"I;) CJ II ISSN: /1

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1 ULU-ENG CVL ENGNEERNG STUDES ) c STRUCTURAL RESEARCH SERES NO. 54 ";) C SSN: / <4y*3 SESMC DESGN STUDES OF LOW-RSE STEEL FRAM-ES By seon D. SCHFF WLlA,.. HALL DOUGLAS A. FOUTCH.. :... A Techncal Repo o Reseach Suppoed by he NATONAL SCENCE FOUNDATON Unde Gan No. DFR DEPARTMENT OF CVL ENGNEERNG UNVERSTY OF LLNOS AT URBANA-CHAMPAG-N URBANA, LLNOS AUGUST 988,/ /.,

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3 REPORT DOCUMENTATON /.,.,REPORT NO. PAGE UUC-ENG Tle and Suble SESMC DESGN STUDES OF LOW-RSE STEEL FRAMES _-.. _ Auho(s) S. D. Sch. W.. Hall and D. A. Fouch 9. Peom na Oaanlzaon Name and Addess Unvesy o llnos a Ubana-Champagn Depamen o Cvl Engneeng 205 N. Mahews Avenue Ubana, L 680.,. ReoHn'a Acc:enon No. 5. Repo Dae Augus Peomlna O,...nlulon Rap. No. SRS PojK/Task/Wolc Un No.. Conac(C) o Gan(G, No. (C) (G) D FR Sponsolna O,...nlzaon Name and Addess 3. Type o Repo & Peod Coveed Naonal Scence Foundaon Washngon, D. C Techncal Repo Supplemenay Noes [ j 6. Absac (Lm: 200 wods) n hs nvesgaon, he nelasc behavo o low-se buldngs wh seel momen-essng ames povdng he laeal essance o song gound moons was examned. The nelasc behavo o ames s dependen on seveal paamees such as desgn base shea, beam-o-column sengh ao, momen-essng connecon behavo, nonsucual elemen pacpaon, ec. The nluence o hese paamees was deemned by peomng nelasc me-hsoy analyses. The dec desgn pocedue adoped n he 988 edon o he Unom Buldng Code was used n he sesmc desgn o he ames. Povsons egadng he equed laeal sness o he ame and sengh and ducly o he membes wee used o popoon he columns, beams and panel zones o each laeal oce-essng ame desgn. The nelasc behavo (maxmum soy ds and sheas, ducles, enegy dsspaon) compued n he me-hsoy analyss o each ame model was compaed o he expeced behavo chaacezed by he code. The nvesgaon concludes wh obsevaons abou he nelasc behavo o he ames wh egad o he numecal modellng o he assumed load-deomaon behavo. n addon, he sucual peomance o ames desgned wh he dec desgn pocedue conaned n he 988 edon o he Unom Buldng Code was evaluaed 7. Documen Analyss a. D.Klpo Eahquake, Ressan Desgn, nelasc Behavo, Dynamc Analyss, Buldng Codes, Sucual Modellng L b. denles/open Ended Tem...: c. COSAT Aeld/Goup 8. Avalably Saemen Release Unlmed (See ANS Z39.8) s.. nsucons on Revese 9. Secuy Class (Ths Repo) 2. No. o Paaes UNCLASSFED Secuy Class (Ths Paae) 22. Pce UNCLASSFED OPTONAL FORM 272 (4-7n (Fomely NTS-35) Depamen o Commece

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5 SESMC DESGN STUDES OF LOY-RSE STEEL FRAMES BY SCOTT D. SCHFF YllAH. HALL DOUGAS A. FOUTCH, [ A Repo on a Reseach Pojec Sponsoed by he NATONAL SCENCE FOUNDATON Reseach Gan No. DFR ].,:, j UNVERSTY OF LLNOS AT URBANA-CHAKPAGN DEPARTMENT OF CVL ENGNEERNG URBANA: LLNOS AUGUST 988

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7 ] ABSTRACT SESMC.DESGN STUDES OF LOY-RSE STEEL FRAMES n hs nvesgaon, he nelasc behavo o low-se buldngs wh seel momen-essng ames povdng he laeal essance o song gound moons was examned. The nelasc behavo o ames s dependen on seveal paamees such as desgn base shea, beam-o-colwnn sengh ao, momen-essng connecon behavo, nonsucual elemen pacpaon, ec. peomng nelasc me-hsoy analyses. The nluence o hese paamees was deemned by The dec desgn pocedue adoped n he 988 edon o he Unom Buldng Code was used n he sesmc desgn o he ames. Povsons egadng he equed laeal sness o he ame and sengh and ducly o he membes wee used o popoon he columns, beams and panel zones o each laeal oce-essng ame desgn. The nelasc behavo (maxmum soy ds and sheas, ducles, enegy dsspaon) compued n he me-hsoy analyss o each ame model was compaed o he expeced behavo chaacezed by he code. The nvesgaon concludes wh obsevaons abou he nelasc behavo o he ames wh egad o he numecal modellng o he asswned '....; load-deomaon behavo. n addon, he sucual peomance o ames desgned wh he dec desgn: pocedue conaned n he 988 edon o he Unom Buldng Code was evaluaed.

8 v ACKNOYLEDGMENTS Ths dsseaon was pepaed by Sco Davd Sch and submed o he Gaduae College o he Unvesy o llnos a Ubana-Champagn n paal ulllmen o he equemens o he Doco o Phlosophy degee n Cvl Engneeng. The dsseaon was compleed unde he supevson o Poessos Wllam. Hall and Douglas A. Fouch. The nvesgaon was a pa o a eseach pogam sponsoed by he Naonal Scence Foundaon unde gan NSF DFR 84-99, Sudes Towads New Sesmc Desgn Appoaches Any ndngs o ecommendaons expessed n hs dsseaon ae hose o he auhos and do no necessaly elec he vews o he Naonal Scence Foundaon. n he lae sages o pepang hs dsseaon, suppo was eceved om he Robe H. Andeson Fellowshp n Cvl Engneeng and s deeply appecaed. The numecal esuls wee obaned usng he DRAN-2D compue pogam unnng on he Has machne o he Depamen o Cvl Engneeng. The pos-pocessng o esuls o poduce gaphcal plos was peomed on he Depamen o Cvl Engneeng newok o Apollo DN3000's and DN4000's woksaons and magen lase pnes. The auhos acknowledge he usage o hese compue acles. The auhos wsh o hank Poessos Leonad A. Lopez, Mee A. Sozen and Nabey Khachauan o he consucve asssance, suggesons and commens. The auhos also ae gaeul o he conbuon povded by Ms. Susan Wasaw n he pepaaon o he manuscp. \

9 v TABLE OF CONTENTS ( CHAPTER NTRODUCTON Backgound Dec Desgn Pocedue o Sesmc Foces Fame Desgn and Modellng Pevous Wok.. Pupose o Sudy Scope o Repo. Page APPLCATON OF DRECT DESGN PROCEDURE FOR STEEL FRAMES 4 { noducon Deemnaon o Equvalen Laeal Foces Sness, Sengh and Ducly Requemens Equvalen Laeal Foces and Membe Selecons Fve-Soy Fame Desgns: DA and DB... Fve-Soy Fame Desgns: D2A, D2B and D2C Fve-Soy Fame Desgn: D3 Two-Soy Fame Desgn: D4 Summay ANALYSS AND MODELLNG OF FRAME STRUCTURES noducon.... Analyss Appoach Repesenaon o Desgn Eahquake Beam-o-Column Connecon Modellng Rgd Connecon Behavo..... Flexble Connecon Behavo Nonsucual Elemen Pacpaon Lnea Load-Deomaon Behavo Tlnea Load-Deomaon Behavo P-Dela Eecs Developmen o Numecal Models

10 v 4 PARAMETRC STUDES AND RESULTS Page noducon Selecon and Pesenaon o Oupu Daa nluence o Gound Moon on Sucual Response Developmen o Paamec Sudes nvesgaon o Beam-o-Column Sengh Rao nvesgaon o Beam-o-Column Connecon Behavo nvesgaon o Nonsucual Elemen Pacpaon nvesgaon o Fame Conguaon..... nvesgaon o Desgn Base Shea and P-Dela nvesgaon o Deecve Connecon nvesgaon o Buldng Hegh Oveall Summay l ( 5 CONCLUSONS AND DESGN MPLCATONS APPENDX A A.l A.2 A.3 A.3.l A. 3.2 A. 3.3 A.4 A.4.l A.4.2 A.4.3 A.4.4 A.5 A.6 Conclusons.. Desgn mplcaons DETALS OF DRAN-2D COMPUTER PROGRAM noducon DRAN-2D Pogam Capables... Fomulaon o Mass, Dampng and Sness Maces Mass Max... Dampng Max Sness Max..... Behavo o Fne Elemens Beam-Column Elemen Beam Elemen Connecon Elemen Shea Panel Elemen Equaons o Moon Enegy Expessons L LST OF REFERENCES l

11 v LST OF TABLES [ Table Page 2. Unom Dead Loads Soy Weghs o Fve-Soy Buldng 25 "' 2.3 Soy Weghs o Two-Soy Buldng Laeal Foces o he DA and DB Desgns 29 Membe Selecons o he DA Desgn Membe Selecons o he DB Desgn Le? E' a Foces o he D2A, D2B and D2C Desgns Membe Selecons o he D2A Desgn Membe Selecons o he D2B Desgn Membe Selecons o he D2C Desgn 36, 2. Laeal Foces o he D3 Desgn (D) Laea: Foces o he D3 Desgn (Sess) !'emb' Selecons o he D3 Desgn Laeal Foces o he D4 Desgn 40 :. 2.5 '\b S'lecons o he D4 Desgn 4 3. S.:.; acos o Eahquake Acceleogams :'!>a,. c ame Desgns o Paamec Sudes 8 -} :.!.;

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13 v LST OF FGURES Fgue a 3.2b a 3.6b a Plo o Coecen, C, o Seveal Sols... Desgn Specum o Ths Sudy Plan Vew o he DlA, DB and D2A Desgns Elevaon Vew o Fame o he DlA, DB and D2A Desgns Plan Vew o he D2B, D2C, D3 and D4 Desgns Elevaon Vew o Fame o he D2B Desgn Elevaon Vew o Fame o he D2C and D3 Desgns Elevaon Vew o Fame o he D4 Desgn Unscaled Eahquake Acceleogams Unscaled Elasc Response Speca o Fve Pecen Dampng Scaled Elasc Response Speca o Fve Pecen Dampng Exaggeaed Deomaon o a Panel Zone Dmensons o Typcal neo Fame. Fee Body Dagam o a Typcal Beam Elemen Foces Acng a an neo Panel Zone. Foces Acng on Uppe Pa o Senes Model o Sness and Sengh o Panel Zone Momen-Roaon Relaonshp o Connecon Elemen Aachmen o a Shea Panel Elemen Load-Deomaon Behavo o Nonsucual Elemens Load-Deomaon Behavo o a Soy wh Nonsucual Elemens Aached o he Fame o he Full-Scale Tes.. Elemen Numbeng o Fve-Soy, Fve-Bay Fame Page

14 x 3.l2b Sa Node Numbeng o Fve-Soy, Fve-Bay Fame. Typcal Enegy Tme Hsoes o a Fame Model Subjeced o he Scaled Eahquake Acceleogams D-Tme Hsoes o Fs Soy o Smla Modellng o DA and DB Fames Subjeced o Thee Eahquakes Shea-D Hsoes o Fs Soy o Smla Modellng o DA and DB Fames Subjeced o Thee Eahquakes Soy D and Shea Envelopes o Smla Modellng o DA and DB Fames Subjeced o Thee Eahquakes Cumulave Enegy Quanes o Smla Modellng o DA and DB Fames Subjeced o Thee Eahquakes Page b 4.Sc lla 4.llb 4.llc 4.l2a Hyseec Enegy Dsbuons o Smla Modellng o DA and DB Fames Subjeced o Thee Eahquakes Hyseec Enegy Locaons o Smla Modellng o DA and lb Fames Subjeced o Thee -Eahquakes D-Tme Hsoes o Fs Soy o Deen Connecon Modellng o DB Fame Subjeced o Thee Eahquakes.. " 00 Shea-D Hsoes o Fs Soy o Deen Connecon Modellng o DB Fame Subjeced o El Ceno Shea-D Hsoes o Fs Soy o DEeen Connecon Modellng o DB Fame Subjeced o Pakeld Shea-D Hsoes o Fs Soy o Deen Connecon Modelllng, o B Fame Subjeced o Ta Sov D and Shea Envelopes o Deen Connecon Mode L.F, 0 :;: B Fames Sub j ec ed o Thee Eahquakes 04 CWDU a V E!"'' gv Quan es o Deen Connecon ModellLng o DS Fame Subjeced o El Ceno Hyseel( EL'gv Dsbuons o Deen- Connecon Modellng o DB Fame Subjeced o El Ceno Hyseec Enegy Dsspaons o Deen Connecon Modellng o DB Fame Subjeced o El Ceno Cumulave Enegy Quanes o Deen Connecon Modellng o DB Fame Subjeced o Pakeld {,- l! 'L

15 } x Page - 4.l2b j 4.l2c 4.l3a 4.l3b 4.l3c l9a 4,9b 4.9c 4.20a 4.20b _ 4.20c Hyseec Enegy Dsbuons o Deen Connecon Modellng o DB Fame Subjeced o Pakeld Hyseec Enegy Dsspaons o Deen Connecon Modellng o DB Fame Subjeced o Pakeld Cumulave Enegy Quanes o Deen Connecon Modellng o DB Fame Subjeced o Ta Hyseec Enegy Dsbuons o Deen Connecon Modellng o DB Fame Subjeced o Ta Hyseec Enegy Dsspaons o Deen Connecon Modellng o DB Fame Subjeced o Ta D-Tme Hsoes o Fs Soy o DB Fame wh Nonsucual Elemens Subjeced o Thee Eahquakes. 6 Shea-D Hsoes o Fs Soy o DB Fame wh Nonsucual Elemens Subjeced o El Ceno Shea-D Hsoes o Fs Soy o DB Fame wh Nonsucual Elemens Subjeced o Pakeld Shea-D Hsoes o Fs Soy o DB Fame wh Nonsucual Elemens Subjeced o Ta 9 Soy D and Shea Envelopes o DB Fame wh Nonsucual Elemens Subjeced o Thee Eahquakes Cumulave Enegy Quanes o DB Fame wh Nonsucual Elemens Subjeced o El Ceno Hyseec Enegy Dsbuons o DB Fame wh Nonsucual Elemens Subjeced o El Ceno Hyseec Enegy Locaons o DB Fame wh Nonsucual Elemens Subjeced o El Ceno. Cumulave Enegy Quanes o DB Fame wh Nonsucual Elemens Subjeced o Pakeld Hyseec Enegy Dsbuons o DB Fame wh Nonsucual Elemens Subjeced o Pakeld Hyseec Enegy Locaons o DB Fame wh Nonsucual Elemens Subjeced o Pakeld ',!,

16 ! x Page. 4.2la Cumulave Enegy Quanes o DB Fame wh Nonsucual Elemens Subjeced o Ta lb Hyseec Enegy Dsbuons o DB Fame wh Nonsucual Elemens Subjeced o Ta lc 4.22 Hyseec Enegy Locaons o DB Fame wh Nonsucual Elemens Subjeced o Ta D-Tme Hsoes o Fs Soy o D2A, D2B and D2C Fames Subjeced o Thee Eahquakes. 26 3, 4.23 Shea-D Hsoes o Fs Soy o D2A, D2B and D2C Fames Subjeced o El Ceno Shea-D Hsoes o Fs Soy o D2A, D2B and D2C Fames Subjeced o Pakeld Shea-D Hsoes o Fs Soy o D2A, D2B and D2C Fames Subjeced o Ta a 4.27b Soy D and Shea Envelopes o D2A, D2B and D2C Fames Subjeced o Thee Eahquakes Cumulave Enegy Quanes o D2A, D2B and D2C Fames Subjeced o El Ceno. Hyseec Enegy Dsbuons o D2A, D2B and D2C Fames Subjeced o El Ceno c Hyseec Enegy Locaons o D2A, D2B and D2C Fames Subjeced o El Ceno a Cumulave Enegy Quanes o D2A, D2B and D2C Fames Subjeced o Pakeld b Hyseec Enegy Dsbuons o D2A, D2B and D2C Fames Subjeced o Pakeld c 4.29a 4.29b Hyseec Enegy Locaons o D2A, D2B and D2C Fames Subjeced o Pakeld. Cumulave Enegy Quanes o D2A, D2B and D2C Fames Subjeced o Ta Hyseec Enegy Dsbuons o D2A, D2B and D2C Fames Subjeced o Ta l

17 x Page 4.29c 4.30 Hyseec Enegy Locaons o D2A, D2B and D2C Fames Subjeced o Ta... 4 D-Tme Hsoes o Fs Soy o Smla Modellng o DB and D2A Fames Subjeced o Thee Eahquakes D-Tme Hsoes o Fs Soy o DB and DlB-PD Fames Subjeced o Thee Eahquakes [ a D-Tme Hsoes o Fs Soy o D2A and D2A-PD Fames Subjeced o Thee Eahquakes Shea-D Hsoes o Fs Soy o Smla Modellng o DB and D2A Fames Subjeced o Thee Eahquakes 50 Soy D and Shea Envelopes o Smla Modellng o DB and D2A Fames Subjeced o Thee Eahquakes Cumulave Enegy Quanes o Smla Modellng o DB and D2A Fames Subjeced o Thee Eahquakes b 4.35c , j la 4.4lb Hyseec Enegy Dsbuons o Smla Modellng o DB and D2A Fmes Subjeced o Thee Eahquakes Hyseec Enegy Locaons o Smla Modellng o DB and D2A Fames Subjeced o Thee Eahquakes 53 D-Tme Hsoes o Fs Soy o Smla Modellng o D2C and D3 Fames Subjeced o Thee Eahquakes D-Tme Hsoes o Fs Soy o Smla Modellng o D2C-TNE and D3-TNE Fames Subjeced o Thee Eahquakes 55 Shea-D Hsoes o Fs Soy o Smla Modellng o D2C and D3 Fames Subjeced o Thee Eahquakes.. " 56 Shea-D Hsoes o Fs Soy o Smla Modellng o D2C-TNE and D3-TNE Fames Subjeced o Thee Eahquakes 57 Soy D and Shea Envelopes o Smla Modellng o D2C and D3 Fames Subjeced o Thee Eahquakes Cumulave Enegy Quanes o Smla Modellng o D2C and D3 Fames Subjeced o Thee Eahquakes Hyseec Enegy Dsbuons o Smla Modellng o D2C and D3 Fames Subjeced o Thee Eahquakes j -, ;

18 x Page 4.4lc Hyseec Enegy Locaons o Smla Modellng o D2C and D3 Fames Subjeced o Thee Eahquakes a Cumulave Enegy Quanes o Smla Modellng o D2C-TNE and D3-TNE Fames Subjeced o Thee Eahquakes 6 -, 4.42b Hyseec Enegy Dsbuons o Smla Modellng o D2C-TNE and D3-TNE Fames Subjeced o Thee Eahquakes c 4.43 Hyseec Enegy Locaons o Smla Modellng o D2C-TNE and D3-TNE Fames Subjeced o Thee Eahquakes D-Tme Hsoes o Fs Soy o D2C and D2C-D Fames Subjeced o Thee Eahquakes Shea-D Hsoes o Fs Soy o D2C and D2C-D Fames Subjeced o Thee Eahquakes. 67 ; a 4.46b 4.46c Soy D and Shea Envelopes o D2C and D2C-D Fames Subjeced o Thee Eahquakes. Cumulave Enegy Quanes o D2C and D2C-D Fames Subjeced o Thee Eahquakes. -. Hyseec Enegy Dsbuons o D2C and D2C-D Fames Subjeced o Thee Eahquakes. Hyseec Enegy Locaons o D2C and D2C-D Fames Subjeced o Thee Eahquakes , 4.47 D-Tme Hsoes o Fs Soy o D4 and D4-TNE Fames Subjeced o Thee Eahquakes Shea-D Hsoes o Fs Soy o D4 and D4-TNE Fames Subjeced o Thee Eahquakes Soy D and Shea Envelopes o D4 and D4-TNE Fames Subjeced o Thee Eahquakes a Cumulave Enegy Quanes o D4 and D4-TNE Fames Subjeced o Thee Eahquakes b A.l A.2 Hyseec Enegy Dsbuons o D4 and D4-TNE F ame s Sub j ec ed o The.e Eahquakes..... Physcal nepeaon o End Eccences. Decomposon o Momen-Roaon Relaonshp

19 --+.j xv Page A.3a Geneal Shape o neacon Suace 99, A.3b neacon Suace o Seel -Secon 99 A.4 dealzaon o Beam-o-Column Connecon 202 : - j _ O -

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21 xv LST OF SYMBOLS The mpoan symbols and noaons used n hs dsseaon ae dened whee hey ae s used n he ex and gven below: A Q be C Coss seconal aea o membe. Reducon aco o yeld sess o panel zone. Wdh o column lange. Numecal coecen o calculae desgn base shea o dec desgn pocedue. C Numecal coecen o esmae a sucue's undamenal peod o vbaon o dec desgn pocedue. DL db de Ox EQ Axal oce n column om desgn dead load. Deph o beam secon. Deph o column secon. Relave soy d beween level x and level x-l. Axal oce n column om equvalen laeal oces o dec desgn pocedue. Allowable compessve sess o membe. Poon o desgn base shea o dec desgn pocedue ha s concenaed a op o sucue. Fx Equvalen laeal oce appled o level x o dec desgn pocedue. Yeld sess o membe. Fequency o vbaon, n hez. G Shea Modulus o panel zone web. L ll,x Hegh, n ee, above he base o level o x o sucue. Hegh, n ee, above he base o op level o sucue. mpoance aco o sucue o dec desgn pocedue.

