PRELIMINARY STUDY ON DISPLACEMENT-BASED DESIGN FOR SEISMIC RETROFIT OF EXISTING BUILDINGS USING TUNED MASS DAMPER

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1 Not: this papr was not abl to b rviwd in accordanc with DEST rquirmnts. PRELIMINARY STUDY ON DISPLACEMENT-BASED DESIGN FOR SEISMIC RETROFIT OF EXISTING BUILDINGS USING TUNED MASS DAMPER Chang-Yu Chn 1 and Kuo-Chun Chang 2 1. Assistant Rsarch Fllow, National Cntr for Rsarch on Earthquak Enginring, Taipi, Taiwan 2. Profssor and Chairman, Dpt. of Civil Enginring, National Taiwan Univrsity, Taipi, Taiwan ABSTRACT According to th quivalnt linar systm, this papr prsnts a prliminary displacmnt-basd dsign (DBD) procdur for sismic rtrofit of xisting buildings using tund mass dampr (TMD) undr th spcifid sismic loading. Th dsign mthod is primarily controlling th roof displacmnt of th building, and this mthod uss th nonlinar pushovr analysis in th dsign procdur. Th concpt of optimum dsign for th TMD would b usd in th dsign procdur. Th dsign rsults ar compard with thos computd from th dynamic inlastic tim history analyss. It is shown from nonlinar tim history analyss that th maximum nonlinar rsponss of th rtrofittd building with TMD can b rasonably capturd by th prsntd mthod. Kywords: tund mass dampr, displacmnt-basd dsign, sismic rtrofit dsign

2 1. INTRODUCTION Th purpos of this study is to confr th displacmnt-basd dsign (DBD) mthod for sismic rtrofit of xisting buildings using tund mass dampr. Th dsign mthod is primarily controlling th displacmnt, and this mthod rplacs th nonlinar tim history analysis by th nonlinar pushovr analysis in th dsign procdur. This mthod prdicts th maximum rspons of th nonlinar structur by using th quivalnt linar systm. Thr ar many rfrncs that discuss th valuation of quivalnt linar systm. Nvrthlss, this study calculats th quivalnt linar systm by using th avrag nrgy mthod and proposs th displacmnt-basd dsign mthod for sismic rtrofit of xisting multi-story buildings using tund mass dampr. In addition, th DBD mthod considrs th ffct of multipl mods. This study, first studis th simulation of TMD by using SAP2000N and PISA3D nonlinar analysis program and thn proposs th DBD mthod for sismic rtrofit of xisting multi-story buildings using tund mass dampr. Th dsign rsults ar compard with thos calculatd from nonlinar tim history analysis and thn summaris som conclusions. 2. SIMULATION OF THE TUNED MASS DAMPER In th figur 1, th mchanics of th tund mass dampr ar includd th stiffnss and th damping dvics which ar in paralll connction. Th stiffnss may b linar or nonlinar, and th damping may also b linar or nonlinar. Th motion quations of th multi-story building quippd with TMD ar as follows: [ M ][ && y] + [ C][ y& ] + K[ y] = [ M ][ L] u&& + [ P] mz && + cz& + kz = m && && ( yn + ug ) whr [ P ] = [ 0,...0, cz& + kz] T, m =mass of th TMD, c =damping of th TMD, k =stiffnss of th TMD, & y& N =acclration of th roof, u& & g =th ground motion, [M ] =mass matrix of th structur, [C] =damping matrix of th structur, [K] =stiffnss matrix of th structur, [y] =story displacmnt of th structur. g (1) k m c z(t) [ y] Figur 1 Th structur quippd with TMD

