INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 2, No 1, 2011

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1 INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volum, No, Copyrght All rghts rsrvd Intgratd Publshng srvcs Rsarch artcl ISSN 9 99 An conomc comparson of Drct dsplacmnt basd Dsgn wth IS-9 Rspons Spctrum mthod for Sunl S. Mayngbam, Choudhury.S - Rsarch Scholar, Dpartmnt of Cvl Engnrng, NIT Slchar, Inda - Profssor, Dpt. of Cvl Engnrng, NIT Slchar, Inda sunl_mayngbam@hotmal.com ABSTRACT Dsplacmnt basd dsgn dals wth th lvl of damag of structur by dsgnng a structur wth a spcfd targt dsplacmnt. Tradtonal codal Forc-basd mthod of dsgn cannot dsgn structurs for targt dsgn objctvs undr a spcfd hazard lvl. An conomc comparson btwn a smplr form of Drct Dsplacmnt-basd Dsgn and IS- 9 Rspons Spctrum mthod for rnforcd concrt fram buldngs s rportd hr. Buldngs of two dffrnt plans, thr dffrnt hghts ar dsgnd wth th mthod for th prformanc lvls achvd from thos dsgnd by th codal mthod and thr rspctv costs of structural fram mmbrs ar compard. It has bn found that th fram buldngs dsgnd wth th mthod s mor conomcal than thos dsgnd wth th codal mthod for th prformanc lvls achvd by th sad codal undr smlar condtons of modlng and prformanc lvls. Kywords: Drct dsplacmnt basd dsgn; IS-9 rspons spctrum mthod; dffrncs n procdur; prformanc lvls; smlar condton; structural costs.. Introducton Ssmc dsgn of buldngs has tradtonally bn forc-basd. In th forc-basd codal mthod of dsgn, th bas shar s computd basd on prcvd ssmc hazard lvl, mportanc of th buldng and probabl rducton n dmand du to nonlnar hystrss ffcts. Th computd bas shar s dstrbutd at floor lvls wth som prscrbd or stmatd dstrbuton pattrn. It s wdly undrstood now that t s not th forc but dsplacmnt, whch can b drctly rlatd to damag. Th constancy of stffnss n forcbasd dsgn s also not tnabl (Prstly 99, ). Through forc-basd mthod of dsgn an ngnr cannot dlbratly dsgn structur for an ntndd prformanc lvl. Th altrnatv approachs ar dsplacmnt-basd dsgn and prformanc-basd dsgn whch ar gradually bcomng popular n rcnt tms. In ths mthods th dsgn s don for an ntndd dsplacmnt or, an ntndd prformanc undr a prcvd hazard lvl. Dsplacmnt-basd dsgn procdurs hav bn rportd n th ltraturs (Aschhm, Paulay, Q and Mohl 99, tc). An offshoot of th dsplacmnt-basd dsgn s Drct Dsplacmnt-basd Dsgn (DDBD) whch has bn rportd by svral authors (Pttnga and Prstly ; Xu tc.). Th DDBD mthod for hollow-tub R.C. fram buldngs by Pttnga and Prstly () appars to b appalng whr th buldng s dsgnd for som spcfd ntrstory drft lmt (%) by consdrng an Equvalnt Sngl Dgr of Frdom (ESDOF) systm of th buldng. Undr th spcfc modlng and targt drft condton, dynamc amplfcaton of story shar, column momnt and story drft ar consdrd and modfd to achv th targt ntr story drft. Rcvd on Octobr, Publshd on Novmbr

