Influência dos modelos de carbonização na análise não linear geométrica de treliças de madeira em situação de incêndio

Abstract

In this work, a numerical study about the geometric nonlinear analysis of plane timber trusses in fire situations was carried out. The analysis was based on a positional formulation of the finite element method. The effects of fire exposure were considered by the carbonization and loss of the timber element's cross section according to the effective section method. The normative guidelines about carbonization models from the revision project of the Brazilian Standard ABNT NBR 7190, the European Standard EN 1995-1-2, and the Australian Standard AS 1720.4 were adopted in the analysis. Three truss systems were proposed for study, and five hardwoods and two softwoods were considered. In the models associated with the revision project of the Brazilian Standard, the charring rates of timber were defined according to experimental values from literature, while the charring rate values suggested by the normative guidelines were adopted in the models from European and Australian Standards. For the geometric nonlinear analysis, the finite element formulation was performed from the total potential energy minimization, whose nonlinear equations system was related to the nodal positions of the structure and solved by the Newton-Raphson method. The critical instability loads of truss systems were estimated by a procedure called iterative process of apparent critical load, which was proposed to reduce the number of iterations necessary for convergence. Computational codes were developed in the MATLAB language to process the analyses and the graphic design, as structural models and diagrams. Regarding the results obtained for a maximum time of fire exposure of 20 minutes, the geometric nonlinear analysis allowed more precise values than a simple geometric linear analysis for normal stresses, internal forces and displacements. In some cases, the results referring to the fire exposed models analyzed from the revision project of the Brazilian standard guidelines exhibited little variation relating to the Australian standard, while the final parameters obtained from the European standard procedures were less conservative in general. The iterative process of apparent critical load, when compared to a conventional procedure, promoted iterations and time reductions greater than 80% for convergence of the truss critical instability load.