22 xv Momen o nea o membe. Elasc sness o panel zone. San hadenng sness o panel zone. Elasc sness o connecon elemen.. j Ke LL San hadenng sness connecon elemen. Axal oce n column om desgn lve load. Soy hegh o level x. Plasc momen o membe. b Plasc momen o beam. Yeld momen o connecon elemen. p Rw s SA SV T c v Axal oce o column a panel zone. Axal yeld oce o column a panel zone. Response modcaon aco o dec desgn pocedue. Se coecen o dec desgn pocedue. Specal pseudoacceleaon. Aveage specal acceleaon. Specum nensy. Specal pseudovelocy. Fundamenal peod o vbaon, n seconds, o he sucue n he decon unde consdeaon. Thckness o panel zone web ncludng any double plaes. Thckness o column lange. Desgn base shea o dec desgn pocedue. Requed sengh o shea essance o panel zone. Yeld sengh o shea essance o panel zone. Ulmae sengh o shea essance o panel zone.. j \! (

23 xv Wegh o sucue o dec desgn pocedue. z Wegh o level o x o sucue o dec desgn pocedue. Sesmc zone aco o dec desgn pocedue.,

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25 CHAPTER NTRODUCTON. Backgound Compeen desgn o eahquake essan sucues depends on he ably o esmae he sucual demand assocaed wh he gound excaon. Howeve, he demand on a sucue om a gven eahquake s dependen upon he buldng's supply o' sness and sengh. n sesmc desgn, s mpeave o accuaely assess he sness and sengh o a buldng, so ha judgemen as o he wohness (ably o whsand he demand) o he desgn o ess majo eahquakes whou endangemen o human lves can be made. Ths sudy concenaed on he assessmen o sness and sengh o low-se seel ame buldngs and he demand on he laeal oce-essng sysems om sevee gound moons. A majoy o buldngs consuced n he Uned Saes ae low-se n naue. Howeve, becaus he sucual engneeng poon o he oal buldng cos s mno as compaed o h-se consucon, sophscaed echnques o he sesmc desgn and analyss o low-se buldngs ae no employed, excep unde unusual ccumsances. nsead, paccng engnees ely on smpled desgn pocedues ha use equvalen laeal oces o epesen dynamcally nduced oces ha ase om a majo eahquake o assess he adequacy o a desgn. Mos buldng codes, ncludng model buldng codes n he Uned Saes, conan povsons o a dec desgn pocedue (an equvalen laeal oce mehod) o sesmc essan desgn [3,4,6,23,24,43]. The moe ecen dec desgn pocedues ound n he buldng codes ae based n pa on pncples mplcly elaed o elasc

26 2 esponse speca o sngle-degee-o-eedom (SDOF) sysems moded o nelasc eecs, he so-called nelasc speca [37]. Theeoe an,,- essenal undelyng assumpon o he usage o any dec desgn pocedue s ha he dynamc esponse o he sucue should be domnaed by he s anslaonal (laeal) mode o vbaon and s elaable o he behavo o a SDOF sysem. s hs undelyng assumpon as well as ohe assumpons held by he code ha om he bass o hs nvesgaon. hese assumpons ae vald o a buldng, hen wll he esponse om a majo eahquake be smla o he expeced esponse o he code and, moe mpoanly, wll he desgn gve sasacoy peomance? n conas, he assumpons ae nvald o some degee o a buldng, how wll he esponse compae o he expeced esponse anc. wll he desgn peom sasacoly unde sevee gound excaon? : he usage o dec des gn pocedues esul n buldngs havng undesable behavo, wha modcaons can be made o he dec desgn pocedues o mpove he sucual peomance o buldngs L l l hough bee desgn pocedues. Also he sesmc desgn equemens n he codes ae. :n a. elaed o he pas peomance o buldngs whch omed a "daab.:s(, cc'.:anng he acual behavo o buldngs. Theeoe, s eal s c :. 0 ('),;*" c:' good peomance o new buldng desgns whch ae no epesened..," \socal daabase? n he lae l: '. S U' he aemah o he Febuay 97, San Fenando Eahquake, he Ap:d Technology Councl (ATC) developed a enave model buldng code o se smc desgn, encompassng moden sucual dynamcs eaues [4]. The Sucual Engnees Assocaon o Calona (SEAOG) \ l subsequenly evsed he "blue book", a buldng code o sesmc desgn, by

27 3 ollowng some o he ecommended desgn pocedues o he ATC code [43]. n addon, he Buldng Sesmc Saey Councl (BSSC) pepaed o he Fedeal Emegency Managemen Agency (FEMA) he NEHRP Recommended Povsons o he Developmen o Sesmc Regulaons o New Buldngs, hs lae documen s a model buldng code lagely based on he ATC model buldng code [6]. The sesmc desgn povsons n he "blue book" became he ; conesone o he laes edon o he Unom Buldng Code (UBC), whch was adoped by he nenaonal Coneence o Buldng Ocals n 988 [24]. The Unom Buldng Code s adoped by mos muncpales wes o he Msssspp Rve. The povsons conaned n he 988 UBC egadng he sesmc desgn o sucues have been updaed o elec he cuen vews o he demand on he sness, sengh and ducly, and peomance o he laeal oce-essng sysem o a buldng shaken dung a majo eahquake. calculaon o he desgn base shea and dsbuon o he desgn base shea no equvalen laeal oces ae pesened n a moe aonal oma han n he pevous edons o he Unom Buldng Code. Alhough, he des gn base shea and dsbuon o he desgn base shea o a ducle seel momen-essng ame sucue havng a sho undamenal peod o,'baon ae he same as ha gven by he 985 UBC [23]. The.. Dec Desgn Pocedue o Sesmc Foces The Sucual Engnees Assocaon o Calona, as well as mos ohe sucual engnees, endose he ollowng phlosophy:. A buldng mus ess a mno eahquake whou damage; 2. n modeae eahquakes some nonsucual damage s allowed;

28 4 3. Dung a majo eahquake, a buldng mus no collapse, bu some sucual as well as nonsucual damage may occu. The pncpal concen o buldng codes egadng he sesmc desgn o a sucue s le saey and no mgaon o sucual o nonsucual damage. The hd pon gven n he above desgn phlosophy peans o le saey, whle he s wo pons pean pmaly o damage mgaon. Thus, he povsons gven n he 988 UBC o sesmc desgn addess he peomance and suvvably o a sucue n he even o a majo eahquake. Howeve, s pesumed ha by adequaely addessng he { hd pon, he ohe wo pons also wll be sased. One o he pncpal obj ecves o sesmc desgn s o comply wh hs desgn phlosophy n he mos cos-eecve manne. A sucue could be desgned o have a pncpally elasc esponse dung a majo eahquake whch would nduce dsoons ha cause lle sucual o nonsucual damage. The cos o such an elasc desgn pobably would be economcally neasble, especally consdeng he ae occuence o a majo eahquake dung he "leme" o a gven buldng. Theeoe conolled and lmed nelasc behavo s pemed by he buldng code dung he esponse o a ( a sucue subjeced o song gound moon. O couse, ncued damage as a esul o nelasc behavo may ende he sucue unsuable o uhe occupancy. The esponse dung a modeae eahquake should no cause he laeal oce-essng sysem o expeence sgncan nelasc deomaons o sucual damage. Even so, he damage o nonsucual elemens can be consdeable snce hese elemens end o be less ducle han he laeal oce-essng sysem. Damage o nonsucual elemens can be lessened by L L

29 ( 5 solang hem om he sucual ame. Fo nsance, he aachmen o exeo claddng o he sucual ame usually oleaes some elave laeal movemen beween adj acen soes o peven he claddng om necessaly beng a pa o he laeal oce-essng sysem. Howeve n many cases, bndng o he connecons o nsucen solaon om he sucual ame cause he claddng o pacpae n he esponse o he sucue whch esuls n he claddng cayng shea oces. The advanage o he dec desgn pocedue s ha he laeal loads can be deemned "declyll wh a vey l:nmum o nomaon abou he popees o he sucue o he expeced gound excaon om uue l eahquakes. n he case o dynamc laeal oce pocedues such as modal o me-hsoy analyss, he desgn pocess nvolves eaon snce he laeal loads ae dependen on he popees o he sucue and gound moon. Snce vey lle nomaon s equed o he dec desgn pocedue, he mehod s que geneal and he aco o saey o any pacula desgn s dcul o assess. The dec desgn pocedue adoped by he 988 edon o he Unom Buldng Code s lmed o he desgn o "egula" sucues, whch have elavely unom dsbuon o buldng mass and sness and no majo physcal dsconnues n plan o elevaon. The code explcly saes unde wha condons a sucue s classed as beng egula because he dynamc behavo s no adequaely chaacezed by he assumed behavo consdeed n he dec desgn pocedue. A dynamc analyss, ehe modal o me-hsoy, s equed o he desgn o egula sucues and may be used o egula sucues.

30 6 An assumpon o he dec desgn pocedue s ha he dsbuons o laeal sness and sengh o a sucue ae popoonal o he desgn soy sheas, so ha he nelasc deomaons (ducly demands) a each soy level ae aly unom houghou he hegh o he buldng dung sevee excaon. n pacce, hee ae many easons why he acual dsbuons o sness and sengh may no be popoonal o he desgn shea oces, whch subsequenly can cause nonunom nelasc deomaons ove he hegh o he sucue. hs happens, much lage soy ds han ancpaed by he code may occu n a ew soes and much lage membe and connecon ducles wll be equed o dsspae he enegy demand snce ewe elemens ae shang he load. A hough nelasc behavo o a sucue s ancpaed dung a maj o eahquake, he dec desgn pocedue nvolves an elasc analyss o he sucue loaded wh he speced combnaons o dead, lve and eahquake loads. As n he consucon o an nelasc desgn specum, he desgn o a sucue usng a se o educed laeal oces should geneae nelasc deomaons whn he desed age deomaon unde he acual loadng. The sably and suvvably o a sucue dung a! majo eahquake s pesumed o be ensued when he soy ds and membe oces om he dec desgn pocedue ae less han he allowable values gven by he code. The dec desgn pocedue o he code povdes a mehod o calculae equvalen laeal oces and check he adequacy o a desgn. Howeve, he L oveall laeal oce-essng scheme s le o he sucual engnee o devse. The code also dcaes ha he sucual model o desgn and analyss mus be able o epesen he behavo o he sucue o he

31 level needed o adequaely pedc he sgncan eaue o he sucual esponse. Howeve, he code gves no gudance as o how o pedc and model he sucual behavo...2 Fame Desgn and Modellng When labo coss wee small n compason o maeal coss, he leas expensve desgn geneally equed he leas amoun o maeal. Howeve 7 as labo coss have nceased moe apdly hough he yeas snce, he abcaon, eecon and nspecon coss have had a geae conbuon n avng a he oal cos o he desgn. Theeoe he leas-wegh desgn may no necessaly be he leas-cos desgn. The sness and sengh equemens o a ame may allow he column secons o become lghe n he uppe soes o ypcal buldngs, bu om a cos pon o vew may be moe economcal o connue a column secon hough adj acen soes. The cos o he addonal "unneeded" maeal s ose by he educon n equed column splces and n me o consucon. Typcally, he lengh o a secon avalable om he mll., dcaes he change n secons o a column lne. Also, may be less { :; a expensve o use he same secon o all he columns o a soy and he same secon o all he beams o a soy, snce ewe deals ae equed o he connec ons and snce epe on o abcaon and bee bulk pcng o maeal ae acheved. - n yeas pas, all o he ames n a seel ame buldng geneally \ ".; wee desgned w h momen-essng connecons o ess laeal oces. Ths appoach povded he geaes amoun o edundancy and locaons o dsspaon o hyseec enegy o a buldng. Pesumably hs appoach

32 l 8 also povded a geae magn o saey. Howeve, o educe he numbe o momen -es s ng connecons equed and cons uc on me has become j nceasngly popula o only he pemee ames o be desgned o ess laeal oces. The connecons o he neo ames ae assumed o be 4 pnned, and hus he neo ames ess only vecal oces o he buay aea. n ac, some sucual engnees n Souhen Calona ae uhe educng he numbe o momen-essng connecons by employng long bay spacngs and even escng he numbe o bays (somemes o a sngle bay) n he pemee ames ha ess laeal oces. The educon n oal numbe o momen-essng connecons o a sucue has wo man dawbacks. The s dsadvanage s hee pobably wll be a educon n he oveall sengh o he sucue Even hough all o he desgns wll have o sasy he equemens o he code, he ably o mach moe closely hose equemens wll be wh desgns usng ewe membes o ess laeal loads. The laeal sness and sengh ae no ndependen snce olled -secons ae used as he columns and beams. Theeoe, an unaccouned o addonal magn o saey o he sengh o he sucue s educed ceang moe nelasc behavo unde sevee gound excaon. The ohe dsadvanage o educng he numbe o momen-essng connecons s he decease n edundancy o he sucue. Unde excaon om a majo eahquake, nelasc deomaons o he laeal oce-essng sysem may cause damage and evenual alue o he membes o connecons because o he necessy o dsspae a lo o enegy n a ew locaons. The nably o edsbue he oces because o lowe edundancy also may lead o geae nsably o he sucue. [ L [! \..

33 9 The modellng o he load-deomaon behavo o a seel ame ypcally s deved om he sness and sengh o he columns and beams. The beam-o-column connecons ae assumed o be nnely gd, whch means ha hee s no elave oaon beween he columns and beams amng no a jon. The lenghs o he column and beams ae based on he membe cenelne-o-cenelne dmensons o he ame. The conbuon o he nonsucual elemens, such as claddng, neo ames, neo walls, ec., o he load-deomaon behavo o he sucue s gnoed n he modellng o he sucue. Even hough shea sesses whn he panel zone cause dsoons, he sness and sengh o beam-o-column connecons geneally ae no consdeed n he analyss o a ame. The lexbly o he panel zones s compensaed o n an analyss by usng he cenelne-o-cenelne dmensons o he lenghs o he membes nsead o he clea spans. Moe mpoan o he load-deomaon behavo o he sucue s he yeld sengh o he panel zone. he panel zone yelds po o yeldng o he columns o beams, he momen acng a he ends o he columns o beams may neve each he yeld momen. Nonsucual elemens ae hose buldng elemens whch ae no desgned o conbue o he sucual capacy o he buldng. Even hough he sness and sengh o nonsucual elemens geneally ae gnoed n he desgn pocess, hese elemens can pacpae n he dynamc and, o ha mae, n he sac esponse when nsucen solaon om he sucual sysem exss. Because he nonsucual elemens do neac wh he sucual ame, he dynamc behavo o he buldng can be que deen om he behavo o jus he bae sucual ame.

34 0 Typcally, only he so-called sucual membes ae consdeed n he dec desgn pocedue...3 Pevous Wok The dec desgn pocedues dealed n codes o he Uned Saes have evolved ove he pas eghy yeas. n he begnnng, he desgn base shea was smply a pecenage o he buldng wegh whou egad o he popees o he sucue. Many nvesgaos have conbued n he yeas snce o evse he dec desgn pocedues no a moe aonal oma, whch s dependen on he load-deomaon elaonshp o he sucue, sol-sucue neacon and desed esponse [7,2,20,2,3, 35,36]. Sll, he evoluon o he dec. desgn pocedues s no compleed snce nvesgaons no he cuen desgn pocedues eveal decences n he peomance o sesmcally desgned sucues [4,8,0,,4,9]. As an example, he deomaons and ducly demands ae lage han expeced o desed o sucues desgned n accodance wh he cuen dec desgn pocedues. n ecen yeas sgncan aenon has been gven o he behavo o. momen-essng connecons unde lage dsoons [6,5,27,28,29,30,38, 39,40]. Ths eseach has poduce mehods o esmang he sness, sengh and hyseec enegy dsspaon capacy o he panel zone. The ncluson o he behavo o connecons n a ne elemen model o a ame can esul n bee pedcon o he oveall load-deomaon elaonshp. The behavo o nonsucual elemens and he conbuon o he oveall sness and sengh o he sucue also s a cuen eseach

35 opc [5,3,26,42,45,46,47]. Ths eseach has shown ha nonsucual elemens can sgncanly ncease he sness o a buldng and aec he dynamc popees o he sucue. The assessmen o he sness and sengh conbuon o nons uc ual elemens s dcul, snce degadaon occus ae epeaed cyclc moon..2 Pupose o Sudy To desgn ecen and eecve sucues o ess song gound excaon, a dec desgn pocedue mus consde he acual dynamc behavo o he sucue. n addon, he modellng o a sucue mus sucenly pedc he load-deomaon behavo o ensue ha esul s om an analyss o a sucue pedc he acual demand on he sucue. The pupose o hs sudy s o deemne he elaonshps beween sesmc desgn and esponse and beween modellng and esponse o low-se seel ame sucues. he dec desgn pocedue conaned n he 988 edon o he Unom Buldng Code can be moded o be moe sensve o he acual behavo o sucues, hen he peomance o sucues unde sevee excaon should mpove. Low-se seel ames, desgned n accodance wh he dec desgn povsons o he 988 edon o he Unom Buldng Code, wee suded o deny he above elaonshps. was oeseen ha he consdeable nelasc deomaons allowed by he code o ducle seel ames may esul n sgncan dspay beween he assumed behavo o he code and he acual esponse o he ame unde sevee excaon. Seveal ne elemen models o each ame desgn wee developed o usage n dynamc ;...

