Benefts of Vertcally Dstrbuted Isolaton Devces for an 8-storey Structure wth Complex Geometry T.J. Sullvan Unversty of Pava, Pava, Italy A. Lago Skdmore, Owngs and Merrll LLP, S.F., USA, formerly ROSE School, IUSS Pava, Pava, Italy G.M. Calv IUSS Pava, Pava, Italy SUMMARY: The constructon of structures wth curved or rregular geometry s becomng ncreasngly common as modern archtects strve to create conc buldngs. However, the realzaton of complex buldng forms creates sgnfcant challenges n regons of hgh sesmcty, snce ths ntroduces sgnfcant uncertantes n the lkely plastc mechansm, wth questons on the lkely performance of connectons and doubts about the probable loadpaths. Ths paper examnes the benefts of a novel sesmc desgn strategy that uses solaton devces dstrbuted vertcally up a buldng between the exteror structure (of complex-geometry) and the heavy nternal core. An nnovatve Drect DBD methodology s used to desgn an 8-storey case study buldng n whch vscoelastc devces are used. Non-lnear tme-hstory (NLTH) analyses are then conducted on a 3-dmensonal model of the buldng and the results ndcate that the target dsplacement and drfts for both the nternal and external structures are well controlled by the desgn soluton. Keywords: complex geometry, dagrd, dsplacement based desgn, vsco-elastc damper.. INTRODUCTION The realsaton of structures wth curved or rregular geometry s becomng ncreasngly common, wth conc buldngs such as Guggenhem n Blbao, the Seattle publc lbrary, the Brdsnest Stadum n Bejng, and the Gherkn n London, all dstngushng themselves by ther unusual form and composton. Ths growng tendency to propose complex buldng forms creates sgnfcant challenges for structural engneers n regons of hgh sesmcty, where t s hghly recommended that structures are regular n form, wth clearly establshed loadpaths and plastc mechansms, n order to provde relable sesmc performance. If a structure possesses an unusual geometrcal form, ths ntroduces sgnfcant uncertantes n the lkely plastc mechansm, wth questons on the lkely performance of connectons and doubts about the probable loadpaths. Recently, Lago et al. () undertook prelmnary testng of a novel sesmc desgn strategy for structures wth complex geometry, that ams to acheve relable sesmc behavour through the ntroducton of specal sesmc solaton devces vertcally dstrbuted up the heght of the buldng. Ths paper extends on the work undertaken n Lago et al. () by consderng the 3D response of an 8-storey buldng wth vertcally dstrbuted solaton devces. The structure s desgned usng a Drect dsplacement-based desgn (DBD) approach (Prestley et al. 7) and non-lnear tme-hstory (NLTH) analyses are undertaken wth b-drectonal exctaton n order to gauge the performance of the nnovatve structural scheme.. THE CONCEPT OF VERTICALLY DISTRIBUTED ISOLATION DEVICES The sesmc response of a buldng wll be affected by ts mass, stffness, strength and deformaton capacty. The proposed concept of vertcally dstrbuted solaton devces s to solate a stff, lght exteror structure, whch wll have lmted strength and nelastc deformaton capacty, from the heavy
mass at a buldng s core. One possble means of dong ths s llustrated n Fg.., where a curved exteror structure s connected to a relatvely regular, heavy nteror structure through the use of specal sesmc solaton devces. The nternal columns and beams would be detaled to resst gravty loads and undergo sesmc movements wthout developng sgnfcant resstance, whereas the core walls and floors would be used as man lateral load resstng structural elements, together wth the exteror structure. The solaton devces are szed to control the transfer of nerta forces from the core and lmt the dsplacements mposed on the exteror structure. The use of the term solaton s not completely approprate snce both the exteror and the nteror structures are drectly connected to the ground and are therefore not base solated. However, the term solaton s used to reflect the partal solaton of the complex exteror structure from the heavy nternal porton of the buldng. Roof supported by nternal core, solated from exteror Columns detaled to resst gravty loads only Sesmc solaton devces between floors and complex exteror structure Sdes of exteror structure are self-supportng Interor RC walls Fgure.. Vertcally dstrbuted solaton concept for a buldng wth complex geometry If very stff and strong devces are used then the exteror structure wll dsplace together wth the nteror structure, whereas f very flexble or low-strength devces are used then the exteror structure s dsplacements wll be very small but the zone between the floor slabs and the exteror structure wll have to sustan larger dfferental dsplacements. These concepts can be useful for optmsng the propertes of the sesmc devces. Lago et al. () nvestgated the use of vscoelastc devces, whch transmt both dsplacement- and velocty-dependent forces. Fgure. depcts the relatve dsplacements of the nternal and external systems at two dfferent nstants of structural moton: (a) at peak core dsplacement and (b) peak core velocty (Fg..