Applied Science, Faculty of
Engineering, School of (Okanagan)
DSpace
UBCO
Odikamnoro, Ikenna H.
Master of Applied Science - MASc
University of British Columbia
This thesis focuses on the exploration of a now-popular performance-based design approach - Direct Displacement-Based Design (DDBD), its application in the de- sign of new structural archetypes, non-linear static and dynamic analysis of these structures, and their seismic risk assessment. First, this study sought to validate a modified direct displacement-based design procedure for post-tensioned timber structures fitted with dissipative bracing systems, after which an Opensees numerical model to simulate the behaviour of the designed frame was validated by calibrating the hysteretic behaviours of the numerical models with results from an experimental model which was tested during the development of this modified direct displacement-based design procedure. After the validation of this modified direct displacement-based design procedure and the Opensees numerical model, the concepts were extended to a 6-storey post-tensioned mass timber building fitted with dissipative bracing systems. A numerical model for this 6-storey structure was created in Opensees and subjected to static and dynamic non-linear analysis using 60 bi-directional spectral compatible ground-motion records from PEER and KiK-net databases to test the accuracy of this new direct displacement-based design procedure. The results affirm the accuracy of this modified direct displacement-based design procedure for post-tensioned mass timber structural systems fitted with dissipative bracing. Next, this thesis focuses on the Opensees numerical modeling, static and dynamic non-linear analysis, and seismic-risk assessment of a hybrid reinforced concrete cross-laminated-timber structure (RC-CLT) which has already been designed using direct displacement-based design procedure. The non-linear dynamic analysis was carried out using a set of 40 hazard-consistent ground motion pairs selected from PEER and KiK-net databases, and reflect the recently developed 6th generation seismic hazard model of Canada (SHM6). The results show the accu- racy of direct-displacement-based design in predicting the behaviour of structures when exposed to target harzard levels and also showed improved performance of the hybrid structure due to the addition of CLT and dissipators.
DIRECT DISPLACEMENT-BASED DESIGN ANDSEISMIC PERFORMANCE ASSESSMENT OF NOVELHYBRID MOMENT-RESISTING FRAMESTRUCTURES FITTED WITH VARIOUSHYSTERETIC DAMPING DEVICESbyIkenna H. OdikamnoroB.Sc., The University of Nigeria, Nsukka (UNN), 2019A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE COLLEGE OF GRADUATE STUDIES(Civil Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Okanagan)May 2023© Ikenna H. Odikamnoro, 2023The following individuals certify that they have read, and recommend to the Col-lege of Graduate Studies for acceptance, the thesis entitled:DIRECT DISPLACEMENT-BASED DESIGN AND SEISMIC PERFOR-MANCE ASSESSMENT OF NOVEL HYBRID MOMENT-RESIST-ING FRAME STRUCTURES FITTED WITH VARIOUS HYSTERETICDAMPING DEVICESsubmitted by Ikenna H. Odikamnoro in partial fulfillment of the requirements forthe degree of Master of Applied ScienceExamining Committee:Solomon Tesfamariam, School of EngineeringSupervisorSiddiqua Sumi, School of EngineeringSupervisory Committee MemberHenry Burton, The University of California, Los AngelesSupervisory Committee MemberiiAbstractThis thesis focuses on the exploration of a now-popular performance-based designapproach - Direct Displacement-Based Design (DDBD), its application in the de-sign of new structural archetypes, non-linear static and dynamic analysis of thesestructures, and their seismic risk assessment.First, this study sought to validate a modified direct displacement-based de-sign procedure for post-tensioned timber structures fitted with dissipative bracingsystems, after which an Opensees numerical model to simulate the behaviour ofthe designed frame was validated by calibrating the hysteretic behaviours of thenumerical models with results from an experimental model which was tested dur-ing the development of this modified direct displacement-based design procedure.After the validation of this modified direct displacement-based design procedureand the Opensees numerical model, the concepts were extended to a 6-storey post-tensioned mass timber building fitted with dissipative bracing systems. A numer-ical model for this 6-storey structure was created in Opensees and subjected tostatic and dynamic non-linear analysis using 60 bi-directional spectral compati-ble ground-motion records from PEER and KiK-net databases to test the accuracyof this new direct displacement-based design procedure. The results affirm theaccuracy of this modified direct displacement-based design procedure for post-tensioned mass timber structural systems fitted with dissipative bracing.Next, this thesis focuses on the Opensees numerical modeling, static and dy-namic non-linear analysis, and seismic-risk assessment of a hybrid reinforced-concrete cross-laminated-timber structure (RC-CLT) which has already been de-signed using direct displacement-based design procedure. The non-linear dynamicanalysis was carried out using a set of 40 hazard-consistent ground motion pairsiiiselected from PEER and KiK-net databases, and reflect the recently developed 6thgeneration seismic hazard model of Canada (SHM6). The results show the accu-racy of direct-displacement-based design in predicting the behaviour of structureswhen exposed to target harzard levels and also showed improved performance ofthe hybrid structure due to the addition of CLT and dissipators.ivLay SummaryTimber-based structural systems are fast becoming popular and necessary to aid therace to sustainability. But The knowledge of the design and construction of build-ings with timber-based products is limited and hence is still subject to research anddevelopment. In this thesis, a relatively new design framework is used to designtimber-based structural systems, and the performance of these buildings is checkedusing simulations. The results show that these structural systems are resilient andperform satisfactorily under seismic forces. Moreso, this design framework cor-rectly predicts the behaviour of the buildings. This makes for a more accuratedesign of resilient infrastructure.vPrefaceThis thesis work is based on the research work conducted in the School of Engi-neering at the University of British Columbia Okanagan Campus under the super-vision of Dr. Solomon Tesfamariam. Chapter 4 is a collaborative effort of Pro-fessor Solomon Tesfamariam, Dr. Prakash Badal Singh, Professor Henry Burton,and Ikenna Harold Odikamnoro, and is a publication in the journal of Infrastructurepreservation and resilience. All other literature reviews, mathematical calculations,and simulations for other chapters of the thesis are carried out by the author. A listof publications at the University of British Columbia is listed as follows.Journal Papers• Odikamnoro, I., Badal, P. S., Burton, H., Tesfamariam, S. (2022). Seismiccollapse risk of RC-timber hybrid building with different energy dissipa-tion connections considering NBCC 2020 hazard. Journal of InfrastructurePreservation and Resilience, 3(1), 14. I carried out the modeling, analysis,and writing of the original draft, Dr. Prakash Badal Singh carried out con-ceptualization, methodology, modeling, formal analysis, writing, and review,Professor Henry Burton carried out Conceptualization, methodology, review,and editing, while Professor Solomon Tesfamariam carried out conceptual-ization, methodology, review, editing, supervision and funding acquisition.viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiList of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Aims and Objectives . . . . . . . . . . . . . . . . . . . . . . . . 21.4 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4vii2.1 Seismic Design of Structures . . . . . . . . . . . . . . . . . . . . 42.2 Limit States for seismic design . . . . . . . . . . . . . . . . . . . 42.3 Force-Based Design . . . . . . . . . . . . . . . . . . . . . . . . . 52.4 Direct Displacement Based Design . . . . . . . . . . . . . . . . . 62.5 Major Differences Between FBD and DDBD . . . . . . . . . . . 102.6 Bibliometric Study DDBD . . . . . . . . . . . . . . . . . . . . . 112.7 Equivalent Viscous Damping (EVD) . . . . . . . . . . . . . . . . 162.8 Section Analysis of Jointed Ductile Connection using MMBA pro-cedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.8.1 Find Decompression Moment, Mdec . . . . . . . . . . . . 222.8.2 Impose a rotation, θimp . . . . . . . . . . . . . . . . . . . 232.8.3 Assume a neutral axis depth c . . . . . . . . . . . . . . . 242.8.4 Determine the force in the unbonded post-tension elements 252.8.5 Evaluate the force in the non-post-tensioned reinforcing el-ements (Ts and Cs) . . . . . . . . . . . . . . . . . . . . . 252.8.6 Evaluate the force in the timber at the beam-column inter-face (Ct) 262.8.7 Check for equilibrium . . . . . . . . . . . . . . . . . . . 272.8.8 Obtain the moment for the given connection rotation inves-tigated above . . . . . . . . . . . . . . . . . . . . . . . . 273 DDBD Verification and Numerical Model Validation of Post-tensionedTimber Frame with Dissipative Bracing System . . . . . . . . . . . 293.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.2 DDBD Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . 313.3 Details of Experimental Model . . . . . . . . . . . . . . . . . . . 363.4 DDBD Verification . . . . . . . . . . . . . . . . . . . . . . . . . 363.5 Numerical Modelling of Post-tensioned Timber Buildings with Dis-sipative Bracing System Using OpenSees . . . . . . . . . . . . . 373.6 Verification Through Non-linear Time History Analysis . . . . . . 373.6.1 Numerical Validation of UHP dampers . . . . . . . . . . 383.6.2 Numerical Validation of Post-tensioned Beam-Column Joint 38viii3.6.3 Validation of Hysteretic Behaviour of Column-FoundationConnection . . . . . . . . . . . . . . . . . . . . . . . . . 383.6.4 Beams, Columns and Braces . . . . . . . . . . . . . . . . 393.7 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 404 Direct Displacement Based Design of Self-Centering Moment Resist-ing Mass Timber frame Building Fitted With Dissipative BracingSystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.1.1 Modified DDBD Procedure . . . . . . . . . . . . . . . . 434.1.2 Frame Description . . . . . . . . . . . . . . . . . . . . . 444.2 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.2.1 Equivalent SDOF system . . . . . . . . . . . . . . . . . . 444.2.2 Bare Frame and Hysteretic Bracing Contributions . . . . . 454.2.3 Beam, Column and Brace Design . . . . . . . . . . . . . 464.2.4 Design of Dissipative Bracing System . . . . . . . . . . . 644.2.5 Design of Post-tensioning . . . . . . . . . . . . . . . . . 644.3 Non-linear Structural Modelling of the 6-storey Mass Timber Frame 664.3.1 Modelling of Structural Frame Elements . . . . . . . . . . 674.3.2 Foundation Modelling . . . . . . . . . . . . . . . . . . . 684.3.3 Modelling of Dissipative Bracing System . . . . . . . . . 684.3.4 Modelling of Post-tensioned Beam Column Joint . . . . . 684.4 Seismic hazard and GM selection per NBCC 2020 . . . . . . . . . 694.4.1 Seismic hazard . . . . . . . . . . . . . . . . . . . . . . . 694.4.2 Hazard-consistent ground motion selection . . . . . . . . 704.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724.5.1 Pushover analysis . . . . . . . . . . . . . . . . . . . . . . 724.5.2 Maximum and Residual Inter-storey Drift Ratios . . . . . 734.5.3 Incremental Dynamic Analysis . . . . . . . . . . . . . . . 744.5.4 FRAGILITY . . . . . . . . . . . . . . . . . . . . . . . . 764.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 76ix5 Seismic collapse risk of RC-timber hybrid building with differentenergy dissipation connections considering NBCC 2020 hazard . . . 785.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785.2 Design details of the RC-CLT hybrid building with steel slit dampers 815.3 Nonlinear structural modeling of the RC-CLT hybrid building . . 835.3.1 CLT modeling . . . . . . . . . . . . . . . . . . . . . . . 845.3.2 RC frame modeling . . . . . . . . . . . . . . . . . . . . . 855.3.3 RC-CLT-Damper modeling . . . . . . . . . . . . . . . . . 865.4 Seismic hazard and GM selection per NBCC 2020 . . . . . . . . . 875.4.1 Seismic hazard . . . . . . . . . . . . . . . . . . . . . . . 875.4.2 Hazard-consistent ground motion selection . . . . . . . . 885.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 915.5.1 Pushover analysis . . . . . . . . . . . . . . . . . . . . . . 915.5.2 Incremental Dynamic Analysis . . . . . . . . . . . . . . . 915.5.3 Fragility assessment . . . . . . . . . . . . . . . . . . . . 925.5.4 Residual deformation . . . . . . . . . . . . . . . . . . . . 945.5.5 Collapse risk assessment . . . . . . . . . . . . . . . . . . 945.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 956 Conclusions and Recommendations for Future Research . . . . . . 986.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 986.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 996.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 996.4 Recommendations for future research . . . . . . . . . . . . . . . 100Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101xList of TablesTable 2.1 Limit states for maximum inter-storey drift ratios . . . . . . . . 5Table 2.2 Equivalent viscous damping expressions for different structuralsystems and hysteresis types . . . . . . . . . . . . . . . . . . . 18Table 2.3 Equivalent viscous damping expressions for different structuralsystems and hysteresis types . . . . . . . . . . . . . . . . . . . 19Table 2.4 Equivalent viscous damping expressions for different structuralsystems and hysteresis types . . . . . . . . . . . . . . . . . . . 20Table 3.1 Summary of the equivalent SDOF system . . . . . . . . . . . . 36Table 3.2 Characteristics of the braced post-tensioned frame . . . . . . . 37Table 4.1 Summary of the equivalent SDOF system . . . . . . . . . . . . 45Table 4.2 Characteristics of the braced post-tensioned frame . . . . . . . 46Table 4.3 Maximum design loads in Glulam Beams of BRBF (all floors) 48Table 4.4 Maximum design loads in Gravity Glulam Columns (Floor no.1 to 12) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50Table 4.5 Maximum design loads in Glulam Beams of BRBF (all floors) 54Table 4.6 Maximum design loads in Gravity Glulam Columns (Floor no.1 to 12) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56Table 4.7 Maximum design loads in Gravity Glulam Columns (Floor no.1 to 12) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60Table 4.8 Column, beam and brace design summary . . . . . . . . . . . 64Table 4.9 Moment demand at beam-column joints . . . . . . . . . . . . 66xiTable 4.10 Spectral value and deaggregation tuples for contributing tec-tonic regime for Vancouver site and Sa(3.0 s) corresponding toa return period of 2475 years. . . . . . . . . . . . . . . . . . . 71Table 5.1 Design summary for 6-story RC-CLT hybrid building. . . . . . 83Table 5.2 Spectral value and deaggregation tuples for contributing tec-tonic regime for Vancouver site and Sa(1.17 s) correspondingto a return period of 2475 years. . . . . . . . . . . . . . . . . . 89Table 5.3 Collapse fragility parameters and associated seismic risk for theRC-CLT hybrid building with different energy dissipators . . . 95xiiList of FiguresFigure 2.1 Fundamentals of Direct Displacement-Based Design (DDBD).Adapted from [99] . . . . . . . . . . . . . . . . . . . . . . . 7Figure 2.2 Schematic Representation of Direct Displacement-Based De-sign (DDBD) Procedure. . . . . . . . . . . . . . . . . . . . . 10Figure 2.3 Bibiometric study of direct displacement-based design . . . . 16Figure 2.4 Rotation contributions to a post-tensioned timber beam-columnjoint. Adapted from [107] . . . . . . . . . . . . . . . . . . . 22Figure 2.5 MMBA nomenclature for a beam-column joint. Adapted from[107] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Figure 2.6 Analytical model verification for MMBA procedure. Adaptedfrom [107] . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Figure 3.1 Schematic of 3-storey single bay post-tensioned timber framefitted with dissipative bracing system. Adapted from [36] . . . 30Figure 3.2 DDBD procedure: (1) Displaced shape, (2) Idealized Hys-teretic Response, (3) EVD and Damped displacement responsespectra, (4) Equivalent contributions of bare-frame and dissi-pative bracing system, and (5) Design of members. . . . . . . 31Figure 3.3 Fundamentals of Post-tensioned frame structure with dissipa-tive bracing system. Adapted from [96] . . . . . . . . . . . . 32Figure 3.4 DDBD procedure. Adapted from [96] . . . . . . . . . . . . . 35Figure 3.5 Target response spectra according to Italian seismic code and7 spectra compatible ground motion records. Adapted from [96] 38xiiiFigure 3.6 (a) Hysteretic behaviour of dissipators from OpenSees numer-ical model when subjected to ground motion, and (b) Compar-ison of hysteretic curves for dissipator behaviour from experi-mental tests and OpenSees model. Adapted from [94] . . . . . 39Figure 3.7 (a) Hysteretic behaviour of post-tensioned beam-column jointfrom OpenSees numerical model when subjected to groundmotion, and (b) Comparison of hysteretic curves for post-tensionedbeam-column joint behaviour from experimental tests, OpenSees,and SAP2000 Numerical Models. Adapted from [35] . . . . . 40Figure 3.8 (a) Hysteretic behaviour of column-foundation connection fromOpenSees numerical model when subjected to ground motion,and (b) Comparison of hysteretic curves for column-foundationconnection behaviour from experimental tests, OpenSees, andSAP2000 Numerical Models. Adapted from [37] . . . . . . . 41Figure 3.9 Depiction of elastic behaviour of beam, column and brace ele-ments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Figure 4.1 DDBD procedure: (1) Displaced shape (2) Idealizaed Hys-teretic Response (3) EVD and Damped displacement responsespectra (4) Equivalent contributions of bare-frame and dissipa-tive bracing system (5) Design of members. . . . . . . . . . . 43Figure 4.2 Schematic representation of Post-tensioned timber frame build-ing fitted with dissipative bracing system. Adapted from [107] 44Figure 4.3 Acceleration and displacement response spectra . . . . . . . . 46Figure 4.4 Hysteretic behaviour of analytical and nonlinear OpenSees nu-merical model for internal and external beam-column joints ofthe mass timber moment resisting frame fitted with dissipativebracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65Figure 4.5 Schematic sub-assembly of the nonlinear structural model forthe mass timber moment resisting frame fitted with dissipativebracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67xivFigure 4.6 PSHA results based on the NBCC 2020 seismic hazard model(a) Seismic hazard curve and (b) deaggregation based on Sa(3.0s)for the Vancouver site . . . . . . . . . . . . . . . . . . . . . . 69Figure 4.7 Scaled selected records targeted at the hazard and deaggrega-tion corresponding to the Vancouver site. (a) Pseudo-responsespectra of individual records. Thick broken lines mark the97.5%ile and 2.5%ile values, (b) target conditional mean forthe three tectonic regimes and (c) target log-standard deviationfor the conditional spectra. The conditioning period is 3.0 s. . 71Figure 4.8 (a) Static pushover curve for post-tensioned timber frame fittedwith dissipative bracing system (b) Cyclic pushover curve forpost-tensioned timber frame with dissipative bracing system . 72Figure 4.9 (a) Maximum ISDR (b) Residual ISDR . . . . . . . . . . . . 74Figure 4.10 (a) IDA for A 6-storey post-tensioned mass timber frame fittedwith dissipative bracing system. (b) Fragility curve for the 6storey post-tensioned mass timber frame fitted with dissipativebracing system . . . . . . . . . . . . . . . . . . . . . . . . . 75Figure 5.1 DDBD procedure: (a) Structure description, (b) EquivalentSDOF system and its displaced shape, (c) Bi-linear force-displacementrelationship of the SDOF system, (d) EVD-µ relationship forthe different structural types, (e) Displacement response spec-tra, and (f) Distribution of the seismic design load along thebuilding height. . . . . . . . . . . . . . . . . . . . . . . . . . 82Figure 5.2 Details of the six-story RC-CLT hybrid building [118]. . . . . 83Figure 5.3 Schematic sub-assembly of the nonlinear structural model forRC-CLT hybrid building system. . . . . . . . . . . . . . . . . 84Figure 5.4 Cyclic responses of the (a) steel slit damper and (b, c) flag-shaped dampers with (b) βF = 0.8 and (c) βF = 0.6 obtainedusing OpenSees. For steel slit dampers, the comparison of ex-perimental hysteretic response is also presented. . . . . . . . . 85xvFigure 5.5 Cyclic responses of the (a) steel slit damper and (b, c) flag-shaped dampers with (b) βF = 0.8 and (c) βF = 0.6 obtainedusing OpenSees. For steel slit dampers, the comparison of ex-perimental hysteretic response is also presented. . . . . . . . . 87Figure 5.6 (a) Change in seismic hazard from NBCC 2015 to NBCC 2020for selected locations in Canada, from east to west. Inten-sity measure- Sa(0.2); Return Period- 2475 year; Site Class- C(Vs30 = 450 m/s). (b) Response spectrum for Vancouver basedon the NBCC 2015 and NBCC 2020 seismic hazard models. . 88Figure 5.7 PSHA results based on the NBCC 2020 seismic hazard model.(a) Seismic hazard curve and (b) deaggregation based on Sa(1.17 s)for the Vancouver site. . . . . . . . . . . . . . . . . . . . . . 