36 2 me-hsoy analyses o nvesgae he nluence o vaous paamees on he sucual peomance o he seel momen-essng ames. \ The paamees seleced o hs nvesgaon eaued he laude allowed by he code n he dec desgn pocedue o a momen-essng seel ame. The nluence o beam-o-column sengh ao, beam-o-column connecon behavo, pacpaon o nonsucual elemens, conguaon o laeal oce-essng ame, desgn base shea level and buldng hegh on he dynamc esponse and behavo wee suded. n addon, a laeal oce-essng ame wh only one bay was seleced o nvesgae he nluence o deecve momen-essng connecons. ".3 Scope o Repo An ovevew o hs nvesgaon has been dscussed n hs s chape. Backgound nomaon and he exen o pevous eseach elaed o sesmc desgn and nelasc behavo o seel ame sucues ndcae a need o uhe sudy he elaonshp beween dec desgn pocedues and dynamc esponse. Undesandng hs elaonshp may lead o bee sesmc peomance o laeal oce-essng desgns. The applcaon o he dec desgn pocedue conaned n he 988 edon o he Unom Buldng Code o he seel momen-essng ames consdeed n hs nvesgaon ae gven n Chape 2. Some devaon concenng he colwnn-o-beam sengh ao, desgn base shea level and ame conguaon ae gven n hs code and hese aspecs wee exploed n he ame desgns. The modellng and analyss pocedue o he seel ames ae pesened n Chape 3. Modellng o a sucue's load-deomaon behavo equed l l. l

37 3 makng assumpons egadng he ndvdual behavo o he elemens. The ne elemen mesh o he ame models and modellng he beam-o-colunn connecons and nonsucual elemens o he me-hsoy analyses ae explaned n hs chape. Seveal hsocal gound excaon ecods, epesenave o he desgn eahquake, wee used n he me-hsoy analyses as he base moon. An explanaon o he scalng algohm o he eahquake acceleogams s gven n hs chape. The developmen, esuls and conclusons o each o he paamec sudes ae pesened n Chape 4. The selecon o he esuls om he me-hsoy analyses used o quany he nelasc behavo o he ame models also ae addessed. Each paamec sudy was developed o deemne he nluence o a pacula paamee on he nelasc esponse. The esuls o he paamec sudes ae dscussed and pesened n gaphcal om. The conclusons o each paamec sudy ocus on he mpoance o nluence o he paamee. The oveall conclusons elaed o he desgn, modellng and analyss o seel ame sucues ae dealed n Chape 5. Snce one o he goals o hs sudy was o mpove he sesmc peomance o sucues hough bee desgn, ecommendaons o he dec desgn pocedue o he 988 edon o he Unom Buldng Code also ae gven. \!

38 4 CHAPTER 2 APPLCATON OF DRECT DESGN PROCEDURE FOR STEEL FRAMES 2. noducon Sucual engnees paccng n Souhen Calona wee consuled o hs sudy o ascean he cuen sae o he desgn o low-se seel ame sucues. Fame desgns n hs sudy wee usually conssen wh he sae o pacce o low-se seel ame sucues consuced n a hghly sesmc egon. Howeve some ame desgns wee chosen o bound a ange o a pacula paamee beng nvesgaed and may no epesen cuen pacce o even "good" pacce o sesmc desgn.. n hs sudy, seel momen-essng ames along he pemee o he sucue povded he laeal oce essance and sably. These ames wee desgned o ess sesmc nduced oces n accodance wh he dec desgn pocedue conaned n he 988 edon o he Unom Buldng Code. Povsons peanng o boh osonal and ohogonal (bdeconal gound excaon) ecs wee gnoed n he sesmc desgn o hese ames snce he laeal lodd domaon behavo o he me-hsoy analyses o each sucue was ped by plana modellng o he momen-essng ames n a speced.c:on. The ncluson o osonal o ohogonal eecs n he d ee: <:!*,. : pocedue pobably would have nceased he laeal sness and s..:-; o a ame bu would have gven msleadng esuls (unconsevavej oa he me-hsoy analyses o hs nvesgaon. The s s:cf n he dec desgn pocedue s o deemne he desgn base shea and vecal dsbuon o he base shea. A sac elasc analyss o he sucue, loaded wh he gavy oces and, j L l

39 5 equvalen laeal oces, s hen peomed o deemne soy ds, membe oces and oveunng momens. The soy ds and membe oces ae checked o code complance wh he laeal sness equemens o he momen-essng ame and sengh and ducly equemens o he columns, beams and panel zones. The calculaon and dsbuon o he desgn base shea o he dec desgn pocedue o each ame desgn consdeed n hs sudy ae descbed n hs chape. The code povsons used o check he laeal sness equemens o he ame and sengh and ducly equemens o he columns, beams and panel zones ae explaned n some deal. nally, he movaon behnd he calculaon o he desgn base shea, he conguaon seleced o he laeal oce-essng ame and he olled seel -secons chosen as he columns and beams o each ame desgn ae pesened n hs chape. 2.2 Deemnaon o Equvalen Laeal Foces The desgn base shea, whch s he sum oal o he equvalen laeal oces appled o he sucue n he dec desgn pocedue, s gven by \' _ 2 C\ R" And (2.) The sesmc zone aco, Z, epesens he eecve peak acceleaon (EPA) o he desgn eahquake pacula o a gven se locaon. Z has a value o zeo o egons whou sesmc hazad and anges up o a maxmum value o ou-enhs o egons o song sesmcy. The aco,, coesponds o he mpoance o he acly. Sandad occupancy sucues have an

40 6 value equal o uny, whle essenal occupancy sucues have an value equal o one and a quae. The mpoance aco,, ases he aco o saey o he desgn by nceasng he equed sness and sengh o he sucue, whch wll esul n smalle nelasc deomaons dung sevee gound excaon. The sesmc wegh, W, s he dead load plus applcable poons o lve load and snow load and should coespond o he wegh o he buldng mass ha can nduce neal oces dung gound excaon. The esponse modcaon aco, Rw, pmaly accouns o nheen ducly and hyseec enegy dsspaon capably o he laeal oce-essng sysem and addonal, bu unpedcable, sengh o he nonsucual elemens. The esponse modcaon aco o laeal oce-essng sysems nceases as he ducly nceases. The desgn coecen, C, s dened by c.25 S T2/3 (2.2) whee S s dependen on he sol chaacescs a he se and T s he esmaed undamenal peod o vbaon, n seconds, o he sucue n he decon unde consdeaon. n hs sudy, he value o Z was aken o be he maxmum, ou-enhs. The mpoance aco,, was aken o be uny, so ha he nelasc behavo was no educed as a esul o a moe consevave desgn. The esponse modcaon aco, Rw, was aken o be welve, snce he laeal oce-essng sysem was assumed o be specal momen-essng space ames (SSF). The calculaon o C was based on a value o S aken o be.2, whch coesponds o a pole o s o dense sol. l [ \ L

41 7 Shown n Fgue 2. ae plos o he desgn coecen, C, veses undamenal peod o sucue o each sol pole classcaon. The value o C geneally deceases as he undamenal peod o he sucue nceases. C has a maxmum value o 2.75 o he s sols (ypes and 2) and a maxmum value o 2.25 o so sols (ypes 3 and 4). The code allows he usage o C equal o 2.75 whou egad o he undamenal peod - -_ o sol pole. Fo long peod sucues, usng a value o C equal o 2.75 geneally s que consevave, especally o sucues ounded on s sols "" (s =.0) (S =.2) u o (S =.5) (S = 2.0) , FGURE 2. T (sec) Plo o Coecen, C, o Seveal Sols j The plos gven n Fgue 2. can be vsualzed concepually n he conex o elasc esponse speca, whch ae used o ancho he desgn specum o a gven sol ype. The desgn specum o hs sudy, S equal

42 8 o.2, s shown n Fgue 2.2. The odnae o Fgue 2.2 s he desgn base shea gven as a pecenage o he buldng wegh. Snce he maxmum value o C need no exceed 2.75 o sol ype 2, he desgn base shea need no exceed 9.2 pecen o he buldng wegh. The 988 UBC mandaes ha he ao o G/Rw shall no be less han 0.075, heeoe he mnmum desgn base shea o hs desgn specum n Fgue 2.2 s compued o be 3.0 pecen o he buldng wegh T (sec)., L l. " l FGURE 2.2 Desgn Specum o Ths Sudy l The poduc o ZCW would be he desgn base shea he sucue was o eman elasc om excaon by he desgn eahquake. Theeoe he desgn base shea o a sho peod sucue would need o be a leas one hunded and en pecen o he buldng wegh (V W -.lw). } nelasc behavo s ncopoaed no he dec desgn pocedue by

43 9 dvdng he "elasc" desgn base shea by he esponse modcaon aco, Rw. The expeced soy ds, elasc and nelasc conbuons, mplc n he 988 UBC ae hee-eghs o Rw ds. mes he allowable soy The educon om he "elasc" esponse specum o he desgn specum s welve o a specal momen-essng space ame, and ye he ancpaed soy ds ae only ou and a hal mes he allowable soy ds. The deence beween hese wo acos s nconssen wh he nelasc desgn speca conceps appled o sngle-degee-o-eedon sysems [37], whch geneally om he bass o cuen dec desgn pocedues. One explanaon o hs dscepancy s ha Rw accouns o ohe acos such as he addonal, bu unpedcable, sengh o nonsucual elemens, ahe han jus he nnae ducly o he laeal oce-essng sysem. Snce he undamenal peod o a sucue s geneally unknown a he onse o he desgn pocess, he ollowng equaon s gven n he code o esmae he undamenal peod o he nal desgn phase: (2.3) whee C s equal o o seel ames and s he hegh, n ee, o he op level o he sucue. Howeve, he value o C s aken o be equal o 2.75, hen an esmaed undamenal peod s no needed o oban a desgn base shea. The esmaed undamenal peod gven by Equaon 2.3 usually s shoe han he acual peod o he sucue. An expesson ha was dawn hough he ecoded es daa o undamenal peod o vbaon o. ;..'l. -

44 20 -. nsumened seel ame buldngs shaken dung he 97 San Fenando eahquake s smla o Equaon 2.3, excep ha he coecen, 0.049, s used nsead o [4,6]. The lowe value was seleced o he dec desgn pocedue, because wll end o be moe consevave by gvng a lage desgn base shea when T s subsued no Equaon 2.2. The equvalen laeal oces o he vecal dsbuon o he desgn base shea o he dec desgn pocedue ae gven by.., (V - F ) Wx Wh (2.4) whee Fx s he equvalen laeal oce appled a level x, Wx s he wegh o level x and hx s he hegh o level x. concenaed oce appled o he op o he sucue and s gven by O.07TV. (2.5) F accouns o he pacpaon o hghe modes n he esponse o long peod sucues. F can be negleced when T s less han seven-enhs o, a second (sho peod sucues) and need no exceed weny-ve pecen o he desgn base shea o long peod sucues. The dsbuon o equvalen laeal oces o sho peod sucues wh consan soy heghs and weghs lnealy nceases om zeo a he base o a maxmum value a he oo. Ths dsbuon coesponds o an assumed lnea shape o he s laeal mode o vbaon. Thus, he dynamc esponse o he sucue should be domnaed by he s mode, so ha he dsbuon o he desgn oces esemble he maxmum soy sheas obaned dung sevee \ gound excaon. The eec o F shs he vecal dsbuon o he

45 2 base shea owads he uppe levels o he sucue, whch anslaes o lage soy sheas n he uppe soes and moe oveunng momen. 2.3 Sness, Sengh and Ducly Requemens The dec desgn pocedue enals peomng a sac elasc analyss o he sucue-loaded-whany applcable loadng combnaons conanng eahquake loads. To saeguad agans collapse o he sucue dung he desgn eahquake, he dec desgn pocedue has wo componens - a d desgn and a sess (sengh) desgn - whch ogehe ae assumed o ensue sably o he sucue by conollng he soy ds and nelasc behavo o he sucual membes. The.compued soy ds o a sucue o less han sxy-ve ee n hegh shall no exceed (2.6) whee Ox s he maxmum allowable soy d o level x and x s he soy hegh o level x. The maxmum allowable soy d ao (soy d dvded by soy hegh) o a specal momen-essng space ame (SMRSF) o whch Rw s equal o welve s compued o be one-hd o a pecen. Fo specal momen-essng space ames desgned n accodance wh he povsons o he 988 UBC, he maxmum soy d as a esul o excaon om he desgn eahquake ae expeced o be ou and a hal (O.375Rw) mes Ox o one and a hal pecen o he soy hegh. n ac egadless o laeal oce-essng sysem, he expeced maxmum soy d aos ae one and a hal pecen. Ths s because he smalle soy

46 22 d mulple o a less ducle sysem (smalle Rw) s ose by a, '. lage allowable soy d. Many povsons n he code ae based on he expeced maxmum soy ds. Fo nsance a he expeced maxmum soy d, he deomaon compably o all amng elemens no equed by desgn o be pa o he laeal oce-essng sysem shall have adequae vecal load-cayng capacy when dsplaced o hs level, sepaaon o adjacen buldngs shall elmnae conac a hs level so ha poundng s pevened dung excaon and connecons shall allow o hs level o soy d. Accepable peomance o he sucue beyond he one and a hal pecen soy d ao s no egulaed by he code mus be avoded collapse o he sucue s o be pevened dung sevee excaon. Some o he sengh equemens ensue ha he calculaed sesses n he columns and beams om he desgn oces ae less han an allowable level. The neacon equaons conaned n he code, whch ae dencal o he equaons conaned n he ASC lanual o Seel Consucon [2], wee used o check he desgn sesses. n hs nvesgaon, he loadng combnaon o lve, dead and eahquake loads conolled he desgns, even hough he allowable sesses o hs load combnaon wee nceased by a aco o one-hd. The calculaed sesses n he columns o he laeal oce-essng ames om vecal dead and lve loads wee small compaed o he s esses om he laeal oces because he buay aea o vecal loads was much smalle han he buay aea o laeal oces. The code also conans povsons egadng mnmum compued sengh o he columns. The axal oce capacy o he columns mus be geae han he axal oces asng om he desgn eahquake as a esul o oveunng eecs o he sucue. The compessve sengh o each l ( l L

47 23 column mus sasy (. 0 ) D L + (0. 8) LL + ( ) EQ. 7 FaA (2.7) and he ensle sengh mus sasy (0. 85) DL + ( ) EQ F y A, (2.-S) whee DL s he axal oce om he dead loads, LL s he axal oce om lve loads, EQ s he axal oce om he equvalen laeal oces, Fa s he allowable compessve sess, Fy s he yeld sess and A s he coss seconal aea. The sengh o he panel zone mus have he capacy o ess he pescbed shea oces appled o he panel zone. The mnmum shea sengh o he panel zone s deved om he beam bendng momens as a esul o he loadng combnaon o gavy loads plus.85 mes he equvalen laeal oces. Howeve, he panel zone need no have he shea sengh o develop moe han eghy pecen o he sum oal o plasc momen o he beams amng no he jon. Addonal ducly equemens o specal momen-essng space ames (SMRSF) ae povded o ensue ha he sucue can expeence sgncan nelasc deomaon whou non-ducle alue modes. he ducly equemens o a specal momen-essng space ames ae no ; j, j sased, hen he momen-essng space ame s classed as odnay. The esponse modcaon aco, Rw, o an odnay momen-essng space ame s egh. The beams and columns o a specal momen-essng space ame mus be capable o omng plasc hnges whou any local bucklng o he langes o web.

48 24 -, The deemnaon o he equvalen laeal oces n he dec desgn pocedue s ahe sagh owad. Once he laeal oce-essng sysem and hegh o he buldng s seleced, and he sol pole o he se s deemned, he desgn base shea can be calculaed. Because so lle nomaon s equed o a desgn, he aco o saey o any buldng could have much vaance dependng on he acual behavo o he sucue n compason o he desgn assumpons. L 2.4 Equvalen Laeal Foces and Membe Selecons All sucues consdeed n hs sudy had plan dmensons o 44 ee by 08 ee and had soy heghs o 4 ee o he s soy and 2 ee o he uppe soes. The pemee momen-essng ames wee used o ess he laeal oces and povde laeal sably o he ene sucue. The neo ames essed vecal oces om he gavy loads o he ndvdual buay aeao Snce he nelasc behavo o momen-essng ames n he decon paallel o he 44 oo, dmenson (he long decon) was o nees n hs nvesgaon, only hose columns, beams and connecons essng laeal oces n hese ames wee desgned and suded. n ac, only one o he exeo ames needed o be modelled because o he assumed symmey o he sucue. One-hal o he desgn base shea o he decon unde consdeaon was essed by each exeo ame. The loo and oo decks wee assumed o be gd enough o anse he nea oces n he cene o he buldng o he exeo ames n he even o an eahquake. The unom dead loads lsed n Table 2. wee used n he wegh calculaons o each sucue. The oal sesmc wegh o buldngs ",.! l [!

49 25 ypcally s calculaed om he dead loads and ull paon load. The pa on load should accoun o any lve load acng on he sucue. The soy weghs, gven n Table 2.2 o a ve-soy model and Table 2.3 o a wo-soy model, wee deemned om he plan aea o he loos o oo and he vecal buay aea o he exeo claddng. TABLE 2. Unom Dead Loads Roo Concee Slab wh Deckng 42 ps Mechancal and Eleccal 6 ps Celng 5 ps Sucual 5 ps nsulaon and Membane ps Toal 89 ps,"..- - Floo Concee Slab wh Deckng 42 ps Mechancal and Eleccal 6 ps Celng 5 ps Sucual 20 ps Paons 20 ps Toal Facade Claddng (exeo wall aea) 03 ps 5 ps :A Soy Weghs o Fve-Soy Buldng.",. }!.... \, ()"'! 4)(08)(0.089) + 2( )( 6)(0.005) = 399 kps..:.. :... )(08)(0.03) + 2( )(2)(0.005), kps \.;3... )(08)(0.03) + 2( )(2)(0.005) """ 632 kps, W 2 :.. 4)(08)(0.03) + 2( )(2)(0.005) == 632 kps W (44)(08)(0.03) + 2( )(3)(0.005) = 635 kps, 7930 kps

50 26 TABLE 2.3 Soy Weghs o Two-Soy Buldng W 2 (oo) (44)(08)(0.089) + 2( )( 6)(0.005) == 399 kps W (44)(08)(0.03) + 2( )(3)(0.005) kps 3034 kps! Thee deen desgn base shea levels wee used o he desgn o he ve-soy sucues. The D sees had a desgn base shea based on an assumed value o C equal o The D2 sees had a desgn base shea based on he esmaed undamenal peod o vbaon o he buldng. The D3 sees was based on moe ealsc value o he undamenal peod o vbaon deemned om he calculaed undamenal peod o vbaon o one o he ames n he D sees. A desgn. base shea based on he esmaed undamenal peod o vbaon o he wo-soy buldng was used n he D4 sees Fve-Soy Fame Desgns: DLA and DB The plan vew o he sucual layou o ehe he DA o DB ame desgns s shown n Fgue 2.3. The bay spacng n boh decons s 8.0 ;- ee, whch pobably s smalle han used n pacce o ypcal seel ame buldngs o oday. The elevaon vew o Fame (o Fame 7) s shown n Fgue 2.4. The ve-soy buldng s classed as a "egula" sucue snce he dsbuon o mass hough he hegh o he buldng s aly unom and hee ae no egulaes n plan o elevaon. n ac, he buldng s symmec n boh sness and mass, hus elmnang { l any "calculaed" oson. n accodance wh ends n pacce and o \ L

51 27 smply he loadng condon o he cone columns, baxal bendng can be elmnaed by usng pnned connecons o he aachmen o he beams n Fames and 7 o he cone columns. The pnned connecons wee placed n Fames and 7, because hese ames had moe bays han he Fames A and o he pependcula decon. Snce h_ laal oce-essng s he same n boh decon he desgn base shea o each decon also s he same. The neo beam-o-column connecons n he end bays o Fames and 7 also wee pnned because momen-essng connecons wee no needed o sasy he laeal sness and sengh equemens o he ame. Theeoe, he beams n he wo end bays ess only vecal gavy loads.. j and do no conbue o he laeal sness o sengh o he ame. CD Co CD FGURE 2.3 8' 44' Plan Vew o he DA, DB and D2A Desgns, co

52 CD B5 B5 B5 B5 B5 B5.n.n.n.n.n.n.n u B4 U B4 u B4 u B4 u B4 u B4 u "<' "<' "<' "<' "<' "<' "<' u B3 u B3 u B3 u B3 u B3 u B3 u " C\ M M M M u B2 u B2 u B2 u B2 u B2 u B2 u N N c:"\ c:"\ c:"\ c:"\ c:"\ u B u B u B u B u Bl u Bl u -<... -< u u u u u u u // // 8-' = 44-' Noe: (3 = Pnned Connecon FGURE 2.4 Elevaon Vew o Fame o he DA, DB and D2A Desgns " -,., [ n he DA and DB ame desgns, he calculaon o he desgn base shea was based on an assumed value o C equal o 2.75 (allowed by he code), even hough a value o C based on he esmaed undamenal peod was smalle. Tnus. he des gn base shea was 9.2 pecen o he buldng wegh. The usa" o such an assumed value o C s geneally consevave, especally 0:- s: '.,-- :'...;es havng an esmaed o acual undamenal peod longe han 0 5 ;onds_ Snce he sucue was desgned wh a base shea,. lage han h- ((' s: n base shea esablshed om he esmaed undamenal peod, as: l '.!.j songe sucue han would be equed C was based on he... :-:!<l!u nal peod was necessay. Snce se sucues ypcally base shea dung excaon (as llusaed by he calculaon o C). he addonal magn o saey due o he consevave value o C s unclea. The desgn base shea and equvalen laeal oces l o hese desgns ae shown n Table 2.4. \ l