2 An conomc comparson of Drct dsplacmnt basd Dsgn wth IS-9 Rspons Spctrum mthod for Th Prformanc-Basd Dsgn (PBD) apparntly startd wth th Frman s Capacty Spctrum Mthod (Frman 9), dvlopd fast wth th contrbuton from vast rsarch communty and wth th publcaton of varous documnts by Appld Tchnology Councl and Fdral Emrgncy Managmnt Agncy. Th prformanc lvls of th buldngs ar dscrbd n trms damag lvl rflctd by nlastc rotaton n mmbrs dffrntatd as Immdat Occupancy (IO) lvl, whr damag lvl s last; Lf Safty (LS) lvl, whr damag lvl s ntrmdat and lf s not thratnd undr strong ground moton; and, Collaps Prvnton (CP) lvl whr damag s substantal and th structur s on th vrg of collaps.. DDBD dsgn procdur Th dsgn s don by a smplr DDBD mthod smlar to Pttnga and Prstly (). Th targt dsgn drft and prformanc lvl of th buldng ar dcdd. Th bam dpth has bn drvd from UPBD (S. Choudhury t al, communcatd to Earthquak Spctra n ). Th bam wdth vars from on-thrd to half of bam dpth as pr gnral dsgn practc. Th column szs ar so adjustd that th column stl s rstrctd % of column sctonal ara. Dsplacmnt (m) IS-Dsplacmnt Spctra % % % % % Prod (sconds) Fgur : IS-Dsplacmnt spctra for.g, mdum typ sol. Howvr, for rady rfrnc th dsgn stps ar laboratd blow, wth mnton of dffrnc wth DDBD mthod of Pttnga and Prstly (), whrvr applcabl. Th quvalnt sngl dgr of frdom systm proprts ar dtrmnd as follows m d = m m m = d () () Volum Issu 9

3 An conomc comparson of Drct dsplacmnt basd Dsgn wth IS-9 Rspons Spctrum mthod for m h H = () m Hr, m, h and ar rspctvly th mass, hght from bas and dsplacmnt for th story. d s targt (spctral) dsplacmnt, m s quvalnt mass, H s th ffctv hght of th ESDOF systm. Th dsplacmnt spctra corrspondng to dsgn acclraton spctra ar gnratd for varous dampng shown n fgur. Th dflcton profl suggstd by Pttnga and Prstly (), as shown n Eq. (a) and (b), has bn usd. Hr, Ø s th mod shap coffcnt of buldng at th floor and n s total numbr of story. h n<=, φ = H n>, φ = h H h (a) (b) H Story dsplacmnt, n stp and s gvn by c = φ φc () Whr, c and ϕ c ar th crtcal story dsplacmnt and th corrspondng mod shap at th crtcal story lvl. Th dampng n th systm s computd from ductlty as gvn blow: Th yld dsplacmnt ( y ) of ESDOF systm s gvn by Eq. () and fram ductlty (µ) s gvn by Eq. (). Now quvalnt ffctv dampng (ξ) n th systm s obtand from Eq. (). y =θ yf H () µ = d / y. µ ξ = + % () π Th dsgn bas shar s computd as follows. Th ffctv tm prod (T ) s obtand from dsplacmnt spctra corrspondng to th curv for dampng ξ and th valu of targt dsplacmnt d. Effctv stffnss for ESDOF systm s gvn by Eq. (9) and bas shar s gvn by Eq. (). () Volum Issu

4 An conomc comparson of Drct dsplacmnt basd Dsgn wth IS-9 Rspons Spctrum mthod for K m = π (9) T P ffct s consdrd as pr Pttnga and Prstly, () whr stablty rato (Ө P ), post yld stablty rato unaffctd (r o =.,assumd) and affctd (r p ) by P ffct and ovrall momnt (M B ) ar gvn by Eq. (a), (b) and (c) rspctvly. P θ P = VBH ro θ P rp = θ M B P = K D H ( µ ) + rp P rp ( µ ) D (a) (b) (c) Th ovrall momnt has drctly bn convrtd to Dsgn bas shar for asy applcaton M V = B b () H Th bas shar s thn dstrbutd at floor lvls as pr Eq. (a). If th buldng s mor than -story hgh, thn to tak nto account th ffct of hghr mods, Eq. (b) s usd, n whch F t s typcally % of bas shar appld at roof lvl. m F = Vb m (a) m F = Ft +. 9V b m (b) Th dsgn s don wth xpctd matral strngths. Th load combnatons ar as blow: D+ L (a) D + L± (b) F x D + L± (c) F y Whr, D and L stand for dad load and lv load rspctvly. F x and F y stand for ssmc load n two mutually prpndcular drctons of th buldng for th floor concrnd obtand from Eq. ().In th dsgn stag ffctv mmbr stffnss as spcfd n FEMA- ar consdrd. Unlk th gnral DDBD, th typcal ffctv stffnss factors for bams and columns ar. and. rspctvly. Capacty dsgn s carrd out to nsur wak-bam strong-column. Columns ar nsurd to bhav as lastc mmbr. In th gnral DDBD, bottom ground story columns ar dsgnd to bhav as lastc mmbrs. Shar falur of bams ar also avodd. Th column szs ar Volum Issu

