Robust Design Optimization- Ensuring Robustness Against Uncertain.pdf

Clemson University TigerPrints All Dissertations Dissertations 8-2013 ROBUST DESIGN OPTIMIZATION: ENSURING ROBUSTNESS AGAINST UNCERTAINTY IN STRUCTURAL DESIGN Zhifeng Liu Clemson University, zhifenl@g.clemson.edu Follow this and additional works at: https://tigerprints.clemson.edu/all_dissertations Part of the Civil Engineering Commons Recommended Citation Liu, Zhifeng, "ROBUST DESIGN OPTIMIZATION: ENSURING ROBUSTNESS AGAINST UNCERTAINTY IN STRUCTURAL DESIGN" (2013) All Dissertations 1157 https://tigerprints.clemson.edu/all_dissertations/1157 This Dissertation is brought to you for free and open access by the Dissertations at TigerPrints It has been accepted for inclusion in All Dissertations by an authorized administrator of TigerPrints For more information, please contact kokeefe@clemson.edu ROBUST DESIGN OPTIMIZATION: ENSURING ROBUSTNESS AGAINST UNCERTAINTY IN STRUCTURAL DESIGN _ A Dissertation Presented to the Graduate School of Clemson University _ In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Civil Engineering _ by Zhifeng Liu August 2013 _ Presented to: Dr Sez Atamturktur, Committee Chair Dr C Hsein Juang, Co-Chair Dr Weichiang Pang Dr Yongxi Huang ABSTRACT In structural design, if robustness is overlooked in design process, the acquired design is likely to have large variation in its performance due to uncertainties In that there is no design specification that explicitly considers the robustness against such uncertainties, this dissertation elucidates design methodologies for use in selecting the optimal design parameters to minimize the effect of the hard to reduce or irreducible uncertainties on structural performance, i.e., maximizing the robustness However, due to limited resources, structural designs are also constrained by available resources and budget Consequently, in that a tradeoff relationship exists between the robustness and cost (i.e the more robust the design, the greater the cost) Therefore, optimizing robustness and cost are conflicting objectives Thus, an explicit consideration of this tradeoff relationship between robustness and cost necessitates formulating a robust design optimization (RDO) as a multi-objective optimization problem, with robustness, cost and other metrics of interest as objectives The outcome of an RDO is a Pareto front, the optimum set reflecting tradeoff between competing objectives, in which the acquired Pareto front designs are more robust and more economical than all other designs Furthermore, with the acquired Pareto front, a more informed decision can be achieved This dissertation applies proposed RDO to two distinct problems, in which the reliability index in foundation design and seismic demand in steel moment resisting frame design are the considered performance measures These measures, in turn, lead to a confidence level based robust design optimization, second order reliability based design optimization, and robust design optimization of steel moment resisting frame ii ACKNOWLEDGEMENTS I would like to thank my advisers Dr Atamturktur and Dr Juang for their valuable guidance and scholarly input Without their guidance and input, I would not have been able to finish my dissertation The discussion with them has made my Ph.D study a thoughtful and rewarding journey I would also like to extend my gratitude to my committee members: Dr Pang and Dr Huang for their review and valuable suggestions Finally, I would like to thank my family, who have supported and helped me by giving encouragement and providing emotional support along the course of this dissertation iii TABLE OF CONTENTS Page TITLE PAGE i ABSTRACT ii ACKNOWLEDGEMENTS iii LIST OF TABLES vi LIST OF FIGURES viii CHAPTER CHAPTER I: INTRODUCTION 1 Motivation Background Overview Problem Statement Dissertation Overview Main Contribution of this Dissertation Dissertation Organization CHAPTER II: CONFIDENCE LEVEL BASED ROBUST DEISGN OF CANTILEVER RETAINING WALL IN SAND Introduction Current Approaches for Treating Uncertainty in Geotechnical Design Framework for the Proposed Confidence Level (CL)-Based Design Approach 10 Case Study: Design of Cantilever Retaining Wall in Sand 13 Simplified Equations for Implementation of CL-Based Design 26 Summary 35 CHAPTER III: SECOND ORDER RELIABILITY-BASED DESIGN OF DRILLED SHAFTS FOR TRANSMISSION LINE STRUCTURES 36 Introduction 36 Background 38 