88Figure 5.8 Scaled selected records targeted at the hazard and deaggrega-tion corresponding to the Vancouver site. (a) Pseudo responsespectra of individual records. Thick broken lines mark the97.5%ile and 2.5%ile values, (b) target conditional mean forthe three tectonic regimes and (c) target log-standard deviationfor the conditional spectra. The conditioning period is 1.17 s. 90Figure 5.9 Pushover curves for the (a) 6-story bare RC frame, (b) RC-CLT hybrid building with steel slit dampers, and (c) RC-CLThybrid building with flag-shaped dissipators . . . . . . . . . . 92Figure 5.10 IDA curves for the 6-story RC-CLT hybrid building with (a)steel slit dampers, and (b, c) flag-shaped dissipators having (b)βF = 0.8, and (c) βF = 0.6 obtained using 40 pairs of NBCC2020-compliant site-specific ground motion records. IDRmaxrepresents the maximum interstory drift ratio. . . . . . . . . . 93Figure 5.11 Collapse fragility curves for the 6-story RC-CLT hybrid build-ing with (a) steel slit dampers, and (b, c) flag-shaped dissipa-tors having (b) βF = 0.8, and (c) βF = 0.6 . . . . . . . . . . . 93Figure 5.12 Maximum interstory drift ratio (IDRmax) versus the residualinterstory drift ratio (IDRres) for the RC-CLT hybrid buildingwith different energy dissipators. The broken line representsthe 45◦ case for equal maximum and residual values. . . . . . 94xviList of AbbreviationsCLT Cross-Laminated TimberCMS Conditional Mean SpectrumCS Conditional SpectrumDDBD Direct Displacement-Based DesignEVD Equivalent Viscous DampingIDA Incremental Dynamic AnalysisIDR Inter-Story Drift RatioIM Intensity measureMMBA Modified Monolithic Beam AnalogyNBCC National Building Code of CanadaPSHA Probabilistic Seismic Hazard AnalysisRC Reinforced ConcreteSHM6 6th Generation Seismic Hazard ModelUFP U-shaped Flexural PlatexviiList of SymbolsAb Area of the beamAc Area of the columnApt Area of post-tensioningAscr Area of column face screw reinforcingAt Total area in compressionB Width of framebb Beam section widthbL Length of the loaded areac position of neutral axisCt Timber compressive forceEpt Post-tensioning modulus of elasticityEt,para Timber parallel-to-grain Modulus of ElasticityEt,perp Timber perpendicular-to-grain Modulus of ElasticityF ForceFDB Force in dissipative bracing systemFi Force on storey iFS,u Ultimate force in equivalent bare frameFS,y Yield force of bare post-tensioned frameFu Ultimate forceGt Shear modulus of timberxviiiH Height of frameHb Height of beamHe Effective heighthb Beam section depthhc Column section depthhi height of the ith storeyHn Total building heighth1 Height of the first storeyIb Beam modulus of inertiaIc Column modulus of inertiaKe Effective stiffnesskgap Modulus of elasticity modification factorkint Interface compression rotation factorKs Stiffness of bare post-tensioned framekscr Modification factor for screw reinforcementkss Modification factor for stress spreadingKS,0 Initial elastici stiffness of bare post-tensioned frameK0 Initial elastic stiffness of frameLb Beam lengthLcant Distance from the interface to the point point of contraflexurels Total length of screwlub Un-bonded length of the post-tensioningMcl Moment at the column center of a beam-column joint connectionMdec Decompression momentMpt Moment due to post-tensioning forceMt Total moment capacity of systemme Effective massmi Mass of storey ixixngap Number of gap openingsr post-yield stiffness ratioSa(Te) Spectral acceleration corresponding to effective periodSd(Te) Spectral displacement corresponding to effective periodSTOT Total elastic displacement of frameTe Effective periodTpt Post-tensioning forceTpt,initial Initial Post-tensioning forceTs Tension force of the mild steel dissipative reinforcementTs Compression force in the mild steel dissipative reinforcementVbase Base shearypt Edge distance to the post-tensioning reinforcement levelys,c Edge distance to the compression reinforcement levelys,t Edge distance to the tension reinforcement levelαs,cl Shear coefficient to convert average shear to centroidal shearβ Recentering ratio∆S,y Yield displacement of bare post-tensioned frame∆S,i Interstorey displacement for equivalent bare frame∆s Elongation of dissipative reinforcing∆DB,y Yield displacement of dissipative bracing system∆d Design displacement∆i Displacement of storey i∆y Yield displacement∆pt Elongation of the post-tensioning∆Tpt Change in post-tensioning force∆εpt Strain increase in post-tensioningxxεeq,v Viscous dampingεeq,h,v Equivalent hysteretic dampingεt Strain in timberεy Yield strain of the materialη Scaling factor for displacement response spectraλ Slenderness ratioµ DuctilityµDB Ductility of dissipative bracing systemθy Yield driftθd Code drift limit for the limit state consideredθimp Imposed rotationθint Interface compression rotationθcl Centre line rotationθc Column rotationθb Beam rotationθ jp Joint panel rotationθcon Connection rotationθgap Gap rotationξeq Equivalent Viscous dampingξ0 Initial elastic dampingξe Damping due to elastic responseξhyst Damping due to inelastic responseφdec Decompression curvatureω˙θ Reduction factor that accounts for the higher mode amplification of driftxxiAcknowledgmentsI want to express my gratitude to the UBC faculty and staff for their continuedassistance, guidance, and direction. Special thanks goes to my supervisor Pro-fessor Solomon Tesfamariam for firstly, trusting my potential for research output,offering me a position in his research group, and providing invaluable mentorship,guidance, and feedback without which this master’s thesis could not have become asuccess. I also need to thank my supervisory committee members, Professor HenryBurton, and Dr. Sumi Siddiqua for their valuable feedback. In extension, I wouldlike to thank other research students under my supervisor - Biniam Teweldebrhan,Yishak Sewasew, Han TongChen, Sourav Das, Haile Woldesellasse, Edel Martinez,Konstantinos Skandalos, and Madihe Kh -, and his post-doc Dr. Prakash BadalSingh for continuous morale support, feedback, technical assistance, and guidanceevery step of the journey. I want to thank my family, siblings, and close friendsfor being there for me in times of need. Finally, I want to appreciate the fundingfrom British Columbia Forestry Innovation Investment’s (FII) Wood First Programand Natural Science and Engineering Research Council of Canada (Grant/AwardNumber: RGPIN 2019-05013), without which this this thesis could have been quitechallenging if not impossible.xxiiDedicationThis thesis is dedicated to all researchers who strive to add value to already exist-ing body of knowledge.xxiiiChapter 1IntroductionIf I have seen farther it is by standing on the shoulders of Giants.— Sir Isaac Newton (1855)1.1 BackgroundEarthquakes are a natural phenomenon, and while it may be impossible to datethe very first earthquake, documented records of earthquake occurrences date asfar back as 1831 BC. Older buildings were designed to carry self and imposedloads, but, in seismic-prone areas, this design is largely insufficient to protect abuilding from collapse in the event of an earthquake. This birthed the seismicdesign of buildings which attempts to fortify a building against lateral loads causedby earthquake ground motions. The study of earthquakes was all but impossibledue to the fact that earthquakes lasted only a few seconds to a couple of minutes[3], so it was a great challenge to study them in real-time. Only recently, thanks toadvancements in technology, did the study of earthquakes and seismology becomeachievable. And in the 1970s, seismic hazard studies were birthed [3] to helpmankind understand and prepare adequately against earthquake occurrences.The El Centro earthquake in 1940 was among the first major earthquakes to berecorded by a strong-motion seismograph [52], and that record in particular, alongwith other records that have become available over the years, has been extensivelyused by the research community for the design, analysis, and even the seismic risk1assessment of conceptual and existing structures.Concrete, and eventually steel over the past couple of decades have been thematerials of choice for the construction of civil engineering structures. But re-cently, timber has become an increasingly promising material for construction inthe civil engineering space. With the focus shifting to environmentally friendlyand lightweight construction, it is easy to see why timber is fast becoming a choicematerial. Not without its limitations, one of the benefits of using timber for con-struction in seismic zones is its light weight which will attract a lesser amount ofseismic force when compared to concrete or steel structures of the same size andcomplexity. One of the major setbacks of the use of timber is its meager energy-dissipating capabilities. To combat this, timber frames are usually fitted with steeljoints to aid energy dissipation.This thesis presents 2 different 6-story moment resisting frame structures - con-crete and timber - fitted with CLT and braces respectively, and different kinds ofdissipators to aid energy dissipation. Seismic risk assessment is carried out for thehybrid RC-CLT structural system, while the seismic performance of the moment-resisting mass timber frame fitted with dissipative bracing is evaluated.1.2 Problem StatementWhile sustainable structural systems are the new trend, there are limitations to par-ticipation by industry professionals. This is partly because these new structuralsystems have unknown force reduction factors (R0 and Rd) without which theirdesign using the already popular force-based design methodology becomes impos-sible. The alternative is to use performance-based design methodologies.1.3 Aims and ObjectivesThe aims and objectives of this thesis are outlined below:1. Replicate the Direct Displacement-based design of experimental model car-ried out by Ponzo et al [96]2. Validate the numerical model for the above-stated experimental model23. Carry out a seismic risk assessment of RC-CLT hybrid building fitted withdifferent energy dissipation connections4. Carry out Direct Displacement-based design of post-tensioned mass timberbuilding with dissipative bracing system5. Validate the DDBD design of the above-stated frame through non-linearstatic and dynamic analysis1.4 Thesis OverviewThis thesis is organized into 6 chapters:Chapter 2 provides a thorough literature review on direct displacement-baseddesign, equivalent viscous damping, and modified monolithic beam analogy (MMBA)which is used in the analytical modelling of post-tensioned timber joints.Chapter 3 contains the replication of the direct displacement-based design pro-cedure carried out by Ponzo et al [96], the numerical modelling of the experimentalmodel discussed by ponzo et al [96], and validation of the design and numericalmodel through non-linear dynamic analysis.Chapter 4 contains the seismic risk assessment of a hybrid RC-CLT framestructure fitted with dissipators at the CLT-beam connection which was designedusing direct displacement-based design by [76].Chapter 5 contains the direct displacement-based design, numerical modelling,and non-linear dynamic analysis of a post-tensioned timber frame fitted with dis-sipative bracing system. It also contains the design of the post-tensioned beam-column joint using the MMBA procedure.3Chapter 2Literature ReviewIf I have seen farther it is by standing on the shoulders of Giants.— Sir Isaac Newton (1855)2.1 Seismic Design of StructuresAlthough early seismic design was crude and was largely inaccurate, it has evolvedover the years and has gotten more refined. Before performance-based design tookthe center stage, force-based design has been in use for decades. In the 1980s, itwas observed that structures with larger masses had greater response to seismicexcitation [82]. Hence, emphasis shifted from strength to ductility, as it had beenthe case to focus on strength in the past.While force-based design is by no means inefficient, it does have some flawswhich are addressed by performance-based design methodologies, and in particu-lar, direct-displacement-based design.2.2 Limit States for seismic designDirect displacement-based design lends itself to design based on the desired per-formance target. This performance target can be in terms of drift, displacement etc.Limit states (Damage states) based on the inter-storey drift ratios are enumeratedin table 2.14Table 2.1: Limit states for maximum inter-storey drift ratiosDamageStateDescription Maximum inter-storey drift ratio(MaxISDR) (%)ImmediateOccupancy(IO)No structural realignment is required for structuralstability, but non-structural and mechanical com-ponents that are sensitive to building alignmentsmay need adjusting and maintenance. (e.g., ele-vator rails, curtain walls, and doors).0.4Life Safety(LS)To regain the margin of safety for lateral stabil-ity, major structural realignment is necessary; how-ever, the necessary realignment and restoration ofthe structure may not be economically and prac-tically viable. (i.e., the structure might be a totaleconomic loss).2.5CollapsePrevention(CP)Due to large residual drift, the building is at dan-ger of collapsing from earthquake aftershocks. (Itshould be noted that this performance point mightbe close/similar to collapse but with more uncer-tainty.).4.52.3 Force-Based DesignForce-based design generally follows the procedure of base shear calculation usinginitial elastic stiffness and acceleration response spectrum [42]. The obtained baseshear is then distributed to upper stories using the equivalent lateral force procedurewhich entails the distribution of the base shear to upper floors in a way that elicitssimilar response from the structure as when it is subjected to an earthquake.Thisusually involves distribution of the base shear to floors - as this is where mass isconcentrated [42] - in proportion to their height from the ground level [93].A few short falls of force-based design include:In force-based design, the distribution of forces for the structural element isbased on the estimation of initial stiffness of the structure. This is not quite ac-curate since resizing of members at the end of the design - assuming member di-5mensions need to be modified - leads to a change in the initial stiffness and hence,the distributed forces are rendered invalid [82]. Again, stiffness is dependent onmember strengths which cannot be known until the end of the design.Also, FBD assumes that all members in a structure yields simultaneously whichis far from correct for several structural types.Force reduction factors are unknown for novel hybrid systems. The over-strength and ductility factors used in force-based design for various structural typesare the results of extensive research and rigorous experiments. As these factors arenot available for novel structural systems, it becomes quite challenging if not im-possible to accurately design new structural types using FBD.Yet another inaccuracy of force-based design is that it uses the force- reductionfactors on all modes. Inelastic response relates only to first mode. As such, forcereduction factors should not be used on higher mode effects. In FBD higher modeeffects are not adequately accounted for since force reduction factors are used onthem.DDBD is proactive while FBD is reactive in the sense that FBD uses dis-placement/deformation only to check if a building falls within acceptable limits atthe end of the design, whereas DDBD targets a certain deformation/displacementbased on the limit state intended to be reached.2.4 Direct Displacement Based DesignDDBD is an emerging branch of performance-based design that has only very re-cently gained popularity. DDBD aims to design a structure to attain a certain limitstate rather than be bounded by it under a specified seismic loading [82]. In DDBD,a substitute SDOF system is used to represent the actual structure, and the structureis designed to achieve a certain limit state by targeting the corresponding displace-ment/deformation/drift level for that given limit state.The procedure for the direct-displacement based design is shown in the Figure2.1 and is enumerated below:1. Develop the design displacement profile: The design displacement profile of65Figure 2.1: Fundamentals of Direct Displacement-Based Design (DDBD).Adapted from [99]the building can be obtained using the formula∆i = ω˙θθdhi(4Hn−hi4Hn−h1)(2.1)where ω˙θ is a reduction factor that accounts for the higher mode amplifica-tion of drift, and is given by 1.15−0.0034Hn < 1.0, Hn is the total buildingheight,h1 is the height of the first storey, hi is the height of the ith storey, andθd is the code drift limit for the limit state considered.From the above, the design displacement, ∆d of the building can be obtainedusing the formula∆d =∑ni=1 mi∆2i∑ni=1 mi∆i(2.2)where mi and ∆i are ,respectively, the mass and displacement of any givenstorey.72. Determine the characteristics of the equivalent single degree of freedom sys-tem: DDBD involves the simplification of the structure to be designed intoan equivalent single degree of freedom system by reducing the masses ofall floors to an effective mass, and the height of the building to an effectiveheight. This can be seen schematically in the Figure 2.1 and is expressedmathematically as:me =∑ni=1 mi∆i∆d(2.3)He =∑ni=1 mi∆ihimi∆i(2.4)Where all parameters retain the same definition as in step 1 above.3. Design Ductility: This is an important parameter necessary for the estima-tion of the Equivalent Viscous Damping value of a system. The ductilityof a system is the ratio between the the design displacement and the yielddisplacement of the structure and can mathematically be expressed as:µ =∆d∆y(2.5)where ∆d is the design displacement and ∆y is the yield displacement. Theyield displacement can be obtained using the equation below:∆y = θyHe (2.6)and θy is given as:θy = 0.5εyLbHb(2.7)where θy represents the yield drifts of the different bays for a given floorlevel, εy represents the yield strain of the material, while Lb and Hb representthe length and height of the beam, respectively.4. Estimate the equivalent viscous damping (EVD): Equivalent Viscous Damp-ing is an essential part of DDBD and is one of the key elements that sets itapart from FBD. EVD is the sum of the elastic and hysteretic damping of a8structure, and in a simplified form can be expressed as:ξeq = ξe+ξhyst (2.8)where ξe accounts for damping due to elastic response from the structurewhile ξhyst accounts for damping due to inelastic response of the structure.Extensive literature has been published on both elastic and hysteretic damp-ing values and equations for different structural types and these will be ex-plored in the following section.5. Obtain the effective period: This can be obtained by using a scaling factordependent on the equivalent viscous damping as expressed in equation 2.9on a displacement spectra. Then a combination of the new scaled displace-ment spectra and the design displacement can be used to obtain the effectiveperiod. This is graphically illustrated in figure 2.1η =√105+ξeq(2.9)6. Calculate the effective stiffness: The effective stiffness is calculated as thesecant stiffness from the point of maximum displacement of the substitutestructure and shares a relationship with effective mass and effective periodas shown in equation 2.10Ke =4π2meT 2e(2.10)7. Obtain the base shear: The base shear can then be obtained using the equa-tionF =Vbase = Ke∆d (2.11)The base shear can then be distributed to all floors using the equationFi =Vbase(mi∆i)∑ni=1(mi∆i)(2.12)after the distribution of base shear to the different floors, the building is thendetailed.9A simplistic flowchart showing the Direct Displacement Based Design proce-dure is shown below:Design DuctilityEquivalent SDOF Properties of systemDesign Displacement ProfileEquivalent Viscous DampingEffective Period Effective Stiffness Base ShearDistribution of Base ShearDesign and analysis of sectionsFigure 2.2: Schematic Representation of Direct Displacement-Based Design(DDBD) Procedure.2.5 Major Differences Between FBD and DDBDWhile most Force-based design approaches use the acceleration response spec-trum, Direct-displacement based design method focuses on the use of displacementresponse spectra. Another difference is that while FBD uses initial elastic stiffnessin its calculation, which does not account for the inelastic response of the struc-ture, DDBD uses the secant stiffness of the structure from the point of maximumdisplacement as shown in figure 2.1Another major difference between force-based design and direct-displacementbased design is that while FBD tries to use account for energy dissipation through10damping and inelastic response using force reduction factors and damped responsespectra, DDBD accounts for this using equivalent viscous damping (EVD).2.6 Bibliometric Study DDBDDDBD was proposed in the late twentieth century, and it is a design proceedure thatattempts to achieve a specified limit state for a given structural system under prede-termined levels of seismic intensity [98] This method closely matches uniform riskdesign spectra philosophy because unlike FBD it does not rely on initial elasticproperties (such as stiffness and damping) which are quite diificult to accuratelyascertain. Rather, DDBD depends on effective stiffness at maximum response,equivalent viscous damping (elastic and hysteretic damping) and displacement re-sponse spectra. DDBD is a versatile design procedure and although initially wasused for concrete building and bridge designs, over the years has evolved over theyears and encompasses various structural systems and types (timber, steel, hybridsystems etc), (buildings, bridges, etc)In 