53 29 TABLE 2.4 Laeal Foces o he DA and DB Desgns T 0.035(62)3/4 = 0.77 sec (Esmaed) C (Assumed) V -= 0.4(.0)(2.75)(7930)/2 = 727 kps (VjW = 0.092) 0.07(0.77)(727) = 39.2 kps F - Soy Wx. hx Wxhx Wxh x F x * Level (kps) () (k-) Wh (kps) * Fs ncludes F DlA Fame - The membe selecons o he laeal-oce essng ames wee conolled by he laeal oces o he sesmc desgn, ahe han he lve loads and dead loads. To sasy he laeal sness equemens he n-plane bendng sness (momen o nea) o he columns was mpoan o conollng he ds. The -secons seleced o he columns wee deepe han nomal o povde as much sness as possble o he gven coss seconal aea. The -secons chosen o hs ame desgn ae shown n Table 2.5. These secons sased he laeal sness equemen, and mached as closely as possble he sengh equemens. Smalle column and beam secons wee chosen as allowable! j hough he hegh o he sucue. n geneal, he columns and beams wee songe han necessay, because laeal sness, no he sengh o he membes, conolled he desgn o he ame. -secons havng sucen momen o nea (sness) exceeded he equemens o he sengh o

54 30 he secon. Alhough, he shea capacy o he panel zones as a esul o he column web hckness was no sucen and double plaes wee needed. The dynamc behavo o hs desgn was song beam-weak column ll, because he sum o he yeld momens o he columns a a connecon was geneally less han he sum o he beams. The yeld momen o each column was based on he neacon beween he momen and axal oce acng on he column (see Appendx A). TABLE 2.5 Membe Selecons o he DlA Desgn Soy Column l\ Beam l\ Level Secon (n4) (n-k) Secon (n4) (n-k) 5 W2lx 'W8x \.2lx 'W24x W2lxlOl 'W24x W2lxlll 'W24x W2lxlll 'W24x DB Fame - The DB ame was smla o he DA ame, excep ha songe columns o oughly he same sness wee chosen o ansom he l dynamc behavo o be "song column-weak beam ll The column secons o he DB ame wee no as deep as he columns o he DA ame. The coss seconal aea, and consequenly he un wegh pe oo, o he columns ( nceased consdeably o acque a secon wh he same momen o nea. The - sec ons chosen o hs desgn ae shown n Table 2.6. Agan, he column and beam secons wee educed as allowable n he uppe soes o he sucue. L

55 - 3 TABLE 2.6 Membe Selecons o he DB Desgn Soy Column Beam Level Secon (n4) (n-k) Secon (n4 ) (n-k) 5 W4x W8x W4x W24x W4x " 520. W24x W4x W24x W4x W24x The nelasc behavo o he DA and DB ames was nvesg"aed n a paamec sudy o deemne he nluence o he beam-o-column sengh ao snce hs was pncpal deence beween hese wo ames. The DB ame also was used n paamec sudes o beam-o-column connecon ] behavo, nonsucual elemen pacpaon and desgn base shea level Fve-Soy Fame Desgns: D2A, D2B and D2C The value o C o he D2A, D2B and D2C ame desgns was based on he esmaed peod gven by Equaon 2.3 o he sxy-wo oo hgh, seel ame sucue, nsead o he consevave value o C equal o Each o hese D2 ame desgns had a deen conguaon o he laeal oce-essng sysem. The desgn base shea was he same o each desgn, because he esmaon o he undamenal peod was ndependen o ame conguaon. The desgn base shea and equvalen laeal oces o all hee desgns ae shown n Table 2.7. The desgn base shea o hese hee ames was 5.9 pecen, whch s appoxmaely wo-hds o he desgn base shea coespondng o a value o C equal o The columns and beams o he lowe hee soes wee each o he same secon as wee columns and

56 32 beams o he uppe wo soes. Theeoe, boh he soy ds and sesses om he dec desgn pocedue wee geneally less han he allowable lms. - TABLE 2.7 Laeal Foces o he D2A, D2B and D2C Desgns T = 0.035(62)3/ sec (Esmaed) C =.25(.2)/(0.77)2/ V = 0.4(.0)(.78)(7930)/2 = 470 kps (VjW = 0.059) F = 0.07(0.77)(470) = 25.3 kps Soy W x hx Wxhx Wxhx F x * Level (kps) () (k-) Wh (kps). "\("\ :: V.L,;}...O * F5 ncludes F [ D2A Fame - The plan vew o he sucual layou and he elevaon vew o he ame conguaon o he D2A desgn s dencal o he DA [ o DB desgns (see Fgues 2.3 and 2.4). The smalle desgn base shea pemed lghe secons o be used o he columns and beams han he DA ame. The -secons chosen o hs desgn ae gven n Table 2.8. The secons wee no changed as allowed, bu he same secons wee used o he lowe hee soes and deen secons wee used o he uppe wo soes. Theeoe, boh he sness and sengh equemens o some soes wee exceeded. Alhough hs selecon o membes pobably s moe epesenave o acual pacce. L

57 :- j, Soy 33 TABLE 2.8 Membe Selecons o he D2A Desgn Column Mp Beam Level Secon (n4) (...,_l,\ \..U- Secon (n4 ) (n-k) 5 'W2lx W2lx W2lx W2lx 'W2lx W2lx 'W2lx W2lx 'W2lx W2lx D2B Fame - The plan vew o he sucual layou and he elevaon vew o he ame conguaon o he D2B desgn s shown n Fgues 2.5 and 2.6. The bay spacng o hs ame was nceased o 28.8 ee, whle he oveall lengh emaned unchanged. was a The advanage o longe bay spacngs educon n he numbe o momen-essng connecons and n he numbe o membes ha need o be eeced. should be noed ha bay wdhs o up o 40 ee n lengh have been used n moden seel ame consucon. Howeve, he longe bay spacngs ncease he eecve lenghs o he columns, whch n un lowe he allowable sesses o he columns. Theeoe, he maeal ecency acually may decease when longe bay spacng ae used. The oal dead wegh o he D2B ame wh 28.8 oo bay spacngs nceased by weny pecen ove he D2A ame wh 8.0 oo bay spacngs. The ncease wegh and maeal cos o he D2B.: j ame s ose by he savngs n he abcaon and eecon coss. The -secons chosen o hs desgn ae gven n Table 2.9. Agan, he same secons wee used o he lowe hee soes and uppe wo soes. n hs desgn he same column deph was used houghou he hegh o he sucue, bu wo deen beam dephs wee used.

58 ,..., CD " c::o a...; " :" CD FGURE " = 44" Plan Vew o he D2B, D2C, D3 and D4 Desgns B5 B5 B5 B5 B5 u L() L() L() L() u B4- B4- B u B4 u B4 B3 u B3 u B3 u B3 u B3 B2 M M M M u B2 u B2 u B2 u B2 B N N N N u B u B u B u -u u -u -u... -"'" // // 28.8" = 44" Bl Noe: C3 = Pnned Connecon FGURE 2.6 Elevaon Vew o Fame o he D2B Desgn

59 ] :-\ " j j " j TABLE Membe Selecons o he D2B Desgn Soy Column l\ Beam Level Secon (n4) (n-k) Secon (n4) (n-k) 5 W2lx W24x W2lx W24x W2lx W27xl W2x W27x W2lx W27xl D2C Fame - The plan vew o sucual layou o he D2C desgn s dencal o he D2B desgn (see Fgue 2.5). The elevaon vew o he ame conguaon o he D2C desgn s shown n Fgue 2.7. Only he cene bay, whch povdes all o he laeal essance and sably, has momen-essng connecons. The edundancy o he sucue and possble yeld locaons o hyseec enegy dsspaon was deceased by he elmnaon o momen-essng connecons. The loss o laeal sengh o he ame om sucual damage o a momen-essng connecon n hs conguaon can have a sucue. gven n Table 2.0. emendous mpac on he suvvably o he The -secons chosen o he cene bay o hs desgn ae The same secons wee used o he lowe hee soes and deen secons wee used o he uppe wo soes. only a Snce ew membes ae povdng he ene laeal oce essance and sably, he sze o hese membes ae que deep and heavy. n ac, achecual consdeaons may be necessay o allow he usage o such deep membes. The membe selecons o he ohe columns and beams would be based scly on he vecal gavy loads and would be much smalle.

60 @ 36,.. B5 L"<o,,,,d,.,, l() u '"'..q. u B4 l() u..q. l.-:l... e:) -.::< -- - N B3 u M M u u N u B2 N u -.::< B l.... u -u // / 28.8" = 44"!.> - l - Noe: G = Pnned Connecon FGURE 2.7 Elevaon Vew o Fame o he D2C and D3 Desgns TABLE 2.0 Membe Selecons o he D2C Desgn Soy Column Mp Beam Mp Level Secon (n4) (n-k) Secon (n4 ) (n-k) 5 w27x w27x w27x w27x 'W'30x w30x2l 'W'30x 'W'30x2ll w30x 'W'30x [ l. The desgns o he D2A, D2B and D2C ames o a ve-soy buldng wee based on he same desgn pocedue. The deence beween he hee ames was he conguaon o he laeal-oce essng sysem. paamec sudy compang he nelasc esponse o he hee ames was peomed. The D2A and D2C ames also wee used n a paamec sudy o A \ l: T

61 37 desgn base shea level. n addon, he D2C was used n paamec sudes whch examned he nluence o nally deecve momen-essng connecons and pacpaon o nonsucual elemens., Fve-Soy Fame Desgn: D3 The desgn base shea o he D2A, D2B and )2Caesgns- was- calculaed wh an esmaed peod (Equaon 2.3) o he sucue. Howeve, he code.. ""T! j pems C o be deemned om a moe ealsc value o he undamenal peod o he sucue. The peod gven by Equaon 2.3 s ypcally shoe han he calcualed peod o he bae sucue ame, hus he desgn base shea s heoecally lage han necessay. The value o C used o he d desgn (sness equemens) s calculaed om Equaon 2.2, whee T s he calculaed undamenal peod o he D2C ame. Howeve, he code speces he value o C o he sess desgn (sengh equemens), may no be less han eghy pecen o he value oba n by Equaons 2.2 and 2.3. Theeoe, he D3 des gn has wo ndependen ses o equvalen laeal oces one se o checkng sness equemens and one se o sengh equemens. The lm n he educ on o C o he sess desgn s o saeguad agans usng a value o T n-.a 5 oo long and esuls n a sucue o quesonable j.-..l: (j..-," consequence o usng a smalle desgn base shea o he d d' 50 p-. l!. h.. he sess desgn may conol he selecon o membes and any unac( o,;..'d o addonal aco o saey o he sengh s elmnaed. A hough. he laeal sness o he sucue s moe han necessay. The desgn base sheas and equvalen laeal oces o he d and sess desgn ae shown n Tables 2. and 2.2, especvely.

62 38 TABLE 2. Laeal Foces o he D3 Desgn (D) T =.48 sec (Peod o D2C) C =.25(.2)/(.48)3/4 -.6 (Full educon) V = 0.4(.0)(.6)(7930)/2-307 kps (V;W = 0.039) F = 0.07(.48)(307) = 3.8 kps Soy Wx hx Wxhx Wxhx F * x Level (kps) () (k-) Wh (kps) * Fs ncludes F l """ %: l TABLE 2.2 Laeal Foces o he D3 Desgn (Sess) c = 0.80(.78) =.42 (Reducon om D2C) V = 0.4(.0)(.42)(7930)/2 = 375 kps (V /w "'" O. 047) F = 0.07(.48)(375) = 38.9 kps Soy W x hx Wxhx Wh x x F x * Level (kps) () (k-) Wh (kps) * Fs ncludes F. The plan vew o he sucual layou and he elevaon vew o he ame conguaon o he D3 desgn s he same as he D2C desgn (see Fgues 2.5 and 2.7). The D2C desgn was seleced o ecalculang he

63 39 desgn base shea, because damac changes n membe szes occu when ewe membes exs n he ame. The -secons chosen o hs desgn ae gven n Table The same secon dephs ae used n he D2C and D3 ames, alhough he weghs pe un lengh ae less o he D3 ame. TABLE 2.3 Membe Selecons o he D3 Desgn Soy Level Column Secon Mp (n-k) Beam Secon Mp (n-k) n W27xl4 W27x4 W30x9 T'T') ('\ 0 WV<...:7... W30x9l :7.../V ')/. ') ') Q L,...,..L.L.v W27x94 W27x94 W30x73 W30x73 W30x The D3 ame, sngle bay povdng he laeal essance and sably o he ve - soy sucue was used n paamec sudes nvesgang he pacpaon o nonsucual elemens and desgn base shea level Two-Soy Fame Desgn: D4 A wo-soy buldng, D4 desgn, was suded n some deal, because he undamenal peod o a wo-soy sucue s geneally shoe han a ve-soy sucue. The esmaed undamenal peod s locaed on he maxmum plaeau on he desgn speca. The plan vew o he sucual layou and he elevaon o he ame conguaon o he D4 desgn s, gven n Fgues 2.5 and 2.8. The desgn base shea and equvalen laeal ) oces o hs desgn ae shown n Tables 2.4. The -secons chosen o hs desgn ae gven n Table 2.5. The same column secon was used n j

64 40 boh soes o he D4 ame, hus elmnang he need o any column splces. n addon, he same secon was used o all o he beams n he ame. The laeal sness o he second soes and he sengh o he... membes n he soy wee moe han equed by he code. B2 B2 B2 B2 B2 B C\ C\ C\ C\ u B u B u u u u // / 28.8/ = 44/ FGURE 2.8 u B Noe: G = Pnned Connecon Elevaon Vew o Fame o he D4 Desgn TAB 2.4 Laeal Foces o he D4 Desgn 0.40 sec (Esmaed) T 0 0])(26)3/ - 4 C 2)(.2)/(0.40)2/3 = 2.76 (Use C = 2.75) V 0... ( 0)(2.75)(3034)/2, kps (VW = 0.092) F - 0 k.ps (T < 0.7 sec). Soy hx 'Wxhx 'Wxhx Fx Leve l l! l..l P S () (k-) 'W h (kps). "-""'":- ='!. -.. 'j : 3: { ') : -- :L u B -""' ; L. L..-

65 4 TABLE 2.5 Membe Selecons o he D4 Desgn Soy Column Level O W8x76 Secon,. b, \n' ) M p Beam Mp (n-k) Secon (n4 ) (n-k) W8x W8x W8x The D4 ame desgn was used n a paamec sudy ha nvesgaed he nluence o he undamenal peod o vbaon o a sucue. Snce he esmaed undamenal peod o he wo-soy sucue was shoe han he ve-soy, he mnmum desgn base shea level as a pecenage o he buldng wegh was lage o he wo-soy ame. The pacpaon o nonsucual elemens, whch had he same sness and sengh as n he ve-soy ames, also was nvesgaed o he wo-soy ame. 2.5 Summay - The desgn o he ames o hs sudy llusae he wde laude gven n he code o he desgn o he laeal oce-essng sysem o a buldng. As s geneally he case o desgn, hee s no a "coec" solu on. bu many possble soluons. Howeve dependng on he des gn cea. one o he desgns may be peeable ove ohe desgns. The magn ude o he desgn base shea was he pncpal deence beween he Dl, D2 and D3 ame desgns o he momen-essng ames o j he ve-soy sucue. The desgn base shea o he Dl ames was 9.2 pecen o he buldng wegh, whle he desgn base shea o he D2 ames was 5.9 pecen o he buldng wegh. The desgn base shea o he D3 ame was 3.9 pecen o he buldng wegh o he d desgn and 4.7

66 42 pecen o he buldng wegh o he sess. The mehod o calculae he L desgn base shea o he D2 ames s ypcal o cuen pacce. The desgn base shea o he Dl ames s consevave and, as a consequence, he expeced soy ds should be less han he D2 ames. The D3 desgn may be unconsevave because he calculaed peod used n he desgn was based only on a bae sucual ame. The acual peod o he sucue,. may be geae han he esmaed peod gven by he code, bu he acual peod s ceanly geae han he calculaed peod o he al desgn. The magnude o he desgn base shea used n he D4 ame desgn o he momen-essng ames o he wo-soy sucue was 9.2 pecen o he buldng wegh. The desgn base shea was lmed by he gven uppe lm o he code, and heeoe a lage base shea need no be used o a seel ame sucue o hs hegh. The bele ha a se and songe sucue s moe consevave (smalle ds and less nelasc behavo) uses an assumpon ha he esponse specum o he gound moon does no ncease sgncanly as he undamenal peods n he ange unde consdeaon decease. Fo he eahquake acceleogams o hs sudy, he elasc esponse speca wee L { l: aly unom ove he equency ange o he lowe modes o vbaon o he vaous ames nvesgaed. L

67 , 43 CHAPTER 3 ANALYSS AND KODELLNG OF FRAME STRUCTURES 3. noducon n ode o deemne he pobable sucual demand on he laeal oce-essng sysem o a buldng dung a majo eahquake, a numecal modellng o he buldng and an acceleaon-me hsoy o he gound moon s necessay. Snce nehe he "exac" load-deomaon behavo o a buldng o he gound moon o uue eahquakes s known, seveal alenaves o boh need o be exploed o deemne a ange n esponse. ""'! j The pocedue o analyze he sucual esponse and selecon o he hsocal eahquake acceleogams ae examned n hs chape. n addon, he modellng o he beam-o-column connecons (panel zones), nonsucual elemens and P-Dela eecs ae pesened n some deal. Ths chape also conans a dscusson concenng he developmen o he numecal models o he me-hsoy analyses. 3.2 Analyss Appoach nelasc me-hsoy analyses wee employed n hs sudy o compue he dynamc esponse o numecal models o vaous ame desgns exced by a se o hsocal gound acceleaon ecods. The esmaon o sucual esponse o a gven gound excaon wh me-hsoy analyss s compuaonally nensve, especally when nelasc behavo s o be consdeed. Much nomaon egadng he popees and behavo o a sucue s equed n a me-hsoy analyss. The soluon pocedue o an nelasc me-hsoy analyss assumes ha he sness o he

68 - 44 sucue emans consan dung each me sep and ha changes n sness only can occu beween successve me seps. The elably o any me-hsoy analyss s dependen on accuae modellng wh ne elemens o he sucue's load-deomaon behavo and he numecal pocedue o solvng he nonlnea equaons o moon. The compue pogam, DRAN-2D, was used o calculae he dynamc esponse o he ame models. The behavo o he ne (o moe aply dscee) elemens used n hs sudy whch wee avalable n he DRAN - 2D elemen "L lbay and he soluon pocedue o he equaons o moon ae explaned n some deal n Appendx A. 3.3 Repesenaon o Desgn Eahquake Eahquake acceleogams, epesenave o he desgn eahquake o he 988 edon o he Unom Buldng Code, wee used n he me-hsoy analyses o compue he nelasc esponse o low-se buldngs usng momen-essng seel ames o he laeal oce-essng sysem. Snce he gound moon o uue eahquakes s unknown and nealy mpossble o pedc. seveal gound excaon ecods, whch ae plausble o a gven se, geneally ae used o deemne he pobable nelasc esponse o a buldng. The adequacy o a sesmc desgn can be judged ae sudyng he esponse om each o he seleced gound moons. Fo smla easons, [ hee hs ocal eahquake acceleogams wee seleced o epesen -he desgn eahquake n hs sudy. All o he me models n hs sudy wee subjeced o each o he eahquake acceleogams. The SOOE componen o he 940 El Ceno eahquake, he N65E componen o he 966 Pakeld eahquake and he S69E componen o he 952 Ta L

69 45 eahquake wee seleced o he base excaon ecods o he me-hsoy analyses. These eahquake ecods wee chosen because o he deen chaacescs n he gound moons. The El Ceno ecod conans a boad equency ange o gound acceleaon and has seveal peods o song gound moon. The Pakeld ecod has a sngle bus o song gound moon and s composed o lowe equency gound acceleaon. The Ta ecod has hghe equency gound acceleaon and a long duaon o modeae gound moon. n hese hee eahquakes mos o he song gound moon occued whn he s weny seconds o excaon. As a consequence, he me-hsoy analyses wee peomed usng only he s weny seconds o gound excaon o each ecod. The acceleogams o each o he hee eahquakes ae shown n Fgue 3.. The eahquake acceleogams needed o be scaled o abou he same level o "nensyll, so ha he esponse calculaed om each eahquake could be compaed. n addon, he scalng o each eahquake ecod was supposed o poduce excaon epesenave o he desgn eahquake o enable compasons beween he calculaed esponse and he ancpaed esponse o he code. The "desgn" eahquake, as chaacezed by vaous. buldng codes, has he capably o geneae sgncan nelasc deomaons n he laeal oce-essng sysem - ducles n he ange o ou o ve o momen-essng seel ames. An assumpon n he 988 UBC s ha he chance o exceedng he nensy o he desgn eahquake s esmaed o be en pecen n y yeas [4,6,43]. should be noed ha hs denon o he desgn eahquake does no epesen he maxmum cedble eahquake o he egon bu only he maxmum pobable eahquake.. -

70 46 -: "!. --. Z 0 -E-4 < u -< El Ceno z 0.25 o OO -H-M $ < Pakeld z 0.25 o OO +HW $ < TME (sec) Tal ' FGURE 3. Unsealed Eahquake Aeeeleogams

71 47 A smoohed elasc esponse specum s used o ancho he desgn, specum n he 988 edon o he Unom Buldng Code. n acualy, he code only uses equaons o oban he desgn base shea, bu a plo o hese equaons can be hough o as a smoohed elasc esponse specum and a desgn specum. The smoohed elasc esponse specum, based on a ( j.. j ve pecen damped sngle-degee-o-eedom sysem, has a maxmum specal acceleaon o. g o hghly sesmc egons (zone 4). Nau and Hall [33] showed ha a scalng pocedue based on sucual esponse, ahe han peak gound moons, gave less dspeson n he esponses om seveal ecods. n a moe ecen sudy [] egadng he deemnaon o he desgn eahquake, one concluson ound om hs sudy also was ha peak gound moons ae no an accuae paamee o classy he nensy o a gound moon. Snce he desgn specum s anchoed o an elasc esponse specum, he elasc esponse speca o he eahquake acceleogams wee used o deemne he scalng o he seleced hsocal acceleogams. The elasc esponse speca o a ve pecen damped sngle-degee-o-eedom sysem exced by he s weny seconds o each eahquake ae shown n Fgue 3.2a along wh he elasc esponse specum used o ancho he desgn specum o hs nvesgaon. A wo sep pocedue was used o calculae he scalng acos.o he acceleaon values o each eahquake acceleogam. The s sep n he scalng pocedue was o nomalze he eahquake ecods, so ha hey all j had he same specum nensy ove a speced equency ange. The specum nensy s gven by SV() d; (3.)

