Issues with the seismic design of mixed MRF Systems

Transcription

1 Issues wth the sesmc desgn of mxed MRF Systems T.J. Maley EUCE TRE, Pava, Italy T.J. Sullvan Unversty of Pava, Italy S. Pampann Unversty of Canterbury, ew Zealand SUMMARY: Engneers may be asked to desgn mxed MRF buldngs n whch a change n materal occurs at a certan level n a buldng. Ths work revews current code desgn recommendatons for such scenaros. Followng ths, a seres of -storey mxed MRF systems of steel and renforced concrete (RC) constructon are desgned usng both the drect dsplacement-based desgn (DDBD) method (Prestley et al., 7) and the ASCE-SEI 7-1 (ASCE, 1) equvalent lateral force (ELF) method for ULS. The ELF method of ASCE-SEI 7-1 produces desgns that are governed by drft lmts and s shown to be conservatve for the scenaros consdered durng assessment usng non-lnear tme-hstory analyses (NTHA). For the DDBD method, peak dsplacements of the systems match the desgn dsplacements well. Overall, the study ndcates that changes n nelastc behavour can, however, nfluence the response of mxed MRF systems, partcularly for what regards hgher mode drft response and resdual deformatons. Keywords: DDBD, FBD, Mxed systems, Steel MRF, Renforced Concrete MRF 1. MIXED MRF SYSTEMS In practce t s common for a buldng to be constructed makng use of dfferent materals to take advantage of the strengths and weaknesses of varous materals for structural purposes. It s, however, less common for a sesmc lateral force resstng system to use mxed constructon that nvolves a change n materal at a certan pont or ponts n the structure. Cases do exst of mxed systems where a complete change n constructon materal occurs at some pont over the heght of a buldng as depcted n Fgure 1.1. Such a transton n materals requres specal attenton to ensure the adequate transfer of desgn actons and consderaton of contnuty of both strength and stffness. For example, durng the 1995 Kobe earthquake the change n constructon materal from steel encased renforced concrete (SRC) constructon to renforced concrete (RC) only or to steel only constructon was dentfed as a contrbutng factor n many md-storey collapses observed n frame buldngs (Chung, 199). These two scenaros, SRC to RC and SRC to steel constructon, can be consdered ndcatve of a lack of contnuty of strength and of stffness, respectvely. Gven such complcatons, the use of a sngle materal system s generally favoured for smplcty and may, n fact, be a requrement of buldng standards. However, when permtted, ether as a retroft or new buld scenaro, a key dffculty for any desgner consderng the use of mxed constructon for sesmc lateral force resstng systems s that buldng standards and desgn codes generally lack provsons for mxed systems. Desgn code procedures are tradtonally based on a sngle materal type and often contan materal specfc assumptons or models. In the desgn for gravty and wnd loadng, a pecewse approach can be taken when usng dfferent constructon materals provded approprate attenton s gven to detalng of mxed connectons. However, for sesmc desgn, where non-lnear