Limit States for Design of Drilled Shafts of Electrical Transmission Line Structure, Subject to Compression under Undrained Load Conditions 41 iv Table Of Contents (Continued) Page Probabilistic characterization of uncertain parameters 45 Development of simplified closed-form models for reliability index 46 Comparison with MRFD and LRFD Approach 58 Relation between ULS Reliability Index and SLS Reliability Index 62 Reliability-based Design Approach 63 Second order reliability-based design approaches 76 10 Summary 84 CHAPTER IV: PERFORMANCE BASED ROBUST DESIGN OPTIMIZATION OF STEEL MOMENT RESISTING FRAMES CONSIDERING GROUND MOTION VARIABILITY 86 Introduction 86 Performance based robust design 88 Methodology: multi-objective optimization and non-dominated sorting genetic algorithm II 92 Steel Moment Resisting Frame Case Study 93 Parametric Analysis 107 Summary 110 CHAPTER V: RELIABILITY BASED MULTI-OBJECTIVE ROBUST DESIGN OPTIMIZATION OF STEEL MOMENT RESISTING FRAME CONSIDERING SPATIAL VARIABILITY OF CONNECTION PARAMETERS 112 Introduction 112 IK Model and its Statistics 114 Case Study Structure: Initial Design 116 Evaluating Seismic Sensitivity of Connection Parameters 117 Evaluating the Importance of Spatial Variability of Connection Parameters 123 Multi-objective Reliability based Robust Design Optimization 128 Summary 135 CHAPTER VI:CONCLUDING REMARKS 136 Summary of Research 136 Major Findings of the Presented Research 137 Limitations and Recommendation for Future Work 142 CITED REFERENCES 143 v LIST OF TABLES Table Page Chapter II Table Sample statistics for example retaining wall 15 Table Mean and cov of cov of soil parameters 15 Table List of design parameters and key results for each of the 16 designs on the Pareto front obtained by the CL-based design method 25 Table.4 Ranges of sample statistics and design parameters for calibration 28 Chapter III Table Summary of probability distribution for random variables 44 Table Values of design parameters for drilled shaft design cases, ULS general failure mode for full factor design of experiment 47 Table Resistance factors for ULS general shear failure mode – LRFD and MRFD 59 Table Accuracy and precision (in terms of β and max) for MRFD approach 60 Table Ranges of FS and Ψc obtained using the regression equation for target reliability index =3.2 61 Table Summary of the drilled shaft unit construction costs (adapted from R S Means Co 2007) 70 Table Coefficient of approximation equations under each covβ 79 Chapter IV Table List of columns and beams 90 Table Characteristics of the ground motions at 2%/50 year seismic hazard level 96 Table 10 Steel section size and objective values of selected designs 100 Chapter V Table Statistics for each parameter of the IK model (Lignos and Krawinkler 2011) 115 Table Correlation coefficient for the IK model parameter (Lignos and Krawinkler 2011) 116 vi List Of Tables (Continued) Table Page Table Ground motions for performing incremental dynamic analysis, as adopted from Vamvatsikos and Cornell (2004) 120 Table Correlation coefficient table for the various spatial variability studies124 Table Section size and objective values for the designs selected from the Pareto front 134 vii LIST OF FIGURES Figure Page Chapter II Figure CL-based design process 13 Figure Illustration of cantilever retaining wall 14 Figure Comparison of accuracy of MCS, new PEM and Taylor expansion in calculating μβ and ζβ 20 Figure Reliability index of different assumed cov for randomly generated designs 21 Figure Distribution of reliability index for a typical design 22 Figure Pareto front and dominated designs 24 Figure Relationship between μβ–ζβ and μβ–CL for sliding failure 27 Figure μβ–ζβ relations and regression equations for different H and all data for sliding failure 29 Figure μβ–ζβ relations and regression equations for different H and all data for bearing capacity failure 30 Figure 10 μβ–ζβ relations and regression equations for different H and all data for eccentricity 31 Figure 11 Regression of ζβ versus μβ for different H for sliding failure 31 Figure 12 μβ-versus-CL plot of all data for sliding failure mode 32 Figure 13 μβ-versus-CL plot of all data for bearing capacity failure mode 32 Figure 14 μβ-versus-CL plot of all data for eccentricity failure mode 33 Figure 15 Relationship between μβ and CL for all failure modes 33 Chapter III Figure Relation between FS and β for all designs for ULS general