1997 Priestly and Calvi explored the basic concepts and principles of DDBDand summarized the design proceedure/methodology for a simple multi-span bridgestructure as well as displacement based assessment of existing buildings and bridges.over the years, DDBD evolved from the use of an inelastic SDOF system for repre-senting the MDOF system to the use of an equivalent linear system of the MDOFsystem in the step involving the estimation of the seismic deformation of the sys-tem [24] Although use of an equivalent linear system remains a non-integral partof displacement-based design.In 2001, Chopra et al. developed a DDBD procedure using concepts of inelasticdesign spectra and explored the performance of elastic and inelastic displacementspectra in correctly predicting the displacement and ductility demands of a struc-ture using DDBD as the design procedure, and found that not only did the DDBDprocedure using inelastic spectra perform better in estimation of displacement andductility demands, it also correctly satisfied plastic rotation constraints and otherdesign criteria unlike the DDBD procedure involving elastic displacement spectra.in 2002, Lin et al. developed a procedure for seismic displacement-baseddesign for old and novel buildings that had passive energy dissipation system-11s/devices. Prior to this, the already established DBD procedures were used fornew buildings while two methods stood out as displacement-based seismic retrofitmethods for existing buildings - coefficient method and capacity-spectrum meth-ods proposed by FEMA273 and ATC-40, respectively. This procedure proposed byLin et al., similar to the already established standard method of DDBD, involvedthe use of substitute structure, target/design displacement, effective period, etc andonly differed due to the fact that this new procedure had to account for the me-chanical properties of the passive energy dissipation devices. This methodologywas verified using non-linear time history analysis and proved to be an easy andreliable method for prognosticating the behaviour of buildings in the linear andnon-linear ranges.After undergoing several iterations and improvements since its conception inthe last decade of the twentieth century, Priestly et al. in 2007 outlined the state-of-the-art DDBD procedure for basic structural systems - frame buildings, wallbuildings, bridges, dual wall/frame buildings, wharves and seismically isolatedstructures - using a wide range of materials - reinforced concrete, structural steel,masonry, timber, prestressed (precast) concrete, etc [101]. A brief outline of theDDBD procedure has already been delineated in section 2.4In 2008, Priestly, Calvi, and Sullivan developed a direct displacement-baseddesign proceedure for frame-wall structures [109]. In their methodology, the designdisplacement profile is obtained from strength proportions assigned to the frameand wall. The said structure is then represented as a single degree of freedomsystem using knowledge of the displacement profile and damping contributions ofthe frame and wall elements separately. Their method showed sufficient levels ofaccuracy for structures of 20 stories in height or lower, and for structures with RCwalls having aspect ratios of greater than 3. For structures with walls having aspectratios of more than 3, shear deformations must be given further consideration. Theaccuracy of this novel DDBD approach was verified using non-linear time historyanalysis (NLTHA).Similar to already established DDBD methodology, in 2009, Sullivan devel-oped a DDBD procedure for dual structures made of RC wall with steel eccentri-cally braced frames (EBFs) equipped with visco-elastic dampers at link positions[111]. This methodology involves a predetermination of strength proportions of12the wall and EBFs at the beginning of the design procedure, and this permits thedesigner to be in control of the forces developed in the structure. The displacedshape at peak response, and hence the single degree of freedom properties of thestructure (effective height, effective mass, and effective stiffness) are determinedby the strength proportioning carried out at the beginning of the design. A novelaspect of this DDBD procedure was its ability to fairly accurately determine theequivalent viscous damping of a structural system fitted with extra dampers. ThisDDBD proceedure was carried out on an 8 storey structure and is fairly easy to im-plement, requires less time, and can be completed without the need of a computermodel.In 2010, Cardone, Palermo and Dolce developed a DDBD proceedure for RCstructures fitted with different seismic isolation systems [22]. Borrowing a leaffrom the already established DDBD procedure established by Priestly et al. in2007 [101], Cardone et al. in their novel DDBD proceedure, defined the targetdisplacement profile using maximum interstory drift and displacement of the base-isolation systems. This robust DDBD procedure accounted for different cyclicresponses of a wide multiplicity of isolation systems (friction pendulum system,high-damping rubber bearings, lead rubber bearings, etc) which are determined byvaried force-displacement relationships.In 2011, Malekpour et al. developed a direct displacement-based design proce-dure for regular steel moment resisting frames [77] with attention paid to the reli-ability of the design methodology within certain performance levels, and in 2012,in order to provide some sort of automation to the thus far established DDBD pro-cedure, Sullivan et al. developed a computer program for DDBD [110]. Though,the software is limited to only RC frame and wall buildings. Sullivan and Nievasin 2014 also extended the DDBD procedure to include strong frame-weak wallstructures, since past research had focused almost solely on weak frame-strongwall structures [85].DDBD was also extended in 2014 to include seismic assess-ment of structures [92]. In the paper, Chu Peng et al. successfully modelled andsimulated the response of seismically-deficient frames through pushover analysis,using a non-linear finite element analysis method. A software which facilitates theDDBD procedure by comparing the capacity of the structure against code-basedvalues was also developed.13In 2018, Yang Lu et al, developed a direct displacement-based design proce-dure for flexible-base structures subjected to pulse-like ground motions [74]. Thisnovel DDBD approach approaches the construction of the displacement responsespectra with a different approach which accounts for the effect of pulse period. Thedesign process also captures SSI (soil structure interaction) effects using a single-degree-of-freedom oscillator with a fixed base. From their results from verifyingthis DDBD procedure using NLTHA, they discovered that inelastic design spectrashowed to be more compatible with this DDBD proceedure than elastic linearisa-tion method in the estimation of actual responses of structures designed with thismethod against pulse-like ground motions. Their results also showed that for struc-tures with high ductility demand, soil structure interaction has insignificant effectsand as such need not be modelled. Hence, a simple fixed base can be used.In the past, DDBD procedure for buckling restrained braces involved itera-tions, and in an attempt to improve upon this, Lu Liu et al in 2018, developeda non-iterative DDBD procedure called R−CR DDBD for steel frames equippedwith self-centring buckling restrained braces (SCBRBs) [68]. In this DDBD pro-cedure, a predetermined drift ratio is used to determine the yield strength and yielddisplacement of the structure using the relation of constant strength inelastic dis-placement response spectra (CR sprectra) and strength reduction factor (R). A ben-efit of this novel DDBD procedure is that it can be extended to other structuraltypes as long as the expression R−CR relationship is available.In 2019, Kun ye et al, extended the basic DDBD procedure to base-isolatedbuildings with lead rubber bearings (LRBs) [129]. This was achieved by incor-porating the 2 degree-of-freedom models of base-isolated buildings to the DDBDprocedure for regular buildings. further research is required before this DDBD ap-proach can be extended to other base-isolated building structures with other base-isolation elements. In thesame year, Pourali et al proposed an algorithm for inves-tigation of p−∆ effects in DDBD procedures. This research serves as a precursorfor other research efforts that would ascertain the amount of allowance necessaryto incorporate more accurately p− ∆ effects in buildings designed with DDBDwhen non-linear behaviour is considered. Yan et al., in thesame year, developeddisplacement profiles for RC-frame structures within the DDBD framework [128].This novel displacement profile expression incorporated column-to-beam strength14ratio, maximum interstorey drift, first-order elastic mode, and even height-widthratio, as well as the drift at first plastic hinge formation. This novel expressionhowever, is only ideal for DDBD of structures whose vibration is dominated byfirst mode.In 2020, a novel DDBD procedure which involved the use of multi-degree-of-freedom equivalent system was developed by Muho et al. [81] for plane moment-resisting frames. As a direct consequence of not using an equivalent single-degree-of-freedom system, this new DDBD procedure better accounts for p−∆ and highermode effects in the structure. The results is the design of frames with closer defor-mation responses to target responses, which in turn means greater predictability ofstructural behaviour which in turn translates to use of lesser construction materi-als. Two concepts central to this new DDBD procedure is the use of design modaldisplacements and deformation dependent equivalent modal damping ratios. Thisnovel DDBD proceedure was extended in 2022 by Kalapodis et al. [61] to includesteel moment resisting frame structures (MRFS), buckling restrained braced framestructures (BRBFS), and steel eccentrically braced frame (EBFS), and considereddesign modal displacements and deformation-dependent equivalent modal damp-ing for ratios for the first few modes. This method produces more accurate resultsfor high-rise buildings where higher mode effects have greater effect on the overallresponse of the structure.In 2021, Yi Xiao et al developed an efficient DDBD procedure for structureswith viscoelastic dampers [127]. For long, design of viscoelastic dampers haveposed a problem both to conventional force-based and direct displacement-basedapproaches due to high nonlinearity of the viscoelastic dampers. This issue isresolved in this new DDBD procedure by the establishment of mathematical rela-tionship between the viscoelastic damper and the structure’s period. Though veri-fied through NLTHA of a 24 storey building and showed satisfactory results, thisDDBD procedure is based on assumptions [127] that are subject to further research.The diagram 2.3 shows citation of authors on the subject of direct displacement-based design15Figure 2.3: Bibiometric study of direct displacement-based design2.7 Equivalent Viscous Damping (EVD)With the emergence of Direct Displacement Based Design (DDBD), EquivalentViscous Damping (EVD) Parameter has gained relevance as it as it eliminates thevery popular iterative and computationally intensive approaches and provides amore direct design approach [69]. Equivalent viscous damping can be defined asa concept used in structural engineering to model the energy dissipation capacityof a building during an earthquake or other vibration event. It is the amount ofviscous damping that would be required in a hypothetical linear viscous damper todissipate the same amount of energy as the building during a given vibration event.Determination of equivalent viscous damping parameter for different novel struc-tural systems is an area of ongoing research. In Loss et al’s paper [69], a formulafor the evaluation of EVD for timber frame structures with dowel type metal fas-tener connection was proposed. Although other formulations - for example, one by[100] - are already available in existing literature, it must be noted that Priestley’sformulation is wildly used for steel and reinforced concrete and has found onlyvery few applications in timber structures. The development of the formulation16for EVD in the paper [69] is based on the Jacobsen’s energy approach [58] and byresults of experiments which show that the dissipative capabilities of timber framestructures are highly concentrated at the joints [69].For buildings with intermediate to long periods, there has been the problemof overestimation of equivalent damping values with the use of jacobsen’s equiva-lent damping approach combined with the secant stiffness method (JDSS) - whichwere the popular and accepted methods - and this led to underestimation of dis-placements. This was discovered in an evaluation carried out by Kowalky et al.in 2006 [41]. They also discovered that there was an underestimation of dampingin buildings with short periods which unsurprisingly led to overestimation of thedisplacement of the buildings. This was due to a couple of problems one of whichwas the basic assumptions inplicit to the JDSS method (for example, the assump-tion that the loading which the structure undergoes can be expressed by a simplesinusoidal function) which does not apply to real earth quake ground motions [41].In an attempt to solve this problem, Kowalky et al. [41] developed expressionsfor equivalent damping for four structural systems using four hysteretic models- Ring spring(Flag-shaped), large Takeda, small Takeda and Elasto-plastic. Theresults from these new hysteretic models when assessed, led to significantly moreaccurate predictions of inelastic displacements. The expressions were proposed tobe used in conjunction with the secant stiffness approach and considered the effectsof the different hysteretic model types.Over the years, different expressions for Equivalent Viscous Damping for dif-ferent structural systems have been developed and has been summarized in tables2.2, 2.3 and 2.4. EVD is relevant to the DDBD procedure because it is a way ofcharacterizing the energy dissipation properties of a building in terms of a sim-ple, linear damping model, and allows engineers to analyze the building’s behaviormore easily and accurately, and to design effective damping systems to mitigate theeffects of earthquakes and other vibrations. The value of equivalent viscous damp-ing for a building depends on a number of factors, including its mass, stiffness, anddamping properties, as well as the characteristics of the ground motion or other vi-bration event. It is typically expressed as a percentage of the critical damping ratio,which is the damping level that would just prevent the building from oscillatingindefinitely.17Table 2.2: Equivalent viscous damping expressions for different structuralsystems and hysteresis typesDescription EVD ExpressionSteel concentricallybraced frame [126]ξeq = 0.03+(0.23− λ15)(µ−1) ∀ µ ≤ 2;ξeq = 0.03+(0.23− λ15) ∀ µ ≥ 2Hybrid-timber struc-tures [4]5+ 62×λ0.4π (1− 1√µ );λ = HBBilinear hystereticmodel for steel mem-bers [112]ξeq = ξ0+a(1− 1µb )(T c)Bilinear elastoplasticsystem [104]ξeq = ξ0+ 2π(1−r)(µ−1)µ−rµ+rµ2Takeda model [48] ξeq = ξ0+0.2(1− 1√µ )Elastic and Coulombslip elements [57]ξeq = ξ0+0.0587(µ−1)0.371Takeda model [40]ξeq = ξ0+ 2π RLA where RLA = 1− 34µα−1γ− 14 [ rβµγ (1− 1µ )+1][2−a(1− 1µ )−µα−1γ]− 14 [ rβ2µγ (1− 1µ )2]and γ = rµ− r+1Ramberg OsgoodModel [89]1π (1− 2γ+1)(1− 1µ FFy )Takeda model α = 0.5and β = 0 [63]ξeq = ξ0+ 1π (1− 1−r√µ − r√µ)Notes: µ: Ductility, λ = H/B: Slenderness ratio, H: Height of frame, B: Width of theframe, a, b, and c: Constants, T : Period, r: Post-yield stiffness ratio, β : Recentering ratio,F : Force, Fy: Yield force.18Table 2.3: Equivalent viscous damping expressions for different structuralsystems and hysteresis typesDescription EVD Expression Parameter definitionsRC frames[102]5+ 120π (1− 1√µ ) µ: DuctilityRC Columnsand walls [102]5+ 95π (1− 1√µ ) µ: DuctilityPrecast con-crete walls andframes [102]5+ 25π (1− 1√µ ) µ: DuctilityRC frame build-ings [102]0.05+0.565[ µ−1µπ ] µ: DuctilityRC frame [73] ξeq =√100−6.5(µ−5)2 forµ < 5.0µ: Ductility, ξeq: EquivalentViscous DampingRC columnsand beams[108]ξeq = 4.7 for µ < 1.0 else,ξeq =−0.4µ2+7.1µ−2 µ: Ductility, ξeq: EquivalentViscous DampingRC frame [47] ξeq = ξ0+ 8π (5+−6µ1.8 +0.2µ1.8) µ: Ductility, ξeq: EquivalentViscous DampingRC columnsand beams[108]ξeq = 4.7 for µ < 1.0 else,ξeq =−0.4µ2+7.1µ−2 µ: Ductility, ξeq: EquivalentViscous DampingRC frame [47] ξeq = ξ0+ 8π (5+−6µ1.8 +0.2µ1.8) µ: Ductility, ξeq: EquivalentViscous Damping, ξ0: Initialelastic dampingBRB-RC framestructure [43]ξeq = 0.05+0.519( µ−1µπ ) µ: Ductility, ξeq: EquivalentViscous DampingSteel braced RCframe [47]ξeq = ξ0 + 70π (1 − 43µ4 − 4.7 ×10−5µ4)µ: Ductility, ξeq: EquivalentViscous Damping, ξ0: Initialelastic dampingInfilled-RCframe [64]ξhyst = 0.804 µ+0.83µπ ;ξhyst = 0.804 µ+0.05µπ for µ ≤ 1;ξhyst = 0.83 µ−0.07µπ for µ ≥ 0 ;µ: Ductility, ξhyst : HystereticDampingSteel Members[102]5+ 150µπ (µ−1) µ: Ductility19Table 2.4: Equivalent viscous damping expressions for different structuralsystems and hysteresis typesDescription EVD Expression Parameter definitionsTakeda modelα = 0.5 andβ = 0 [63]ξeq = ξ0+ 1π (1− 1−r√µ − r√µ) µ: Ductility, ξeq: EquivalentViscous Damping, ξ0: Ini-tial Elastic Damping, r: post-yielding stiffnessBilinear hys-teretic system[53]ξeq = 2π(µ−1)(1−r)µ2 µ: Ductility, ξeq: EquivalentViscous Damping, r: post-yielding stiffnessRC structuressubjected toblast loads [72]ξeq = 0.05+ 1π(1−r)(µ−1)µ[1+r(µ−1]) µ: Ductility, ξeq: EquivalentViscous Damping, r: post-yielding stiffnessHysteretic mod-els [15]ξeq = aπ (1− 1µb )(1+ 1(T+c)d )N µ: Ductility, ξeq: Equivalentviscous damping, N: normal-izing factor, a, b, and c are re-gression constantsHystereticModels [15]ξeq = aπ (1− 1µb )(1+ 1(T+c)d ) 1N µ: Ductility, ξeq: Equivalentviscous damping, N: normal-izing factor, a, b, and c are re-gression constantsHystereticmodels (Wherethe value of Cvaries depend-ing on the shapeof the hysteresisloop) [41]ξ = ξv+Ci( µ−1πµ ) µ: Ductility , ξ : EquivalentViscous DampingSteel frame withCLT infill [12]ξ0 + C(µ−1µπ);C =[0.43 + 0.5 × A + 0.015 ×B + (1.27 × 10−3Ct) + (3.75 ×10−4×D)−0.054×E−(2.74×10−4A×Ct)− (1.01× 10−3A×D) − 0.019 × A × E + (2.62 ×10−5 × B×D)− (3.2× 10−4 ×Ct ×D)−0.135×A2− (1.045×10−4 × B2) − (1.98 × 10−6 ×C2t )+(5.9×10−3×E2)]C: constant, A, B, C, D, andE: modelling variables20Review of Self-Centering Moment-ResistingBeam-Column JointsThe ratio between the moment capacity provided by the post-tensioning and themoment capacity provided by the entire system is referred to as the recenteringratio β , and usually ranges from 0.6 to 0.8 for post-tensioned timber frame struc-tures [96]. For the system discussed in chapter 4, this ratio is closer to 1.0 becauseof the absence of dissipative reinforcement at the beam-column joint. This can bemathematically expressed as:MptMt= βThe beam-column connection of post-tensioned frame structures is usually de-signed using the Monolithic Beam Analogy (MBA). The benefit of this methodol-ogy is that it can be used irrespective of the material of the frame. Modified Mono-lithic Beam Analogy (MMBA) is an adaptation of the MBA procedure specificallyfor timber structures due to some of its material peculiarities which include theorthotropic behaviour of timber, its lesser strength compared to concrete and steelend effect - which is the local crushing of timber fibres at the beam-column jointwhich results in a 70%, decrease in timber stiffness, etc. These modifications wereabsolutely necessary to ensure accurate results.This methodology involves the capture of the behaviour of the joint in twosegments - before decompression, and before yielding of the post-tensioning ten-don. It should be ensured that the beams and columns remain elastic, as such,the strain in the beam and column should not exceed the elastic limit strain of thetimber material used. This can be ensured by calculating the strain in timber εt ,for every imposed rotation θimp at the beam-column joint, and checking that thevalue εt does not exceed the elastic limit strain of the timber material. This can bemathematically expressed as:εt = c(3θimpLcant+φdec)(2.13)where εt is the strain in the timber, θimp, is the imposed rotation at the con-nectino, φdec is the decompression curvature, c is the position of the neutral axis,and Lcant is the distance from the interface to the point point of contraflexure - this21is taken as half of the beam length when structure is subjected to seismic forcesonly.section analysis for jointed ductile connections involve moment and corre-sponding rotations. The rotation at a beam-column joint is comprised of elasticrotation components - beam rotation θb, column rotation θc and rotation of jointpanel θ jp - and inelastic rotation which comprises the connection rotation θcon2.8 Section Analysis of Jointed Ductile Connection usingMMBA procedureA brief outline of the MMBA procedure is outlined in this section, and is usedin the analytical and numerical modelling of post-tensioned timber frame joints inthe chapters that follow. before the MMBA procedure is outlined, it is necessaryto understand the sources of rotation contributions. This has been depicted in thefigure 2.4Figure 2.4: Rotation contributions to a post-tensioned timber beam-columnjoint. Adapted from [107]2.8.1 Find Decompression Moment, MdecIdeally zero rotation occurs prior to decompression moment, but due to the lowstrength of timber in perpendicular to the grain direction, there is a rotation thatoccurs