Comparison of several variants of the response spectrum method and definition of equivalent static loads from the peak response envelopes

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1 Comarson of severa varans of he resonse secrum mehod and defnon of equvaen sac oads from he ea resonse enveoes Q.S. Nguen S. Ercher & F. Marn EGIS Indusres 4 rue Doorès Ibarrur SA Monreu cede France. SUMMARY: he resonse secrum mehod s based on he defnon of a suabe combnaon of he sesmc ea resonses of severa snge-degree-of-freedom oscaors reresenng he modes of he anaed srucure. Dfferen varans es assocaed wh dfferen was of accounng for he smuane of ea resonses of hsca dsnc quanes. Pea smuane can be rgorous reaed b he (her-esod ea resonse enveoes. Frs a nove nerreaon of hese enveoes s roosed based on he noon of coeffcens of he near combnaon of moda eas. hen an agorhm aowng he aromaon of a her-esod b a ohedron s anaed. Moreover a rocedure based on he ea resonse enveoes s roosed o defne sac force feds equvaen o he sesmc acon. In he as ar of he arce four dfferen mehods ncudng he her-esod enveoes and he equvaen sac force feds are used o comue and comare he oa renforcemen demands of a renforced concree budng. Kewords: Her-esod resonse enveoe ohedra aromaon of esods equvaen sac oads 1. INRODUCION he resonse secrum mehod s a ouar mehod of sesmc srucura anass based on he assumon of near easc srucura behavor. he sesmc resonse s comued as a suabe combnaon of he ereme resonses o he gven earhquae of severa snge-degree-of-freedom oscaors each one assocaed wh one mode of he anaed srucure. he man dffcu n he acaon of hs mehod s he defnon of he combnaon rues among moda ea resonses o ge he goba resonse of he whoe srucure. he we-nown Comee Quadrac Combnaon - CQC (Der Kureghan 1979 defnes a combnaon of ea moda resonses accounng for he coung effecs due o cose modes. Moreover he sueroson of he effecs of dfferen sesmc drecons s usua made b a quadrac combnaon rue or b he Newmar s combnaons aroach (Newmar Fna he smuaneous occurrence of ea vaues of hsca dfferen quanes (e.g. a norma effor and a bendng momen n a beam secon was suded b Gua and Sngh (1977 Lebond (1980 Menun and Der Kureghan (2000ab among ohers. hese wors conrbued o he defnon of he noon of her-esod ea resonse enveoe whch s nvesgaed here. In he frs ar of he aer a nove nerreaon of he ea resonse enveoe s roosed based on he noon of enveoe of he coeffcens of he near combnaon of moda eas (Marn 2004 named here α-enveoe. he reaonsh beween he α-enveoe and he cassca defnon of ea resonse enveoes (Menun and Der Kureghan 2000ab s dscussed (Secon 2. A dscreaon rocedure of a her-esod based on he use of an enveong ohedron w be resened n Secon 3: s an eenson of he mehod resened b Lebond (1980. Acua hs eended dscreaon rocedure was roosed b Vén e a. (2007 and he resen aer dscusses n more dea some roeres of hs agorhm. Noce ha oher dscreaon mehods are suggesed n ASCE (2009. hen he α-enveoe s used o defne severa seudo-acceeraon feds where each

2 fed defnes a robabe dsrbuon of acceeraons smuaneous acng on each on of a srucure durng he gven earhquae. hese acceeraons feds are used o defne severa sac oad cases equvaen o he gven earhquae (Secon 4. he second ar of he arce (Secon 5 regards he acaon of four varans of he resonse secrum mehod o a renforced concree srucure: ( Sueroson of he ea moda resonses n each earhquae drecon usng he Comee Quadrac Combnaon (CQC mehod foowed b Newmar s combnaons o oban he goba resonse due o dfferen earhquae drecons; ( Sueroson of he ea moda resonses usng he CQC mehod for each earhquae drecon foowed b quadrac combnaons o consder he effecs of dfferen earhquae drecons and ermuaons of generaed forces sgns o esmae he mos crca enveoe; ( Her-esod enveoe of smuaneous generaed forces; (v Sac oad cases defned b usng moda near combnaons of acceeraons. he resus are comared n erms of he oa renforcemen quan and of esmaed ea resonses for severa she eemens of he srucure. 