(a) and (b) respectvely). By usng vscoelastc devces, forces are transmtted to the external structure when the nternal system velocty s a maxmum (due to the velocty dependent (dampng) characterstcs of the devces) and when the nternal system dsplacement s a maxmum (due to the stffness characterstcs of the devces). Ths s benefcal snce the relatve dsplacements between the external structure can be lmted but effectve solaton can stll be obtaned. If, say, vscous dampng devces were used nstead of vscoelastc devces, the external system s not dsplaced when the core reaches dsplacement, mplyng that the connecton between the exteror and the core wll requre detalng for much larger relatve dsplacements. Despte ths apparent advantage of vscoelastc dampers compared to vscous dampers, there are some drawbacks related wth these devces, snce they have a temperature dependent behavour and they are prone to creep when subjected to permanent loads (see Chrstopoulos and Flatrault (6) for further detals). Temperature dependence studes are outsde the scope of ths work and t should be part of future research works. Instead, as dscussed n Lago et al. (), n order to avod creep problems for the type of structural system consdered here, one could consder two dfferent solutons: () a selfsupportng exteror structure that does not mpose gravty loads on the devces, or () use of devces realsed wth multple elements arranged to provde the equvalent of vscoelastc behavour wth, for example, the use of vscous dampers n parallel wth flexble plates or beams.
External dsplacement functon of stffness of the vsco-elastc devces Exteror dsplacement functon of dampng coeffcent of vsco-elastc devces Core dsplacement s greater than that of the external dagrd At peak velocty the core dsplacement s zero Deformed Poston Intal Poston (a) Peak Dsplacement of Core Buldng (b) Peak Velocty of Core Buldng Fgure.. Plan vew of a structural system at (a) peak dsplacement of core and (b) peak velocty of core when complex exteror structure s vertcally solated wth vsco-elastc devces (modfed from Lago et al. ). Wth the above n mnd, t s consdered that the system merts some development ncludng the dentfcaton of a desgn methodology that can properly account for the non-lnear response of the core together wth the dampng offered by the vsco-elastc devces... Desgn Procedure One of the man dffcultes faced n the desgn of structures wth complex geometry s that every structure s lkely to be dfferent and as such, t s dffcult (f not mpossble) to assgn ratonal behavour factors or provde other general desgn gudelnes for such systems. However, by adoptng the vertcal solaton strategy the level of complexty can be drastcally reduced, snce the non-lnear behavour can be desgned to occur only n the ductle core structure. As such, what s requred s a sesmc desgn procedure that can properly account for the non-lnear response of the core together wth the dampng and stffness offered by the solaton devces and exteror structure. Ths secton wll brefly revew a Drect DBD procedure (from Sullvan (9) and Lago et al. ) that can account for these characterstcs. In secton 3 the method wll be appled to a case study structure n order to verfy ts ablty of controllng the structural response under b-drectonal earthquake exctaton. The fundamentals of the Drect DBD from Prestley et al. (7) are llustrated n Fgure.3. The method utlses the substtute structure approach (see Shbata and Sozen, 974) to characterze the non-lnear response of a MDOF system wth an equvalent SDOF system characterzed by a secant stffness K e, and effectve mass, m e, together wth a ductlty dependent equvalent vscous dampng value. These concepts are llustrated n Fg..3a to.3c. n 3 H e M e d F u F n K y rk K e d Equvalent Vscous Dampng.5..5..5 Elasto-Plastc RC Frame RC Brdge 4 6 Dsplacement Ductlty Spectral Dsplacement [m].5.4.3.. ξ = 5% d ξ = % T e 4 6 Perod [s] (a) SDOF representaton (b) Effectve stffness, K eff (c) Equvalent Vscous Dampng (d) Dsplacement Spectrum Fgure.3. Fundamentals of DDBD (adapted from Prestley et al. [7])
