Reliability assessment of concentrically braced frames. Risk-based seismic performance assessment of Eurocode conform design

Gulyás, Gyöngyi and Zsarnóczay, Ádám and Vigh, László Gergely (2014) Reliability assessment of concentrically braced frames. Risk-based seismic performance assessment of Eurocode conform design. In: EUROSTEEL 2014, 10-12. September 2014, Naples, Italy.

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Abstract

The concept and methodology of structural reliability analysis is controlled by the Eurocode 0 (EC0, [1]) standard in Europe for several common scenarios: basic rules and requirements including reliability differentiation of structures and the target probability of failure (or reliability index) are prescribed by the code. Eurocode 8-1 (EC8-1, [2]) requires design checks of buildings at two performance objective levels: a) no-collapse (ultimate limit state); b) damage limitation (serviceability limit state); for which states, however, there is no custom target value of the reliability index defined. Furthermore, no comprehensive study is available on the reliability of the simplified capacity design procedures in EC8-1. This paper examines a common structural solution – Concentrically Braced Frames (CBF) – and assesses the collapse probability of a set of typical representations of such structures to provide information on the reliability of Eurocode conform structural design. The seismic performance assessment methodology is based on the FEMA P695 [3] framework using incremental dynamic analysis (IDA), and extended with the calculation of failure probability. A total of 6 archetype CBF structures with X-bracing were designed varying the storey number (2-4-6 stories) and the dissipation capacity (quasi-elastic or dissipative structure with q = 1.5 or 4.0, respectively). A peak ground acceleration agR = 0.3 g is considered; with ground type D and Type I response spectrum. The considered dead load is 6.5 and 4.5 kN/m2, while the live load is 3.0 and 1.0 kN/m2 on the intermediate and roof floors, respectively. Combination factor of the live load is 0.3. The floor area is 30x24 m. Design of the buildings is completed by using modal response spectrum analysis and capacity design rules in accordance with EC8-1. For the non-linear dynamic analysis, numerical models for the structures are developed in the OpenSees [4]. Simplified planar models with non-linear material models and equivalent geometric imperfections are applied. The time-history analysis results in IDA curves. Fragility curve reflecting the conditional probability of failure with given seismic intensity is determined from the IDA results, and modified to handle additional sources of uncertainties. Site specific hazard curve describing the relationship between seismic intensity and the probability of occurrence of ground motions with such intensity is generated using EFEHR [5]. The collapse probability density function is obtained as the product of the hazard probability density function and the fragility curve. The total probability of collapse is calculated by numerically integrating the collapse PDF over the entire spectral acceleration domain. The obtained reliability index values fall within the range of 2.25 ~ 3.06 and 3.14 ~ 3.79 in case of the dissipative and the quasi-elastic structures, respectively. These values are lower than the target values prescribed by EC0 for ultimate limit state (RC2, BETAtarget = 3.8, meaning 0.01% probability of failure over lifetime, [1]). This observation may be interpreted as the design provisions of EC8-1 conflict EC0 rules and the minimum safety level is not assured. Note that, however, it is only possible to achieve the 0.01% probability of failure if the designed structure does not collapse from a ground motion with 0.01% probability of occurrence over the lifetime of the structure. Such a ground motion is extremely rare and the authors believe that it is not economical to design a structure to resist such rare effects. Accordingly, one may conclude to that seismic specific target values of reliability index shall be introduced. By accepting the compliance of EC8-1, the target value should be lower than 2.25, i.e. higher risk can be associated to seismic events. Such distinction is also made by JCSS [6]. For further details on the research refer to [7]. ACKNOWLEDGMENT This paper was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences. REFERENCES [1] EN 1990:2005 Eurocode: Basis of structural design. Brussels: CEN. [2] EN 1998-1:2008 Eurocode 8: Design of structures for earthquake resistance – Part 1: General rules, seismic actions and rules for buildings. Brussels: CEN. [3] FEMA P695. 2009. Quantification of building seismic performance factors, Federal Emergency Management Agency (FEMA), Washington, D.C. [4] McKenna F., Feneves G.L. 2012. Open system for earthquake engineering simulation, Pacific Earthquake Engineering Research Center [5] European Facility for Earthquake Hazard and Risk (EFEHR), Available at: www.efehr.org [6] Joint Committee on Structural Safety (JCSS): Probabilistic Model Code, 2000. [7] Gulyás Gy. 2013. Reliability analysis of steel building structures in high seismicity zones – Analysis of quasi-elastic and dissipative concentrically braced frames. MSc thesis. BME Dept. Struct. Eng.

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