at the beam-column joint as a result of the initial post-tensioning force.This is called interface rotation and can be calculated using the formular below:θint = kintTpt,initialhcEt,perph2bbb(2.14)22kint =1KscrKss(2.15)kscr = 1+54AscrAt(lshc)1.26(2.16)kss =hcbLln(hcbL+1) (2.17)The formular for the decompression moment is given by:Mdec =Tpt,intialZbAb(2.18)The decompression moment corresponds with the interface rotation on themoment-rotation plot.2.8.2 Impose a rotation, θimpThe desired moment-rotation relationship is obtained by plotting a summation ofrotation experienced by post-tensioning, and rotation caused by interface compres-sion deformation by the corresponding moment sustained. But the starting pointis to determine the drift for which the moment-rotation relationship is to be deter-mined. This can be summarized in a few simple steps.1. Find the centre line rotation, θcl: This can simply be obtained by dividingthe horizontal displacement to which the joint under consideration is sub-jected by the height of the joint from its base. It has thesame mathematicaldefinition as drift ratio.2. Obtain the connection rotation (θcon): This is obtained by subtracting thebeam, column, and joint panel rotations, (θb,θc,θ jp) from the centre linerotation and transposing the difference. As can be observed from figure2.4, plotting moment-rotation relationship of the post-tensioning using cen-tre line rotation can lead to erroneous results. This is due to the fact that theentire rotation experienced by the beam-column joint does not come exclu-sively from the post-tensioning. As such, in order to obtain accurate results,23the rotation contributions from the beam, column and joint panels have to besubtracted. Formulars for obtaining beam, column and joint panel rotationsusing centre line rotation as obtained from [107] are expressed below:θb =Mcl(Lb−hc)L2b((Lb−hc)26EtIb+2αs,clGtAb)(2.19)θc = Mcl(H6EtIc+2αs,clGtAcH)(2.20)θ jp =3Mcl2αs,clAchbGtLb−hcLb(2.21)θcon =θcl−θb−θc−θ jp(1− hcL−b) (2.22)3. Obtain gap rotation (θgap): The gap rotation is the actual rotation associatedexclusively to the post-tensioning and is obtained by subtracting the interfacerotation from the connection rotation. This can be mathematically expressedbelow:θgap = θcon−θint (2.23)A detailed review and derivation of expressions for all contributing rotationsin jointed ductile connection for timber frame buildings can be obtained in[107]2.8.3 Assume a neutral axis depth cThis value is iterated until equilibrium condition is satisfied. The neutral axis depthhere, is measured from the suffit of the beam as can be observed from the figure2.524Figure 2.5: MMBA nomenclature for a beam-column joint. Adapted from[107]2.8.4 Determine the force in the unbonded post-tension elementsThe force in the unbonded post-tensioned element can be obtained as the sum-mation of the initial post-tensioning force and an additional post-tensioning forcewhich manifests as a result of the rocking of the joint during a seismic event. Thiscan be mathematically expressed as shown below:Tpt = Tpt,initial +∆Tpt (2.24)∆Tpt = ∆εptEptApt (2.25)∆εpt =ngap∆ptlub(2.26)∆pt = θgap(ypt − c) (2.27)2.8.5 Evaluate the force in the non-post-tensioned reinforcingelements (Ts and Cs)This is an optional step and should be used if dissipating reinforcement is incorpo-rated at the beam-column joints. The exact equation to be used here also dependson the exact type of non-post-tensioned reinforcement used. But it would be a25function of the displacement undergone by the dissipating reinforcement. This canbe expressed mathematically as:Ts = f (∆s,t) = 0 (2.28)Cs = f (∆s,c) = 0 (2.29)∆s,c = θcon(c− ys,c) (2.30)∆s,t = θcon(c− ys,t) (2.31)2.8.6 Evaluate the force in the timber at the beam-column interface(Ct)In a design where the beam and column are protected via capacity design, theyremain elastic. In such a scenario, only the beam-column joint experiences non-linearity. As the beams and columns are assumed elastic, the elastic strain of thematerial is not to be exceeded. This has already been expressed in equation 2.13but is repeated here for convenience.εt = c(3θgapLcant+φdec)φdec =2Tpt,initialKgapEt,parabbh2b(2.32)The force in the timber element is determined mathematically using the equa-tion below:Ct = 0.5KgapεtEt,parabbc (2.33)262.8.7 Check for equilibriumAll the above calculations depended on a neutral axis depth, c. Now the value of cis iterated until the equation below is satisfied.Ct +Cs−Ts−Tpt = 0 (2.34)2.8.8 Obtain the moment for the given connection rotationinvestigated aboveThe corresponding moment for the given connection rotation investigated aboveis obtained by taking moment about the neutral axis of the beam. A triangulardistribution is assumed for the stresses in the timber element. This moment plottedagainst the connection rotation gives the moment-rotation relation for the post-tensioning. The experimental and analytical results from [107] were extracted andcompared to an analytical model based on the same experimental frame used in[107], and there was a perfect match. This is shown in figure 2.6.27-100-80-60-40-20020406080100-0.03 -0.02 -0.01 0 0.01 0.02 0.03Connection Moment (kNm)Connection Rotation (Rads)PT ONLY 200kN- -0.02 -0.01 0 0.01 0.02 0.03Connection Rotation (Rads)PT ONLY 250kNAnalytical Model VerificationExperimental and Analytical model results from Smith et. al (2014)Figure 2.6: Analytical model verification for MMBA procedure. Adaptedfrom [107]28Chapter 3DDBD Verification andNumerical Model Validation ofPost-tensioned Timber Framewith Dissipative Bracing System3.1 IntroductionJointed Ductile Connections and in particular post-tensioned systems have con-tinued to gain popularity due to their recentering capability since an excessiveresidual inter-storey drift ratio can result in the eventual decommissioning of abuilding even if the building exhibited a desirable response to seismic loading. Inthis chapter, the DDBD procedure and numerical models for Post-tensioned tim-ber buildings with dissipative bracing systems developed by Ponzo et al. in [96]are replicated. This is relevant because the DDBD procedure and numerical modelused in the chapter 4 of this thesis is an extension of the numerical model cal-ibrated by Ponzo et al. in [96] using experimental model testing results. Theexperimental model used by Ponzo et al. is a three-storey one-bay post-tensionedtimber frame with and without dissipative steel reinforcement at the frame-braceconnection and at the column-base connection. A detailed description of the ex-29perimental and numerical models used in that research can be found in [17, 33, 33–35, 37, 55, 96, 105, 106, 106, 107, 107]A schematic representation of the experimental and numerical models investi-gated by Ponzo et al. is shown in figure 3.1Figure 3.1: Schematic of 3-storey single bay post-tensioned timber frame fit-ted with dissipative bracing system. Adapted from [36]303.2 DDBD ProcedureAs the original DDBD methodology was first proposed for bare concrete systems,slight modifications have to be made to accommodate novel structural archetypes[14, 45, 115–118, 120]. The DDBD procedure delineated by Ponzo et al. [96] forpost-tensioned timber buildings with dissipative bracing systems is a slight varia-tion of the standard DDBD procedure already articulated in chapter 2, and is elab-orated below:Define Design DisplacementIn post-tensioned timber systems for short or medium-storey buildings, the dis-placed shape of the building can be assumed linear. This corresponds to a givendesign displacement (∆d) for a given earthquake intensity of interest [96]. Aschematic representation of this is shown in figure 3.2dme HeDefine Design Displacement Assume Flag shape design parameters: 𝛽ி; μ; r0204060801001201401600 2 4 6 8 10 12Displacement (mm)PeriodDesign SpectrumDamped Design Spectrum𝜼=√(𝟏𝟎/(𝟓+𝝃𝒆𝒒))Evaluate equivalent viscous damping, 𝝃𝒆𝒒y dFuFyrKiKiKeμ𝛽ி𝐹௬FsoFsysy drKiKsμDisp DBy dFDBKDBμDispDBy dFuFyrKiKiKeμDetermine equivalent DOF: Te;Ke;Fu;Fi and equivalent contributions: Fs; FDB51 2 34 Design Members and Joint Connections• Beams• Columns• Dissipative bracing system• Post-tensioning𝛽ி𝐹௬sFigure 3.2: DDBD procedure: (1) Displaced shape, (2) Idealized HystereticResponse, (3) EVD and Damped displacement response spectra, (4)Equivalent contributions of bare-frame and dissipative bracing system,and (5) Design of members.31Assume Flag Shape Design ParametersThe flag-shaped hysteretic behaviour, which combines the corresponding responseof bare post-tensioned frame with the response of an equivalent dissipative bracingsystem, makes up the equivalent force-displacement of the braced post-tensionedframe [96], and this is represented schematically in the figure 3.3. The threeflagshape parameters are ductility µ , recentering ratio of system βF , and post-yieldstiffness ratio r, which have average values of (1.5-3.0), (0.6-1.0), and (0.1-0.3),respectively.S,yFs,yDisplForcey dFuFyrKiKiKeμ𝛽ி𝐹௬DisplForceFlag-shapeHysteretic modelForceDB Displ𝐹஽஻Bilinear elastic modelFB BDF𝑀௉் 𝑀௉்Bare post-tensioned Frame (F) Dissipative Braces (DB)F𝑀௉் 𝑀௉்FB BDBraced post-tensioned Frame (BF)Figure 3.3: Fundamentals of Post-tensioned frame structure with dissipativebracing system. Adapted from [96]Evaluate Equivalent Viscous DampingThis can be defined as the sum of energy dissipated by the bare post-tensionedtimber frame and the dissipative bracing system. k is a reduction factor appliedto the hysteretic damping of the dissipative bracing system. Typical values of krange from 0.6 - 1.0; More details of this can be found in [96]. The equations forequivalent viscous damping and hysteretic damping are given in equations 3.1 and3.232εeq = εeq,v+ kεeq,h,v (3.1)εeq,h,v =β f (µ−1)µπ[1+ r(µ−1)] (3.2)Determine Equivalent SDOFThe SDOF properties of the frame - effective mass, (Me), effective height, (He),and design displacement, (∆d) are evaluated using the same equations expressed insection 2.4, but is repeated here for convenience.me =∑ni=1 mi∆i∆dHe =∑ni=1 mi∆ihimi∆i∆d =∑ni−1(mi∆2i )∑ni−1(mi∆i)(3.3)From the above equations, the effective stiffness and base shear of the framecan be estimated using the equations 3.4, and 3.5.Sd(Te) = Sa(Te)(Te2π)2; Ke = me(2πTe)2(3.4)Fu = Ke∆d ; Fy =Fu1+ r(µ−1) (3.5)Calculate the Equivalent ContributionsThe behaviour of the system is characterized by contributions from the bare post-tensioned frame and the dissipative bracing system. In this step, the total baseshear is discretized into contributions from the two above-mentioned componentsof this system [96]. Figure 3.3 shows the conceptual contributions of the barepost-tensioned frame and the dissipative bracing system as well as their combinedcontribution. The equations necessary for this discretization are detailed below:FDB =βF2Fy; ∆DB,y =∆dµDB; KDB,y =FDB∆DB,y(3.6)The ultimate force, yielding force, and yield displacement of the bare post-33tensioned frame can be obtained using the analytical equations expressed below:FS,u = Fu−FDB; FS,y = Ks.∆S,y; ∆S,y = FS,u− rk0∆dkS,0− rk0 (3.7)Design Members and Joint ConnectionsHere, the members of the structural system are designed. The post-tensioningbeam-column joint is designed using the Modified Monolithic Beam Analogy (MMBA)which has been detailed in section 2.7. Also, the properties - Force, yield displace-ment, ductility, etc - of the bare post-tensioned frame and the dissipative bracingsystem are distributed to the different storeys using the equations detailed below:KDB,i = rkkS,i; rk =kDBkS,0; kS,i =1∆si∑iFi; Fi = Fumi∆i∑ni=1(mi∆i)(3.8)FDB,i = rFFS,y,i; rF =FDBFS,y; FS,y,i = kS,i∆S,y,i; ∆S,y,i =∆siSTOT∆S,y (3.9)KDB,i, j =KDB,inDB,i; FDB,i, j =FDB,inDB,i(3.10)KDB,i, j =KD,i, j.kB,i, jKD,i, j +KB,i, j; FD,i, j = FDB,i, j (3.11)From here, the beam, column and braces are analysed and designed (sized)using relevant timber design codes. The above DDBD procedure is covered ingreater detail in [96]Verify Design AssumptionsIn this step, the structural system is modeled in software, in our case, OpenSees,and subjected to static or dynamic non-linear analysis. The resulting ultimate dis-placement, ∆u or drift, θu is compared with the design displacement, ∆d or drift, θdobtained from the DDBD procedure outlined above. The difference between both34values should fall within an acceptable margin, ε , otherwise, the DDBD procedureis repeated by assuming new values for the design parameters.Mathematically put, if |∆u − ∆d | or |θu − θd | < ε , the Design is Complete,else, repeat the DDBD procedure choosing new design parameters. A schematicrepresentation of the above DDBD procedure is shown in figure 3.41. Define design displacement: 𝜟𝒅𝝁2. Assume flag shape parameters: 𝜷𝑭; 𝒓; 𝝁𝝃𝒆𝒒3. Evaluate equivalent damping: 𝝃𝒆𝒒4. Determine the equivalent SDOF: 𝑻𝒆; 𝑲𝒆 ; 𝑭𝒖 ; 𝑭𝒊5. Calculate equivalent contributions: 𝑭𝒔 ; 𝑭𝑫𝑩6. Design members and joint connections6.1 Determine PT force (MMBA procedure)6.2 Design of dissipative bracing system at storey i7. Verify design assumption: Δ௨ − Δௗ < 𝜀DESIGN COMPLETEYESNOFigure 3.4: DDBD procedure. Adapted from [96]The above-outlined DDBD procedure is carried out on the experimental modeldescribed by Ponzo et al. in [17, 33, 33–35, 37, 55, 96, 105, 106, 106, 107, 107].A brief description of the details of the model is rendered in section 3.3:353.3 Details of Experimental ModelThe experimental model used is a three-dimensional, three-storey one-bay post-tensioned timber frame with a dissipative bracing system. The system is post-tensioned at the beam-column joint in both directions and is scaled to a factorof 2/3. The scaled floor dimension is 4m by 3m, and the scaled height of eachstorey is 2 m. The floor, beams, and columns were designed according to Eurocodeassuming that the building is to be used as an office space [96]. A live load of3kN/m2 was used on each floor except the roof which was subjected to a live loadof 2kN/m2 to represent garden utilization, and GL32H was the specification ofGluLam used for the beams, columns, and bracing with dimensions 200 mm by305 mm, 200 mm by 320 mm, and 175 mm by 190 mm, respectively.3.4 DDBD VerificationThe DDBD procedure outlined in section 3.2 is carried out on the frame describedin section 3.3 and similar results are obtained as detailed in [96]. The same targetresponse spectrum and ground motion as explored by Ponzo et al. is used in thisvalidation process. The target drift, θ was taken as 1.25%, recentering ratio, βFwas taken as 0.8, ductility, µ as 2.5, post-yield stiffness ratio, r as 0.2, reductionfactor, k as 0.85, elastic damping, εe as 0.02, hysteretic damping, εhyst as 0.12, andequivalent viscous damping, εeq was taken as 0.1199. After SDOF properties of thesystem was obtained and DDBD carried out, the effective mass, me was obtainedas 0.01449kNs2/mm, effective stiffness, ke as 1.2372kN/mm, effective height, Heas 4666.7mm, design displacement, ∆d as 58.3mm, effective period, Te as 0.68s,base shear, Fu as 72.17kN, and yield force, Fy was gotten to be 55.51kNTable 3.1: Summary of the equivalent SDOF systemstoreyNo.Height(mm)∆i(mm) mi(kNs2/mm)mi∆i mi∆i2 mi∆ihi3 6000 75 0.005635 0.4226 31.70 2535.882 4000 50 0.005635 0.2818 14.09 1127.061 2000 25 0.005635 0.1409 3.52 281.7636Table 3.2: Characteristics of the braced post-tensioned framestoreyNo.Fi(kN) ∆Si(mm) Fs,y,i(kN)Ks,i FDB,i KDB,i FDB,i, j KDB,i, j3 36.08 25 17.54 1.44 4.924 0.861 2.462 0.43052 24.06 25 43.85 2.41 12.31 1.435 6.155 0.71751 12.03 25 105.25 2.89 29.54 1.722 14.77 0.86103.5 Numerical Modelling of Post-tensioned TimberBuildings with Dissipative Bracing System UsingOpenSeesAfter the DDBD procedure has been successfully replicated, and results matchthose obtained by Ponzo et al. in [96], a numerical model is created and is sub-jected to the seismic risk for which it was designed and the expectation is thatthe numerical model behaves in a predetermined fashion. But first, this numericalmodel has to be calibrated using an experimental model. This process was carriedout by Ponzo et al. in [17, 33, 33–35, 37, 55, 96, 105, 106, 106, 107, 107] usingSAP2000, Ruaumoko and OpenSees software. The numerical model explored inthis thesis was created using just OpenSees software and results compared withthose obtained by [96]. Observations show that the OpenSees model accuratelypredicts the non-linear hysteretic behaviour of the various elements of the struc-ture.3.6 Verification Through Non-linear Time HistoryAnalysis7 spectra-compatible ground motion records were selected from the European strongmotion database and with those, NLTHA was carried out on the frame. The resultsobtained were compared to results obtained by Ponzo et al. [96] and both resultswere tallied.37Figure 3.5: Target response spectra according to Italian seismic code and 7spectra compatible ground motion records. Adapted from [96]3.6.1 Numerical Validation of UHP dampersFor the test frame having dissipative bracing system, the type of dissipation usedis the UHP damper which is correctly modeled using RambergOsgoodSteelor Steel02 material models in OpenSees. The hysteretic behaviour of the testframe after being subjected to a suite of ground motion records [94] is recorded,and this result is compared to the results of NLTHA conducted on the OpenSeesmodel. A considerable match is observed and is shown in figure 3.63.6.2 Numerical Validation of Post-tensioned Beam-Column JointThe behaviour of the beam-column joint is accurately represented with a multi-linear elastic OpenSees model used in parallel with a linear elastic model to repre-sent the moment contribution of the joint panel. This can be modeled analyticallyusing the MMBA procedure already discussed in chapter 2. Results obtained fromexperimental tests [35] are compared with numerical models from Sap2000 andOpenSees subjected to the same set of ground motion records and a perfect matchwas obtained and is shown in figure 3.73.6.3 Validation of Hysteretic Behaviour of Column-FoundationConnectionThe behaviour of the beam-column joint is accurately represented with a com-bination of three different OpenSees material models as shown in figure 3.1 -38-2.00E+01-1.00E+010.00E+001.00E+012.00E+01-5.00E+01 -2.50E+01 0.00E+00 2.50E+01 5.00E+01Opensees Model Opensees ModelExperimental ModelDissipator Response(a) (b)Figure 3.6: (a) Hysteretic behaviour of dissipators from OpenSees numeri-cal model when subjected to ground motion, and (b) Comparison ofhysteretic curves for dissipator behaviour from experimental tests andOpenSees model. Adapted from [94]Steel02, and two different ElasticMultiLinear models to represent mo-ment contributions by gravity and seismic forces. The OpenSees modelling of thecolumn-foundation connection used in this thesis is discussed in [95]. A near-perfect match in hysteretic behaviour of the experimental model subjected to se-lected spectra-compatible ground motion records and the OpenSees model sub-jected to identical ground-motion records is obtained, and is shown in Figure 3.8.3.6.4 Beams, Columns and BracesA simplistic approach for the modelling of the beam, column and brace elementsis utilized. Capacity design was already factored into the design. This means thatthe dissipators are designed to fail first, then post-tensioned beam-column jointsfollow, and finally the beams, columns and braces. These elements are designedto remain elastic even in the face of MCE (Maximum Credible Earthquake). Thatsaid, the beams, columns, and braces were thus modelled as elastic elements usingelasticBeamColumn, and truss element models in OpenSees both usingelastic uniaxial material models. This is shown in Figure 3.9.39Sap ModelExperimental ModelOpenSees Model-20-15-10-505101520-2.00E-02 -1.00E-02 0.00E+00 1.00E-02 2.00E-02Opensees ModelBeam-Column Joint Response(a) (b)Figure 3.7: (a) Hysteretic behaviour of post-tensioned beam-column jointfrom OpenSees numerical model when subjected to ground motion, and(b) Comparison of hysteretic curves for post-tensioned beam-columnjoint behaviour from experimental tests, OpenSees, and SAP2000 Nu-merical Models. Adapted from [35]3.7 Chapter SummaryIn this chapter, the three-storey post-tensioned timber frame with dissipative brac-ing system experimentally and numerically modelled and tested by Ponzo et al.in [96] was designed using Direct Displacement Based Design and modelled us-ing OpenSees software. Similar results were obtained between the results fromthe model explored in this chapter and models created by Ponzo et al. Thus, thisDDBD procedure and model have been validated and thus can be extended to largerstructural systems. This is explored in Chapter 4.40-10-5051015202530-3.50E-02 -2.50E-02 -1.50E-02 -5.00E-03 5.00E-03 1.50E-02 2.50E-02 3.50E-02Free rocking (Experimental)Dissipative rocking (Experimental)OpenSees ModelColumn-Foundation Joint ResponseOpensees Model(a) (b)Figure 3.8: (a) Hysteretic behaviour of column-foundation connection fromOpenSees numerical model when subjected to ground motion, and (b)Comparison of hysteretic curves for column-foundation connection be-haviour from experimental tests, OpenSees, and SAP2000 NumericalModels. Adapted from [37], θF, MδFigure 3.9: Depiction of elastic behaviour of beam, column and brace ele-ments.41Chapter 4Direct Displacement BasedDesign of Self-Centering MomentResisting Mass Timber frameBuilding Fitted With DissipativeBracing SystemIf I have seen farther it is by standing on the shoulders of Giants.