Pre and post-cracking behavior of steel-concrete composite deck subjected to high cycle load

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1 Fratr Mhani Conrt Conrt Strtr - High Prforman, Fibr Rinford Conrt, Spial Loading Strtral Appliation- B. H. Oh, t al. (d) 2 Kora Conrt Intitt, ISBN Pr pot-raking bhavior tl-onrt ompoit dk bjtd high yl load C. Fjiyama & K. Makaa Th Univrity Tokyo, Tokyo, Japan E. Gbryohann Addi Ababa Univrity, Addi Ababa, Ethiopia ABSTRACT: Strtral prforman tl-onrt ompoit dk i imlatd in ing thr dimnional nonlinar finit lmnt analyi by inorporating th intrfa modl rprod Mohr-Colomb frition btn tl onrt. Th ompoit mhanim ith rgard th mhanial lok by tl rib intrfa frition i analyzd. Firt, th fft intrfa frition i prntd. Sond, th pro intrnal rak onrt i xplaind bad on th mhanial intrlok ith diffrnt rib hap. Finally, th fft pot-raking bhavior i xamind by high-yl fatig analyi INTRODUCTION. Bakgrond Rnt dvlopmnt in th fild omptr imlation thnology hav ld a rnd intrt in fatig problm onrt. In Japan thr ha bn a lot rinford onrt (RC) bridg dk damag rportd in 96. To ork ot from thi problm, diffrnt grop rarhr intalld a hl-typ moving load tting mahin (Mada & Mati 984). Vario xprimnt hav bn ondtd in 98 (Mati 987, Pdikari & Bim 989). Bad pon th rlt th xprimntal tdi, thy old om p vral inflning far in fatig problm. Sh a minimm thikn lab a rtain rqirmnt rbar arrangmnt r rnd in dign od. It a fftiv in pratial fild. Nmrial analyi takling thi problm ha bn rportd by Makaa t al (26a). Thy hav dvlopd a thr dimnional nonlinar finit lmnt analyi framork COM3 flly tra mhanial damag platiity ndr high yl rptition load in logarithmi alratd tim intgration. Th appliability th analytial ytm ha bn vrifid for RC lab ndr both high-yl fixd moving load (Makaa t al. 26b). Enginr hav bn alo dvloping intrt tiliz tl-onrt ompoit lab for bridg dk in th pat dad. Thi i d th fat, thi typ lab rqir l amont pporting girdr in ontrtion. Compoit dk i partilarly appliation for in a long pan itation, hr th RC lab i not faibl. A many bridg dk ffr from high-yl moving load, invtigation ompoit lab bjtd high yli load i rqird. Hakin & Mithll xamind th rpon ompoit lab ith diffrnt typ har onnr ndr both mononi rvral yli har (984). Thy pointd ot failr mod i gratly inflnd by th mhanial proprty har onnr. Sakrai t al. hav xamind th ndran limit th ompoit dk onit botm tl plat, tl rib onrt both xprimntally in ing FE analy (25). Exprimntal rlt implid a tl-onrt ompoit trtr, hih onit th botm tl plat, tl rib onrt, tnd tart onrt rak from th tip tl mmbr ndr high-yl load. Fjiyama & Makaa analyzd th xprimnt don by Sakrai t al. ing th nh modl COM3 inlding th intrfa frition modl for tl-onrt ompoit dk (29). Aording thi tdy, progr dfltion ha bn flly imlatd a ll a a partilar rak dvlopmnt from th tip tl rib ndr th high-yl moving load a hon in Figr. Thi papr fo on th fft ompoit mhanim on th raking pot-raking bhavior fatig onrt. In partilar, th fft mhanial intrlok by tl rib, td th fft intrfaial frition i did xtnivly.