2 behavour s often allowed to occur and dsplacement compatblty and dynamc effects are of greater sgnfcance, such a pecewse desgn approach may no longer be consdered vald and a system level approach s requred. Consequently, the dffculty les n the sesmc desgn of such mxed systems and the applcaton of code desgn procedures ntended for use wth a sngle materal-type system. Ths presents a major uncertanty for the sesmc desgn of mxed systems and forms the bass for the motvaton of the research. The work presented here summarses the results of ntal studes on the ssues faced durng system level desgn and assesses the performance of case study frames desgned usng both Dsplacement-based desgn (DBD) and Force-based desgn (FBD) procedures. Fgure 1.1. Examples of concrete/steel and concrete/tmber mxed constructon wth a change n constructon materal over the heght n North Carolna (mage courtesy of the Independent Weekly) Moment resstng frame systems (MRFs) provde a natural startng pont for nvestgatng the sesmc desgn of mxed systems. Columns and beams of dfferent composton may be used together and/or changed over the system heght. Due to ther flexble nature, the desgn of MRFs s usually controlled by lmtng the nterstorey drft response meanng that the drft or dsplacement response of the system must be adequately allowed for durng desgn. For taller MRFs, hgher mode drft amplfcaton becomes a sgnfcant factor requrng consderaton to ensure adequate desgn level response. Dfferent materals and non-lnear behavour wll have dfferng effects on the dsplacement response and the magntude of drft generated by hgher modes, thus for mxed MRF systems the nfluence of changng propertes on these response quanttes requres careful consderaton.. DBD OF MIXED MRF SYSTEMS Drect dsplacement-based desgn (DDBD) has been developed by Prestley et al. (7) as a more ratonal approach to sesmc desgn than tradtonal FBD methods as desgn carred out to a target dsplacement or drft from the outset. Recent development of the method has seen the publcaton of a dsplacement-based desgn model code DBD1 (Sullvan et al., 1). In DDBD the dsplacement response of the system under desgn s the focus and the system strength, and subsequently stffness, s set wth the goal of achevng the target level response for a desgn level earthquake. The method uses the substtute structure approach of Shbata & Sozen (197), together wth equvalent vscous dampng (EVD) expressons as explaned by Prestley et al. (7). Fgure.1 presents a bref outlne of the DDBD method where the mult-degree of freedom (MDOF) system s converted nto a sngle-degree of freedom (SDOF) substtute structure to represent the fundamental mode response (Fgure.1a). Ths SDOF structure s defned by an equvalent system mass and heght and s charactersed by the secant or effectve stffness at the peak dsplacement (Fgure.1b). For desgn, a target peak dsplacement response s set accordng to deformaton lmt states correspondng to the desred performance level of structural and non-structural elements. At ths pont, knowledge of the yeld dsplacement of the structure s requred n order to estmate the system

3 dsplacement ductlty at the peak response and allow an estmaton of the system EVD (Fgure.1c). If the yeld dsplacement can be establshed ndependently of the strength wthn the system, the system ductlty demand s gven drectly wthout the need for teraton. Fgure.1. Key steps of DBD for MODF systems: (a) equvalent SDOF system, (b) effectve stffness and ductlty, (c) EVD vs. ductlty, (d) desgn dsplacement spectra (adapted from Prestley et al., 7) In order to estmate the EVD from the ductlty of the system at maxmum response, an approprate dampng-ductlty relatonshp calbrated to the expected hysteretc response of the system s used as llustrated n Fgure.1c. The EVD represents the combned effects of elastc and hysteretc energy dsspaton wthn the system. Thus, wth the EVD and the desgn dsplacement of the system known, the requred secant or effectve perod of the system s obtaned from the reduced desgn dsplacement response spectrum as shown n Fgure.1d. From ths effectve perod, the desgn base shear of the system s gven drectly by smple calculaton from Equatons 1 and. K e = (1) π me / Te V = () B K e d where K e s the effectve stffness, m e the effectve mass, T e the effectve perod, V B the desgn base shear, and d the equvalent SDOF system desgn dsplacement. It s also noted that for MRF systems the desgn base shear s appled to the structure usng the dstrbuton gven by Equaton (3) where 9% percent of the base shear s appled n proporton to the mass and the expected dsplacement profle whlst the reman 1% s appled at the roof level of the structure. The use of ths redstrbuton of 1% of the base shear to the roof level, smlar to that prescrbed by the New Zealand code NZS (NZS, ) s to ad n the control of hgher modes. F = F t ( m ) ( m ) n +.9V (3) B = 1 where F t =.1V B for the top level and F t = everywhere else. For DDBD, the system EVD, ξ sys, may be found from Equaton where the EVD of each storey s estmated and then weghted by the work done of the storey (storey shear, V and storey drft, θ ) over the heght of the system to gve an estmate for the system EVD. Vθ ξ ξ sys = () Vθ Equaton 5 and Equaton are gven by Prestley et al. (7) for estmatng EVD as a functon of ductlty µ for concrete and steel frame systems respectvely.