For the Drect DBD of complex geometry systems wth vertcally dstrbuted solaton devces, one must frst dentfy performance crtera whch could nclude peak storey drft lmts, stran lmts of structural elements or resdual deformaton lmts (see Sullvan et al. ). An expected dsplaced shape at peak response s then dentfed and the desred vscous dampng level for the system s selected. The dsplaced shape of systems such as that shown n Fg.. can be set assumng that the walls wll control the deformed shape (see Lago et al. () for further dscusson of ths assumpton). Consequently, for walls wth aspect rato (heght dvded by length) greater than 3., the desgn dsplacement profle s defned accordng to Eqn... φ h yw = h 3 + θ ph H (.) n where h s the heght of level above the wall base, H n s the total heght, θ p s the desgn plastc rotaton of the wall base hnge and φ yw s the wall yeld curvature that can be obtaned from sectonal moment-curvature analyss or usng approxmate expressons provded n Prestley et al. (7) and Sullvan et al. (). The desgn plastc rotaton can be found from: θ p φ θ c yw H n = ( ls yw ) p φ φ L (.) where θ c s the code desgn storey drft (to lmt damage to non-structural elements), φ ls s the wall curvature lmt for the desgn lmt state and L p s the length of the base plastc hnge n the walls (see Prestley et al. 7 or Sullvan et al. for further detals). Knowng the dsplacement profle of the system the equvalent sngle degree of freedom propertes of desgn dsplacement, d, effectve heght, H e and effectve mass, m e, are computed as: d = m (.3) m m h H e = (.4) m m e m = (.5) d where s the desgn dsplacement, m s the sesmc mass, and h s the heght, of level. To proceed wth the desgn t s proposed that a desred level of system vscous dampng, ξ sys be selected based on engneerng judgement (a value of between % and 3% can typcally be effectve). Havng obtaned the desgn dsplacement from Eqn..3 and havng selected the desgn equvalent vscous dampng, a hghly damped desgn dsplacement spectrum should be obtaned and an effectve perod dentfed, as llustrated n Fgure.3d. There are many dfferent rules n the lterature to construct hghly damped spectra and n ths work the followng expresson s used n whch the hghly damped dsplacement spectrum, S d,ξ, s obtaned from the 5% elastc spectral dsplacement demands, S d,5% as a functon of the desgn value of the equvalent vscous dampng ξ :.5 S d, ξ = Sd,5% (.6) 5 + ξ
Wth the requred effectve perod known, t s possble to compute the necessary effectve stffness, K e, and base shear, V b, as follows: m K = V = K (.7) e e 4π b e d Te Note that, for smplcty, the above expresson does not nclude an allowance for p-delta effects and nterested readers should refer to Sullvan et al. () for such detal. Wth the desgn base shear establshed, the member strengths and the propertes of solaton devces should be set n order to respect the ntally assumed system dampng value. To facltate ths, t s helpful to frstly choose the proportons of lateral load that wll be ressted by the nternal core and the exteror structure. As the exteror structure s of complex geometry and should reman n the elastc range, elastc analyses of the exteror system could be conducted to dentfy a safe desgn level of lateral force. Such elastc analyses should nvolve applcaton of a set of equvalent lateral forces, F, dstrbuted accordng to: m Fe, = VExt (.8) m where m and are respectvely the mass and the dsplacement of floor. A unt base shear can be used at frst for V Ext so that the rato of the desgn force to the desgn resstance n all elements of the external frame can be computed. The maxmum rato wll ndcate the crtcal element and can also be dvded nto the unt base shear n order to estmate the maxmum allowable transfer force, V Ext,max. However, n practce one should am to ncorporate some margn of safety by adoptng a lower transfer force than V Ext,max, consderng that hgher mode effects, sesmc exctaton of the frame tself and capacty desgn consderatons wll tend to ncrease the demands on the exteror frames. The safe transfer force could be consdered a lmt to both the velocty-dependent and stffnessdependent forces n the solaton devces. To facltate a drect DBD soluton, the rato of the stffnessdependent transfer force to the total stran energy wll be denoted usng the symbol ψ as recommended by Lago et al. (). Assumng that the dampers and the structure have the same desgn dsplacement (whch should be vald when dampers are provded at all floors) the proporton can be referred n terms of the total base shear nstead of the total stran energy, such that: V V + V V = V ( ψ ) (.9) Tot = Stru Ext Stru Tot where the total base shear at maxmum dsplacement, V Tot, s carred by the core structure, V Stru, and by the elastc stffness-dependent forces n the dampers, set equal to V Ext. At maxmum velocty (zero dsplacement) t s useful to expresson the proporton of total base shear carred by the vscous part of the dampers as β, such that: V = β (.) FD V Tot The proportons ndcated n Eqns..9 and. are useful for the calculaton of the system dampng, as shown by the followng equaton (see Lago et al., for detaled dervaton): β ξ = FD D sys = ( ψ ) ξstru + ψξ Ext + V Tot e (.)