2. A NOVEL INERPREAION OF PEAK RESPONSE ENVELOPES In hs Secon a new nerreaon of ea resonse enveoes s roosed based on near combnaons of moda resonse eas. he noon of enveoe of he coeffcens of he near combnaon of moda eas s nroduced and comared wh he cassca defnons Lnear combnaons of moda resonse eas Consder an N-degree-of-freedom near and cassca damed srucure for whch N rea egenmodes can be cacuaed. For sesmc acaons on n N modes are usua reaned b guaranng ha he sum of effecve masses of he n modes s hgh enough or nroducng a seudomode. he sesmc effecs are esmaed b consderng hree earhquaes (reresened b seudoacceeraon secra one er each drecon ( =. For an earhquae n drecon he 3Ncomonens dsacemen vecor u ( can be wren b a near combnaon of modes: where 1 2 N 1 2 N 1 2 N [ u u... u u u... u u u... u ] = u = r ( φ (2.1 φ s he 3N-comonens egenvecor for mode u ( s he arcaon facor for mode and he earhquae drecon and s he dsacemen n he drecon ( of he node due o he earhquae n he drecon. Each erm u = r ( φ reresens a srucura dsacemen roorona he -h mode shae. he me-funcon r s he souon of dnamcs equaon of he & : snge-degree-of-freedom oscaor reresenng he mode under he gven acceerogram ( & r 2 + 2ξ ω r& + r = u& (2.2 ( ω ω and g where ξ are he usaon and he damng coeffcen of he mode resecve. When ω are nown for a gven mode Eqn. 2.2 can be soved and he mamum absoue dsacemen ( ξ can be comued: R ma r = Sd ( ω ξ = (2.3 ~ R = ma r eads o sgh conservave resus Observe ha he use of Eqn. 2.3 nsead of [ ] 2 (Menun and Der Kureghan 2000a. he seudo-acceeraon becomes S ( ω ξ ω S ( ω ξ u g a =. d

3 Usng Eqns. 2.1 and 2.3 he dsacemen vecor u ( can be rewren as a near combnaon of he moda ea dsacemen vecors U = R φ : where = α R φ = α U wh 1 = 1 u r α (2.4a R α are named here coeffcens of he near combnaon of moda eas. he oa dsacemen due o he earhquaes n he hree drecons reads: = u = u U α (2.4b Le us consder a (generaed force f e.g. an aa force a bendng momen ec. n a secon or eemen of he srucure. B vrue of srucura near one can awas fnd a vecor d such ha: f d u = = ( = = d U = s he vaue of α ( α (2.5 f F where F d U f corresondng o he ea dsacemen vecor for he mode and he drecon. Eqns. 2.4ab show ha a an me he dsacemen of a ons (nodes of a srucure can be deermned b a near combnaon of he moda ea dsacemen vecors U. Lewse Eqn. 2.5 shows ha a (generaed force f can be deermned b a near combnaon of α. F usng he same coeffcens ( 2.2. Her-esod enveoe of near combnaons coeffcens (α-esod In order o esmae he robabe mamum vaue of he (generaed force f due o an earhquae n he drecon one can use he Comee Quadrac Combnaon (Der Kureghan 1979: f ma = ρ F F (2.6 where ρ s he moda cross-correaon coeffcen beween he modes and ha can be cacuaed as foows (Der Kureghan 1979: ρ = 8 ξξ ωω ( ωξ + ω ξ ωω ( ω ω + 4ξ ξ ω ω ( ω + ω + 4ω ω ( ξ + ξ hus n he sense of robab: f = α F f or ( ma F F H F where [ ] α 1 α 2... α n [ ] = F F F and [ ] U α (2.7a & 2.7b α = s he vecor of he (me-deenden combnaon coeffcens F n H = ρ. he condon n Eqns. 2.7 can be eended o he case of hree sesmc drecons usng a quadrac combnaon of f : ma