— Sir Isaac Newton (1855)4.1 IntroductionSince its inception, direct displacement-based design has been modified to accom-modate the challenges and nuances that come with various structural archetypes.Ponzo et. al in their paper [96] outlined a DDBD procedure for post-tensioned tim-ber buildings with dissipative bracing system. This DDBD procedure involves thediscretization of forces acting on the system into forces acting on just the bare-frame and dissipative bracing system respectively. The DDBD procedure waschecked using an experimental setup and was validated using non-linear time his-42tory analysis [17, 33, 33–35, 37, 55, 96, 105–107, 107].dme HeDefine Design Displacement Assume Flag shape design parameters: 𝛽ி; μ; r0204060801001201401600 2 4 6 8 10 12Displacement (mm)PeriodDesign SpectrumDamped Design Spectrum𝜼=√(𝟏𝟎/(𝟓+𝝃𝒆𝒒))Evaluate equivalent viscous damping, 𝝃𝒆𝒒y dFuFyrKiKiKeμ𝛽ி𝐹௬FsoFsysy drKiKsμDisp DBy dFDBKDBμDispDBy dFuFyrKiKiKeμDetermine equivalent DOF: Te;Ke;Fu;Fi and equivalent contributions: Fs; FDB51 2 34 Design Members and Joint Connections• Beams• Columns• Dissipative bracing system• Post-tensioning𝛽ி𝐹௬sFigure 4.1: DDBD procedure: (1) Displaced shape (2) Idealizaed HystereticResponse (3) EVD and Damped displacement response spectra (4)Equivalent contributions of bare-frame and dissipative bracing system(5) Design of members.Ponzo et al.’s tweak on the DDBD approach for design of post-tensioned timberbuildings with dissipative bracing systems [96] proved fairly accurate and thus wasused in this study for the design of a 6 storey mass timber post-tensioned bracedframe as described in section 4.1.2 and in figure 4.2A brief summary of the DDBD procedure used by Ponzo et al. for the frameunder consideration is also outlined in section 4.1.1 and in the figure 4.14.1.1 Modified DDBD ProcedureThe seismic demand of this building is estimated using a modified DDBD proce-dure espoused by Ponzo et al. in their paper [96] for the design of post-tensionedframes. This procedure has also been summarized in chapter 3 for convenience. Aschematic representation of this DDBD procedure is shown in figure 4.1.43159 m6 m9 m6@ 3.65m = 21.9mElevation9 m6 m9 m7@ 6m = 42mPlanCase study building:6-Storey moment-resisting mass timber building fitted with dissipative bracing system.Figure 4.2: Schematic representation of Post-tensioned timber frame build-ing fitted with dissipative bracing system. Adapted from [107]4.1.2 Frame DescriptionThe frame to be designed using this DDBD approach is a 6-story 3-bay mass timberbuilding fitted with dissipative bracing systems in the outer bays. The beams arefitted with post-tensioned cables to ensure re-centering of the frame, while thebraces are fitted with UFP dampers at their connection to the beams to aid energydissipation. The building’s seismic force-resisting system is made up of two sets ofdissipative bracing systems on all floors fitted at the extreme bays in the north-southdirection of the building as depicted in figure 4.2.4.2 Design4.2.1 Equivalent SDOF systemA summary of the equivalent SDOF of the system is summarized in the table 5.1,and the summary of the SDOF parameters are outlined in table ??. The mass ofthe building was calculated based on the dimensions of the elements and a fractionof the live load of the building as specified by NBCC 2020. The building wasdesigned for a drift capacity of 2.5 % which corresponds with Life Safety (LS) limitstate and is generally the maximum drift design limit for post-tensioned timbertimber buildings [96, 122]. The equivalent damping parameters for the system issummarized in table ??44The building is located on a site in Vancouver with coordinates (49◦15′00′′ N,123◦7′12′′ W) having an average shear wave velocity of 450m/s at a maximumdepth of 30m. The damped and undamped acceleration and displacement responsespectra for the site of interest are shown in figure 4.3 and is based on 2% in 50 yearreturn period. The values for hysteretic damping, equivalent viscous damping, andresponse spectrum reduction factor were calculated based on formulas expressedin chapter 2, while the elastic damping component of the building was assumedto be 2% which is typical for most timber buildings [96]. The target drift, θ wastaken as 2.5%, recentering ratio, βF was taken as 0.8, ductility, µ as 1.7, post-yield stiffness ratio, r as 0.2, reduction factor, k as 0.6, elastic damping, εe as 0.02,hysteretic damping, εhyst as 0.094, and equivalent viscous damping, εeq was takenas 0.0835. After SDOF properties of the system was obtained and DDBD carriedout, the effective mass, me was obtained as 0.7074kNs2/mm, effective stiffness, keas 1.117kN/mm, effective height, He as 15568.1mm, design displacement, ∆d as389.2mm, effective period, Te as 5s, base shear, Fu as 434.8kN, and yield force, Fywas gotten to be 381.4kNTable 4.1: Summary of the equivalent SDOF systemStoryNo.Height(mm)∆i(mm) mi(kNs2/mm)mi∆i mi∆i2 mi∆ihi6 21900 547.5 0.1290 70.63 38669.7 15467875 18250 456.3 0.1496 68.23 31131.8 12452734 14600 365.0 0.1496 54.59 19924.4 7969743 10950 273.8 0.1496 40.94 11207.5 4482982 7300 182.5 0.1496 27.29 4981.1 1992441 3650 91.3 0.1496 13.65 1245.3 498114.2.2 Bare Frame and Hysteretic Bracing ContributionsA summary table detailing the characteristics of the braced post-tensioned frameis shown in figure 4.2. Results for this table are then used for the beam, columnand brace design. The analysis of the frame was carried out using ETABS. Thestiffnesses and forces in the dissipative bracing system are used for the design of450200400600800100012000 2 4 6 8 10 12Sd (mm)Period (s)Displacement Response Spectra5% Damped Spectrum8.6% Damped Spectrum0% Damped Spectrum00.20.40.60.811.21.41.60 2 4 6 8 10 12Sa(T)(g)Period (s)Acceleration Response Spectrum5% Damped Spectrum8.6% Damped Spectrum0% Damped SpectrumFigure 4.3: Acceleration and displacement response spectrathe UFP dissipators fitted at the connection between the beam and braces. As theeffects of the rigidity of diaphragms on seismic performance of the building isbeyond the scope of this study, a rigid diaphragm is assumed which ensures thatthe total base shear is equally distributed between the frames [107].Table 4.2: Characteristics of the braced post-tensioned frameStoryNo.Fi(kN) ∆Sy,i(mm) Fs,y,i(kN)Ks,i FDB,i KDB,i FDB,i, j KDB,i, j6 111.53 46.33 96.33 2.08 59.94 1.85 14.98 0.465 107.75 46.33 189.38 4.09 117.84 3.63 29.46 0.914 86.20 46.33 263.83 5.69 164.16 5.06 41.04 1.273 64.65 46.33 319.66 6.90 198.90 6.13 49.73 1.532 43.10 46.33 356.88 7.70 222.06 6.85 55.52 1.711 21.55 46.33 375.50 8.10 233.64 7.20 58.41 1.804.2.3 Beam, Column and Brace DesignThe beams, columns and braces were first analysed in ETABS and then designedusing the Glulam grade DFL 20f-E and DFL 16c-E. First, gravity load analysis wascarried out and all beams and columns were designed based on gravity loads only.Then the seismic force resisting system - the outer bays of the frame as shown in46figure 4.2 - was analysed and designed, and the most critical section for the beam,column and brace was used in the OpenSees model for simplicity. A summary ofthe beam, column and brace design calculations and result tables for the differentfloors is shown in the table 4.847Design of Glulam Beams of Braced Post-tensioned frame For Gravity LoadsThe force in beams are obtained from the ETABS model. The design calculationsprovided in this section are for the most critical case only. Since the design checksfor beams do not involve interaction, both checks (shear and moment) may corre-spond to different load combinations. The design values for the beam are obtainedfrom ETABS as given below:Table 4.3: Maximum design loads in Glulam Beams of BRBF (all floors)Vf M f(kN) (kN-m)62 67Material Properties:Grade for glulam beam is selected as Wood species DFL 20f-E. The properties ofthis grade of timber are given by Table 7.3 of CSA O86-14.Modulus of elasticity (E) : 12400 MPaStrength in compression parallel tograin ( fc): 30.2 MPaStrength in tension parallel to grain atgross section ( ftg): 15.3 MPaStrength in bending ( fb) : 25.6 MPaLongitudinal shear ( fv) : 2.0 MPaCross-sectional Properties:Consider Wood species DFL 20f-E glulam beam : 215 mm × 342 mm.Area of the beam (A = bd) : 215 × 342 = 73530 mm2Moment of inertia (I) :Ix = bd312 = 7.1670×108 mm4Iy = db312 = 2.8324×108 mm4Section modulus (S) :Sx = bd26 = 4.1912×106 mm3Sy = db26 = 2.6348×106 mm348Design against Bending Moment:According to CSA O86-14 (Cl. 7.5.6.5.1), the factored bending moment resistance, Mrshall be taken as the minimum of Mr1 or Mr2, as followsMr1 = φFbSKX KZbgMr2 = φFbSKX KLφ : 0.9Fb = fb(KDKHKSbKT ) : 25.6 MPaS = Sx : 4.1912×106 mm3KX = Curvature factor = 1.0 (Cl. 7.5.6.5.2 of CSA O86-14)KZbg =(130b)0.1(610d)0.1(9100L)0.1=(130215)0.1(610342)0.1(91007920)0.1 = 1.02CB (=√Led/b2) :√1.92×7920×342/2152 = 10.61 ¿ 10KL : 0.98The bending moment resistance is,The bending moment resistance, Mr = min(Mr1,Mr2)Mr = 0.9×25.6×4.1912×106×1.0×min(1.02,0.98)/106 = 95 kN-mFactored bending moment resistance (Mr) = 95 kN-m ¿ 67.3589 kN-m (Table 4.5)Design against Shear:According to CSA O86-14 (Cl. 7.5.7.2), the factored shear resistance, Vr is given byVr = φFv2Ag3φ : 0.9Fv = fv(KDKHKSvKT ) : 2.0 MPaAg = A : 73530 mm2The factored resistance is,Vr = 0.9×2.0× 2×735303 = 88 kN > 62 kNFinal Cross-section:Thus, DFL 20f-E Glulam beam of 215 mm × 342 mm is adequate.49Design of Glulam Columns of Braced Post-tensioned frame For GravityLoadsThe forces in columns are obtained from analysis carried out on the ETABS model.The design calculations provided in this section are for the most critical case only.Checks for all cases are similarly carried out. The design values for column areobtained from ETABS as given below:Table 4.4: Maximum design loads in Gravity Glulam Columns (Floor no. 1to 12)Vf M f ,x M f ,y N f ,comp N f ,ten(kN) (kN-m) (kN-m) (kN) (kN)57.9002 102.974 0.3391 106.3295 0Material Properties:Grade for glulam column is selected as Wood species DFL 16c-E. The properties ofthis grade of timber are given by Table 7.3 of CSA O86-14.Modulus of elasticity (E) : 12400 MPaStrength in compression parallel tograin ( fc): 30.2 MPaStrength in tension parallel to grain atgross section ( ftg): 15.3 MPaStrength in bending ( fb) : 14.0 MPaLongitudinal shear ( fv) : 2.0 MPaCross-sectional Properties:Consider Wood species DFL 16c-E glulam column : 315 mm × 456 mm.Area of the column (A = bd) : 315 × 456 = 143640 mm2Moment of inertia (I) :Ix = bd312 = 2.4890×109 mm4Iy = db312 = 1.1877×109 mm4Section modulus (S) :Sx = bd26 = 1.0917×107 mm3Sy = db26 = 7.5411×106 mm350Design against Compression Loads:Unbraced length of column (L) : 4.035 mAs the column is pinned supported at both ends,Effective length factor (Ke) : 1.2 (Table A.6.5.6.1 of CSA O86-14)Effective length (Le = KeL) : 4.842 mSlenderness ratio (Cc) : 4.035 / 0.315 = 12.8 < 50According to CSA O86-14 (Cl. 7.5.8.4.2), the factored compressive resistance parallelto grain, Pr = φFcAKZcgKC.φ : 0.8fc : 30.2 MPaKD : 1.0 (Table 5.3.2.2 of CSA O86-14)KH : 1.0 (Cl. 7.4.3 of CSA O86-14)KSc : 1.0 for dry service condition (Table 7.4.2 ofCSA O86-14)KSE : 1.0 for dry service condition (Table 7.4.2 ofCSA O86-14)KT : 1.0 treatment factor (Cl. 7.4.4 of CSA O86-14)Fc = fc(KDKHKScKT ) : 30.2 MPaVolume, Z = Lbd : 4.035 × 0.315 × 0.456 = 0.580 m3KZcg (min{0.68 (Z)−0.13,1}) : 0.68 ×(0.580)−0.13 = 0.730From Cl. 7.5.8.5 of CSA O86-14, the slenderness factor KC is given by,KC =[1.0+ FcKZcgC3c35(0.87E)KSE KT]−1=[1.0+ 30.2×0.730×12.8335×(0.87×12400×1.0×1.0]−1= 0.83Therefore, factored compressive resistance is,Pr = 0.8×30.2×143640×0.730×0.83 = 2090.0 > 106.3 kN (Table 4.7)Design against Tensile Loads:According to CSA O86-14 (Cl. 7.5.11), the maximum factored tensile force,Tr = φFtgAgφ : 0.9ftg : 15.3 MPaFtg = ftg(KDKHKScKT ) : 15.3 MPaAg = A : 143640 mm2Therefore, the factored tensile resistance is,Tr = 0.9×15.3×143640 = 1978 > 0 kN (Table 4.7)51Design against Bending Moment:According to CSA O86-14 (Cl. 7.5.6.5.1), the factored bending moment resistance, Mrshall be taken as the minimum of Mr1 or Mr2, as followsMr1 = φFbSKX KZbgMr2 = φFbSKX KLX-X axis:φ : 0.9Fb = fb(KDKHKSbKT ) : 14.0 MPaS = Sx : 1.0917×107 mm3KX = Curvature factor = 1.0 (Cl. 7.5.6.5.2 of CSA O86-14)KZbg =(130b)0.1(610d)0.1(9100L)0.1=(130315)0.1(610456)0.1(91004035)0.1 = 1.02CB (=√Led/b2) :√1.92×4035×456/3152 = 5.97 ¡10KL : 1.00The bending moment resistance is,The bending moment resistance, Mr = min(Mr1,Mr2)Mr = 0.9×14.0×1.0917×107×1.0×min(1.02,1)/106 = 138 kN-mFactored bending moment resistance (Mr) = 138 kN-m ¿ 102.974 kN-m (Table 4.7)Y-Y axis:φ : 0.9Fb = fb(KDKHKSbKT ) : 14.0 MPaS = Sy : 7.5411×106 mm3KX = Curvature factor = 1.0 (Cl. 7.5.6.5.2 of CSA O86-14)KZbg =(130b)0.1(610d)0.1(9100L)0.1 = (130315)0.1(610456)0.1(91004035)0.1 = 1.02CB (=√Led/b2) :√1.92×4035×456/3152 = 5.97 ¡10KL : 1.00The bending moment resistance, Mr = min(Mr1,Mr2)Mr = 0.9×14.0×7.5411×106×1.0×min(1.02,1)/10(6) = 95 kN-mFactored bending moment resistance (Mr) = 95 kN-m ¿ 0.3391 kN-m (Table 4.7)52Design against Shear:According to CSA O86-14 (Cl. 7.5.7.2), the factored shear resistance, Vr is given byVr = φFv2Ag3φ : 0.9Fv = fv(KDKHKSvKT ) : 2.0 MPaAg = A : 143640 mm2The factored resistance is,Vr = 0.9×2.0× 2×1436403 = 172 kN > 57.9002 kNDesign against combined Bending Moment and Axial Load:Members subject to combined bending and compressive or tensile axial loads shall bedesigned to satisfy the appropriate interaction equation,(PfPr)2+M fMr[11− PfPE]≤ 1TfTr+M fMr≤ 1Pf (Compressive load) : 106 kNPr (Compressive resistance) : 2090 kNM f (Factored bending moment) :M f ,x = 102.974 kN-mM f ,y = 0.3391 kN-mMr (Factored bending moment resis-tance):Mr,x = 138 kN-mMr,y = 95 kN-mTf (Tensile load) : 0 kNTr (Tensile resistance) : 1978 kNPE = Euler buckling load in the plane of the applied moment,PE,x =π2E05KSE KT IxL2e= 1.130×104 kNPE,y =π2E05KSE KT IyL2e= 5.394×103 kN(PfPr)2+M f ,xMr,x[11− PfPE,x]+M f ,yMr,y[11− PfPE,y]=(1062090)2+103138[11− 1061.13×104]+0.395[11− 1065.39×103]= 0.76 < 1.0TfTr+M f ,xMr,x+M f ,yMr,y=01978+103138+0.395= 0.75 < 1.0Final Cross-section:Thus, DFL 16c-E Glulam column of 315 mm × 456 mm is adequate.53Design of Glulam Beams of Braced Post-tensioned frame For Lateral LoadsThe force in beams are obtained from the ETABS model. The design calculationsprovided in this section are for the most critical case only. Since the design checksfor beams do not involve interaction, both checks (shear and moment) may corre-spond to different load combinations. The design values for the beam are obtainedfrom ETABS as given below:Table 4.5: Maximum design loads in Glulam Beams of BRBF (all floors)Vf M f(kN) (kN-m)3 6Material Properties:Grade for glulam beam is selected as Wood species DFL 20f-E. The properties ofthis grade of timber are given by Table 7.3 of CSA O86-14.Modulus of elasticity (E) : 12400 MPaStrength in compression parallel tograin ( fc): 30.2 MPaStrength in tension parallel to grain atgross section ( ftg): 15.3 MPaStrength in bending ( fb) : 25.6 MPaLongitudinal shear ( fv) : 2.0 MPaCross-sectional Properties:Consider Wood species DFL 20f-E glulam beam : 215 mm × 342 mm.Area of the beam (A = bd) : 215 × 342 = 73530 mm2Moment of inertia (I) :Ix = bd312 = 7.1670×108 mm4Iy = db312 = 2.8324×108 mm4Section modulus (S) :Sx = bd26 = 4.1912×106 mm3Sy = db26 = 2.6348×106 mm354Design against Bending Moment:According to CSA O86-14 (Cl. 7.5.6.5.1), the factored bending moment resistance, Mrshall be taken as the minimum of Mr1 or Mr2, as followsMr1 = φFbSKX KZbgMr2 = φFbSKX KLφ : 0.9Fb = fb(KDKHKSbKT ) : 25.6 MPaS = Sx : 4.1912×106 mm3KX = Curvature factor = 1.0 (Cl. 7.5.6.5.2 of CSA O86-14)KZbg =(130b)0.1(610d)0.1(9100L)0.1=(130215)0.1(610342)0.1(91007920)0.1 = 1.02CB (=√Led/b2) :√1.92×7920×342/2152 = 10.61 ¿ 10KL : 0.98The bending moment resistance is,The bending moment resistance, Mr = min(Mr1,Mr2)Mr = 0.9×25.6×4.1912×106×1.0×min(1.02,0.98)/106 = 95 kN-mFactored bending moment resistance (Mr) = 95 kN-m ¿ 5.5172 kN-m (Table 4.5)Design against Shear:According to CSA O86-14 (Cl. 7.5.7.2), the factored shear resistance, Vr is given byVr = φFv2Ag3φ : 0.9Fv = fv(KDKHKSvKT ) : 2.0 MPaAg = A : 73530 mm2The factored resistance is,Vr = 0.9×2.0× 2×735303 = 88 kN > 3 kNFinal Cross-section:Thus, DFL 20f-E Glulam beam of 215 mm × 342 mm is adequate.55Design of Glulam Columns For Braced Post-tensioned frame for LateralLoadsThe force in columns are obtained from the ETABS model. The design calculationsprovided in this section are for the most critical case only. Checks for all cases aresimilarly carried out. The design values for column are obtained from ETABS asgiven below:Table 4.6: Maximum design loads in Gravity Glulam Columns (Floor no. 1to 12)Vf M f ,x M f ,y N f ,comp N f ,ten(kN) (kN-m) (kN-m) (kN) (kN)30.3875 55.4571 0 0 363.7596Material Properties:Grade for glulam column is selected as Wood species DFL 16c-E. The properties ofthis grade of timber are given by Table 7.3 of CSA O86-14.Modulus of elasticity (E) : 12400 MPaStrength in compression parallel tograin ( fc): 30.2 MPaStrength in tension parallel to grain atgross section ( ftg): 15.3 MPaStrength in bending ( fb) : 14.0 MPaLongitudinal shear ( fv) : 2.0 MPaCross-sectional Properties:Consider Wood species DFL 16c-E glulam column : 315 mm × 456 mm.Area of the column (A = bd) : 315 × 456 = 143640 mm2Moment of inertia (I) :Ix = bd312 = 2.4890×109 mm4Iy = db312 = 1.1877×109 mm4Section modulus (S) :Sx = bd26 = 1.0917×107 mm3Sy = db26 = 7.5411×106 mm356Design against Compression Loads:Unbraced length of column (L) : 4.035 mAs the column is pinned supported at both ends,Effective length factor (Ke) : 1.2 (Table A.6.5.6.1 of CSA O86-14)Effective length (Le = KeL) : 4.842 mSlenderness ratio (Cc) : 4.035 / 0.315 = 12.8 < 50According to CSA O86-14 (Cl. 7.5.8.4.2), the factored compressive resistance parallelto grain, Pr = φFcAKZcgKC.φ : 0.8fc : 30.2 MPaKD : 1.0 (Table 5.3.2.2 of CSA O86-14)KH : 1.0 (Cl. 7.4.3 of CSA O86-14)KSc : 1.0 for dry service condition (Table 7.4.2 ofCSA O86-14)KSE : 1.0 for dry service condition (Table 7.4.2 ofCSA O86-14)KT : 1.0 treatment factor (Cl. 7.4.4 of CSA O86-14)Fc = fc(KDKHKScKT ) : 30.2 MPaVolume, Z = Lbd : 4.035 × 0.315 × 0.456 = 0.580 m3KZcg (min{0.68 (Z)−0.13,1}) : 0.68 ×(0.580)−0.13 = 0.730From Cl. 7.5.8.5 of CSA O86-14, the slenderness factor KC is given by,KC =[1.0+ FcKZcgC3c35(0.87E)KSE KT]−1=[1.0+ 30.2×0.730×12.8335×(0.87×12400×1.0×1.0]−1= 0.83Therefore, factored compressive resistance is,Pr = 0.8×30.2×143640×0.730×0.83 = 2090.0 > 0.0 kN (Table 4.7)Design against Tensile Loads:According to CSA O86-14 (Cl. 7.5.11), the maximum factored tensile force,Tr = φFtgAgφ : 0.9ftg : 15.3 MPaFtg = ftg(KDKHKScKT ) : 15.3 MPaAg = A : 143640 mm2Therefore, the factored tensile resistance is,Tr = 0.9×15.3×143640 = 1978 > 363.7596 kN (Table 4.7)57Design against Bending Moment:According to CSA O86-14 (Cl. 7.5.6.5.1), the factored bending moment resistance, Mrshall be taken as the minimum of Mr1 or Mr2, as followsMr1 = φFbSKX KZbgMr2 = φFbSKX KLX-X axis:φ : 0.9Fb = fb(KDKHKSbKT ) : 14.0 MPaS = Sx : 1.0917×107 mm3KX = Curvature factor = 1.0 (Cl. 7.5.6.5.2 of CSA O86-14)KZbg =(130b)0.1(610d)0.1(9100L)0.1=(130315)0.1(610456)0.1(91004035)0.1 = 1.02CB (=√Led/b2) :√1.92×4035×456/3152 = 5.97 ¡10KL : 1.00The bending moment resistance is,The bending moment resistance, Mr = min(Mr1,Mr2)Mr = 0.9×14.0×1.0917×107×1.0×min(1.02,1)/106 = 138 kN-mFactored bending moment resistance (Mr) = 138 kN-m ¿ 55.4571 kN-m (Table 4.7)Y-Y axis:φ : 0.9Fb = fb(KDKHKSbKT ) : 14.0 MPaS = Sy : 7.5411×106 mm3KX = Curvature factor = 1.0 (Cl. 7.5.6.5.2 of CSA O86-14)KZbg =(130b)0.1(610d)0.1(9100L)0.1 = (130315)0.1(610456)0.1(91004035)0.1 = 1.02CB (=√Led/b2) :√1.92×4035×456/3152 = 5.97 ¡10KL : 1.00The bending moment resistance, Mr = min(Mr1,Mr2)Mr = 0.9×14.0×7.5411×106×1.0×min(1.02,1)/10(6) = 95 kN-mFactored bending moment resistance (Mr) = 95 kN-m ¿ 0 kN-m (Table 4.7)58Design against Shear:According to CSA O86-14 (Cl. 7.5.7.2), the factored shear resistance, Vr is given byVr = φFv2Ag3φ : 0.9Fv = fv(KDKHKSvKT ) : 2.0 MPaAg = A : 143640 mm2The factored resistance is,Vr = 0.9×2.0× 2×1436403 = 172 kN > 30.3875 kNDesign against combined Bending Moment and Axial Load:Members subject to combined bending and compressive or tensile axial loads shall bedesigned to satisfy the appropriate interaction equation,(PfPr)2+M fMr[11− PfPE]≤ 1TfTr+M fMr≤ 1Pf (Compressive load) : 0 kNPr (Compressive resistance) : 2090 kNM f (Factored bending moment) :M f ,x = 55.4571 kN-mM f ,y = 0 kN-mMr (Factored bending moment resis-tance):Mr,x = 138 kN-mMr,y = 95 kN-mTf (Tensile load) : 363.7596 kNTr (Tensile resistance) : 1978 kNPE = Euler buckling load in the plane of the applied moment,PE,x =π2E05KSE KT IxL2e= 1.130×104 kNPE,y =π2E05KSE KT IyL2e= 5.394×103 kN(PfPr)2+M f ,xMr,x[11− PfPE,x]+M f ,yMr,y[11− PfPE,y]=(02090)2+55.5138[11− 01.13×104]+095[11− 05.39×103]= 0.40 < 1.0TfTr+M f ,xMr,x+M f ,yMr,y=3641978+55.5138+095= 0.59 < 1.0Final Cross-section:Thus, DFL 16c-E Glulam column of 315 mm × 456 mm is adequate.59Design of Glulam Braces for Lateral LoadsThe force in braces are obtained from the ETABS model. The design calculationsprovided in this section are for the most critical case only. Checks for all cases aresimilarly carried out. The design values for braces are obtained from ETABS asgiven below:Table 4.7: Maximum design loads in Gravity Glulam Columns (Floor no. 1to 12)Vf M f ,x M f ,y N f ,comp N f ,ten(kN) (kN-m) (kN-m) (kN) (kN)0.3595 0 0 192.4581 0Material Properties:Grade for glulam column is selected as Wood species DFL 16c-E. The properties ofthis grade of timber are given by Table 7.3 of CSA O86-14.Modulus of elasticity (E) : 12400 MPaStrength in compression parallel tograin ( fc): 30.2 MPaStrength in tension parallel to grain atgross section ( ftg): 15.3 MPaStrength in bending ( fb) : 14.0 MPaLongitudinal shear ( fv) : 2.0 MPaCross-sectional Properties:Consider Wood species DFL 16c-E glulam column : 175 mm × 190 mm.Area of the column (A = bd) : 175 × 190 = 33250 mm2Moment of inertia (I) :Ix = bd312 = 1.0003×108 mm4Iy = db312 = 8.4857×107 mm4Section modulus (S) :Sx = bd26 = 1.0529×106 mm3Sy = db26 = 9.6979×105 mm360Design against Compression Loads:Unbraced length of column (L) : 4.035 mAs the column is pinned supported at both ends,Effective length factor (Ke) : 1.2 (Table A.6.5.6.1 of CSA O86-14)Effective length (Le = KeL) : 4.842 mSlenderness ratio (Cc) : 4.035 / 0.175 = 23.1 < 50According to CSA O86-14 (Cl. 7.5.8.4.2), the factored compressive resistance parallelto grain, Pr = φFcAKZcgKC.