shear failure mode 49 Figure Effect of each design parameter on β for ULS, general shear failure mode 50 Figure Actual β (obtained by FORM) vs predicted β for all design cases for ULS general shear failure mode 52 Figure Effect of each design parameter on β for SLS, general shear failure mode 53 Figure Actual β (obtained by FORM) vs predicted β for all design cases for SLS general shear failure mode 54 Figure Effect of each design parameter on β for ULS, local shear failure mode 55 viii C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an List Of Figures (Continued) Figure Page Figure Actual β (obtained by FORM) vs predicted β for all design cases for ULS local shear failure mode 56 Figure Effect of each design parameter on β for SLS, local shear failure mode 57 Figure Actual β (obtained by FORM) vs predicted β for all design cases for SLS local shear failure mode 58 Figure 10 Relation between ULS β and SLS β under different ya for general shear failure mode 63 Figure 11 Relation between ULS β and SLS β under different ya for local shear failure mode 63 Figure 12 A target FS for a given target reliability index for the ULS, general shear failure: (a) βT =2.8; (b) βT =3.2; (c) βT =3.6; (d) βT =4.0 65 Figure 13 A target FS for a given target reliability index for the ULS, local shear failure: (a) βT =2.8; (b) βT =3.2; (c) βT =3.6; (d) βT =4.0 66 Figure 14 A design example of the drilled shaft in an undrained compression 70 Figure 15 The Pareto front designs and the dominated design for the design example of the reliability based design approach 71 Figure 16 The dimensions for the dominated and Pareto front designs 73 Figure 17 The Pareto front for different assumed covsu 75 Figure 18 The μβ versus the βTR curve under several assumed covβ 78 Figure 19 The predicted βTR versus the actual βTR 80 Figure 21 The contour plot of μβ and δβ for ULS, local shear failure mode of drilled shaft 81 Figure 22 The contour plot of βTR for ULS, the general failure mode and the local shear failure mode of the drilled shaft 82 Figure 23 Pareto front designs and dominated design for a true reliability based design approach 83 Chapter IV Figure Elevation view and plan view of the example steel moment resisting frame 94 Figure Sa and Sd response spectrum for 2%50 year seismic hazard level Los Angles ground motions with 5% damping 97 Figure Modified IK deterioration model (a).Monotonic curve (b) Cyclic determination curve (Lignos and Krawinkler 2011) 97 Figure Pareto Front and dominated designs (a) 3D view; (b) Relation between weight and ζdrift; (c) Relation between weight and μdrift; (d) Relation between μdrift and ζdrift 99 Figure CDF of inter-story drift of six selected designs 101 ix Stt.010.Mssv.BKD002ac.email.ninhd.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj.dtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an consider both safety (reliability) and cost With this novel enumeration and visualization method, designers may also easily construct a Pareto front without any multi-objective optimization 6) The SRBD (Second Order Reliability-Based Design) approach improves the robustness of the reliability-based design approach against the uncertainty in the estimated statistics of input parameters The proposed SRBD approach requires little extra effort over the calculation of the traditional reliability index on the part of the user In fact, closed-form simplified equations are available for SRBD 7) Based on the Pareto front acquired for various design conditions using both the RBD and SRBD approaches, the criterion ―D/B ≤ 3.7‖ was employed for ensuring cost effective designs of drilled shafts for transmission line structures under compression in undrained loading conditions Using this criterion, a cost effective design can be achieved that does not require the development of either a complex optimization processes or Pareto front based designs 8) The developed closed-form equations for the RBD and SRBD approaches, implemented in either site-specific FS-based procedure or Pareto front-based procedure, are shown effective in designing drilled shafts for transmission line structures that are subjected to compression in an undrained loading condition Similar development processes can be undertaken to create applicable simplified equations, much like the calibration of LRFD factors to solve different geotechnical problems using different geotechnical models Findings and observations from the performance based robust design (Chapter IV): 1) The performance based robust design methodology proposed can provide a set of competing designs that are economical, safe and robust in the form of a Pareto front, 139 Stt.010.Mssv.BKD002ac.email.ninhd.