72 48 whee SV() s he specal pseudovelocy and s he equency n Hez. Housne's denon o specum nensy has negaon lms o 0.4 and 0.0 Hez [22]. Howeve, he negaon lms used n hs nvesgaon wee 0.5 and 3.0 Hez; hs ange had bee coelaon wh he naual ;.. -. \ equences domnang he esponse o he modelled ame sucues and also was he egon o he esponse speca conolled by velocy. The specum nenses o each eahquake ae gven n Table 3.. The values gven n he column labeled "SF " wee he scale acos ha esuled n equal spec un nens es. The usage o hese scale acos ended o goup ogehe he elasc esponse speca. The absolue vecal poson o he hee speca was deemned om he second sep o he scalng pocedue, whch shed he speca as a goup FREQUENCY (cps)..! l FGURE 3.2a Unsealed Elasc Response Speca o Fve Pecen Dampng L

73 TABLE Scalng Facos o Eahquake Acceleogams Recod Sv SF Sa SF z SF (njsec z ) (g's) El Ceno Pakeld ( Ta The second sep o he scalng pocedue conssed o posonng he hee esponse speca. A new specum was ceaed by aveagng a each equency he pseudoveloces o each esponse specum scaled wh he coespondng scale aco calculaed n he s sep o he scalng pocedue. The aveage specal acceleaon o he new specum was calculaed ove he equency ange o 2.0 o 4.0 Hez. The lowe lm o 2.0 Hez was oughly he locaon whee acceleaon begns o conol a ypcal esponse specum. The uppe lm was seleced, because bounded he desd quency ange and povded a wde enough equency ange o scalng. The aveage specal acceleaon s dened as. \ 4.0 Hz 0 SA() d, (3.2) 2.0 Hz whee SA (.' s.," specal pseudoacceleaon. The.v.. :.lf' spec al acceleaon o he aveage o he hee scaled ecods was c"d o be. g, maxmum acceleaon o elasc esponse envsoned by he code, bu was calculaed o be.3 g o he aveage o he hee scaled acceleogams. Theeoe, he second scale aco, SF z, s

74 50 equal o. dvded by.3. The nal scale acos o each ecod, gven n he column labeled "SF" n Table 3., ae he poduc o he scale acos, SF, calculaed n he s sep and he scale aco, SF z, o he second sep. The nal poson o he scaled elasc esponse speca ae shown n Fgue 3.2b along wh he elasc esponse specum used o ancho he desgn specum. should be noed ha he Pakeld acceleogam was. o - - scaled down o he level o he desgn eahquake, because hs ecod was vey song n he equency egon unde consdeaon n hs sudy_ FGURE 3.2b FREQUENCY (cps) Scaled Elasc Response Speca o Fve Pecen Dampng The maxmum esponse quanes o a ame model wh an elasc o nealy elasc esponse would be appoxmaely he same as a excaon wh each scaled ecod. esul o As would be expeced, he deences,. beween he calculaed esponses om each eahquake acceleogam would be

75 5 moe pevalen as he level o nelasc esponse nceased. The vaaon n esponse can be judged (vsually) by nong ha he calculaed esponse o he ame models n hs sudy anged om soy ds smalle han he desgn levels o soy ds lage han en mes he desgn levels. 3.4 Beam-o-Column Connecon Modellng The load-deomaon behavo o a seel sucual ame s dependen on he sness and sengh o he columns and beams, and also on he sness and sengh o he connecons beween he columns and beams. n one o he paamec sudes o hs nvesgaon, he nluence o he beam-o-column connecons on he nelasc behavo was examned. The nheen lexbly and yeld sengh o he beam-o-column connecons aec he naual equences o a sucue and he locaons o hyseec enegy dsspaon dung nelasc excusons. The assumed behavo o he beam-o-column connecons n he me-hsoy analyses was dependen on he assumpons made dung he modellng phase o each ame. The panel zone o a gd ype beam-o-column connecon s he lengh o he column locaed beween he beam langes a a jon. equed o sasy he sengh o sably equemens o he code, column web senes and/o double plaes can be added o he panel zone. Shea, l j sesses ae developed n he panel zone when an unbalanced momen exss beween he beams amng no he jon. n he case o a sngle beam amng no a jon, he end momen o ha beam s he unbalanced momen. Shea sesses n he panel zone cause shea deomaon and possbly yeldng o he panel zone. Dsoon o he panel zone ales he angle beween he columns and beams amng no he jon. An exaggeaed vew

76 52 o shea deomaon n a panel zone om unbalanced beam momens appled o a ypcal neo beam-o-column connecon s shown n Fgue 3.3. FGuRE 3.3 Exaggeaed Deomaon o a Panel Zone The connec:,on elemen avalable n he DRAN-2D elemen lbay was ulzed n :h,! a:::l models so ha, desed, shea deomaon n a panel zone co-:c.! ).odelled wh a blnea momen-oaon elaonshp, The momen anseed by he connecon elemen was el. '. c ::-.e elave oaon beween he ends o he columns and beams a: a. :: The pa a:!:': - s:: udv o connecon behavo -was compsed o ou models o pod-,le '- ] 0 o wh deen sness and sengh. The oveall behavo o a jon was dependen on he chaacescs o he.. columns, beams and panel zone locaed a a jon. The physcal meanng o each connecon model s descbed nex: \ l :.

77 53 ) No Panel Zone (NPZ) model denoes a gd connecon allowng no elave oaon beween he columns and beams amng no a jon and havng plasc hnge locaons o he columns and beams a he nesecpn o he membe cenelnes o he jon - he ypcal behavo o beam- o-column connecons n ne elemen models o momen-essng ames; 2) Rgd Panel Zone (RPZ) model denoes a gd connecon allowng no elave oaon beween he columns and beams amng no a jon and havng plasc hnge locaons o he columns and beams a he connecon aces o he jon; 3) Elasc Panel Zone (EPZ) model denoes a lexble connecon allowng elave oaon beween he columns and beams amng no a jon, havng he elasc sengh o develop he ull plasc momen o he beams amng no each jon and havng plasc hnge locaons o he columns and beams a he nesecon o he membe cenelnes o he jon; 4) nelasc Panel Zone (PZ) model denoes a lexble connecon allowng elave oaon beween he columns and beams amng no a jon, havng he nelasc sengh, ae yeldng o he panel zone web, o deve lop he ull plasc momen o he beams amng no each jon and havng plasc hnge locaons o he columns and beams a he nesecon o he membe cenelnes o he jon Rgd Connecon Behavo n boh o he gd connecon models desgnaed as NPZ and RPZ, no elave oaon occued a a jon. n he s gd connecon model,

78 54 he nluence o he panel zone was compleely neglec ed. The lexble lenghs o he columns and beams, as shown n Fgue 3.4, wee aken o be equal o he cenelne-o-cenelne dmensons. The ncease n ame -. lexbly due o he usage o cenelne dmensons s hough, n common pacce, o compensae o neglecng he lexbly o he connecon. The 988 edon o he Unom Buldng Code allows he deomaon n he panel o be gnoed, cenelne dmensons ae used n he soy d calculaons and he sengh o he panel zone s above a speced level. Membe Cenelnes ;., L Face - o - Face Dmenson s, FGURE 3.4 Dmensons o Typcal neo Fame Yeldng o a column o beam end occued when he momen acng a an end exceeded he yeld momen capacy o he secon. Dependng on he elave yeld momens o he columns and beams a a j on, he plasc \

79 55 hnge locaons would ehe om n he column o he beam ends. Howeve, hs s no he bes physcal epesenaon o he acual behavo o he connecon because yeldng o ehe he columns o he beams would occu a he connecon ace whee he momen s maxmum o he clea span poon o he beam. j : j The panel zone web o he ohe gd connecon model was assumed o be gd. The deomaon mode o he panel zone was a gd body moon, so no yeldng o deomaon occued wh he panel zone egon. An eccenc y a each end o he columns and beams equal o hal o he column deph o he beams and hal he beam deph o he columns was speced o move he plasc hnge locaon om he end o he membe o he connecon ace. Theeoe, he lexble lenghs, as shown n Fgue 3.4, o he columns and beams wee aken o be equal o he ace-o-ace dmensons (clea span). Face-o-ace dmensons poduce he ses modellng o a ame. The ncease n sness can be que sgncan o ames wh deep secons, snce he laeal sness o a column s nvesely elaed o he lexble lengh cubed. Yeldng o a column o beam a he connecon ace occued when he momen a he connecon ace exceeded he yeld momen capacy o he secon. A ee body dagam o a ypcal beam elemen whou any oces ; appled along he lengh o he membe s shown n Fgue 3.5. n ac, any oces along he membes ae conveed o equvalen nodal loads n he j \ j DRAN-2D compue pogam. Snce no oces ae appled along he membe, he shea n he membe s consan and he momen vaes lnealy om one end o he ohe. Theeoe, he maxmum momen and any yeldng always occu a an end o a membe.

80 56 2. de 2. de 2 2 l--p:l_ :a_ml_e:n:_ -)- \ V LE: :... Face _ o _ Face Dmenson..: : M RE,-- "',, Cenelne - o - Cenelne Dmenson, -..', : : End Eccences o Beam : : A,,,,,, :: Shea Dagam :: V LE ;...; ;...;.-.;...,;, V RE, ALE MLF Dagam. " '' l FGURE 3.5 Fee Body Dagam o a Typcal Beam Elemen L L

81 57, ) As shown n Fgue 3.5, he momen a he end o he membe s appled o he node and mus be n equlbum wh he ohe momens acng a he node. n addon, he momen a he end o a membe s equal o he momen a he connecon ace plus he shea acng a he connecon ace mes he dsance beween he end node and connecon ace (end eccency). The momen acng a he ace o he connecon s always less han he, momen acng a he end o a membe n double (evese) cuvaue, whch s geneally he case o he columns and beams o a laeal oce -essng ame wh small vecal loads. n ac, he end momens o each o he beams amng no a jon s appoxmaely he same and acng n he same decon, because he exenal oces appled o he beams ae elavely small compaed o he laeal oces Flexble Connecon Behavo The connecon models desgnaed as EPZ and PZ wee boh assumed o be lexble. The oces acng a a ypcal neo beam-o-column connecon ae shown n Fgue 3.6a. The oces, Fh and Fv, ae he exenally appled oces (nea, sac o boh) o he jon. No axal oces ae pesen n he beams o hs sudy because he beams ae assumed o be axally gd. A ee body dagam o he uppe pa o web plae senes o a panel zone wh plae senes s shown n Fgue 3.6b. The shea oce, V pz ' acng above and below he panel zone egon s essed by he web o he panel zone and he langes o he columns. s que possble ha he shea sengh o he panel zone can conol he amoun o momen ha can be anseed beween he columns and beams a a jon. j

82 58 "'" {., c MA c - :;"., l VA «'L ( ML ;:::::::::;:::::::::::::::::::::;:;:::::::::::;::::::::::::::::::::':::::::::::=,::':::::'" v) TH Fv... VB M lvr ) \--.- _._ O=VA-VB+F H o = P A - P B + V L - db V R + Fv 0= MA +MB -ML-MR j (. l FGURE 3.6a Foces Acng a an neo Panel Zone (. [ V PZ ) '- FGURE 3.6b Foces Acng on Uppe Pa o Senes

83 ) 59, The shea oce couple a whch yeldng o he panel zone web naes s gven by whee O.55Fy s he yeld shea sess, de s he deph o he column and s he hckness o he panel zone web ncludng any double plaes., The model o he sengh and sness calculaons o a panel zone, shown n Fgue 3.7, was developed by Kawnkle [29]. The eecve shea aea o he panel zone web has dmensons o nney- ve pecen o he column deph and nney-ve pecen o he beam deph. The panel zone web, whch has an elasc-peecly plasc behavo, yelds a he shea oce gven by Equaon 3.3. The column langes conbue o he shea sengh ae yeldng o he panel zone web and unl he shea deomaon eaches ou mes he yeld shea san. The equaon gven n he 988 UBC o deemne he shea sengh o a panel zone s based on he equaon developed by Kawnkle. The maxmum shea oce couple ha heoecally can be appled o he panel zone s gven by (3.4) whee be s he wdh o he column langes, e s he hckness o he j column langes. The s em conaned n he backes o Equaon 3.4 coesponds o he sengh deved om sheang o he panel zone web, whle he second em elaes o he sengh conbuon om bendng o he column langes a he cones o he panel zone.

84 60 O.95d b FGURE 3.7 Y V Rgd Boundaes V,. O.95d c -"/ l Panel Zone Web Ky : 0 S Y s Yy! Column Flange Hnges ; Ky : Yy s Y s 4yy Model o Sness and Sengh o Panel Zone The behavo gven by Equaons 3.3 and 3.4 can be expessed wh a blnea load-deomaon elaonshp. The elasc shea sness o he beam-o-column connecon, whch s he elasc sness o panel zone web, o he blnea elaonshp s dened as (0.95d c )G, (3.5) whee G s he shea modulus o he panel zone web. The shea-deomaon ealonshp o he panel zone web s assumed o be elaso-plasc. The san hadenng shea sness o he beam-o-column connecon, whch s he bendng sness o column langes, o he blnea elaonshp s \!.. dened as

85 6.04 bcg 0.95d b (3.6) l A vecal oce acng above he panel zone educes he yeld shea sess o he panel zone web. The educon aco gven by von Mses yeld ceon s expessed as: ; a (3.7) whee P s he axal column oce a he desgn level and P y s he yeld axal oce o he column. Howeve, he educon aco was gnoed n hs sudy, because axal desgn oce o each column was small n compason o he yeld capacy. Snce he shea load-deomaon behavo o a panel zone s modelled wh a DRA-2D connecon elemen (oaonal spng), he shea sness, san hadenng and sengh o he beam-o-column connecon ae conveed no momen - oaon elaonshps. As shown n Fgue 3.8, he elave oaon beween he columns and beams amng no a jon s he same as he shea d!omd:on n he panel zone. The elave oaon beween he colu::s a)c... a.:xs. amng no a jon s elaed o he momen anse. The o:a:o..a: elas:c sness o he connecon elemen s dened by Ke - {C C K--y - (0.95)(0.95dc)G. (3.8) The oa: lona: s:an hadenng sness o he connecon elemen s expessed as (3.9) ',

86 62 The yeld momen o he connecon elemen s wen as (3.0). v v FGURE 3.8 Momen-Roaon Relaonshp o Connecon Elemen n hs sudy, boh lexble connecon models o he beam-o-column connecons wee desgned o have he capably o anse an unbalanced beam momen equal o he sum oal o he plasc momen o he beams. The desgn shea oce couple acng above and below he panel zone om he unbalanced beam momen s dened as (3.) ;..,, whee Hpb s sum oal o he plasc yeld momen o he beams and O.95d b s he eecve deph o he beams amng no he jon. The s modellng o he panel zone o a lexble connecon had he sengh equed o develop he ull plasc momen o he beams deved enely om he panel zone web. Theeoe, he beam-o-column connecons

87 . 63 vually emaned elasc dung he gound excaon. The panel zone web hckness was deemned om Equaon 3.3, whee Vy was equal o he shea ] oce gven by Equaon 3., and can be expessed as (3.2) n he ohe model o he panel zone o a lexble connecon, he equed sengh o he panel zone was developed om boh he panel zone web and he column langes. Ths beam-o-column connecon model yelded po o developng he ull plasc momen o he beams, bu could develop he momen ae he shea san eached ou mes he yeld san. The panel zone web hckness was deemned om Equaon 3.4, whee Vu was equal o he shea oce gven by Equaon 3., and can be expessed as b (3.3) The san hadenng aos gven by Equaon 3.9 geneally wee less ] han ou pecen and even as low as one and a hal pecen. Howeve, es esuls o panel zone yeldng ypcally had san hadenng aos o moe "'\ han ve pecen. Thus, he san hadenng aos n hs sudy wee assumed o be ve pecen, egadless o he popees o he panel zone. The phys cal deence beween he wo lexble connecons was he hckness o he panel zone web. The web hckness o he elasc panel zone was geae han he web o he nelasc panel zone. The elasc panel zone had a yeld momen equal o he sum oal o he plasc yeld momen o he beams. Howeve, because o he hghe san hadenng ao o he panel zone elemen, he majoy o yeldng occued n he beams

88 64 (assumng song column-weak beam desgn) ahe han yeldng o he panel zone web. The nelasc panel zone had a yeld value less han he sum oal o he plasc yeld momen o he beams o a jon. Theeoe, yeldng occued n he panel zones unl he nelasc deomaons ae lage enough o cause he yeldng o develop n he beams. The boh lexble connecon models o he panel zone had he shea sengh o develop he ull plasc momen o he beams amng no he jon. Howeve, he 988 UBC saes ha he sengh o he panel zone need no develop moe han eghy pecen o he ull plasc momen o he beams. he eghy pecen lmaon was ollowed, mos o he yeldng a a jon would occu n he panel zone, because he panel zone would mos lkely no have he ably o anse enough momen o he beams o cause hem o yeld. 3.5 Nonsucual Elemen Pacpaon The nonsucual elemens n a buldng can be negleced, he nonsucual elemens ae solaed om he laeal oce-essng ame. n mos nsancs, especally dung nal excaon, he nonsucual elemens e ec h> "sponse, because he nonsucual elemens ae no compleely so:dc and hey possess laeal sness and sengh as evden by ac U.c: '.'4' ses calculaed peods o vbaon, obseved dampng and maxmum soy!.h'as. n ac, he 9bseved undameal peod o buldngs can be $lgcanly hghe po o any degadaon o he nonsucual elemes. The sness and sengh o he nonsucual elemens (claddng, neo walls, neo ames, ec.) wee no consdeed n he dec {. \ l l \ L