φ : 0.8fc : 30.2 MPaKD : 1.0 (Table 5.3.2.2 of CSA O86-14)KH : 1.0 (Cl. 7.4.3 of CSA O86-14)KSc : 1.0 for dry service condition (Table 7.4.2 ofCSA O86-14)KSE : 1.0 for dry service condition (Table 7.4.2 ofCSA O86-14)KT : 1.0 treatment factor (Cl. 7.4.4 of CSA O86-14)Fc = fc(KDKHKScKT ) : 30.2 MPaVolume, Z = Lbd : 4.035 × 0.175 × 0.19 = 0.134 m3KZcg (min{0.68 (Z)−0.13,1}) : 0.68 ×(0.134)−0.13 = 0.883From Cl. 7.5.8.5 of CSA O86-14, the slenderness factor KC is given by,KC =[1.0+ FcKZcgC3c35(0.87E)KSE KT]−1=[1.0+ 30.2×0.883×23.1335×(0.87×12400×1.0×1.0]−1= 0.40Therefore, factored compressive resistance is,Pr = 0.8×30.2×33250×0.883×0.40 = 284.2 > 192.5 kN (Table 4.7)Design against Tensile Loads:According to CSA O86-14 (Cl. 7.5.11), the maximum factored tensile force,Tr = φFtgAgφ : 0.9ftg : 15.3 MPaFtg = ftg(KDKHKScKT ) : 15.3 MPaAg = A : 33250 mm2Therefore, the factored tensile resistance is,Tr = 0.9×15.3×33250 = 458 > 0 kN (Table 4.7)61Design against Bending Moment:According to CSA O86-14 (Cl. 7.5.6.5.1), the factored bending moment resistance, Mrshall be taken as the minimum of Mr1 or Mr2, as followsMr1 = φFbSKX KZbgMr2 = φFbSKX KLX-X axis:φ : 0.9Fb = fb(KDKHKSbKT ) : 14.0 MPaS = Sx : 1.0529×106 mm3KX = Curvature factor = 1.0 (Cl. 7.5.6.5.2 of CSA O86-14)KZbg =(130b)0.1(610d)0.1(9100L)0.1=(130175)0.1(610190)0.1(91004035)0.1 = 1.18CB (=√Led/b2) :√1.92×4035×190/1752 = 6.93 ¡10KL : 1.00The bending moment resistance is,The bending moment resistance, Mr = min(Mr1,Mr2)Mr = 0.9×14.0×1.0529×106×1.0×min(1.18,1)/106 = 13 kN-mFactored bending moment resistance (Mr) = 13 kN-m ¿ 0 kN-m (Table 4.7)Y-Y axis:φ : 0.9Fb = fb(KDKHKSbKT ) : 14.0 MPaS = Sy : 9.6979×105 mm3KX = Curvature factor = 1.0 (Cl. 7.5.6.5.2 of CSA O86-14)KZbg =(130b)0.1(610d)0.1(9100L)0.1 = (130175)0.1(610190)0.1(91004035)0.1 = 1.18CB (=√Led/b2) :√1.92×4035×190/1752 = 6.93 ¡10KL : 1.00The bending moment resistance, Mr = min(Mr1,Mr2)Mr = 0.9×14.0×9.6979×105×1.0×min(1.18,1)/10(6) = 12 kN-mFactored bending moment resistance (Mr) = 12 kN-m ¿ 0 kN-m (Table 4.7)62Design against Shear:According to CSA O86-14 (Cl. 7.5.7.2), the factored shear resistance, Vr is given byVr = φFv2Ag3φ : 0.9Fv = fv(KDKHKSvKT ) : 2.0 MPaAg = A : 33250 mm2The factored resistance is,Vr = 0.9×2.0× 2×332503 = 40 kN > 0.3595 kNDesign against combined Bending Moment and Axial Load:Members subject to combined bending and compressive or tensile axial loads shall bedesigned to satisfy the appropriate interaction equation,(PfPr)2+M fMr[11− PfPE]≤ 1TfTr+M fMr≤ 1Pf (Compressive load) : 192 kNPr (Compressive resistance) : 284 kNM f (Factored bending moment) :M f ,x = 0 kN-mM f ,y = 0 kN-mMr (Factored bending moment resis-tance):Mr,x = 13 kN-mMr,y = 12 kN-mTf (Tensile load) : 0 kNTr (Tensile resistance) : 458 kNPE = Euler buckling load in the plane of the applied moment,PE,x =π2E05KSE KT IxL2e= 4.543×102 kNPE,y =π2E05KSE KT IyL2e= 3.854×102 kN(PfPr)2+M f ,xMr,x[11− PfPE,x]+M f ,yMr,y[11− PfPE,y]=(192284)2+013[11− 1924.54×102]+012[11− 1923.85×102]= 0.46 < 1.0TfTr+M f ,xMr,x+M f ,yMr,y=0458+013+012= 0.00 < 1.0Final Cross-section:Thus, DFL 16c-E Glulam column of 175 mm × 190 mm is adequate.63Table 4.8: Column, beam and brace design summaryStory no. Column Design(mm)Beam Design(mm)Brace design(mm)Gravity load design1,2,3,4,5,6 315×456 215×342Seismic force resisting system1,2,3,4,5,6 315×456 215×342 175×1904.2.4 Design of Dissipative Bracing SystemThe dissipative bracing system consisted of timber braces made of Glulam gradeDFL 16c-E in series with two U-shaped Flexural Plates dampers of C60 steel type[36]. The dissipators are designed using stiffness and force damand on the dissi-pative bracing system. These values are detailed in table 4.2 and can be obtainedusing method detailed in section 3.24.2.5 Design of Post-tensioningUnlike BRB-glulam frame which does not have moment carrying capacity at thebeam-column joints [39], glulam frame fitted with dissipative bracing system [96]is a moment-resisting frame and has moment demand on its beam-column joints.After analysis in ETABS, the moment demands at all the beam-column joints wereobtained, and critical values at each storey extracted. A summary of the criticalmoment demand at the different stories is shown in the table 4.9. The joints weredesigned using the Modified Monolithic Beam Analogy (MMBA) and a design mo-ment of 133.33 kNm was obtained as the design moment for the joints. A momentrotation relationship was developed for the beam column joint consisting primarilyof three sections - Before decompression, after decompression but before yieldingof the timber in compression and after yielding of the timber in compression. Thethree zones use prestressing forces 0.7 fpy, fpy, and fpu, respectively. The largestmoment demand at the joints obtained from the analysis of the frame using ETABSis used as the critical moment demand for the design of the beam-colmn joints in64the frame. This value is taken as 120 kNm. A 7 wire strand post-tensioning cablewith minimum ultimate strength of 2060 MPa and minimum yield strength of 1770MPa and having a diameter and cross-sectional area of 27.9 mm (1.1”) and 625mm2respectively was used. As a single post-tensioning tendon of any given dimensionor strength was unable to supply the moment demand at the design rotation, twotendons were placed in parallel to provide the design moment demand.As the dimension of the internal and external bays differ, the moment-rotationresponse of the beam-column joints in the internal and external joints also differ.Both responses were modeled analytically and numerically using the same materialmodels in OpenSees and is depicted in figure 4.4-300-200-1000100200300-0.15 -0.1 -0.05 0 0.05 0.1 0.15Rotation (Rads)Moment (kNm)Beam-Column Joint ResponseInternal Bay Beam-Column Joint ResponseExternal Bay Beam-Column Joint ResponseFigure 4.4: Hysteretic behaviour of analytical and nonlinear OpenSees nu-merical model for internal and external beam-column joints of the masstimber moment resisting frame fitted with dissipative bracing65Table 4.9: Moment demand at beam-column jointsStoryNo.Mi(kNm)6 33.635 77.504 100.003 114.502 120.101 115.00Base 554.3 Non-linear Structural Modelling of the 6-storey MassTimber FrameA regular 6-storey, 3-bay mass timber moment resisting frame symmetric in both xand y axes, and fitted with dissipative bracing system, was modelled in OpenSeessoftware. The OpenSees is a script-based software framework used for investigat-ing the behaviour of structural and geotechnical systems when subjected to a widerange of static and dynamic loads. The building was modelled as a 2-dimensionalstructure and torsional effects were ignored both in analysis and design due to sym-metry in the building plan.A phenomenological model (lumped plasticity model) was used to representthe 6-storey moment resisting frame in OpenSees, as this gives a fairly accuraterepresentation of the response of the structure under several kinds of loading whilesimultaneously requiring less computational time. Lumped plasticity models takeadvantage of results from experimental data and thus account for complex interac-tions which are not easily modelled in isolation e.g. bar pull-out, strain penetration,etc. The concentrated/lumped plasticity model was used and details of the mod-elling can be found in the sections below.664.3.1 Modelling of Structural Frame ElementsThe six-storey moment resisting mass timber frame with dissipative bracing wasmodelled in OpenSees as a 2D system with three degrees of freedom - displacementalong x, displacement along y, and rotation about z. The model employs a leaningcolumn to account for P-Delta effects.The beams, columns and braces were modelled using linear elasticBeamColumnelement - whose compulsory arguments are only the cross-sectional area, Young’smodulus and second moment of area about the Z axis, while a non-linear zerolength element which is a parallel combination of two rotational springs - linearelastic (joint panel) and multilinear elastic (post-tensioning tendons) - accountedfor the behaviour of the beam-column joint. This element is defined by 2 nodesat the same location connected by 2 uniaxial material objects representing themoment-rotation relationship of the element as can be observed from figure 4.5.The modulus of elasticity for timber used is 12400 MPa, and the yield strength ofthe post-tensioning tendon used is 1770 MPa. The leaning column was also mod-elled using elasticbeamcolumn element, but was connected to the beam byhorizontal trusses.19Figure 4.5: Schematic sub-assembly of the nonlinear structural model for themass timber moment resisting frame fitted with dissipative bracingThe frame was subjected to gravity analysis, modal analysis, and static pushover67analysis from which the periods and pushover curve of the building were obtained.These values were used in the non-linear analysis of the structure.4.3.2 Foundation ModellingThe moment capacity of the base of the first floor column of the structure inves-tigated in this study is 55 kNm as can be seen from table 4.9. This is modelledusing non-linear parallel rotational springs as described by Ponzo et al. in [95].The capacity of the base of the column investigated by Ponzo et al. in [95, 96]is23 kNm. As such, the numerical model for the structure investigated in this studyis obtained by applying a factor of 2.5 on the stiffness and moment capacity of thenumerical model discussed by Ponzo in his work [95], which was calibrated usingan experimental model.4.3.3 Modelling of Dissipative Bracing SystemThe dissipative bracing system was modelled as a series connection of a truss ele-ment and a zero-length element. The truss arguments needed to define the truss el-ement are the cross-sectional area of the timber - which is obtained from the framedesign as described in section 4.2.3 - and the material model used, which in thiscase is the linear elastic material model. The zero-length element used was mod-elled using steel02 material model which described the hysteretic response ofthe UFP dampers which provided energy dissipation for the system. The argumentsrequired to define the steel02 are the yield strength of the steel, its stiffness, andits post-yield stiffness ratio. The values for yield strength and stiffness can be ob-tained from the design section 4.2.2 above, while the post-yielding stiffness ratio istaken as 0.08. On each floor, the bracing was fixed to the beam below it using thefix command in OpenSees, and the top of the bracing was connected to the abovebeam through the UFP dampers as shown in figure 4.5.4.3.4 Modelling of Post-tensioned Beam Column JointThe post-tensioned beam-column joints were modelled using two zero-length rota-tional spring elements connected in series containing linear elastic and multilinear-elastic material models to replicate the behaviours of the joint panel and post-68tensioning tendons respectively. The values inputed in the material models are themoment-rotation values obtained from the design of the beam-column joint usingMMBA procedure.4.4 Seismic hazard and GM selection per NBCC 20204.4.1 Seismic hazardFrom what it used to be in 2015, the seismic hazard model of Canada has been up-dated in 2020. This 6th generation seismic hazard model is constituted by a 25-50percent increase in seismic hazard [88]. The figure 4.3 shows the response spec-trum of Vancouver corresponding to 2% in 50 year return period. For the structureunder consideration in this chapter, its fundamental first mode period is 2.81 sec-onds, and has a corresponding spectral acceleration value of 0.175g. Figure 4.6ashows the hazard curve for the Vancouver site (49◦15′00′′ N, 123◦7′12′′ W) withan average shear wave velocity to 30 m depth, Vs30 = 450 m/s. The hazard curveis shown for the intensity measure, Sa(3.0 s) i.e., the spectral acceleration corre-sponding to the first mode. The deaggregation results for Sa(3.0 s) correspondingto a 2475 year return period is shown in Figure 4.6b. Three contributing tectonicregimes are considered for southwestern British Columbia [114, 121] - Active shal-low crust, subduction interface and in-slab(source id- IntraSlab55).050 9101550 8Distance (km)100Magnitude7150200 62505300Figure 4.6: PSHA results based on the NBCC 2020 seismic hazard model (a)Seismic hazard curve and (b) deaggregation based on Sa(3.0s) for theVancouver site694.4.2 Hazard-consistent ground motion selectionGround motion records were selected to depict the tectonic characteristics of south-western British Columbia. Investigated in this study are a number of site- andstructure-specific conditional spectra (CS). The conditional mean spectrum (CS),which is specific to a tectonic regime, includes the mean and covariance betweenseveral spectral ordinates [10]. The CMS accounts for the conditionality of spectralordinates by defining the parameter ε , as follows:ε(T ∗) =lnSa(T ∗)−µlnSa(T ∗)σlnSa(T ∗), (4.1)where Sa(·) is the spectral acceleration; T ∗ is the conditioning period; and µlnSa(·)and σlnSa(·) are obtained from a suitable ground motion model for deaggaregtedmagnitude-distance (M,R). Further, the CMS is expressed as:ln[Sa(T )|Sa(T ∗)] = µlnSa(T )+ρε(T ),ε(T ∗)σlnSa(T )ε(T ∗), (4.2)where ρε(T ),ε(T ∗) is the correlation coefficient between Sa(T ) and Sa(T ∗).Table 4.10 shows the modal earthquake tuples (M,R)with the highest contribu-tion for each tectonic regime using SHM6. The corresponding deaggregation wasshown earlier in Figure 4.6b. The table also lists the spectral shape at 3.0 s for eachtectonic regime. The ground motion models for each tectonic regime is selectedfrom the corresponding logic tree of the tectonic regime used during ProbabilisticSeismic Hazard Analysis (PSHA).Figure 4.7 shows the results of the ground motion selection based on the targetCS. Each tectonic regime’s contribution to the site hazard is directly correlated withthe quantity of records from that regime used in the non-linear dynamic analysisof the model under consideration. Thus, there are 12 Active Surface Crust, 11Subduction, and 7 In-Slab records. The NGA West-2 database [5] has been usedfor crustal and in-slab records, whereas the KiK-net database [83] has been used forthe subduction records. The Vs30 values are between 300 and 600 m/s. Figure 4.7b–c show the target and achieved mean and dispersion of the three conditional spectra.A computationally-efficient algorithm is employed to select the ground mo-tion suite [60]. The scaling factor is limited to 5 [121]. Further, a restriction of70Table 4.10: Spectral value and deaggregation tuples for contributing tectonicregime for Vancouver site and Sa(3.0 s) corresponding to a return pe-riod of 2475 years.T Deaggregation Parameters Active SurfaceCrustSubduction Inslab Total3.00sContribution 44.00% 40.00% 16.00% 100%No. of GMs 11.00 10.00 4.00 25Adjusted No. of GMs 12 11 7 30Magnitudes 7.35 8.85 7.45Distance 10 150 50RJB > 20 km is imposed to exclude near-field records. A maximum magnitude dif-ference of 1.5 from the modal magnitude is allowed. The Vs30 values are between300 and 600 m/s. Figure 4.7b–c show the target and achieved mean and disper-sion of the three conditional spectra. An excellent match reflects the versatility ofthe considered database and selection algorithm. The seismic harzard, deaggre-gation plot, and ground motion selection was achieved using a tool developed byTesfamariam et. al in 2023 [119]Figure 4.7: Scaled selected records targeted at the hazard and deaggregationcorresponding to the Vancouver site. (a) Pseudo-response spectra ofindividual records. Thick broken lines mark the 97.5%ile and 2.5%ilevalues, (b) target conditional mean for the three tectonic regimes and (c)target log-standard deviation for the conditional spectra. The condition-ing period is 3.0 s.714.5 Results4.5.1 Pushover analysisThis is a type of nonlinear static analysis used to evaluate the seismic performanceof a structure. It involves applying a series of increasing lateral load distributionproportional to the modal shape of the structure - in this case, linear - to a systemand analyzing the resulting deformation and internal forces. It is a simplified ap-proach to modeling the nonlinear behavior of a structure under seismic loading,and is based on the assumption that the structure’s behavior can be represented bya single mode of deformation, which is usually the first mode.The figure 4.8 shows the pushover and cyclic pushover curves for the 6 storeypost-tensioned timber frame fitted with dissipative bracing systems. For the pushovercurve, the base shear at 2.5% drift is about 450 kN which tallies with the designvalue from the DDBD procedure outlined in section 4.2 - 434.8 kN. The backboneof the cyclic pushover curve is identical to that of the static pushover curve. Italso shows the amount of energy dissipated in the system as well as some level ofrecentering.01002003004005006007008000 0.01 0.02 0.03 0.04 0.05Base Shear (kN)Roof Drift RatioPushover Curve-800-600-400-2000200400600800-0.05 -0.03 -0.01 0.01 0.03 0.05Base Shear (kN)Roof Drift RatioCyclic Pushover Curve(a) (b)Figure 4.8: (a) Static pushover curve for post-tensioned timber frame fittedwith dissipative bracing system (b) Cyclic pushover curve for post-tensioned timber frame with dissipative bracing systemA brief summary of the DDBD procedure used by Ponzo et al. for the frameunder consideration is also outlined in section 4.1.1 and in the figure 4.1724.5.2 Maximum and Residual Inter-storey Drift RatiosMaximum Interstory Drift Ratio (MIDR) is a measure of the amount of lateraldeformation or movement that can occur between adjacent floors of a buildingduring a seismic event. Mathematically, it is the ratio of the displacement betweenthe two adjacent floors divided by the height of the story. The maximum interstorydrift ratio is a limit that is commonly used in seismic design to ensure that thebuilding’s deformation during an earthquake is within acceptable limits. The limitvaries depending on the building’s occupancy type, height, and seismic zone. thestructural system under investigation in this study has a target maximum interstoreydrift ratio of 2.5% which corresponds to the life safety limit state. A set of 60bi-directional ground motion records were selected as described in section 4.4.2were used to carry out non-linear time history analysis on the structure and themaximum interstorey drift ratio on each floor for each of the 60 ground motionrecords is recorded and plotted as shown in figure 4.9. The average MISR for allfloors is also plotted and highlighted in blue. The average MIDR does not exceed2.5% for any floor, as such, the structural system successfully passes this designconstraint. Exceeding the maximum interstory drift ratio during an earthquake canresult in significant damage to the building and compromise its structural integrity,leading to potential collapse.Residual Interstory Drift Ratio (RIDR) is a measure of the amount of interstorydrift that remains in a building after an earthquake or other lateral load event. It isthe difference between the maximum interstory drift ratio experienced during theevent and the amount of drift that is recovered or dissipated over time. This is animportant parameter in evaluating the seismic performance of buildings becauseit can indicate the extent of damage that has occurred and the potential for futuredamage during subsequent earthquakes. If the RIDR is high, it suggests that thebuilding has suffered significant damage and may not be able to withstand futureseismic events. On the other hand, a low RIDR indicates that the building has per-formed well and has the potential to resist future earthquakes. The target RIDR forthe structure under consideration here is 0.1% which was achieved after Non-lineartime history analysis was carried out on the structure using 60 bi-directional care-fully selected ground motion records. Therefore, the building exhibits satisfactory73performance.0 1.25 2.5 3.75 5MaxISDR (%)246Story0 0.2 0.4 0.6 0.8 1ResISDR (%)Figure 4.9: (a) Maximum ISDR (b) Residual ISDR4.5.3 Incremental Dynamic AnalysisThis is a very helpful procedure to aid the examination of the range of behaviourof a structure when subjected to a suite of possible earthquake ground motions.Similar to static pushover analysis where a series of steadily increasing lateral loadsare imposed on a structure in order to observe its range of behaviour from elastic, toinelastic, and finally failure, IDA involves subjecting a structure to a series of scaledaccelerograms so as to examine the range of possible behaviours of the structurefrom elastic, to inelastic, and finally, to the onset of dynamic instability (rangeof rapidly increasing deformations for very infinitesimal increases in monotonicscalable ground motion intensity measures [123]). This is achieved by scaling upthe intensities of the earthquake load.After IDA, a predetermined Damage measure (DM) is examined from the re-sults to ascertain the behaviour of the structure [123]. Also, two or more DMs canbe decided upon in order to investigate