EVALUATION OF PUSHOVER ANALYSIS PROCEDURES FOR FRAME .

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EVALUATION OF PUSHOVER ANALYSIS PROCEDURESFOR FRAME STRUCTURESA THESIS SUBMITTED TOTHE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCESOFMIDDLE EAST TECHNICAL UNIVERSITYBYSERMİN OĞUZIN PARTIAL FULFILLMENT OF THE REQUIREMENTSFORTHE DEGREE OF MASTER OF SCIENCEINCIVIL ENGINEERINGAPRIL 2005

Approval of the Graduate School of Natural and Applied SciencesProf. Dr. Canan ÖzgenDirectorI certify that this thesis satisfies all the requirements as a thesis for the degree of Master ofScience.Prof. Dr. Erdal ÇokçaHead of DepartmentThis is to certify that we have read this thesis and that in our opinion it is fully adequte, inscope and quality, as a thesis for the degree of Master of Science.Asst. Prof. Dr. Ahmet YakutSupervisorExamining Committee MembersProf. Dr. Polat Gülkan(METU, CE)Asst. Prof. Dr. Ahmet Yakut(METU, CE)Prof. Dr. Haluk Sucuoğlu(METU, CE)Asst. Prof. Dr. Sinan Akkar(METU, CE)Asst. Prof. Dr. Burcu Güneş(ATILIM UNIVERSITY)

I hereby declare that all information in this document has been obtained andpresented in accordance with academic rules and ethical conduct. I also declare that,as required by these rules and conduct, I have fully cited and referenced all materialand results that are not original to this work.Name, Last name : Sermin OĞUZSignatureiii:

ABSTRACTEVALUATION OF PUSHOVER ANALYSIS PROCEDURESFOR FRAME STRUCTURESOğuz, SerminM.S., Department of Civil EngineeringSupervisor : Asst. Prof. Dr. Ahmet YakutApril 2005, 156 pagesPushover analysis involves certain approximations and simplifications that someamount of variation is always expected to exist in seismic demand prediction of pushoveranalysis. In literature, some improved pushover procedures have been proposed toovercome the certain limitations of traditional pushover procedures.The effects and the accuracy of invariant lateral load patterns utilised in pushoveranalysis to predict the behavior imposed on the structure due to randomly selectedindividual ground motions causing elastic and various levels of nonlinear response wereevaluated in this study. For this purpose, pushover analyses using various invariant lateralload patterns and Modal Pushover Analysis were performed on reinforced concrete andsteel moment resisting frames covering a broad range of fundamental periods. Certainresponse parameters predicted by each pushover procedure were compared with the 'exact'results obtained from nonlinear dynamic analysis. The primary observations from thestudy showed that the accuracy of the pushover results depends strongly on the load path,properties of the structure and the characteristics of the ground motion.Pushover analyses were performed by both DRAIN-2DX and SAP2000. Similarpushover results were obtained from the two different softwares employed in the studyiv

provided that similar approach is used in modeling the nonlinear properties of members aswell as their structural features.The accuracy of approximate procedures utilised to estimate target displacementwas also studied on frame structures. The accuracy of the predictions was observed todepend on the approximations involved in the theory of the procedures, structuralproperties and ground motion characteristics.Keywords: Pushover analysis, seismic performance evaluation, nonlinear response, ModalPushover Analysis, approximate proceduresv

ÖZÇERÇEVE YAPILARDA İTME ANALİZİ YÖNTEMLERİNİNDEĞERLENDİRİLMESİOğuz, SerminYüksek Lisans, İnşaat Mühendisliği BölümüTez Yöneticisi : Y. Doç. Dr. Ahmet YakutNisan 2005, 156 sayfaElastik ötesi itme analizinin bazı basitleştirilmiş yaklaşımlar içermesi,elastik ötesi itme analizi sismik davranış tahminlerinin gerçek davranıştan herzaman bir miktar farklı olmasına neden olmaktadır. Geleneksel elastik ötesi itmeanalizinin içerdiği bazı kısıtlamaları gidermek için literatürde gelişmiş elastik ötesiitme analizi yöntemleri önerilmiştir.Bu çalışmada, elastik ötesi itme analizinde kullanılan sabit yatay yükdağılımlarının, rastgele seçilen yer hareketleri nedeniyle elastik ve farklı rilmiştir. Bu amaçla, farklı sabit yatay yük dağılımları kullanılarakelastik ötesi itme analizleri ve Modal Elastik Ötesi İtme Analizi geniş bir birincimod periyodu aralığını kapsayan betonarme ve çelik çerçevelerde uygulanmıştır.Herbir analiz yöntemi tarafından tahmin edilen bazı davranış parametreleri elastikötesi dinamik analizden elde edilen gerçek sonuçlarla karşılaştırılmıştır. Yapılanvi