5 An conomc comparson of Drct dsplacmnt basd Dsgn wth IS-9 Rspons Spctrum mthod for rstrctd n way that th maxmum stl n columns s %. Nomnal rnforcmnt of bam was takn as.% at ach fac for ductl bhavor. Hr, n contrast to th gnral DDBD mthod, dynamc amplfcaton s not consdrd n th dsgn. Th targt drft has bn achvd by assumng tral rducd dsgn drft untl t s achvd. Morovr, th purpos of ths rport s just to compar th structural cost undr smlar modlng condton and prformanc lvl.. Dffrncs btwn th two procdurs Th dffrnc btwn DDBD and IS rspons spctrum mthod ar statd as follows. Th frst s a dsplacmnt basd dsgn whch uss xpctd matral strngth n th dsgn stag. It also uss constant bam scton for a partcular fram; load combnaton as pr Eq. (); nlastc st mod dsplacmnt profl (Eq. (a) and (b)); latral load dstrbuton accounts for hghr mod ffct for buldngs abov -story as n Eq. (b); P- ffct as n Eq. (a), (b) and (c). Th lattr s a forc basd dsgn whr charactrstc matral strngth s usd. Hr, t uss varabl bam sctons accordng to th dmand and rang of prcntag rnforcmnt; load combnaton: ().(DL+IL), ().(DL+IL±EL), ().(DL±EL), ().9DL±.EL, whr DL stands for dad load, IL for mposd load and EL for ssmc load along th fram; th numbr of mods dpnds on th sum total of thr modal mass to mak up at last 9% of th total ssmc mass; latral load dstrbuton dos not accounts for hghr mod ffct; mssng mass corrcton byond % for hghr mod ffct. Forc-basd dsgn mthods for othr cods ar mor or lss smlar rgardng th basc assumptons mntond abov. Howvr, som assumptons lk factor of safty for loadng apart from th basc lmt stat dsgn may vary. So, thy ar xpctd to bhav smlarly spcally n nlastc tm hstory analyss for smlar condtons and also thr structural cost.. Prformanc valuaton and cost comparson For structural cost comparson btwn th two dsgn mthods, two plans dsgnatd as plan I and Plan II as shown n fgur a and fgur b hav bn consdrd. Th hghts of buldngs consdrd ar -story, -story and -story for both plans. Th nomnclatur of th buldngs and targt prformanc objctvs has bn lstd n Tabl. Symbols IS and DDBD rprsnts buldngs dsgnd by I.S. rspons spctrum mthod and DDBD rspctvly. Th scond numrcal fgur ndcats th typ of plan and th last numrcal fgur n buldng nam rflcts th total numbr of story n th buldng. Tabl : Nomnclatur and targt prformanc objctvs of buldngs consdrd. Buldng Catgory No. Plan No. usd Buldng nomnclatur Dsgn mthod I IS-, IS-, IS- IS-9 II IS-, IS-, IS- IS-9 I DDBD-, DDBD-, DDBD- DDBD II DDBD-, DDBD-, DDBD- DDBD Volum Issu

