Probabilistically modelled geometrical imperfections for reliability analysis of vertically loaded steel frames: Fid-Bau Portal

Probabilistically modelled geometrical imperfections for reliability analysis of vertically loaded steel frames

Jindra, Daniel / Kala, Zdeněk / Kala, Jiří

Abstract The article explores the stochastic modelling of 3D steel frames under static vertical load, with a main focus on random initial geometrical imperfections. The random input parameters for initial geometrical imperfections are derived from the tolerance criteria in accordance with European standard. In order to derive statistical parameters from the corresponding standard tolerances, two methods noted as #RSS (random storey sway) and #RSP (random storey position) have been utilized and compared. Both of these methods are used along with the first-order reliability method (FORM) and the advanced finite element method (FEM) – geometrically and materially nonlinear imperfect analysis (GMNIA) to numerically analyse several geometries of steel frame structures. Ultimate resistances of these structures are monitored and basic sensitivity studies are conducted. The results are also compared with the deterministic approach of the European standard. The stochastic approach of the FORM to estimate the ultimate resistance of steel frame structures serves as a verification tool of the classic, in engineering praxis widely used, deterministic approach. This study provides useful provisions for the advanced numerical analyses of steel frames of various geometries. Additionally, the estimations of ultimate resistance by the deterministic European standard approach is verified for selected frame geometries.

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Highlights • Stochastic modelling of 3D multi-story steel frames with random geometrical imperfections. • Verification of the European Steel standard by first order reliability method (FORM). • First order reliability method (FORM) with semi-probabilistic approach used for design resistence. • Geometrically and materially nonlinear analysis of ultimate resistance of geometrically imperfect steel frame structures. • Two methods to consider stochastic values of the initial parameters to define the geometrical imperfections.