4 or 2 = F f = f ( ma ma = f α = ρ F F (2.8a f F F H F α wh α = [ α α α ] F [ F F F ] ~ = and H 0 0 ~ H = 0 H 0 (2.8b 0 0 H From Eqns. 2.7b and 2.8b suosng ha he mar H s nverbe one can rove ha: 1 α α 1 and α H α 1 (2.9a & 2.9b H ~ 1 Eqns. 2.9ab gve he defnon of wo her-esods wh dmensons n and 3n. We name hem α - esod and α-esod resecve. Each on α beongng o he α-esod reresens a robabe near combnaon of moda resonse eas. As a consequence he se of ons nsde he α- esod defnes a he robabe confguraons of he srucure durng he sesmc even. he revous formuas can be eas modfed when a seudo-mode s consdered (Vén e a Her-esod enveoe of generaed forces (F-esod In a gven ar of a srucure (e.g. a beam secon S dfferen generaed forces ma ac smuaneous (e.g. he norma force N and he bendng momen M. In hs aragrah he robem of he smuane of he eas of hese dfferen forces s dea wh. In dea we are neresed n he defnon of he enveoe of a robabe smuaneous generaed forces (e.g. a he robabe coues (NM n a secon S due o a gven earhquae. Reca ha he eressons gven n he revous Secon on concern he case of a snge (generaed force. Le [ ( ( ( ] = f1 f 2... f be a vecor of smuaneous (generaed forces due o an earhquae n drecon and e R = [ F 1 F 2... F ] be a mar whose coumns [ F F F ] F m 1 m 2 m... n m = are he vecors of ea moda vaues of he force (. B vrue of near one can rove ha: fm X 1 = ( R H R 1 1 = α H α 1 (2.10a where X = R H R and he nequa foows from Eqn. 2.9a. In he case of hree sesmc drecons one can aso rove ha: where ~ 1 1 X = α H α 1 (2.10b X = and = X. Eqns. 2.10ab consdered as denes defne wo her-esods of dmenson ha we name f -esod and f-esod resecve. Each on of he f-esod corresonds o a robabe combnaon of smuaneous generaed forces f1 f2... f. Eqn. 2.10b mes ha a on of he f-esod corresonds o one and on one on α of he α- esod (Eqn. 2.9b. 3. POLYHEDRAL APPROXIMAION OF HYPER-ELLIPSOID ENVELOPES For racca acaon uroses he number of combnaons of smuaneous generaed forces (n oher words he number of chosen ons on he f-esod surface shoud be reave sma. he aroach roosed b Lebond (1980 for cases =2 and =3 consss n reacng he her-esod

5 b a ohedron enveong he her-esod. Oher dscreaon aroaches are roosed n ASCE (2009.he eenson of Lebond s aroach o he genera case wh >3 dmensons can be made accordng o he foowng fve-se rocedure: Se 1: Dagonae he mar X defnng he f-esod.e. fnd he dagona mar ( λ λ... λ Y = dag and he mar D such ha 1 2 egenvaues of X. X = DY D. Noce ha λ λ... λ are he 1 2 Se 2: ransform he f-esod no a her-shere wh un radus b he affn 1/ 2 ha u : S a V = Y. S u : R a R such Se 3: Defne a ohedron havng ( [ ] 2 ons enveong a un her-shere: V = ± a ± a... ± 1... ± a wh = = 1... and a = ( (he comonen of V equa o us or mnus 1 s he -h Se 4: ransform he ohedron enveong he her-shere (Se 3 no a ohedron enveong he her-esod n he dagonaaon reference: S ( 1/ 2 ( [ ] = Y λ λ... ± λ... ± a. V = ± a 1 ± a 2 Se 5: ransform he ohedron defned a Se 4 no a ohedron enveong he her-esod ( ( n he orgna reference: = D S. Acua hs rocedure s equa o he one roosed b Lebond (1980 for he case =3. However n he case >3 s necessar o rove ha no nersecon occurs beween he un her-shere and he ohedron defned a above se 3. hs corresonds o rove ha each one of he 2 her-anes ( 1 ( 2 ( defned b he ons V V... V (=1 2 has a dsance from he reference on O greaer han 1. For he -h her-ane hs dsance can be cacuaed as foows: d ( 1 ( 2 ( ( O V V... V de = ( 1 ( 2 ( 1 ( 3 ( 1 ( ( 1 [ V ( V ( V... ( V ] ( 2 ( ( ( 1 ( V... ( V ( ( ( V 1 2 abe 1. Dsance from he reference on o he her-ane defned b he ons V V... V ( 1 ( 2 ( ( O V V V d... λ ( ( ( he dsances are greaer han 1. hs means ha he ohedron s awas arger han he un shere. Hence hs agorhm s conservave. he margn becomes arger when he dmenson ncreases. 4. EQUIVALEN SAIC LOAD CASES For some acaons ma be usefu o reresen he sesmc acon on a srucure b one (or severa equvaen sac oad(s usua defned a each srucura node as he roduc beween he noda mass and suabe noda acceeraon(s. In hs Secon a rocedure s roosed o defne such acceeraon feds usng he α-esod and a arcuar case of f-esod. From Eqn. 2.4a and Eqn. 2.4b one can defne he dsacemen n he drecon assocaed wh a node of he srucure: u he seudo-acceeraon a ( and he nera force (