6 An conomc comparson of Drct dsplacmnt basd Dsgn wth IS-9 Rspons Spctrum mthod for Fgur : (a) Plan No. I of buldngs and (b) Plan No. II of buldngs. Dsgn spctrum consdrd s as pr IS-9 at acclraton lvl.g for mdum typ sol. A cornr prod xtnson of sconds has bn appld to tackl largr dsplacmnt dmand (also to ncorporat th sgnfcanc of magntud on th cornr prod as pr Faccoll t al., ) for hghr story buldngs dsgnd by DDBD. Th spctrum compatbl ground motons (SCGM) hav bn constructd by usng th softwar dvlopd by Kumar () whr th phas angl, frquncy contnt and duraton of th background arthquak ar ncorporatd n th SCGM hghlghtd n Tabl. Th match btwn th IS dsgn spctrum and SCGM rspons spctrums at % dampng ar shown n fgur a.th Fnal mmbr szs of varous buldngs hav bn furnshd n Tabl. Concrt of cub strngth MPa and rnforcng stl wth yld strngth MPa hav bn usd. Expctd matral strngths as pr FEMA- hav bn usd n dsgn and non lnar tm hstory analyss. Tabl : Dtals of artfcal ground motons Sl. No. Nam Background Earthquak Rcord No. Duraton (sc) GM Duzc 999 Duzc, (ERD).9 GM El Cntro 9 N-S Componnt. GM Gazl 9 Karakyr, 9. GM Kocal 999 Sakarya, 9 (ERD). GM N. Palm Sprng 9 9, USGS staton. Howvr, charactrstc matral strngths hav bn usd n dsgn stag for th I.S. cod mthod. Th post-lastc forc-dformaton bhavor has bn takn as pr FEMA- shown n fgur b. Buldngs hav bn modld usng SAP v.. Effctv scton proprts of bams and columns hav bn usd for all consdrd buldngs for non lnar analyss. Th yld momnts ar obtand from dsgn stl. Th ffctv bam flxural rgdty s gvn by Eq. (a), n whch E s modulus of lastcty of concrt, I ff, bam s ffctv momnt of nrta of bam, M yb s bam yld momnt and Ø yb s bam yld curvatur gvn by Eq. (b) Volum Issu

7 An conomc comparson of Drct dsplacmnt basd Dsgn wth IS-9 Rspons Spctrum mthod for Sa/g... GM- GM- GM- GM- GM- IS Prod (sc) (a) Normalzd forc CP LS IO Plastc rang Dformaton or dformaton rato (b) Fgur : (a) Dsgn IS spctrum Vs. SCGM rspons spctrum and (b) Forc-dformaton bhavour (FEMA-). Tabl : Mmbr sz of th buldngs consdrd. Buldng Nams Column Sz (mm) Bam Sz (mm) Dpth wdth Long-drcton Short-drcton IS- to to to IS- to to to IS- to to to IS- to to to IS- to to to IS- to to to DDBD- to DDBD- to DDBD- to DDBD- to DDBD- to DDBD- to Effctv flxural rgdty of column s gvn by Eq. (c), n whch I ff, column s ffctv momnt of nrta of column, M c s column momnt corrspondng to axal load n column undr gravty load and s obtand from ntracton dagram of column at xpctd strngth lvl of matrals. Ø yc s yld curvatur of column gvn by Eq. (d), n whch b c s column dpth undr drcton of arthquak undr consdraton. Eq. (a) through (d) s aftr Prstly (). M yb EI ff, bam = (a) φyb y φ yb =. (b) b h ε M c EI ff, column = (c) φyc Volum Issu

8 An conomc comparson of Drct dsplacmnt basd Dsgn wth IS-9 Rspons Spctrum mthod for φ = b (d) yc.ε y / c Th buldngs ar subjctd to Nonlnar Tm hstory analyss (NLTHA) undr spctrum compatbl ground motons (SCGM). As th dsgn s don for dsgn spctrum, th nrgy lvl of th ground motons ar st to lvl of dsgn spctrum, whch s assurd through SCGM. Th buldngs dsgnd by th IS mthod ar frst chckd for thr prformanc through NLTHA whr som of th buldngs prformanc lvl has bn found to byond CP whch s not an dal lvl for comparson. Irrspctv of thr ral prformanc lvl, just to mak an dal ground for comparson, columns wr arbtrarly modld as lastc mmbrs so that hngs wr mad to form only n bams through capacty dsgn (strong column wak bam) whch s also don n cas of DDBD. IS- long GM- GM- GM- GM- GM-... IS- short... IS- long IS- short 9 IS- short... IS- long... Fgur : IDR dagram n th mntond drcton for IS-9 dsgnd buldngs. Capacty dsgn has bn prformd as pr EC-, M Rc =. M Rb. () Whr, M Rc rprsnts th sum of th dsgn momnts of rsstanc of th columns framng nto th jont and M Rb s th corrspondng sum of th dsgn momnts of rsstanc of th bams. Volum Issu