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj.dtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an with which structural engineers and stakeholders can make informative tradeoff decisions in a preferred manner 2) Pareto front designs are superior to dominated designs in terms of cost, safety and robustness, while traditional trial and error method would most probably result in a dominated design (inefficient design) rather than a Pareto front design (efficient design), as Pareto front designs only occupy a small proportion of all designs in solution space 3) For identical mean value of seismic demand, variation of seismic demand can be reduced through adjusting design variables and a safer design can be achieved 4) Uniformity drift ratio can be served as design efficiency indicator effectively Efficient designs generally have smaller uniformity ratio, while inefficient designs generally have larger uniformity ratio Required uniformity drift ratio for each range of maximum inter-story drift for ensuring efficient designs is suggested With the suggested requirement enforced, efficient designs can be achieved with the trial and error process without complex optimization 5) The Pareto front solution is just marginally influenced by the selected connection model The Pareto front based on R=8, satisfied the much stricter strength requirement with a smaller R factor (R=3) Pareto front solutions with a greater R factor are observed to dominate solutions obtained with a lesser R factor Findings and observations from the multi-objective reliability based design (Chapter V): 1) The proposed multi-objective reliability based design optimization methodology improved the collapse prevention reliability, even with an inherent parameter uncertainty, resulting in a tradeoff between how well this methodology would 140 Stt.010.Mssv.BKD002ac.email.ninhd.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj.dtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an prevent a collapse and the cost of using this methodology Consequently, a tradeoff decision is deemed necessary to finalize the design based upon the Pareto front 2) A sensitivity study based upon pushover analysis determines that the pre-capping rotation (Өp), the post yield strength ratio (Mc/My), the effective yield moment to yield moment ratio (My/My,p) and the yield strength (Fy) influenced the pushover curve as soon as the frame yields Additionally, the post-capping rotation (Өpc) exert no influence on push-over curve until the capping point is exceeded, with κ showing the effect on the push-over curve later than all other parameters Of all the parameters, My/My,p, and Fy shows a greater effect on the pushover curve 3) A sensitivity study based upon an incremental dynamic analysis determines that the My/Myp, Fy, Mc/My and Өpc exhibit the most significant effect on the median incremental dynamic analysis curve, while the effect of Өp and the cyclic deterioration ratio (ᴧ) is almost negligible The effect of the residual strength ratio (κ) on median IDA curve, is not negligible, however, with the effect (κ) ratio exhibiting much later than all other parameters 4) A spatial variability study based on incremental dynamic analysis determines that the perfect uncorrelated correlation assumption leads to a larger variation in seismic response when the maximum inter-story drift ratio is small (less than 3% in the example frame studied) Inversely, the perfect correlation assumption results in a larger variation in seismic response as the maximum inter-story drift ratio became larger For the larger maximum inter-story drift ratio (larger than 3% in the example studied), the perfect correlation assumption is very conservative 5) A smaller maximum inter-story drift ratio determines that an increase in the interfloor correlation correspondingly decreases the dispersion of median incremental 141 Stt.010.Mssv.BKD002ac.email.ninhd.