where ξ Stru, s the structural equvalent vscous dampng constant of the system, gven by the sum of the nherent dampng and the nelastc structural dampng (f the man structural system s enterng ts nelastc range); ξ D, s the damper equvalent vscous dampng value offered by the devces; ξ Ext, s the external structure dampng; and V Ext, s the base shear carred by the external structural system (that s the same as the elastc porton carred by the vscoelastc dampers V Ext = V FD,el ). If the velocty-dependent shear obtaned n ths way s greater than the frame desgn lmt (.e. V Ext ), t s necessary to reduce the system dampng value (to permt a reducton n the stran energy proporton β). Another soluton nstead can be to upgrade the desgn the external frame to carry the force mparted by the vscous part of the damper and repeat the desgn. The velocty-dependent base shear obtaned from Eqn. (.) s then used to fnd a set of floor dampng forces, F d,, dstrbuted usng a modfed form of Eqn. (.3) n whch the dfferental dsplacement profle between the core structure and the external frame, -δ fr,, replaces the desgn dsplacement of each level,. Wth the requred dampng forces known, the relatve dampng constant, C, at each level can be determned wth the followng expresson: C TF = = π TF e d, e d, ( δ ) π fr, damper, (.3) where δ fr, s the frame dsplacement at level and damper, s the damper dsplacement for level. The damper dsplacement as utlzed n Eqn. (.3) assumes that between the external frame and the nternal core the dsplacements are n phase. However, the response s out of phase and consequently t should be determned through the followng expresson from Lago et al., (): damper, = sn atan δfr, cos atan δ fr, δ fr, (.4) Fnally, the requred damper elastc stffness can be obtaned usng the elastc forces determned of Eqn..8, as shown n Eqn..5. Fe, K = (.5) damper, Havng determned the requred propertes of the addng dampng system the subsequent step s to desgn the core wall. The base shear carred by the core walls, V wall, can be found drectly from the system total base shear as: V wall = V b V Ext. Furthermore, the overturnng moment carred by the walls, M wall, can be calculated as the product of the respectve base shears by the effectve heght, H e. At ths pont the DDBD procedure s complete, snce the requred strength for each structural system has been establshed. The next step would be to undertake capacty desgn of the elements not ntended to yeld and determne necessary renforcement quanttes. Furthermore, capacty desgn requrements are needed for the vscoelastc elements but ths s outsde the scope of ths paper and nterested readers should refer to Lago et al. []. The above revewed step-wse procedure for complex geometry structures wth vscoelastc dampng devces s summarzed n Fg. 3. 3. APPLICATION TO AN 8-STOREY CASE-STUDY STRUCTURE The sesmc desgn procedure descrbed n the prevous secton has been appled by Lago et al. () to the 8-storey structure shown n Fg. 3. for D response. Ths paper extends on the work undertaken by Lago et al. () to consder the 3D response of the buldng and a smplfed modellng approach.
