Lateral Behaviour and DirectDisplacement Based Design of a NovelHybrid Structure: Cross LaminatedTimber Infilled Steel MomentResisting FramesbyMatiyas BezabehB.Sc., Addis Ababa University, 2011A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE COLLEGE OF GRADUATE STUDIES(Civil Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Okanagan)August 2014c© Matiyas Bezabeh, 2014AbstractRecently, an innovative hybrid structure has been developed as an alter-native lateral-load resisting system at The University of British Columbia.The hybrid structure incorporates Cross Laminated Timber (CLT) shearpanels as an infill in steel moment resisting frames (SMRFs). In order toincrease the applicability of the proposed system, in this thesis, a direct dis-placement based design methodology has been developed and analyticallyvalidated.Initially, a nonlinear time history analysis (NLTHA) was carried out tostudy the lateral behaviour of the proposed hybrid structure. For this pur-pose, a total of 162 different hybrid buildings were modeled and analyzedin OpenSees by using twenty earthquake ground motions (2% probabilityexceedance in 50 years). Post-earthquake performance indicators (Maxi-mum Interstory Drift (MISD) and Residual Interstory Drift (RISD)) wereobtained from the analyses. To assist the post-seismic safety assessment ofthe hybrid buildings, surrogate models for MISD and RISD were developedusing Response Surface Methodology and Artificial Neural Network (ANN).By using the ANN surrogate models as fitness functions for the Genetic Al-gorithm, optimal modeling parameters of the hybrid system were obtained.Secondly, to represent the energy dissipative capacity of the hybrid sys-tem, an equivalent viscous damping (EVD) equation was developed. To for-mulate the EVD equation, 243 single-storey single-bay CLT infilled SMRFmodels were developed and subjected to monotonic static and semi-staticcyclic analysis. The EVD of each model was calculated from the hystereticresponses based on Jacobsen’s area based approach and later calibrated us-iiAbstracting NLTHA.Finally, an iterative direct displacement based design method was de-veloped for the proposed hybrid structure. A detailed description of theproposed methodology is presented with a numerical example. In orderto verify the proposed method, hybrid buildings with 3-, 6-, and 9- storeyheights were designed. A calibrated EVD-ductility relationship was used toobtain the energy dissipation of the equivalent SDOF system for all casestudy buildings. Nonlinear time history analysis using twenty ground mo-tion records was used to validate the performance of the proposed designmethodology. The results indicate that the proposed design method effec-tively controls the displacements resulting from the seismic excitation of thehybrid structure.iiiPrefaceThis research work is carried-out at The University of British Columbiaunder direct supervision of Dr. Solomon Tesfamariam and Professor Sigi F.Stiemer. All the literature review, simulations and mathematical calcula-tions of this thesis are carried-out by the author. A list of my journal andconference publications at The University of British Columbia are listed asfollows.Journal Papers1. Bezabeh, M. A., Tesfamariam, S., Stiemer, S.F. 2014. ”Equivalent Vis-cous Damping for CLT Infilled Steel Moment Resisting Frames”, Jour-nal of Structural Engineering,ASCE, Prepared for submission (Versionof Chapter 4).2. Bezabeh, M. A., Tesfamariam, S., Stiemer, S.F. 2014. ”Prediction ofMaximum Interstorey Drift of Cross laminated Timber Infilled SteelMoment Frames from Post-Earthquake Residual Interstorey Drift: Re-sponse Surface Methodology”, Structures, Prepared for submission(Version of Chapter 3).3. Bezabeh, M. A., Tesfamariam, S., Stiemer, S.F. 2014. ”Coupled Arti-ficial Intelligence and Genetic Algorithm for the Multi-objective Op-timization of CLT infilled Steel Moment Resisting Frames”, Journalof Computing in Civil Engineering, ASCE, Prepared for submission(Version of Chapter 3).ivPreface4. Dickof, C., Stiemer, S. F., Bezabeh, M. A., and Tesfamariam, S. 2013.CLT-Steel Hybrid System: Ductility and Overstrength Values Basedon Static Pushover Analysis. Journal of Performance of ConstructedFacilities, ASCE [Accepted].5. Bezabeh, M. A., Tesfamariam, S., Stiemer, S.F. 2014. ”Direct Dis-placement Based Design of CLT Infilled Steel Moment Resisting Frames”,Canadian Journal of Civil Engineering, Prepared for submission (Ver-sion of Chapter 5).6. Tesfamariam, S., Stiemer, S. F., Dickof, C., and Bezabeh, M. A. 2013.Seismic Vulnerability Assessment of Hybrid Steel-Timber Structure:Steel Moment Resisting Frames with CLT Infill. Journal of EarthquakeEngineering [Accepted].Conference Papers1. Bezabeh, M. A., Tesfamariam, S., Stiemer, S.F. 2014. ”EquivalentViscous Damping of CLT Infilled Steel Moment Frames”, World Con-ference on Timber Engineering (WCTE), August 10-14, Quebec City,Canada. (Accepted)(Version of Chapter 4).2. Bezabeh, M. A., Tesfamariam, S., Stiemer, S.F. 2014. Residual DriftDemands of CLT Infilled Steel Moment Frames. In the 7th EuropeanConference of Steel and Composite Structures (EUROSTEEL 2014),September 10-12, 2014, Naples, Italy. (Accepted)3. Bezabeh, M. A., Tesfamariam, S., Stiemer, S.F. 2014. ”Applicationof Soft Computing to Quantify the Optimal Modeling Parameters ofCross Laminated Timber Infilled Steel Moment Resisting Frames”,12th International Conference on Applications of Statistics and Prob-ability in Civil Engineering, ICASP 12, July 12-15, 2015, Vancouver,Canada. Submitted (Version of Chapter 3).vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . xviDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiChapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Research methodology . . . . . . . . . . . . . . . . . . . . . . 41.3 Organization of the thesis . . . . . . . . . . . . . . . . . . . . 5Chapter 2: Literature review . . . . . . . . . . . . . . . . . . . . 72.1 Cross Laminated Timber (CLT) walls . . . . . . . . . . . . . 72.2 Advancements on CLT infilled SMRFs at UBC . . . . . . . . 122.3 Force based design . . . . . . . . . . . . . . . . . . . . . . . . 192.4 Performance based design . . . . . . . . . . . . . . . . . . . . 202.5 Direct displacement based design (DDBD) . . . . . . . . . . . 222.6 Review on DDBD of structures with lateral load resistingsystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22viTABLE OF CONTENTSChapter 3: Studying lateral behaviour of CLT infilled SM-RFs via artificial intelligence, Genetic Algorithm,and Response Surface Method . . . . . . . . . . . . 373.1 Predicting MISD of CLT infilled SMRFs: Response SurfaceMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.1.1 Building design and modeling . . . . . . . . . . . . . . 393.1.2 Seismic input . . . . . . . . . . . . . . . . . . . . . . . 433.1.3 Maximum and residual interstorey drift results . . . . 463.1.4 Surrogate Model for MISD . . . . . . . . . . . . . . . 483.1.5 Statistical validation of the proposed equation . . . . 553.2 Multi-objective optimization of drift demands of CLT infilledSMRFs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.2.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . 573.2.2 Surrogate Model using artificial intelligence . . . . . . 593.2.3 Multi-objective optimization using Genetic Algorithm 613.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Chapter 4: Equivalent viscous damping of CLT infilled steelmoment resisting frames . . . . . . . . . . . . . . . 654.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 684.3 Formulation for yielding point . . . . . . . . . . . . . . . . . . 704.4 Parametric study . . . . . . . . . . . . . . . . . . . . . . . . . 744.4.1 Monotonic pushover analysis . . . . . . . . . . . . . . 744.4.2 Semi-static cyclic analysis . . . . . . . . . . . . . . . 754.5 Equivalent viscous damping . . . . . . . . . . . . . . . . . . . 774.6 EVD calibration using nonlinear time history analysis . . . . 844.6.1 Results of calibration . . . . . . . . . . . . . . . . . . 914.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92Chapter 5: Direct displacement based design of CLT infilledsteel moment resisting frames . . . . . . . . . . . . 945.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94viiTABLE OF CONTENTS5.2 Basics of Direct displacement based design (DDBD) . . . . . 975.3 Proposed DDBD approach for CLT infilled SMRFs . . . . . . 1015.4 Nonlinear Time History Analysis . . . . . . . . . . . . . . . . 1185.4.1 Results of nonlinear time history analysis . . . . . . . 1195.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126Chapter 6: Conclusions and future research perspectives . . . 1276.1 Summary and conclusions . . . . . . . . . . . . . . . . . . . . 1276.2 Future research perspectives . . . . . . . . . . . . . . . . . . . 131Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151Appendix A: Surrogate models of MISD and RISD using ArtificialNeural Network . . . . . . . . . . . . . . . . . . . . . 151A.1 Designing the ANN network . . . . . . . . . . . . . . . . . . 151A.2 Training the ANN network . . . . . . . . . . . . . . . . . . . 152Appendix B: Approximate method of structural analysis . . . . . . 155Appendix C: Design checks . . . . . . . . . . . . . . . . . . . . . . 160viiiList of TablesTable 2.1 Performance levels, corrsponding damage state anddrift limits ([Gho01] By permission from publisher) . . 21Table 2.2 Proposed earthquake hazard levels ([Gho01] By per-mission from publisher) . . . . . . . . . . . . . . . . . 21Table 3.1 beam design details . . . . . . . . . . . . . . . . . . . . 40Table 3.2 column design details . . . . . . . . . . . . . . . . . . . 40Table 3.3 Ground Motion properties . . . . . . . . . . . . . . . . 43Table 3.4 Definition of input variables . . . . . . . . . . . . . . . 50Table 3.5 ANOVA table . . . . . . . . . . . . . . . . . . . . . . . 51Table 3.6 Equation coefficients . . . . . . . . . . . . . . . . . . . 52Table 4.1 Modeling variables . . . . . . . . . . . . . . . . . . . . 70Table 4.2 Modeling variables . . . . . . . . . . . . . . . . . . . . 85Table 4.3 Results of the semi-static cyclic analysis on model M4 90Table 5.1 Characteristics of equivalent SDOF . . . . . . . . . . . 107Table 5.2 Average frame ductility . . . . . . . . . . . . . . . . . 109Table 5.3 Base shear proportions between frame and walls . . . . 112Table 5.4 Beams and columns required moment strength . . . . 113Table 5.5 Details of sections . . . . . . . . . . . . . . . . . . . . 116Table 5.6 Details of DDBD design . . . . . . . . . . . . . . . . . 118ixList of FiguresFigure 1.1 CLT infilled SMRF ([TSDB14] Adapted with permis-sion from publisher) . . . . . . . . . . . . . . . . . . . 2Figure 1.2 Outline of the thesis . . . . . . . . . . . . . . . . . . . 6Figure 2.1 Five-layer Cross Laminated Timber (CLT) element([SHE10] Adapted with permission from publisher) . 8Figure 2.2 Test set-up used for the CLT walls tests . . . . . . . . 9Figure 2.3 Test set-up used for the CLT walls tests . . . . . . . . 10Figure 2.4 Failure modes of the bracket connections at late stageof testing for a) wall with spiral nails; and b) wall 04with annular ring nails . . . . . . . . . . . . . . . . . 10Figure 2.5 CLT wall and connection configuration. ([SST+13]Adapted with permission from publisher) . . . . . . . 13Figure 2.6 Monotonic envelope curves of connection tests, sawsand pinching4: (a) perpendicular to grain for Connec-tion A; and (b) longitudinal to grain for ConnectionA. ([SST+13] Adapted with permission from publisher) 14Figure 2.7 Hysteretic response of connection tests, Saws modeland Pinching4 model for Connection C: (a) Test andSaws for longitudinal to grain; (b) Test and Pinch-ing4 for longitudinal to grain; (c) Test and Saws forperpendicular to grain; and (d) Test and Pinching4for perpendicular to grain. ([SST+13] Adapted withpermission from publisher) . . . . . . . . . . . . . . . 15xLIST OF FIGURESFigure 2.8 Single Bay, Single Storey, CLT Infilled Frame withBracket Locations ( [DSBT14] Adapted with permis-sion from publisher) . . . . . . . . . . . . . . . . . . . 16Figure 2.9 Details of the 6-storey frame, a) base building floorplan, b) one infilled bay configurations, b) two infilledbay configurations, and, b) three infilled bay config-urations ([DSBT14] Adapted with permission frompublisher) . . . . . . . . . . . . . . . . . . . . . . . . 17Figure 2.10 a) storey sway mechanism b) rigid body rotatio of ithstorey ([WR] Adapted with permission from publisher) 24Figure 2.11 Flow chart on DDBD procedure of CBF structures([WR] Adapted with permission from publisher) . . . 25Figure 2.12 Geometry of frame-wall structures used in the evalua-tion ([GSC10] Adapted with permission from publisher) 26Figure 2.13 Flowchart of DBD for dual systems ([GSC10] Adaptedwith permission from publisher) . . . . . . . . . . . . 27Figure 2.14 Flowchart of DDBD for steel braced reinforced con-crete frames . . . . . . . . . . . . . . . . . . . . . . . 30Figure 2.15 Geometry of steel braced reinforced concrete framesused in the evaluation ([MGD13] Adapted with per-mission from publisher) . . . . . . . . . . . . . . . . . 31Figure 2.16 Plan and elevation of the 8-storey dual-system case-study building ([Sul09] Adapted with permission frompublisher) . . . . . . . . . . . . . . . . . . . . . . . . . 32Figure 2.17 Flowchart of DDBD for RC wall-steel EBF dual sys-tem with added dampers . . . . . . . . . . . . . . . . 33Figure 3.1 Typical building plan . . . . . . . . . . . . . . . . . . 40Figure 3.2 CLT infill distributions of 6-storey typical building,a) Frame with infill only in the middle bay (0-1-0);b) Frame with infill in two exterior bays (1-0-1), andc) Frame with infill in all bays (1-1-1) . . . . . . . . . 41Figure 3.3 Details of connection, Gap and CLT infill panels . . . 41xiLIST OF FIGURESFigure 3.4 Significant duration definition according to ([TB75])for Imperial Valley, 1979 earthquake . . . . . . . . . 45Figure 3.5 Comparison of mean and target response spectra forprobability of exceedance of 2 % in 50 years . . . . . 46Figure 3.6 Performance matrix for residual and maximum inter-storey drift . . . . . . . . . . . . . . . . . . . . . . . 47Figure 3.7 Displacement time histories of a typical 3 storey build-ing, a) Bare frame; b) Frame with infill in the middle(0-1-0); c) Frame with infill in two exterior bays (1-0-1), and d) Frame with infill in all bays (1-1-1) . . . 48Figure 3.8 Effect plots of modeling parameters . . . . . . . . . . 49Figure 3.9 Response surface plot for interactions between; a) in-fill Pattern and storey Number and b) infill patternand bracket spacing . . . . . . . . . . . . . . . . . . . 53Figure 3.10 Response surface plot for interactions between; a)seismicity and infill pattern and b) panel thicknessand storey Number . . . . . . . . . . . . . . . . . . . 54Figure 3.11 Validation plot; Predicted vs. Actual (red dots . . . . 56Figure 3.12 Response surface plot for MISD with infill patternand bracket spacing . . . . . . . . . . . . . . . . . . . 58Figure 3.13 Response surface plot for RISD with infill pattern andbracket spacing . . . . . . . . . . . . . . . . . . . . . 58Figure 3.14 Outline of the methodology . . . . . . . . . . . . . . . 60Figure 3.15 ANN model for prediction of objective function . . . 61Figure 3.16 Pareto-optimal solutions . . . . . . . . . . . . . . . . 62Figure 3.17 Higher order plot for variables corresponding to Paretocurve that trained using trainlm . . . . . . . . . . . . 63Figure 4.1 Hysteretic response area of one cycle . . . . . . . . . 66Figure 4.2 Framework for formulation . . . . . . . . . . . . . . . 69Figure 4.3 Compression strut action for the hybrid system . . . 71Figure 4.4 Compression strut action for the hybrid system . . . 71Figure 4.5 Five layer CLT . . . . . . . . . . . . . . . . . . . . . . 72xiiLIST OF FIGURESFigure 4.6 single strut representation of the hybrid system . . . 73Figure 4.7 Sample monotonic pushover analysis results . . . . . 75Figure 4.8 CUREE cyclic loading protocol . . . . . . . . . . . . 76Figure 4.9 Sample semi-static cyclic analysis results . . . . . . . 77Figure 4.10 Response surface plot for the effect of interactions be-tween bracket spacing (A) and post yielding stiffnessratio (E) . . . . . . . . . . . . . . . . . . . . . . . . . 79Figure 4.11 Response surface plot for the effect of interactionsbetween Panel strength (D) and Gap (B) . . . . . . . 80Figure 4.12 Response surface plot for the effect of interactionsbetween post stiffness yield ratio (E) and Gap (B) . 80Figure 4.13 Response surface plot for the effect of interactionsbetween Panel strength (D) and Panel thickness (Ct) 81Figure 4.14 Validation plot; Predicted vs. Actual . . . . . . . . . 81Figure 4.15 Damping ductility law for various modeling parame-ters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83Figure 4.16 Comparison of EVD expressions with different re-searches . . . . . . . . . . . . . . . . . . . . . . . . . 84Figure 4.17 Calibration process for EVD . . . . . . . . . . . . . . 86Figure 4.18 Comparison between mean and target spectrum forselected ground motion . . . . . . . . . . . . . . . . . 88Figure 4.19 Displacement spectra at 5% damping level from thescaled ground motion . . . . . . . . . . . . . . . . . . 88Figure 4.20 8.2% damped average displacement spectrum . . . . 91Figure 4.21 Calibrated hysteretic damping vs. ductility for bracketspacing of (a) 0.4 m ; b) 0.8 m; c) 1.6 m . . . . . . . 92Figure 5.1 Basics of DDBD approach (adopted from Priestley etal. 2007) . . . . . . . . . . . . . . . . . . . . . . . . . 98Figure 5.2 Framework of DDBD for CLT infilled SmRfs . . . . . 102Figure 5.3 Building floor plan . . . . . . . . . . . . . . . . . . . . 103Figure 5.4 Elevation view of the 3 storey 2D frame . . . . . . . . 103Figure 5.5 Shear distribution between CLT walls and steel frame 105xiiiLIST OF FIGURESFigure 5.6 Moment and shear distribution of frame and CLT wallalong the height of the building . . . . . . . . . . . . 105Figure 5.7 CLT panel representation with a compression strut . 108Figure 5.8 Equivalent viscous damping . . . . . . . . . . . . . . 110Figure 5.9 Effective period from damped displacement spectrum 111Figure 5.10 Inflection point on the deflected shape of the momentresisting frame . . . . . . . . . . . . . . . . . . . . . . 113Figure 5.11 Detail results of approximate method of analysis . . . 114Figure 5.12 Elevation view of six and nine storey buildings . . . . 117Figure 5.13 Response of 3 storey CLT infilled SMRF in Northridge1994 earthquake . . . . . . . . . . . . . . . . . . . . . 120Figure 5.14 Maximum storey displacement of 3 storey hybrid build-ing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121Figure 5.15 Maximum storey displacement of 6 storey hybrid build-ing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121Figure 5.16 Maximum storey displacement of 9 storey hybrid build-ing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122Figure 5.17 Maximum interstorey drift of 3 storey hybrid building 122Figure 5.18 Maximum interstorey drift of 6 storey hybrid building 123Figure 5.19 Maximum interstorey drift of 9 storey hybrid building 123Figure 5.20 Residual interstorey drift of 3 storey hybrid building . 124Figure 5.21 Residual interstorey drift of 6 storey hybrid building . 125Figure 5.22 Residual interstorey drift of 9 storey hybrid building . 125Figure A.1 MATLAB toolbox window for MLP training . . . . . 152Figure A.2 Regression outputs for MISD . . . . . . . . . . . . . 153Figure A.3 Regression outputs for RISD . . . . . . . . . . . . . . 154Figure B.1 Shear proportion between interior and exterior columns156Figure B.2 Simplified steel moment frames with assumed hinges . 157Figure B.3 Column shear . . . . . . . . . . . . . . . . . . . . . . 158Figure B.4 Details of joint M, beam MN, and column MI . . . . 159Figure C.1 Detail results of approximate method of analysis . . . 161xivLIST OF FIGURESFigure C.2 Details of exterior column . . . . . . . . . . . . . . . . 162xvAcknowledgmentsFirst of all, I would like to express my deepest appreciation and thanksto my supervisors Dr. Solomon Tesfamariam and Professor Siegfried F.Stiemer, for offering me the MASc student position, their support, guidance,and unlimited hours of supervision required to complete this thesis. Theiradvice on both academic and non-academic matters have been priceless.Besides, I would like to thank my friends in UBC Okanagan, for theinteresting discussions, for the great Ping-Pong games, and for all of the funwe had in the last 18 months. Also I thank my roommate Dessalegn Amenu,for being with me in peaks and valleys of life during my days of MASc.Finally, I wish to thank my parents especially my sisters Tsgae andKalkidan. Without your love and blessings, as well as your moral support,this thesis would not have been possible.xviDedicationDedicated to my mother for her endless love from the Heavenxvii1IntroductionDuring the last decade, the use of hybrid structural systems has in-creased across North America. A hybrid system combines two or morematerials and allows them to work jointly. Its main advantages are con-structability, cost effectiveness, construction speed, and aesthetics. Consid-ering the height limitation on timber as a structural material, feasibilitystudies have been carried out at The University of British Columbia (UBC)on hybridizing timber with steel to meet the current performance require-ment [SDT12, STKP12, DST12, Dic13, DSBT14]. The proposed hybridsystem incorporates Cross Laminated Timber (CLT) as an infill in steel mo-ment resisting frames (SMRFs)(Figure 1.1). The proposed system proved tohave higher seismic resistance and lower the seismic vulnerability [TSDB14].Moreover, the proposed system can be applied to strengthen existing build-ings after a seismic event. The CLT panels are characterized by high stiffnessto weight ratio, which makes them appropriate material for the seismic de-sign of buildings.1Chapter 1. Introduction2D elastic shell element for CLT 2 node link element Elastic Shear deformation Compression gap Stress force Tension gap $Fy (-ve value) $gap (-ve value) $E $gap (+ve value) $Fy $E Nonlinear displacement based Gap elements Beam-column element Figure 1.1: CLT infilled SMRF ([TSDB14] Adapted with permission frompublisher)The hybrid system under study is achieved by using L-shaped steel brack-ets as a connector between the CLT panel and steel frame. These connectionbrackets are bolted to the steel frame and nailed to the CLT panel. Thor-ough experimental studies have been carried out on the seismic behaviourof the bracket connections at UBC for the past four years [SKP+13]. Theseconnections provided to ensure full confinement between the structural ele-ments and prevent out of plane failure of the infill panels during a seismicevent. The interface between the CLT infill wall and the steel frame isprovided with a small gap to allow the connection brackets to deform un-der lateral load. This permits the frame and panel to act independentlyand influence each other under lateral loading, which makes the interactioncomplex.21.1. Motivation1.1 MotivationAs discussed in previous paragraphs, the proposed hybrid system canbe an alternative construction practice for medium- and high-rise buildings.In the literature, extensive researches have been carried out for masonryand concrete infilled steel frames [EDEH03, Mog04, MTM08, SR78, DSS89,ED02, CGA02]. However, using CLT as a structural infill panel is not thor-oughly explored. The hybridization of timber with steel as shown in Figure1.1 is promising to increase the height requirement on timber buildings.Moreover, the investigation on the composite action under extreme seismicevents also creates a new research dimension.In order to make this type of hybrid system ready for designers andbuilders, the first step is to make sure that the system is seismic resistant.Design guidelines and standards are needed for the proposed system. Incompliance with the current design philosophy, force based design, the latestCanadian code does not have appropriate Rd and Ro factors to performthe design of the proposed hybrid system. Therefore, the objectives of thecurrent study are to examine the lateral behaviour under seismic excitationand to develop a performance based design methodology for the hybridsystem. This design method will be used as a baseline to develop the designguide rules that can be applied to prepare design standards. In addition,this type of construction method offers the following advantages:(a) The hybrid building system elements are suitable for prefabrication.This can result rapid erection time and avoids on site constructionerrors.(b) The proposed structural typology, CLT as an infill in SMRFs, can beused for the strengthening of existing buildings after a seismic event.(c) This type of building system avoids the use of formworks and scaffold-ings which yields quality construction and safe project area.