4 µ 1 ξ = µπ (5) µ 1 ξ = µπ () 3. FBD OF MIXED MRF SYSTEMS As explaned n the ntroducton there s lttle gudance avalable for an engneer when desgnng a mxed system n usng current code (force-based) desgn methods. The work presented here focuses on the equvalent lateral force (ELF) procedure gven by ASCE/SEI 7-1 (ASCE, 1) whch does gve some gudance for the horzontal or vertcal combnaton of framng systems. In contrast, n the European and New Zealand codes (Eurocode (CEN, ) and NZS (NZS, ) respectvely) no drect consderaton of such systems s gven. The ELF method of ASCE/SEI 7-1 s applcable to all structures wthout vertcal rregulartes that do not exceed 1ft or.m and structures hgher than ths wth no rregulartes although wth a restrcton on the fundamental perod of 3.5 tmes the corner perod of the desgn acceleraton spectrum. For the ELF method, the fundamental perod can be estmated from approxmate equatons based upon heght and structural type that tend to underestmate actual perod values. For vertcal rregularty, ASCE/SEI 7-1 (ASCE, 1) gves weak or soft storey rregularty lmts that are relatve to the strength and stffness of the storey or storeys above a gven storey. Thus, f any change n stffness over the heght of a mxed MRF system s lmted to a reducton n stffness wth heght, and ncreases n stffness wth heght are avoded, these rregularty lmts are satsfed. Such a restrcton on the stffness propertes can be consdered prudent for desgn n areas wth sgnfcant sesmcty. A further weght or mass rregularty lmt of no storey havng a mass greater than 15% of any adjacent storey wth the excepton of the roof level s gven. Ths s perhaps the only lkely vertcal rregularty lmt that may not always be met for mxed systems due to large dfferences n mass between steel & RC systems. Fgure 3.1. Outlne of ASCE/SEI 7-1 ELF method based on the fundamental mode response Fgure 3.1 summarses the man steps of the ELF method of ASCE/SEI 7-1 graphcally where the estmated fundamental mode response s used to defne a sesmc coeffcent from an nelastc desgn spectrum. The sesmc coeffcent s then combned wth the sesmc weght of the system to gve the desgn base shear that s appled to the structure usng a trangular dstrbuton. Note that the elastc desgn spectrum s reduced as a functon of the response modfcaton factor R to gve an nelastc spectrum. In addton to ths, a dsplacement check s carred out under these desgn lateral loads to ensure that, when the dsplacements obtaned from statc analyses are amplfed by the deflecton amplfcaton factor C d, the drft lmt s respected. Exceedng the drft lmt requres the desgn process to be repeated wth a reduced response modfcaton factor R. ASCE/SEI 7-1 gves desgn coeffcents for MRF systems of steel, RC, and steel and RC composte

5 constructon for use wth the ELF or modal response spectrum (MRS) procedures n addton to means of estmatng the ntal perod of such systems. The values gven for these systems are gven n Table 3.1 below based on the type or ductlty class of the system beng desgned. Table 3.1. ASCE/SEI 7-1 desgn coeffcents for RC, steel, & RC & steel composte MRFs Response modfcaton Deflecton MRF Type Overstrength factor, Ω factor, R o amplfcaton factor, C d Specal MRF Intermedate MRF 5 (.5) 3.5 () Ordnary MRF 3 (3.5) 3.5 (3) *where gven values n brackets are for steel only MRFs For the vertcal or horzontal combnatons of framng systems n the same drecton the provsons of ASCE/SEI 7-1 state that the most strngent of the applcable structural lmtatons must be appled. An excepton s granted for vertcal combnatons where the upper system has a smaller response modfcaton factor, R, than the lower system. In ths case the desgn coeffcents R, Ω o, and C d of the upper system can be used for the upper system and the larger R and correspondng coeffcents Ω o and C d may be used for the lower system provded the forces transferred between the upper and lower systems are amplfed by the rato of the larger R coeffcent to the smaller R coeffcent. Fnally, for completeness t s noted that a two-stage ELF method, where upper and lower portons are desgned separately, s allowed under certan crcumstances. However, one of the condtons s that the stffness of the lower porton must be at least 1 tmes the stffness of the upper porton whch s lkely to be excessvely restrctve for MRF only systems.. DBD & FBF OF CASE STUDY SYSTEMS Followng the DBD model code DBD1 (Sullvan et al., 1) and the ELF procedure of ASCE/SEI 7-1 (ASCE, 1), DBD and FBD solutons have been found for -storey MRF systems of steel, renforced concrete (RC), and mxed RC and steel constructon where the lower -storeys are of RC constructon and the upper -stores are of steel constructon (Fgure.1). For both the DBD and FBD solutons the desgn response spectrum has been taken from ASCE/SEI 7-1 for a hgh level of sesmcty (Fgure.) and an allowable drft level of.5% has been assumed for the ultmate lmt state (ULS). In all cases rgd full strength connectons have been assumed ncludng column base connectons to a rgd foundaton. Fgure.1. Generc elevaton for case study MRFs consdered For each of the desgns 5% elastc dampng has been assumed and the sesmc weght kept constant. For the DBD of the MRFs unform RC beam and column sectons have been consdered of.x.m and.5x.5m, respectvely, over the heght of the system. For steel members, the W1 and W1