6 = u U α (2.11a 2 = ω U = a ( α A α (2.11b 2 = m ω U = α ( α (2.11c P Anaogous eressons can be wren for drecons and eadng o he foowng noda force fed a he generc me : = P ( α ( N 1 2 N 1 2 N where [ ] P P P... P P P... P P P... P = s he vecor of he moda ea forces. Usua he combnaon coeffcens are no nown and he robem o hand s he defnon of a sueroson rue of he moda ea forces P n each drecon. A ossbe rocedure s he use of he Comee Quadrac Combnaon. hus for each earhquae drecon here s a force fed 1 2 N = [ ] ma ma... wh ma = ρ P P o be aed o he srucure. he Newmar s ma rue can be used o combne he force feds assocaed wh he hree earhquae drecons. A nove rocedure o defne a sac oad for sesmc anass s roosed herenafer usng he noon of moda near combnaons and α-esod. Frs observe ha a a gven me he vecor of forces ( α and corresonds o one sac oad case. Moreover n Eqn deends on he vecor ( s roven n Secon 2.2 ha he ocus of robabe vaues of he combnaon coeffcens α s he α-esod defned b Eqn. 2.9b. As an equa for n modes he α-esod beongs o he sace of 3n dmenson 3n. Is ohedra enveoe woud have 3 n 2 ons. hs number s oo arge for racca cacuaons eseca for mu-moda srucures whose number n of sgnfcan modes can be ver moran. Acua nsead of fndng a he ons α aromang he α-esod a remnar seecon of he mos moran ones (accordng o some engneerng crera coud be erformed. For nsance s ossbe o oo for he 6 ons α beongng o he α-esod and F F F M M M a he mamng he oa shear sesmc forces ( ( ( and momens ( ( ( base of he budng (or a anoher gven eve of he srucure. However hese s cases do no accoun for coung effecs beween hese s generaed forces. Acua a comee descron of robabe sesmc forces a he base of he budng s rovded b he corresondng 6D heresod (named here -esod: each on = [ F F F M M M ] of hs -esod reresens one robabe combnaon of he oa forces and momens a he base. Hence s roosed o oo for he ons α fufng Eqn. 2.9b and such ha he corresondng vecor of oa forces and momens a he base beongs o -esod. In racce he -esod can be aromaed b a 6Dohedron wh 384 verces and he number of α ons o comue s 384. hs s made b he anaca rocedure roosed hereafer. Frs observe ha a on of he -esod can be wren as a funcon of α : ( α = [ c α c α c α c α c α c α ] = (2.13 c c1 c2... cn c1 c2... cn c1 c2... cn = For nsance he comonens of [ ]

7 whch has dmenson 3n are equa o c = P. he roof s sraghforward and s omed for brev. hs means ha c s he oa horona force (for a he nodes ndcaed b he nde n he drecon for he mode and due o an earhquae n he drecon. Le us consder now one of he 384 nown verces of he ohedron enveong he -esod. We name hs vere A = [ a a a a a a ]. hen s ossbe o rove ha he on 1 [ b b b b b b ] B = A A X A = es on he surface of he -esod. Moreover B s he nersecon beween he -esod and he segmen nng he orgn and he on A. As a consequence he robem ha we have o sove can be wren as foows: ~ 1 Fnd α such ha α H α = 1 and ( α = = B (2.14 hs means ha α mus be a on of he α-esod (of dmenson 3n and ( α mus be a on of he 6D her-esod of he oa forces and momens (-esod. he souon α of he robem (2.14 s aso he souon of he foowng omaon robem: Fnd α such ha α = ARG ma 1 ( ( α ~ α : α H α = 1 1 [ X B] (2.15 Accordng o he Lagrange muer mehod Eqn s equvaen o: Fnd α such ha = ARG ma ( α 1 Pose c [ c c c c c c ] X B =. hs eads o 1 ~ 1 ( [( X B + λ( α α 1 ] α α H 1 λ = ± c H c and 2 H c α = ± (2.16a & 2.16b c H c he vecor α corresondng o he on A on he ohedron reads: A A 1 α = α X A (2.17 A Each vecor α A can be nroduced no Eqn n order o defne a sac oad fed o be aed o srucura nodes. Acua here are 384 ons A hus 384 vecors α A and 384 sac oad cases. A hese oad cases reroduce some robabe combnaons of he hree oa sesmc forces and momens a he budng bass. 5. APPLICAION In hs ar sesmc effecs o a budng n renforced concree w be suded usng he foowng four aroaches: 1. Comee Quadrac Combnaons of he moda resonses n one drecon and Quadrac Combnaon of hree drecons (CQC-Quadrac Combnaon 2. Comee Quadrac Combnaons of he moda resonses n one drecon and Newmar s Combnaons of hree drecons (CQC-Newmar s Combnaons 3. Her-esod enveoe of smuaneous she (or beam effors n each eemen of he mode.e. = [ N N N M M M ] accordng o he noaon of Sec. 2.3 where ( N N N ( M M are membrane effors and M are bendng momens