3 Th simulation of th TMD by using th 3D nonlinar analysis programs can b combind with th stiffnss and damping link lmnts. Th stiffnss and damping link lmnts ar connctd paralll to ach othr. Th stiffnss and damping paramtrs may b input linar or nonlinar according to th practic application Th accuracy of th analysis rsults simulatd from 3D nonlinar analysis programs such as SAP2000N and PISA3D would b studid by using an analytical xampl. A plan six storis and two-bay stl fram would b slctd as th analytical xampl. Th sction of columns for th bas fram is H300x300x10x15mm, and bams for th bas fram is H200x200x8x12mm. Th story high is 2.6m and th distanc of on bay is 6m. Th story mass is 10 ton. Th TMD is installd at th roof of th bas fram. Ths analysis rsults would b compard with thos from th numrical calculation of stat spac analysis. It can b found that th simulat rsults by using SAP2000N and PISA3D nonlinar analysis programs ar rathr consistnc with th numrical calculation from th stat spac analysis. Figur 2 show th analytical rsults of roof displacmnt and roof acclration for th bas fram with and without TMD. Th vrtical coordinat of figur 2(a) rprsnts th roof displacmnt (m), whil th horizontal coordinat rprsnts th tim (sc). In addition, th vrtical coordinat of figur 2(b) rprsnts th roof acclration (m/s 2 ), whil th horizontal coordinat rprsnts th tim (sc). Th rduction rsponss in th figur 2(a) and 2(b) ar both corrsponding to th bas fram with TMD. Thrfor, it can obtain th larg rduction rsponss by quipping with th combination of simpl mchanics which should b corrctly dsignd. In anothr word, th stiffnss and damping should b dsignd according to th optimum dsign mthod. "#$%&'(")*+,-*&-($")(*.-+/--)*/'+,*%)0*/'+,"1+*234*1)0-&*56*-)+&"*-%&+,71%8- "#$%&'(")*+,-*&-($")(*.-+/--)*/'+,*%)0*/'+,"1+*234*1)0-&*56*-)+&"*-%&+,71%8- A bad dsign of TMD would rsult in magnifying th rspons of th bas fram. :;=> < :;= = > D""E*D-F%+'G-*4'($F%B-#-)+A#C :;:> 9:;:> : : > =: => 9:;= E""F*E-G%+'H-*ICC-G-&%+'")B#J(-C? D? ; ; :; :@?;?@ A; A@ >; >@ 9? H'+,"1+*234 9> 9= K'+,*234 K'+,"1+*234 9:;=> 9:;< (a) Figur 2'#-A(-BC 2 Rduction of th rspons for fram with TMD 9< 9:; 2'#-B(-CD (b) 3. DISPLACEMENT-BASED DESIGN Basd on th quivalnt linar systm mthod, this study proposs th displacmnt-basd dsign for sismic rtrofit of th xisting multi-story buildings quippd with TMD. Th dsign objct is th control of th displacmnt. Th dsign procdur would rpat th stps until th dsign displacmnt bing satisfid th objct critria. Th nonlinar static analysis and simpl linar dynamics analysis will substitut for nonlinar tim history dynamics analysis. Finally, th dsign rsults will b compard with th rsult calculatd from nonlinar tim history dynamics analysis. Th dsign procdur is as shown in figur 3. Th ky stps for th dsign mthod ar th TMD optimum dsign and valuation of th quivalnt linar systm. Thr ar many rfrncs that discuss th optimum dsign of linar stiffnss TMD for th linar lastic structurs. [Tsai t al., 1993] But, th rfrncs about optimum dsign mthod of TMD

4 for th nonlinar structurs ar lss. In this study, th dsign of linar stiffnss TMD for th nonlinar structurs would b usd in th DBD procdur. Th optimum dsign mthod of TMD which contains nonlinar stiffnss would b study in th futur. Th dtrmination of th quivalnt linar systm would b dtrmind as quation 2 and 3. [Chn, 2003] Th quivalnt damping ratio is dtrmind from th contribution of th structural inlasticity, dampr forc, and inhrnc damping ratio of th structur. Th TMD would b simulatd as th quivalnt fram undr th nonlinar pushovr analysis. M T = 2 (2) K ( inlasticity) + ( dampr) ( inhrnc) = + (3) Whr T is th quivalnt priod, M is th quivalnt mass, K is th quivalnt stiffnss, is th quivalnt damping ratio, ( inlasticity) is th damping ratio contributd from th inlasticity of th structur, (dampr) is th damping ratio contributd from th dampr forc, (inhrnc) is th inhrnc damping ratio of th structur. Whn prforming th nonlinar pushovr analysis, th latral story forcs distribution [F] ar proportional to th quation 4. Th quivalnt mod shap [ ] is calculatd from quation 5. [ F ] = [ K][ ] (4) [ 1 d d ] = $ S (#," )[ ] + $ S (#," )[ ] (5) In which [K] is th stiffnss matrix of th structur with TMD, i is th frquncy corrsponding to th i th mod of th structur with TMD, i is th damping ratio corrsponding to th i th mod of th structur with TMD, ] is th mod shap corrsponding to th i th mod of structur with TMD, i is th partition factor corrsponding to th i th mod of structur with TMD, S d is th displacmnt dtrmind from th spctrum. According to th quivalnt linar systm, th maximum nonlinar roof displacmnt of th structur with TMD would b calculatd from th lastic rspons spctrum corrsponding to th quivalnt priod T and quivalnt damping ratio. As shows in figur 4, th maximum nonlinar roof displacmnt of th structur with TMD can b valuatd as follows: u = " S T, ) (6) Whr roof d ( [ ][ M ][1] " = [ ][ M ][ ] [ i u roof