2 J = ) D ( h, T h Tranvr Cntr Longitdi- Prinipal train CL Th proportionality fiint D(h,T) moitr prmability it i a nonlina th rlativ hmidity h tmpratr & Najjar 972). Th moitr ma balan th variation in tim th atr ma volm onrt (atr ontnt ) b q divrgn th moitr flx J (a) Obrvd rak in xprimnt (Sakrai t al. 25) (b) Simlation by FE analyi (Fjiyama t al. 29) = J Figr. Intrnal rak tl-onrt ompoit dk ndr high-yl moving load. t v E opn opn E lo lo (a) Normal tiffn Figr 3. Intrfa frition modl for tl-onrt ompoit trtr. v For opning () 開口時 G opn G opn Th atr ontnt an b xprd a a. Nglting thir diffrn (Xi t al. Comprion Tnion th vaporabl atr (apillary a Shar tranfr vapor, adorbd atr) th non- Contit- Str - Strain Str - Strain (hmially Shar trbond) - Slip or Strain atr tiv n (Mil = E lo K T ε Pantazopolo & Mill 995). It i ra E A ε = ε + ε p am th vaporabl atr i a f K E = E K C ε rlativ hmidity, h, dgr hydration dgr ilia fm ration, α, i.. = ε π / 2 εp ε ε = ε + ε p = ag-dpndnt = R ( ω, δ, θ ) inθdθ orption/dorption π / 2 (Norling Mjonll 997). Undr thi am Enh Fratr paramtr K onidr Fratr paramtr K T onidr Amlatd path fntion X rd modl by btitting Eqation in Eqati tim dpndnt platiity & tim dpndnt fratring yli har aoiatd ith yli fatig fratring yli fatig fatig damag obtain damag for damag dkt = Fdt + Gdε + Hdε KC K C High dkc = dt + dε t ε = X ( δ, ω) Tim dpndnt Cyli fatig fntion + ( D original h) modl + yl fratring Fatig Tim dpndny Cyli fatig X = log{ + ( / )} damag. Makaa t al. 23, Hia 25 d δ ω K = λ ~ hnfk = ε hr / i th lop th orption/ K Contat dnity modl by Li & Makaa 989, Fk Fk = iothrm (alo alld moitr apa + λ ~ hnfk = Modifiation amlatd path fntion by ε ε K govrning qation Gbryohann (Eqation 26 3) mt b 3 4 λ = K ( K ) g R by appropriat bondary initial onditi El-Kahif Makaa 24 Th rlation btn th amont Phyial Dra tiffn Dra tnion tiffn by atr Dra har rlativ tranfr hmidity normal i alld maning platiity amlation by bond fatig iothrm rak by ontino if mard dtrioration ith inraing ontino fratring onrt hmidity rogh rak rfa dorption iothrm in th Figr 2. Intrnal rak tl-onrt ompoit dk ndr high-yl moving load. th folloing, orption iothrm ill b rfrn both orption dorption By th ay, if th hytri th iothrm old b takn in aont, rlation, vaporabl atr v rlativ hmi For b (2) 閉合時 lor d aording th ign th varia rlativity hmidity. μ Th hap th iothrm for HPC i inflnd by many p pially tho infln G lo xtnt hmial ration, in trn, dtrm trtr por iz ditribtion (atr- G ratio, mnt lo hmial ompoition, SF ring tim mthod, tmpratr, mix t.). In th litratr μ vario formlatio (b) fond Shar tiffn drib th orption iothrm onrt (Xi t al. 994). Hovr, in th papr th mi-mpirial xprion pro Norling Mjornll (997) i adoptd b Proding FraMCoS-7, May 23-28, 2

3 .2 J = D ( Shm h, T ) h high yl fatig analyi () Th fatig imlation by COM3 i bad on th dirt Th path proportionality intgral hm fiint (Makaa D(h,T) t al. i 23). alld Thr moitr bai prmability ntial modl it for i onrt a nonlinar d fntion hrin ar th omprion, rlativ hmidity tnion h tmpratr rak har T (Bažant modl along & Najjar rak 972). plan. Th Th moitr thr ma modl balan ar rqir importan th variation trat th in mlativ tim th fatig atr ma damag pr nit tim volm dpndnt onrt fft (atr (Fig. ontnt 2.). Simlation ) b qal i ondtd divrgn by