çalışma üzerindeki temel gözlemler elastik ötesi itme analizi sonuçlarının yükdağılımı, yapı ve yer hareketi özelliklerine son derece bağlı olduğunu göstermiştir.Elastik ötesi itme analizleri DRAIN-2DX ve SAP2000 programları ileyapılmıştır. Her iki programın da elastik ötesi eleman özellikleri ve yapısalözellikleri modellemede benzer yaklaşımlar kullanması nedeniyle programlardanbenzer elastik ötesi itme analizi sonuçları elde edilmiştir.Maksimum global deplasman tahmin edilmesinde kullanılan yaklaşıkyöntemlerin doğruluk derecesi de çerçeve yapılar üzerinde değerlendirilmiştir.Tahminlerin doğruluk seviyesinin yöntemlerin teorisinde yer alan basitleştirilmişyaklaşımlar, yapısal özellikler ve yer hareketi özelliklerine bağlı olduğu gözlemlenmiştir.Anahtar Kelimeler : Elastik ötesi itme analizi, sismik performans değerlendirmesi,elastik ötesi davranış, Modal Elastik Ötesi İtme Analizi, yaklaşık yöntemlervii

ACKNOWLEDGMENTSThis study was conducted under the supervision of Asst. Prof. Dr. Ahmet Yakut. Iwould like to express my sincere appreciation for the support, guidance and insights thathe has provided me throughout the study.I am thankful to Serhat Bayılı and Ufuk Yazgan for their helps in this study.Nazan Yılmaz Öztürk is highly acknowledged for her supports and closefriendship throughout my graduate life.I would like to thank my friends at Structural Mechanics Laboratory; Emre Akın,Seval Pınarbaşı, Sezgin Küçükçoban, Beyhan Bayhan, Dilek Okuyucu, Gökhan Özdemir,Emrah Erduran, Hakan Erdoğan, Okan Özcan, Tuğba Eroğlu and Barış Erdil for theirfriendship during my assistantship at METU.My dear friend Emre Kara deserves thanks for his invaluable friendship.I would like to express my deepest appreciation to my parents -the most preciouspeople in my life- for their confidence in me and for the support, love and understandingthat they have provided me throughout my life.viii

TABLE OF CONTENTSPAGEPLAGIARISM . iiiABSTRACT. ivÖZ . viACKNOWLEDGMENTS . viiiTABLE OF CONTENTS. ixCHAPTER1. INTRODUCTION. 11.1BACKGROUND . 11.2METHODS OF ANALYSIS. 21.2.1 Elastic Methods of Analysis. 21.2.2 Inelastic Methods of Analysis . 31.2.3 Summary . 41.3DESCRIPTION OF PUSHOVER ANALYSIS. 41.3.1 Use of Pushover Results. 51.3.2 Limitations of Pushover Analysis . 61.3.3 Summary . 91.4 OBJECTIVE AND SCOPE . 9ix

PAGE2. REVIEW OF PREVIOUS RESEARCH . 112.1GENERAL . 112.2PAST STUDIES ON SIMPLIFIED NONLINEARANALYSIS PROCEDURES. 112.3PAST STUDIES ON PUSHOVER ANALYSIS . 153. PUSHOVER ANALYSIS WITHDRAIN-2DX vs SAP2000 . 213.1GENERAL . 213.2PUSHOVER ANALYSIS PROCEDURE . 213.3PUSHOVER ANALYSIS WITH DRAIN-2DX. 233.3.1 Implementation of Pushover Analysis byDRAIN-2DX .233.3.2 Element Description of DRAIN-2DX.243.4PUSHOVER ANALYSIS WITH SAP2000 . 263.4.1 Element Description of SAP2000 .313.4.2 Force-Displacement Relationships.323.4.2.1 Default vs User-Defined HingeProperties for Steel Sections .343.4.2.2 Default vs User-Defined HingeProperties for Concrete Sections .353.5COMPARISON OF PUSHOVER ANALYSIS WITHDRAIN-2DX vs SAP2000 . 394. SEISMIC DEMAND PREDICTION BY PUSHOVERANALYSIS FOR FRAME STRUCTURES. 494.1INTRODUCTION . 494.2DESCRIPTION OF CASE STUDY FRAMES . 50x