6 AISC (AISC, 1) secton groups and ther characterstc Z/I propertes have been used. These secton propertes have been consdered for both the FBD and DBD solutons durng the performance assessment carred out n the followng secton. The resultng desgn solutons as summarsed n Table.1 and Table. for the DBD and FBD procedures respectvely. Spectral Acceleraton (g) Desgn Average GM Record Spectral Dsplacement (m) Perod (s) Perod (s) Fgure.. Desgn acceleraton spectra (left panel) and dsplacement spectra (rght panel) wth spectra from ground moton set used for NTHA 1... Table.1. Desgn results for DBD systems Steel Mxed Concrete µ sys ξ sys (%) T e (s) V b (kn) V b/w t R * F T 1 (s) T (s) T 3 (s) Table.. Desgn results for FBD systems Steel Mxed Concrete R * C d * T a (s) V b (kn) V b/w t C s..5. T 1 (s) T (s) T 3 (s).5.3. * values used to comply wth storey drft lmt of.5% 5. THA PERFORMA CE ASSESSME T OF DESIG SOLUTIO S In order to assess the performance of each of the desgn solutons, NTHAs usng RUAUMOKO3D (Carr, ) have been carred out. For these analyses lumped mass and plastcty models have been used to assess the system response of the desgns usng the spectrally matched accelerograms gven prevously n Fgure. (Pennucc et al., 9). In all cases the member stffness propertes used are those related to the desgn member strength and the expected secton yeld curvature (EI=M/ϕ y ), analogous to the secant to yeld stffness, thus approxmatng cracked secton propertes for the RC sectons. Capacty desgn s enforced for the analyses by permttng hnges to form only at the beam ends and the column bases thus mposng a beam-sway mechansm. Gravty loads have been neglected durng modellng and were not consdered when settng member strengths. The b-lnear and Takeda fat (α =.3, β=.) hysteretc rules are used to characterse the rgd connecton steel and renforced concrete (RC) frames respectvely (see Carr, ). Note that for the column base level the Takeda thn (α =.5, β=) hysteretc rule has been used to smulate the behavour of RC sectons under bendng and axal load. For all cases a post-yeld moment-curvature stffness rato of. has been assgned. A tangent stffness proportonal dampng approach has been adopted for ths study over the more

7 tradtonal elastc stffness proportonal dampng followng the reasonng outlned n Prestley et al. (7). As pure tangent stffness proportonal dampng s not avalable wthn Ruaumoko3D (Carr, ) for MDOF systems, tangent-stffness Raylegh dampng has been used wth an adjustment made to the elastc dampng for a dampng level of 5% usng the procedure gven by Prestley et al. (7). For ths study P- effects have been neglected. Usng these modellng assumptons the resultng perods are gven n Table.1 and Table. for the respectve desgn scenaros consdered. The peak drft results for all of the desgn solutons presented n ths work are gven n Fgure 5.1. Note that the results from the DBD and FBD methods dffer sgnfcantly. The DBD solutons respond at a level consstent wth the drft lmt used durng desgn whlst the FBD solutons respond at a level sgnfcantly below the drft lmt. Ths relatve dfference n response s not unexpected consderng the ncreased desgn base shear requred by the FBD method over the DBD method as can be seen n Table.1 and Table.. The FBD method requres a desgn base shear of to. tmes that of the DBD method whch reduces the average drft response level from around.5% for the DBD method to around %, where much of the system undergoes lttle nelastc behavour. It s worth notng that the altered base shear dstrbuton used for DBD to help control hgher mode effects reduces the response n the upper levels and results n more unform drft response, thus assgnng strength more effcently Indv. NLTH Mean Desgn Fgure 5.1. NTHA peak drft results for steel (left panels), mxed (central panels), and concrete (rght panels) systems for DBD (upper panels) and FBD (lower panels) systems at 1% of the desgn ntensty Between the dfferent scenaros consdered n Fgure 5.1, the effect of the reducton n stffness at mdheght of the mxed system (where there s a transton from RC to steel constructon) s notceable for both desgn methods, although more so for the FBD soluton due n part to the altered strength dstrbuton used for DBD. To examne more closely the response of the mxed systems, peak dsplacement and resdual drft profles are gven together wth the peak drft profles n Fgure 5. where t can be seen that the reducton n stffness and change n hysteretc behavour at the transton also nfluences resdual drft levels.

8 Indv. NLTH Mean DBD Profle... Dsplacement (m) Resdual Indv. NLTH Mean FBD Profle... Dsplacement (m) Resdual Fgure 5.. NTHA peak dsplacement (left panels), drft (central panels), and resdual drft (rght panels) results for DBD (upper panels) and FBD (lower panels) mxed systems at 1% of the desgn ntensty Fgure 5.3 presents the same results for analyses run at 15% of the desgn ntensty where smlar effects are observed wth the response ncreasng for the upper levels wth the change n constructon type although to a lesser degree than observed for the 1% ntensty level. Subsequent work reported n Maley et al. (11) has found the lessonng of ths effect to be due to dfferences n the hysteretc rules used to characterse the steel and RC behavour that become apparent when ductlty levels become sgnfcant. As an example, the effect of ths s hghlghted n Fgure 5. where the b-lnear (BL) hysteretc model has been replaced wth the Takeda thn (TT) rule, whch could be used to characterse the behavour of steel T-stub connectons, for the FBD mxed system. The result s an ncrease n the peak transent response when compared to the prevous results. Whlst t s acknowledged that the ncreases n system transent response due to a reducton n stffness could be expected to be captured usng modal response spectrum (MRS) methods, the effect of dfferent nelastc propertes can not. Gven the sgnfcant effect of the reducton n stffness on the response, t could be argued that an MRS procedure should be requred by ASCE/SEI 7-1 where a sgnfcant reducton n stffness occurs as s the case for other major codes. Returnng to Fgure 5.3, the altered base shear dstrbuton used for the DBD method, gven by Equaton 3, agan results n a more unform dstrbuton n the drft response and effectvely controls the hgher mode response. It could be sad that the FBD system gves a more desrable response due to the lower transent and resdual drfts, but f such a response were desred the DBD method could provde for ths by desgnng to a reduced drft lmt. Fnally, t s noted that for both ntensty levels the resdual drfts observed n the upper steel constructon levels tend to be notceably hgher than those for the lower levels wth RC constructon. Ths s despte transent drfts showng dfferng trends and s lkely due to the ncreased unloadng stffness of the b-lnear hysteretc rule used to characterse the nelastc behavour of the steel members.

9 Indv. NLTH Mean Dsplacement (m) Resdual Indv. NLTH Mean Dsplacement (m) Resdual Fgure 5.3. NTHA peak dsplacement (left panels), drft (central panels), and resdual drft (rght panels) results for DBD (upper panels) and FBD (lower panels) mxed systems at 15% of the desgn ntensty Indv. NLTH Mean (TT) Mean (BL).... Dsplacement (m) Resdual Fgure 5.. NTHA peak dsplacement (left panel), drft (central panel), and resdual drft (rght panel) results for FBD mxed systems wth Takeda thn (TT) rule used for steel porton of frame at 15% of the desgn ntensty 5. CO CLUSIO S The applcaton of the DDBD (Prestley et al., 7) and ASCE-SEI 7-1 (ASCE, 1) desgn provsons for mxed MRF systems has been revewed and the desgn procedures have been appled to an -storey steel/rc case study mxed MRF system. For comparson, the methods have also been appled to steel only and RC only systems. The revew has found that the methods can be appled

10 relatvely easly to mxed MRF systems and the desgn and subsequent NTHA assessment of the mxed case study buldng has shown smlar trends to steel and RC only systems for both procedures. By runnng NTHAs, the change n constructon materal has been shown to have greatest nfluence on the resdual drfts whch s somethng a desgner should be aware of when consderng such systems. The DDBD method was found to gve more economcal desgns and an mproved response overall due to the superor ablty of the method to control the level and form of the response. On ths later pont, the altered base shear dstrbuton used by the DBD method has been shown to mprove the system performance and ad n the control of the hgher mode response. The use of the DDBD method can be seen as advantageous for performance based desgn where the more accurate control of system response offered by DDBD wll mprove performance estmates. It s noted that more advanced modellng could be used n future research to strengthen conclusons made here, especally to consder local effects n systems wth such changes n materal constructon. Fnally, t s noted that further research on the topc has shown that changes n nelastc behavour can have a sgnfcant nfluence on the transent drft response of mxed MRF systems (Maley et al., 11). AKC OWLEDGEME T The authors gratefully acknowledge that the research leadng to these results has receved fundng from the European Unon's Research Fund for Coal and Steel (RFCS) research programme under grant agreement n [RFSR-CT-1-9]. REFERE CES AISC (1). Manual of Steel Constructon, 3rd Edton, Amercan Insttute of Steel Constructon Inc., Chcago, USA. ASCE (1). Mnmum Desgn Loads for Buldngs and Other Structures, Amercan Socety of Cvl Engneers. Carr, A.J. (). Ruaumoko 3D A program for Inelastc Tme-hstry Analyss, Department of Cvl Engneerng, Unversty of Canterbury, New Zealand. CEN (). Eurocode : Desgn of structures for earthquake resstance -Part 1: General rules, sesmc actons and rules for buldngs, Comté Européen de Normalsaton (CEN), Brussels, Belgum. Chung, R., Ballantyne, D., Comeau, E., Holzer, T., Madrzykowsk, D., Schff, A., Stone, W., Wlcosk, J., Borcherdt, R., Cooper, J., Lew, H., Moehle, J., Sheng, L., Taylor, A., Buckle, I., Hayes, J., Leyendecker, E., O Rourke, T., Sngh, M., and Whtney, M. (199) January 17, 1995 HyogokenNanbu (Kobe) Earthquake: Performance of Structures, Lfelnes, and Fre Protecton Systems, NIST SP 91 (ISCCS TR1), Natonal Insttute of Standards and Technology, Gathersburg, MD. Maley, T.J., Sullvan, T.J., Pampann, S. (11). Sesmc Desgn of Mxed MRF Systems, (n press), IUSS Press, Pava, Italy. NZS (). NSZ Structural Desgn Actons, Part 5: Earthquake Actons-New Zealand. Standards New Zealand, New Zealand. Pennucc, D., Calv G. M., and Sullvan T. J. [9] "Dsplacement-Based Desgn of Precast Wall wth Addtonal Dampers," Journal of Earthquake Engneerng 13:1, 5. Prestley, M.J.N., Calv, G.M., and Kowalsky, M.J. (7). Dsplacement-Based Sesmc Desgn of Structures, IUSS Press, Pava, Italy. Shbata, A., and Sozen, M. (197). Substtute Structure Method for Sesmc Desgn n Renforced Concrete, ASCE Journal of Structural Engneerng, 1:1, 1-1. Sullvan, T.J., Prestley, M.J.N., Calv, G.M. (1). A Model Code for the Dsplacement-Based Sesmc Desgn of Structures, IUSS Press, Pava, Italy.