(d) Given the aim of maximizing the use of timber in buildings, among con-struction industry stakeholders hybrid tall buildings become prevalent.31.2. Research methodologyThe proposed hybrid system is an ideal candidate as a high seismicresistant tall building.1.2 Research methodologyInitially, a thorough investigation is carried out to study the lateral be-haviour of the proposed hybrid system and to identify the optimal modelingparameters that results in minimum damage on the building during theseismic event. For the purpose, a total of 162 different hybrid buildings aremodeled in OpenSees [MMS+06] by varying six decision variables: buildingstorey [3-, 6- 9-], CLT infill configuration [one-bay infilled, two-bays infilledand three-bays infilled], CLT panel thickness [99, 169, 239 mm] and strength[17.5, 25, 37.5 MPa], and connection bracket spacing 800 and 1600 mm.Twenty earthquake ground motions (with 2% probability exceedance in 50years) have been used as an input for the analysis. In order to identify theoptimal modeling variables, prediction equations and black box functionsare developed using Response Surface Methodology (RSM) and ArtificialIntelligence, respectively. Multi-objective optimization procedures are ap-plied to identify the optimal modeling parameters. The result highlightsthat the drift demands of the proposed hybrid systems are quite differentfrom the bare SMRFs. Therefore, rather than considering the CLT infill asa non-structural element, it is of a great advantage to consider it during thedesign process. For this reason, a design philosophy that incorporates de-formation as an input parameter during the design process is chosen. Theseprocedures are called performance based design methods, specifically, Di-rect Displacement Based Design (DDBD) method. As a first step for theDDBD method, the energy dissipative capacity of the proposed system isquantified through equivalent viscous damping (EVD). This process leadsto the development of EVD-ductility law that can be used in the design.Initially this law is developed using Jacobsen′s approach and then correctedusing inelastic time history analysis. Subsequently, a new iterative directdisplacement based design method for the proposed system has been devel-oped and tested by designing 3-, 6-, and 9- storey hybrid buildings. Finally,41.3. Organization of the thesisthe performance of the proposed design method is verified using nonlineartime history analysis.1.3 Organization of the thesisThis thesis contains 6 chapters. The outline of this thesis is depictedin Figure 1.2. The introduction chapter includes, an overview to innovativehybrid system (CLT infilled SMRF), motivation, research methodology, andorganization of thesis. Chapter 2 presents a thorough literature review in-cluding research development at UBC on the proposed hybrid system. Inaddition, it reviews some notable researches on DDBD of structural systemswith additional lateral load resisting systems. Chapter 3 provides the pre-diction equation for the maximum interstorey drift (MISD) of the hybridsystem from modeling parameters and residual interstorey drift (RISD). Itapplies RSM procedure with D-Optimal experimental design technique forthe prediction equation development. Moreover, Chapter 3 presents the ap-plication of soft computing (Artificial Intelligence and Genetic Algorithm)for the multi-objective optimization of drift demands of the hybrid system.Chapter 4 provides an EVD-ductility law for the DDBD design of CLT-SMRF system. Initially, this law was developed using Jacobsen‘s area basedapproach and then corrected using inelastic time history analysis from atotal of 8640 simulations. Chapter 5 presents the DDBD methodology thatis developed for the proposed hybrid system. The developed design methodis presented with a numerical example for a 3 storey hybrid building. Inaddition, this chapter includes design verification using nonlinear time his-tory analysis. Finally, the conclusions and future research perspectives arepresented in Chapter 6.51.3. Organization of the thesisTitle Introduction Literature review Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Conclusions and future research perspectives Studying lateral behaviour of CLT infilled SMRFs via Artificial Intelligence, Genetic Algorithm, and Response Surface Method Lateral Behaviour and Direct Displacement Based Design of a Novel Hybrid Structure: Cross Laminated Timber infilled Steel Moment Resisting Frames Equivalent viscous damping of CLT infilled steel moment resisting frames Direct displacement based design of CLT infilled steel moment resisting frame Figure 1.2: Outline of the thesis62Literature review2.1 Cross Laminated Timber (CLT) wallsCross Laminated Timber (CLT) panel is an engineered wood productwith several cross layers of lumber arranged orthogonally that are gluedtogether by adhesives or fasteners. The cross-section of CLT panel has oddnumbers of layers in order to create symmetry at the central layer. Softwoodlumber and adhesives are the main materials to produce CLT panels. Panelsizes may vary on the specification of the manufacturer; typically in BritishColumbia (BC), thickness range is 99-309 mm with maximum available panelsize of 3 x 12.2 m. Figure 2.1 shows typical arrangement of CLT layers.72.1. Cross Laminated Timber (CLT) wallsFigure 2.1: Five-layer Cross Laminated Timber (CLT) element ([SHE10]Adapted with permission from publisher)Generally, several researches have been conducted in Canada and otherparts of the world on the seismic behaviour of CLT structural systems.These systems include connections between CLT components, CLT walls,and entire CLT building tests. Review on some of notable researches ispresented in subsequent sections.Popovski et al. [PKC11] Seismic Performance ofcross-laminated timber buildingsFP innovation conducted a series of quasi-static tests on CLT wall panels.The purpose of the study was to assess the seismic performance of CLT panelwall systems. Several tests, for various wall configurations and connectiontypes, were carried out. Connections applied at the base of walls to connectwalls with floors underneath. The test set-up used for the walls is indicatedin Figure 2.2.82.1. Cross Laminated Timber (CLT) wallsFigure 2.2: Test set-up used for the CLT walls tests( c© 2011, FPInnovation, by permission)The CLT walls, during the tests, behaved as a rigid body with smallshear deformation. Moreover, static tests revealed that much deformationoccurred in the brackets while considerable deformation was observed on thefasteners for cyclic tests. This observation also varied the peak deformationand deformation as shown in Figure 2.3. Moreover, some observed connec-tion failures of brackets with spiral nails and annular ring rails is depictedin Figure 2.4.92.1. Cross Laminated Timber (CLT) wallsFigure 2.3: Test set-up used for the CLT walls tests( c© 2011, FPInnovation, by permission)Figure 2.4: Failure modes of the bracket connections at late stage of testingfor a) wall with spiral nails; and b) wall 04 with annular ring nails( c© 2011, FPInnovation, by permission)In general, results showed that adequate seismic performance was achievedwhen steel brackets used with nails or slender screws. The authors also es-timated the seismic reduction factor (R) factors for the CLT systems incompliance with National Building Code of Canada (NBCC)[NRC05]. Aconservative estimate of Rd = 2 and Ro = 1.5 is suggested. Furthermore,102.1. Cross Laminated Timber (CLT) wallsthe authors briefly discuss the application of capacity design method for theCLT structures.Ceccotti and Follesa [CF06] Seismic behavior of multi-storeyXLam buildingsAs a part of SOFIE (Fiemme house constructive system) project, a col-laboration of Trees and Timber Institute of National Research Council ofItaly (CNR-IVALSA), National Institute for Earth Science and Disaster Pre-vention In Japan (NIED), Shizouka University, and the Building ResearchInstitute (BRI) in Japan leads to a shaking table tests on the 3- storey CLTbuilding. The test was carried out in the laboratory of NIED in Japan.The dynamic test carried out for 3 different earthquakes at two levels ofPGA. The simulated earthquakes applied in three different configurations(distinct opening layout) in order to capture the effect of wall length and tor-sional behaviour of the building system under seismic excitation. “The testhouse survived 15 destructive earthquakes without any severe damage, i.e.any damage that couldn′t allow for any further reparation of the building“[CF06].Ceccotti et al. [CSY10] Seismic behaviour of multistorybuilding cross-laminated timber buildingsAs a continuation is the 3- storey CLT building test in the above section,another notable shaking table test was carried out in Japan on a 7- storeyCLT building. The design of building was conducted by using a behaviourfactor (q) value of 3 and importance factor of 1.5. A 100% of Kobe Earth-quake (M = 7.2) record was applied in all orthogonal directions. From thedynamic test under, it is observed that the maximum interstorey drift of thesystem is less than the drift that cause the connections to fail.112.2. Advancements on CLT infilled SMRFs at UBC2.2 Advancements on CLT infilled SMRFs atUBCAs a basic components of building system, timber and steel have beenused independently. However, the height limitation on timber as a mainstructural element and the trend to build tall wood buildings makes hy-bridization a feasible solution. In general, hybridization offers an efficientuse of the best engineering properties from each material it constitutes. Thishybridization can be done in different scale: system level and building level.A novel hybrid structure that incorporates Cross Laminated Timber (CLT)as an infill panel in steel moment resisting frames (SMRFs) is developed atUBC [SDT12, STKP12, DST12, Dic13, DSBT14, TSDB14]. In this section,a brief summary of previous researches at UBC on the development of inno-vative hybrid system is presented. The review is started with the researchmade on the experimental investigation of steel bracket connection systembetween CLT and steel frame [SKP+13]. This followed by a review on thefinite element validation of the experiments by [SST+13]. Review on theresearch that combined the above two studies to develop the CLT infilledSMRF hybrid system by [DSBT14] is also included. Finally a probabilisticassessment of the CLT- SMRF system by Tesfamariam et al. [TSDB14] ispresented.Schneider et al. [SKP+13] Damage assessment of connectionused in cross laminated timber subject to cyclic loadsA total of 98 different CLT bracket connections are examined undervertical (parallel to the grain) and horizontal (perpendicular to the grain)directions. The authors focused on studying the damage indices and theircorrelation with the observed damages under monotonic and cyclic loading.In their work, the authors also calibrated the Kraetzig‘s energy based modelby using the data from experiments. Moreover, a damage scale ranges from1-5 was defined using 24 experimental tests. This damage scale was alsoverified using 37 cyclic loading tests. The test results revealed that the pull-122.2. Advancements on CLT infilled SMRFs at UBCout failure of connectors was common type of observed failure mechanismfor the tests in the parallel to the grain direction. However, wood crushingof the outer layer was predominant failure mode for tests in perpendicu-lar to the grain direction. From the analysis, Bracket A with spiral nailsand ring shank nails offers the largest ductility value. From the observedfailure modes, the authors noticed the dependency of failure modes on thegrain orientation of CLT element. In general, from their study, the authorsconcluded that the failure on most of the brackets are occurred when theaverage damage index reaches 0.8.Shen et al. [SST+13] Hysteresis behaviour of bracketconnection in cross laminated timber shear wallsCalibration of Pinching4 [LMA03] and Saw models [FF01] of Opensees[MMS+06] for the experimental tests performed by ([Sch09, SST+12] is themain goal of the research. The experimental test results of three typesof connection systems, i.e., one bracket (Bracket A of [SKP+13] ) and 3fastener types were considered for the calibration purpose. Figure 2.5 showsthe connection details that are considered in the study.eNf1, eNd2, eNf2, eNd3, eNf3, eNd4, eNf4) are used to d fine the re-sponse envelope. That’s closer to the actual cyclic envelope of theconnection than Stewart’s nine parameters-plywood model. Twounload–reload paths and pinching behavior are defined with 6parameters (rDispP, rFoceP, uForceP, rDispN, rFoceN, uForceN).rDispP and rDispN respectively refer to the pinched ratio of thedeformation at which reloading or unloading occurs to the historicdeformation demand of each cycle. rForceP and rForceN individu-ally indicate the pinched ratios of the forces corresponding to thehistoric deform tion demand of each cycl under reloading andunloading. uForceP and uForceN represent the pinched ratios ofstrengths under reloading and unloading, respectively.There are 16 parameters to control increasing unloading stiff-ness degradation, accelerated reloading stiffness degradation andstrength degradation under cyclic loading. The damage indicesdki, ddi, and dfi are assumed to be a function of displacement historyand energy accumulation when setting the damage type as‘‘energy’’, which is based on a general damage index proposed byPark and Ang [37]. The form of each damage rule is the same, illus-trated as follows:di ¼ ðg1ðdmaxÞg3 þ g2ðEi=EmaxÞg4 Þ 6 glim ð5aÞdmax ¼ max½dP=defP;dN=defN ð5bÞEi ¼ZdE ð5cÞwhere di is a general damage index ranged between 0.0 and 1.0(specifically, dki as the unloading stiffness damage index at timeith, ddi as the reloading stiffness damage index at time ith, dfi asthe envelope strength degradation at time ith). The parameters(g1, g2, g3, g4, glim) are used to fit the damage rule to the experimen-tal data. Emax equal to the energy corr sponding to r sponse enve-lope defined before. Ei is the cumulative hysteretic energy at timeith.def P and def N are, respectively, the positive and negative failuredeformations defined previously, actually def P equal to ePd4 and defN equal to eNd4. dp and dN are respectively the positive and negativemaximum deformation demands in the loading circle. The unload-ing stiffness (ki), reloading deformation (dmax,i), strength(fmax,i) attime ith should be calculated according to:ki ¼ k0ð1 dkiÞ ð6aÞdmax;i ¼ dmax;0ð1 þ ddiÞ ð6bÞfmax;i ¼ f max;0ð1 dfiÞ ð6cÞwhere k0 is the initial unloading stiffness for the case of no damage,dki represents unloading stiffness damage index at the time ith,dmax,0 is the maximum historic deformation demand without degra-dation of reloading stiffness, ddi is the value of reloading stiffnessdamage index at the time ith, fmax,0 is the initial envelope maximumstrength for the case of no damage, and dfi indicates the value ofstrength damage index at time ith.Both models describe the degrading reloading stiffness in differ-ent ways. For Saws model, the current reloading stiffness is calcu-lated based on a function of last loading history; for Pinching4model, the current reloading stiffness is defined based on the cur-rent loading history. Saws model only can describe a symmetryhysteretic behavior while Pinching4 model can be used for anasymmetry hysteretic behavior because of respective definitionof the positive and negative hysteretic curves. Saws model predictsthe connection failure to occur when the linear degrading back-bone intercepts the positive pinched line and the calculation stops.As to the Pinching4 model, connection failure happens when dis-placement de and exceeds the envelope curve defined before.The calculations continue to run and the failure segment of theenvelope curve is characterized by the horizontal line.3. Load-slip connection test: hysteretic model calibrationThe CLT samples for connection and full size wall tests are94 mm thick (three layers that are divided in 30 mm-34 mm-30 mm) [8]. The CLT wall configuration and connection configura-tion are shown in Fig. 3. The three types of bracket connectionsconsist of ‘‘SIMPSON StrongTie bracket 90 48 3.0 116’’ andvarious fasteners combinations (18 spiral ails 16d-3 1/200, 18screws 4-70 mm, 10 screws 5-90 mm). Typical for orthotropicmaterials, the vertical direction of a CLT shear wall is parallel toouter layer gain and the horizontal direction is perpendicular toouter layer gain for practical application. In the connection sliptests, the load parallel to outer layer grain and perpendicular toouter layer gain were measured for each bracket connection basedon displacement control under monotonic and cyclic loading,respectively. The three connections, denoted by Connections A, B,C, are shown in Fig. 4.Fig. 2. Pinching4 model.Fig. 3. CLT wall and connection configuration.982 Y.-L. Shen et al. / Construction and Building Materials 48 (2013) 980–991Figure 2.5: CLT wall and connection configuration. ([SST+13] Adaptedwith permission from publisher)The results of calibration process using finite element (FE) study arediscussed as follows. Comparison between results of the (FE) models andexperimental tests are depicted in Figure 2.6a and b for monotonic tests in132.2. Advancements on CLT infilled SMRFs at UBCparallel and perpendicular direction, respectively. From the Figure 2.6a itcan be inferred that the both analytical models predict very well for testin perpendicular to the grain direction. However, in Figure 2.6b the SAWmodel failed to capture failure point after degradation from the peak load.The cyclic connection tests were conducted according to ASTM-CUREE protocol [38] where each phase consists of a primary cycleat a certain percent of the reference deformation D and a couple ofthe trailing cycles with 75% of amplitude of the primary cycle. Thereference displacement is the displacement at 80% of the peak loadon the degradation segment for monotonic envelope curve. Thecyclic displacement schedules in two directions are presented inFig. 5(a) and (b).3.1. Monotonic and cyclic envelope curves for Saws model andPinching4 modelQuantifying the monotonic and cyclic envelope curves, for thebracket connections, is important as it directly influence accuracyof the modeling shear walls. A total of 3 connection specimensare tested under CUREE loading protocols and the correspondingaverage monotonic and cyclic envelope test curves are plotted inFigs. 6–8 (perpendicular and longitudinal to grain). These experi-mental results are used to calibrate Saws model and Pinching4model. Parameter estimations for both models are determined byleast-squares method based on force response at correspondingdisplacement. For the three types of bracket connections, theparameters of monotonic envelope curves and hysteretic curvesbased on Saws model and Pinching4 model are summarized inTables A1 and A2. For example, for Connection A, the test resultsshow good agreement with both models’ prediction for perpendic-ular (Fig. 6a) and longitudinal (Fig. 6b) to grain direction.From Fig. 6(a), it can be observed that the backbone curve (it re-fers to the envelope curve) of Saws model is smooth and Pinching4model is relatively coarse with multi-linear envelope. In Fig. 6(b),the monotonic backbone, after peak load, exhibits a rapid drop instrength and later stabilizes to a constant value. Saws model quan-tifies degradation segment after the peak load as a linear line anddoes not capture the strength stabilization component of the enve-lope. For Pinching4 model, failure of the connection happens whendisplacement demand exceeds the envelope curve defined before,characterized by the horizontal line in the last degrading segment.This feature can be used to describe the constant trend in thedegrading backbone. Furthermore, based on above description, itis postulated that for the wall tests, Saws model would not ableFig. 4. Three types of bracket connection.Fig. 5. The cyclic schedules of connection slip test in two directions: (a) parallel tograin; and (b) perpendicular to grain.Fig. 6. Monotonic envelope curves of connection tests, saws and pinching4: (a)perpendicular to grain for Connection A; and (b) longitudinal to grain forConnection A.Y.-L. Shen et al. / Construction and Building Materials 48 (2013) 980–991 983Figure 2.6: Monotonic envelope curves of connection tests, saws and pinch-ing4: (a) perpendicular to grain for Connection A; and (b) longitudinal tograin for Connection A. ([SST+13] Adapted with permission from publisher)Figure 2.7 shows the comparison of the analytical model responses andexperimental tests for connections under cyclic loading. Considering reload-ing stiffness and degrading slope, the Pinching4 model is found to be thebetter analytical model.142.2. Advancements on CLT infilled SMRFs at UBCenergy elastic–plastic (EEEP) [38] are summarized in Table 1. Theparameters used to define the envelopes are: Ke is equivalent elastic stiffness. Ppeak is the peak load of the envelope curve. Dpeak is the corresponding displacement at the peak load. Pu is defined to the ultimate load corresponding to failure limitstate which is at 80% of the peakload. Du is the corresponding displacement at the failure load (Pu). Pyield is equivalent yield load but actually there is no significantyield point on the hysteretic envelope curve. Dyield is the displacement at the yield load. D is ductility factor defined as the ratio of the ultimate displace-ment (Du) and the yield displacement (Dyield).Stiffness, strength, and ductility of the connections are impor-tant safety factors [39] and compared in the following, respec-tively. In terms of longitudinal to grain direction test, ConnectionA has the greatest Ke value (9.18 kN/mm), ext is Connection B(6.2 kN/mm) and the last is Connection C (5.1 kN/mm). Similartrend are observed for Pu values. Connections A and B have higherPpeak value (48.9 kN and 49.2 kN) than Connection C (45.8 kN).Connection A shows higher ductility ratio (D = 6.12) than Connec-tion B (D = 3.8) and Connection C (D = 3.01).For loading perpendicular to grain direction, Connection A stillhas the highest Ke value of 5.11 kN/mm, followed by ConnectionsB (4.11 kN/mm) and C (4.21 kN/mm). Connection B achieved thehighest Ppeak (50.4 kN) and Pu (40.3 kN) values. However, in termsof ductility ratio, Connection A shows higher ductility ratio(D = 4.83) than Connection C (D = 3.82) and Connection B(D = 3.67). Based on the above calculation, the ductility factors ofall connections are higher than 3.0.3.2. Cyclic hysteretic models for Saws model and Pinching4 modelThe cyclic connection tests have shown that the slack responseoccurs. Fastener’s group loses partial contact with the surroundingwood because of permanent deformation produced by previousloading. The slack response results in the accelerated reloadingstiffness degradation with increasing displacement loading. BothTable 1Summary of hysteretic response of test and modeling for three types of connections.Ke (kN/mm) Fy (kN) Dy (mm) Ppeak (kN) Dpeak (mm) Pu (kN) Du (mm) D = Du/DyLongitudinal to grain directionConnection A 9.1 44.6 4.9 48.9 20 39.1 30 6.12Connection B 6.2 43.6 7.1 49.2 21 37.3 27 3.8Connection C 5.1 40.2 7.9 45.8 18 36.6 23.8 3.01Perpendicular to grain directionConnection A 5.1 41.5 8.1 46.7 24 37.4 39.2 4.83Connection B 4.1 44.5 10.8 50.4 26 40.3 39.7 3.67Connection C 4.2 40.2 9.6 46.4 24 37.1 36.7 3.82Fig. 9. Hysteretic response of connection tests, Saws model and Pinching4 model for Connection C: (a) Test and Saws for longitudinal to grain; (b) Test and Pinching4 forlongitudinal to grain; (c) Test and Saws for perpendicular to grain; and (d) Test and Pinching4 for perpendicular to grain.Y.-L. Shen et al. / Construction and Building Materials 48 (2013) 980–991 985Figure 2.7: Hysteretic response of connection tests, Saws model and Pinch-ing4 model for Connection C: (a) Test and Saws for longitudinal to grain;(b) Test and Pinching4 for longitudinal to grain; (c) Test and Saws for per-pendicular to grain; and (d) Test and Pinching4 for perpendicular to grain.([SST+13] Adapted with permission from publisher)Furthermore, the authors implemented the analytical models of the con-nection in the CLT wall to compare FE results with experimental tests con-ducted by [Sch09]. From their study, it is found that Bracket-A with spiralnail 16×3(1/2) is an excellent connector of CLT system with steel members.From a computational point of view, the Pinching4 analytical model showedgood result in simulating the behavior of CLT wall under both static andcyclic loads.152.2. Advancements on CLT infilled SMRFs at UBCDickof et al. [DSBT14] CLT-steel hybrid system: ductilityand overstrength values based on static pushover analysisIn this paper, the authors extended the development of an innovativesteel-timber hybrid structure from [SDT12, STKP12, DST12, Dic13]. Theproposed system incorporates a CLT infill shear panels inside a steel momentresisting frame. Figure 2.8 shows the developed innovative hybrid structure.Figure 2.8: Single Bay, Single Storey, CLT Infilled Frame with BracketLocations ( [DSBT14] Adapted with permission from publisher)The hybrid system is achieved by using steel bracket connections thatwere tested by [Sch09, SST+12]. In order to study the effect of physicalproperties of CLT shear panels inside steel frames, the authors performed athorough parametric study on the single bay single storey of the proposedsystem. From the analysis they found out that CLT thickness, crushingstrength and gap between CLT and steel frame affect the ultimate strength,ultimate drift, and post peak behavior of the system. Subsequently, an ana-lytical study has been carried out on the multi-degree-of-freedom (MDOF)of the proposed system. 3-, 6- and 9- storey frames with different infilltopology (Figure 2.9) were considered.162.2. Advancements on CLT infilled SMRFs at UBCa) b) c) d) Figure 2.9: Details of the 6-storey frame, a) base building floor plan, b)one infilled bay configurations, b) two infilled bay configurations, and, b)three infilled bay configurations ([DSBT14] Adapted with permission frompublisher)Monotonic pushover analysis was performed to establish preliminary val-ues of the over-strength and ductility factors. A thorough discussion is alsoincluded on the definition of first yielding point. It is indicated that bracketyielding occurs at an early stage of loading with very little influence on the172.2. Advancements on CLT infilled SMRFs at UBCinitial stiffness of the system. In this case, calculating the system ductilitywith the bracket yielding deformation will create unrealistic ductility de-mand. Therefore, the authors chose to use a system yielding deformation.Finally, in order to perform a force based design of the proposed hybridstructure, the authors suggested a ductility and over-strength values of 2.5and 1.25, respectively.Tesfamariam et al. [TSDB14] Seismic vulnerabilityassessment of hybrid steel-timber structure:steel momentresisting frames with CLT infillThis paper performs a probabilistic seismic vulnerability assessment onthe innovative hybrid system that was developed at UBC by [SDT12, STKP12,DST12, Dic13, DSBT14]. The study is conducted on the buildings designedfor the earthquake hazard level of Vancouver, Canada. Three, six and ninestorey buildings with three different infill configurations were considered.Moreover, in order to quantify the effect of ductility class of the steel frames,the study considers both Limited Ductile (LD) and Ductile (D) categories ofNBCC 2010 [NRC10]. A global system response parameter, peak interstoreydrift ratio (PISD), is adopted as a performance indicator. The spectral ac-celeration at 5% damping is chosen as an intensity measure (IM) to developthe fragility curves. In order to obtain PISD, a nonlinear time history analy-sis was carried out using 10 earthquake ground motions scaled to the hazardlevel of 2%, 5%, 10%, and 40% in 50 years return period. From the paramet-ric studies, significant reduction in the fundamental period of structure wasobserved as the infill bays increased from bare to all bays infilled frame. Forall bays infilled systems, the effect of ductility class on PISD was found to beminimal. From the fragility curves, it can be inferred that the incorporationof CLT shear panels decreases the vulnerability of the system. Generally,the study shows that the proposed hybrid system can be a substitute con-struction type in moderate and high seismic regions. Moreover, the authorsrecommended further research on the residual drift demand of the proposedsystem as it can be high with the stiffening behavior of the shear panels.182.3. Force based design2.3 Force based designGenerally, most design codes use a force based design approach (FBD)for the seismic design of structures. This method calculates the elastic designbase shear and reduces it by using a force reduction factor (R) to performinelastic design that considers ductility and over-strength of structures. TheNational Building Code of Canada (NBCC)[NRC10] uses a combined duc-tility related (Rd) and over-strength related (Ro) reduction factors to reachto inelastic design. The details and necessary steps of FBD method canbe found elsewhere [Dic13, PCK07b]. Medhekar and Kennedy [MK00b],Priestley [Pri00], and Priestley et al. [PCK07b], pointed out the limitationsof current FBD method. The following list includes some issues that arerelated to the FBD method.1. FBD method requires the fundamental period of the structure at thestart of the design process. Building design codes suggest empiricalequations to determine the fundamental period of structures. Theseequations are solely dependent on the type and geometry of a struc-ture. Moreover, these equations are conservative and are not conve-nient for structures with irregularities [YA13].2. The R factors that are used reduce the elastic base shear is formu-lated based on an equal displacement approach. Priestley [Pri00] andPriestley et al. [PCK07b] pointed out the problem associated withthis approach for short and long period structures. Moreover, it isstated that the approach becomes questionable for the system havinghysteretic behaviour different from elasto-plastic.3. In FBD method displacements are only checked at the end of the de-sign process. This may create large deformation when R factors greaterthan 1.0 are used for the design. This large displacement can resultin poor performance of non-structural elements under earthquakes re-lated to serviceability limit state. Moreover, this large displacementcan result in structural instability at ultimate limit state.192.4. Performance based designAs the proposed CLT infilled SMRFs achieved by L-shaped steel brack-ets to connect CLT panel with steel frame, the hysteresis behaviour of thesystem is quite different from elasto-plastic. Moreover, the hysteresis be-haviour of the hybrid system is dependent on the gap between CLT andsteel frame, panel thickness, panel strength, and connection bracket spac-ing. In addition, NBCC [NRC10] does not specify appropriate ductility andoverstrength factors for the proposed hybrid structure. Due to these rea-sons, it is of a great advantage to develop the displacement based designapproach for CLT infilled SMRFs that avoids the illogical assumptions ofthe FBD method.2.4 Performance based designOver the last 50 years, seismic design of structures shows considerableadvancement. One of the key advancement during the last 20 years is thedevelopment and progress of performance based engineering. Performancebased engineering provides guidelines to design, construct, and maintain allkinds of civil infrastructures to meet prefixed performance level for the givenseismic hazard. Performance based seismic design (PBSD) is one componentof performance based engineering where the design criteria are defined toachieve prescribed performance objectives when the structure is subjectedto a certain level of seismic hazard [Gho01]. Four notable researches are con-sidered as the corner stone of PBSD, i.e. [Com95, ATC96, UC97, Fed97].SEAOC Vision 2000 [Com95] aimed at developing a framework to designa structure to meet multiple performance objectives. The document in-cludes four performance levels, i.e. fully operational, operational, life safety,and near collapse. Moreover the document suggests elastic and inelasticdesign methods. Conventional force and strength, displacement based de-sign, energy approaches and prescriptive design are among the suggesteddesign methods [Com95]. ATC 40 (Applied Technological Council)[ATC96]document, provides a design and analysis methods for concrete buildings inCalifornia. The document uses performance based methodology for the eval-uation and retrofit design of buildings by considering certain performance202.4. Performance based designobjectives. Development and application of capacity spectrum method forthe performance assessment of existing buildings is presented in detail. TheFederal Emergency Management Agency (FEMA) [UC97, Fed97] also de-fined performance levels and ranges to meet multiple objectives for a givenground motion intensity. The document proposes limits on drift values forvarious types of main structural and non-structural elements. Four differ-ent analytical procedures are discussed in detail, i.e. Linear Static, LinearDynamic, Nonlinear Static, and Nonlinear Dynamic to be applied for sys-tematic rehabilitation. Moreover in the document, stiffness, strength, andductility characteristics of different structural elements are presented fromthorough laboratory and analytical studies. Ghobarah [Gho01] grouped theperformance levels and earthquake hazard from the above research docu-ments as shown in Table 2.1 and Table 2.2, respectively.Table 2.1: Performance levels, corrsponding damage state and drift limits([Gho01] By permission from publisher)Performance level Damage state DriftFully operational, Immediate occupancy No damage <0.2%Operational, Damage control, Moderate Repairable <0.5%Life safe-Damage state Irreparable <1.5%Near collapse, Limited safety, Hazard reduced Severe <2.5%Collapse >2.5%Table 2.2: Proposed earthquake hazard levels ([Gho01] By permission frompublisher)Earthquake frequency Return period in years Probablity of exceedenceFrequent 43 50%in 30 yearsOccasional 72 50%in 50 yearsRare 475 10%in 50 yearsVery rare 970 5%in 50 years or 10%in 100 yearsExtremely rare 2475 2%in 50 years212.5. Direct displacement based design (DDBD)2.5 Direct displacement based design (DDBD)Direct Displacement Based Design (DDBD) is a subset of performancebased seismic design wherein the performance objectives are defined basedon the level of damage sustained in the structure. The sustained damage instructures is related to the displacement and drift values during the responseunder seismic excitation [GEAA00]. DDBD was first introduced by Priestly[Pri93], with the aim of designing structures for specific target displacement.The details of the DDBD of structures is presented in Chapter 5.2.6 Review on DDBD of structures with lateralload resisting systemsMedhekar and Kennedy [MK00b] Displacement-basedseismic design of buildings-theoryA thorough theoretical discussion on performing a displacement baseddesign of SDOF and MDOF steel buildings is carried out in the paper.Clear limitations of spectral acceleration method of National Building Codeof Canada (NBCC 1995) [NRC95] are also discussed. This is followed bythe discussions on the displacement based design of a SDOF concentricallybraced frame (CBF). The authors established the displacement based de-sign for the MDOF system by assuming a harmonic response according tothe initial displaced shape. The other notable assumption on the paper isthe base shear due to earthquake excitation of the MDOF system and thesubstitute SDOF is equal. The design procedures suggested for MDOF sys-tems is to first transform the MDOF system to an equivalent SDOF andthen to design it using the procedure developed for SDOF systems. More-over, suggestions are included to consider torsional effects in the process ofbuilding design. Accounting for the center of mass translation at the startof the design process and subsequent considerations of twisting displace-ments on iterative basis are suggested for building with asymmetry in plan.Finally, some issues regarding the application of the proposed method to222.6. Review on DDBD of structures with lateral load resisting systemsdesign bridge structures (masses and stiffness are lumped in parallel) havebeen raised.Medhekar and Kennedy [MK00a] Displacement-basedseismic design of buildings-applicationAs a continuation of the theoretical study by Medhekar and Kennedy[MK00b], this research applied the displacement based design method forconcentrically braced frames. Two and eight storey frames that are locatedin Vancouver (Canada) are presented as a case study to apply the pro-posed design method. Both elastic and inelastic designs are performed forthe buildings. Subsequently, the performance of the designed buildings ischecked by using nonlinear static and time history analysis. Moreover, theexample case studies are extended to consider torsion due to asymmetricbuilding layout, column shortening, and higher mode effects.Wijesundara and Rajeev [WR] DDB seismic design of steelconcentric braced frame structuresIn this research much development on consideration of the appropriatelevel of equivalent viscous damping and yielding displacement of CBF struc-tures is made. Contrary to the design approach by [MK00b], this paper usedan equivalent viscous damping expression as a function of ductility and braceslenderness ratio that is developed by Wijesundara et al. [WNS11]. In thepaper, the yielding displacement profile is derived by considering both braceyielding and axial column deformation. Considering sway mechanism thatresults the change in brace length with rigid body rotation of the storeythat induces an column deformation as shown in Figure 2.10, the authorsformulated the interstorey yielding displacement (∆y,i) expression as follows.232.6. Review on DDBD of structures with lateral load resisting systems- 12 - SAITM Research Symposium on Engineering Advancements (SAITM – RSEA 2012) Figure 1: Fundamentals of Direct Displacement-Based Design (Priestley, 2007). The yield displacement profile is developed in this study on the basis of following two assumptions: (1) buckling of the compression braces and yielding of the tension braces at all the storey levels occur simultaneously; and (2) the force-deformation curve is approximated to be bi-linear. Then, the lateral displacement at each storey level is basically induced due to storey sway mechanism resulting in the brace elongation in tension and shortening in compression and the rigid body rotation of the storey resulting in the axial deformations of the outer columns in the braced bay as shown in Figure 2 (a) and (b), respectively. Figure 2: (a) Filtered velocity time history at 4th floor in E-W direction and (b) its fast Fourier transformation (FFT) plot. Based on the deformed geometry shown in Figure 2(a), Δsy,i the lateral displacement induced by the sway mechanism at yielding of the ith storey can be expressed as in Eq 1 neglecting the second order terms (Δsy,i)2 and (εyLud,i)2. iyiudyisy hBLcossin2 2 ,, (1) where α is the angle of the brace to the horizontal line, B is the bay width, Lud,i is the undeformed and the brace at ith storey, εy is the yield strain of the brace steel material and hi is the storey height. Tension and compression forces developed in outer columns in the braced bay, resulting in brace buckling in compression and yielding in tension, are significantly different to each other for the intermediate and slender braces. However, the gravity loads diminish the difference by decreasing the tension force and conversely increase the compression force. As consequence of that, it is reasonable to assume that the axial elongation and shorting of the outer column in tension and compression, respectively are approximately equal. Thus, Δry,i the lateral displacement induced by the rigid rotation at yielding of the ith storey can be expressed in the following form in Eq. 2. tan2, iyciiiry hhBh (2) where εyc is the yield strain of the column steel material and β is the ratio of the design axial force to the yielding force of the column section at ith storey. Finally, the total interstorey yield displacement at the ith storey Δyi is: tancossin, iyciyiy hh (3) The design displacement profile proposed by Priestley et al. [6] referring the first inelastic mode shape of RC moment resisting frame structures is used in this study as the design displacement profile for CBFs as well. The design displacement profile is obtained from a normalised inelastic mode shape δi, and the displacement of the lowest floor Δ1 as given in Eqs. 4,5 and 6: 11 ii (4) 4 nHHnii (5) 44134 nHHHHninii (6) where the normalised inelastic mode shape depends on the height Hi, and roof height Hn. All the steps in the DDBD procedure for steel CBF structures are summarized in the flow chart shown in Figure 3 Figure 2.10: a) storey sway mechanism b) rigid body rotatio of ith storey([WR] Adapted with permission from publisher)∆yi = (ysinαcosα)hi + (βychi)tanα (2.1)where, y is yield strain of the brace steel, α is the brace angle in unreformedshape, hi is the storey height, β is the ratio of the axial to yielding force ofthe column, β is the ratio of the design axial force to the yielding force of thecolu n section at ith storey, and yc is yield strain of the column. A designdisplacement profile that is suggested for frame structures by Priestley et al.[PCK07b] is adopted with the conventional equations to transform MDOFCBF to a SDOF system. Figure 2.11 outlines the developed flowchart of theDDBD of steel CBF structures. By using the formal procedure of DDBDmethod, as a case study, the authors designed four and eight storey CBFMDOF frames. Moreover, the buildings were designed for a 1% target drift.In order to avoid conservative estimates of brace sizes, the material over-strength and strain hardening ratios were not considered. After obtainingthe design base shear the braces were sized to resist the entire shear ineach floor. Moreover, beams and columns of the system were designed tobe elastic under gravity loads and lateral loads (specifically during nonlin-ear response of braces). Finally the performance of designed building are242.6. Review on DDBD of structures with lateral load resisting systemschecked using nonlinear dynamic analyses (NDA) under seven earthquakeground motions. For all building heights and bracing types an agreementwas obtained between the average NDA response and initial assumed shape.- 13 - SAITM Research Symposium on Engineering Advancements (SAITM – RSEA 2012) Figure 3: (a) Flow chart on DDBD procedure of CBF structures 3. NONLINEAR DYNAMIC ANALYSES Two CBF structures are four and eight storeys with inverted-V bracing configuration and continuous middle column that links the brace-to-beam intersection points at each floor level directly to the foundation. The height of each storey is 3.5m and the bay width of each of braced and unbraced bays is 7m. All the frames are designed for the ground motion which has the probability of exceedance equal to 10% in 50 years (i.e., return period of 475 years) with the peak ground acceleration of 0.3g. 5% damped displacement spectrum as defined in EC8 [1] is used for the design with the corner period (Tc) of 4s. In order to investigate the performance of the buildings designed according to the DDBD procedure, nonlinear dynamic analyses are performed using the OpenSEES finite element computer program. The steel CBFs are modelled in 3-D rather than in 2-D to permit the braces to buckle in the out-of-plane direction of the frame since all the braces are designed and detailed to develop the out-of-plane buckling. The behaviour of all the frame elements except the braces is limited to in-plane displacement by restraining the translational degree of freedom in the perpendicular direction to the plane of the frame and the rotational degrees of freedom in the out-plane directions. The column-to-base and the beam-to-column connections are modelled as pinned connections while the columns are modelled as continuous members. All the braces are modelled using the inelastic beam-column brace model proposed by Uriz [7]. All the columns and beams are also modelled using nonlinear beam-column elements available in OpenSEES frame work. The corotational theory was used to represent the moderate to large deformation effects. Seven real accelerograms are selected from PEER data base in order to carry out the nonlinear dynamic analyses and scaled to match with the design displacement spectrum. Figure 4 shows the 5% damped displacement spectra of the individual accelerogram and average of the individual accelerogram together with the design displacement spectrum, in the period range of 0 to 4s. The average displacement spectrum of the individual accelerogram is matched well with the design displacement spectrum. 00.10.20.30.40.50.60.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0Period (s)Displacement (m)AverageDesign Spectrum Figure 4: Displacement spectra from the scaled natural accelerogram at 5% damping 4. RESULTS AND DISCUSSION The average profiles of peak inter-storey drift ratios of the two buildings resulting from NDA are compared with the corresponding design profiles. Figure 5(a) and (b) illustrate the average peak displacement and drift ratio profiles for 4 and 8 storeys CBFs with IVMC configuration, respectively. It is clear that the resultant average displacement profile of 4 storey frame is almost linear and well matched to the design displacement profile. The average drift ratio is 4% below the design drift ratio at the 1st storey while 30% below at the top storey. In the case of 8 storey frame, the average displacement profile is fairly matched with the design displacement profiles ensuring that average displacements do not exceed the design displacements corresponding to the presumed displacement shape significantly as shown in Figure 5(b). The average drifts at storey levels 5, 6 and 7 are slightly higher than the design drifts, and the maximum of 16% higher drift is observed at 7th storey level. Figure 2.11: Flow chart on DDBD procedure of CBF structures ([WR]Adapted with permission from publisher)252.6. Review on DDBD of structures with lateral load resisting systemsGarcia et al. [GSC10] Development of a DBD method forsteel frame-RC wall buildingsThis research is a direct extension of the displacement based design pro-cedure developed by Sullivan et al.[SPC06] for RC frame wall structure.In this paper, the applicability of the DDBD method is validated for steelframe-RC wall structures. This type of system is a typical steel-concretehybrid system at a building level. The flow chart used to design this sys-tem which is adopted from Sullivan et al.[SPC06], is shown in Figure 2.13.Important steps of the flowchart are discussed in the following paragraphs.Figure 2.12: Geometry of frame-wall structures used in the evaluation([GSC10] Adapted with permission from publisher)262.6. Review on DDBD of structures with lateral load resisting systemsstructure characteristics, the design displacement and the development of the designdisplacement spectra. The design method proposed in this article uses this DDBDprocedure to obtain the design forces, as outlined next. In particular, the next sectiondemonstrates how the design displacement profile and equivalent viscous damping of thedual systems can be established as a function of strength assignments.3. Proposed DDBD Methodology for Steel Frame-RC Wall BuildingsThe flowchart describing the proposed design method for dual steel frame-RC wallsystems is depicted in Fig. 2. The several steps involved in the process are outlined inthe following sections.Determine effective height, h , effective mass, m ,and design displacement, ΔeedCalculate the ductility demands on steel framesand RC walls. Are ductility demands excessive?Determine equivalent viscous dampingvalues for steel frames and RC wallsNOReduce driftlimit.YESUse proportions of overturning moment resisted by the steelframes and RC walls to factor damping values and obtainan equivalent system damping value ξ sysPlot displacement spectra at system dampinglevel and use design displacement to obtainrequired effective period, T .eDetermine effective stiffness, K ,and design base shear, V = K Δeeb dDistribute base shear up the height inproportion to displacement of masses.Substract frame shears from total shears toobtain wall shears and thereby moments.Obtain beam and columnstrengths by factoring strengthproportions by shear base.Perform capacity design with allowance for highermode effects to obtain strengths in non-yieldingelements, and design shears in frames and wallsAssign strength proportions toframes and wallsSelect a beam group from steeltables or chartsSteps1 & 2DDBDSteps4 to 8Step3Step9Step10Determine RC wall inflection height, hinfDetermine yield displacementsof RC walls and yield drift ofsteel framesCalculate design displacement profileFIGURE 2 Flowchart of DBD for dual systems [adapted from Sullivan et al., 2006].256 R. Garcia, T. J. Sullivan, and G. D. CorteDownloaded by [The University of British Columbia] at 18:03 03 July 2014 Figure 2.13: Flowchart of DBD for dual systems ([GSC10] Adapted withpermission from publisher)272.6. Review on DDBD of structures with lateral load resisting systemsOne of the critical advancements of this design methodology is its flexi-bility to assign strength proportion at the start of the design process. Thestrength assignment is carried out by allocating a portion of the total baseshear for the frames and walls. The design displacement profile is then gov-erned by the assigned strength proportions. By using the relative strengthdistribution of frame elements, the frame shear profile is calculated by usingEquation 2.2.Vi,frame =∑Mb,i +∑Mb,i−12(hi − hi− 1)(2.2)where, Vi,frame is the frame shear at level i, Mb,i, and Mb,i−1 are the beamstrengths at i and i-1 storeys, and hi and hi−1 are the storey heights forlevel i and i-1. The total shear profile is estimated from Equation 2.3.Vi,totalVb= 1−i(i− 1)n(n+ 1)(2.3)where, Vi,total is the total shear at level i, n is the total number of storeys,and Vb is the design base shear. Then the base shear carried by the wall(Vi,wall) can be calculated by deducting the frame shear from the total shear.From the shear profiles developed through the above equations, the mo-ment diagram of the wall can be drawn to calculate the height of inflection.The height of inflection is then used to calculate the properties of equivalentSDOF system. Another contribution of this research is the expression of theequivalent viscous damping ξhyst which is a weighted average between thewall and frame based on their overturning moment capacity given below inEquation 2.4.ξsys =Mwallξwall +MframeξframeMwall +Mframe(2.4)where, ξsys is the system equivalent viscous damping and Mwall, ξwall,Mframe, ξframe are the wall overturning moment, equivalent viscous damp-ing for wall, overturning moment of frames, and equivalent viscous dampingfor frame, respectively. Finally 4-, 8-, 12-, 16-, and 20- storey buildings weredesigned using the proposed method. Two dimensional time history analyseshave been carried out to check the performance of buildings by comparing282.6. Review on DDBD of structures with lateral load resisting systemsresponse displacement profiles with the initial target profile. For the casestudy buildings, the proposed method worked very well in controlling thedeformations.Malekpour et al. [MGD13] DDBD of steel braced reinforcedconcrete framesThis research work develops a direct displacement based design methodfor steel concrete hybrid system. The system consists of reinforced concreteframes with steel cross bracing. The authors applied the concept of ini-tial strength proportion assignment for frames and bracing to obtain thedesign displacement profile based on the idea of Sullivan et al. [SPC06]. Si-multaneous iterative calculations of equivalent viscous damping [Bla04] anddesign process were carried out until the trial effective period converged tothe effective period from the displacement spectra corresponding to designdisplacement. Figure 2.14 shows the developed flowchart of the DDBD ofRC steel braced frames (Figure 2.15).292.6. Review on DDBD of structures with lateral load resisting systemset al. (2006) came to the conclusion that the braced frame has more ductility and can resist greater lateralload. Maheri and Ghaffarzadeh (2008) investigated the amount of the interaction force between the RCframe and the steel bracing analytically and experimentally using the experiments conducted on RC mo-ment-resisting frames and RC frames with steel bracings. In this study, considering the ever-increasingdevelopment of the DBD and its use in RC buildings in addition to the use of steel bracing systems inRC frames as a new structural system, steps of the displacement-based design method are developedfor RC frames with steel bracings.2. GENERAL REVIEW OF THE DDBD METHODAs also mentioned by Moehle (1992) and Kowalsky et al. (1995), the DDBD procedure could beconsidered as reverse of the force-based design method. In this method, the structure is designed with apre-defined limit state, which predicts response of the structure and uses the design methods that are basedon response control of the structure. Thus, this method beginning with the analysis of the structuralcomponents ends in their design. Also, it should be noted that thismethod uniformly predicts the nonlinearbehavior with no need of the various suggestions about the force reduction factors (Priestley, 2003;Gulkan and Sozen, 1974; Shibata and Sozen, 1976). According to the points mentioned above, theDBD method presents a reasonable approach for seismic design of the structures. Figure 1 displays thesteps that should be followed for seismic design of the dual frame-bracing systems. According toFigure 1. DDBD flowchart for RC braced frames.1424 S. MALEKPOUR, H. GHAFFARZADEH AND F. DASHTICopyright © 2012 John Wiley & Sons, Ltd. Struct. Design Tall Spec. Build. 22, 1422–1438 (2013)DOI: 10.1002/talFigure 2.14: Flowchart of DDBD for steel braced reinforced concrete framesThe storey yield displacement of bracing is computed using Equation 2.5by assuming the tension yielding of bracings ([GA07]).4yi =FyLbriEcosθi(2.5)where Fy is the yield strength of the brace, Lbri is the length of bracing, Eis the modulus of elasticity of the steel, and θi is the angle of bracing withhorizontal. The design displacement profile is calculated by using Equation2.6 that considers the design drift. The design drift (θd) is reduced as given302.6. Review on DDBD of structures with lateral load resisting systemsin Equation 2.7 to account for higher mode effects ([SPC06]).4i = 4iy + (θd)(hi) (2.6)θd = θd,limit[1−N − 5100(MOT,frameMOT,total+ 0.25)]≤ θd,limit (2.7)In order to calculate the equivalent viscous damping, the initial effective(Te,trial) period is computed as:Te,trial =N6√µsys (2.8)where N is the number of storeys of the building under consideration and µsysis the system ductility. Once the equivalent viscous damping is developedthe usual procedure of DDBD method was followed to calculate the designbase shear.the steps are being comfortably handled and provide a proper control for displacement and inter-storydrift of the structure.4. INVESTIGATED STRUCTURES AND RESULTS OF THE DIRECT DISPLACEMENT-BASED DESIGNIn this study, an internal 2D frame is selected from each of the 4-story, 8-story and 12-story buildings.The frames are 3.5m in height and have three spans with 5m in width. The structures are assumed tobe residential, placed in a very high seismicity region with soil type II and according to the IranianCode of Practice for Seismic Resistant Design of Buildings (Standard No.2800, 2005). The structuresare all composed of reinforced concrete frames and steel bracings, as shown in Figure 5. The structuresare regular in plan with dual syst ms of RC frames plus steel bracings providing the lateral strengthand stiffness. The bracings are directly connected to the frames, and the profiles used for the bracesand the material properties are as follows:f0c ¼ 30 MPa EC ¼ 25 740 MPa fy ¼ 400 MPa Es ¼ 200 000 MPaResults of the six steps leading to DDBD of the 4-story, 8-story and 12-story models are given in thissection. The final design results and strength values of beams, columns and bracings are given in Tables 2and 3. It should be noted that in this methodology, the columns are designed regarding their axial loadshare and the b ams and bracings are controlled according to capacity-based design (the provisions ofstrong column–weak beam) after they have been designed using this approach to retain their elasticbehavior in the event of an earthquake. The beams and bracings are also designed regarding their assignedproportion of the base shear.Figure 5. Plan and elevation of the models.Table 2. Initial design results of the structures.4 stories 8 stories 12 storiesDrift limit θd 0.025 0.025 0.025Frame yield rotation θy 0.0125 0.0110 0.0100Braced yield displacement Δy (mm) 25.4 50.8 76.2Effective mass me (kg) 229836 462550 694873Effective height He (mm) 9670 18390 27140Design displacement Δd (mm) 230 414 587Braced ductility m 9.06 8.15 7.7Braced damping xbraced 14.82 14.28 14.03Frame damping xframe 12.56 13.14 12.82Equivalent damping xeq 13.62 13.64 13.49Effective period T (s) 1.70 2.65 3.30% base shear assigned to brace 60% 60% 50%DDBD OF STEEL-BRACED RC FRAMES 1431Copyright © 2012 John Wiley & Sons, Ltd. Struct. Design Tall Spec. Build. 22, 1422–1438 (2013)DOI: 10.1002/talFigure 2.15: Geometry of steel braced reinforced concrete frames used inthe evaluation ([MGD13] Adapted with permission from publisher)Finally the performance of the designed buildings were investigated usingnonlinear time history analysis. From the responses, it is found that theinterstorey drift of four and eight storey buildings is lower than the initialtarget value. However, due to buckling of the braces at the lower stories theinterstory drift for the 12 storey building is greater than 2.5%.312.6. Review on DDBD of structures with lateral load resisting systemsSullivan [Sul09] DDBD of a RC wall-steel EBF dual systemwith added dampersA direct displacement based design method is developed and verifiedfor an eight- storey hybrid RC wall-steel eccentrically braced frame (EBF)with visco-elastic dampers. The structural system and the developed designmethod are shown in Figures 2.16 and 2.17, respectively.2009.pdf168 DIRECT DISPLACEMENT-BASED DESIGN A method for the Direct DBD of Frame-Wall dual systems has been developed and tested by Sullivan et al. [3] and a methodology for the Direct DBD of systems with added damping has been proposed by Christopoulos and Filiatrault [4]. However, to the author’s knowledge, a Direct DBD procedure has not previously been developed for the combination of structural systems incorporated in the case-study building. Furthermore, the methodology for systems with added damping [4] is iterative and therefore not very practical. As will be shown in this paper, the Direct DBD methodology developed for frame-wall dual systems by Sullivan et al. [3] can be relatively easily adapted to the case study structure, and the added damping devices can be accounted for without iteration. General Procedure The basic process of the Direct DBD procedure developed principally by Priestley et al. [1] is illustrated for a dual system in Figure 3. The first two steps in the procedure, shown as Fig. 3(a) and Fig. 3(b), aim to establish the effective mass, (me), height (he) and design displacement (∆d) of an equivalent SDOF system representation of the MDOF building, responding to a selected deformation limit (associated with either material strain or non-structural storey drift limits). This is based on the Substitute Structure approach pioneered by Gulkan and Sozen [5] and Shibata and Sozen [6]. As indicated in Figure 3(c), the ductility demand expected at the design deformation limit is then used to set an equivalent viscous damping value for the equivalent SDOF system. This equivalent viscous damping represents the energy dissipated by the structure and therefore the damping values vary depending on the hysteretic properties of the structural system being designed. To account for the impact that energy dissipation has on the dynamic response, the design displacement-spectrum is then developed at the expected equivalent viscous damping level. As shown in Figure 3(d), the design displacement is then used to enter the highly-damped spectrum and read off the effective period that will ensure the design displacement is not exceeded. The effective period, Te, can be related to an equivalent SDOF effective stiffness, Keff, using Equation 1. 224eTemK eff π= (1) where me is the effective mass of the equivalent SDOF system (established in steps a & b of the design procedure). Finally, the design base-shear, Vb, is obtained by multiplying the required effective stiffness by the design displacement, as shown in Equation 2. deffKbV ∆= (2) Figure 2: Plan and Elevation of the 8-storey dual-system case-study building (not to scale). 05101520251 2 3 4 5Elasto-PlasticRC FrameRC BridgeEquivalent Viscous DampingDisplacement DuctilityEquivalent Viscous Damping 00.10.20.30.40.50.60 2 4 6ξ=17%ξ=5%Spectral Displacement (m)Period (s)Teff∆dSpectral Displacement (m)(a) SDOF representation (b) Effective Stiffness, Keff (c) Equivalent Viscous Damping (d) Displacement Spectrum Figure 3: Fundamentals of Direct Displacement-Based Design (adapted from [3]). PLAN SIDE ELEVATION Damper 6 m RC walls 8.0 m 8.0 m 8.0 m 9.2 m 8.0 m 8.0 m 8.0 m 7.15 m 7.15 m 4.0 m 18.3 m 4.0 m 8-storeys at 4 m cc. Pinned Connections Internal steel framing (non lateral-load resisting) Excitation Direction Considered F me he Displacement Fd rKKeffKi ∆y ∆dForce Figure 2.16: Plan and elevation of the 8-storey dual-system case-study build-ing ([Sul09] Adapted with permission from publisher)322.6. Review on DDBD of structures with lateral load resisting systems169 As such, the design procedure is relatively simple. The challenge for dual-system case-study structures is to establish the appropriate equivalent viscous damping and the equivalent SDOF system values of effective mass, height and design displacement. As will be seen in the next section, these equivalent SDOF parameters can be established with knowledge of the design displacement profile expected for the building at the design deformation limit. By considering the results of shake table tests on RC frame-wall systems, Sullivan et al. [7] found that the displacement profile of RC frame-wall systems is dependent on the curvature profile in the RC walls, which in turn is a function of the proportions of strength assigned to the walls and frames. Based on this observation, the design methodology presented in Figure 4 was developed by Sullivan et al. [3] for dual systems possessing RC walls and frames. This methodology will be extended here for the case-study building being examined. Figure 4: Design methodology for RC frame-wall systems [3] and extended here for the case-study building. Design Displacement Profile for the Dual System As indicated in Figure 4, strength proportions are assigned at the start of the design procedure to give the design displacement profile. This is done by using the strength proportions to establish the moment profile and subsequently the curvature profile in the RC walls at peak response. Integration of the curvature profile then provides the displacement profile. Sullivan et al. [7] found that the displacement profile in RC frame-wall systems is well represented by summing the elastic displacement profile of the walls together with a linearly increasing displacement profile associated with inelastic rotation of a base plastic hinge in the RC walls, as shown by Equation 3. icfyWalldiyi hh.2 ⎟⎟⎠⎞⎜⎜⎝⎛ −+∆=∆ φθ (3) where ∆i is the design displacement for level i θd is the design storey drift limit φyWall is the wall yield curvature (Equation 5) hi is the height to level i hcf is the contra-flexure height in the walls and ∆iy is, given by Equation 4. 622cfyWallicfyWalliyhhh φφ −=∆ for hi > hcf (4a) cfiyWalliyWalliy hhh6232 φφ −=∆ for hi < hcf (4b) The contraflexure height in the walls, hcf, can be obtained with knowledge of the strength proportions, as explained in subsequent paragraphs. The yield curvature for U-shaped walls bending in the axis of the web can be approximated with reasonable accuracy [8] using only the longitudinal reinforcement yield strain and the wall length, as shown by Equation 5 [9]. Yield curvature expressions for other section shapes are available in [1]. wyyWall Lεφ 4.1= (5) The yield displacement profile given by Equation 4 assumes a linear variation in wall curvature from the yield curvature at the base to zero at the contra-flexure height. As argued by Priestley and Paulay [10] this approach approximately accounts for tension shift and higher mode effects and as shown by Sullivan et al. [7] it appears to work relatively well for RC frame-wall systems. For the case study dual system examined here, the assumption that the curvatures in the walls will dictate the displacement profile of the building, is made considering that the stiffness of the large wall sections is considerably greater than that of the EBF columns. One might anticipate that the diagonals of the EBF system would render the EBF very stiff and that therefore, these should be considered in setting the displaced shape. However, the diagonals are not connected directly to each floor level and are instead only connected to the top and bottom of the EBF columns. As such, the deformed shape of the structure from the ground to roof level is dependent on the curvatures of the stiffest elements, which are the wall sections. The EBF system resistance is still expected to influence the displaced shape, but in a secondary fashion through changes to the moment and therefore curvature profile in the walls. Note that the results of non-linear time-history analyses presented later in this paper also support the validity of this displaced shape assumption. As such, Equations 4 and 5 can be used to estimate the building’s displaced shape, provided that the strength proportions of the EBF relative to the RC walls are considered in establishing the wall contraflexure height. Contraflexure develops in a wall when a parallel structural system causes the upper levels of the wall to be bent in an opposite sense relative to the lower levels. This occurs in frame-wall structures because the frames tend to restrain the upper levels of the walls. It should also be expected for the case study structure being considered if the EBF system restrains a large amount of the lateral load. Figure 5 illustrates how the shear forces and bending moments are expected to vary according to the proportion of resistance assigned to the walls and EBFs respectively. Two cases are shown in order to demonstrate that with a large portion of the overturning assigned to the EBF system, the walls are expected to undergo reverse bending over their upper levels, developing a point of contraflexure at a height, hcf. The contraflexure height is expected to reduce as the proportion of resistance carried by the EBF system increases. 1. Assign Strength Proportions to establish design displacement profile 2. Use design displacement profile to obtain equivalent SDOF properties me, he, and ∆d 3. Estimate equivalent viscous damping of dual system by considering ductility demands and relative work done of the separate systems. 4. Undertake Direct DBD to obtain design base shear Vb (as per Figure 3) 5. Set element strengths to provide Vb, respecting the strength proportions assigned in step 1. Figure 2.17: Flowchart of DDBD for RC wall-steel EBF dual system withadded dampersThe design method is started by assuming strength proportions to theEBF and RC wall to develop the co tra-flexure height and the correspondingdesign displacement shape. The displaced shape at the peak displac m ntis calculated using Equations 2.9-2.11.∆i = ∆iy +(θd −φyWallhcf2)hi (2.9)where ∆i is the design displacement for level iθd is the design storey drift limitφywall is the wall yield curvaturehi is the height to the level ihcf is the contra-flexure height in the walls∆iy is given in Equa ions 2.10 and 2.11∆iy =φywallhcfhi2−φywallh2cf6for hi > hcf (2.10)332.6. Review on DDBD of structures with lateral load resisting systems∆iy =φywallh2i2−φywallh3i6hcffor hi ≤ hcf (2.11)In this paper, the equivalent viscous damping is calculated by superposingthe dissipated energy of different structural elements. The system equivalentviscous damping (ξsys) is calculated based on the amount of base shear (Vb)and damping force (Fdamper) of the hybrid system. The equation used tocalculate the system equivalent viscous damping is given in Equation 2.12.ξsys =2Vwallξwall + 2VEBF ξEBF + Fdamper2Vb(2.12)where Vwall,VEBF , ξwall, ξEBF are wall shear, EBF shear, equivalent viscousdamping for wall, and equivalent viscous damping for EBF, respectively. Af-ter this step, the procedure of DDBD Priestley et al. [PCK07b] is followedto calculate the design base shear. 85% of the total overturning momentis used to design the flexural reinforcement for the RC walls. EBF mem-bers were designed by considering both maximum displacement and velocityconditions. Moreover, the required damping stiffness is computed that canbe used to manufacture a visco-elastic damper. From the validation usingtime history analysis, the displaced profile of the system is matched withthe initial design profile. The author of this thesis believes that the methodof establishing equivalent viscous damping without requiring extensive dy-namic analysis on the assumed hysteretic behaviour is a novel contribution.Christopoulos [CPP04] Seismic design and response ofbuildings including Residual DriftThis paper contributes a novel approach to account the residual defor-mation in the initial stage of the DDBD process of frame structures. Thepaper initially discusses the residual deformation damage index and suggeststhe use of combined residual and maximum drift performance matrix for as-sessing structures. Subsequently, a procedure to evaluate the global damageof the MDOF system based on a combined performance matrix is presented.The global performance level is defined by aggregating the contribution of342.6. Review on DDBD of structures with lateral load resisting systemsindividual storey levels with appropriate weighting factors. In order to incor-porate residual drift in to the design process, the authors developed inelasticresidual drift spectra using 20 ground motion records for ductility values of2, 3, 4, and 5. The developed inelastic residual drift spectra were aimed atextending the extensive research on residual deformation of SDOF systemby Kawashima et al. [KMHN98]. Two types of hysteretic rules i.e., Takedadegrading stiffness (TK) and bilinear elasto-plastic (EP) were considered.Plots of maximum and residual displacement response with elastic periodand effective period are produced from the analyses. A relationship is pro-vided to derive the residual drift of MDOF (RDMDOF ) systems from theresidual drift of SDOF (RDSDOF ) systems using amplification factors givenin Equation 2.13. The factors fMDOF and fp−4 are incorporated to accountfor higher modes and P-4 effects, respectively.RDMDOF = RDSDOF .fMDOF .fP−4 (2.13)Having the residual displacement response spectra using SDOF oscillatorwith an expression to generate the equivalent residual drift of MDOF system,the authors proposed a DDBD procedure that incorporates residual drift atthe initial stage of DDBD. The proposed method introduces one more stepon the conventional DDBD procedure of Priestley et al. [PCK07b]. Afterobtaining an equivalent SDOF system using conventional DDBD method[PCK07b], a check for residual deformation is added before calculating thedesign base shear. From the target displacement and effective period ofequivalent SDOF, the residual displacement can be obtained from the resid-ual displacement spectra. By using Equation 2.13, the residual drift ofMDOF system can be calculated using the appropriate amplification fac-tors. If the obtained RDMDOF is within the acceptable limit then the pro-cess can proceed to calculate the design base shear. However, if the residualdrift has exceeded the limit, the properties of equivalent SDOF should bemodified and all the steps will be repeated. Finally, the paper presentsrecommendations to control the residual drift of MDOF frame structures.352.6. Review on DDBD of structures with lateral load resisting systemsAlaee [MASR] Towards a DDBD procedure for cold-formedsteel frame / wood panel shear wallsTwo important inputs of direct displacement based design method, equiv-alent viscous damping (EVD) and design displacement profile, are formu-lated for cold-formed steel frame / wood-panel (CFSFWP) systems. Forthis purpose, several nonlinear time history analyses are carried out to de-velop the EVD as a function of ductility for different effective periods of agiven hysteretic law. Moreover, for low rise systems, verification is includedto use a linear displacement profile for DDBD. The EVD ξe expression isdeveloped for thin and fat hysteretic models in terms of ductility (µ) and isgiven in Equation 2.14.ξe = 0.05 + 0.478(µ− 1µpi)(2.14)In addition, for the DDBD procedures the authors suggested the follow-ing expression for equivalent viscous damping (Equation 2.15) that needssmall trial and error.ξe =0.095µ− 0.045 if1 ≤ µ ≤ 20.145 ifµ > 2(2.15)As part of recommendation to use linear displacement profile, a plotof mean interstorey drift with the assumed profile is given that shows theapplicability of the assumption for 3 storey CFSFWP structures.363Studying lateral behaviour of CLT infilledSMRFs via artificial intelligence, GeneticAlgorithm, and Response Surface Method3.1 Predicting MISD of CLT infilled SMRFs:Response Surface MethodThe 1995 Hyogo-ken Nanbu (Kobe, Japan), the 1985 Michoacan earth-quake (Mexico City, Mexico) and the 1994 Northridge earthquake (Califor-nia, US) caused significant damage to the infrastructure. Generally, thedamage sustained in the buildings can be related to the structural defor-mation [KMA03, EY04, MK05, GAEB99, KC04]. Also, several reinforcedconcrete buildings damaged by the 1985 Michoacan earthquake were demol-ished due to large permanent (residual) drift [RM86]. Recent studies arehighlighting the importance of residual drift in the post-earthquake perfor-373.1. Predicting MISD of CLT infilled SMRFs: Response Surface Methodmance assessment of new and existing structures [CPP03, PCP03, CP04,LBC04, BCMM04, YD08]. Gupta and Krawinkler [GK99] reported theresidual drift demands SMRF frames and highlighted the increase in un-certainty along with the intensity of ground motions. In order to satisfy areparability limit state, Iwata et al. [ISK06] suggested that the maximumresidual inter-storey drift angle for steel moment-resisting frames (SMRFs)buildings should be limited to 1/90. McCormick et al. [MAIN08] proposedresidual drifts of 0.5% as permissible value on the study conducted in Japan.Wu et al. [WLYL04] showed the combination of maximum and residualdeformation is effective to evaluate structural performance under seismicexcitation. Pampanin et al. [PCP03] developed performance matrix us-ing interstorey and residual drift as a framework for an alternative per-formance assessment. Erochko et al. [ECTC10] developed an equationto express the residual drifts as function of peak drifts and damage con-centration factor. More recently, Christidis et al. [CDHB13] proposeda simple method to evaluate the maximum seismic roof displacement ofsteel framed structures from their residual drifts. These studies promptedthe need to develop an equation for rapid and direct evaluation of thepost-earthquake performance of steel-timber hybrid structures. Recently,[SDT12, STKP12, DST12, Dic13, DSBT14] investigated the potential useof Cross Laminated Timber (CLT) as an infill in steel moment resistingframes to couple the light and stiff behaviour of timber with a strong andductile steel frame. In addition, Tesfamariam et al.[TSDB14] studied theseismic vulnerability of this hybrid system with consideration of MISD.The primary objective of this section is to develop an equation to predictMISD from post-earthquake residual interstory drift (RISD) and modelingparameters of CLT infilled SMRFs. For this purpose, two-dimensional (2D)dynamic analysis of the proposed hybrid system was performed for variousmodeling parameters, i.e. building height, infill pattern, CLT panel thicknessand strength, and connection bracket spacing. The analyses were carried outby using OpenSees [MMS+06] FE software for twenty maximum consideredearthquake (MCE) ground motions (2% in 50 years). Response surfacemethodology (RSM) with D-Optimal experimental design technique was383.1. Predicting MISD of CLT infilled SMRFs: Response Surface Methodadopted for the development of prediction equation. Finally, the proposedequation is statistically validated to check its capability of prediction fordata points other than the model training data set.3.1.1 Building design and modelingDesign of BuildingsA typical 3-, 6- and 9- storey steel frame office building, with regulargeometric shape, was considered. The plan view is shown in Figure 3.1.The buildings were designed for the seismic events of the magnitude possi-bly occurring in Vancouver, Canada. The buildings were modeled as two-dimensional structure and, due to its symmetry in plan, accidental torsionwas neglected both in design and analysis phase. For the seismic load, theequivalent static load (ESL) procedure as suggested by NBCC 2010 [NRC10]was used. The buildings were designed to meet the requirement of moderateductility (with Rd = 3.5, and Ro = 1.5) as specified in CSA S16 [CSA09].Only building frames along the north-south directions were considered forthe design and analysis. All steel sections used in design were based onCSA G40.21-04 [CSA09] specification and the section details are presentedin Table 3.1 and 3.2.393.1. Predicting MISD of CLT infilled SMRFs: Response Surface MethodFigure 3.1: Typical building planTable 3.1: beam design detailsBuilding storey Storey number External Internal3 1−2 W310×60 W310×603 W310×52 W310×5261−3 W310×79 W310×794−5 W310×74 W310×746 W310×60 W310×6091−6 W310×86 W310×864−5 W310×74 W310×746 W310×60 W310×60Table 3.2: column design detailsBuilding storey Storey number External Internal3 1−3 W310×67 W310×866 1−3 W310×107 W310×10791×6 W310×107 W310×1184−6 W310×67 W310×867−9 W310×67 W310×67403.1. Predicting MISD of CLT infilled SMRFs: Response Surface Method4.5 m 3.65 m TYP Figure 3.2: CLT infill distributions of 6-storey typical building, a) Framewith infill only in the middle bay (0-1-0); b) Frame with infill in two exteriorbays (1-0-1), and c) Frame with infill in all bays (1-1-1)Displacement based beam-column element Elastic shell element for CLT Non-linear spring for connection Gap elements (B) Elastic beam column element Bracket Spacing (C) Panel Thickness(D) Figure 3.3: Details of connection, Gap and CLT infill panels413.1. Predicting MISD of CLT infilled SMRFs: Response Surface MethodModeling of building structuresDetailed modeling of both structural members and CLT infill panels wereperformed using OpenSees FE software [MMS+06]. The details are providedin the subsequent paragraphs.Modeling of structural frames elements: spread plasticityprincipleThe structural frame elements have been modeled using combinationof linear and nonlinear elements. Linear elastic and non-linear displace-ment based beam-column elements used for the center and end of the framemember respectively are shown in Figure 3.3. Modified Ibarra KrawinklerDeterioration model [LK10] used with a bilinear material property basedon moment-curvature relationships are given in the ASCE 41 [C+07] fornonlinear parts of the frame elements.Modeling of CLT panelsCLT panels were modeled as a linear elastic shell element as shown inFigure 3.3. For simplicity, the section of CLT panel was modeled as singlelayer with linear elastic- isotropic wood material property of Quad elementsof OpenSees. The material model used for these quad elements was thendMaterial-ElasticIsotropic. The CLT mechanical properties used for mod-eling can be found elsewhere [Dic13, DSBT14, TSDB14].Modeling of connection between CLT panels and steel framesThe connection between the steel frames and CLT walls was achievedby using steel brackets; which were bolted with steel and nailed to CLTpanels. Non-linear spring model was used to represent the behaviour ofthe bracket that connects CLT with steel frame. A more realistic charac-terization of the CLT to frame connection could be accomplished with theso-called Pinching4 material model of OpenSees [SST+13]. Figure 2.7 showsa good agreement between experimental test data and Pinching4 analytical423.1. Predicting MISD of CLT infilled SMRFs: Response Surface Methodmodel. Therefore, the calibrated Pinching4 model was used to model thenon-linearity of the bracket connection. The OpenSees twoNodeLink andElastic Perfectly Plastic Gap (EPPG) elements were used to model con-nection and gap respectively. The bracket behaviour was assigned both inthe shear and axial direction. Additionally, the EPPG gap property wasmodeled in parallel formulation with the axial behaviour of bracket.3.1.2 Seismic inputTwenty ground motions records were obtained from the Pacific Earth-quake Engineering Center [PEE05] database by comparing the ratio of seis-mic motion (A/V) to Vancouvers A/V. The A/V (A in g and V in m/s) ofVancouver is close to 1.0 and an average of 0.97 was obtained from selectedground motions. All GMRs were obtained from stations on soil class C ofNBCC, 2010 [NRC10]. The events had moment magnitudes in range of 5.42- 7.36 with in epicentral distance of (14.4-76 km). Table 3.3 summarizes theselected GMRs for this paper.Table 3.3: Ground Motion propertiesNo. Earthquake Station Mw PGA/PGV D(Km) tD(Sec) AI(m/s)1 San Fernando, 1971 CDMG 24303 LA - Hollywood Storage FF 6.4 1.11 39.49 9.26 0.762 San Fernando,1971 CDMG 24271 Lake Hughes 6.61 0.81 26.1 7.93 0.833 Parkfield,1966 CDMG 1016 Cholame-Shandon Array 12 6.19 0.98 6.18 25.81 0.834 Northridge,1994 CDMG 24461 Alhambra - Fremont School 6.69 1.02 40.15 7.45 0.745 Northridge,1994 CDMG 24283 Moorpark - Fire Sta 6.69 1.03 31.45 6.98 0.866 Livermore,1980 CDMG 57064 Fremont - Mission San Jose 5.8 1.2 37.28 5.41 0.367 Coaglina,1983 CDMG 46175 Slack Canyon 6.36 1.016 33.52 7.53 0.68 Morgan Hill,1984 CDMG 57064 Fremont - Mission San Jose 6.19 0.91 31.83 30.28 0.539 Morgan Hill,1984 CDMG 57383 Gilroy Array 6 6.19 1.196 36.34 23.94 1.0910 Loma Prieta, 1989 CDMG 57383 Gilroy Array 6 6.93 1.092 34.47 15.89 0.9311 Gazli USSR, 1976 9201 Karakyr 6.8 1.047 12.82 14.9 5.912 Northridge, 1994 USC 90015 LA - Chalon Rd 6.69 0.929 14.92 9.01 0.8513 Northridge, 1994 USC 90020 LA- W 15th St 6.69 1.04 29.59 19 0.7614 Northridge, 1994 UCSB 78 Stone Canyon 6.69 1.107 14.41 8.31 1.1715 Imperial Valley, 1979 UNAMUCSD 6621 Chihuahua 6.53 0.923 18.8 23.97 1.3516 Iprina Italy, 1980 ENEL 99999 Rionero In Vulture 6.2 0.92 29.83 27.35 1.2317 Iprina Italy, 1980 ENEL 99999 Calitri 6.9 0.83 15.04 31.36 1.3518 Kern Country, 1952 USGS 1095 Taft Lincoln School 7.36 1.132 43.49 29.88 1.4519 Hecotr Mine, 1999 SCSN 99999 Hector 7.13 0.895 26.53 11.26 1.0820 Hector Mine, 1999 CDMG 12647 Joshua Tree N.M 7.13 1.15 75.38 11.9 0.89Two additional characteristics of the selected records are found in theTable 2; significant duration (tD) and Arias Intensity (AI). Significant du-ration (tD) is estimated as suggested by [TB75], which is a time inter-433.1. Predicting MISD of CLT infilled SMRFs: Response Surface Methodval at which 5% and 95% of the Arias Intensity (AI) accumulates. Al-though it is believed that strong motion duration does not have any signif-icant effect on the response structure [SCBC98, BC94], some recent stud-ies [MP97, Cha05, DM01] show that there is indirect relationship betweenstrong ground motion duration and seismic response. Therefore, in this workseismicity was characterized by significant duration (tD), calculated usingSeismoSignal V 5.1.0 software. Figure 3.4 shows the definition of the tD forImperial Valley, 1979 record.The selected GMRs were scaled to match with the response spectra ofVancouver at specified period range. Matching was done with in the periodrange of (0.2T − 1.5T); 0.138 sec - 4 sec, where T is the fundamental periodof the building. The ground motion matching was accomplished by matchingthe spectrum for a probability of exceedance of 2% in 50 years of NBCC 2010[NRC10]. Figure 3.5 shows the scaled spectra with the mean and targetspectrum for considered hazard value.443.1. Predicting MISD of CLT infilled SMRFs: Response Surface MethodFigure 3.4: Significant duration definition according to ([TB75]) for ImperialValley, 1979 earthquake453.1. Predicting MISD of CLT infilled SMRFs: Response Surface Method0 1 2 3 400.511.522.53Time (sec)Acceleration (g) MeanTargetFigure 3.5: Comparison of mean and target response spectra for probabilityof exceedance of 2 % in 50 years3.1.3 Maximum and residual interstorey drift resultsTwo dimensional nonlinear time history analysis was carried out to cal-culate MISD and RISD to develop the prediction equation. The factors andtreatment levels that were used for dynamic analysis were chosen by consid-ering market availability and simulation running time. Three, six , and ninestorey frames were considered with with one (0-1-0), two (1-0-1) and three(1-1-1) bays infill, as shown in Figure 3.2. Bracket spacing of 0.8m and 1.6mwere chosen by considering computational simplicity. A panel thickness of(99 mm, 169 mm, and 239 mm) and panel strength of (17.5 MPa, 25 MPaand 37.5 MPa) were selected by considering market availability. Analyseswere carried out for each combination of factors considered and treatmentlevels. The results of dynamic analyses are presented in the form of perfor-463.1. Predicting MISD of CLT infilled SMRFs: Response Surface Methodmance matrix of MISD and RISD as shown in Figure 3.6. This plot wasdeveloped from 3240 scatter data points for only the storey in each build-ing that has the largest drift for each seismic excitation. The higher driftscatter is for less infill patterns (0-1-0), large bracket spacing and 9-storeybuilding. Some overlapped observations are depicted in the performancematrix, which indicates that there are some factors in the dynamic analysisthat have a minimal effect on both MISD and RISD. This conclusion willbe verified in subsequent sections using sensitivity analysis of input factors.0 0 .5 1 1.5 2 2.500 .511.522.5M ISD (% )RISD (%) 3 story 0 -1-0 infill3 story 1-0 -1 infill3 story 1-1-1 infill0 0 .5 1 1.5 2 2.500 .511.522.5M ISD (% )RISD (%) 6 story 0 -1-0 infill6 story 1-0 -1 infill6 story 1-1-1 infill0 0 .5 1 1.5 2 2.5 300 .511.522.5M ISD (% )RISD (%) 9 story 0 -1-0 infill9 story 1-0 -1 infill9 story 1-1-1 infillFigure 3.6: Performance matrix for residual and maximum interstorey driftMore specifically, Figure 3.7 depicts the time history of the top horizontaldisplacement for 3-story bare and CLT infilled frames. These plots are forbracket spacing, panel thickness and panel strength of 0.8m, 99mm and25 MPa, respectively. As expected, the residual displacement (Uresidual)is decreases when the infill number increases. Significant reduction was473.1. Predicting MISD of CLT infilled SMRFs: Response Surface Methodobserved at the maximum roof displacement (Umax) for 1-0-1 and 1-1-1infill patterns.a) b) c ) c ) Figure 3.7: Displacement time histories of a typical 3 storey building, a)Bare frame; b) Frame with infill in the middle (0-1-0); c) Frame with infillin two exterior bays (1-0-1), and d) Frame with infill in all bays (1-1-1)3.1.4 Surrogate Model for MISDSensitivity AnalysisA screening process using sensitivity analysis was needed to improvethe efficiency of RSM for equation development. The process was used toidentify input variables that have larger influence on the output. Figure 3.8shows the effect plots of MISD with each indicated variable by keeping theother variables at their median value.483.1. Predicting MISD of CLT infilled SMRFs: Response Surface MethodStory Number (A)3 6 9MISD (%)1.01.31.72.0Infill Pattern (B)1 2 3MISD (%)1.01.31.72.0A B Bracket Spacing (C) (m)0.80 1.60MISD (%)1.01.31.72.0Panel Thickness (D) (mm)99.00 169.00 239.00MISD (%)1.01.31.72.0C D Panel Strength (E) (MPa)17.50 27.50 37.50MISD (%)1.01.31.72.0 Seismicity (F) (sec)5 12 18 25 31MISD (%)1.01.31.72.0E F Figure 3.8: Effect plots of modeling parametersThe effect plots of bracket spacing, panel thickness and panel crushingstrength revealed that their extent of influence is small. There is no strong493.1. Predicting MISD of CLT infilled SMRFs: Response Surface Methodevidence to reject these variables from further predictive equation devel-opment. However, MISD has been found to be sensitive to the significantduration (tD), infill pattern, and number of storey.Predictive equation using response surface methodologyResponse surface methodology (RSM) consisted of a group of techniquesused in the empirical study of the relationship between the response y andnumber of input variables x1, x2, ...,xk [Mon97]. This relationship can beestimated with models from certain experimental data points. In this work,a D-Optimal deterministic experimental design technique was used for effi-cient sampling of design points of the dynamic analysis result. This type ofdesign minimizes the overall variance of the estimated regression coefficients[KM10]. Moreover, this method is suitable for deterministic computer mod-els and for simulations with an irregular experimental region [Mon97]. Thefactors and treatment levels that were used as input for experimental designwith their upper and lower bound values are shown in Table 3.4. In thistable RISD (output from dynamic analysis) is included as one input factorwith 3240 levels.Table 3.4: Definition of input variablesFactor Name Units Type Subtype levels Minimum MaximumA Storey Number - Numeric Discrete 3 3 9B Infill pattern - Numeric Discrete 3 1 3C Bracket Spacing m Numeric Discrete 2 0.8 1.6D Panel Thickness mm Numeric Discrete 3 99 239E Panel Strength MPa Numeric Discrete 3 17.5 37.5F Seismicity (tD) sec Numeric Discrete 20 5.41 31.36G RISD % Numeric Discrete 2160 0.25 2.68A second degree polynomial of the form shown in Equation 4.13 wasused to set up relationship between y and x1, x2, ...,xk; and used to predictMISD for the given settings of the modeling variables and RISD.y = β0 +k∑i=1βixi +k∑i=1βix2i +∑∑i<jβijxixj (3.1)503.1. Predicting MISD of CLT infilled SMRFs: Response Surface MethodIn Equation 4.13, y is a regression function, and β0, βi and βij arethe regression coefficients. In order to obtain the coefficients for the abovesecond degree model, 87% of the data points from dynamic analyses wereused for the model training, while the rest was kept aside for statisticalvalidation. Analysis of Variance (ANOVA) test for significance level (α =0.05) was performed in Design Expert V8 [SE10] software to identify factorsand their interactions that influence the response (MISD). Table 3.5 showsa standard ANOVA result with a corresponding degree of freedom, meansquare and F-value for each factor and their interactions. Table 3.5 showsthe only factors and interactions influencing the response, which possessesa P-value of less than 0.05.Table 3.5: ANOVA tableSource Sum of square df Mean Square F V alue P valueModel 676.38 20 33.82 374.84 0.0001A-Storey No 22.95 1 22.95 254.33 0.0001B-Infill pattern 142.04 1 142.04 1574.28 0.0001C-Bracket Spacing 0.22 1 0.22 2.46 0.1166D-Panel Thickness 0.36 1 0.36 4.04 0.0444E-Panel Strength 0.00293 1 0.00293 0.032 0.857F-Seismicity (tD) 1.02 1 1.02 11.28 0.0008G-RISD 0.089 1 0.089 0.99 0.3204AB 47.71 1 47.71 528.75 0.0001AC 3.73 1 3.73 41.36 0.0001AD 0.26 1 0.26 2.92 0.0875AE 0.2 1 0.2 2.2 0.1381BC 1.61 1 1.61 17.87 0.0001BD 0.51 1 0.51 5.63 0.0177CG 0.81 1 0.81 9.01 0.0027DE 0.27 1 0.27 2.95 0.0861FG 0.57 1 0.57 6.3 0.0121A2 0.99 1 0.99 10.96 0.0009B2 60.1 1 60.1 666.09 0.0001F2 0.36 1 0.36 3.97 0.0463G2 0.42 1 0.42 4.69 0.0304The model adequacy was checked for the ANOVA assumptions of nor-mality and constant variance, during which nothing unusual was found.After this, regression analysis was performed based on the significant fac-513.1. Predicting MISD of CLT infilled SMRFs: Response Surface Methodtors and interactions in order to estimate the coefficients of the proposedequation. Table 3.6 summarizes the coefficients for the proposed polynomialequation based on both normalized and actual factors.Table 3.6: Equation coefficientsSource Normalized Coefficients Actual CoefficientsIntercept 1.22 2.304A 0.12 0.055836B -0.34 -1.42639C 0.029 -0.029398D 0.017 1.19E-03E -1.51E-03 2.14E-03F -0.074 7.77E-03G -0.04 0.43916AB -0.097 -0.032272AC 0.023 0.019398AD 7.17E-03 3.42E-05AE 6.13E-03 2.04E-04BC 0.03 0.073855BD -0.02 -2.89E-04CG -0.065 -0.15923DE -0.015 -2.08E-05FG -0.071 -5.41E-03A2 1.00E-02 1.14E-03B2 0.31 0.31086F2 -0.037 -2.17E-04G2 -0.095 -0.091808The effect of interactions was described using response surface plot inFigure 3.9 and 3.10 . These plots were constructed for the indicated axislabels while keeping the other parameters at their median value.523.1. Predicting MISD of CLT infilled SMRFs: Response Surface Method(A) () Figure 3.9: Response surface plot for interactions between; a) infill Patternand storey Number and b) infill pattern and bracket spacing533.1. Predicting MISD of CLT infilled SMRFs: Response Surface Method(A) () Figure 3.10: Response surface plot for interactions between; a) seismicityand infill pattern and b) panel thickness and storey Number543.1. Predicting MISD of CLT infilled SMRFs: Response Surface MethodThe lower infill patterns and nine storey building resulted in larger MISDas shown in Figure 3.9a. This observation is better supported by the largerabsolute values of the normalized coefficients in the prediction equation ofTable 3.6. It is also clear from Figure 3.9b that, MISD is heavily influencedby the infill pattern rather than the bracket spacing. This observation is re-versed for a heavily infilled frame (1-1-1). From the above response surfaceplots it can be inferred that the addition of infilled bays decreases MISD sig-nificantly, which is strongly correlated with the increasing number of panels.Also, in Figure 3.10a the infill pattern is more dominant factor than the sig-nificant duration of the ground motions. Nine storey frames with 0-1-0 infillpattern experienced more storey drift than the other models. Focusing onthe Panel thickness, Figure 3.10b indicates their minimal effect on MISD,which was consistent throughout effect plots and ANOVA test results ofthese two parameters.3.1.5 Statistical validation of the proposed equationStatistical tests such as F-test and R2 test are widely used to validateregression models. However, due to the absence of random error they areincompatible with the current problem. Therefore, two alternate validationstechniques [SPKA97] using the original and additional data points were ap-plied. The former method uses validation using the adjusted R2 (modelsum of squares divided by total sum of squares) on the training data set.The latter one adopts statistical error measuring indexes such as averageabsolute error (%AvgErr) and root mean square error (%RMSE) of addi-tional validation data points. For the second method, 432 randomly selectedMISD values used from the results of dynamic analysis. Equations 3.2 and3.3 show formulas that used to calculate the defined indexes.AvgErr = 100×1N∑Ni=1 yi − yj1N∑Ni=1 yi(3.2)553.1. Predicting MISD of CLT infilled SMRFs: Response Surface MethodRMSE = 100×√1N∑Ni=1 (yi − yj)21N∑Ni=1 yi(3.3)00. 511. 522. 530 0. 5 1 1. 5 2 2. 5 3Actual Predicted Figure 3.11: Validation plot; Predicted vs. Actual (red dotsAdjusted R2 value of 0.73 was obtained from the first method, whichshows how good the model fits with the original experimental data points.The statistical error measuring indexes (%AvgErr) and (%RMSE) values are2.6% and 18.04%, respectively. The plot of predicted vs. actual values isshown in Figure 3.11. This plot possesses an R2 value of 0.63 which confirmsthat the prediction equation approximates well the value of MISD.563.2. Multi-objective optimization of drift demands of CLT infilled SMRFs3.2 Multi-objective optimization of driftdemands of CLT infilled SMRFsThe primary objective of this section is to identify optimized modelingparameters of CLT infilled SMRFs by considering MISD and RISD as anobjective functions. Responses surface plots are developed for MISD andRISD independently to study the effect of modeling parameters on the driftdemands. For this purpose, 3 story building results of section 3.1 are used.Figures 3.12 and 3.13 show these two drift demands are conflicting eachother as the number of infill bays is increased. Also as discussed in section3.1.4, the infill pattern (which is directly related to the CLT wall length inthe system) is the main factor that affect the drift demands of the hybridsystem. This reason prompted the need to optimize the modeling parame-ters for the given conflicting objectives, i.e. MISD and RISD. To develop amore accurate models of objective functions, a concept of artificial intelli-gence is applied to all the dynamic results of section 3.1. Artificial NeuralNetwork (ANN) model is trained and validated to predict MISD and RISDfor further optimization. Finally, optimized modeling parameters were iden-tified using Genetic Algorithm’s multi-objective optimization capability thatsimultaneously minimizes MISD and RISD by defining the non-dominatedPareto front of design solutions.3.2.1 MethodologyA framework that used to optimize the modeling parameters of the pro-posed hybrid system is depicted in Figure 3.14. The first step in the frame-work is to perform parametric study on the modeling variables using non-linear time history analysis. The Modeling variables for the problem aredetermined by considering market availability and simulation running time.Three, six, and nine storey frames with regular geometry were used for thisstudy. The first modeling variable (x1) building height and the second vari-able (X2) is infill pattern. One (0-1-0), two (1-0-1) and three (1-1-1) baysinfill were considered, as shown in modeling section of Figure 1. Bracket573.2. Multi-objective optimization of drift demands of CLT infilled SMRFs(A) Figure 3.12: Response surface plot for MISD with infill pattern and bracketspacingFigure 3.13: Response surface plot for RISD with infill pattern and bracketspacing583.2. Multi-objective optimization of drift demands of CLT infilled SMRFsspacing (X3) of 0.8m and 1.6m were chosen considering computational sim-plicity. A panel thickness (X4) of (99 mm, 169 mm, and 23 9mm) and panelstrength (X5) of (17.5 MPa, 25 MPa and 37.5 MPa) were selected by consid-ering market availability. Seismicity is represented by significant duration(X6) obtained from the seismic hazard of Vancouver, Canada. The objectivefunctions (RISD and MISD) are found from the result of time history anal-ysis and depicted in Figure 3.14 as performance matrix plot. The detailsof this step are well discussed in subsequent sections. From this step foreach combination of time history analyses the surrogate network functionfor RISD and MISD were obtained using ANN training method. Finally,multi-objective optimization using Genetic Algorithm (GA) is carried outto optimize the modeling parameters.3.2.2 Surrogate Model using artificial intelligenceArtificial Neural NetworkArtificial Neural Network (ANN) is a subset of Artificial Intelligence thatsimulates the behaviour of human brain that helps machines and computersto learn. ANN is a system that has a capability to simulate, learn and storeknowledge for future usage [ASAH11]. ANN has been applied for variousaspects of structural capacity predictions and yields accurate results whencompared to experimental results and code justified formulations [Sel12,DAGT09, BBS07, CKS03, MDLZ04, CNS06]. In order to obtain a moreaccurate predictions of MISD and RISD, in this thesis, ANN is trained andvalidated using results from nonlinear time history analysis. The Multilayerpreceptors (MLP) are the most widely used feed-forward networks consistingof input layer, hidden layer and output as shown in Figure 3.15. As shownin Figure 3.15, the input layer comprised of building height, bracket spacing,infill pattern, CLT panel thickness and strength, and seismicity (tD). Theoutput layer is representing MISD and RISD. The details of training andvalidation of the surrogate models are given in Appendix A.593.2. Multi-objective optimization of drift demands of CLT infilled SMRFsModeling Time History Analysis Drift performance matrix Maximum and Residual Drifts Multi-Objective Optimization using GA 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.200.10.20.30.40.50.60.70.80.9MISD (%)RISD (%) 3 story 0-1-0 infill3 story 1-0-1 infill3 story 1-1-1 infill Artificial Neural Network Model Training and Validation Minimize F(X) s.t 3 ≤ 𝑥1 ≤ 91 ≤ 𝑥2 ≤ 30.8 ≤ 𝑥3 ≤ 0.699 ≤ 𝑥4 ≤ 23917.5 ≤ 𝑥5 ≤ 37.55 ≤ 𝑥6 ≤ 32 Where X = (x1, x2, x3, x4, x5, x6), F(X) = f(x) and g(x) g, f: ℝ6 𝑦𝑖𝑒𝑙𝑑𝑠 ℝ, f(x) = MISD and g(x) = RISD Figure 3.14: Outline of the methodology603.2. Multi-objective optimization of drift demands of CLT infilled SMRFs Building Height Infill Pattern Bracket Spacing Panel Thickness Panel Strength Seismicity … … Hidden Neurons Input Layer Output Layer MISD (%) RISD (%) Figure 3.15: ANN model for prediction of objective function3.2.3 Multi-objective optimization using Genetic AlgorithmRecently, Tesfamariam et al. [TBS14] optimized the modeling parame-ters of CLT infilled steel moment frames using the objective functions thatare developed using response surface method. From their research they con-cluded that RISD and MISD are conflictive drift objectives with respectto the infill topology in the frame. Their conclusion gives imputes to per-form multi-objective optimization of modeling parameters using black boxfunctions developed using ANN analysis of previous section.Genetic algorithm (GA) is a stochastic method to search the optimalpoint using population solution for multi-objective optimization problems[Deb01]. The optimization problem defined for the case understudy is givenby:minimizexF (X)subject to =3 ≤ x1 ≤ 91 ≤ x2 ≤ 30.8 ≤ x3 ≤ 1.699 ≤ x4 ≤ 23917.5 ≤ x5 ≤ 37.55 ≤ x6 ≤ 32where X = (x1, x2, x3, x4, x5, x6), F(X) = f(x) and g(x) and g, f: R6 → R,613.2. Multi-objective optimization of drift demands of CLT infilled SMRFsf(x) = MISD and g(x) = RISDThe network is simulated and the outputs are assigned as fitness func-tion for GA for the optimization process. A MATLAB tool box [MAT13] isused for the current problem with a population size of 250 for each of theiterations. Constraint dependent and intermediate functions were assignedfor mutation and crossover, respectively. The generated Pareto-optimal so-lutions are presented in Figure 3.16.0 . 85 0 . 9 0 . 95 1 1.05 1.1 1.15 1.20.0 90 .10 .110.120.130.140.150.160.17M ISD %RISD %Figure 3.16: Pareto-optimal solutionsResults and DiscussionThis section presents the results of the optimization and correspondingvariables of Pareto-front curve shown in Figure 3.16. 3-story building ap-pears to be optimal building height. The variables corresponding to Pareto-front curve of Figure 3.16 are depicted by using a higher-dimension matrixscatter in Figure 3.17. The matrix scatter plot shows the relationship be-tween each optimal variable with respect to the height of the building. Forthe current optimization problem infill pattern in two bays (1-0-1) is alwaysoptimal. Bracket spacing in the range of [0.8 - 0.845 m], panel thickness [110623.3. Summary- 130 mm], and panel strength [17.5 - 35 MPa] are other optimal modelingparameters.Bra Sp Infil l PattPanel Str Panel Th SeismicityBra SpInfill PattPanel StrPanel ThSeismicity5 10 15110 120 13020 25 30 35-4 -2 0 2 4 60.8 0.805 0.81 0.81551015110120130202530351230.80.8050.810.815Figure 3.17: Higher order plot for variables corresponding to Pareto curvethat trained using trainlm3.3 SummaryThis chapter proposed surrogate models for MISD and RISD of the CLTinfilled SMRFs to identify optimum modeling parameters. For this purpose,two-dimensional (2D) time history analyses of the 162 hybrid buildings wereperformed utilizing 20 earthquake ground motions. Building height, infillpattern, CLT panel thickness and strength, and connection bracket spacingwere selected as input decision variables for the analyses. In the first section,Response surface methodology with D-Optimal computer experimental de-sign technique was adopted for the development of prediction equation of633.3. SummaryMISD from modeling parameters and RISD. The developed second orderpolynomial equation was validated by statistical techniques with originaland additional data sets. In the second section, more accurate surrogatemodels of MISD and RISD were developed using Artificial Neural Network.Subsequently, optimum modeling variables for the proposed hybrid systemwere identified. The optimization process adopts ANN based objective func-tions that are trained using Levenberg-Marquardt algorithm. This studyadopted multi-objective optimization approach using Genetic Algorithm forconflicting objective functions. The obtained optimal modeling variableswill be used as a starting point for the direct displacement based design ofCLT infilled SMRFs in Chapter 5.644Equivalent viscous damping of CLT infilledsteel moment resisting frames4.1 BackgroundGenerally, displacements due to seismic excitations are related to dam-age sustained in structures and associated failure [KMA03, EY04, MK05,GAEB99, KC04]. In performance based seismic design, the major advance-ment is to consider structural deformations as a main input for the deignprocess [PCK07b]. These methods are specifically known as direct displace-ment based seismic design. Direct Displacement Based Design (DDBD) uti-lizes a virtual representation of the nonlinear structures with an equivalentlinear system through secant stiffness (Ke) and equivalent viscous damping(ξeq) at peak displacement (4d) as illustrated in Figure 5.1. This methoduses equivalent viscous damping (EVD) to represent the energy dissipativecapacity of the structural system. As shown in Figure 5.1d, the target654.1. Backgrounddisplacement is used to obtain an effective period of the structure for thegiven level of EVD. From this step, the design base shear can be calcu-lated from the effective mass (meff ), secant stiffness (Ke), effective period(Teff ), and target displacement (4d)[PCK07b]. In this chapter, the moti-vation is to develop an EVD coefficient for a new steel-timber hybrid system[SDT12, STKP12, DST12, Dic13, DSBT14].The EVD concept was introduced by Jacobsen [Jac60], which is basedon the idea that nonlinear systems and equivalent linear system under sinu-soidal excitation dissipate an equal amount of energy per cycle of response(Figure 4.1). The approach proposed by Jacobsen is called the area basedapproach and is shown in Equation 4.1.Figure 4.1: Hysteretic response area of one cycleξhyst =12piAhystFmUm(4.1)ξeq = ξo + ξhyst (4.2)where Ahyst is the value of dissipated energy; Fm and Um are the maximumforce and displacement for the loop, respectively (Figure 4.1). The equiva-lent viscous damping ξeq in Equation 4.2 is the summation of elastic damp-ing ξo and hysteretic component of damping ξhyst ([PCK07a]). Rosenblueth664.1. Backgroundand Herrera [EI64] developed the EVD expression based on secant stiffness.Priestley [Pri93] adopted this for the DDBD method of structures. Mirandaand Garcia [MRG02] validated Jacobsen′s approach with secant stiffness todetermine the inelastic displacement demand of a Single Degree of FreedomSystem (SDOF) system. A comprehensive investigation of the accuracyof Jacobsen′s approach was performed by [DK04] for the Takeda hysteresismodel using 100 earthquake records. Kowalsky and Ayers [KA02] found thatthe equivalent linear system based on Jacobsen′s approach, using effectiveperiod at maximum response, yields a good result for the assessment of anon-linear response for majority of considered cases. Blandon and Priestley[BP05] compared the EVD based on Jacobsen′s approach and EVD from theiterative time history analyses for six different hysteretic models. They con-cluded that Jacobson′s approach overestimate EVD values and proposed thecorrected equations for DDBD method. Recently, the EVD was investigatedfor different types of structural systems [DKN07, WNS11, GJT12, LS06].Dwairi et al. [DKN07] proposed a hyperbolic damping ductility law basedon nonlinear ductility at peak displacement as follows:ξhyst = C(µ− 1µpi)(4.3)where C is a constant and µ is a ductility ratio. The authors have pro-posed values of C for unbonded post tensioned concrete systems, reinforcedconcrete beams, reinforced concrete walls and steel members in terms ofthe effective period. Wijesundara et al. [WNS11] derived the EVD ex-pression for a concentrically braced frame based on Jacobsen′s method andcalibrated the expressions using iterative time history analyses. They havealso highlighted that pinching significantly affects the EVD. Ghaffarzadeh etal. [GJT12] proposed new EVD equations for the reinforced concrete (RC)moment resisting frames and RC concentrically braced frames. Lu and Silva[LS06] estimated EVD for seismic and blast loads for individual and mul-tiple RC members. However, the EVD expression is not yet developed forthe steel-timber hybrid system.Since there is no definite hysteresis law to characterize the response of674.2. Methodologythe proposed hybrid system, 243 single storey-single bay hybrid systemsare analytically investigated to compute the EVD based on Jacobson′s areabased approach and corresponding ductility. Different parameters are var-ied: gap between CLT panel and steel frame, bracket (connection) spacing,CLT panel thickness and strength, and post stiffness yield ratio of steelmembers. A least square regression method is used to calculate the valueof C (Equation 4.3) for each system. An expression for the coefficient Cas a function of different modeling parameters is developed using ResponseSurface Method (RSM). Subsequently, an expression is proposed to com-pute EVD from ductility and modeling parameters. Finally, an iterativenonlinear time history analyses is conducted using 20 spectrum compatibleearthquake ground motions to calibrate EVD from Jacobsen′s area basedapproach.4.2 MethodologyThe method followed to formulate the EVD for the hybrid system isoutlined below. A conceptual representation of the hybrid system is shown inFigure 3.3. Single-storey single-bay frame with the following model variablesare considered:− Three levels of bracket spacing were considered (A): 0.4 m, 0.8 m, and1.6 m.− Gap magnitude between steel frame and CLT infill (B) of 20, 50, and80 mm, panel thickness (Ct) of (99, 169, 239 mm), panel strength (D)of (17.5, 25, and 37.5 MPa), and post stiffness yield ratio (E) of (1, 3,and 5 %) were selected.Once the analytical models are developed, the procedure depicted inFigure 4.2 is followed to establish the EVD-ductility law. Monotonic staticpushover and semi-static cyclic loading analysis are carried out for all con-sidered models. The parameters considered in this study are summarizedin Table 4.1. The total combination of all parameters constitutes the 243models considered.684.2. MethodologyEquivalent Viscous Damping ൌࢼ ࢼୀ ࢼ ࢼୀୀୀ Area based approach for ߦ௬௦௧ Response Surface Plot ۱ = ࣆࣆି Damping Coefficient C Single storey hybrid system EVD -ductility law Damping –Ductility with Gap … M1 M2 M243 Calibration of EVD 0 1 2 3 4020406080Time (sec)Displacement (cm) MeanTargetAverage displacement spectra 0 1 2 3 400.511.522.53Time (sec)Acceleration (g) MeanTargetIterative ITHA New EVD -ductility law 0481216200 2 4 6 8 10[ hyst (%) µ M1M2M3081 62 43 24 00 2 4 6 8 10[ hyst(%) µ 20 mm30 mm40 mm50 mm60 mm80 mmFigure 4.2: Framework for formulation694.3. Formulation for yielding pointTable 4.1: Modeling variablesA:Bracket-Spacing(m)B:Gap(mm) Ct: PanelThickness(mm)D: PanelStrength(MPa)E: Post YieldStiffness (%)0.4 20 99 17.5 10.8 50 169 25 31.6 80 239 37.5 5The results of the pushover analysis are used to calculate the yielding andultimate displacement of each hybrid system. Subsequently, the EVD andductility of each system are computed from the hysteretic responses. Designof computer experiments and response surface methodology were applied toformulate the damping-ductility law. Finally, calibrations of sample modelsare carried out using nonlinear time history analysis (NLTH).4.3 Formulation for yielding pointIn order to establish the yielding point of the proposed hybrid sys-tem, a preliminary finite element analysis was carried out under monotonicpushover loading. Figure 4.3 shows the stress distribution of the CLT in-fill panel. As is shown in Figure 4.3, the compression strut response isformed under the lateral load that is accompanied with high compressionstress at the corner of the panels. The panel crushing is indicated as aneffective way of to dissipate energy and is simpler for maintenance purposes[Dic13, DSBT14, TSDB14]. The yielding point is obtained as discussed be-low and taken as the smaller of steel yielding or panel crushing values inconnection brackets for all predetermined models. The steel yielding pointsare determined from the outputs of the finite element analysis. An expres-sion is developed to calculate the panel crushing displacement using a simplemechanistic approach. The proposed single story hybrid system (Figure 3.3)is simplified to Figure 4.4 by representing the panels with compression andtension struts. Only the corner spring connection was considered to simulatethe extreme case of crushing of panels. At this point it is to be noted thatthe tensile load (Ft) on steel members due to connection brackets is ignoredfor simplicity. Within the simplified free body diagram, Fs represents the704.3. Formulation for yielding pointcrushing strength of the panel in the brackets and can be mathematicallyexpressed as shown below.Figure 4.3: Compression strut action for the hybrid systemb c F S g dc A B Ray R by F Scos F Ssin R by P Ray C x b x C y F Scos A y g L H o F S P F tcos X Y Figure 4.4: Compression strut action for the hybrid systemConsidering the system equilibrium of forces in x direction and moment714.3. Formulation for yielding pointat point o of Figure 4.4 will give:− Fscosθ + Cx + bx + P = 0 (4.4)Fscosθ(bc2+ g)− P(HL)(dc2)− bxH = 0 (4.5)Substituting Equation 4 in to Equation 5 gives:P =FscosθLH(bc + 2g −Hdc −H)(4.6)The compression resistance of the CLT wall (Fs) at a point of yielding canbe calculated by the composite K theory as follows: For CLT the crushingstrength is given by [GP11]fc,90,eff = fc,0k4 (4.7)where fc,0 is the crushing strength and k4 is given by:k4 =E90E0+(1−E90E0)(a(m−2) − a(m−1) + ...± a1am)(4.8)where E90 and E0 are the modulus of elasticity in bending in perpendic-ular and parallel to the major strength direction, respectively. The param-eters am and am−i are shown in Figure 4.5.ܽ݉ ܽ݉-2 ܽ݉-4 Figure 4.5: Five layer CLTThe stiffness of cross layers for CLT is:724.3. Formulation for yielding pointE90 =E030(4.9)The crushing strength (Fs) is calculated by multiplying the perpendicu-lar crushing strength f(c,90,eff) with the area of contact. The area of contactis calculated based on the macro modeling concept for masonry infill usingthe single strut approach as shown in Figure 4.6.W d H hw L Lw Figure 4.6: single strut representation of the hybrid systemFs = fc,90,effwt (4.10)where t is the thickness of CLT panel and w can be calculated as follows[Sta67]:w = 0.175d(h 4√Ewtwsin2θ4EIhw)(4.11)734.4. Parametric studyFinally, substituting Equations 4.10 and 4.11 in to Equation 4.6, theapplied force that crushes the CLT element is:P =fc,90,effcosθ.L.w.tH(bc + 2g −Hdc −H)(4.12)The displacement that corresponds to the value of P (Equation 4.12)obtained from the pushover analysis is defined as the yield point for panelcrushing in connection brackets.4.4 Parametric study4.4.1 Monotonic pushover analysisStatic monotonic pushover analysis was carried out for the 243 models.Results of the pushover analysis are used to calculate the yield and ultimatedisplacement of the system (Figure 4.7). The displacement correspondingto the point where 20% decrease in lateral capacity is defined to be theultimate displacement of the hybrid system. The yield point of the hybridsystem is established based on the displacement corresponding to the smallerof the crushing of panel and yielding of steel. Samples from the results ofmonotonic pushover analysis are depicted in Figure 4.7. As shown in theFigure 4.7, models having thicker and stronger CLT panels with larger postyield stiffness ratio possess larger load carrying capacity.744.4. Parametric study0 50 100 150 200 250 300 350 400 45005001000150020002500300035004000Displacement (mm)Force (kN) A=0.8m,B=20mm,Ct=99mm,D= 17.5MPa, E=1%A=0.8m,B=50mm,Ct=99mm,D= 17.5MPa, E=1%A=0.8m,B=20mm,Ct=239mm,D= 37.5MPa, E=5%A=0.8m,B=50mm,Ct=239mm,D= 37.5MPa, E=5%Figure 4.7: Sample monotonic pushover analysis results4.4.2 Semi-static cyclic analysisA hysteretic response of base shear with lateral displacement is obtainedby applying a cyclic displacement history at the top node of each model.The cyclic loading test is conducted according to the CUREE-Caltech Woodframe project protocol [KPI+01] (Figure 4.8). The ultimate displacementobtained from the monotonic pushover analysis is used for cyclic test with acorrection factor of 0.4 to account for the difference in deformation capacitybetween monotonic test and cyclic test [KPI+01].754.4. Parametric study-160-120-80-40040801201600 200 400 600 8 00 1000 1200Displacement (% of Max) Time (seconds ) Figure 4.8: CUREE cyclic loading protocolSamples from the results of semi-static cyclic analysis are depicted inFigure 4.9. The responses shown in Figure 4.9a and b are characterized byfat hysteresis loops with large energy dissipation. Also from Figure 11a andb, it is clear that the thinner (Ct = 99 mm) and weaker panels (D = 17.5MPa) show less pinching behaviour. However, in Figure 4.9c and d, modelswith thicker (Ct = 239 mm) and stronger panels (D = 37.5 MPa) withhigher post yield stiffness ratio (5%) are characterized by a higher degree ofpinching. This pinching causes significant reduction in energy dissipation,which creates thinner hysteretic loops.764.5. Equivalent viscous damping-3000-2000-10000100020003000Force (kN)-3 0 0 -2 0 0 -1 0 0 0 1 0 0 2 0 0 3 0 0-3 0 0 0-2 0 0 0-1 0 0 001 0 0 02 0 0 03 0 0 0Displacement (mm)Force (kN)-3 0 0 -2 0 0 -1 0 0 0 1 0 0 2 0 0 3 0 0Displacement (mm)a) b)c) d)A = 0. 8mB = 20mmCt = 99mmD = 17. 5 MPaE = 1%A = 0. 8mB = 50mmCt = 99mmD = 17. 5 MPaE = 1%A = 0. 8mB = 20mmCt = 239mmD = 37. 5 MPaE = 5%A = 0. 8mB = 50mmCt = 239mmD = 37. 5 MPaE = 5%Figure 4.9: Sample semi-static cyclic analysis results4.5 Equivalent viscous dampingThe hysteretic damping corresponding to the cyclic response is calcu-lated for each model based on Equation 1. Then a least square regressionwas applied to calculate the value of C for Equation 4.3 from hystereticdamping (ξhyst) and ductility values. All the variables in the RSM analysisare continuous. Response surface methodology (RSM) with the D-Optimalcomputer experimental design technique was used to develop an expressionfor C using the results from least square regression analysis. A second degreepolynomial of the form shown in Equation ?? was used to set up relationshipbetween C and the modeling variables (A, B, Ct, D, and E); In Equation 13,C is a regression function, and β0, βi and βij are the regression coefficients.774.5. Equivalent viscous dampingy = β0 +k∑i=1βixi +k∑i=1βix2i +∑∑i<jβijxixj (4.13)In order to develop the desired relationship, data points are selectedon the basis of optimality criteria, which are based on the proximity ofthe predicted response C to the mean response. In order to obtain thecoefficients for the proposed second degree equation, 80% of the data pointsfrom the least square regression analysis were used for the model training,while the rest were kept aside for statistical validation.After obtaining significant factors and interactions from RSM, the fi-nal expression for C, given in Equation 4.14, is developed using modelingparameters of Table 4.1.C =(0.43 + 0.5A+ 0.015B + (1.27E − 03Ct) + (3.75E − 04D)− 0.054E − (2.74E − 04A.Ct)− (1.01E − 03A.D)− (0.019AE) + (2.62E − 05BD)− (3.2E − 04Ct.D)− 0.135A2− (1.045E − 04B2)− (1.98E − 06C2t ) + (5.9E − 03E2))(4.14)It can be inferred from the Equation 4.14 that the value of C is depen-dent on the complex interaction between the gap, panel properties and postyielding stiffness ratio of steel frames. The effect of variable interactionsis illustrated using response surface plot in Figure 4.10,4.11,4.12, and 4.13.Figure 4.10 shows a decrease in the value of C with an increase in the postthe yield stiffness ratio. As discussed earlier, the higher degree of pinchingfor systems with a large post yield stiffness ratio prohibits the formationof fat hysteresis loops that in turn decreases the value of C. Moreover, inFigure 4.10, for the hybrid systems with larger bracket spacing, the value ofC showed an increase in a linear fashion. It is also clear from Figure 4.11that the value C is heavily influenced by increasing the magnitude of the gapbetween CLT panel and steel frame. Originally, the gap was provided to ac-784.5. Equivalent viscous dampingcommodate construction tolerances and to develop the hysteretic behaviour.The increase in the gap allows the connection to deform and dissipate energythat increases the value of C. Equation 14 is statically validated for 43 datapoints outside of the training data set. R2 value of 0.97 was obtained forthe plot of actual vs. predicted values of C, as shown in Figure 4.14.Figure 4.10: Response surface plot for the effect of interactions betweenbracket spacing (A) and post yielding stiffness ratio (E)794.5. Equivalent viscous dampingFigure 4.11: Response surface plot for the effect of interactions betweenPanel strength (D) and Gap (B)Figure 4.12: Response surface plot for the effect of interactions between poststiffness yield ratio (E) and Gap (B)804.5. Equivalent viscous dampingFigure 4.13: Response surface plot for the effect of interactions betweenPanel strength (D) and Panel thickness (Ct)00.511.50 0.5 1 1.5Actual Predicted Figure 4.14: Validation plot; Predicted vs. ActualThe variation of the hysteretic damping ( ξhyst) of the hybrid system un-der study with different modeling variables is given in Figure 4.15. Figure814.5. Equivalent viscous damping4.15 shows the effect of modeling variables on the ξhyst by keeping the othervariables at their median value. Figure 4.15a shows the variation of ξhyst andductility µ for different levels of gap between the CLT wall and steel frame.As discussed in previous sections, the larger gap provided allows the con-nection brackets to deform and to dissipate energy. Figure 4.15(a) confirmsthis concept because the hysteretic damping is increasing with increase inthe gap magnitude. However, the effect of increasing the gap magnitude willdiminish for the gaps that are more than 40 mm. Bracket spacing and panelstrength shows minimal effect on the hysteretic damping as shown in Figure4.15b and c. Even though it is small, the hysteretic damping will increase forthe models with larger bracket spacing. As can be seen from Figure 4.15dthe value of hysteretic damping is heavily influenced by the magnitude ofpost yielding stiffness ratio of steel frame members. The higher degree ofpinching for systems with large post yielding stiffness ratio prohibits theformation of fat hysteresis loops that in turn decreases the ξhyst. However,the sensitivity of ξhyst is smaller for models with post yield stiffness ratiomore than 3%.824.5. Equivalent viscous damping010203040[hyst(%) 20 m m30 m m40 m m50 m m60 m m80 m m 0.4 m0. 8 m1.2 m1.6 m0 2 4 6 8 10010203040Ductility, P[hyst (%) 17.5 MPa 25 MPa 37.5 MPa0 2 4 6 8 10Ductility, P 0%1%2%3%4%5%d)b)a)c )Figure 4.15: Damping ductility law for various modeling parametersFigure 4.16 compares the results obtained using the new expression ofC (Equations 4.3 and 4.14) with the results obtained from other notablestudies. In general, the current study obtained the maximum value of ξhystin the range of 18%-37% for a ductility value of 10. Referring to Figure15, results of the proposed equation are between the damping ductility lawgiven by [Pri03] for bare steel frame and [GJT12, WNS11] for the concen-trically braced steel frames and concentrically braced reinforced concrete.The damping ductility law given by [DK04], for a steel member, is largerthan the EVD of the current study. The damping ductility law suggestedby [LDT] for reinforced concrete frames with masonry infill is similar to thehighly pinched models of the proposed hybrid system. In general, the pro-posed equation proved to be in agreement with laws developed for frameswith infill wall and bracings.834.6. EVD calibration using nonlinear time history analysis1 2 3 4 5 6 7 8 9 100102030405060Du ctility, P[hyst (%) Current studyPriestley (20 03)Dwairi et al . (20 0 7 )Landi et al . 2012Wi jesundara et al . 2011Ghaffarzadeh et al . 2012Figure 4.16: Comparison of EVD expressions with different researches4.6 EVD calibration using nonlinear time historyanalysisThe methodology used to calibrate an EVD was computed based onJacobsens area based approach in earlier sections is presented here. Thepurpose of calibration is to improve the agreement between the area-basedapproach and the time history analysis for the substitute structure. Onlynine models with the gap magnitude of 20 mm are considered for the calibra-tion purpose. Models with 20 mm gaps are shown to have stable hystereticbehaviour with less strength and stiffness degradation [DSBT14, Dic13].Moreover, panel thickness and strength are shown to have minimal effecton EVD; therefore, for the calibration process here, they are fixed to be 99mm and 17.5 MPa, respectively. Nonlinear time history analysis (NLTHA)844.6. EVD calibration using nonlinear time history analysisusing 20 spectrum compatible earthquakes are used for the calibration pro-cess. An iterative NLTHA analysis is applied for each model until the topdisplacement of the hybrid system from NLTHA matches the initial consid-ered displacement from the semi-static cyclic analysis ([WNS11]). The stepsfollowed are outline below with an example. Figure 4.17 shows the iterativesteps used to calibrate EVD.Step 1: Selection of models to be calibratedThe nine models considered for the current calibration process are givenin Table 4.2. The models were selected based on their design implication forthe DDBD of the hybrid system.Table 4.2: Modeling variablesModels A:Bracket-Spacing(m)B:Gap(mm) Ct: PanelThickness(mm)D: PanelStrength(MPa)E: Post YieldStiffness (%)M1 0.4 20 99 17.5 1M2 0.4 20 99 17.5 3M3 0.4 20 99 17.5 5M1 0.8 20 99 17.5 1M1 0.8 20 99 17.5 3M1 0.8 20 99 17.5 5M1 1.6 20 99 17.5 1M1 1.6 20 99 17.5 3M1 1.6 20 99 17.5 5Step 2: Force and displacement of considered hysteretic loopfrom semi-static cyclic loading analysisThe top node displacement (4j) and corresponding force (Fj) for eachloop (j) of each model are obtained from the semi-static cyclic loading anal-ysis. A total of 24 loops were obtained for each model, and subsequently, 24force (Fj) and displacement (4j) values for the model under considerationare obtained.Step 3: Calculate the ξhyst and µ for each loop (j)The hysteretic damping (ξhyst) was calculated by using area based ap-proach (Equation 4.1) and the ductility (µ) is obtained by dividing 4j of854.6. EVD calibration using nonlinear time history analysisEnd of test for M i ? No Yes Average (∆ NLTHA ) =േ5%(߂) ? ∆j = Average (∆ NLTHA ) No … M1 M2 M9 -0.4-0.3-0.2-0.100.10.20.3-2-1.5-1-0.500.511.52x 106Force (N)Displacement (m)01234020406080Time (sec)Displacement (cm) MeanTarget∆ j and F j Displacement spectra ൌ ࢤ Nonlinear time history analysis For hysteretic loop j Calculate ܖ܉܌ђ͗ • ൌ •ࣆൌࢤ ࢤ loop j + 1 Yes M (i+1) Figure 4.17: Calibration process for EVD864.6. EVD calibration using nonlinear time history analysiseach loop by the yielding displacement (4y).Step 4: Effective period (Teff)The effective period (Teff ) can be obtained from the scaled averagedamped displacement spectra of Figure 4.19 with appropriate factor (Equa-tion 4.16) corresponding to each 4j . The details of development and scalingof the average displacement spectra will be discussed in step 6.Step 5: Effective mass (meff)The effective mass (meff ) is calculated by using Equation 4.15 as follows:meff =(Fj4j)(T 2eff4pi2)(4.15)Step 6: Nonlinear time history analysis (NLTHA)NLTHA is conducted by lumping half of meff on each of the two topnodes of the model in the gravity direction. Opensees [MMS+06] finite el-ement software tool with a tangent stiffness based 3% Rayleigh damping isused for the analysis. Twenty spectrum compatible earthquake ground mo-tions of section 3.1.2 scaled to Vancouver′s design spectrum NBCC 2010[NRC10] were used for the analysis (Figure 4.18). The ground motionrecords were obtained from the Pacific Earthquake Engineering Center [PEE05]database by comparing the ratio of seismic motion (A/V) to Vancouver′sA/V. The average 5% damped displacement spectrum from all the groundmotions considered is compared with Vancouver′s design spectrum as shownin Figure 4.19. As it can be inferred from Figure 4.19, the mean and thetarget 5% damped displacement spectrum are in good agreement.874.6. EVD calibration using nonlinear time history analysis0 0 .5 1 1.5 2 2.5 3 3.5 400 .511.522.53Time (sec)Acceleration (g) MeanTargetFigure 4.18: Comparison between mean and target spectrum for selectedground motion0 0 .5 1 1.5 2 2.5 3 3.5 401020304050607 08 0Time (sec)Displacement (cm) MeanTargetFigure 4.19: Displacement spectra at 5% damping level from the scaledground motion884.6. EVD calibration using nonlinear time history analysisA scaling factor obtained from Equation 4.16 EC8 [dN98] is used toobtain the highly damped displacement spectrum corresponding to ξhyst forthe hysteretic loop under consideration. By using the new spectrum, theTeff corresponding to each 4j was obtained.Rξ =√72 + ξ≥ 0.55 (4.16)Step 7: Outputs from the analysis and check for convergenceThe average of maximum top displacement (4NLTHA) that is obtainedfrom step 6 is compared with the initial considered displacement (4j). If thedifference is within 5% error, the corresponding ξhyst and µ are consideredas the true hysteretic damping and ductility values and the analysis willcontinue for the next loop (j+1). If the difference is significant, anotherξhyst and µ value will be calculated based on the new 4NLTHA and allthe procedures starting from step 2, will be repeated until convergence isobtained.Step 8: Analysis for other modelsSteps 1-7 were repeated for all 9 models considered.A detailed numerical example is presented in order to clearly show thesteps followed for the calibration process. The hysteretic loop details ob-tained from semi-static cyclic analysis for model M4 are given in Table 4.3.The yielding (panel crushing) displacement (4y) for this model is obtainedfrom Equation 12 and the monotonic pushover analysis is 28.3 mm.894.6. EVD calibration using nonlinear time history analysisTable 4.3: Results of the semi-static cyclic analysis on model M4No ofCycleFj (kN) 4j (m) Ahyst ξhyst1 378184 0.0135 76.18 0.0022 547052 0.02025 1561.037 0.0223 463256 0.01512 1411.148 0.034 463258 0.01512 1227.049 0.0275 463258 0.01512 1227.05 0.0276 463258 0.01512 1227.05 0.0277 463258 0.01512 1227.05 0.0278 711921 0.027 4431.471 0.0369 571507 0.02025 1983.32 0.02710 571519 0.02025 1672.793 0.02311 571519 0.02025 1672.797 0.02312 571519 0.02025 1672.799 0.02313 571519 0.02025 1672.799 0.02314 1158190 0.054 32446.2 0.08215 909964 0.0405 17769.8 0.07616 907065 0.0405 17710.76 0.07617 1349150 0.081 106901 0.15518 1060970 0.06075 55594.1 0.13719 1060960 0.06075 48881.85 0.1220 1478120 0.108 201085.7 0.221 1203500 0.081 111006.8 0.18122 1557650 0.189 536739.4 0.2923 1200120 0.14175 270829 0.25324 1558390 0.27 786884.7 0.297For simplicity, lets consider loop 14 with Fj = 1158.1 kN and 4j = 54mm. The corresponding ξhyst and µ are 8.2 % and 1.9, respectively. Fromstep 4, the damped displacement spectrum corresponding to ξhyst = 8.2 %is obtained from Figure 4.20. The scaling factor associated with equivalentdamping level is obtained using Equation 16. As suggested by [BP05], theinfluence of initial damping in the elastic range was not included in theprocess of time history calibration process. From Figure 17, the effectiveperiod (Teff ) associated with 4j = 54 mm and ξhyst = 8.2% is 0.72 sec. Byusing Equation 15 of step 5, the effective mass (meff ) is 281.923 ton. TheNLTHA is carried out by lumping half of the effective mass calculated oneach top node in the gravity direction.904.6. EVD calibration using nonlinear time history analysis0 0.5 1 1.5 2 2.5 3 3.5 40102030405060Time (Sec)Dsiplacement (cm) Average = 8.2%Figure 4.20: 8.2% damped average displacement spectrum4.6.1 Results of calibrationThe final calibrated EVD-ductility laws for the hybrid system understudy are given in Figure 18. Figure 4.21a, b, and c shows the variation ofthe corrected EVD-ductility law for various post yield stiffness ratios of thesteel members with bracket spacing of 0.4m, 0.8m, and 1.6m, respectively.As can be inferred from Figures 4.21a, b, and c, irrespective of the bracketconnection spacing, models with higher post yield stiffness ratio dissipateless amount of energy.914.7. Summary0 5 100510152025Ductility, P[hyst (%) 0 5 100510152025Ductility, P 0 5 100510152025Ductility, P[hyst (%) M1M2M3M4M5M6M7M8M9b)a)c)Figure 4.21: Calibrated hysteretic damping vs. ductility for bracket spacingof (a) 0.4 m ; b) 0.8 m; c) 1.6 m4.7 SummaryThis chapter proposes an equivalent viscous damping-ductility law forCLT infilled SMRFs. For this purpose, an analytical investigation was car-ried out for 243 predetermined single-storey single-bay CLT infilled SMRFsby varying the modeling parameters that affect the hysteretic behaviour ofthe system. The equivalent viscous damping and ductility of each modelwere obtained from the hysteretic responses of semi-static cyclic analysis.Then an expression is developed for equivalent viscous damping as a func-tion of ductility and various modeling parameters. Finally, an iterative924.7. SummaryNLTHA is conducted using 20 spectrum compatible earthquake ground mo-tions to calibrate EVD from Jacobsen′s area based approach. The calibratedEVD-ductility law will be used in direct displacement based design (Chapter5) of CLT infilled SMRFs to represent the energy dissipation of the hybridsystem.935Direct displacement based design of CLTinfilled steel moment resisting frames5.1 BackgroundDirect Displacement Based Design (DDBD) is a performance based seis-mic design, where the performance objectives are defined by the designerbased on the desired level of damage sustained in the structures [GAEB99].The damage sustained is associated with the displacement and interstoreydrift values during seismic excitation [KMA03, EY04, MK05, GAEB99,KC04]. In this chapter, the motivation is to develop a DDBD method fora new steel-timber hybrid system introduced by [SDT12, STKP12, DST12,Dic13, DSBT14].The idea of incorporating displacements in the design process of struc-tures through a concept of substitute-structure was first implemented byShibata and Sozen [SS74]. Gulkan and Sozen [GS74] developed a method945.1. Backgroundto estimate the design base shear of structures by considering their inelasticresponse. Moehle [Moe92] established a displacement-oriented approach forthe design of reinforced concrete structures. Moreover, the author showsthe simplicity and effectiveness of a displacement based method over theconventional ductility based approach. A true displacement based designphilosophy is introduced by Priestley [Pri93] as an alternative over the spec-tral based design method.Kowlasky et al. [KPM95] examines the applicability of DDBD method ofPriestley [Pri93] on single-degree-of-freedom (SDOF) bridge columns. Theapplied method provides additional flexibility for the designers that satisfiesthe initial target displacement with an acceptable margin of error. Calviand Kingsly [CK95] showed the application of the DDBD method to designmulti-degree-of-freedom (MDOF) bridge structures. The authors appliedthe concept of transforming the MDOF system to an equivalent SDOF sys-tem to calculate the required secant stiffness. The proposed procedure waseffective for relatively symmetrical bridges. However, the authors pointedout the deficiency of the method related to bridges with multiple dominantmodes of vibration. A more interesting application of inelastic design spec-tra to the direct displacement based design is presented by Chopra and Goel[CG01]. In this research, the authors showed the deficiencies associated withthe application of elastic design spectra in estimating ductility and displace-ment demands. Priestley and Kowalsky [PK00] applied the DDBD methodto design MDOF reinforced concrete frames and wall buildings based on aninitially estimated displacement profile.Recently, the applicability of the DDBD procedure has been examinedfor different types of structures and hysteretic systems [MK00a, MK00a,SPC06, WR, MGD13, MASR, RHA13, GSC10, Sul09, CPP04, PR09, PR07,PvdLP12, FF02, vdLRPP12].Medhekar and Kennedy [MK00a, MK00a] formulated the DDBD methodand applied it to the design of two and eight storey concentrically bracedsteel frames. For both building types, the authors used 5% elastic damp-ing as an effective damping. Recommendations are forwarded to includethe hysteric component of damping to represent the total energy dissipative955.1. Backgroundcapacity of the structures. A more comprehensive DDBD of concentricallybraced steel frames is presented by Wijesundara and Rajeev [WR]. In thisresearch, the authors used calibrated equivalent viscous damping with ayield displacement profile. Sullivan et al. [SPC06] proposed a novel DDBDapproach to design reinforced concrete frame-wall structures. The developedmethodology was applied to 4, 8, 12, and 16 storeys frame-wall structures byconsidering different configurations of both frames and walls. In their paper,strength proportions between walls and frames are assigned initially to cal-culate the characteristics of an equivalent SDOF system. Malekpour et al.[MGD13] applied Sullivan’s [SPC06] concept of initial strength proportionassignment to design steel concentrically braced reinforced concrete frames.As a step towards a DDBD approach for cold-formed steel frame wood panelshear walls, [MASR] derived an expression to calculate EVD and the designdisplacement profile. A work by Christopoulos [CPP04] modified the DDBDprocedure of Priestley [Pri99] to incorporate residual deformation into thedesign process through the residual/maximum displacement spectra.Even though wood structures have been effective with regards to col-lapse prevention and life safety in recent earthquakes (Loma Prieta 1999and Northridge in 1994), the economic losses associated with these struc-tures was enormous [PR09]. This reason prompted the need for a designmethod that satisfies both life safety and damage limit state. To addressthis concern, recently a DDBD approach was applied to wood frame struc-tures [PR09, PR07, FF02, vdLRPP12]. Pang and Rosowski [PR09] appliedthe DDBD approach to design mid-rise regular wood-framed buildings. Thisprocedure is intended to satisfy both the damage and safety limit states. Intheir research, a normalized modal analysis is used to develop the inter-storey drift spectra. Moreover, the authors showed the applicability of themethod by designing both commercial and residential type buildings. Filia-trault and Floz [FF02] and van de Lindt et al. [vdLRPP12] also outlined aDDBD procedure for wood frame buildings. Although the above researcheshave adopted the DDBD procedure for reinforced concrete, steel , and woodbased structures, the procedure is not yet developed for the steel-timberhybrid system that incorporates CLT as an infill panel in SMRFs.965.2. Basics of Direct displacement based design (DDBD)In this chapter, an iterative direct displacement based design method isdeveloped for a CLT infilled steel moment resisting frame structure. Theiterative design procedure is started by assuming the following initial model-ing variables: gap between CLT panel and steel frame, bracket (connection)spacing, CLT panel thickness and strength, and post yield stiffness ratio ofsteel members. Subsequently, the design displacement profile is developedby assigning an initial relative strength between the CLT wall and frameelements. This profile is used to obtain the characteristics of an equivalentsingle degree of freedom (SDOF) system. A system ductility value is estab-lished based on the proportions of the overturning moment resistance of theCLT wall and steel moment frame. A calibrated EVD-ductility relationshipis used to obtain the energy dissipation of the equivalent SDOF system. Ef-fective period and secant stiffness of the system are calculated to obtain thefinal design base shear. Hybrid systems of three bays, 3-, 6-, and 9-storeysheight buildings with an infilled middle bay are designed using the proposedmethod. Nonlinear time history analysis using twenty earthquake groundmotion records is used to validate the performance of the proposed designmethodology. The results indicate that the developed method effectivelycontrols the displacements due to seismic excitation of the hybrid system.5.2 Basics of Direct displacement based design(DDBD)A through discussion on the fundamentals of the DDBD method for dif-ferent types of structures is given in [PCK07b]. In this section, the basicsteps and key equations of DDBD method are discussed. Figure 5.1 showshow DDBD utilizes a virtual representation of the nonlinear structures withan equivalent Single Degree of Freedom (SDOF) system through secant stiff-ness Ke and equivalent viscous damping ξeq at peak displacement ∆d.975.2. Basics of Direct displacement based design (DDBD)F y F u K i rK i K e ѐy ѐd F m eff h eff a) SDOF representation b ) Effective stiffness c) EVD vs. ductility d) Design displacement spectra 05101520250 2 4 6 8 10[ hyst (%) Ductility, µ M1M2M30 1 2 3 4020406080Time (sec)Displacement (cm) MeanTargetFigure 5.1: Basics of DDBD approach (adopted from Priestley et al. 2007)One of the critical steps in the process of DDBD is the transformationof MDOF system in to an equivalent SDOF system. The equivalent SDOFsystem is represented by secant stiffness (Ke) at the maximum response.For this transformation process, a design displacement profile is needed.For frame type building, the design displacement is depends on the driftlimits of lower stories [PCK07a]. The displacement profile suggested forframe structures in [PCK07a] is given by Equation 5.1.∆i = δi(∆cδc)(5.1)where δi is the inelastic mode shape as given by Equation 5.2, ∆c is thedesign displacement at the first floor (level c), and δc is the value of mode985.2. Basics of Direct displacement based design (DDBD)shape at level c.for building framesfor n ≤ 4 δi =HiHnfor n > 4 δi = 43(HiHn)(1− Hi4Hn )(5.2)where Hi and Hn are the heights of level i and total height of the building,respectively. The characteristics of equivalent SDOF system, i.e., designdisplacement (∆d), effective mass (meff ) and effective height (heff ) aregiven in Equations 5.3, 5.4, and 5.5, respectively [SL12].∆d =∑ni=1mi∆2i∑ni=1mi∆i(5.3)me =∑ni=1mi∆i∆d(5.4)he =∑ni=1mi∆ihi∑ni=1mi∆i(5.5)where n is the number of storeys and mi and hi are the mass and height ofstorey i, respectively. Representation of the energy dissipative capacity ofthe structures using equivalent viscous damping frame structures requiresknowledge of structural ductility demand. The ductility of a structural sys-tem can be calculated from the geometry of the cross section of its members.The yield drift of frame structures given by [PCK07a] is:θy = C2yLbHb(5.6)where C2 is 0.5 and 0.65 for concrete and steel members, respectively; Lb andHb are the beam span and depth, respectively; and y is the flexural yieldingstrain for steel members. The yield displacement (∆y) and the associated995.2. Basics of Direct displacement based design (DDBD)ductility (µ) are given in Equations 5.7 and 5.8, respectively.∆y = he × θy (5.7)µ =∆d∆y(5.8)In DDBD the energy dissipative capacity of the structures is representedby EVD. Several authors derived the law of EVD ductility law for differentstructural systems (hysteretic laws) (details are given in Chapter 4). ThisEVD (ξeq) contains both the elastic and hysteretic components of damping.With the assumption of 5% elastic damping, Priestley [PCK07b] proposedthe EVD-ductility law as follows:ξeq = 0.05 + C(µ− 1µpi)(5.9)where the coefficient C is in the range of 0.1 to 0.7 for various structuralsystems (hysteresis rules). Once the ductility demand is known it is possibleto calculate the EVD using 5.9. Once, the design displacement (∆d) andEVD (ξeq) are established, the required effective period can be obtained fromthe displacement spectra (Figure 5.1d) for an appropriate EVD (ξeq) level.The average elastic displacement spectra can be scaled with the coefficient(η) to a highly damped spectra using Equation 5.10 [dN05].η =√105 + ξ(5.10)The corresponding effective stiffness, Ke (Figure 5.1b), for the equivalentSDOF system can be obtained from Equation 5.11.Ke =4pi2meT 2eff(5.11)Finally, design base shear (Vb) can be calculated from the effective stiff-1005.3. Proposed DDBD approach for CLT infilled SMRFsness (Ke) and design displacement ∆d as follows.Vb = Ke∆d (5.12)To select member sections with adequate strength, the structure should beanalyzed under lateral forces distributed as shown Equation 5.13.Fi = Vbmi4i∑ni=1mi4i(5.13)where Fi is the shear force at level i.5.3 Proposed DDBD approach for CLT infilledSMRFsThe basics of DDBD method are discussed thoroughly in Chapter 2. Theproposed framework to design CLT infilled SMRFs is outlined as shown inFigure 5.2. The proposed DDBD procedure is illustrated with a case study3 storey - 3 bays (middle bay infilled steel moment resisting frame). Thefloor plan and elevation view of the case study building are given in Figures5.3 and 5.4, respectively. The height of each storey of the building is 3.2 m.A constant bay width of 6 m is used for the entire building.1015.3. Proposed DDBD approach for CLT infilled SMRFs Assume model ing para met ers of CLT infi ll ed stee l moment resisting frames • Gap betwee n CLT and stee l frames • CLT thi ckne ss and strengt h • Connec ti on bracke t spac ing • Post y ie ld stiffne ss rati o of stee l members Assign stre ngth proporti ons bet wee n CLT shea r panel s and stee l moment frames Deve lop design displac ement profil e ௧ܸ௧ൌ ܸ ܸ ் Chara ct eri stic s of equi val ent SDOF sy stem • Design displa ce ment ( οௗሻ • Effe ct ive mass ( ݉ሻ • Effec ti ve height ( ݄ሻ Sy stem duct il it y ( ߤ௦௬௦ሻ using proporti ons of over turni ng moment resistanc e bet wee n CLT infi ll and stee l moment frame Sy stem equi val ent viscous damping ( ߦሻ ߤ௦௬௦ൌܯ்ߤ௪ܯߤܯ்ܯ Scal e the design displa ce ment spec trum to get effe ct ive period ( ܶ)for corre sponding οௗ Sܿܽ𝑙𝑖݂݊݃ܽܿݎݐ ߟൌଵହାక ͲǤͷͷ Dete rimne the effe ct ive stiffne ss ( ܭ) and design base shea r ( ሻ Distri bute the base shea r and perform struc tural analy sis Sele ct the member size s and det ermine the require d CLT prope rti es yes CLT prope rti es and brac ket spac ing are ok? End ܨൌ ܸ ݉οσ ݉οୀଵ No Figure 5.2: Framework of DDBD for CLT infilled SmRfs1025.3. Proposed DDBD approach for CLT infilled SMRFs6 m 6 m 6 m 6 m 6 m 6 m 6 m N A A Figure 5.3: Building floor planFigure 5.4: Elevation view of the 3 storey 2D frameThe building is assumed to be situated on a very dense soil and softrock (site class C) with a peak ground acceleration 0.48g in Vancouver,Canada. The building is modeled as a two-dimensional structure and due to1035.3. Proposed DDBD approach for CLT infilled SMRFsits symmetry in plan, accidental torsion is neglected both in the design andanalysis phase. Both beam and column elements are detailed based on CSAG40.21 with a yielding strength of Fy = 350 MPa and modulus of elasticity(Es) of 200 GPa. A constant floor seismic weight (including the CLT panels)of 253T was obtained by performing gravity load structural analysis using acommercial software SAP 2000 [HW05]. The proposed design methodologyis comprised of 11 steps and presented in detail for the case study building.Step 1: Assume modeling parameters of CLT infilled steelmoment resisting framesResults from multi-objective optimization of Chapter 3 are used to setthe initial modeling parameters CLT infilled SMRFs. A bracket spacing0.8 m, panel thickness and strength of 99 mm and 17.5 MPa, respectively,are used as a starting parameters for the current example. Steel memberswith a smaller post yield stiffness ratio dissipate a relatively large amount ofenergy. Therefore, based on the results of Chapter 4, the post yield stiffnessratio of 1% is used as an initial starting point.Step 2: Assign strength proportions between CLT shearpanels and steel moment framesA concept of initial strength assignment to calculate the characteristicsof an equivalent SDOF is adopted Sulliavn et al. [SPC06]. The CLT shearpanels are not continuous (disconnected at the bottom and top of eachstorey) and deform in a pure shear behaviour. Therefore, it is reasonableto assign the shear strength proportion at the start of the process as theirbending strength is not important. For the proposed hybrid system, Figure5.5 shows the shear resistance proportions between the CLT shear panelsand steel moment resisting frames. Since the steel frame shear resistancedepends up on the beams strength, constant beam strength are used upto the roof level based on recommendation of Pauley [PP]. As depicted inFigure 5.6, 70% of the total shear is directly assigned to the frames. Theshear resistance for the CLT wall is calculated by subtracting the frame1045.3. Proposed DDBD approach for CLT infilled SMRFsshear from the total shear as given by Equation 5.14 [SPC06].Vi,CLTVb=Vi,totalVb−Vi,frameVb(5.14)where Vb is total design base shear, Vi,CLT is the shear resisted by the CLTinfill panels at story i, and Vi,total is the total shear at story i. The totalshear of the system is established as a function of design base shear, storeynumber (i) and total number of storeys (n) by [SPC06] as given in Equation5.15.Figure 5.5: Shear distribution between CLT walls and steel frameVi,totalVb= 1−i(i− 1)n(n+ 1)(5.15)- 0 .5 0 0 .5 1 1.5Shear (% o f Vb)-5 0 5 100123O verturning mo ment (% o f Vb)Level TotalFrameWallFigure 5.6: Moment and shear distribution of frame and CLT wall along theheight of the building1055.3. Proposed DDBD approach for CLT infilled SMRFsThe shear and overturning moment proportion distribution throughoutthe height of the building are shown in Figure 5.6. As shown in Figure 5.6,the inflection point for the wall starts above the first storey. At this point,the shear proportions can be tuned to effectively utilize the CLT panels thatwill give an optimum inflection height.Step 3: Develop design displacement profileThe properties of an equivalent SDOF system are depends on the driftlimit of the lower stories of moment frames and an assumed displacementprofile. This displacement profile is corresponds to the inelastic first moderesponse of the structure under seismic excitation [PCK07b]. To ensurethe satisfactory performance of the structures under seismic event, buildingcodes specify limits on lateral storey drift values. The NBCC 2010 [NRC10]puts a 2.5% interstorey drift limit to represent extensive damage on thebuildings. Previous studies [DST12, Dic13, DSBT14] on the CLT infilledSMRFs suggest that the CLT panel crushing can be an effective way ofenergy dissipation and easy for maintenance purposes. In their research,the authors showed that panel crushing occurs before the 2.5% interstoreydrift limit of the system. Therefore, the drift limit θd of 2.5% correspondingto lower storey drift demand of the hybrid system is selected as a target driftlimit. The displacement profile is established using Equation 5.16 [SPC10].∆i = ωθθdhi(4Hn − hi4Hn − h1)(5.16)where ∆i is the displacement at level i, hi is the height of ith floor from theground, Hn is the total building height, ωθ is the factor to account for theeffects of higher modes and is given as:ωθ = 1.15− 0.0034Hn ≤ 1 (5.17)1065.3. Proposed DDBD approach for CLT infilled SMRFsStep 4: Characteristics of equivalent SDOF systemEquations 5.18, 5.19, and 5.20 [SL12] are used to calculate the designdisplacement (4d), effective mass (meff ), and effective height (Heff ), recep-tively, for the substitute equivalent SDOF system from the masses lumpedin each storey (mi) and height of each storey from the base (hi).∆d =∑ni=1mi∆2i∑ni=1mi4i(5.18)meff =∑ni=1mi∆i∆d(5.19)heff =∑ni=1mi∆ihi∑ni=1mi∆i(5.20)The summary of the equivalent SDOF system are summarized in Table5.1.Table 5.1: Characteristics of equivalent SDOFStorey h ∆i θi mi mi∆i mi∆2i mi∆ihi ∆d meff heff3 9.6 0.196 1.59 253 49.68 9.75 476.92 0.156 680.9 7.282 6.4 0.145 2.04 253 36.8 5.35 235.521 3.2 0.08 2.5 253 20.24 1.61 64.7680 0 0 0 0 0 0 0Step 5: System ductility (µsys) using proportions ofoverturning moment resistance between CLT infill and steelmoment frameAs CLT panels crush at low drift values, the ductility associated withthem is large. However, for the steel moment frames the inelastic responseoccurs at a relatively larger drift value. The displacement ductility value ofCLT panels and frames is calculated as follows:µCLT =∆d∆crush,CLT(5.21)1075.3. Proposed DDBD approach for CLT infilled SMRFsThe crushing displacement for the CLT wall (∆crush,CLT ) is calculatedusing the deflected shape of the CLT panel (Figure 5.7) as follows.ȟ ȟ௨௦ǡ ் ȟ௨௦ǡ ் 3.2 m 6 m d Figure 5.7: CLT panel representation with a compression strutEo =fCLTCLT=fCLT4cd=d.fCLT4c.cosθ(5.22)4crush,CLT =d.fCLTEo.cosθ(5.23)where Eo, fCLT , and CLT are the modulus of elasticity, crushing strengthof CLT panel, and strain of the CLT panel, respectively. The displacementductility of the steel moment resisting frame is calculated using Equation5.24 [GSC10].µframe,i =4i −4i−1hi − hi−1(1θy,steelframe)(5.24)where µframe,i is the ductility demand of ith storey and θy,steelframe is theyield drift of the steel frame as given by Equation5.25 [PCK07b].1085.3. Proposed DDBD approach for CLT infilled SMRFsθy,steelframe = 0.65yLbhb(5.25)where Lb and hb are the beam span length and depth, respectively. For thisexample, a trial beam depth of 500 mm based on initial gravity load analysisis used that gives θy,steelframe of 13.65 mm. As suggested by Pauley [PP],it is advantageous to use the constant beam sections throughout the heightof the building. As such, it is possible to take the average frame ductilitydemand of each floor to get the overall frame ductility. Table 5.2 summarizesthe ductility demands of each story and the average ductility (µaverage).Table 5.2: Average frame ductilityStorey h ∆i µframe,i0 0 0 01 3.2 0.08 1.832 6.4 0.145 1.493 9.6 0.196 1.16µframe,average 1.12Having both the CLT panel and frame ductility demands, it is nowpossible to determine the system ductility µsys that is weighted based onthe respective overturning moment resistance using Equation 5.26 [GSC10].For the case study building, the calculated system ductility (µsys) is 2.217.µsys =MCLTµCLT +Mframeµframe,averageMframe +MCLT(5.26)Step 6: System equivalent viscous dampingAn expression and plots of equivalent viscous damping of SDOF hybridsystem are developed in Chapter 4. Figure 5.8 shows the damping ductil-ity law corresponding to the assumed modeling variables of step 1. Fromthe plot, the hysteretic component equivalent viscous damping (µhyst) cor-responding to the system ductility of step 5 is 11.5%. The total equivalentdamping of the system µeq is found by adding 3% elastic damping on µhyst.1095.3. Proposed DDBD approach for CLT infilled SMRFs0 2 4 6 8 100510152025Ductility, P[eq (%)Figure 5.8: Equivalent viscous dampingStep 7: Effective period of the systemThe effective period of the equivalent SDOF system is obtained from thehighly damped displacement spectrum. The average elastic displacementspectrum of chapter 4 is used by scaling with an appropriate scaling factor.A scaling factor is calculated using Equation 5.27 [dN98] to obtain the highlydamped displacement spectra corresponding to µeq = 14.5 %. Figure 5.9shows the damped spectrum used to calculate the system effective period(Teff ). An effective period of 2.26 sec is obtained from the plot.η =√10(5 + ξ(5.27)1105.3. Proposed DDBD approach for CLT infilled SMRFs0 1 2 3 40102030405060Time (Sec)Displacement (cm) Average[e q = 14.5 %d=15.6 c mFigure 5.9: Effective period from damped displacement spectrumStep 8: Effective stiffness and design base shearThe effective period and design base shear are calculated in Equations5.28 and 5.29 as follows:Keff = 4pi2meffT 2eff= 5257.4 kN (5.28)Vb = Keff4d = 824.04 kN (5.29)Step 9: Distribute the base shear and perform a structuralanalysisThe above calculated design shear force is distributed to perform thestructural analysis of the system. Equation 5.30 [SL12] is used to calculate1115.3. Proposed DDBD approach for CLT infilled SMRFsthe design shear forces at each level of the building (Fi).Fi = KVbmi4i∑ni=1mi4i(5.30)Table 5.3 summarizes the proportions of shear for frames (Vframe) andCLT wall VCLT at each storey level of the building.Table 5.3: Base shear proportions between frame and wallsStorey mi∆i Fi(kN) Vi,total(kN) Vframe(kN) Vwall(kN)3 49.68 383.60 383.60 268.52 115.082 36.8 284.15 667.75 467.42 200.321 20.24 156.28 824.03 576.82 247.210 0 0 0 0 0The structural analysis is carried out using the approximate method. Aportal method of analysis has been chosen to perform the analysis due to itssimplicity and accuracy. As indicated in Figure 5.10, the inflection point forthe bottom columns is taken to be at 60% of the storey height (hs). Thisprovision will avoid any soft storey mechanisms (formation of yielding pointon the top of the lower story columns). However, for other columns of theframes, this inflection point is set at the mid height of the given storey. Themethod of structural analysis is illustrated in detail in Appendix:1125.3. Proposed DDBD approach for CLT infilled SMRFs* * * * * * * * * * * * 0 . 6 h s h s 0.5h s Figure 5.10: Inflection point on the deflected shape of the moment resistingframeThe final results for beams, columns, and joints of the frame are depictedin Figure 5.11.Step 10: Beam and column strengthsThe plastic moment strengths for the beams and columns are summa-rized and shown in Table 5.4. The detailed moment strengths for all beamsand columns in the building are indicated in Figure 5.11. Subsequently, theplastic section modulus are calculated to choose an appropriate section thatsatisfies the demand.Table 5.4: Beams and columns required moment strengthStorey Beam moment Interior column moment Exterior column moment3 71.6 143.13 71.62 196 249.28 124.641 247.7 369.13 184.5It should be noted at this point that the selection of steel cross sectionsis accomplished with the following assumptions and provisions:1. Gravity and seismic load actions (moment and shear) are not com-1135.3. Proposed DDBD approach for CLT infilled SMRFs268.52 kN 198.9 kN 23.85 71.56 44.73 23.85 71.06 23.85 223.79 23.85 223.79 71.56 71.56 71.56 23.85 71.56 23.85 89.46 223.79 134.33 44.73 71.56 71.56 23.85 23.85 143.16 143.13 89.46 44.73 89.46 44.83 23.85 124.14 196 71.56 196 223.79 165.53 165.53 196 165.53 65.33 65.33 89.26 65.33 143.136 196 249.28 99.19 165.53 65.33 65.33 155.8 196 249.28 249.28 155.8 155.8 77.9 89.26 89.26 124.14 124.14 77.9 23.85 134.33 23.85 134.33 71.56 71.56 23.85 71.56 23.85 89.46 134.33 44.87 143.16 143.16 23.85 44.87 23.85 44.87 71.56 23.83 44.73 71.56 71.56 23.83 143.16 143.13 89.46 89.46 143.16 143.13 44.73 44.73 23.83 23.83 196 99.19 196 99.19 65.33 65.33 89.46 143.136 196 249.28 33.85 99.19 65.33 65.33 155.8 196 89.46 196 33.85 196 33.85 65.33 65.33 65.33 77.9 196 124.14 89.46 44.87 71.56 44.73 33.85 23.83 249.28 249.28 155.8 155.8 77.9 89.26 89.26 124.14 124.14 77.9 109.4 kN 77.9 89.26 123.04 247.84 124.14 247.84 91.7 91.7 247.84 91.7 82.61 65.33 171.83 82.61 249.28 247.53 249.28 55.24 91.7 82.61 82.61 192.26 247.87 246.09 369.13 155.8 155.8 96.13 171.77 171.77 123.04 184.56 96.13 247.53 51.24 247.53 55.24 82.61 82.61 155.8 249.28 196 249.28 18.78 55.24 65.33 65.33 192.8 247.53 89.46 82.61 96.3 247.83 123.04 171.77 77.9 18.78 89.16 247.53 18.78 247.53 18.78 82.61 82.61 96.13 246.09 369.13 155.8 155.8 96.13 171.77 171.77 123.04 184.56 96.13 Figure 5.11: Detail results of approximate method of analysis 1145.3. Proposed DDBD approach for CLT infilled SMRFsbined to select the element sections. Rather, the selection process isdone with only the governing load (seismic actions). This assumptionis correct for building designs in high seismic regions. Moreover, Pinto[Pin97], found negligible difference in seismic response of structureswith or without gravity loads. Priestley [PCK07b] strongly argued thefallacy associated with combining DDBD seismic actions with gravityactions for the DDBD process. The addition of gravity moments withseismic moments, in DDBD, will result larger in sections. This willresult a false sense of lower seismic response than the initial target dis-placement. In line with Priestley et al.[PCK07b], the element sectionsare selected for the higher of gravity and seismic moments. Since thebuildings are designed for high seismic regions, for all buildings in thisresearch the seismic loads governs the design.2. As indicated in Chapter 4, the post yielding stiffness of the steel mem-bers is critical in the inelastic response and energy dissipation of thesystem. Garcia [GSC10], recommended a reduction factor on the de-sign strength of members as seen in Equation 5.31. Since, at the startof the design process the post yielding stiffness is considered to be 1%,the reduction factor for the case study building is 1.002.factor = 1 + r(µframe − 1) (5.31)3. As required by CSA S16-09, both beams and columns are assumed tobe constructed by considering bracing against lateral torsional buck-ling.With the above assumptions, the member selection is carried out for beamsand columns in the lower stories. Uniform cross sections of beams, exte-rior column, and interior columns are used through out the height of thebuilding. The section modulus of beams and columns are used to selectthe sections from the CISC Handbook [CIS10]. Table 5.5 summarizes theselected sections for the case study building.1155.3. Proposed DDBD approach for CLT infilled SMRFsTable 5.5: Details of sectionsMember Section Zprovided(103mm3) Mr,provided(kN.m)Beam W310x52 841 261Interior column W360x79 1430 444Exterior column W310x45 708 220The design checks for class of a selected section, overall member strength(OMS), and lateral buckling strength (LTBS) of members of the buildingis provided in Appendix. The design checks have been carried out basedon CSA S16-09 regulations and conceptual suggestions from Filiatrault etal.[FRC+13].Check for CLT propertiesIn this section, design checks have been carried out on initially assumedCLT panel properties. As discussed in Chapters 3 and 4, panel strength has alittle effect on the dynamic behavior of the hybrid system. Numerical valuesfrom Structurlam manufacturing guideline [Strnd] are used to perform thedesign check. From the guideline, three layers CLT wall under pure shearcan carry up to 304 kN load. However, the maximum shear demand onCLT walls for the case study building is 89.1 kN. Therefore, the CLT panelthickness (99 mm) that was considered at the start of the design process isacceptable. The steel connection brackets transfer the shear and axial loadsfrom the steel frame to the CLT wall. The brackets in this hybrid systemare under 3 different loads: shear, axial or their combination. Calibrationof the Pinching4 model [LMA03] of OpenSees [MMS+06] by [SST+13] fromthe experimental tests performed by Schneider et al.[SST+12] on the bracketconnections indicates that these connection type can carry up to 45 kN bothin shear and axial directions. At the start of the design process, a total of16 brackets are applied at the top and bottom of the panel. These bracketsare under pure shear and combined axial-shear response. Therefore, thesebrackets transfer 16 × 45 kN shear and axial force with out failure. Themaximum shear demand on the CLT wall is less than the bracket shear forcetransferring capability. Therefore, the initially assumed bracket spacing is1165.3. Proposed DDBD approach for CLT infilled SMRFsis acceptable. However, the capability of the brackets under combined shearand axial loading needs further research and is not considered in the designcheck for this thesis.For the detailed design of structures, a capacity design should be per-formed after this step. The application of this concept will vary membersections along the height of the building. Moreover, the column sizes willbe expected to increase. Application of the capacity design is outside thescope of this thesis. More information on the application of capacity designprinciples in DDBD of hybrid structures can be found elsewhere [SPC06].The above steps have been followed to design the middle bay CLT infilled sixand nine storey 2D buildings of Figure 5.12. The floor plan for the buildingsis shown in Figure 5.3.3.2 m TYP Figure 5.12: Elevation view of six and nine storey buildings1175.4. Nonlinear Time History AnalysisThe final results of DDBD of 3, 6, and 9 storey buildings are summarizedin Table 5.6. It should be noted at this point that all design checks wereperformed for the design of 6 and 9 storey buildings.Table 5.6: Details of DDBD design3 storey 6 storey 9 storeyProportion of Vb assigned to frames (%) 70 50 50Design storey drift, thetad(%) 2.5 2.5 2.5Design displacement (detald) (m) 0.156 0.28 0.409Effective Height, heff (m) 7.28 13.5 19.73Effective Mass, meff (T) 680.8 1287.3 1887.5µCLT 12.05 21.7 31.4µframe,average 1.123 1.22 1.28µsys 2.21 7.53 10.21ξSDOF (%) 14.5 20.5 21Effective period, Teff (sec) 2.26 3.2 4.2Keff (KN/m) 5257.4 4957.9 4219.9Vb (kN) 824.04 1399.8 1726Beam section W310×52 W310×67 W360×79Interior column section W360×79 W360×91 W360×110Exterior column section W310×45 W310×52 W360×64Beam strength, Mb,i (KN.m) 261 326 444Interior column strength, Mint.col,i (KN.m) 444 552 640Exterior column strength, Mext.col,i (KN.m) 220 261 3545.4 Nonlinear Time History AnalysisIn order to perform nonlinear time history analysis (NLTHA), OpenSees[MMS+06] finite element tool is used to model the designed hybrid struc-tures. The details of the structural modeling are discussed in Chapter 3.Twenty earthquake ground motions that have been used to calibrate theEVD in Chapter 4 are used to perform NLTHA. Figure 3.5 shows the scaledspectra with the mean and target spectrum for considered hazard value. Theaverage 5% damped displacement spectrum from all the ground motions iscompared with Vancouver design spectrum as shown in Figure 16(b). Thedesigned elements are modeled with their respective moment strength and1% post yield stiffness ratio. Rigid floor systems are assumed for the build-1185.4. Nonlinear Time History Analysising. Accidental torsion and P-∆ effects were not considered in the validationanalysis. Seismic weight which is compromised of the self weight of the struc-ture is applied at beam column connections. Since the structure is designedfor high seismic region the structural elements are capable of carrying addi-tional gravity loads. However, this assumption mat not work for the designsin moderate and low seismic regions.5.4.1 Results of nonlinear time history analysisThe proposed DDBD method is validated by comparing its displacementresponses with the initially assumed target displacement profile. In orderto reduce the potential damage on the structures during the seismic event,maximum interstorey drift (MISD) of the building should be less than thetarget interstorey drift value (2.5%). In addition, according to Chapter 3,the residual interstorey drift (RISD) response should be checked as it canbe high in the proposed hybrid structure. Sample seismic response of the 3storey building in Northridge earthquake is given in Figure 5.13.1195.4. Nonlinear Time History Analysis- 0. 3- 0. 2- 0. 100.10.20.30.40 20 40 60 80 10 0Acceleration (g) No rthridge, 1994 - 0.2 25- 0. 15- 0. 07500.07 50.150 20 40 60 80 10 0Roof displacement (m) Time (Sec) Residual displacement Maximum displacement Figure 5.13: Response of 3 storey CLT infilled SMRF in Northridge 1994earthquakeThe storey displacement response of 3, 6, and 9 storey buildings aregiven in Figures 5.14, 5.15, and 5.16, respectively.1205.4. Nonlinear Time History Analysis0 0 .05 0 .1 0 .15 0.2 0 .250123Displacement (m)Level EQ-iTargetAverageFigure 5.14: Maximum storey displacement of 3 storey hybrid building0 0 .1 0 .2 0 .3 0 .40123456Displacement (m)Level EQ-iTargetAverageFigure 5.15: Maximum storey displacement of 6 storey hybrid building1215.4. Nonlinear Time History Analysis0 0 .1 0 .2 0 .3 0 .4 0 .5 0 .6 0 .70123456789Displacement (m)Level EQ-iTargetAverageFigure 5.16: Maximum storey displacement of 9 storey hybrid buildingThe maximum intersorey drift response of 3, 6, and 9 storey buildingsare given in Figures 5.17, 5.18, and 5.19, respectively.0 0 .5 1 1.5 2 2.5 3 3.5023M ISD (% )Level EQ-iTargetAverageFigure 5.17: Maximum interstorey drift of 3 storey hybrid building1225.4. Nonlinear Time History Analysis0 0 .5 1 1.5 2 2.5 30123456M ISD (% )Level EQ-iTargetAverageFigure 5.18: Maximum interstorey drift of 6 storey hybrid building0 0 .5 1 1.5 2 2.5 30123456789M ISD (% )Level EQ-iTargetAverageFigure 5.19: Maximum interstorey drift of 9 storey hybrid buildingIt is evident from Figures 5.14-C.5 that the target displacement anddrift profiles are close to the average responses from the NLTHA. Irrespec-tive of the height of the building, average displacement and intersorey drift1235.4. Nonlinear Time History Analysisdemands are less than the initially assumed target values. This clearly indi-cates the capability of the proposed method in controlling the responses ofstructures under seismic excitation. However, the values of the design driftand displacement profiles for the top storeys of 6 and 9 storey buildings arenot close enough to the average responses of NLTHA. This lower response isdue to the application of uniform beam and column cross sections throughout the height of the structure. This leads to lower drift values at the topof the buildings. The importance of residual interstorey drift is highlightedin Chapter 3. For brevity, the plots for the variation mean and individualRISD with the height of the building is given in Figures 5.20-5.22. The 3storey building experienced RISD values of 0.01 - 0.3 %. A dispersed scatterplot is obtained for this building as shown in Figure 5.20. The RISD valuesfor the six and nine storey buildings under each earthquake vary in the rangeof 0.01 - 1.35 % and 0.01 - 0.9 %, respectively. Values more than 0.5 % indi-cates extensive damage on the building. The mean RISD values are shownto increase linearly with the building height. However, large variability withground motions is observed in the RISD responses.0 0 .06 0 .12 0.18 0 .24 0 .3 0 .360123RISD (% )Level EQ-iAverageFigure 5.20: Residual interstorey drift of 3 storey hybrid building1245.4. Nonlinear Time History Analysis0 0 .2 0 .4 0 .6 0 .8 1 1.2 1.40123456RISD (% )Level EQ-iAverageFigure 5.21: Residual interstorey drift of 6 storey hybrid building0 0 .2 0 .4 0 .6 0 .8 10123456789RISD (% )Level EQ-iAverageFigure 5.22: Residual interstorey drift of 9 storey hybrid building1255.5. Summary5.5 SummaryA new iterative direct displacement based design method SMRFs withCLT infill walls has been developed and tested by designing 3-, 6-, and9- storeys hybrid buildings. In summary, the developed method provedto effectively control seismic interstorey drifts and displacements. A robustfinite element model of the hybrid structure that accounts for the CLT paneland frame interactions was used for the validation process. Initial shearproportions between the wall and frame are assigned at the start of thedesign process. The system ductility and equivalent viscous damping areexplicitly accounted. Better control of storey drifts and displacement wereachieved for low rise hybrid buildings.Future research should aim at investigating the method to account forresidual interstorey drift values (RISD). The RISD values that are obtainedfrom NLTHA are between 0.2 - 0.6 %. RISD responses more than 0.5 % rep-resent extensive damage on the buildings. Christopoulos [CPP04] indicatedan effective way of controlling RISD in the DDBD method. Moreover, a fur-ther extension of the developed method is to couple it to the capacity designprinciples. This will make the method more rational for the designers.1266Conclusions and future researchperspectives6.1 Summary and conclusionsThis thesis has developed an iterative DDBD method for the Timber-Steel hybrid structure. The hybrid structure incorporates CLT shear panelsas an infill in steel moment resisting frames (SMRFs). This structure hasbeen developed at The University of British Columbia to overcome the heightlimitation of timber as a main structural element. The proposed hybridsystem couples the ductile behaviour of steel moment resisting frames withthehigh stiffness to weight ratio of CLT shear panels.The proposed hybrid structure is achieved by using L-shaped steel bracketconnectors that are bolted to the steel frame and nailed to the CLT panel.These brackets are experimentally tested in axial and shear directions bySchneider et al. [SKP+13]. Analytical calibrations of the experimental tests1276.1. Summary and conclusionson the brackets were performed by Shen et al. [SST+13]. A composite ac-tion is obtained by providing a gap between the frame and the CLT panelthat allows the brackets to deform and disspiate energy. Preliminary over-strength and ductility factors were suggested for the system by Dickof et al.[DSBT14]. This hybrid system has proven to be efficient in decreasing theseismic vulnerability of steel moment resisting frames in high seismic regionsTesfamariam et al. [TSDB14]. The main motivation of this research was todevelop a DDBD method for the proposed hybrid structure.Initially, a polynomial predictive equation to quantify MISD was de-veloped from corresponding RISD and significant modeling parameters bystudying the seismic behaviours of 162 different hybrid buildings. The vali-dation process confirmed that the equation can provide a good approxima-tion of MISD for the proposed hybrid structures. Response surface method-ology technique was successfully applied to develop the prediction equation.The developed equation does not need the dynamic characteristics of thestructure in order to perform the post-seismic safety assessment of hybridstructures. Moreover, the dynamic analysis results were used to identifyoptimal modeling parameters of the hybrid structure. The optimizationprocess adopts ANN based objective functions that are developed by usingthe Levenberg-Marquardt algorithm. A Pareto-front of optimal design so-lutions was obtained by applying a multi-objective optimization approachusing the Genetic Algorithm. The obtained optimized values of modelingvariables will result in the possible minimum RISD and MISD values underextreme seismic event. The following conclusions can be made based on theresults of the parametric studies in Chapter 3:− MISD can be estimated from the modeling parameters and RISD effec-tively. The validation process confirmed that the equation can providegood approximation of MISD for the proposed hybrid structures.− Response surface methodology technique can be successfully applied todevelop the prediction equation. D-Optimal deterministic experimen-tal design technique was used for efficient sampling of design pointswithout requiring additional dynamic analyses.1286.1. Summary and conclusions− The developed equation can be used for post-seismic safety assessmentof hybrid structures without requiring the dynamic characteristics ofthe structure under consideration.− MISD and RISD can be estimated from the modeling parameters byusing ANN surrogate models.− The proposed optimum values of modeling variables will result inthe possible minimum RISD and MISD values under extreme seismicevents.− Adopting the proposed modeling parameters during the design processof the hybrid system will decrease the damages resulting from theearthquake events.In Chapter 4, an EVD model was developed and calibrated for the hy-brid structure under study. For this purpose, an analytical investigation wascarried out for 243 single-storey single-bay CLT infilled SMRFs by varyingthe modeling parameters that can affect the hysteretic behaviour of thesystem. The equivalent viscous damping and ductility of each model wereobtained from the hysteretic responses of semi-static cyclic analysis. Thenan expression was developed for equivalent viscous damping as a functionof ductility and various modeling parameters. Finally, an iterative non-linear time history analyses was conducted using 20 spectrum compatibleearthquake ground motions to calibrate EVD from Jacobsen′s area based ap-proach. The calibration process using NLTHA revealed that the Jacobsensarea based approach overestimates the EVD ratio. The calibrated EVD-ductility law was found to be dependent on the gap between the frame andCLT panel, bracket spacing and the post yield stiffness ratio of the hybridsystem. The following conclusions can be drawn based on the results of theresearch in Chapter 4− The coefficient C of damping ductility law of Equation 4.1 is expressedas function of modeling variables of CLT infilled steel moment frames.This law can be used for the direct displacement based design methodthat allows simultaneous calibration and design procedure [MGD13].1296.1. Summary and conclusions− In general, the hysteretic damping is found to be higher for the hybridsystem modeled with larger gap and bracket spacing. Hybrid systemswith smaller gap between CLT and steel with larger post yield stiffnessratio experienced a higher degree of pinching. This pinching effectcaused the systems to dissipate less amount of energy under cyclicloading.− The effect of panel strength and thickness on damping is found tobe minimal. This suggests that changing the thickness and crushingstrength of panels will not influence the hysteretic behaviour of thesystem.− Hybrid systems with larger post yielding stiffness ratio dissipate lessamount of energy which results in a lower value of hysteretic damping.− From the comparison graphs of Figure 4.16, it is concluded that fora given level of gap, post yield stiffness ratio, panel thickness andstrength, and bracket spacing, the hysteretic damping is increasedlinearly up to ductility (µ) value of 2.− The calibration process using NLTHA revealed that the Jacobsen′sarea based approach overestimates the EVD ratio. The calibratedEVD-ductility law was found to be dependent on the bracket spacingand the post yield stiffness ratio of the hybrid system.− The calibration process utilized NLTHA on SDOF hybrid systems andthe effective period is in the range of (0.7 to 3.38 sec). Consistent withother researchers by [WNS11, PCK07b] the developed EVD-ductilitylaws in this paper can be applied to the direct displacement baseddesign of MDOF of proposed hybrid structures.Finally in Chapter 5, a new iterative direct displacement based designmethod for CLT infilled SMRFs has been developed and tested by design-ing 3-, 6-, and 9- storey hybrid buildings. A robust finite element modelof the hybrid structure that accounts for CLT panel and frame interactionswas used for the validation process. Initial shear proportions between the1306.2. Future research perspectivespanels and frames were assigned at the start of the design process. Thesystem ductility and equivalent viscous damping are explicitly accounted.Design checks have been carried out on a the class of section, lateral bucklingstrength, and overall member strength. In summary, the developed methodeffectively controls seismic interstorey drifts and displacements. There wasgreater control of storey drifts and displacements for low rise hybrid build-ings. The following conclusions can be made based on the results of theresearch in Chapter 5:− A new iterative direct displacement based design method for CLTinfilled SMRFs has been successfully developed and tested by deigning3-, 6-, and 9- storey hybrid buildings.− The developed method proved to effectively control the seismic inter-storey drifts and displacements of CLT infilled SMRFs.− Better control of storey drifts and displacement were achieved for lowrise hybrid buildings. .− The developed method paves a path for designers to consider DDBDmethod as an alternative design approach for CLT infilled SMRFs.perfomr6.2 Future research perspectivesThe following list includes some aspects of the proposed DDBD pro-cedure that needs further study in order to increase its applicability androbustness.1. Validate EVD-ductility law of Chapter 4 by using full scale Experi-mental tests. Moreover, important properties such as diagonal CLTpanel crushing displacement and bracket behaviours in a combinedaxial and shear loads can be extracted from the tests.2. Incorporate residual storey drift values as an input for the design pro-cess. The RISD values that are obtained from NLTHA of Chapter 51316.2. Future research perspectivesare between 0.2 - 0.6 %. RISD responses more than 0.5 % representextensive damage to the buildings. Christopoulos [CPP04] indicatedan effective way of controlling RISD in the DDBD method.3. Extend the proposed method to include torsion due to irregularity inbuilding layout. Moreover, further investigation is needed to controlhigher mode effects.4. A more comprehensive performance evaluation of the designed build-ings can be done by using FEMA P695 [41] methodology.5. Extend the method to consider different CLT panel configurations.6. 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In 14th. world conferenceon earthquake engineering, 2008. → pages 38149Appendix150ASurrogate models of MISD and RISD usingArtificial Neural NetworkA.1 Designing the ANN networkThe design of network topology is carried out after obtaining data forobjective functions (MISD and RISD) from nonlinear time history analysis.From Figure 3.15, it is shown that the input layer consists of 6 membersand the output layer is comprised of 2 members. The design of topologyis then literally means determining the number of hidden layers, which wasobtained by trial and error approach. The selection of network topologywas based the regression coefficient (R) for the training and validation as atarget objective. The network design and analysis was carried out by usingNeural Network toolbox [DB93] in MATLAB numerical computing program[MAT13]. The Neural Network Toolbox was used to design, implement, testand validate the proposed network. Later, for optimization process, the code151A.2. Training the ANN networkfrom tool box was exported for further manipulation.A.2 Training the ANN networkThe training process is adjusting the weights for each of the iterationsin order to create the largest possible regression coefficient (R). For thisthesis, a Levenberg-Marquardt back propagation (trainlm) back propagation(trainbr) algorithm is used. A network topology of 6-9-9-1 for both RISDand MISD is obtained to be good by trial and error approach and is shownin Figure A.1. After implementing the proposed topology, the regressionoutputs are shown in Figure A.2 and A.3 for MISD and RISD, respectively.Figure A.1: MATLAB toolbox window for MLP training152A.2. Training the ANN network1 2 3 40.511.522.533.54TargetOutput ~= 0.81*Target + 0.29Training: R=0.89975 DataFitY = T1 2 30.511.522.533.5TargetOutput ~= 0.78*Target + 0.36Validation: R=0.86146 DataFitY = T1 2 3 40.511.522.533.54TargetOutput ~= 0.87*Target + 0.21Test: R=0.88686 DataFitY = T1 2 3 40.511.522.533.54TargetOutput ~= 0.81*Target + 0.29All: R=0.89138 DataFitY = TFigure A.2: Regression outputs for MISD153A.2. Training the ANN network0.5 1 1.50.20.40.60.811.21.41.61.8TargetOutput ~= 0.54*Target + 0.12Training: R=0.72573 DataFitY = T0.5 1 1.50.20.40.60.811.21.41.6TargetOutput ~= 0.47*Target + 0.14Validation: R=0.59398 DataFitY = T0.5 1 1.50.20.40.60.811.21.41.6TargetOutput ~= 0.37*Target + 0.16Test: R=0.49947 DataFitY = T0.5 1 1.50.20.40.60.811.21.41.61.8TargetOutput ~= 0.51*Target + 0.13All: R=0.67725 DataFitY = TFigure A.3: Regression outputs for RISDAs can be shown in Figures A.2 and A.3, the regression coefficient forthe RISD is smaller than MISD. This is due to the fact the RISD values ofthe system are highly nonlinear that makes it difficult to develop statisticalrelationship between inputs and outputs.154BApproximate method of structural analysisThe inflection point for the frame structures occurs at a point where thecurvature of the member changes its sign. Figure 5.10 shows the approxi-mate inflection point locations and deflected shape of the structure underdistributed horizontal shear forces. The internal columns of the structurecarry two times larger shear than the exterior columns. It should be notedat this point that the structure is considered as it is made from different sin-gle storey single bay elements as shown in Figure B.1 to support the aboveassumption.155Appendix B. Approximate method of structural analysisV 1 2Vs 2Vs 2Vs Figure B.1: Shear proportion between interior and exterior columnsIn each storey, based on the assumption it is possible to express theshears in either of the columns in terms of the other column. From thisassumption a total of 9 equations can be obtained.Column shearThe column shears are calculated by passing an imaginary horizontallines (a-a, b-b, and c-c) at the bottom of each storey as depicted in FigureB.2156Appendix B. Approximate method of structural analysis a a b b c c 26 8. 52 kN 10 9. 4 kN 198. 9 kN A B D C F E G I H P O N M L K J Figure B.2: Simplified steel moment frames with assumed hingesConsidering portion of frame above the imaginary cutting line, the freebody diagram that is shown in Figure B.3 is obtained. Based on the previousdiscussions, the shear carried by internal columns is taken as twice of theexterior columns. Equilibrium of forces in horizontal direction is used tocalculate shear force carried by each column as indicated in Figure B.3.157Appendix B. Approximate method of structural analysis ൌ 2 6 8 . 5 2 ൌെെെ ൌǤૠ ൌ 2 6 8 . 5 2 ૢૡǤ ૢൌെെെ ൌૠૠǤ ૢ ൌ 2 6 8 . 5 ૢૡǤ ૢૢǤൌെെെ ൌૢǤ 268.52 kN V 3 2 V 3 2 V 3 V 3 268.52 kN 198.9 kN V 2 2 V 2 2 V 2 V 2 268.52 kN 109.4 kN 198.9 kN V 1 2 V 1 2 V 1 V 1 Figure B.3: Column shearColumn moments, beam moments, and axial forcesThe moments in columns are obtained by applying moment equilibriumcondition at inflection points. For clarity, the detail analysis of the columnMI, beam MN and joint M will be discussed as shown in Figure B.4.158Appendix B. Approximate method of structural analysis26 8.5 2 kN Q MI M MN M NM Q MN M S1 S1 Q MI Q MI M M I M M I z Q MN Q MN M MN M MN Q MN Q MN z Figure B.4: Details of joint M, beam MN, and column MISince the shear on column MI is known it is advantageous to start theanalysis from the left top corner side of the frame. The column moment(MMI) of Figure B.4 is determined by applying equilibrium condition of∑Mz = 0 at the inflection point of the column. The column axial forces(QMN ) are found by applying equilibrium equation∑My = 0 at the inflec-tion point of the beam (MN). Using the same approach all the shear, axialand moment of beam and column have been quantified.159CDesign checksExterior beam in first storyIn this section, the exterior beam on the left side of the lower storeyis checked. The details of the beam are shown in Figure C.1. For ductiledesign of frames, the beam section should meet a width-thickness ratio ofclass 1 of CSA S16-09 [CSA09].The limiting requirement from CSA S16-09[CSA09] for flange and web are indicated below in Equations C.1 and C.2,respectively.160Appendix C. Design checks91. 7 247. 84 82. 61 82. 61 91. 7 247. 84 Figure C.1: Detail results of approximate method of analysisFlange =b2t<145√fy= 7.75 (C.1)Web =hw<1100√fy= 58.79 (C.2)where b, t, h, and w are flange width, flange thickness, web depth, and webthickness, respectively. The cross-sectional properties of the selected beamsection are given below. The calculated requirements and checks are given.A = 6670 mm2 d = 318 mmIx = 119 E6 mm4 b = 167 mmZx = 841 E3 mm3 t = 13.2 mmry = 39.2 mm w = 7.6 mmFlange =b2t= 6.32 (C.3)Web =hw=d− 2tw= 38.36 (C.4)As shown in Equations C.3 and C.4, the web and flange slendernessrequirements are with in the limit. Therefore the section used for the beamis Class 1. Moreover, the shear resistance of the beams is 495 kN. The beamsection considered here satisfies both shear and moment requirement.161Appendix C. Design checksOther beamsAs suggested by Pauley [PP] and Garcia [GSC10], beams of equal strengthare used for the entire height of the structure. This recommendation is basedon the idea of facilitating the construction time. However, this recommen-dation is not valid for buildings designed with non-uniform gravity loaddistrbution among floor levels [GSC10].Exterior column in first story before yielding due to seismicforcesThe first storey columns, as discussed in section 5.3 are allowed to yieldat their bottom. Due to this ductile behavior, according to CSA S16-09[CSA09] the section should be Class 1. The formation of the plastic hingesin the upper parts of the bottom storey columns is avoided by providing ap-propriate corrections for the inflection points. Therefore, the base columnsshould remain elastic up to the point of yielding to satisfy the requirementsagainst premature failures. Even though the columns are assumed to bebraced, design checks against overall member strength and (OMS) and lat-eral buckling strength (LTBS) are carried out. The verification against theclass of the section, OMS and LTBS are calculated as follows.96. 13 96. 13 184.56 171.77 171.77 123.04 Figure C.2: Details of exterior columnThe cross-sectional properties of the selected beam section are given be-162Appendix C. Design checkslow. The calculated requirements and checks are shown below.A = 5690 mm2 d = 318 mmIx = 99.2 E6 mm4 b = 166 mmZx = 708 E3 mm3 t = 11.2 mmry = 38.8 mm w = 6.6 mmFlange =b2t= 7.41 (C.5)Web =hw=d− 2tw= 44.78 (C.6)As shown in Equations C.5 and C.6, the web and flange slenderness re-quirements are with in the limit. Therefore, the section used for the exteriorcolumns is Class 1.Overall member strength (OMS)The overall member strength for columns that are under combined axialand bending loadings is checked using Equation C.7 of CSA S16-09[CSA09]section 13.8.2.OMS :CfCw+0.85U1xM1xMrx≤ 1 (C.7)where Cf and Crx are the applied axial load and factored axial compressiveresistance for column, respectively. In addition, Mf and Mrx are the appliedbending moment and factored moment resistance for column, respectively.Mrx is calculated without considering lateral torsional buckling. U1x is thefactor to account for the second order effect due to deformation of a mem-ber in its end and taken here as 1.0. The axial compressive resistance iscalculated using Equation C.8.Cr = φAfy(1 + λ2n)−12n (C.8)where φ is compression resistance factor and is given as 0.9. A is crosssectional area and n is a factor associated with residual stress patterns for163Appendix C. Design checksgroups of W shape sections. For cold formed non-stress relived sections nis 1.34. The non-dimensional slenderness parameter (λ) is calculated byEquation C.9.λ =KLr√Fypi2E(C.9)For the exterior column understudy, K (effective length factor), is takenas 1.0. Then the slenderness ratio KL/r in both direction x and y axis are24.4 and 82.47, respectively. The axial compressive resistance Crx and Cryare 1731.72 and 975.71 KN, respectively. Therefore, the OMS check is:CfCrx+0.85U1xM1xMrx=171.771731.72+0.85.1.123.04220= 0.57 < 1.0 (C.10)From the above calculation, it can be concluded that the exterior columnswill remain elastic prior to yielding.Lateral buckling strength (LTBS)The lateral buckling strength for columns that are under combined axialand bending loadings is checked using Equation C.11 of CSA S16-09 section13.8.2 [CSA09].LTBS :CfCry+0.85U1xM1xMrx≤ 1 (C.11)CfCry+0.85U1xM1xMrx=171.77975.1+0.85× 1× 123.04220= 0.65 < 1.0 (C.12)From the above calculation, it can be inferred that the exterior columnsare safe against lateral torsional buckling and will remain elastic prior toyielding.164Appendix C. Design checksCheck for axial bending and tensionCSA S16-09 [CSA09] requires the following design checks of Equation(C.13) for member under combined axial tension and bending. As can beinferred from Figure 5.11, the lower storey exterior column in the right sideis subjected to both axial tension and bending.TfTr+MfMr≤ 1.0 (C.13)where Tf and Tr are the axial applied load and resistance of the column.From the analysis, it is verified that the column can handle the uplift forcewith the applied bending moment. To shorten construction time, the samecross-sections of interior and exterior columns used throughout the heightof the building. Therefore, the design checks for the upper storeys columnsare omitted.165
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Lateral behaviour and direct displacement based design of a novel hybrid structure : cross laminated… Bezabeh, Matiyas 2014
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Title | Lateral behaviour and direct displacement based design of a novel hybrid structure : cross laminated timber infilled steel moment resisting frames |
Creator |
Bezabeh, Matiyas |
Publisher | University of British Columbia |
Date Issued | 2014 |
Description | Recently, an innovative hybrid structure has been developed as an alternative lateral-load resisting system at The University of British Columbia. The hybrid structure incorporates Cross Laminated Timber (CLT) shear panels as an infill in steel moment resisting frames (SMRFs). In order to increase the applicability of the proposed system, in this thesis, a direct displacement based design methodology has been developed and analytically validated. Initially, a nonlinear time history analysis (NLTHA) was carried out to study the lateral behaviour of the proposed hybrid structure. For this purpose, a total of 162 different hybrid buildings were modeled and analyzed in OpenSees by using twenty earthquake ground motions (2% probability exceedance in 50 years). Post-earthquake performance indicators (Maximum Interstory Drift (MISD) and Residual Interstory Drift (RISD)) were obtained from the analyses. To assist the post-seismic safety assessment of the hybrid buildings, surrogate models for MISD and RISD were developed using Response Surface Methodology and Artificial Neural Network (ANN). By using the ANN surrogate models as fitness functions for the Genetic Algorithm, optimal modeling parameters of the hybrid system were obtained. Secondly, to represent the energy dissipative capacity of the hybrid system, an equivalent viscous damping (EVD) equation was developed. To formulate the EVD equation, 243 single-storey single-bay CLT infilled SMRF models were developed and subjected to monotonic static and semi-static cyclic analysis. The EVD of each model was calculated from the hysteretic responses based on Jacobsen's area based approach and later calibrated using NLTHA. Finally, an iterative direct displacement based design method was developed for the proposed hybrid structure. A detailed description of the proposed methodology is presented with a numerical example. In order to verify the proposed method, hybrid buildings with 3-, 6-, and 9- storey heights were designed. A calibrated EVD-ductility relationship was used to obtain the energy dissipation of the equivalent SDOF system for all case study buildings. Nonlinear time history analysis using twenty ground motion records was used to validate the performance of the proposed design methodology. The results indicate that the proposed design method effectively controls the displacements resulting from the seismic excitation of the hybrid structure. |
Genre |
Thesis/Dissertation |
Type |
Text |
Language | eng |
Date Available | 2014-08-26 |
Provider | Vancouver : University of British Columbia Library |
Rights | Attribution-NonCommercial-NoDerivs 2.5 Canada |
DOI | 10.14288/1.0074372 |
URI | http://hdl.handle.net/2429/50200 |
Degree |
Master of Applied Science - MASc |
Program |
Civil Engineering |
Affiliation |
Applied Science, Faculty of Engineering, School of (Okanagan) |
Degree Grantor | University of British Columbia |
GraduationDate | 2014-09 |
Campus |
UBCO |
Scholarly Level | Graduate |
Rights URI | http://creativecommons.org/licenses/by-nc-nd/2.5/ca/ |
AggregatedSourceRepository | DSpace |
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