9 An conomc comparson of Drct dsplacmnt basd Dsgn wth IS-9 Rspons Spctrum mthod for Fgur : Hngs n typcal IS cod dsgnd frams wth th mntond drctonal SCGMs. Tabl : Structural cost wth prformanc lvl for IS cod dsgnd buldngs. Buldng nams Structural Costs Prformanc lvl (Rs.) Long drcton Short drcton IS-,,.% LS.% LS IS-,,.% LS.% LS IS-,,9.% LS.% LS IS-,,9.% LS.% LS IS-,9,9.% LS.% LS IS- 99,,99.9% LS.% LS Tabl : Structural cost wth prformanc lvl for DDBD dsgnd buldngs. Buldng nams Structural Costs (Rs.) Targt Prformanc Lvl Achvd Prformanc lvl Cost wth rspct to IS cod buldngs Long drcton Short drcton DDBD-,,.% LS.% LS.% LS -.% DDBD-,,9.% LS.% LS.% LS -.% DDBD-,9,9.% LS.% LS.% LS -.% DDBD-,9,.% LS.% LS.% LS -9.% DDBD-,,.% LS.% LS.% LS -.% DDBD-,,.% LS.% LS.% LS -.% Th prformanc lvls of rsultng buldngs hav bn found dal shown n Tabl, th ntr story drft dagrams (%IDR) bn shown n fgur whr th %IDR coms around.9% to.%. Th mmbr hng formaton at last stp n tm hstory analyss for typcal cass of IS cod dsgnd buldngs has bn hghlghtd n fgur. Th pnk and th blu hngs on th fram mmbrs of fgur and fgur ndcat IO and LS lvl rspctvly. Hr, th maxmum mmbr prformanc s LS. Any targt Volum Issu

10 An conomc comparson of Drct dsplacmnt basd Dsgn wth IS-9 Rspons Spctrum mthod for prformanc lvl, spcally % IDR for DDBD s not xpctd to b achvd through NLTHA wthout slght dvatons bcaus of dynamc amplfcatons (not consdrd), dsgn rrgularts and othr mnor factors lk mprcal consdraton of hghr mod ffct n th dsgn procdur, tc. Buldngs of tral targt prformanc lvl by DDBD hav bn tstd through NLTHA for thos achvd by th IS mthod (Tabl and Tabl ). untl a clos, prfrably lssr prformanc lvl s achvd. Th ntrstory drft dagrams for DDBD dsgn buldngs hav bn shown n fgur and hngs formaton at last stp n tm hstory analyss ar also found to b LS, typcal cass has bn hghlghtd n fgur. Th structural costs.. th costs of th total volum of concrt and stl usd only for bams and columns has bn valuatd for both th catgors of buldngs (Tabl and Tabl ) accordng to Dlh Schdul of Rats. Th rato of volum of concrt and stl provdd aganst buldng hghts s shown n fgur 9a. Th rato s lssr by a sgnfcant amount n cas of th IS cod dsgnd buldngs than th othr showng that th volum of stl s domnant for th codal buldngs. DDBD- long... DDBD-long... DDBD- long DDBD-long DDBD-long DDBD- long... Fgur : IDR dagram n th mntond drcton for DDBD dsgnd buldngs. Volum Issu

11 An conomc comparson of Drct dsplacmnt basd Dsgn wth IS-9 Rspons Spctrum mthod for Snc, th cost of rnforcng stl s usually hghr than that of concrt, th volum of stl s on of th mpld factors (rsultng from th dffrncs n th two dsgn mthods) rsponsbl for th hghr cost (fgur 9b). For smlar prformanc lvls, buldngs dsgnd wth DDBD has found to b mor conomcal avragng to about -.% of th buldngs dsgnd wth IS rspons spctrum mthod for th consdrd buldngs undr smlar condtons of modlng. Th sam study can also b prformd for forcd-basd dsgn cods of othr countrs to montor thr dffrncs wth DDBD, th most mportant bng thr conomc aspcts. Hght IS IS DDBD DDBD Hght IS IS DDBD DDBD Vc/Vs (a) Cost (Rs.)x (b) Fgur 9: (a) Rato of volum of concrt and stl Vs. hght and (b) Structural costs Vs. hght.. Concluson Th costs of R.C fram buldngs dsgnd wth drct dsplacmnt basd dsgn has bn compard wth thos dsgnd wth I.S. rspons spctrum mthod at th prformanc lvl gvn by th lattr. Fram buldngs of two plans and dffrnt hghts hav bn dsgnd wth I.S. rspons spctrum mthod. Th prformanc of th buldngs has bn valuatd Volum Issu

12 An conomc comparson of Drct dsplacmnt basd Dsgn wth IS-9 Rspons Spctrum mthod for through nonlnar tm hstory analyss usng fv spctrum compatbl ground motons. Th sam catgory of buldngs has bn dsgnd wth drct dsplacmnt basd dsgn for th prformanc lvls gvn by thos dsgnd wth I.S. rspons spctrum mthod. Th prformanc of th buldngs has bn valuatd and chckd through nonlnar tm hstory analyss usng fv spctrum compatbl ground motons. Rsults hav bn prsntd for varous rspons quantts. Th structural costs of both th catgors of buldngs hav bn valuatd. It has bn found that buldngs dsgnd wth drct dsplacmnt basd dsgn ar mor conomcal than thos dsgnd wth th IS rspons spctrum mthod.. Rfrncs. Aschhm, M (), Ssmc dsgn basd on th yld dsplacmnt, Earthquak Spctra, (), pp -.. Ezo Faccol t al. (), Dsplacmnt spctra for long prods. Earthquak Spctra, (), pp.. Frman, S.A., Ncoltt, J.P. and Tyrll, J.V (9), Evaluaton of xstng buldngs for ssmc rsk: A cas study of Pugt Sound naval shpyard, Brmrton, Washngton, Procdngs of th US Natonal Confrnc on Earthquak Engnrs, EERI, Brkly, Calforna.. Kumar, A (), Softwar for gnraton of spctrum compatbl tm hstory, Procdngs of th World Confrnc on Earthquak Engnrng, Aug. -, Canada, Papr No. 9.. Paulay, T (), An stmaton of dsplacmnt lmts for ductl systms, Earthquak Engnrng and Structural Dynamcs,, pp Pttnga, J.D. and Prstly, M.J.N (), Dynamc bhavor of rnforcd concrt frams dsgnd wth drct dsplacmnt-basd dsgn, Journal of Earthquak Engnrng, 9(), pp 9-.. Pttnga, J.D. and Prstly, M.J.N (), Accountng for p-dlta ffcts n structurs whn usng drct dsplacmnt-basd dsgn, Rsarch Rport ROSE (Europan School for Advancd Studs n Rducton of Ssmc Rsk), IUSS Prss, Pava.. Prstly, M.J.N (), Myths and fallacs n arthquak ngnrng, Rvstd, Europan School for Advancd Studs n Rducton of Ssmc Rsk, 9 th Mallt-Mln Lctur. 9. Q, X. and Mohl, J.P (99), Dsplacmnt dsgn approach for rnforcd Concrt Structurs Subjctd to Earthquaks, Rport No. UCB/EERC-9/.. Xu, Q (), A drct dsplacmnt-basd ssmc dsgn procdur of nlastc structurs, Engnrng Structurs,, pp -.. SAP V.. (), Nonlnar, Educatonal vrson. Structural analyss program, Computr and Structurs Inc., Brkly, CA. Volum Issu 9

13 An conomc comparson of Drct dsplacmnt basd Dsgn wth IS-9 Rspons Spctrum mthod for. Dlh Schdul of Rats (), Cntral Publc Works Dpartmnt, Nw Dlh.. FEMA- (), Prstandard and commntary for th ssmc rhabltaton of buldngs, US Fdral Emrgncy Managmnt Agncy,. Volum Issu