The structure conssts of a curved exteror dagrd structure realsed wth steel elements, and two Cshape RC walls. A secondary framng system s also present n order to assst n resstng gravty loads. The dagrd desgned to be self-supportng under gravty loads, and vsco-elastc devces are dstrbuted vertcally up the heght at the dagrd-floor nterface. The sesmc desgn of the buldng s carred out for a a peak ground acceleraton of.4g usng the sol type C EC8 type spectrum (CEN, 4) and a desgn storey drft lmt of.%. Spectra of a set of 7 pars of spectra compatble accelerograms (from Lago et al. ) used for the NLTH analyses are shown n Fg. 3.. + + = Daphragms & gravty columns Core External frame of complex geometry Whole structure Fgure 3.. Case study structure wth core and complex dagrd structural systems (after Lago et al., ).6. Mean.8 Records Dsplacement [cm] Acceleraton [g] Desgn.4 5 5 4 Perod [s] 6 8 4 Perod [s] 6 8 Fgure 3.. Ground motons pars for NLTHAs: (a) acceleraton and (b) dsplacement spectra (Lago et al., ) To adjust the desgn for 3D effects, the desgn procedure of Secton 3 was appled n the global X and Y drectons separately, wth torson effects gnored owng to the relatvely concentrc mass, stffness and strength dstrbuton. The damper characterstcs were set consderng ther contrbuton to the nplane drecton of the dagrd walls. In other words, the damper contrbuton assocated wth the outof-plane response of the dagrd was gnored n the desgn. The b-drectonal characterstcs were, however, specfed for the non-lnear tme-hstory analyses used to gauge the performance of the system, as explaned n the next secton. Followng the above consderatons the structure s equpped wth four vscous dampers per floor (two per man prncpal drecton as shown n Fg. 3.3). Vscoelastc Damper st Floor 4th Floor 8th Floor Fgure 3.3. Plan vews of the case study structure at three levels ndcatng damper locatons (Lago et al., )
4. SEISMIC PERFORMANCE OF THE NEW SCHEME The desgn of the structural system n both prncpal drectons has lead to defne the propertes of the vscoelastc devces n both drectons. The relatve desgn propertes are shown n Table 4. and detaled calculatons are provded n Lago et al. (). Table 4.. 8-storey desgn propertes for both prncpal drectons Prncpal Drecton M n,wall (knm) I (m4 ) C Damp. (kns/m) K (kn/m) Damp X 9574 3.6 6 93 Z 53.94 343 698 The results for the major response parameters are shown for both drectons n Fg. 4.. The fgures show that the average NLTHAs results are very close to the desgn values and the overall structural response s well predcted n terms of dsplacements and drfts. The stuaton s slghtly dfferent lookng at the response n terms of wall shears and moments snce hgher modes effect amplfy the demand. However, good capacty desgn methods should overcome ths ssue (see the capacty desgn requrements for structures wth vscoelastc dampers proposed by Lago et al. ). Smlar remarks can be made lookng at the response for the solaton devces. The dsplacement demands are very well predcted but the velocty s underestmated due to dfferences between the pseudo-velocty and the real spectral velocty and hgher modes effect (agan, see Lago et al. ). Relatve Heght.8.6.4...3.6.8.6.4. 3.8.6.4. 3.8.6.4. 3.8.6.4. ì.8.6.4...4 Dsplacement [m] Drft [%] Wall Shears [kn] Wall Moments [knm] Damper Velocty [m/s] Damper Dsplacement [m] X-Drecton Z-Drecton Desgn Fgure 4.. Case study structure NLTH results for both prncpal drectons (Lago et al., ) In lght of these results, one notes that torsonal effects were not predomnant, llustratng a beneft of the vertcal dstrbuted solaton approach. Indeed, the stuaton s completely dfferent n the case the nternal and external system works together wth the core system, as shown n Lago et al. (). Havng demonstrated the valdty of the proposed soluton for the structural case under consderaton n the followng secton an alternatve modellng approach s proposed that can be used as a more drect and easy way to deal wth complex geometry structure proposed n ths work. 4.. Smplfed Analyss Approach Due to the modellng dffcultes ntrnsc wth structures of complex geometry, a smplfed model s proposed heren that can help for ntal stages of desgn of these structural typologes n order to grasp the capacty of the solaton system to furnsh a valuable scheme compared to other structural systems. The dea s to use smple MDOF models that have smlar propertes of the full complex geometry structure n such way the analyses can be run very quckly (compared wth the long analyses of the full model). The proposed soluton s shown n Fg. 4. where the complex geometry s smplfed by a mult-stck model lnked to the core by vsco-elastc lnks.