traing th th moitr voltion flx J miroopi mat- th rial tat at ah momnt. Logarithmi intgral mthod alrat ompting for high yl problm = J (2) a ll. t For fll 3D imlation, Makaa t al. ha xtndd Th atr in-plan ontnt 2D RC an modl b xprd inlding a tim th m dpndny th vaporabl rp atr 3D orthogonal (apillary pa atr, ytm atr by vapor, man adorbd th projtion-ompoition atr) th non-vaporabl mthod (23). (hmially Thi ompoition bond) atr thniq n i (Mill rgardd 966, a a impl Pantazopolo xtnion & Mill th 995). mlti-dirtional It i raonabl nonorthogonal am fixd th rak vaporabl approah. atr Thi omptational a fntion framork rlativ hmidity, ha alrady h, dgr bn vrifid hydration, ndr lo-yl α, tati dgr dynami ilia fm load. ration, Whatvr α, i.. th omplxity = (h,α,α ) th = ag-dpndnt loading hytri orption/dorption i, th mlti-axial iothrm trarrying (Norling mhanim Mjonll 997). i formlatd Undr thi a amption a linar ombination by btitting D b-mhanim Eqation in rprnting Eqation 2 on th rakd obtain onrt rinformnt a propod by Collin & Vhio (982). To rpliat th atal tr tranfr btn th tl mmbr + ( D onrt, h) = α& intrfa + α& lmnt + & i propod ith mhanial proprti a indiatd in Fig- n (3) r 3. Th bhavior i bad pon Colomb frition la. hr Th frition / i th fiint lop i th amd orption/dorption b ontant iothrm dring (alo load. alld Th intrfa moitr modl apaity). do not tak Th in govrning aont qation th rdtion (Eqation 3) tiffn mt b ompltd ridal train by appropriat d high bondary yl loading. initial ondition. Th rlation btn th amont vaporabl atr rlativ hmidity i alld adorption 2 iothrm MECHANISM if mard OF COMPOSITE ith inraing ACTION rlativity hmidity dorption iothrm in th oppoit 2. a. Compoit Nglting dk thir modl diffrn (Xi t al. 994), in Th th folloing, tl-onrt orption ompoit iothrm dk ill invtigatd b d hr ith onit rfrn botm both orption tl plat, I-hap dorption tl ondition. rib, rinforing By th bar ay, if onrt. th hytri Th modl i th imply moitr pportd iothrm on old id b takn in th in vrtial aont, dirtion. diffrnt Th inplan rlation, dimnion vaporabl th atr lab v i.5 rlativ m x hmidity,.5 m having mt a gro b d dpth aording 69 mm, th inlding ign th 9 mm variation thik botm th plat. rlativity hmidity. Th hap th orption iothrm I-hap for tl HPC rib i ar inflnd t only by in many th tranvr paramtr, dirtion pially 3 tho mm paing. infln Rib xtnt hav nithr rat td th nor hmial hol for ration intrloking, ith in trn, rronding dtrmin onrt. por Rib trtr ar ldd por iz th ditribtion botm plat (atr--mnt any othr har ratio, onnr mnt hmial do not xit ompoition, in thi dk. SF Intrfa ontnt, lmnt ring tim modl i mthod, propod tmpratr, for th ontat mix additiv, rfa btn t.). In tl th litratr plat vario onrt formlation a indiatd an in Figr fond 3. Aording drib th Rabbat orption iothrm Rll (985), normal th b fritional onrt (Xi fiint t al. 994). for normal Hovr, trngth in th onrt prnt ith papr dry th ondition, mi-mpirial an b xprion amd propod b.6, a by a ontant. Norling Mjornll Th rrnt (997) intrfa i modl adoptd do ba not tak it in xpliitly aont aont th rdtion for th voltion tiffn hydration ridal train ration d high SF yl ontnt. loading. Thi orption iothrm rad Rinforing bar oniting D3/25 mm in th longitdinal dirtion provid ingl RC layr on th I- hap rib, ovr dpth rinforing bar i 42 