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Master's Dissertation
DOI
10.11606/D.3.2005.tde-20022006-150915
Document
Author
Full name
Henrique Furia Silva
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2005
Supervisor
Committee
Silva, Valdir Pignatta e (President)
Savassi, Walter
Soares, Carlos Alberto
Title in Portuguese
Formulação do problema da torção uniforme em barras de seção transversal maciça.
Keywords in Portuguese
função empenamento
mecânica dos sólidos
teoria da elasticidade
torção uniforme
Abstract in Portuguese
O escopo do trabalho é estudar o problema da torção uniforme em barras de seção maciça e resolvê-lo analiticamente para obter o momento de inércia à torção da seção transversal e os deslocamentos ao longo de toda a barra. Este trabalho foi desenvolvido no contexto da Teoria da Elasticidade, utilizando o método semi-inverso para determinar as equações de Saint-Venant para a torção uniforme. As seções em forma de elipse e triângulo eqüilátero foram resolvidas utilizando a função de tensão de Prandtl, a função empenamento e a sua conjugada harmônica. A seção retangular foi resolvida utilizando as funções empenamento e de Prandtl desenvolvidas em séries infinitas. Foi desenvolvida uma formulação matricial utilizando o Método de Galerkin para resolver problemas que não possuem solução fechada.
Title in English
Formulation of the uniform torsion problem in solid section bars.
Keywords in English
elasticity theory
mechanics of solids
uniform torsion
warping function
Abstract in English
The main purpose of this essay is to present the issue of the uniform torsion in solid section bars and to solve it analytically to achieve the moment of inertia to the torsion of the transversal section and the displacements throughout the whole bar. This essay was developed in the Elasticity Theory context, using the semi-inverse method to determine the Saint-Venant equations to the uniform torsion. The sections in ellipse and equilateral triangle were solved using the Prandtl stress function, the warping function and its harmonic conjugate. The rectangular section was solved using the warping and the Prandtl functions developed in infinite series. A formulation based on matrixes was developed using the Galerkin method to solve problems that do not have closed solution.
 
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Defsa61x.pdf (1.11 Mbytes)
Publishing Date
2006-02-21
 
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