4.3NONLINEAR TIME HISTORY ANALYSES. 514.4PUSHOVER ANALYSES. 534.5MODAL PUSHOVER ANALYSIS (MPA) PROCEDURE . 594.6COMPARISON AND INTERPRETATION OF RESULTS. 624.6.1 Global Structure Behavior.624.6.2 Story Displacements.664.6.3 Inter-Story Drift Ratios .774.6.4 Story Pushover Curves .884.6.5 Plastic Hinge Locations.924.6.6 Accuracy of Modal Pushover Analysis (MPA)Predictions.974.7SUMMARY AND DISCUSSION OF RESULTS. 985. ESTIMATION OF INELASTIC DISPLACEMENTDEMAND . 1015.1GENERAL . 1015.2NONLINEAR DYNAMIC ANALYSIS OFEQUIVALENT SDOF SYSTEM . 1025.3CAPACITY SPECTRUM METHOD (ATC-40 PROCEDURE A) . 1075.4DISPLACEMENT COEFFICIENT METHOD (FEMA-356). 1105.5CONSTANT DUCTILITY PROCEDURE (CHOPRA&GOEL). 1115.6COMPARISON AND INTERPRETATION OF RESULTS. 1135.7SUMMARY AND DISCUSSION OF RESULTS. 1246. CONCLUSIONS AND FUTURE STUDYRECOMMENDATIONS . 1266.1SUMMARY . 1266.2CONCLUSIONS . 127xi

PAGE6.3RECOMMENDATIONS FOR FUTURE STUDY . 133REFERENCES. 134APPENDIXA. FRAME DATA AND RESULTS OF PUSHOVERANALYSIS . 140A.1 DESCRIPTION OF CASE STUDY FRAMES . 140A.1.1 REINFORCED CONCRETE FRAMES. 140A.1.2 STEEL FRAMES. 144A.2 STORY PUSHOVER CURVES FOR STEEL FRAMES . 147A.3 PLASTIC HINGE LOCATIONS . 150xii

CHAPTER 1INTRODUCTION1.1 BACKGROUNDNonlinear static analysis, or pushover analysis, has been developed over the pasttwenty years and has become the preferred analysis procedure for design and seismicperformance evaluation purposes as the procedure is relatively simple and considers postelastic behavior. However, the procedure involves certain approximations andsimplifications that some amount of variation is always expected to exist in seismicdemand prediction of pushover analysis.Although, in literature, pushover analysis has been shown to capture essentialstructural response characteristics under seismic action, the accuracy and the reliability ofpushover analysis in predicting global and local seismic demands for all structures havebeen a subject of discussion and improved pushover procedures have been proposed toovercome the certain limitations of traditional pushover procedures. However, theimproved procedures are mostly computationally demanding and conceptually complexthat use of such procedures are impractical in engineering profession and codes.As traditional pushover analysis is widely used for design and seismicperformance evaluation purposes, its limitations, weaknesses and the accuracy of itspredictions in routine application should be identified by studying the factors affecting thepushover predictions. In other words, the applicability of pushover analysis in predictingseismic demands should be investigated for low, mid and high-rise structures byidentifying certain issues such as modeling nonlinear member behavior, computationalscheme of the procedure, variations in the predictions of various lateral load patternsutilized in traditional pushover analysis, efficiency of invariant lateral load patterns in1

representing higher mode effects and accurate estimation of target displacement at whichseismic demand prediction of pushover procedure is performed.1.2 METHODS OF ANALYSISFor seismic performance evaluation, a structural analysis of the mathematicalmodel of the structure is required to determine force and displacement demands in variouscomponents of the structure. Several analysis methods, both elastic and inelastic, areavailable to predict the seismic performance of the structures.1.2.1 Elastic Methods of AnalysisThe force demand on each component of the structure is obtained and comparedwith available capacities by performing an elastic analysis. Elastic analysis methodsinclude code static lateral force procedure, code dynamic procedure and elastic procedureusing demand-capacity ratios. These methods are also known as force-based procedureswhich assume that structures respond elastically to earthquakes.In code static lateral force procedure, a static analysis is performed by subjectingthe structure to lateral forces obtained by scaling down the smoothened soil-dependentelastic response spectrum by a structural system dependent force reduction factor, "R". Inthis approach, it is assumed that the actual strength of structure is higher than the designstrength and the structure is able to dissipate energy through yielding.In code dynamic procedure, force demands on various components are determinedby an elastic dynamic analysis. The dynamic analysis may be either a response spectrumanalysis or an elastic time history analysis. Sufficient number of modes must beconsidered to have a mass participation of at least 90% for response spectrum analysis.Any effect of higher modes are automatically included in time history analysis.In demand/capacity ratio (DCR) procedure, the force actions are compared tocorresponding capacities as demand/capacity ratios. Demands for DCR calculations mustinclude gravity effects. While code static lateral force and code dynamic proceduresreduce the full earthquake demand by an R-factor, the DCR approach takes the fullearthquake demand without reduction and adds it to the gravity demands. DCRsapproaching 1.0 (or higher) may indicate potential deficiencies.Although force-based procedures are well known by engineering profession andeasy to apply, they have certain drawbacks. Structural components are evaluated forserviceability in the elastic range of strength and deformation. Post-elastic behavior of2

structures could not be identified by an elastic analysis. However, post-elastic behaviorshould be considered as almost all structures are expected to deform in inelastic rangeduring a strong earthquake. The seismic force reduction factor "R" is utilized to accountfor inelastic behavior indirectly by reducing elastic forces to inelastic. Force reductionfactor, "R", is assigned considering only the type of lateral system in most codes, but it hasbeen shown that this factor is a function of the period and ductility ratio of the structure aswell [38].Elastic methods can predict elastic capacity of structure and indicate where thefirst yielding will occur, however they don’t predict failure mechanisms and account forthe redistribution of forces that will take place as the yielding progresses. Realdeficiencies present in the structure could be missed. Moreover, force-based methodsprimarily provide life safety but they can’t provide damage limitation and easy repair.The drawbacks of force-based procedures and the dependence of damage ondeformation have led the researches to develop displacement-based procedures for seismicperformance evaluation. Displacement-based procedures are mainly based on inelasticdeformations rather than elastic forces and use nonlinear analysis procedures consideringseismic demands and available capacities explicitly [22].1.2.2 Inelastic Methods of AnalysisStructures suffer significant inelastic deformation under a strong earthquake anddynamic characteristics of the structure change with time so investigating the performanceof a structure requires inelastic analytical procedures accounting for these features.Inelastic analytical procedures help to understand the actual behavior of structures byidentifying failure modes and the potential for progressive collapse. Inelastic analysisprocedures basically include inelastic time history analysis and inelastic static analysiswhich is also known as pushover analysis.The inelastic time history analysis is the most accurate method to predict the forceand deformation demands at various components of the structure. However, the use ofinelastic time history analysis is limited because dynamic response is very sensitive tomodeling and ground motion characteristics. It requires proper modeling of cyclic loaddeformation characteristics considering deterioration properties of all importantcomponents. Also, it requires availability of a set of representative ground motion recordsthat accounts for uncertainties and differences in severity, frequency and durationcharacteristics. Moreover, computation time, time required for input preparation and3

interpreting voluminous output make the use of inelastic time history analysis impracticalfor seismic performance evaluation.Inelastic static analysis, or pushover analysis, has been the preferred method forseismic performance evaluation due to its simplicity. It is a static analysis that directlyincorparates nonlinear material characteristics. Inelastic static analysis procedures includeCapacity Spectrum Method [3], Displacement Coeffi

Nonlinear static analysis, or pushover analysis, has been developed over the past twenty years and has become the preferred analysis procedure for design and seismic performance evaluation purposes as the procedure is relatively simple and considers post- elastic behavior. However, the procedure involves certain approximations and simplifications that some amount of variation is always .

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