the different behaviours of the building. For74this system, inter-storey drift ratio is chosen as the damage measure, and the limitstate considered is life safety limit state which corresponds to 2.5% ISDR.Maximum inter-storey drift ratio for the 6-storey post-tensioned mass timberframe was obtained after non-linear dynamic analysis, and the results of the IDAcarried out are shown in the figure21Objective 3: Seismic Performance AssessmentIDA Curve Fragility CurvePcol <5%CMR = 1.43Figure 4.10: (a) IDA for A 6-storey post-tensioned mass timber frame fittedwith dissipative bracing system. (b) Fragility curve for the 6 storeypost-tensioned mass timber frame fitted with dissipative bracing sys-temEvery point on the figure corresponds to the ISDR demand imposed on thestructure by a given ground motion record at different intensities [123]For most of the ground motion records, the structure exhibits linear behaviourup until the onset of dynamic instability at approximately 5% drift. Thus, followingthe equal displacement rule - For structures with moderate periods, the global in-elastic displacements remain fairly the same with displacements of correspondingelastic models [125]. Only for very few ground motion records did the structurereach dynamic instability before it was subjected to an intensity of ground shakingequal to the design value - 0.175g. For some other ground motion records, thesystem exhibits hardening rather than softening - a phenomenon where a structurerapidly and rather too quickly attains very high drifts from little to no increase inthe intensity of the ground motion - in the post elastic region up until the onset ofdynamic instability.75The IDA curves allow us to observe the range of possible behaviours of thestructure when subjected to a suite of ground motion records. It is also importantto note that it is the pattern and timing, not just the intensity of ground motion thatdictates the level of response of the structure [123]4.5.4 FRAGILITYFragility is a measure of the probability of a structure to reach or exceed a specificdamage state when subjected to various intensities of ground motion or other seis-mic demand parameters [11]. Obtaining the fragility curve involves estimation ofthe fragility function parameters which can be obtained via many methods - fieldobservations of damage, judgment, or static structural analyses, [11] But in thisthesis, the fragility function is derived from Dynamic structural Analysis (DSA)and is an important step in seismic risk assessment procedure.Using the empirical data from the IDA curves, a lognormal distribution is fittedto produce a collapse fragility for the structure under consideration. The fragilitycurve for the 6-storey moment-resisting timber frame fitted with dissipative brac-ing is shown in figure 4.10. The spectral acceleration corresponding to the firstmode Sa(2.81 s) is chosen as the intensity measure. The fragility function showsthat the seismic performance of this structural system is satisfactory, with a col-lapse capacity of approximately 5% This value favorably compares to the target of10% in code-compliant ordinary buildings based on ASCE 7 [6]. Accordingly, thecollapse margin ratio (CMR) defined as the ratio of median collapse capacity to theMCE level spectral acceleration is found to be 1.43. It is to be noted that a highrecentering ratio value βF results in higher collapse capacity. This can be attributedto the large hysteresis loops in the system.4.6 Chapter SummaryTimber is a desirable building material for structural systems due to a global pushfor environmentally sustainable construction. This has led to the development ofnovel structural timber-based archetypes to improve seismic performance in highseismic zones. Performance-based design methodologies are necessary for the de-sign of these novel archetypes until they are accommodated in design codes. Direct76Displacement-based design is a performance-based design methodology popular-ized by Priestly and Kowalsky [101].In this chapter, a Modified DDBD procedure proposed by Ponzo et al. in [96]is carried out on a post-tensioned mass timber building with dissipative bracingsystem to be located in Vancouver, Canada, with the aim of determining the seismicperformance of the building. The 6-storey building contains post-tensioning at thebeam-column joints to aid re-centering. It is also fitted with dissipative bracingsystem to enhance energy dissipation. For nonlinear response history analysis, aset of 60 bi-directional ground motion records representing the tectonic regimesof subduction, shallow crustal, and in-slab are chosen. The results show that thebuilding exhibits satisfactory seismic performance. The building has a base shearof about 435 kN and exhibits MIDR and RIDR within the design limits of 2.5%and 0.1% respectively. The building has a probability of collapse of less than 5%which is satisfactory and has a collapse margin ratio of 1.43.77Chapter 5Seismic collapse risk ofRC-timber hybrid building withdifferent energy dissipationconnections considering NBCC2020 hazardIf I have seen farther it is by standing on the shoulders of Giants.— Sir Isaac Newton (1855)5.1 IntroductionBuildings have become a key point of focus in establishing sustainable develop-ment goals meant to address the growing challenge of climate change [75]. Withrapid population growth in urban areas, non-traditional buildings such as thosewith hybrid structural systems are central to the development of sustainable in-frastructure. Over the past couple of decades, concrete and steel have becomethe materials of choice for the construction of civil infrastructure. With a ro-bust design methodology, traditional concrete and steel structures have dominatedthe construction market. However, with the focus shifting to environmentally78friendly and lightweight structures, timber is fast becoming a viable constructionmaterial [56]. One of the benefits of timber construction in seismic zones is itslightweight, which attracts smaller inertial forces when compared to concrete orsteel structures with the same size and complexity. Aside from being used as astand-alone material for building structural systems as permitted by the various de-sign codes, several hybrid-structural systems using timber have been investigated,e.g. [14, 45, 115–118, 120].Prescriptive design standards, based on a force-based methodology, utilize re-duction factors to account for inherent non-linearity in the structural systems [30].Several researchers have worked to develop the reduction factors for differenthybrid-structural systems [13, 38]. However, existing design codes do not pro-vide the reduction factors for emerging hybrid-structural systems, consequently,force-based design cannot readily be implemented. In an attempt to provide amore robust, accurate, and reliable design approach, the performance-based de-sign methodology was developed [31, 32, 97]. One variation of that methodologyis direct displacement-based design (DDBD) [101]. Starting with the design ofsimple concrete multi-span bridges and building frames [98], the DDBD has beenextensively applied to traditional and novel systems. Examples include structureswith passive energy dissipating devices [67], steel-timber hybrid buildings [14],frame-wall structures [85, 109], frame-wall structures with dissipators [111], struc-tures with seismic isolation systems [22], steel and RC moment-resisting frames[61, 77, 81], traditional light-frame timber structures [70], structures with flexi-ble bases [74], tall hybrid timber buildings [70], self-centering buckling-restrainedbraced frame structures [61, 68], base-isolated building structures [129], dual sys-tems [78], and structures with visco-elastic dampers [127]. Recent developmentshave paved the way for high-rise building design using the DDBD by addressingissues of the displacement profile [128], higher modes, and P-Delta effects [61, 81].An integral part of the DDBD method is estimating the equivalent viscousdamping (EVD) for different structural systems [12, 47]. Over the years, differentresearchers have sought to establish expressions for determining the EVD of differ-ent structural systems, e.g., Table ??. This was generally achieved by using resultsfrom a physical experiment to calibrate a numerical model, and then EVD-ductilityrelationships are developed for a large number of numerical models using an area-79based approach. The ductility, µ , is defined as the ratio of the maximum dis-placement to the yield displacement. In recent years, EVD expressions for hybridbuildings using timber and different dissipation mechanisms have been developed[4, 14, 16, 80, 91, 96, 124]. These studies will facilitate the design and widespreadacceptance of hybrid timber buildings. The present study adopts an RC-timber hy-brid building designed using the DDBD approach [118]. A maximum story driftratio (IDRmax) of 2.5% that corresponds to the collapse prevention limit state is tar-geted. The EVD for the RC-timber hybrid system was developed by Nielsen andImbeault [84]. The hybrid building system utilizes the high strength and stiffnesscharacteristics of the CLT to reduce the induced displacement of the structure andthe energy dissipating characteristics of the hysteretic connectors [65, 118].While it is important that sustainable alternatives to traditional structural sys-tems be developed, attention must be paid to their seismic collapse risk to ensureadequate life safety performance. As such, seismic collapse risk assessment ofbuildings has gained attention [62]. In the present study, the collapse capacity ofthe RC-CLT building reported in [118] is assessed using nonlinear time-historyanalysis. The effects of the energy dissipation devices have been studied by con-sidering an alternative flag-shaped dissipator which has gained widespread inter-est in the last two decades [2, 8, 25, 26, 28, 29]. The hybrid building reported inTesfamariam et al. [118] was designed with the NBCC 2015 [19] seismic hazard.With the newly released updated NBCC 2020 [20] hazard model, it is postulatedthat substantial changes in the seismic hazard will have an impact on the design ofnew buildings and assessment of existing ones, especially in regions with very highseismicity, such as southwestern British Columbia. The seismic hazard of the se-lected Vancouver, British Columbia site, is affected by the interaction of three tec-tonic regimes, viz., Subduction, Shallow Crustal, and In-slab. A hazard-consistent40-paired ground motion records, representing the complex seismicity of Vancou-ver, is selected for nonlinear response history analysis of the hybrid building sys-tem.The present study has three primary contributions—(i) a rigorous ground mo-tion record selection consistent with the complex seismicity of Southwestern BritishColumbia is performed. The record selection follows the latest seismic hazardmodel per NBCC 2020 [20]. (ii) The seismic collapse assessment of an innovative80RC-CLT building system designed using DDBD is assessed, and (iii) the effectsof alternative energy dissipators on collapse capacity and residual deformation areinvestigated.5.2 Design details of the RC-CLT hybrid building withsteel slit dampersA regular 6-story, 3-bay RC moment resisting frame with CLT infill designed byTesfamariam et al. [118] has been considered for the seismic performance assess-ment. The building is 24 m × 42 m in plan with the longer direction having 7 bayseach with a length of 6 m. Figure 5.2 shows the elevation along the shorter andmore critical direction. The CLT infill is a three-ply panel that is 99 mm thick,comprised of three 33 mm thick laminae that are fused together. The CLT infillwas designed with some clearance to the RC frame to avoid shear (brittle) fail-ure in the RC columns due to their interaction [86]. Slit dampers [65] at the topof the CLT infill were provided as an additional energy dissipation mechanism.The steel slit dampers are associated with large hysteretic loops leading to highenergy-dissipation capacity. Given the novel structural system, the RC-CLT build-ing was designed using the DDBD. The target was set to a maximum inter-storydrift IDRmax of 2.5% corresponding to 2% probability of exceedance in 50 years,for the NBCC 2015 hazard level [19].Figure 5.1 summarizes the DDBD procedure as follows:1. Develop the design displacement profile.2. Determine the characteristics of the equivalent single degree of freedom sys-tem.3. Determine the design ductility.4. Estimate the Equivalent Viscous Damping5. Determine the effective period, stiffness and base shear.6. Perform structural analysis and member design.7. Calculate the stiffness of each story.81~~y dFuFyrKiKi Keμ𝜼 =𝟏𝟎𝟓 + 𝝃𝒆𝒒𝑽𝒃 = 𝑲𝒆𝜟𝒅𝑭𝒊 = 𝑽𝒃𝒎𝒊𝜟𝒊∑ (𝒎𝒊𝜟𝒊)𝒏𝒊ୀ𝟏𝐹௜(a)(f)(e)(d)(c)(b)dme HeFigure 5.1: DDBD procedure: (a) Structure description, (b) EquivalentSDOF system and its displaced shape, (c) Bi-linear force-displacementrelationship of the SDOF system, (d) EVD-µ relationship for the differ-ent structural types, (e) Displacement response spectra, and (f) Distri-bution of the seismic design load along the building height.8. Calculate the equivalent stiffness of the CLT and dampers.9. Calculate the number of dampers required for each story.10. Design and validate the structure.A more detailed DDBD procedure for the RC-timber hybrid building is describedin the previous chapter and in Tesfamariam et al. [118]. The elevation of thehybrid building is shown in Figure 5.2. It is noted that the length of the CLT infilland the number of slit dissipators are optimized during the design. A summary ofthe results from the design is given in Table 5.1. All beams are 450 mm× 350 mmin size. The design is governed by the connection with the slit damper and gravityloads on each floor.82DL = 2.0 kPaLLAll floors = 2.4 kPaLL6m-bay = 4.8 kPaLLroof = 2.2 kPaLLroof (6m-bay) = 2.2 kPa9 m 6 m 9 mBABA6 ×3.65 m = 21.9 mWidthDepthSection B-BSection A-AWidthDepthC1C2 C2C1Figure 5.2: Details of the six-story RC-CLT hybrid building [118].Table 5.1: Design summary for 6-story RC-CLT hybrid building.Story Columnsize (mm2)ρb,top ρb,bot ρC1 ρC2 No. ofdampersLCLT (m)6 300×300 2-20M 2-20M 4-25M 4-20M 2 15 300×300 2-20M 2-20M 4-25M 4-20M 2 14 300×300 2-20M 2-20M 6-25M 6-20M 2 13 350×350 2-20M 3-20M 6-25M 6-20M 2 22 350×350 2-20M 3-20M 8-25M 6-25M 2 21 350×350 2-20M 3-20M 8-25M 6-25M 3 3ρb,top,ρb,bot : longitudinal reinforcement at top and bottom of beams;ρC1,ρC2: longitudinal reinforcement in column C1 and C2, respectively;LCLT : length of CLT infill wall.5.3 Nonlinear structural modeling of the RC-CLT hybridbuildingA two-dimensional nonlinear model was considered to be appropriate due to theregularity of the hybrid building. Figure 5.3 provides a schematic representation ofthe key elements of the analytical model. A concentrated plasticity model is usedto capture the non-linearity in the RC frame. Marker 1 shows the modeling detailsof the RC frame whereas Marker 2 describes the details of the RC-CLT dissipator83connections. Different structural components are provided in the following subsec-tions. The P-Delta effects are captured using a leaning column [46]. 5% Rayleighdamping has been considered in the first and the third fundamental mode for all lin-ear elastic elements. Damping in the nonlinear elements has not been modeled asrecommended in the literature [23, 49, 130]. The eigenvalue analysis of the frameresulted in first, second, and third mode periods of 1.17, 0.40, and 0.25 seconds,respectively.Elastic beam-column elementPanel ZoneColumn-end ZoneBeam-end ZoneMulti-point constraints𝑀𝑦𝑀𝑐Basic Strength Det.Post-Capping Strength Det.Unload. Stiff. Det.𝑀𝑟 = 𝑘𝑀𝑦𝑀𝑦𝑀𝐶𝑀𝑟 = 𝑘𝑀𝑦Moment, 𝑀Chord Rotation, 𝜃𝜃𝑝 𝜃𝑝𝑐Deformation, 𝛿Force, 𝐹1Beam Beam nodeConnector nodeDissipatorEqual DOFCLTCLT nodes3-DOF system2-DOF system2Figure 5.3: Schematic sub-assembly of the nonlinear structural model forRC-CLT hybrid building system.5.3.1 CLT modelingThe three-ply 99 mm thick CLT infill panel is modeled using quad elements witha bilinear isoparametric finite element formulation. The CLT infill is formulatedassuming a plane stress condition due to the minimal out-of-the-plane stresses.Because of the connection detail and design of the hybrid building, the assignednDMaterial for the CLT elements are elastic with a modulus E, of 9.5 kN/mm2,and a Poisson’s ratio of 0.16. The CLT and RC frame are connected using steel-slit84-250-150-5050150250-40 -20 0 20 40Force (kN)Displacement (mm)ExperimentalNumerical𝑆𝑡𝑒𝑒𝑙 𝑠𝑙𝑖𝑡 𝑑𝑎𝑚𝑝𝑒𝑟(a)-250-150-5050150250-40 -20 0 20 40Force (kN)Displacement (mm)𝛽𝐹 = 0.8(b)-250-150-5050150250-40 -20 0 20 40Force (kN)Displacement (mm)𝛽𝐹 = 0.6(c)Figure 5.4: Cyclic responses of the (a) steel slit damper and (b, c) flag-shapeddampers with (b) βF = 0.8 and (c) βF = 0.6 obtained using OpenSees.For steel slit dampers, the comparison of experimental hysteretic re-sponse is also presented.dampers. The stiffness of the CLT, KCLT , is approximated as follows [50]:KCLT =12h33EAL +h1000G +hdL f, (5.1)where h, E, A, L, G, d, and f represent the CLT height, elastic modulus, cross-sectional area, wall length, shear modulus, thickness, and bearing capacity factorper CSA O86 [21], respectively.5.3.2 RC frame modelingThe modeling details of a typical RC beam-column joint are shown with Marker 1in Figure 5.3. The RC beam-column joints are designed and detailed to conformwith the highest ductility class specified in the Canadian standard [19]. Thus, flex-ural yielding is expected to precede shear failure. The RC members are modeledusing the hysteretic rules defined by the Ibarra–Medina–Krawinkler (IMK) model[54], which captures strength and stiffness degradation. The key points on thebackbone curve and cyclic deterioration constants are based on the semi-empiricalexpressions developed in the literature [51, 90]. The multi-point constraints for theRC joints are modeled using the joint2D element that incorporates a diagonalcompression strut mechanism [71] and a shear panel is used for the joint deforma-tion.855.3.3 RC-CLT-Damper modelingThe modeling details of the RC-CLT joint including the slit dampers on top ofthe CLT infill are shown with Marker 2 in Figure 5.3. The beam-column ele-ments have 3 degrees of freedom (ux, uy, rz) and the quad element has two (ux,uy). The two elements with different numbers of degrees of freedom are linkedusing connector nodes which are constrained using the equalDOF command. AtwoNodeLink element is used between the connector and RC beam nodes. Thebottom of the CLT infill is anchored to the RC beam by constraining the quad ele-ments at the base of each floor. Due to the dominance of flexural behavior (rz), thechord rotation is used as the deformation measure for the RC members, whereasthe displacement is used as the deformation measure for the energy dissipators dueto their point action along the translational direction (ux).Figure 5.5a shows an example calibration of the hysteretic response of the slitdamper using OpenSees [79], which is modeled using the RambergOsgoodSteeluniaxial material. The experimental data are taken from Lee et al. [65]. Thecalibrated parameters for the RambergOsgoodSteel material are: the yieldstrength Fy = 140 kN, initial elastic modulus E0 = 70 kN/mm, yield offset a =0.002, and the parameter to control the transition from elastic to plastic responsen = 13. Similarly, Figures 5.5b–c show the numerical response of the flag-shapeddampers. Two recentering ratio values, βF = 0.8 and βF = 0.6, have been con-sidered. These values are based on relevant experimental studies [96]. The flag-shaped dampers are modeled using the SelfCentering uniaxial material inOpenSees. In the absence of experimental results for the flag-shaped dampers ofequivalent strength, their key parameters are selected such that the peak strengthand deformation capacity closely resemble that of the steel slit dampers. Nonlinearstatic analyses of these systems are used to confirm this design choice. The adoptedparameters for flag-shaped dissipators are: the forward activation strength Fa = 130kN, initial stiffness k1 = 61.9 kN/mm (corresponding to 2.1 mm of deformation atactivation strength), and post-activation stiffness k2 = 0.03k1.865.4 Seismic hazard and GM selection per NBCC 20205.4.1 Seismic hazardThe 6th generation seismic hazard model (SHM6) described in the NBCC 2020[20] represents a comprehensive change over the NBCC 2015 [19]. Figure 5.6ashows the change in short period seismic hazard for several locations in Canada,from East to West. Such an increment of 25–50% is expected to impact the de-sign and performance assessment of Canadian buildings, especially in regions withvery high seismicity such as southwestern British Columbia. Figure 5.6b showsthe response spectrum for Vancouver corresponding to the 2% in 50 year returnperiod. However, it is noted that for the period of interest in the present study (firstnatural period of the CLT-RC hybrid building, T1 = 1.17s), the two hazard modelsincidentally have approximately the same spectral acceleration value. Figure 5.7ashows the hazard hazard curve for the Vancouver site (49◦15′00′′ N, 123◦7′12′′ W)with an average shear wave velocity to 30 m depth, Vs30 = 450 m/s. The hazardcurve is shown for the intensity measure, Sa(1.17 s) i.e., the spectral accelerationcorresponding to the first mode. The deaggregation results for Sa(1.17 s) corre-sponding to a 2475 year return period is shown in Figure 5.7b. Three contributingtectonic regimes are considered for southwestern British Columbia [114, 121]. Forthe present hazard, their contributions are 41% for Active Shallow Crust, 32% forSubduction Interface, and 27% for In-Slab (source id- IntraSlab55).