Abstract The development of a numerical formulation is presented to describe viscoelastic behavior considering shear effects. The nonlinear positional formulation of the Finite Element Method is used considering plane frame elements with Reissner kinematics. The description of the viscoelastic behavior is considered through the adoption of a stress-strain relation based on Boltzmann rheological model. The used kinematics allows to describe the decoupling between the rotations and the displacements in element cross-sections. This approach allows to evaluate the contribution of shear effects in viscoelastic behavior in an original way. Based on the developments and the results obtained, it is possible to observe that strains and displacements due to viscoelastic behavior are significantly superior to the results obtained considering Bernoulli-Euler kinematics hypothesis. It is possible to notice a better agreement between the obtained numerical results and the results in the literature. Results obtained from the developed formulation allow the assessment of the shear effects on the viscoelastic behavior of plane frames.

RESUMO: A interação entre paredes estruturais e vigas de transição (sistema parede-viga) é um fenômeno que ainda carece de estudos para se realizar sua consideração de forma sistemática na análise de edifícios. No passado, pesquisadores como Wood, Rosenhaupt, Burhouse, Stafford Smith, Navaratnarajah, Davies, Riddington e Armed, realizaram experimentos e buscaram desenvolver modelos de cálculo simplificados para representar esse fenômeno. Entretanto, os estudos se limitaram ao caso de vigas biapoidas e paredes sem aberturas. O estudo apresentado neste artigo teve como objetivo realizar análises por meio de modelagem computacional do sistema parede-viga em situações mais complexas de comportamento, empregando-se um específico modelo de barras equivalentes. Os exemplos elaborados consideraram comportamento elástico linear para os materiais e consistiram na avaliação dos esforços e deslocamentos verticais nas vigas de apoio, além das tensões na base das paredes, para painéis de um edifício real de alvenaria estrutural. A modelagem computacional foi elaborada segundo abordagens bidimensionais e tridimensionais da estrutura. Dentre os resultados obtidos, destaca-se a importância da consideração do efeito das amarrações entre painéis de alvenaria via modelo tridimensional devido à intensa redistribuição de esforços verificada. Também foi realizada a análise de uma possível excentricidade no sistema parede-viga, o que permitiu verificar que a consideração dos momentos de torção influenciou consideravelmente no dimensionamento das vigas de suporte.

ABSTRACT: Wall-beam interaction (wall-beam system) is a phenomenon that requires further investigation in order to be consistently incorporated into structural building analysis. Researchers such as Wood, Rosenhaupt, Burhouse, Stafford Smith, Navaratnarajah, Davies, Riddington and Armed conducted tests on specimens to develop simplified analysis models, emphasizing the behavior of walls without openings under one span beams. The present study performed computational analysis using an specific equivalent frame model in order to study the behavior of the wall-beam system in more complex wall and beam arrangements. The examples considered the linear elastic behavior of materials and consisted of assessing stress distribution and displacements on support beams, in addition to stresses at the bottom of the walls, for panels in a real structural masonry building. Two- and three-dimensional analyses were used and the results showed the importance of three-dimensional analysis of wall interconnections. The effects of eccentricity between the vertical plane of the wall and horizontal support beam axis were also evaluated, showing the strong influence of twisting moments in support beam design.

Abstract The thermal effects of problems involving deformable structures are essential to describe the behavior of materials in feasible terms. Verifying the transformation of mechanical energy into heat it is possible to predict the modifications of mechanical properties of materials due to its temperature changes. The current paper presents the numerical development of a finite element method suitable for nonlinear structures coupled with thermomechanical behavior; including impact problems. A simple and effective alternative formulation is presented, called FEM positional, to deal with the dynamic nonlinear systems. The developed numerical is based on the minimum potential energy written in terms of nodal positions instead of displacements. The effects of geometrical, material and thermal nonlinearities are considered. The thermodynamically consistent formulation is based on the laws of thermodynamics and the Helmholtz free-energy, used to describe the thermoelastic and the thermoplastic behaviors. The coupled thermomechanical model can result in secondary effects that cause redistributions of internal efforts, depending on the history of deformation and material properties. The numerical results of the proposed formulation are compared with examples found in the literature.