Comparison of second order effects in a plane frame through rigorous analysis and simplified methods from NBR 6118/2014 and NBR 8800/2008

Resumo

The analysis of second order effects in structures can be performed in a rigorous, simplified or approxi-
mated approach. The rigorous analysis consists in incremental procedures that modifies structure’s stiffness matrix,

according to changes in its geometry. The simplified analysis divides a nonlinear problem in successive linear pro-
blems. In this context, NBR 6118/2014 and NBR 8800/2008 presents simplified methods like the coefficient γZ

and the amplification coefficient method (MAES) for reinforced concrete and steel structures, respectively. This
work aims to investigate coefficient γZ and MAES performance in determining second order effects by magnifying
the first order efforts. To achieve that, a comparison is performed, following normative recommendations, using a

reinforced concrete plane frame from literature. Python codes are developed to calculate both simplified approa-
ches, using direct stiffness method for first order efforts determination and all considerations present on normative

codes for a simplified second order analysis. Therefore, in this work, the results of two simplified methods for
second order analysis are obtained for the same frame designed structure, and these results are also compared to
those obtained from a geometric nonlinear rigorous data, comparing regular procedures in structure designing.