External Frame System (wth storey stffness k fr, ) Vsco-Elastc Devces Internal Wall System Fgure 4.. Complex geometry smplfed model schematc vew (Lago et al., ) The propertes of the external structure, as stck elements, are smply derved from the propertes of the real structures (but n the case of prelmnary desgn stages tral values of the stffness can be defned). For the complex geometry structure consdered n ths work, the lateral stffness of the elements s computed through the knowledge of the storey stffness, k fr,, defned as the rato of the external frame storey shear, V fr,, to the relatve nterstory dsplacement, δ fr,, as follows: k fr, V fr, = (4.) δ fr, Ths smplfed assumpton s only an approxmaton to the storey stffness but the NLTHA results presently shortly wll llustrate that t s good enough for the sake of graspng the structural capacty of the system. 4.. Analyss of the Smplfed Scheme As explaned above, the exteror structure wth complex can be smplfed through a smply MDOF stck element system whose stffness s defned by Eqn. (4.) and for the 8-storey case study structure under analyss (Fg. 3) the propertes obtaned n ths way are reported n Table 4.. Table 4.. 8-storey smplfed approach complex geometry equvalent stffness Level EI (knm ) X-Drecton EI (knm ) Z-Drecton 38565 36 9465 4646 3 36639 446 4 79956 5655 5 8735 5 6 36 39653 7 873 7 8 398 745 Knowng the propertes of the external frame n the both prncpal drectons and desgnng the nternal core and the dampers wth the same procedure descrbed n Secton 3, t s possble to gauge the performance of the smplfed model for 3D response. The results of NLTH analyses are shown n Fg. 4.3 for the man structural response parameters n both prncpal drectons. The fgures show that the response s very close to that of the full geometrc model and the same conclusons can be drawn about the desgn soluton. Indeed, the dsplacements are very well predcted whle the forces and damper velocty requre the applcaton of capacty desgn rules (see Lago et al. ).
.8.8.8.8.8.8 Relatve Heght.6.4..6.4..6.4..6.4..6.4..6.4...3.6 3 3 5.5..4 Dsplacement [m] Drft [%] Wall Shears [kn] Wall Moments [knm] X-Drecton Z-Drecton Desgn Damper Velocty [m/s] Damper Dsplacement [m] Fgure 4.3. Smplfed model NLTH results for both prncpal drectons (Lago et al., ) 5. CONCLUSIONS A novel sesmc desgn soluton for buldngs wth complex geometres has been revewed. The nnovatve soluton nvolves a vertcal dstrbuton of dampng devces up the heght of the complex structures to partally solate the complex portons of the structure and effectvely use the whole buldng system. A dstnct advantage of ths approach s that t would be applcable to most structures wth complex geometry, provded that the exteror structure s self-supportng under gravty loads. A new Drect DBD formulaton for the systems wth vertcally dstrbuted solaton devces has been developed, followng on from the recommendatons of Sullvan (9) and Lago et al. (). In order to valdate the method for 3D response, an 8-storey complex geometry case study structures has bee desgned and subject to NLTHAs usng a sute of spectrum-compatble accelerograms. The results confrm that the vertcal solaton strategy can be an effectve means of desgnng structures wth complex geometry n sesmc regons and that the proposed DDBD approach could provde effectve control of the response. However, careful capacty desgn s requred, as dscussed n Lago et al. (). Moreover, the results show that the solaton method helps lmt the torsonal nfluence of the complex structure. Fnally, an alternatve smplfed modellng approach has been ntroduced n order to avod complex structural modellng at concept desgn stages. The model was subjected to NLTHAs and the results ndcate that t could predct a response smlar to that of a full geometrc model. REFERENCES CEN (4). Eurocode 8 Desgn Provsons for Earthquake Resstant Structures, EN-998-:4, European Commttee for Standardzaton, Brussels, Belgum. Chrstopoulos, C., Flatrault, A. (6). Prncples of Passve Supplemental Dampng and Sesmc Isolaton, IUSS Press, Pava, Italy. Lago A., Sullvan, T.J., Calv, G.M. (). Sesmc Desgn of Structures wth Passve Energy Dsspaton Systems, ROSE Research Report, n press, IUSS Press, Pava, Italy. Lago A., Sullvan T.J., Calv, G.M. (). A novel sesmc desgn strategy for structures wth complex geometry, Journal of Earthquake Engneerng, 4(S), 69-5. Prestley, M.J.N, Calv, G.M., Kowalsky, M.J. (7). Dsplacement Based Sesmc Desgn of Structures, IUSS Press, Pava, Italy. Shbata, A. and Sozen, M. (974). Substtute structure method for sesmc desgn n renforced concrete. ASCE Journal of Structural Engneerng :, 8. Sullvan, T.J. (9). Drect dsplacement-based desgn of a RC wall-steel EBF system wth added dampers, Bulletn of the New Zealand Socety for Earthquake Engneerng, 4:3, 67-68. Sullvan, T.J., Prestley, M.J.N., Calv, G.M. Edtors (). A Model Code for the Dsplacement-Based Sesmc Desgn of Structures, IUSS Press, Pava, Italy.