Doctoral Thesis
DOI
https://doi.org/10.11606/T.18.2018.tde-21032018-090933
Document
Author
Full name
Rogério de Oliveira Rodrigues
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1997
Supervisor
Committee
Venturini, Wilson Sergio (President)
André, João Cyro
El Debs, Ana Lúcia Homce de Cresce
Laier, José Elias
Pimenta, Paulo de Mattos
Title in Portuguese
Análise dinâmica bidimensional não-linear física e geométrica de treliças de aço e pórticos de concreto armado
Keywords in Portuguese
Comportamento não-linear
Dinâmica estrutural
Abstract in Portuguese
Title in English
Physical and geometrical non-linear two-dimensional dynamic analysis of steel trusses and reinforced concrete frames
Keywords in English
Non-linear behaviour
Structural dynamics
Abstract in English
This work deals with the two-dimensional dynamic analysis of steel trusses and reinforced concrete frames. The physical non-linear effects of these materials as well as the geometrical non-linearity of such structures are studied. In this context, a general equation that describes the behaviour of structures approximated by finite elements is defined, using the Virtual Works Principle for structures in movement. In order to integrate this differential equation along the time an implicit procedure is adopted based on the predictor-corrector process taking into account the Newmark's generalised equations. For the geometrical non-linear analysis, the deformation field is defined by assuming displacements approximated along each finite element by quadratic shape functions. All terms resulting from that assumption are taken into account for the plane trusses, while for plane frame, terms representing higher order products are neglected. In order to describe the equilibrium position of the structural system, during the numeric integration process, the updated Lagrangean formulation is used to give the secant and tangent incremental stiffness matrices. Regarding the steel non-linear physical behaviour, a numerical procedure is achieved based on a bilinear stress-strain curve that is able to describe kinematic, isotropic and independent responses. For the reinforced concrete physical non-linear behaviour the well known CEB and ACI models were taken to derive and implement the numeric process. In this case, the moment of inertia is corrected according to the element level of cracking. These models also consider the material behaviour when cyclic loads are applied causing stress sign inversion. Finally, numeric examples are presented to illustrate the quality and accuracy of obtained results.