5 Dcid th mass ratio TMD optimum dsign Assum th dsign displacmnt Calculat th EQ. linar systm Comparison of th dsign dis. ys No No Dsign dis. Objct dis. ys Evaluat th acclration and chck th srvics ys No Dampr dtail dsign Figur 3 DBD dsign procdur Sd, ) ( T % T Figur 4 Elastic displacmnt rspons spctrum It is intrsting to dmonstrat th dsign procdur by using on analytical xampl. Th xisting 3-story stl fram from th National Cntr for Rsarch on Earthquak Enginring in Taiwan is slctd as th bas fram. Th distanc of th short dirction is 3m and th long dirction is 4.5m. Th story high is 3m. Th mass of 1 st and 2 nd floor is 11209kg, 3 rd floor is 10910kg. Th sction of th columns ar H200x204x12x12mm, th bams ar H200x150x6x9mm. Th dsign arthquak rcord is typ artificial history from Taiwan s sismic dsign provision with pak ground acclration qualing to 0.5g. Th objct roof displacmnt of th rtrofittd fram is 20cm (drift angl=2.2%). Th final paramtrs of linar stiffnss TMD calculatd from th dsign procdur ar summarizd as tabl 1. Th TMD mass ratio µ quals to 1%.

6 Tabl1 Final TMD dsign rsults Mass (KN-s 2 /m) Stiffnss (KN/m) Damping (KN-s/m) TMD Th fundamntal dynamics charactristics of th fram with TMD ar summarizd as tabl2. In addition, in ordr to vrify th accuracy of th final dsign rsults, th nonlinar tim history dynamics analysis is prformd to chck th maximum roof displacmnt of th rtrofittd fram with TMD. In tabl3, it shows that th maximum roof displacmnt of th rtrofittd fram with TMD conforms accuratly th dsign displacmnt. Tabl2 Fundamntal dynamics charactristics of fram with th TMD Priod Modal Mass Partition Mod Shap (sc) (KN-s 2 /m) Factor TMD 3 rd story 2 nd story 1 st story 1 st Mod nd Mod EQ. Mod Tabl3 Comparison btwn DBD and tim history analysis EQ. Priod Damping Ratio Damping Ratio Damping Ratio T (sc) ( inlasticity) (dampr) (inhrnc) Maximum roof dis. (m) EQ. Mod Nonlinar Tim History Analysis CONCLUSIONS Th proposd DBD procdur for th sismic rtrofit of xisting building quippd with TMD is simpl and availabl. It is shown from nonlinar tim history analyss that th maximum nonlinar rsponss of th rtrofittd building with TMD can b rasonably capturd by th prsntd mthod. Howvr, th optimum dsign of th TMD which contains nonlinar stiffnss would b xtndd to rsarch in th futur. In addition, th xprimnt of structur with TMD should also b conductd to vrify th proposd DBD mthod. 5. REFERENCES Chang-Yu Chn (2003), displacmnt-basd dsign for sismic rtrofit of xisting buildings using damping systms, Mastr thsis Dpt. of Civil Eng., National Taiwan Univrsity, Taiwan. Hsiang-Chuan Tsai and Guan-Chng Lin (1993) Optimum tund-mass damprs for minimizing stady-stat rspons of support-xcitd and dampd systms, Earthquak Enginring and Structural Dynamics, Vol.22, pp Rahul Rana and T.T. Song (1998), Paramtric study and simplifid dsign of tund mass damprs, Journal of Enginring Structurs., Vol. 20, No.3, pp T. Pinkaw, P. Lukkunarasit and P. Chatupot (2003), Sismic ffctivnss of tund mass damprs for damag rduction of structurs, Journal of Enginring Structurs., Vol. 25, pp