-250-150-5050150250-40 -20 0 20 40Force (kN)Displacement (mm)ExperimentalNumerical𝑆𝑡𝑒𝑒𝑙 𝑠𝑙𝑖𝑡 𝑑𝑎𝑚𝑝𝑒𝑟(a)-250-150-5050150250-40 -20 0 20 40Force (kN)Displacement (mm)𝛽𝐹 = 0.8(b)-250-150-5050150250-40 -20 0 20 40Force (kN)Displacement (mm)𝛽𝐹 = 0.6(c)Figure 5.5: Cyclic responses of the (a) steel slit damper and (b, c) flag-shapeddampers with (b) βF = 0.8 and (c) βF = 0.6 obtained using OpenSees.For steel slit dampers, the comparison of experimental hysteretic re-sponse is also presented.87025507510012500.511.522.5% Change Sa(0.2) (g)NBCC 2015 NBCC 2020 % Change(a)0 1 2 3 4 500.20.40.60.811.2NBCC 2015NBCC 2020(b)Figure 5.6: (a) Change in seismic hazard from NBCC 2015 to NBCC 2020for selected locations in Canada, from east to west. Intensity measure-Sa(0.2); Return Period- 2475 year; Site Class- C (Vs30 = 450 m/s). (b)Response spectrum for Vancouver based on the NBCC 2015 and NBCC2020 seismic hazard models.10-2 10-1 10010-710-510-310-1(a)05Contribution to Hazard (%)0 91050 8100 7150 200 6250 5300(b)Figure 5.7: PSHA results based on the NBCC 2020 seismic hazard model.(a) Seismic hazard curve and (b) deaggregation based on Sa(1.17 s) forthe Vancouver site.5.4.2 Hazard-consistent ground motion selectionThe ground motion selection is conducted to represent the complex tectonic featureof southwestern British Columbia. A series of site- and structure-specific condi-tional spectra (CS) is considered. Specific to a tectonic regime, the CS includes themean (known as, conditional mean spectrum, CMS) and covariance between dif-ferent spectral ordinates [10]. The CMS accounts for the conditionality of spectral88ordinates by defining the parameter ε , as follows:ε(T ∗) =lnSa(T ∗)−µlnSa(T ∗)σlnSa(T ∗), (5.2)where Sa(·) is the spectral acceleration; T ∗ is the conditioning period; and µlnSa(·)and σlnSa(·) are obtained from a suitable ground motion model for deaggaregtedmagnitude-distance (M,R). Further, the CMS is expressed as:ln[Sa(T )|Sa(T ∗)] = µlnSa(T )+ρε(T ),ε(T ∗)σlnSa(T )ε(T ∗), (5.3)where ρε(T ),ε(T ∗) is the correlation coefficient between Sa(T ) and Sa(T ∗).Table 5.2 shows the modal earthquake tuples (M,R) with the highest contri-bution for each tectonic regime using SHM6. The corresponding deaggregationwas shown earlier in Figure 5.7b. The table also lists the spectral shape at 1.17s for each tectonic regime. The ground motion models for each tectonic regimeis selected from the corresponding logic tree of the tectonic regime used duringProbabilistic Seismic Hazard Analysis (PSHA).Table 5.2: Spectral value and deaggregation tuples for contributing tectonicregime for Vancouver site and Sa(1.17 s) corresponding to a return pe-riod of 2475 years.Tectonic Regime Contributionto HazardM R(km)ε(1.17 s) Ground MotionModelActive Shallow Crustal 41% 7.35 15 0.777 CB14 [18]Subduction Interface 32% 8.85 145 1.797 BCH16 [1]Intra-Slab 27% 7.15 55 1.047 AB03-Sub [7]Figure 5.8 shows the results of the ground motion selection based on the tar-get CS. The number of records from each tectonic regime is proportional to itscontribution to the site hazard. Thus, there are 16 Shallow Crustal, 13 SubductionInterface, and 11 In-Slab records. The NGA West-2 database [5] has been usedfor crustal and in-slab records, whereas the KiK-net database [83] has been usedfor the subduction records. Site classification and flat-files for each database are8910010-210-1100CMS CrustalCMS SubductionCMS In-SlabCrustal recordsSubduction recordsIn-Slab records(a)10010-210-1100Target CrustalTarget SubductionTarget In-SlabActual CrustalActual SubductionActual In-Slab(b)10000.20.40.6Target CrustalTarget SubductionTarget In-SlabActual CrustalActual SubductionActual In-Slab(c)Figure 5.8: Scaled selected records targeted at the hazard and deaggregationcorresponding to the Vancouver site. (a) Pseudo response spectra ofindividual records. Thick broken lines mark the 97.5%ile and 2.5%ilevalues, (b) target conditional mean for the three tectonic regimes and (c)target log-standard deviation for the conditional spectra. The condition-ing period is 1.17 s.available in the literature [9, 131]. The period range of interest is based on theNBCC guidelines [87, 121]. The upper bound of the period range, Tmax is definedas max(2T1,1.5 s), where T1 is the period of vibration in the first mode. The lowerbound of the period range, Tmin is defined as min(0.15T1,T90%), where T90% is thelowest period of vibration that achieves a cumulative mass participation of 90%.For the RC-CLT building, the 0.25 second period corresponds to the third mode.Thus, the period range of interest is [0.18, 2.34]. A computationally-efficient al-gorithm is employed to select the ground motion suite [60]. The scaling factor islimited to 5 [121]. Further, a restriction of RJB > 20 km is imposed to excludenear-field records. A maximum magnitude difference of 1.5 from the modal mag-nitude is allowed. The Vs30 values are between 300 and 600 m/s. Figure 5.8b–cshow the target and achieved mean and dispersion of the three conditional spectra.An excellent match reflects the versatility of the considered database and selectionalgorithm.905.5 Results5.5.1 Pushover analysisFigures 5.9b–c show the pushover curves for the RC-CLT hybrid frame with slitand flag-shaped dampers, respectively. The pushover curves for the latter withβF = 0.8 and βF = 0.6 are identical due to the common backbone curve of bothflag-shaped dissipators. The effect of the recentering ratio is captured in the dy-namic analysis, which is presented in the subsequent sections. The pushover curvesof hybrid frames are compared with the bare RC frame (Figure 5.9a) to observe theeffects of the CLT infill and energy dissipators on the nonlinear static response. Forboth types of dissipators, a significant increase of ≈ 70% is observed in the maxi-mum base shear. While the yield displacements of the hybrid buildings are smallerthan that for the bare frame, the maximum deformation capacity (corresponding toa base shear reduction to 80% of the maximum) increases. Thus, a combination ofCLT infill with energy dissipators enhances the strength as well as the drift capac-ity of the building. The reduction in yield drift is attributed to the presence of thestiffer CLT infills, whereas the higher ultimate deformation is attributed to the highdeformability of steel slit and flag-shaped dampers. The nonlinear static capacityof the hybrid frame with flag-shaped dissipators is similar to the frame with slitdampers. Since the design of frames is based on static analysis, this similarity con-firms the equivalence of the design using both types of dissipators. The marginaldifference in the inelastic capacity of the two dissipators is attributed to the discretenature of the design process.5.5.2 Incremental Dynamic AnalysisThe seismic performance of the RC-CLT hybrid system with different energy dis-sipators is assessed using incremental dynamic analysis (IDA) [123]. Under IDA,increasingly scaled ground motion records are applied to the building until its col-lapse. The statistical distribution of the intensity measure values for each groundmotion record in the suite is used to derive the seismic fragility function. Due tothe unique seismicity of Southwestern British Columbia, a rigorous ground motionselection method is adopted. As discussed earlier, a suite of 40 pairs of ground91(a) (b) (c)Figure 5.9: Pushover curves for the (a) 6-story bare RC frame, (b) RC-CLThybrid building with steel slit dampers, and (c) RC-CLT hybrid buildingwith flag-shaped dissipators.motion records is selected to represent the three tectonic regimes that affect Van-couver, British Columbia. Figure 5.10 shows the IDA curves for RC-CLT buildingswith three design configurations of energy dissipators, viz., one slit damper and twoflag-shaped dissipators with recentering ratio, βF = 0.8 and βF = 0.6. The figurealso shows the 84th and 16th percentile IDA curves. The median collapse capacityof buildings with flag-shaped dissipators is observed to be the highest. This maybe attributed to the recentering capacity of flag-shaped dissipators, which result inrelatively smaller nonlinear deformations. It is noted that the scaling of the groundmotion records for IDA maintains the same spectral shape at different intensities,which may not be a true representation of the hazard. Multiple stripe analysistargeting conditional spectra at different intensities can alleviate this issue [59, 66].5.5.3 Fragility assessmentUsing the empirical data from the IDA curves, a lognormal distribution is fittedto produce a collapse fragility for each building. Figure 5.11 shows the collapsefragility of three RC-CLT hybrid building designs. The spectral acceleration corre-sponding to the first mode Sa(1.17 s) is chosen as the intensity measure. Table 5.3presents the fragility parameters. The fragility functions reaffirm the better seis-mic performance of buildings with flag-shaped dissipators, whose median collapsecapacity is 25–30% more than those with slit dampers. Accordingly, the collapsemargin ratio (CMR) defined as the ratio of median collapse capacity to the MCE920 0.02 0.04 0.06 0.080123Mean84th/16th percentile(a)0 0.02 0.04 0.06 0.080123Mean84th/16th percentile(b)0 0.02 0.04 0.06 0.080123Mean84th/16th percentile(c)Figure 5.10: IDA curves for the 6-story RC-CLT hybrid building with (a)steel slit dampers, and (b, c) flag-shaped dissipators having (b) βF =0.8, and (c) βF = 0.6 obtained using 40 pairs of NBCC 2020-compliantsite-specific ground motion records. IDRmax represents the maximuminterstory drift ratio.level spectral acceleration is found to be 2.8 in the case of slit dampers, whereasit increases to 3.6 and 3.5 for buildings with flag-shaped dissipators. It is notedthat an increase in the recentering ratio βF results in higher collapse capacity. Thiscan be attributed to the larger hysteresis loops for βF = 0.8 compared to that forβF = 0.6, as shown earlier in Figure 5.5. Thus, the flag-shaped dissipator with ahigher recentering ratio provides higher energy dissipation and thus less deforma-tion.0 0.5 1 1.5 2 2.500.51Empirical CDFLognormal CDF(a)0 0.5 1 1.5 2 2.500.51Empirical CDFLognormal CDF(b)0 0.5 1 1.5 2 2.500.51Empirical CDFLognormal CDF(c)Figure 5.11: Collapse fragility curves for the 6-story RC-CLT hybrid build-ing with (a) steel slit dampers, and (b, c) flag-shaped dissipators having(b) βF = 0.8, and (c) βF = 0.6.935.5.4 Residual deformationWhile the maximum interstory drift ratio (IDRmax) is a useful measure for the col-lapse assessment of structures, the post-earthquake safety of a structure is largelydetermined based on the residual drift ratio (IDRres). The literature is rich withstudies on IDRres for single- and multi-degree-of-freedom systems [e.g., 27, 103, 113, 117].Figure 5.12 shows a plot of the residual drift ratio versus maximum drift ratio forall three energy dissipators. It is observed that flag-shaped dissipators significantlyreduce the residual drift. Thus, the recentering capacity of flag-shaped dissipatorsimproves the building performance by reducing residual drift.0 0.02 0.04 0.0600.020.040.06SlitFlag-Shaped, F = 0.8Flag-Shaped, F = 0.6Figure 5.12: Maximum interstory drift ratio (IDRmax) versus the residual in-terstory drift ratio (IDRres) for the RC-CLT hybrid building with dif-ferent energy dissipators. The broken line represents the 45◦ case forequal maximum and residual values.5.5.5 Collapse risk assessmentThe fragility functions developed in the previous section capture record-to-recorduncertainty (βRT R) in the buildings’ seismic performance. Additional sources ofuncertainty were approximated based on the literature [44]. These include (a)uncertainty in design requirements, βDR = 0.10: Superior rating on account ofcapacity-based RC frame obtained using DDBD, (b) uncertainty in test data, βT D =0.20: Good rating due to well-calibrated material and damper properties, and (c)modeling uncertainty, βMDL = 0.35: Fair rating due to modest confidence in therepresentation of the collapse characteristics. Different uncertainty components94are combined using the square root of the sum of their squares. Table 5.3 summa-rizes different measures of collapse for the RC-CLT hybrid building with energydissipators. The probability of collapse at MCE, P(coll|MCE), for the buildingwith slit dampers is found to be 2.7%. As anticipated from the fragility, the valueof P(coll|MCE) for buildings with flag-shaped dissipators is smaller and equalsto 1.7% and 1.9% for βF = 0.8 and βF = 0.6, respectively. These values are fa-vorably compared to the target of 10% in code-compliant ordinary buildings basedon ASCE 7 [6]. The collapse rate, λcoll is estimated using the total probabilitytheorem considering all possible intensity levels. The value of λcoll is assessed as0.65× 10−4 for the hybrid building with slit dampers, whereas λcoll for buildingswith flag-shaped dissipators is found to be 0.42× 10−4 and 0.46× 10−4. Thesevalues again compare favorably to the collapse risk target of 2× 10−4 in ASCE7 [6]. Assuming a Poisson’s distribution for collapse, the probability of collapsein 50 years P(coll)50y is determined as 0.32% for the slit damper case; P(coll)50ytakes the value of 0.21% and 0.23% for the cases with flag-shaped dissipators.These values again comfortably meet the conventional target of 1% for ordinarybuildings [6].Table 5.3: Collapse fragility parameters and associated seismic risk for theRC-CLT hybrid building with different energy dissipatorsGround MotionSuiteµSa(g)βRT R CMR P(coll|MCE) P(coll)50y λcoll(×10−4)Steel slit damper 1.103 0.335 2.8 2.7% 0.32% 0.65SMA (βF = 0.8) 1.435 0.443 3.6 1.7% 0.21% 0.42SMA (βF = 0.6) 1.387 0.443 3.5 1.9% 0.23% 0.465.6 Chapter SummaryA global call for environmentally-sustainable construction is making timber an at-tractive material for building structural systems. The seismic performance of ahybrid timber building located in Vancouver, Canada is studied in this paper. Thelatest 6th generation seismic hazard model described in the NBCC 2020 coupled95with the complex seismotectonic features of southwestern British Columbia make acompelling case for the present investigation. The six-story RC-CLT hybrid build-ing contains steel slit dampers that enhance its energy dissipation mechanism. Ahazard-consistent suite of 40 ground motion records representing three tectonicregimes (Subduction, Shallow Crustal, and In-slab) is selected for nonlinear re-sponse history analysis. The effectiveness of the energy dissipation mechanism us-ing slit dampers is compared to a modern flag-shaped dissipator. Two flag-shapeddissipators are considered to observe the effect of different recentering ratios. Theseismic performance of three building configurations is compared in terms of resid-ual drift ratio. Flag-shaped dissipators are shown to outperform the slit dampers.The following conclusions are drawn from the study:• The CLT infill and steel slit dampers in the building enhance its maximumbase shear capacity by ≈ 70% compared to the bare RC frame. While theyield displacement of the hybrid building is marginally smaller due to thestiffer CLT infills, the maximum deformation capacity is enhanced by steelslit dampers. Thus, a combination of CLT infills and steel slit dampers in-creased both the lateral strength and drift capacity of the building.• Comparable nonlinear static performance is obtained for the hybrid build-ings with flag-shaped dissipators and steel slit dampers. However, when thenonlinear response history is compared, the buildings with flag-shaped dis-sipators outperform the ones with slit dampers.• The median collapse capacity of the buildings with flag-shaped dissipatorsis 25–30% more than those with slit dampers. Correspondingly, the collapsemargin ratio (CMR) is found to be 2.8 in the case of slit dampers, whereas itincreases to 3.5–3.6 for buildings with flag-shaped dissipators.• With an increase in the βF value, the flag-shaped hysteresis provides a betterenergy dissipation mechanism.• Compared to the steel slit damper, the flag-shaped dissipators significantlyreduce the residual drift under seismic excitation.96• The probability of collapse at the MCE for the hybrid building with slit andflag-shaped dissipators (βF = 0.8 and βF = 0.6) was found to be 2.7%, 1.7%,and 1.9%, respectively. These values are deemed favorable when comparedto the 10% target for code-compliant ordinary buildings in ASCE 7 [6].Further, the probability of collapse of the hybrid building in 50 years wascomputed as 0.32%, 0.21%, and 0.23%. These values again outperform theconventional target of 1% for ordinary buildings.97Chapter 6Conclusions andRecommendations for FutureResearchIf I have seen farther it is by standing on the shoulders of Giants.— Sir Isaac Newton (1855)6.1 ConclusionThis thesis has presented a comprehensive look at the seismic performance of post-tensioned timber frames fitted with dissipative bracing systems, as well as the seis-mic risk assessment of a hybrid RC-CLT structural system designed with directdisplacement-based design - a performance-based design methodology.In chapter 4, the principal objective of this thesis, which is to validate the ve-racity of the modified DDBD procedure for post-tensioned timber frame systemsfitted with dissipative bracing systems was carried out. This was achieved by repli-cating the design and numerical modelling for the experimental model used in thedevelopment of this modified DDBD procedure [96], and extending the design andmodelling principles onto a 6-storey 3-bay post-tensioned timber system with dis-sipative bracing systems, and checking that there is a match between design andseismic performance using Non-linear static and dynamic analyses. The numerical98model was subjected to 60 bi-directional ground motion records and satisfactoryseismic performance was achieved.In chapter 5, the seismic risk assessment of a hybrid RC-CLT system was car-ried out and showed that the CLT improved the seismic performance of the struc-ture by enhancing the stiffness property of the system. The nature of the dissipatorused on the system also affects the overall performance of the system. 3 dissipa-tors were used their performances were compared. The flag-shaped dissipator -having self-centering capabilities - led to reduced residual inter-storey drift ratioin the system and thus led to a better overall seismic performance for the systemwhen compared to the other two dissipators. The three types of dissipators, over-all, provided supplemental energy dissipating capabilities to the structural system.The hybrid structure was subjected to non-linear dynamic analysis using a suit of40 ground motions with consideration of the 6th generation seismic hazard modeldescribed in NBCC 2020. The resulting IDA, fragility, MIDR and RIDR resultsshow the improved seismic performance of this novel structural system.6.2 ContributionsAs the use of more sustainable materials in the civil engineering space becomesmore prominent, sustainable timber structural systems are increasingly in demand.As they have not yet been captured by force-based design methodologies, theycan only at the moment be designed using performance-based design approaches.In this thesis, one such sustainable structural system was designed using directdisplacement-based design - a post-tensioned mass timber structure fitted with dis-sipative bracing - and its seismic performance was evaluated. The dissipating brac-ing system can also be used to retrofit post-tensioned mass timber structural sys-tems.6.3 LimitationsThe column-foundation connection of the 6-storey post-tensioned mass timberbuilding with dissipative bracing system was not designed and was assumed tohave the same behaviour as the 3-storey 2/3 scaled experimental model investi-gated by ponzo et al. in [96]. While this could be true, analytical modelling of the99foundation behaviour was not established and an experimental model of the samesize and magnitude was not explored.6.4 Recommendations for future research1. For both structural systems investigated, a rigid diaphragm was assumed.For mass timber structural systems with semi-rigid diaphragms, the resultsfrom this study might not be accurate. Further research has to go into thedevelopment of performance-based design methodologies that incorporatevarious levels of diaphragm rigidity.2. Analytical modelling of the column-foundation connection would aid moreaccurate numerical modelling of similar connection types. Large-scale ex-perimental setups should also be explored to further investigate the hystereticbehaviour of the column-foundation connection.3. Reduction factors for the post-tensioned mass timber structural system fittedwith dissipative bracing can be investigated so it can be designed using aforce-based design approach. Seismic risk assessment can also be carriedout to provide more insight into its seismic performance.4. More dissipative bracing configurations should be investigated to ascertainan optimal configuration that provides better seismic performance for thepost-tensioned mass timber structural system.100Bibliography[1] N. Abrahamson, N. Gregor, and K. Addo. BC Hydro ground motionprediction equations for subduction earthquakes. Earthquake Spectra, 32(1):23–44, 2016. → page 89[2] M. S. Alam, M. Moni, and S. Tesfamariam. 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Civil Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
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Tesfamariam, Solomon
Direct displacement-based design and seismic performance assessment of novel hybrid moment-resisting frame structures fitted with various hysteretic damping devices
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