as forças desconhecidas como de tração, é desenhado.
A soma de momentos sobre D produz uma solução para a força que atua em EF.
As forças inclinadas desconhecidas são resolvidas nos componentes horizontal e vertical.
A condição de equilíbrio para as forças aplicadas ao longo das direções horizontal e vertical resulta em duas equações.
Resolvendo as equações simultâneas, a força ao longo de DC e DF pode ser calculada.

<ol>
	<li>R. C., Hibbeler Engenharia Mecânica Estática, Pearson. Pág. 291-293</li>
	<li>F.P. Beer, E.R. Johnston, D.F. Mazurek, P.J. Cornwell, B.P. Self, Mecânica Vetorial para Engenheiros Estática e Dinâmica Mecânica de Engenharia Estática, Mc Graw-Hill Education. Pág. 217</li>
</ol>

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método das seções

Considere uma estrutura de treliça, conforme mostrado na figura.

<img alt="Figure 1" src="/files/ftp_upload/14285/14285_PT_Fig_1v2.svg" style="text-align: center; height: 350px;" />

Forças F1 e F2 atuam nos nós B e D, respectivamente. O método das seções pode ser empregado para determinar as forças que atuam em membros específicos da treliça, como EF, DC e DF. Essa abordagem é baseada no princípio de que uma treliça em equilíbrio também possui cada um de seus segmentos em equilíbrio.

Para calcular as forças que atuam nesses membros, considera-se um diagrama de corpo livre da treliça. A equação de equilíbrio para momentos em torno do nó A pode ser aplicada para estimar a reação de apoio no ponto E.

<img alt="Equation 1" src="/files/ftp_upload/14285/14285_PT_Equation_1v2.svg" style="text-align: center; height: 13px;" />

Uma seção é feita ao longo de um plano seccional que intersecciona no máximo três membros: EF, DC e DF. Em seguida, um diagrama de corpo livre da parte direita da seção cortada é desenhado, assumindo as forças desconhecidas como tensões.

<img alt="Figure 2" src="/files/ftp_upload/14285/14285_PT_Fig_2v2.svg" style="text-align: center; height: 350px;" />

Uma solução para a força que atua no membro EF pode ser obtida somando momentos ao redor do nó D.
<img alt="Equation 2" src="/files/ftp_upload/14285/14285_PT_Equation_2v2.svg" style="text-align: center; height: 13px;" />

As forças inclinadas desconhecidas, FDC e FDF, são resolvidas em componentes horizontais e verticais. A aplicação da condição de equilíbrio para as forças ao longo das direções horizontal e vertical resulta em duas equações separadas.

<img alt="Equation 3" src="/files/ftp_upload/14285/14285_PT_Equation_3v2.svg" style="text-align: center; height: 13px;" />

<img alt="Equation 4" src="/files/ftp_upload/14285/14285_PT_Equation_4v2.svg" style="text-align: center; height: 13px;" />

As forças ao longo dos membros DC e DF podem ser estimadas resolvendo essas equações simultâneas.

Método das Seções

Considere uma estrutura de treliça, como mostrado na figura.

As forças F1 e F2 atuam nas juntas B e D, respectivamente. O método das seções pode ser empregado para ...

Education

JoVE Core

Mechanical Engineering

Engenharia Mecânica

Unit 1

Unidade 1

Structural Analysis

Análise Estrutural

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

Method of Sections

truss member force analysis by sections

Truss member force analysis by sections finds the force in selected members of a truss. In this problem, forces F1 and F2 act at joints B and D. The goal is to determine the forces in members EF, DC, and DF.

The method uses the idea that a truss in equilibrium also has each of its sections in equilibrium. A free-body diagram of the whole truss is drawn first. The moment equation about joint A is then used to estimate the support reaction at point E.

Next, a cut is made along a sectional plane that passes through no more than three members. Here, the cut intersects EF, DC, and DF. A free-body diagram of the right side of the cut section is then drawn, and the unknown member forces are assumed to be tensile, or pulling away from the cut.

The force in member EF is found by summing moments about joint D. The inclined forces in members DC and DF are then split into horizontal and vertical parts. Finally, equilibrium in the horizontal and vertical directions gives two equations, and solving them gives the forces in DC and DF.

Truss Member Force Analysis by Sections

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Learn how the method of sections uses free-body diagrams, moments, and force balance to find unknown forces in truss members EF, DC, and DF.

Truss Member Force Analysis by Sections | JoVE K12

O JoVE Core Mechanical Engineering oferece vídeos animados concisos e de fácil compreensão que abrangem tópicos-chave como equilíbrio, forças, análise de treliças e mecânica estrutural. Explore suas aplicações no mundo real e observe esses conceitos em ação por meio de experimentos conduzidos por cientistas.

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Truss Member Force Analysis by Sections

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