89 65 desgn pocedue o he momen-essng ames, snce he sengh o he nonsucual elemens was no oblged o povde any laeal essance. The nonsucual elemen conbuon s dcul o assess, snce he nonsucual elemens end o be less ducle han he ame and, hus, yeld and degade ae lmed deomaons. n addon, s beleved o be consevave o gnoe he sness and sengh conbuon o he nonsucual elemens, snce he laeal oce-essng ame would be desgned o ess all o he equvalen laeal oces.,.}, Shea panel elemens, avalable n he DRAN-2D elemen lbay, wee added o seleced ame models o accoun o he pacpaon o he nonsucual elemens. The load-deomaon behavo o he shea panel elemen s explaned n Appendx A. The load-deomaon behavo o he shea panel elemens dd no model any pacula componen o maeal, bu was suppose o possess he compose chaacescs o he elaonshp beween he nonsucual elemens and he laeal oce-essng sysem. The shea panel elemen, as shown n Fgue 3.9, was aached o he ame a he locaon o he beam-o-column connecons. The shea panel elemen dd no conbue o he oaonal sness o a jon and dd no mpnge upon he end oaon o he columns and beams. The laeal sness o he shea panel elemen o each soy mulpled by he soy he gh was consan o all soes n a ame model, snce he "same amoun" o nonsucual elemens was assumed o be n each soy. Thus he absolue ncease n laeal sness and sengh o each soy was he same, bu he elave ncease was much geae o he uppe soes o j

90 66 Membe Cenelnes {' { j 'l:.. FGURE 3.9 Aachmen a o Shea Panel Elemen 3.5. Lnea Load-Deomaon Behavo The nal aemp o deemne he mpac o nonsucual elemens on he dynamc esponse o a ame employed a smple modellng o he behavo o nonsucual elemens. The load-deomaon behavo, as shown n Fgue 3.0, was aken o be lnea wh a alue san (oal loss o sness and sengh) o nches/nch. Ae eachng he alue san, he elemen no longe pacpaed n he esponse o he ame. The desed load-deomaon behavo o he nonsucual elemens could be modelled wh a sngle shea panel elemen pe soy. The lnea shea panel elemens wee added o he DB desgn o a ve-soy ame. The sness o he lnea shea panel elemens was chosen o shoen he calculaed undamenal peod o he ve-soy ame o he esmaed value gven by he 988 UBC. The calculaed peod o he bae sucual sysem o he DB desgn was aound.25 whle he l

91 67 esmaed peod gven by he 988 UBC o a ve-soy buldng was 0.77 seconds. To oban he desed undamenal peod, he laeal sness o he ame model wh nonsucual elemens was appoxmaely wo and a hal mes geae han he laeal sness o he bae sucual ame model.,. j. j -en ; -U < < U U * Falue o Lnea Model 3 Fs Fa.lue o Tlnea Model C3 Second Falue o Thnea Model Thd Falue o Tlnea Model ::; lk:ly::-:l j o FGURE 3.0 STORY DRFT RATO (%) Load-Deomaon Behavo o Nonsucual Elemens Tlnea Load-Deomaon Behavo The lnea shea panel elemens had a esponse o he ames. sgncan nluence on he Snce he alue o hs elemen was ahe abup, he sness and sengh degadaon o he elemen was ened. The load-deomaon daa om he Nonsucual Elemen Tes Phase o he U.S. -apan Coopeave Reseach Pojec on a Full-Scale Seel Tes Fame [45,46,47] was used o oban a moe ealsc behavo o nonsucual elemens. The daa om hs es phase was aken om a sac cyclc

92 68 loadng o a sx-soy sucue wh claddng aached o he exeo ames and nll walls along he neo ame. The es daa o one o he soes s shown n Fgue 3. o cycles o nceasng deomaon. The sness value gven n each plo epesen he slope o lne beween he maxmum excusons n each decon. The hyseess loops shown epesen he load-deomaon behavo o boh he sucual seel ame and nonsucual elemens. Theeoe, some o he degadaon s due o he ame, bu mos o s due o he deeoaon o he nonsucual elemens. The conbuon o he bae seel ame o.v hs soy was esmaed om he esuls o anohe soy n he ame whouc nonsucual elemens. ns ead o us ng one shea panel elemen-. pe soy, hee elemens havng deen load-deomaon chaacescs wee used. Each o he shea pane elemens had a lnea load-deomaon behavo and speced alue san. The load-deomaon behavo om he combnaon o he hee shea panel elemens, shown n Fgue 3.0, degades n sness and sengh a pedened deomaons. The nal sness o he lnea model o nonsucual elemens was dencal o he nal sness o he lnea model o nonsucual elemens. Howeve, he sness was assumed o decease by y pecen ae he shea san eached nches/nch, heeae he shea san was aken o be weny pecen o he n a value unl he shea san eached nches/nch and nally a a shea san o 0.0 nches/nch he lnea nonsucual elemen was assumed o al. Unloadng ae a alue (degadaon) o a nonsucual elemen occued along he dashed lne o he ogn. l l

93 -l o.c. -- <: :::= n. 0 n o K = 350 k/n K = 280 k/n l! V / l ,, l o.c. :::= n. 0 n - l O o.c 200. <: o. :::= n. - - K = 240 k,/n,v K = 20 k,/n - K = 220 k,/n K = 90 k/n u:l STORY DRFT RATO (%) STORY DRFT RATO (%) 2.0 FGURE 3. Load-Deomaon Behavo o a Soy wh Nonsucual Elemens Aached o he Fame o he Full-Scale Tes ' {

94 .}' ; 70 The lnea nonsucual elemens wee added o he DB desgn o a ve-soy ame o examne he nluence o hs assumed nonsucual elemen behavo. n addon, he lnea nonsucual elemens wee added o he ohe ame models, so ha he esponses o hese models wh and whou nonsucual elemens could be compaed. l. 3.6 P-Dela Eecs P-Dela eecs wee no accouned o n he dec desgn pocedue o he momen-essng ames n hs sudy, because he povsons o he 988 edon o he Unom Buldng Code spulae ha sucues locaed n zones 3 and 4 o he Sesmc Zone Map o he 988 UBC and sasyng he d lmaons o he code need no consde -P-Dela eecs. Howeve, P-Dela eecs, asng om he nsably o he neo ames, wee nvesgaed n hs sudy. n low-se sucues n whch all o he ames ae essng laeal oces, P-Dela eecs geneally ae no o concen, because he axal compessve oces n he columns ae no lage enough o cause sgncan second ode dsplacemens. Howeve, he sucues n hs sudy ulzed momen-essng ames along only he pemee o ess he laeal oces. The neo ames havng Gnly pnned beam-o-column connecons povded no laeal essance o sably and wee desgned o cay he gavy loads o he buay aea. Theeoe, he exeo ames no only povded he laeal essance o he sucue, bu also aced o sablze he dsplaced neo ames hough daphagm acon o he loo and oo slabs..,! \ (

95 7 To deemne P-Dela eecs wee sgncan, he me-hsoy analyses o some o he ame models wee peomed wh and whou he ncluson o P-Dela eecs. As an appoxmae means o accoun o P-Dela eecs, he laeal sness o he soes wee educed, so ha lage soy ds wee equed o manan equlbum o he deleced sucue. The modellng o P-Dela eecs could be hough o as applyng a each me sep an addonal shea oce a each soy level equal o he oal wegh acng on he soy mes he soy d dvded by he soy hegh. One advanage o he appoxmaon o P-Dela eecs wh hs ype o modellng s ha no eaon o deemne he P-Dela oces s equed whn a me sep. 3.7 Developmen o Numecal Models Snce a ame model could have many vaaons, he developmen o a genec numecal model whch could be used by all models would be desed, so ha he nepeaon o he esuls would be ease. Thus n some models, elemens ha wee no necessay o model he desed behavo wee used. Fo nsance, n ame models wh gd beam-o-column connecons, a connecon elemen was no necessay, bu could be used he oaon sness and yeld momen was lage n compason o he ohe elemens. The elemen numbeng scheme, shown n Fgue 3.l2a, was used o all ame models o hs conguaon. The columns and beams o an exeo ame, ncludng he membes no essng laeal oces, wee epesened n each ame model. Connecon elemens, wee used n he ame models o aach he columns o he beams a he momen-essng connecons. The sness and sengh o he connecon elemens wee dependen on he

96 72 desed behavo o he beam-o-column connecon. Shea panel elemens 'o he lnea behavo o nonsucual elemens ae shown as he shaded egon n each soy. n he case o he lnea behavo o nonsucual elemens, hee shea panel elemens pe soy wee used Cl Cl Cl ell 7.5 N Cl en?.8:8:<': 7.g.0 ::-:< -:>:::Q. 6.g en 7.. ::: 7.5 :-:',. :<, : ! U N co.0 8.g ee ---- co...;. 8.8 a: co 8.7 ee ---- co N 8.6 ee ---- co eel FGURE 3.l2a Elemen Numbeng o Fve-Soy, Fve-Bay Fame The columns n he addonal bay, shown wh dashed lnes, caed he vecal oces necessay o oban P-Dela eecs..a. The elemen sness max o each o he columns n he addonal bay ncluded geomec sness conbuons. As a consequence o he columns n he addonal [ bay havng pnned end connecons, no laeal sness esuled om he maeal sness o he columns. The oveall laeal sness o each column was negave he axal oce n he column poduced compesson! and posve he axal oce n he column poduced enson. The compessve oce acng n a P-Dela column was equal o he wegh o he soy levels locaed above he column. When P-Dela eecs wee gnoed, he axal oce n each column was zeo, and he P-Dela bay povded no conbuon o he oveall laeal sness o he soes. The beams o ( [

97 73 he addonal bay aced as a lnk o anse he sablzng oces om he acual ame o he P-Dela columns. The node numbeng scheme, shown n Fgue 3.2b, also was used o all ame models o hs conguaon. A pa o nodes was equed a he connecon elemen locaons. One o he nodes, desgnaed wh a B", was he end node o he beams amng no he j on and he ohe node, desgnaed wh a C", was he end node o he columns amng no he jon. The vecal anslaons o each pa o nodes wee consaned o be dencal. The hozonal anslaons o all he nodes n a soy level wee consaned o be dencal, snce he axal deomaons o he beams wee gnoed. The momen anseed beween he columns and beams by he connecon elemen a a momen-essng connecon was a uncon o he elave oaon beween he pa o nodes B 55B 5gB Me 5C 58C.(. 4,2B 44:B.(.8B 43C 45C '('7C 30 3B 33B 37B 32C 3.(.C 36C 9 20B 22B 26B 2C 2SC 25C 8 9B 3B 5B loc 2C l4:c 2 3.( FGURE 3.2b... lb 60C 50B '('9C 39B 38C 28B 27C B 6C : Node Numbeng o Fve-Soy, Fve-Bay Fame 7 j

98 74 CHAPTER 4 PARAMETRC STUDES AND RESULTS 4. noducon The goal o he paamec sudes pesened n hs chape was o deemne, and by how much, cean paamees nluence he nelasc esponse o low- se seel ame sucues asng om song gound moon. s deemned ha a pacula paamee does mpac he + calculaed esponse o a buldng, hen hs paamee may need o be consdeed n he desgn pocess and dealed n he mahemacal model o he analyss o he sucue, so ha he desgn pocess s compable wh he expeced behavo o he buldng. Theeoe, mpovemens o dec desgn pocedues may be needed o oban equvalen laeal oces whch coelae o he expeced nea oces poduced by he desgn eahquake. Sae and ecen laeal oce-essng sysems capable o whsandng he desgn eahquake ae hghly dependen on deemnng he ancpaed nelasc behavo o sucues, so ha unnecessay saey acos can be elmnaed whou saccng le saey. The dec desgn pocedue gven n he 988 edon o he Unom Buldng Code s a vey smplsc appoach o a complcaed poblem because o he dculy n assessng he sness and sengh o a buldng, and he nably o oecas he gound excaon o uue eahquakes. n addon, a sucual engnee geneally can no jusy he cos o a moe dealed analys s (modal o me -hs oy) o a low-se buldng. The poblem s how o manan a smple and geneal desgn pocedue and a he same me poduce desgns ha ae sucually adequae and economcally

99 easble. 75 The ocus o hs sudy s o deemne he cuen dec desgn pocedue o he 988 UBC esuls n buldngs ha behave n he manne expeced by he code wes and moe mpoanly ha peom sasacoly dung a naj o eahquake. Theeoe, seveal paamees ha mayo may no be consdeed n he dec desgn pocedue, bu ha ale he sesmc behavo o a buldng, wll be nvesgaed o deemne he nluence on he sucual esponse. n an analycal sudy o hs ype he amoun o geneaed oupu daa s ovewhelmng. The challenge s o nepe and pocess he sgncan daa, so ha mplcaons as hey pean o paccal desgn applcaons and buldng codes can be deemned. Geneal nomaon elaed o he se lee on 3nd pesenaon o he geneaed daa om he me -hs oy analyses s explaned n hs chape. n addon, nluence o he gound moons seleced o hs sudy on he sucual esponse s dscussed n s one de al. n sepaae secons o hs chape, he developmen o each paamec sudy. along wh esuls and conclusons s gven. The esuls o each paam'c sudy ocuses on he calculaed esponse asng om song,c '..;.nc! o: lons n ode o undesand he nelasc behavo o he S OOle 0 he esuls wee compaed o he dec des gn pocedues o cen:ne he nelasc behavo o he sucue was. epeselav" o he behavo assumed n he code. The chape has an ove a s '.'"!." secon ha eeaes he mpoan conclusons as hey e la e o h" '' 0 mance, des gn o analys s o a momen -es s ng ame sucue o each paamec sudy and also ncludes some geneal conclusons abou he paamec sudes. (

100 Selecon and Pesenaon o Oupu Daa Ae much delbeaon, he nepeaon o he esuls om he me-hsoy analyses o he ame models was chaacezed by sudyng: a) he laeal dsplacemen o each soy level; b) he oal hozonal shea L essed by he membes o each soy; c) he accumulaed npu enegy and dsspaon o he npu enegy; d) dsbuon o hyseec enegy. These quanes wee seleced, because he soy ds and soy sheas povded an oveall pcue as o how he sucue esponded o he gound excaon. n addon, he maxmum soy ds and soy sheas obaned dung each me-hsoy analyss wee compaed o he allowable soy ds o he equvalen laeal oces, he maxmum expeced soy ds om nelasc behavo as a esul o excaon_.wh he desgn eahquake and he desgn soy sheas asng om he equvalen laeal oces o a specal momen-essng space ame (SMRSF). The maxmum compued soy ds also wee compaed o he expeced soy ds poposed n he 988 UBC. The enegy quanes, whch wee a uncon o he esp.onse and.. popees o he ame model, gave an ndcaon as o he manne n whch a sucue dsspaed he npu eney and absobed he hyseec enegy. A subsanal amoun o daa can be geneaed dung each me-hsoy [ analyss o a ame havng many degees o eedom and membes. The amoun o oupu daa geneaed dung he me-hsoy analyses was mnmzed by, only wng he esuls o evey h me sep o he oupu le. The L me sep o each analyss was 0.0 seconds, and he coespondng ncemen beween saved daa pons was 0.05 seconds. Even so he analyss o such a ( massve volume o daa consues a majo ask.!

101 77 The esuls ae pesened n gaphcal om o ease assessmen and compehenson o he esponse and compason wh ohe ame models. Mos o he jaggedness conaned n he aces o vaous plos s a consequence o only samplng evey h me sep. The cones (locaons) o yeldng and unloadng geneally ae he aeas ha eque moe samplng o oupu daa o oban "ue" values o esponse because he sness change can be vey abup. n hs nvesgaon, he hyseec enegy dsbuons by j ; elemens and soes wee based on he hyseec enegy dsspaed by he columns and connecon elemens o an neo column lne o a ame model and he beam ends aached o hs column lne. Howeve, he hyseec enegy dsbuons calculaed o hs column lne ae beleved o be efsenave o he dsbuon o he ene sucue. One ype o plo made o each paamec sudy was a me hsoy o soy d and he soy shea-d hsoy o he s soy. Only he esuls o he s soy wee ploed so ha he geneal behavo o he sucue dung he analyss could be seen. Snce an assumpon o he d ec des gn pocedue was ha he sucue would expeence oughly equal ducles hough he hegh o he sucue, he behavo o he s soy would be epesenave o all he soes. Howeve n many o he analyses, ohe laeal modes han he s laeal mode had sgncan conbuons o he esponse. Thus, he behavo o one soy was no necessaly epesenave o anohe soy. Ohe plos ha wee made o each paamec sudy wee envelopes o maxmum soy ds and sheas o each soy. Alhough hese plo gave an ndcaon o he maxmums, hey dd no elae he numbe o mes ha a level o ducly was eached o nealy eached dung a me-hsoy

102 78.' analyss. Howeve, he nomaon conaned n hs plo can be decly elaed o he dec desgn pocedue.., j- Ba chas wee geneaed showng he oal npu enegy and he " dsspaon no dampng and hyseec enegy o each analyss. The deence beween he oal npu and he sum oal o he hyseec plus dampng enegy was he knec and elasc san enegy assocaed wh he sucue a he end o he me-hsoy analyses. n mos nsances, he deence was mnmal because he gound excaons wee small owads he end o he weny seconds. Theeoe, he esponse was dmnshng a he,... compleon o each me-hsoy analyss. Anohe ba cha ha was geneaed showed he dsbuon o hyseec enegy n he seleced neo column lne by boh elemens and soes o each paamec sudy. n addon o hs ba cha, he same nomaon was dsplayed n a moe gaphcal om o (pehaps) ease evaluaon. An elevaon o hs neo column lne was ploed along wh he amoun o hyseec enegy dsspaed n each locaon. hyseec enegy o a locaon was gven as a do n whch he aea symbolzed he pecenage o he oal hyseec enegy dsspaed a ha locaon. These dagams gave a cleae pcue as whch elemens dsspaed hyseec enegy and how a cean paamee possbly aleed he yeld paen o a ame. The 4.3 nluence o Gound Moon on Sucual Response The me hsoes o he dsbuon o npu enegy no hyseec ( (plasc san), dampng (vscous) and soed (knec plus elasc san) enegy o a ypcal ve-soy ame model subjeced o each o he scaled

103 79 eahquake acceleogams ae shown n Fgue 4.. The npu enegy a any pon n me was he accumulaed enegy mpaed no he sucue dung he excaon. The npu enegy nceased o deceased beween successve me seps, dependng on whehe he gound moon a ha pacula me was o was no opposng he moon o he sucue. The hyseec enegy was he poon o npu enegy dsspaed by nelasc deomaon o he membes. The dampng enegy was he amoun o npu enegy dsspaed hough vscous dampng n he sucue. The deence beween he npu and hyseec plus dampng enegy was he amoun o enegy soed n he sucue. Snce he soed enegy was ehe elasc san enegy o knec enegy, he soed enegy was ecoveable as he sucue came o es. Dependng on he equency conen o he gound moon and he domnang equences o he sucue, he soed enegy a mes had lage oscllaons. The equaons mplemened n he DRAN - 2D compue pogam o calculae he vaous enegy quanes dung he me-hsoy analyses ae gven n Appendx A. The El Ceno acceleogam geneally caused wo egons o sgncan hyseec enegy accumulaon sepaaed by a peod o lull excaon. The Pakeld acceleogam geneaed one egon o subsanal nelasc behavo n whch he sucue expeenced lage d excusons dung hs neval, and hen bascally esponded elascally heeae. The Ta acceleogam gadually accumulaed hyseec enegy ove a consdeable poon o he gound excaon. The excaon om he Pakeld ecod was no ha song o he hghe equency ve- soy ame models and he wo-soy ame models, because he equency band was no as boad as n he El Ceno and Ta.