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj.dtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an dynamic analysis curve caused by uncertainties in the connection parameters For the larger maximum inter-story drift ratio, an increase in the inter-floor correlation causes an increase in the dispersion of the median incremental dynamic analysis curve from the uncertainty in the connection parameters Limitations and Recommendation for Future Work To further expand the work presented in this dissertation, a number of research topics can be undertaken, which include the following: 1) In both confidence level based design and second-order reliability based design approaches, the epistemic uncertainty is from the uncertainty in coefficient of variation of soil parameters The approaches can be extended to consider uncertainty from mean value of soil parameters in future 2) In performance based robust design approach, modal pushover analysis instead of the most rigorous nonlinear dynamic method is employed to calculate seismic demand for computational applicability consideration Though modal push over analysis can provide results with comparable accuracy, result based on nonlinear dynamic method would be more persuading As a result, effort will be made to implement the methodology with nonlinear dynamic method employed 3) The performance based robust design and reliability based multi-objective robust design approaches in this dissertation can be straightforwardly implemented using many other design codes Thus, future study is recommended to further develop this approach according to other building codes (e.g Eurocode) 142 Stt.010.Mssv.BKD002ac.email.ninhd.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj.dtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an CITED REFERENCES CHAPTER I Beyer, H., Sendhoff, B (2007), ―Robust Optimization – A Comprehensive Survey,‖ Computer Methods in Applied Mechanics and Engineering, Vol 196, pp 3190-3218 Charnes, A.; Cooper, W.W (1977), ―Goal programming and multiple objective optimization.‖, part Eur J Oper Res.1, 39–54 Chen W., Wiecek, M., Zhang, J (1999), ―Quality Utility: A Compromise Programming Approach to Robust Design", ASME Journal of Mechanical Design, Vol 121, No 2, pp.179187 Deb, K., Pratap, A., Agarwal, S (2002), ―A Fast and Elitist Multiobjective Genetic algorithm: NSGA-II,‖ IEEE Transactions on Evolutionary Computation, Vol 6, No 2, pp 182-197 Ellingwood, B., Galambos, T V., MacGregor, J G., and Cornell, C A Development of a probability based load criterion for American National Standard A58 NBS Spec Publ 577, National Bureau of Standards (NBS), Washington, D.C.; 1980 Lagaros, N.D., Papadrakakis, M (2007a) ―Robust seismic design optimization of steel structures‖, Struct 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1984 Bourdeau, P L., Amundaray, J I Non-parametric simulation of geotechnical variability Géotechnique 2005; 55(2): 95-108 Coduto, D.P Foundation design: principles and practices, 2nd edn, Prentice Hall, New Jersey; 2010 Coulomb, C A Essai sur une application des regles des maximis et minimis a quelquels problemesde statique relatifs, a la architecture Mem Acad Roy Div Sav., vol 7, 343–387; 1776 Dai, S.H., and Wang, M.O Reliability analysis in Engineering Applications Von Nostrand Reinhold, New York; 1992 Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T A fast and elitist multiobjective genetic algorithm: NSGA-II IEEE Transactions on Evolutionary Computation 2002; 6(2): 182-97 Deodatis, G., and Shinozuka, M Stochastic FEM analysis of nonlinear dynamic problems Probabilistic Methods in Civil Engineering, Proceedings of the 5th ASCE Specialty Conference 1988, ASCE, Blacksburg, VA, 152-155 Duncan, J M Factors of safety and reliability in geotechnical engineering J.Geotech.Geoenviron.Eng 2000; 126(4): 307-316 Ellingwood, B., Galambos, T V., MacGregor, J G., and Cornell, C A Development of a probability based load criterion for American National Standard A58 NBS Spec Publ 577, National Bureau of Standards (NBS), Washington, D.C.; 1980 Harr, M E Reliability-based design in civil engineering, Mc-Graw-Hill, New York; 1987 Huang, B., and Du, X Analytical robustness assessment for robust design Structural and Multidisciplinary Optimization 2007; 34(2): 123-137 Jaksa, M B., Goldsworthy, J S., Fenton, G A., Kaggwa, W S., Griffiths, D V., Kuo, Y L, and Poulos, H G Towards reliable and effective site investigations Géotechnique 2005; 55(2): 109-121 Kulhawy, F H On the evaluation of soil properties ASCE Geotech Spec Publ 1992; 31: 95– 115 Low, B K Reliability-based design applied to retaining walls Géotechnique 2005; 55(1): 63-75 Phoon K K., and Kulhawy, F H Characterization of geotechnical variability Canadian Geotechnical Journal 1999a; 36(4): 612-624 144 Stt.010.Mssv.BKD002ac.email.ninhd.