LIGHTWEIGHT STRUCTURES in CIVIL ENGINEERING CONTEMPORARY PROBLEMS Monograph from Scientific Seminar Organized by Polish Chapters of International Association for Shell and Spatial Structures UTP University of Science and Technology Faculty of Civil and Environmental Engineering and Architecture XXIII LSCE –2017 Bydgoszcz, 1 December, 2017 DESIGN OF STEEL STRUCTURES FOR A GIVEN LEVEL OF RELIABILITY USING PARTIAL SAFETY FACTORS CALIBRATION PROCEDURE J. Szafran 1) K. Juszczyk 2) M. Kamiński 3) 1) Adjunct Professor, Chair of Structural Reliability, Department of Structural Mechanics, Faculty of Civil Engineering, Architecture and Environmental Engineering, Łódź University of Technology, Łódź, POLAND, email: jacek.szafran@p.lodz.pl 2) M.Sc. Eng, Chair of Structural Reliability, Department of Structural Mechanics, Faculty of Civil Engineering, Architecture and Environmental Engineering, Łódź University of Technology, Łódź, POLAND, email: kjuszczyk@compactprojekt.pl 3) Professor, Head of Chair of Structural Reliability, Department of Structural Mechanics, Faculty of Civil Engineering, Architecture and Environmental Engineering, Łódź University of Technology, Łódź, POLAND, email: marcin.kaminski@p.lodz.pl ABSTRACT: The main aim of this study was to perform calibration procedure of partial safety factors, which are used in Eurocodes calculation techniques to ensure necessary level of structural safety. Some representative examples of the slender steel structures were used to present this method including steel chimney and three examples of steel lattice telecommunication towers having different heights. Finite Element Method computational models were used to perform static analysis and the Ultimate Limit State was considered. The main attention of the analysis is focused on bending moments of the chimney basis and axial forces in legs of the towers. The generalized stochastic perturbation technique has been programmed in symbolic algebra package MAPLE and used to determine the first two moments of the necessary structural responses of the chimney and the towers. The characteristic wind pressure has been treated here as the input random variable with given expectation and variability interval for the coefficient of variation. Partial safety factors were calculated for different reliability indices β and different coefficients of variation of the environmental load effects. Keywords: partial safety factors, calibration procedure, structural safety, perturbation method, reliability index 1. INTRODUCTION It is obvious that buildings and engineering structures cannot be designed taking into consideration the mean values of all the environmental and dead loads only. Possible failures of these structures often makes the risk for the people and may also have relatively high economic, social and some environmental consequences. Therefore, the appropriate safety level must be maintained and, at the same time, designing of the structures should be accompanied with some optimization procedures. European Standards suggest all to design civil engineering structures using partial safety factors as the coefficients used for impact effects, load capacity or material properties, which result in the certain safety margins. Identification of the reliability level is done thanks to the reliability index β, which takes into account the accepted or adopted level of statistical scattering of these impact effects, carrying capacity and uncertainty of the model depending on the consequences of failure of the designed structure (Ref. 11). Statistical estimation or probabilistic determination of the partial safety factors is the subject of an extensive theoretical, computational and also experimental research. Hicks and Pennington in Ref. 4 present for instance the results from a reliability analysis of the resistance of composite beams in sagging bending, designed according to Eurocode 4. They evaluate these partial factors related to carrying capacity for the structural steel, concrete and shear connection using a methodology contained in Ref. 1. Calibration procedure of the resistance partial factors in modelling of the steel structures reliability according to Eurocodes is presented in Ref. 13 as well. Casas and Chambi in Ref. 1 describe the methodology for a reliability- based calibration of the partial safety factors used for the confined concrete elements in the design of strengthening or seismic retrofitting of bridge piers using fiber reinforced polymers. New material safety factors for the seismic safety assessment were also proposed by Pereira and Romao in Ref. 10 to characterize strength capacity of the existing buildings. There are many new technologies and materials which could be used in civil engineering due to its easy application and excellent mechanical and chemical properties, however partial or a complete lack of the codes, standards and experience in the long term behavior make these solutions reluctantly used by the designers and engineers. Efficient estimation of partial safety factors for material properties allows getting an appropriate safety margin. Usage of the reliability-based design is also common in geotechnical designing. Partial factors are also often used in these codes to overcome the difficulties in performing probabilistic analysis. In Ref. 8 and Ref. 9 authors develop partial safety factors for different geotechnical design applications, including rock slopes stability and design of the support for a rock wedges in an underground opening. The external loads partial safety factors were estimated in Ref. 7 by Lenner and Sykora. These Authors deal with special purpose heavy vehicles on road bridges and propose a methodology for calibration of the related partial factors. Key steps of this approach consist of assessing static load effect, dynamic amplification, model uncertainty, sensitivity factors and final reliability. There is no versatile procedure to calibrate partial safety factors. One of the available approaches was shown in Ref. 2. A quantile-based approach for calibrating reliability-based partial factors that is based on the equivalence principle between the design quantiles for the random variables and the target reliability was presented. According to the Authors the proposed