104 El Ce.lo. o o '" l n Pa.keld '--,,- 0:: Z -n.!:a:: >- 0:= Z STORED /Ul'/NC TYSTEREC = TME (sec) \ Ta 20.0 l ( FGURE 4. Typcal Enegy Tme Hsoes o a Fame Model Subjeced o he Scaled Eahquake Acceleogams [ l

105 4.4 Developmen o Paamec Sudes 8 The vaous paamec sudes undeaken n hs nvesgaon ae shown n Table 4., along wh he ame desgns ha wee used n each sudy. The s paamec sudy, beam-o-column sengh ao, acually was "unplanned". The goal o he nal desgn o he ve-soy ame was o have a desgn wh "song column-weak beam" behavo, bu due o he neacon beween he axal oces and bendng momens o he columns dung he me -hsoy analyses, he sengh o he columns a a jon geneally was smalle han he sengh o he beams. Reselecon o songe column secons havng he same laeal sness poduced a desgn wh "song column-weak beam" behavo. TALE 4. Usage o Fame Desgns o Paamec Sudes Paamec Sudy DA DB D2A D2B D2C D3 D4 Beam-o-Column Sengh Rao * * Beam-o-Column Connecon Behavo * Nonsucual Elemen Pacpaon * * * * Momen-Ressng Fame Conguaon * * * Deecve Momen-Ressng Connecons * Desgn Base Shea Level & P-Dela * * * * c. l' '! Sucue Hegh (Fundamenal Peod) * * The second and hd paamec sudes ceneed on he vaance o he assumed laeal load-deomaon behavo o he buldng componens whch ulmaely nluence he behavo o he sucue as a whole. The

106 82 "song co lumn-weak beam" ame desgn o he s paamec sudy was used as he bass o he ame models o hese paamec sudes. One o he paamec sudes nvesgaed he nluence o he beam- o- column connecon behavo o he momen-essng connecons, whle he ohe paamec sudy examned he pacpaon o he nonsucual elemens n essng laeal oces. The ouh paamec sudy concenaed on he ame conguaon o he laeal oce-essng sysem. Snce he deemnaon o he desgn base shea and vecal dsbuon o base shea s ndependen o ame conguaon, he equed laeal sness and sengh o each ame desgn wee appoxmaely he same. The h paamec sudy compaed he esponse o ame desgns wh dencal ae conguaons, bu wh deen des gn base shea levels. The 988 UBC has hee mehods o oban he desgn base shea level o he dec desgn pocedue. The nluence o deecve beam-o-column connecons was examned n he nex paamec sudy. A ame conguaon wh one bay n he pemee ames essng laeal oces was chosen o be suded, because he mpac o a couple o deecve (poo qualy) connecons pe ame could be vey sgncan. The las paamec sudy peaned o he nelasc esponse o a wo-soy sucue. The undamenal peod o he wo-soy sucue was n he ange wee he desgn speca s a maxmum and ndependen o he undamenal peod o he sucue. One o he key pons o hs nvesgaon was o deemne he nlasc behavo o he sucue was compable wh he assumed behavo l o he code. The code expecs an even dsbuon o ducly ove he hegh o he sucue and maxmum soy ds o less han one and a hal

107 83 pecen o he soy hegh. Soy ds beyond hs level could seously compomse he suvvably o he sucue because he negy o he connecons would be quesonable and second ode eecs may lead o even moe nsably nvesgaon o Beam-o-Column Sengh Rao The dec desgn pocedue o he 988 edon o he Unom Buldng Code s no only concened wh he laeal sness and sengh o he momen-essng ames, bu also he nelasc behavo o he ame. The 988 UBC advocaes "song column-weak beam" desgn o momen-essng ames, alhough unde cean condons "song beam-weak column" desgn s pemed. The oaonal sengh ao o he columns and beams a a momen-essng connecon mus sasy he ollowng elaonshp, gven n he 988 UBC: >.0, (4.) whee Zc s he plasc secon modulus o each column amng no a jon and Zb s he plasc secon modulus o each beam amng no a jon. FyC and FYb ae he nomnal yeld sess o he columns and beams and a s he maxmum axal compessve sess n a column o all applcable loadng combnaons. The denomnao o Equaon 4. epesens he oal sengh deved { om he beams amng no a plasc momen o he beams. connecon and s smply he sum oal o The numeao o Equaon 4. epesens he oal sengh deved om he columns and s he "adjused" sum oal o

108 [ 84 plasc momen o he columns. The plasc momen o a column s ed.lced, when a compessve axal oce s pesen. The educon aco, a' s a ahe cude (smple) mehod o deemne he poon o he oal sengh ha can be assocaed wh bendng. A educon aco s no needed o he beams because s assumed ha he axal oces ae nsgncan. [ cean beam lm aons o compacness also ae appled o he L columns, he 988 UBC allows he elaonshp gven n Equaon 4. o be gnoed unde ehe o he ollowng condons:. The compessve sess (a) n he columns s less han oy pecen o Fy o all applcable loadng combnaons; 2. The laeal shea sengh o he columns n a soy ae y pecen geae han he soy above. The membes seleced o he DA ame sased he equemens o he s condon gven above, and hus he song beam-weak column ll desgn was pemed. Songe columns wee seleced o he DB ame o oce he behavo o be song column-weak beam". n boh o h ames, he - sec ons o he columns o each s oy changed as equed by he d des gn. Theeoe he dsbuons o he laeal sness and [ sengh wee que unom, alhough he sengh o he DB ame was moe han equed. l The axal oces n he columns o he DA and DB ame desgns esulng om he gavy (dead and lve) loads and equvalen laeal oces wee elavely small. The neacon equaon gven n he seel maeal secon o he code (same as ASC (.6-2)), govenng he desgn o seel membes havng a compessve sess om an appled axal oce smalle han een pecen o he allowable axal sess, was used n leu L L.': ::

109 85 o he neacon equaons havng he same om as ASC (.6-la) and ASC (.6-lb). n accodance wh he 988 UBC, he allowable sesses ae nceased by a aco o one-hd o loadng combnaons conanng eahquake oces. The pmay eason o avodng plasc hngng o he columns s he possbly o local bucklng o he columns nea he plasc hnge locaon o nelasc bucklng o he ene column. Also, bucklng (alue) o he columns ahe han he beams wll cause geae laeal nsably o he ame. Snce he axal oces n he columns o he DA ame desgn wee small, and heeoe, he columns wee sessed pmaly n pue bendng, he allowance o "song beam-weak column" behavo was jusable. Th ne elemen models o he DA and DB ames wee ypcal o he modellng o momen-essng ames snce he nluence o "gd" beam-o-column connecons and nonsucual elemens wee gnoed. The cenelne-o-cenelne dmensons wee used o dene he lexble lengh o he columns and beams. The yeldng o he columns and beams occued n ] concenaed plasc hnges locaed a he ends o he membes. Howeve, he model dd no consde degadaon o he membes as a esul o nelasc behavo. Thus, yeldng o he columns was no moe caasophc han yeldng o he beams. Alhough he behavo o a ame was "song beam-weak column", hen he yeld momen o a column end lucuaed wh he axal oce acng n he column. Compasons o he me hsoes o he s soy d o he DA! and DB ames subjeced o each o he eahquake acceleogams ae shown n Fgue 4.2. The coespondng soy shea-d hsoes o he s soy ae shown n Fgue 4.3. The esponse o he DA and DB ames

110 86 asng om each eahquake acceleogam wee que smla snce, he naual equences o vbaon o he wo ames wee appoxmaely he same as a esul o d conollng he sesmc desgn o boh ames and mno nelasc deomaons. As shown n he s soy hyseess loops, he nelasc deomaons o he s soy o he songe DB ame wee abou hal as much as n he DA ame. The maxmum soy ds and soy sheas obaned dung each o he me-hsoy analyses ae ploed as envelopes n Fgue 4.4. The maxmum.. :. ' "! j values o an envelope dd no occu necessaly a he same me bu wee he maxmum values calculaed o each soy. The envelopes o he maxmum soy d aos ended o be smla, snce hey all had lage ds n he uppe soes. n ac, he ds calculaed n he uppe soes wee aound ou o ve mes he allowable soy ds o he equvalen laeal oces n he dec desgn pocedue and geneally exceeded soy d aos o one and a hal pecen expeced by he 988 UBC om nelasc behavo. Pehaps he lage ducles occued n he uppe soes as a esul o hghe mode pacpaon. The maxmum soy sheas o he DA ame wee wo mes lage han he desgn soy sheas and hee mes lage o he DB ame, alhough he absolue deence n soy sengh deceased owads he op level o he ame. As expeced, he songe DB ame essed moe shea n each o he soes han he [ j ;.. DA ame, even hough he DA ame expeenced lage ds. The sengh ncease above yeldng was vey small even a lage deomaons, so consequenly he yeld sengh dcaed he maxmum soy sheas. The acual shea sengh o he ame was seveal mes lage han he desgn sheas as a esul o he wokng sess desgn o sze he membes.

111 87 The oal npu enegy quanes and dsspaon heeo (hyseec and dampng) a he end o he dynamc analyses ae shown n Fgue 4.Sa. The oal npu eneges coespondng o each eahquake wee nealy he same o boh ames, alhough he hyseec enegy dsspaed n he DA ame was slghly less han n he DB ame. Theeoe, he lage deomaons n he DA ame wee ose by he lage hegh o he hyseess loops o he DB ame. n Fgue 4.5b, he dsbuons o he hyseec enegy dsspaed along an neo column lne ae shown by boh elemens and soes. No supsngly, mos o he hyseec enegy s dsspaed n he columns o he DA ame whch was "song beam-weak column" desgn and n he beams o he DB ame... hch was "song column-weak beam" desgn. The hyseec enegy dsspa:ed a he base was abuable o yeldng o he column a he assumed gd connecon o he gound. The paen n he neo column lne o hyseec enegy dsspaon s gven n Fgue 4.5c. geneally g..a:e yeldng n he uppe soes and changes n locaons o hysee:c negy dsspaon s clealy pesened n hs gue. Th' Ce: $ -;, ase shea o he DA and DB ames was deemned om a The ahe CCd:lV value o C equal o 2.75, and ye some o he nelasc d:s O:-:S.!ca: :he "desgn" eahquake wee sll lage han expeced... he- case o hese wo ames, he -secons equed o "song column-weak beam" desgn weghed appoxmaely seven:), p':('. mee han he columns o he "song beam-weak column" desgn. n s:e o he nceased wegh, hyseec enegy dsspaon s a good ndcao o sucual damage, as s hough o be, and

112 88 songe membes can saely dsspae moe hyseec enegy, hen he DB ame may be moe aacve n ems o suvvably han he DA ame. The queson o whehe a "song beam-weak column" desgn o a ame s accepable depends on he axal oces and bendng momens acng on he columns. Fo he case o ames wh small axal oces, hee appeas o be le deence beween he expeced deomaons o he wo ame behavos. O couse, ame desgns havng boh lage bendng momens and axal oces should be avoded because he neacon o he wo loadng condons educe he allowable sesses and consequenly he ecency o maeal o he membes. One bene o employng a pemee laeal oce-essng sysem s ha he pemee ames ae pncpally desgned o ess bendng momens asng om he laeal oce, because he buay aeas o he gavy oces ae much smalle han hey ae o he laeal oces. Theeoe, he "song beam-weak column" behavo seems o be pemssble n laeal oce-essng schemes ha use pemee momen-essng ames. One ohe ssue ha should be addessed s he pemanen deomaons ha may esul om an eahquake o smalle magnude han he "desgn" l. eahquake. s que possble ha slgh nelasc behavo may ase om a modeae eahquake. Does plasc hngng o he columns, ahe han plasc hngng o he beams ceae lage pemanen ose n he sucue and esc he possble eusage o sgncanly ncease he cos o epa o he sucue? so, egadless o magnude o he axal oces, "song column-weak beam" behavo may be moe advanageous o he owne o he sucue, even hough he nal cos can be hghe. [ [ ' l

113 \ \' l)a --- lb - 0 o.s -E-c < 0:: E-c o.s 0 E-c U. El Ceno la )lb Pakeld _T DA --- lb 0.5, j TME (sec) j FGURE 4.2 D-Tme Hsoes o Fs Soy o Smla Modellng o DA and DB Fames Subjeced o Thee Eahquakes... j

114 C.l :g ]A ]B El Ceno El Ceno T 200..!T.l :g -- A ]B :::l O. C/) > C/).!T.l e- 600 Pakeld -- DA --- B Pakeld O Tal Ta STeR DRFT RATO (%) STORY DRFT RATO (%).0 FGURE 4.3 Shea-D Hsoes o Fs Soy o Smla Modellng o DA and DB Fames Subjeced o Thee Eahquakes l

115 9 :3 e= 0 Eo-«C:.l 5 lesgn BASE - - -, , - la l : B ---- '-..-['" - e - LL_ - :,,,, El Ceno - l :l > 3...:l 0 E- C:l 2 BASE 5,, -, : l-..- -,, - ESGN la lb Pakeld " ::: A a.: :>.;; lb > Q:: 0!n 2 - o ,.- l _-: l.l lesgn : : '-l - - _ '--- - : - : L...'- -: - :!, -, : : -'" -, - '-: LL Ta : BASE,,, o ENVELOPE: DRFT RATO (%) ENVELOPE: SHEAR (kps). FGURE 4.4 Soy D and Shea Envelopes o Smla Modellng o DA and DB Fames Subjeced o Thee Eahquakes

116 92 ';;" 3.0.S 2.0 o.0 < \-... : DA DB DA DB DA DB } ;. npu Dampng Hyseec FGURE 4.Sa Cumulave Enegy Quanes o Smla Modellng o DA and DB Fames Subjeced o Thee Eahquakes 00. ;>-c p;:: Zz - O U - :::> 50. E-c p;:: E-c!Zl!Zl - -p;:: 25. o. DA DB DA DB DA DB FGURE 4.Sb.Q Panel Zones Fh Fouh Thd Beams Second ; Fs 0 e-. Columns Base en Hyseec Enegy Dsbuons o Smla Modellng o DA and DB Fames Subjeced o Thee Eahquakes

117 . 5 (Roo) T 93 T T T T ] j Base DA DB DA DB DA DB E Ceno Pakeld Ta TYPCAL ONT / Boom o Uppe Column. Panel Zone Rgh End o Le Beam -.. Le End o Rgh Beam Top o Lowe Column Noe: seas popoonal o pecenage o hyseec enegy dsspaed a locaon. - FGURE 4.Sc Hyseec Enegy Locaons o Smla Modellng o DA and DB Fames Subjeced o Thee Eahquakes

118 nvesgaon o Beam-o-Column Connecon Behavo n he ypcal ne elemen modellng o momen-essng seel ames, he beam-o-column connecons ae assumed o be gd. Howeve, he meanng o he em "gd" s somewha msleadng o a beam-o-column connecon, because deomaon n he panel zone does occu om shea sesses ha develop as a esul o unbalanced beam momens. The 988 ed on o he Unom Buldng Code eques ha he d calculaons o he dec desgn pocedue consde bendng and shea conbuons ( om he clea spans o he beams and columns, axal deomaons o he columns and oaons and dsoons o he panel zones. Howeve, he d calculaons can be based on beam and column cenelne-o-cenelne dmensons and gnoe he oaon and dsoon o panel zones, he deence beween he wo calculaed ds s less han een pecen o he sengh o he panel zone can develop eghy pecen o he plasc momen o he beams amng no a jon. The 988 UBC does no sae how he conbuon o he panel zone should be ncluded n he d calculaons. Howeve, he equaon gven n he code o calculae he sengh o he panel zone s based on he equaons developed by Kawnkle o assessng he sness and sengh o panel zones. The d calculaons o he ame desgns o hs sudy wee based on he cenelne dmensons whou egad o deomaon n he panel zone, because he panel zones wee desgned o develop one hunded pecen o he plasc momen o he beams amng no a jon. The sandad modellng o he DB ame had gd beam-o-column connecons and he yeldng o he columns and beams occued a he ends l o he membes. Thee ohe connecon models wee assumed o he DB

119 95 ame o deemne he nluence o connecon behavo on he nelasc \ esponse o seel momen-essng ames. One o he connecon models no only assumed ha no elave oaon occued beween he columns and beams amng no a jon, bu also ha yeldng o he columns and beams occued a he connecon aces. n ohe wods, he panel zone was a gd elemen havng only gd body moon. The emanng wo connecon!. models assumed ha hee was elave oaon beween he columns and beams amng no a jon and ha he yeldng o he columns and beams occued a he ends o he membes. The deence beween hese wo lexble connecon models was pncpally he yeld sengh o he panel zone as a esul o deen hcknesses o he panel zone web.. The panel zone o he nelasc lexble connecon model yelded po o he ( developmen o he ull plasc momen o he beams, whle he panel zone o he elasc lexble connecon model yelded a he developmen o he ull plasc momen o he beams. A dscusson o modellng he beam-o-column connecons w h he ne elemens avalable n he DRAN - 2D pogam s conaned n Chape 3. "\, (No j, "l l compue The sandad model o he DB ame wh gd connecons and yeldng o he columns and beams a he ends o he membes was desgnaed DlB-NPZ Panel Zone). The ame model wh gd panel zones was desgnaed DlB-RPZ. The ame model wh lexble connecons havng he elasc sengh o develop he ull plasc momen o he beams was desgnaed DlB-EPZ. The ohe lexble connecon model havng he nelasc sengh o develop he ull plasc momen o he beams was desgnaed DlB-PZ. Compasons o he me hsoes o he s soy d o he DlB-NPZ, DB-RPZ and DB-PZ ames subjeced o each o he eahquakes ae

120 96 j shown n Fgue 4.6. The coespondng soy shea-d hsoes o he s soy ae shown n Fgues 4.7, 4.8 and 4.9 o each eahquake. The me hsoes o soy d and soy shea-d hsoes o he DlB ame model wh elasc panel zones (DlB-EPZ) wee que smla o he ame model wh nelasc panel zones (DB-PZ) and, hus, ae no gven n hese gues. The undamenal peod o vbaon o he ame model wh gd panel zones was oughly weny- ve pecen shoe han he ame models wh he ohe ypes o connecons. As a consequence, he domnang peod o he d- me hsoes o he DB-RPZ model was shoe han he ohe wo shown. The soy shea-d hsoes o he DB-NPZ and DB-PZ wee que smla and agan hs was due o he lmed nelasc behavo o he ame. The maxmum soy ds and soy sheas obaned dung each o he me-hsoy analyses ae ploed as envelopes n Fgue 4.0. The maxmum soy d and soy shea envelopes wee nealy dencal o he DB-PZ and DB-EPZ, hus he DB-EPZ envelopes ae no gven n he gues. The maxmum soy ds, especally n he uppe soes, wee smalle o he DB-RPZ ame model. The soy ds wee que unom om excaon wh he Pakeld ecod, bu he ohe wo ecods poduced lage ds n he uppe soes. n ac, he ds calculaed n he uppe soes o he analyss wh he E Ceno and Ta ecods geneally exceeded he maxmum expeced soy ds o one and a hal pecen o he soy hegh. The maxmum soy sheas o each o he ame models wee oughly he same and usually wee hee mes lage han he desgn soy sheas. The oal npu enegy quanes and he dsspaon heeo ae shown n Fgues 4.lla, 4.2a and 4.3a o he DB ame modelled wh each o!, l

121 . \ - 97 he ou connecon models subjeced o each o he eahquakes. The enegy quanes wee appoxmaely he same, excep o he DB-RPZ model. The deence beween he oal npu enegy o he DB-RPZ model and he ohe models pobably could be conbued o deence n excaon due o he neacon beween undamenal equency o vbaon o he sucue-and equency conen o he gound moon. The dsbuons o he hyseec enegy by elemens and soes o ] each o he ou ame models ae shown n Fgues 4. lb, 4.2b and 4.3b o each eahquake ecod. The DB-NPZ model had mos o he hyseec enegy dsspaed n he beams because o he song column-weak beam" desgn. The DB-RPZ model had even less hyseec enegy dsspaed n he columns han he DB-NPZ, because he educon n momen om he plasc hnge locaon o he end node was geae o he columns han he beams (see Fgue 3.5). The dsbuons by soes o he DB-EPZ and DB-PZ models wee essenally he same. The Pakeld ecod ended o cause he mddle soes o dsspae mos o he hyseec enegy, whle he E Ceno and Ta ecods caused mos o he dsspaon n he uppe soes. Howeve, he dsbuons by elemens wee deen o hese wo ames. The hyseec enegy dsspaed by he columns o he DB-PZ and DlB-EPZ ames wee appoxmaely he same, bu he elaonshp beween he elasc sengh o he beams and he elasc sengh o he panel zone dcaed whch o hese elemens dsspaed mos o he balance o hyseec enegy T. o each ame. The locaons o hyseec enegy dsspaon o an neo column lne ae shown n Fgues 4.llc, 4.2c and 4.3c. As shown n hese gues, mos o he hyseec enegy was dsspaed n he uppe soes.