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj.dtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an Phoon K K., and Kulhawy, F H Characterization of geotechnical variability Canadian Geotechnical Journal 1999b; 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AC-8: 59–60 CHAPTER V American Institute of Steel Construction (AISC) (2010) ―AISC 341 Seismic provisions for structural steel buildings.‖ Chicago American Society of Civil Engineers(ASCE) (2010) ―ASCE-7 Minimum Design Loads for Buildings.‖ Reston Applied Technology Council (ATC) (2005) Improvement of nonlinear static seismic analysis procedures Rep No FEMA-440, Washington, D.C Celika, Ozan C., Ellingwood, Bruce R., (2010) ―Seismic fragilities for non-ductile reinforced concrete frames – Role of aleatoric and epistemic uncertainties‖ Structural Safety, Vol 32, No 1, pp 1-12 Deb, K., Pratap, A., Agarwal, S (2002) ―A Fast and Elitist Multiobjective Genetic algorithm: NSGA-II.‖ IEEE Transactions on Evolutionary Computation 6(2):182-197 Federal Emergency Management Agency (FEMA) (2000) ―Prestandard and commentary for seismic rehabilitation of buildings.‖ Rep No FEMA-356, Washington D.C 151 Stt.010.Mssv.BKD002ac.email.ninhd.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj.dtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an Federal Emergency Management Agency (FEMA) (2009) ―Recommended Methodology for Quantification of Building System Performance and Response Parameters.‖ Rep No FEMA P695, Project ATC-63, Prepared by the Applied Technology Council, Redwood City, CA Foutch, D A., and Shi, S Connection element (type 10) for DRAIN-2DX Dept of Civ Engr., University of Illinois at Urbana-Champaign, Ill; 1996 Fragiadakis M, Lagaros ND, Papadrakakis M Performance-based multiobjective optimum design of steel structures considering life-cycle cost Structural and Multidisciplinary Optimization 2006; 32: 1–11 Ibarra, L.F., Medina, R.A and Krawinkler, H (2005) ―Hysteretic models that incorporate strength and stiffness deterioration.‖ Earthquake Eng Struct Dyn 34, 1489–1511 Jalayer, Fatemeh and Cornell, C Allin (2003) ―A technical framework for probability-based demand and capacity factor design (DCFD) seismic formats.‖ PEER-2003/08, Pacific Earthquake Engineering Research Center, University of California, Berkeley Lagaros, N.D., Papadrakakis, M (2007a) ―Robust seismic design optimization of steel structures‖, Struct Multidisc Optim, Vol 33, pp 457–469 Lagaros, N.D., Fragiadakis, M (2007b) ―Robust performance based design optimization of steel moment resisting frames‖, Journal of Earthquake Engineering, Vol 11(5), pp 752-772 Lignos, D G., Krawinkler, H (2011) ―Deterioration Modeling of Steel Beams and Columns in Support to Collapse Prediction of Steel Moment Frames‖, ASCE Journal of Structural Engineering,Vol 137 (11), pp 1291-1302 Liu, M., Burns, S A., and Wen, Y K (2005) ―Multiobjective optimization for performancebased seismic design of steel moment frame structures‖ Earthquake Engineering and Structural Dynamics 34(3): 289-306 Luco, Nicolas and Cornell, C.Allin (2000) ―Effects of Connection Fractures on SMRF Seismic Drift Demands‖, ASCE Journal of Structural Engineering, Vol 126, No 1, pp.127-136 Kazantzi A K., Righiniotis T D and Chryssanthopoulos M K (2008) ―Fragility and hazard analysis of a welded steel moment resisting frame‖, Journal of Earthquake Engineering, Vol 12, No 4, pp 596–615 Kishi N, Chen WF Moment–rotation relations of semi rigid connections with angles J Struct Engng ASCE 1990, 116(7):1813–33 Nair, V N., Abraham, B., MacKay, J., Nelder, J A., Box, G., Phadke, M S., et al (1992) ―Taguchi's Parameter Design: A Panel Discussion.‖ Technometrics; 34(2): 127-161 Park, Gyung-Jin, Lee, Tae-Hee, Lee, Kwon Hee, Hwang, K-H (2006) ―Robust Design: An Overview,‖ AIAA Journal, Vol 44, No 1, pp 181-191 152 Stt.010.Mssv.BKD002ac.email.ninhd.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj.dtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.vT.Bg.Jy.Lj.Tai lieu Luan vT.Bg.Jy.Lj van Luan an.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an Stt.010.Mssv.BKD002ac.email.ninhd.vT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.LjvT.Bg.Jy.Lj.dtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn