Performance based design optimization of steel concentric braced structures
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The design of an optimal structural configuration is an iterative process which cannot lead to unique solution and can be extremely time-consuming due to the noticeably large number of variables influencing the design process and the structural behaviour.
Although several studies are early available in the literature aiming to provide optimization design tools, no existing design procedures allow designers to account for both the optimal structural performance at each limit state and the control of constructional and repairing costs after severe and/or unexpected loading conditions (namely earthquake, fire, blast, etc.). These considerations motivated our research, which aims to define a conceptual design process to find the optimal structure. To achieve this goal a numerical algorithm for complex structural optimization of building structures has been developed focusing on seismic performance.
In this paper, an advanced complex structural optimization process is presented, which is able to find optimal structural solutions in consideration of performance at several limit states and control constructional costs and risks. The numerical algorithm has been developed in Matlab, while nonlinear structural analyses have been carried out in OpensSEES [1] finite element program. The methodology and the developed algorithm is illustrated through numerical example of optimization of Concentric Braced Frame (CBF) structures.
For the performance assessment and calculating the life cycle probability of exceedance for specific damage states, the Pacific Earthquake Engineering Research Center (PEER) framework [2] has been followed and implemented in the algorithm. The presented methodology is able to assess the performance of CBF using nonlinear static analysis method and can be effectively used by heuristic optimization. According to the Eurocode standards [3, 4], the acceptable damage and risk has been controlled on Damage Limitation (DL), Significant Damage (SD) and Collapse Prevention (CP) performance levels by earthquakes with 40%, 10% and 2% probability of exceedance in 50 years, respectively. Damage functions have been defined according to [4, 5], and implemented in the algorithm in order to carry out a complete risk analysis. Since the pure structural cost has just a small part in the total cost and the cost of pure structural damage also can be easily far smaller than the cost caused by the damage of non-structural elements and contents, the non-structural components have been considered in the cost calculations and the risk analysis as well.
In the consideration of this study, the feasibility of the developed optimization process is verified with analysis of a set of structures with different geometry and loading conditions. In this paper, typical results are illustrated for the optimization of a six-storey office building located in moderate seismicity area (Budapest, Hungary). Four optimized cases are presented. In three cases out of the four, LCC is minimized regarding different states of damage. The fourth case represents IC minimization (risk is not minimized). However, all of the cases are influenced by the risk related to every performance levels through the probability constraints and the penalty function. IC of the structure is defined as the cost of the bracing system (including cost braces, columns and foundation).
As expected, the minIC design results in the cheapest solution: the initial cost is ~7%, ~ 10% and ~13% lower than in case of DL, SD and CP design, respectively. Nevertheless, this minIC design provides higher risk values.
From the minLCC design cases, the highest reduction in the risk can be achieved in case of the CP design due to the fact that (i) the structural collapse governs the failure of all other components, thus increase in the structural capacity has a great effect on the risk of CP related to other components; (ii) increase in the structural capacity causes some shift of fragility curve, which may mean significant change in the risk by lower probabilities.
The results of the analysis confirm that slightly increasing the initial cost of the bracing system can significantly reduce the seismic risk, especially in case of collapse prevention performance objective. The presented results imply the stable and feasible operation of the developed algorithm.
ACKNOWLEDGMENT
This paper was supported by the Janos Bolyai Research Scholarship of the Hungarian Academy of Sciences.
REFERENCES
[1] Pacific Earthquake Engineering Research Center. Open System for Earthquake Engineering Simulation, http://opensees.berkeley.edu/.
[2] Gregory G. Deierlein, 2004. “Overview of a comprehensive framework for earthquake performance assessment”, Proc. of an International Workshop “Performance-Based Seismic Design Concepts and Implementation”, 28 June – 1 July, 2004, Bled, Slovenia, ISBN 0-9762060-0-5, pp. 15-25.
[3] CEN: EN 1998-1:2008 Eurocode 8, Design of structures for earthquake resistance – Part 1.
[4] CEN: EN 1998-3:2005 Eurocode 8, Design of structures for earthquake resistance – Part 3.
[5] H. Aslani, E. Miranda, 2005. Probabilistic Earthquake Loss Estimation and Loss Disaggregation in Buildings, John A. Blume Earthquake Engineering Center Technical Report 157, Stanford, USA.