122 98 The calculaed soy d and sheas om he dynamc analyses o he ame models wh vaous connecon behavos wee que smla, excep o he model wh gd panel zones. The ame model wh gd- panel zones pobably depcs he nelasc behavo o he ndvdual columns and beams bee han he ohe ame models. The plasc hnge locaons o yeldng o he columns o beams would mos lkely be locaed a he ace o he connecons whee he momen s he lages (assumng no exenal oces along he membes) o he clea span o he membe. Howeve, he oal dsegad o deomaon n he panel zone esuled n poo modellng o he oveall load-deomaon behavo o he ame. The code saes ha he sengh o he panel zones need no develop moe han eghy pecen o he ull plasc momen o he beams. n a "song column-weak beam ll Theeoe desgn, he panel zone desgned o hs level usually wll expeence sgncan nelasc behavo beoe ehe o he beams amng no a jon yeld. The bendng momens acng n each o he beams a a jon ae essenally he same magnude and acng n he same decon, snce he vecal oces o a pemee ame ae ahe small. Reseach has shown ha he panel zone s a good locaon o dsspaon o hyseec enegy, excep ha unde sevee dsoon o he panel zone he beam-o-column connecons may al pemauely [27,28,29,30,38,39,40]. The sucual engnee s n "chage" o deemnng he locaon(s) o hyseec enegy dsspaon a a jon by specyng he hckness o he web o a panel zone. he engnee speces he mnmum sengh, hen he yeldng geneally wll occu n he panel zone. Howeve, a " hcke web s speced o he panel zone han he yeldng can occu n he ends o he beams o columns dependng on he elave senghs. L

123 99 Snce he sucual engnee has he capably o deemne whee he yeldng a a connecon wll ake place, he equed ducly can be desgned no hese locaons so ha non-ducle alues ae pevened ae many cycles o nelasc deomaons. The povsons n he 988 VBC encouage he sengh o he panel zone o be able o develop a leas eghy pecen o he ull plasc momen o he beams. Alhough a hs mnmum level, he panel zones wll dsspae mos o he hyseec enegy a a jon. should no be supsng ha he calculaed soy ds and sheas wee no much deen o he hee ame models w hou gd panel zones, because once hee was yeldng a a jon he ne esul was he same - he nably o anse momen om he columns o he beams. The l placemen o plasc hnge locaons a he connecon ace should only be used deomaon n he panel zone can be accouned o n an analyss, because he sness o he ame would be unealscally hgh. Howeve, cae mus be aken n developng he numecal model o a j on so ha calculaed esponse ndcaes whee he yeldng would acually occu n he sucue hn subjeced o a majo eahquake. would be que dcul o mode U... ce! omaon n he panel zone and oce he plasc hnge j locaons c! U" columns and beams o occu a he connecon aces usng he n. '. "*,ls cuenly avalable wh he DRAN-2D pogam. One lm a o :- : he ame models developed o hs nvesgaon was he nably c _LCO'",ln o degadaon o he membes and connecons as a esul o neasc behavo. Pehaps yeldng n he columns would cause } moe degadaon o he oveall sness and sengh o he ame han yeldng n he beams. j

124 B-NPZ B-RPZ B-PZ {' ; 0 -E-c <:: T E-c en -2.0 El Ceno! " E-c <:: Cl::': E-c 0.0 -Cl::': Cl::': 0 E-c en :] 2.0 B-NPZ - B-RPZ B-PZ 0 -E-c < Cl::': 0.0 -Cl::': Pakeld Cl::': E-c CZ -2.0 Ta TME (sec) FGURE 4.6 D-Tme Hsoes o Fs Soy o Deen Connecon Modellng o DB Fame Subjeced o Thee Eahquakes! j.

125 B-NPZ 0 -CT.l. 600.,:,:: --- E Ceno ] B-RPZ lb-pz E Ceno j E Ceno STORY DRFT RATO (%) ]...] FGURE 4.7 Shea-D Hsoes o Fs Soy o Deen Connecon Modellng o DB Fame Subjeced o El Ceno

126 " 02 ;. :; P B-NPZ a 600.! -<.. O. CZl p:= CZl! Pakeld 'o.; P l o. ::: CZl 0 CZl -.. C.l P-4 :g B-RPZ B-PZ Pakeld -< l : l 0 / 0:: /,'/ / / :n // "" z ;:? / / /A / Z / ( 0 /:/, E-- CZl /V.-/ Pakeld STORY DRFT RATO W' \ \70),.. l FGURE 4.8 Shea-D Hsoes o Fs Soy o Deen Connecon Modellng o DB Fame Subjeced o Pakeld, l! -

127 B-NPZ Ta B-RPZ 600. c::: <: O. -en > E- en Ta B-PZ j -en >- D e; Ta STORY DRFT RATO (%) FGURE 4.9 Shea-D Hsoes o Fs Soy o Deen Connecon Modellng o DB Fame Subjeced o Ta

128 04 : 0 Zl 5 : BASE , --,-- _,,-W-!, - - DESGN DB-NPZ )lb-rpz B-PZ El Ceno! - _-, - : --, :..., L.- : L,! :;a > 3 0 E-c en 2 BASE 5 : 0 Zl BASE FGURE 4.0 L.. l : ', L,..!,,..---,, : : u.., ESGN B-NPZ B-RPZ B-PZ Pakeld )ESGN )lb-npz B-RPZ B-PZ Ta o ENVELOPE: DRFT RATO (%) SHEAR ENVELOPE (kps) Soy D and Shea Envelopes o Deen Connecon Modellng o DB Fames Subjeced o Thee Eahquakes,,, : :,, -- : : : :--: :..., :, : -: :!..., :,... :, : ',-- [ : L l. L

129 d Z DB-NPZ DB-RPZ DB-EPZ DB-PZ npu Dampng Hyseec FGURE 4.lla Cumulave Enegy Quanes o Deen Connecon Modellng o DB Fame Subjeced o El Ceno o. DB-NPZ DB-RPZ DB-EPZ DB-PZ Panel Zones Fh Fouh Thd Beams Second >- ::s:: Fs 0 E- Columns Base en FGURE 4.llb Hyseec Enegy Dsbuons o Deen Connecon Modellng o DB Fame Subjeced o El Ceno, (.

130 06 5 (Roo) Base T T T T DB-NPZ DB-RPZ DB-EPZ DB-PZ.. [ TYPCAL ONT Boom o Uppe Column / Panel Zone Top o Lowe Column Rgh End o Le Beam -.. Noe: Aeas popoonal o pecenage o hyseec enegy dsspaed a locaon. Le End o Rgh Beam FGURE 4.llc Hyseec Enegy Dsspaons o Deen Connecon Modellng o DB Fame Subjeced o El Ceno. ( L

131 } ! E; z DB-NPZ 07 DB-RPZ npu DB-EPZ ". Dampng Hyseec DB-PZ FGURE 4.l2a Cumulave Enegy Quanes o Deen Connecon Modellng o DB Fame Subjeced o Pakeld o. DB-NPZ DB-RPZ DB-EPZ DB-PZ Panel Zones Fh...:l Fouh Thd Beams Second >c Fs 0 Columns U Base E-c FGURE 4.l2b Hyseec Enegy Dsbuons o Deen Connecon Modellng o DB Fame Subjeced o Pakeld

132 08 5 (Roo) Base T T T DB-NPZ DB-RPZ DB-EPZ DB-PZ -. TYPCAL ONT /' Boom o Uppe Column. / Panel Zone Rgh End o Le Beam /', Le End o Rgh Beam...- Top o Lowe Column Noe: Aeas popoonal o pecenage o hyseec enegy dsspaed a locaon. FGURE 4.l2c Hyseec Enegy Dsspaons o Deen Connecon Modellng o DB Fame Subjeced o Pakeld L

133 Po.,!:Q.S 2.0 o -- o DB-NPZ DB-RPZ DB-EPZ DB-PZ npu Dampn Hyseec FGURE 4.l3a Cumulave Enegy Quanes o Deen Connecon Modellng o DB Fame Subjeced o Ta 00. >-c Zz o C,.) E--4 ::::> 0:: pa --0::; E-c E--4 U':l O 25. o. DB-NPZ DB-RPZ DB-EPZ DB-PZ Panel Zones Fh e: Fouh E-c 5; Thd e3 Beams Second >-c ::::S Fs 0 Columns.l Ba:!e ::3 FGURE 4.l3b Hyseec Enegy Dsbuons o Deen Connecon Modellng o DB Fame Subjeced o Ta

134 0 5 (Roo) 4 3 T T T { 2 " Base DB-NPZ DB-RPZ DB-EPZ DB-PZ TYPCAL ONT _ /' Boom o Uppe Column,panel Zone Rgh End o Le Beam Le End o Rgh Beam Noe: Aeas popoonal o pecenage o hyseec enegy dsspaed a locaon. Top o Lowe Column FGURE 4.3c Hyseec Enegy Dsspaons o Deen Connecon Modellng o DB Fame Subjeced o Ta l L

135 { nvesgaon o Nonsucual Elemen Pacpaon The povsons n he 988 edon o he Unom Buldng Code o he dec desgn pocedue o he laeal oce-essng sysem o a buldng do no speccally addess he neacon o he nonsucual elemens (claddng, neo paons, mechancal sysems, ec.) wh he laeal deomaon o he bae sucual ame. The sness conbuon o nonsucual elemens s ndecly ncopoaed n he code equaon o he esmaon o he undamenal peod o vbaon o'a sucue. The esmaed undamenal peod o he buldng s shoe han he undamenal peod o he bae sucual ame. Howeve, he sengh conbuon o he nonsucual elemens s gnoed. The povs ons n he code egadng he laeal oce pocedues manan ha he mahemacal model o he sucue should epesen, o he adequacy equed o pedc he sgncan conbuons o he esponse. he load -deomaon behavo o he sucue. Howeve, no econmendao-s ae gven n he code egadng he assessmen o he laeal slns5 ad sengh o nonsucual elemens o ncopoaon o nons ue _:..... enen pacpaon no he desgn and analyss o a sucue ;: modellng o he nonsucual elemens was employed o deeen : :gcance o hese elemens n he calculaed esponse. Shea panel :p5. modellng nonsucual elemens, wee added o each soy o h, $:an.:nc! modellng o he DB ame. The addonal laeal sness om he nonsucual elemens educed he calculaed undamenal \ j peod o he ame model o he esmaed value gven by he code. The load-deomaon behavo o he nal modellng o nonsucual elemens

136 2 was lnea wh a alue s an o one -hal o a pecen, whch also coesponds o a one-hal o a pecen soy d ao. Ae sudyng he esponse o he ame model usng he nonsucual elemens wh a lnea load-deomaon behavo and ealzng ha he nluence can be que poound, an mpoved model o nonsucual elemens was developed. Ths model had a load-deomaon elaonshp wh degadaon o sness and sengh a hee deomaon levels. The anson o alue o he nonsucual elemens o a soy was moe genle. A dscusson egadng he modellng o nonsucual elemens s gven n Chape 3. n hs paamec sudy, he DlB ame model whou nonsucual elemens was desgnaed DlB-NNE (No Nonsucual Elemens). The DlB ame model conanng nonsucual elemens wh a lnea load-deomaon elaonshp was desgnaed as DlB-LNE, whle he ame model conanng nonsucual elemens wh a lnea load-deomaon elaonshp was desgnaed as DlB-TNE. n he DlB-LNE and DlB-TNE models, he sness and sengh conbuon o he nonsucual elemens had a gea nluence n he uppe soes o he ames because he laeal sness and sengh o he soes deceased om he lowe soes o he uppe soes, whle he laeal sness and sengh conbuons o he nonsucual elemens emaned elavely consan houghou he hegh. Theeoe he dsbuon o sness and sengh, whch was aly unom, was no longe popoonal o he soy sheas om he equvalen laeal oces. The compasons o he me hsoes o he s soy d o he DlB-NNE, DlB-LNE and DlB-TNE ame models ae shown n Fgue 4.4. The } deences beween he aces o he hee models om excaon wh he

137 3 El Ceno acceleogam wee small as wee he deences beween he aces om excaon wh he Ta ecod. Alhough, should be noed ha he nonsucual elemens degaded o even aled dung he s ew cycles o song excaon. The Pakeld aces o he models wh nonsucual elemens wee oughly he same. Howeve, he geneal- -amplude o-he esponse o he bae sucual ame model was lage han he ohe wo. Ths ds ncon was abuable o he shng o equences n he models, because he models wh nonsucual elemens had small ds n he uppe soes dung he esponse om he Pakeld acceleogam. Thus, he geneal behavo o hese ame models was a gd body movemen o he uppe. soes espondng on a so s soy. The soy shea-d hsoes om excaon by each eahquake ae shown n Fgues 4. 5, 4. 6 and The degadaon o alue o he nonsucual elemens can be seen n hese aces by he change n slope o he elasc poon o he hyseess loops. The nelasc behavo o he models wh lnea behavo nonsucual elemens was geae because o he complee apd alue o he nonsucual elemens n he lowe ; \ soes. The shea caed by hese elemens was anseed abuply o he sucue as a shock loadng, causng consdeable acceleaons whch consequenly lead o lage soy ds. The soy d and shea envelopes o maxmum esponse ae ploed n, Fgue 4.8. The maxmum soy ds ended o be o smla magnude o he lowe soes, whle. he soy ds n he uppe soes o he bae sucual ame model ended o be lage han n he ame models wh nonsucual elemens. The addon o nonsucual elemens nceased he laeal sness and sengh o he soe uppe soes o he bae

138 4 sucual ame snce he nonsucual elemens o hese soes dd no sue much degadaon. n he uppe soes, he maxmum soy ds o he ame models whou nonsucual elemens appoached o exceeded he expeced nelasc ds, whle he maxmum soy ds o he ame models wh nonsucual elemens wee smalle han he expeced nelasc ds. The deences beween he maxmum soy ds o he ame models wh and whou nonsucual elemens wee que deen he nonsucual elemens o a soy dd no al o sue much degadaon. The maxmum soy sheas, especally o he ame models wh nonsucual elemens, wee consdeably lage han he desgn soy sheas. The oal npu enegy quanes and he dsspaon heeo ae shown n F gu e s 4. 9 a, a, 4. 2la. The npu enegy coespondng o each eahquake usually ee whn en pecen o each ohe. As ndcaed by he hyseec enegy dsbuons gven n Fgues 4.l9b, 4.20b and 4.2lb, he dsspaon o hyseec enegy om he El Ceno and Ta ecods was manly n he u;:,?e soes o he DB-NNE ame model and manly n he lowe soes o he DB-LNE, whle he dsbuon was moe unom n he DB-TNE. The hvs:eec enegy dsspaon o boh o he ame models wh nonsuc:.al elemens was eally concenaed n he lowe soes om exc a ;'.,. h he Pakeld ecod. The locaons o hyseec enegy dsspa:c';; also ae shown n Fgues 4.l9c, 4.20c and 4.2lc. As shown n hee!ues, he addon o henonsucual elemens ended o educe he numbe o locaons o hyseec enegy dsspaon. The pacpaon o nonsucual elemens n hs sudy caused a sgncan change n he dynamc behavo o he model. The nonsucual elemens wh he lnea load-deomaon behavo povded a consdeable

139 5 ncease n laeal sness and sengh, especally as he soy ds., appoached he alue san snce he bae sucual ame had nealy eached s maxmum shea capacy a one-hal o a pecen soy d ao. Theeoe, he dsbuon o sness and sengh o he' ame models consdeng he pacpaon o nonsucual elemens was no compable wh he assumed dsbuon o he 988 UBC. The vaance n he maxmum d o a soy n a ame model w h lnea behavo nonsucual elemens was dependen on he alue o he nonsucual elemen o ha soy. he nonsucual elemen o a soy aled, he maxmum esponse o he soy was oughly he same as he maxmum esponse obaned by he bae sucual ame model. n many buldngs, an aemp s made o solae he nonsucual elemens om he bae sucual ame. Howeve, because o mpope ns a a on o he nons uc u al elemens o nsuc en so la on om he laeal oce-essng sysem, nonsucul elemens wll ulmaely pacpae n he esponse. Dependng on he elaonshp beween he laeal sness and sengh o he bae sucual ame and he nonsucual elemens, he nonsucual elemens can have a subsanal nluence on he esponse. j The modellng o he nonsucual elemens was ahe cude, even o he moe ened model wh he lnea load-deomaon behavo. Even so he mpoance o accounng o he pacpaon o nonsucual ( -; elemens was evden. sucen solaon o he nonsucual elemens om he bae sucual ame s no povded, he ancpaed behavo o he nonsucual elemens should be consdeed n he desgn o pope assessmen as o he adequacy o he laeal oce-essng sysem.. -'

140 E-NNE E-LNE.0 B-TNE.. " }!. -.0 El Ceno ZO B-NNE B-LNE.0 lb-tne Pakeld E-NNE E-LNE.0 E-TNE -.0 Tal TME (sec), FGURE 4.4 D-Tme Hsoes o Fs Soy o DB Fame wh Nonsucual Elemens Subjeced o Thee Eahquakes L

141 7 --. en c,!:Q l::: :.l 0 E-! :.l O B-NNE El Ceno en A.c. '--" B-LNE p:; < O. :.: :.l ). " 0 E-! C.:l ,/ B-TNE / / / / - en /' 0...-, 800. / '--" / / / / / / :.: O. :::: en :>-< 0 E--.l El Ceno El Ceno 2.0 STORY DRFT RATO (%) FGURE 4.5 Shea-D Hsoes o Fs Soy o DB Fame wh Nonsucual Elemens Subjeced o El Ceno

142 8 -- en c:: <: P: o. C:l >c 0:: E--- C:l lb-nne Pakeld lb-lne /,/ /' - / / 0:: / <: O. ::: /, C:l / >- // 0:: A/ / 0 h/ -./ / C:l / /' "/ / _-.L... /,-- "- / Pakeld Q....!: :: < O. -C:l lb-tne >- c:: C:l FGURE 4.6!/ LO STORY DRFT RATO (%) Pakeld Shea-D Hsoes o Fs Soy o DB Fame wh Nonsucua Elemens Subjeced o Pakeld 2.0 :.. \ (

143 B-NNE '-"'"! B-LNE B-TNE Ta Tal ; STORY DRFT RATO (%) Tal 2.0 FGURE 4.7 Shea-D Hsoes o Fs Soy o DB Fame wh Nonsucual Elemens Subjeced o Ta

144 ': ' :, : 4 - Ll--T-l : -.,.L, L! - BASE l l )Es/eN )lb-nne, : - '--l : - -- )lb-lne,, - '-, )lb-tne :, - -. El Ceno!, ', --..,..., - - L,. -, " "" - - -'----,- - ', l 5 : : : 'j 3 2,... - l_l E FGURE )Es/eN, :, - )lb-nne!, )lb-lne )lb-tne --,... - : : '- : -; Pakeld : )Es/eN )lb-nne,,...,,, -- )lb-lne! )lb-tne :, - '.oj : -... : Ta, o. : : -, '-----,- -, L-n - - ', ' LL,, ' U l - '-- -, ENVELOPE: DRFT RATO (%) SHEAR ENVELOPE (kps) Soy D and Shea Envelopes o DB Fame wh Nonsucual Elemens Subjeced o Thee Eahquakes - - [ ( L l

145 S 2.0 o DB-NNE DB-LNE DB-TNE npu Dampng Hyseec FGURE 4.l9a Cumulave Enegy Quanes o DB Fame wh Nonsucual Elemens Subjeced o El Ceno.. o. DB-NNE DB-LNE DB-TNE P<:l Panel Zones Fh...: Fou.h Thd Beams Second ;] Fs 0 Columns Base.l E- FGURE 4.l9b Hyseec Enegy Dsbuons o DB Fame wh Nonsucual Elemens Subjeced o El Ceno