8 4. Sac oad cases usng moda near combnaons and consderng 384 robabe combnaons of hree oa forces and hree oa momens a he base of he srucure (see Secon 4. Observe ha n he 1 s and 2 nd rocedures he smuane of he generaed forces s an aromaed wa. he 3 rd rocedure roer aes no accouns smuane of generaed forces of each eemen of he srucure. he 4 h rocedure s eeced o consder a arge number of robabe saes of he srucure affecng he renforcemen demand. A comarson of hese four aroaches n erms of oa amoun of renforcemen demand w be carred ou Srucure descron and moda anass Le us consder a renforced concree budng wh he foowng dmensons: wdh 16.5m engh 27.5m hegh 31.94m (Fg. 1a. he fne eemen sofware used for he srucura anass s HERCULE. he number of nodes and (she or beam eemens s and resecve. he so under he foundaon raf s modeed b a se of verca and horona near easc srngs. Afer he moda anass (abe 2 35 modes us he seudo-mode are reaned (n=36. A secrum anass s hen carred ou usng he secrum of Fg. 1b. For he earhquae n verca drecon he secrum ordnae s reduced b a facor equa o 2/3. he oad cases used n hs eame ncude he ermanen oad (G and he sesmc oad due o earhquaes n drecons and. Horona drecons % 7% 10% 20% 15% 30% 0.01 Fgure 1. (a Fne eemen mode. (b Pseudo-acceeraon secrum n horona drecons (acceeraon (m/s 2 vs. frequenc (H abe 2. Imoran reaned modes Frequenc Perod Damng Percenage of effecve mass N mode (H (s coeffcen (% (% X Y Z oa of consdered modes Comarson of four aroaches of sesmc effor cacuaon Once he effors are nown for each eemen of he mode he renforcemen can be deermned. abe 3 gves he raos beween he oa renforcemen found b he four aroaches consderng he

9 CQC-Newmar s Combnaons as reference mehod. One can observe ha he resu obaned usng he her-esod s ver cose o he reference one. he renforcemen amoun obaned b he sac oad cases (-esod Secon 4 s more moran. he dfference beween hs aroach and he her-esod enveoe (hrd case n abe 3 can be eaned b he fac ha he 6-dmenson - esod s dscreed b a ohedra enveoe whch s arger han he orgna -esod. As eeced he CQC-Quadrac Combnaon gves he mamum renforcemen demand. abe 3. Comarson of he four mehods of sesmc effor cacuaon n erms of renforcemen quan CQC Newmar combnaons CQC quadrac combnaon Her-esod enveoe oa renforcemen rao Equvaen sac oad case Herenafer he dfference beween he four aroaches w be usraed b ong he ons reresenng he combnaons of he s effors N N N M M M n wo she eemens of he srucure. A 6D sace shoud be consdered. For he fne eemens ndcaed n Fg. 2 he roecons of hese effors n he anes N N and N M are shown n Fgs. 3 and 4. Eemen 6692 Eemen Fgure 2. Eemens consdered N and N (N/m N(N/m and M (Nm/m N N M N Her-esod CQC-Quadrac Combnaon CQC-Newmar's Combnaons Equvaen sac oads Her-esod CQC-Quadrac Combnaon CQC-Newmar's Combnaons Equvaen sac oads Fgure 3. Dsrbuon of forces eemen 6692 Fgs. 3 and 4 show ha ( here are ons obaned b he equvaen sac oad rocedure of Secon 4 whch enveoe boh he ons of he her-esod enveoe of she effors and he CQC-Newmar s ons. ha eans wh he renforcemen demand found b he equvaen sac oad aroach s more moran han ones found b he aroaches 2 and 3; ( he renforcemen quan obaned b he CQC-Quadrac Combnaons s he mos moran. he effors are srong overesmaed eseca when an moran correaon beween she effors ess; ( s ossbe o reduce he renforcemen demand found b he equvaen sac oad aroach b a dfferen defnon of he 6-dmenson -esod enveoe. Wor s n rogress on hs subec.

10 N and N (N/m N(N/m and M (Nm/m N M N N 0 Her-esod CQC-Quadrac Combnaon CQC-Newmar's Combnaons Equvaen sac oads Her-esod CQC-Quadrac Combnaon CQC-Newmar's Combnaons Equvaen sac oads Fgure 4. Dsrbuon of forces eemen CONCLUSION In he frs ar of he aer a nove nerreaon of he so-caed (eca ea resonse enveoes (Menun and Der Kureghan 2000a has been deveoed usng he noon of enveoe of he coeffcens of he near combnaon of moda eas (Marn Moreover he roeres of an agorhm for he dscreaon of a ea resonse enveoe wh a generc dmenson have been dscussed. Fna usng he ea resonse enveoe aroach a rocedure has been roosed o defne severa sac oad cases equvaen o he sesmc acon. In he second ar of he aer he renforcemen demand for a renforced concree budng s comued usng four dfferen rocedures based on he moda secrum mehod. he frs wo aroaches he CQC-Quadrac Combnaon and he CQC-Newmar s Combnaons are cassca mehods of combnng he ea moda resonses comng from he resonse secrum mehod. he hrd rocedure s he ea resonse enveoe mehod (Menun and Der Kureghan 2000a aed on he membrane and bendng effors of each she eemen of he fne eemen mode. he as rocedure s based on he equvaen sac oad feds defned accordng he new mehod roosed n he aer. As eeced he aroach caed CQC-Quadrac Combnaon gves he arges renforcemen demand. For he eame consdered here he cassca CQC-Newmar s Combnaons and he ea resonse enveoe mehod gve amos he same oa renforcemen demand. he equvaen sac oad feds rocedure eads o a renforcemen demand hgher han he CQC-Newmar s Combnaons. Wor s n rogress o mrove he defnon of he dscreaon agorhm used o aromae he her-esods. REFERENCES Marn F. (2004. Probèmes de concomance en anase modae secrae. Combnaons néares de modes Domane de concomance. Inerna reor IOSIS Indusres (n French. Vén J-M. Marn F. Langeore A. and Caadeu S. (2007. Omsaon du dmensonnemen ssmque ar anase secrae en usan e domane de concomance des socaons. Cooque AFPS 2007 (French. Menun C. and Der Kureghan A. (2000a. Enveoes for sesmc resonse vecors. I: heor. Journa of srucura engneerng. Ar Menun C. and Der Kureghan A. (2000b. Enveoes for sesmc resonse vecors. II: Acaon. Journa of srucura engneerng. Ar Gua A.K. and Sngh M.P. (1977. Desgn of coumn secons subeced o hree comonens of earhquae. Nucear Engneerng and Desgn Lebond L. (1980. Cacu ssmque ar a méhode modae. Usaon des réonses our e dmensonnemen. héores e méhodes de cacu N (In French. Der Kureghan A. (1979. On reonse of srucures o saonar ecaon. Earhquae Engneerng Research Cener. Unvers of Caforna Beree. Reor No. UCB/EERC-79/32.. Newmar N.M. (1975. Sesmc desng crera for srucures and faces rans-aasa ene ssem. Proceedngs of he U.S. Naona Conference on Earhquae Engneerng. Earh. Engrg. Ins ASCE 4-09 (2009. Worng Grou on Revson of ASCE Sandard 4. Sesmc anass of safe-reaed nucear srucures Draf.