mm. Rinforing bar onrt abov th rib ar modld a RC lmnt ith bond fft. Th othr on- ( h, α, α ) = G ( α, α ) + ( g α α ) h rt part ar rgardd a plain onrt. Tnion tiffning/tning far i dtrmind for ah onrt (4) lmnt. Figr 4 ho tl fram ( g α αthi ) h lab th K ( α, α ) ro tion rib. Tabl ho mhanial proprti rptiv matrial. hr th firt trm (gl iothrm) rprnt th 2.2 phyially Compoit bond mhanim (adorbd) atr th ond Stl-onrt trm (apillary ompoit iothrm) mhanim rprnt onit th apillary ation atr. Thi in gnral. xprion On i i valid th mhanial only for lo intrlok ontnt oing SF. Th har fiint onnr, G rprnt h a rib th amont td. Anothr atr pr on nit i volm th intrfaial hld frition th gl por btn at % tl rlativ onrt. hmidity, Both mhanial it an b tr-tranfr xprd (Norling th intrfaial Mjornll 997) frition a ontribt onitnt kinmati tl onrt. Th ompoit dk invtigatd hr an b an G ( α, α ) = k α + k α (5) appropriat xampl vg vg analyz th mhanim. Intrloking by tl rib at a th main tr tranfr hr k mhanim aro rib. Th fft intrfa maximm frition amont th botm atr plat pr nit hold volm b inldd an vg k vg ar matrial paramtr. From th fill thi all por tr (both tranfr apillary mhanim por a ll, gl por), no mattr on ho an allat minor rol K it a ha on in obtain thi dirtion. In ontrat, th intrfaial frition i th ol tr tranfr mhanim along th rib ba no har onnr in thi dirtion. g α α.88α +.22α G To xamin th abovmntiond tr tranfr (6) mhanim K ( α, α ) = on th trtral prforman, th athor t for modl for g α analyi α ( Tabl 2). Typ-I ri ha I-hapd rib (tion 2.). Typ-F ri ha rtanglar rib (Fig. 4.). Th hight th rib Th i 5mm matrial hih paramtr i th am k vg a k vg th protyp. g an b alibratd Th thikn by fitting rib xprimntal i mad data b 8mm rlvant o a fr hav (vaporabl) qivalnt momnt atr ontnt inrtia in ith onrt th at I-hapd vario ag rib. (Di Flat Lzio plat & rib Cati hang 29b). tr onntration rak initiation inid onrt, vn thogh it 2.2 tiffn Tmpratr i qivalnt voltion th I-hapd rib. Extrm mall frition fiint,., alo hang tr Not, onntration arly ag, in rak th initiation hmial inid ration onrt. aoiatd Th nmbr ith mnt -6 hydration - t for SF th ration frition fiint, ar xothrmi,.6 th. tmpratr rptivly. fild i not niform for non-adiabati ytm vn if th nvironmntal tmpratr i ontant. Hat ondtion an b 3 dribd ANALYSIS in onrt, FOR INTERNAL at lat for CRACKING tmpratr not xding C (Bažant & Kaplan 996), by 3. Forir Th fft la, hih intrfa rad frition Th q = tati λ T load i applid by diplamnt ontrol at a (7) rat.2 mm/. Th load i applid on a 2mm qar ara at th ntr th lab. A maximm hr q i th hat flx, T i th abolt diplamnt 4 mm i applid bfor th omplt tmpratr, λ i th hat ondtivity; in thi nloading. Proding FraMCoS-7, May 23-28, 2

4 -2 Load J Mid pan dfltion D ( h, T h = ) kn I-6 F- Th I- proportionality fiint D(h,T) moitr prmability F-6 it i a nonlina th rlativ hmidity h tmpratr & Najjar 972). Th moitr ma balan th variation in tim th atr ma volm onrt (atr ontnt ) b q divrgn th moitr flx J RC layr I-hap rib (a) Dimnion analyi modl Tabl. Matrial proprti analyi modl. Nam Strngth Stiffn ν N/mm 2 N/mm 2 Conrt Comprion x 4.7 Tnion 2.5 Rbar (D3) Yild point x 5.3 Botm plat Yild point x 5.3 I-hap rib Yild point x 5.3 Tabl 2. Ca for FE analyi. Ca I-hap rib Flat-plat rib Fition fiint μ=.6 I-6 F-6 Protyp μ=. I- F- = 2 J 3 4 mm Figr 5. Load Mid-pan dfltion. Th atr ontnt an b xprd a Tabl 3. Smmary tati th vaporabl analyi. atr (apillary a vapor, adorbd atr) th non- (hmially bond) atr n (Mil Nam Capaity Pantazopolo Dfltion Botm & Mill plat 995). It i ra Prinipal train am th vaporabl atr i a f kn mm µ rlativ hmidity, h, dgr hydration I-6 97 dgr 7.2 ilia fm 353 ration, α, i.. = I- 84 =. ag-dpndnt 964 orption/dorption (yild) F (Norling 5.2 Mjonll 997). 3 Undr thi am F- 736 by btitting 5.2 Eqation 3 in Eqati obtain Botm plat Srfa onrt + ( D h) + -2 h μ α (b) I-hap rib (I-6, I-) -4 Botm ppr onrt -6 RC layr Top I-hap rib hr / i th lop th orption/ -8 iothrm (alo alld moitr apa Flat-plat rib - govrning qation I-6 (Eqation 3) mt b (Rtanglar) -2 by appropriat bondary I- initial onditi -4 Th rlation btn th amont -6 atr rlativ hmidity i alld Botm plat -8 Srfa botm plat iothrm if mard ith inraing () Flat-plat rib (F-6, F-) Figr 6. Strain ditribtion hmidity along rib dorption at th ntr iothrm pan. in th a. Nglting thir diffrn (Xi t al. Figr 4. Stl-onrt ompoit dk modl for FE analyi. th folloing, orption iothrm ill b Dip x 2 rfrn both orption dorption By th ay, if th hytri th iothrm old b takn in aont, rlation, vaporabl atr v rlativ hmi b d aording th ign th varia rlativity hmidity. Th hap th (a) Dformation iothrm Prinipal for HPC train i a inflnd I- by many p Dpth mm t pially tho infln xtnt hmial ration, in trn, dtrm Dip x 2 trtr por iz ditribtion (atrratio, mnt hmial ompoition, SF ring tim mthod, tmpratr, mix t.). In th litratr vario formlatio fond drib th orption iothrm onrt (Xi t al. 994). Hovr, in th (b) Dformation Prinipal train a F- Figr 7. Strain ditribtion papr along th mi-mpirial rib at th ntr xprion pan. pro Norling Mjornll (997) i adoptd b Proding FraMCoS-7, May 23-28, 2

5 J = Figr D ( h, T ) 5 ho h th load vr mid-pan dfltion rv ndr th tati loading for all a. For () ah Th a, proportionality th tati apaity, fiint mid-pan D(h,T) dfltion i alld moitr th maximm prmability prinipal train it i a nonlinar th botm fntion plat at th pak rlativ load hmidity ar mmarizd h tmpratr in Tabl 3. T (Bažant Ca I- 6 & Najjar ho 972). 3 kn Th highr moitr apaity ma balan omhat rqir tiffr th rpon variation than in tim a th I-. atr ma pr nit volm Th tiffn onrt (atr a ontnt I- tart ) b qal dra th arond divrgn 2 kn. th Thi moitr rdtion flx J indiat lipping at th intrfa btn onrt th tl plat, a a rlt lo frition fiint,.. Figr 6 ho = th Jtrain along th rib at mid-pan ro tion at aload 2 kn. Ca I- ho a noti- (2) t abl Th lip, atr hoing ontnt a diffrn an b xprd in train a th 99μ m btn th vaporabl p tl atr ppr onrt. Evn (apillary atr, atr thogh th train rfa onrt th vapor, adorbd atr) th non-vaporabl botm plat ar almot th am a a I-6. (hmially bond) atr n (Mill 966, Morovr, th diffrnt proprty intrfaial Pantazopolo & Mill 995). It i raonabl frition ha a orrlation ith failr mod. A indiatd in Tabl 3, th prinipal train at th pak load am th vaporabl atr i a fntion rlativ hmidity, h, dgr hydration, α a I- xd yilding point, althogh, dgr ilia fm ration, α a I-6 do not rah yilding., i.. Thi = man (h,α,α ) = ag-dpndnt orption/dorption iothrm th lo frition a I- fail not only by pnhing (Norling Mjonll 997). Undr thi amption har onrt bt alo by yilding th botm by btitting Eqation in Eqation 2 on tl plat. obtain 3.2 Th fft mhanial lok by tl rib intrnal + rak ( D h) + & n (3) Ca F-6 ho 62 kn highr apaity than F-. Th diffrn i d th diffrn intrfa frition, hr / i th lop th orption/dorption vn thogh th tiffn do not ho iothrm (alo alld moitr apaity). Th lar dfrn. Figr 7 ho 2 tim magnifid govrning qation (Eqation 3) mt b ompltd dformation th prinipal train ditribtion at by appropriat bondary initial ondition. th pak load. To fo on th fft th mhanial intrlok tl rib, a I- a F-, Th rlation btn th amont vaporabl atr rlativ hmidity i alld adorption hih ha. th intrfaial frition fiint ar iothrm if mard ith inraing rlativity ompard. hmidity dorption iothrm in th oppoit Figr7(a) illtrat loalization tnil train a. Nglting thir diffrn (Xi t al. 994), in a vrtial rak ndr th loading ara a horizontal rak in a layr inlding flang rib. Th th folloing, orption iothrm ill b d ith rfrn both orption dorption ondition. raon hy th horizontal rak dvlop i By th ay, if th hytri th moitr omprd ppr onrt jt ndr th loading iothrm old b takn in aont, diffrnt ara a vr har dformation rronding rlation, vaporabl atr v rlativ hmidity, mt onrt in th layr inlding flang rib. b d aording th ign th variation th Figr 7(b) ho loalization tnil train rlativity hmidity. Th hap th orption arond th tip rib. Thi loal dformation rat th iothrm horizontal for HPC intrnal i inflnd rak from by th many tip paramtr, rib. In addition, pially tho an opning infln btn xtnt onrt rat th th hmial botm ration plat a ll, a in btn trn, onrt dtrmin por th p trtr rib. Th por rtanglar iz ditribtion rib ithot (atr--mnt flang do not ratio, rtrain mnt onrt hmial in th ompoition, vrtial dirtion. SF ontnt, Thi indiat ring tim I-hap mthod, rib tmpratr, ith flang mix provid additiv, mor ffiint t.). In mhanial th litratr intrlok, vario oing formlation thir an hap b a fond ompard drib th rtanglar th orption rib. iothrm normal onrt On th (Xi bai t al. thi 994). analyi, Hovr, th ombination th prnt intrfa papr th frition mi-mpirial th mhanial xprion lok propod i onidrd. by Norling F- Mjornll F-6 (997) a i th adoptd opning ba btn it onrt xpliitly aont tl in for th arly th voltion tag ba hydration inffiint ration onfinmnt SF ontnt. in th vrtial Thi orption dirtion. iothrm Th intrfa rad frition along th rib m hav a minor rol for thi opning. Th tiffn mainly dpnd on th mhanial proprty th tl part aftr thi opning. That i th raon hy th diffrn in ( h, α, α ) = G ( α, α ) + tiffn i not obrvd larly btn F- F- ( g α α ) h 6 a hon in Figr 5. (4) ( g α α ) h K ( α, α ) 4 POST-CRACKING SUBJECTED TO HIGH- CYCLE MOVING LOAD 4. hr Condition th firt for trm analyi (gl iothrm) rprnt th phyially bond (adorbd) atr th ond High-yl moving load i applid on a 5 mm trm (apillary iothrm) rprnt th apillary idth mm lngth th mid-pan th atr. Thi xprion i valid only for lo ontnt a I-6 F-6. Th load lvl i abot 55 % SF. Th fiint G tati apaity th protyp, rprnt th amont I-6. Th moving atr pr nit volm hld in th gl por at % pd i t a 4. m/. rlativ hmidity, it an b xprd (Norling In addition, anothr a tdy TS-6 i propod. Th tnion tiffning/tning far Mjornll 997) a plan onrt lmnt i hangd from.5.4 in th G ( α vrtial, α ) = k dirtion α + k for α TS-6. Dimnion (5) vg vg proprty tl part ar tally th am a I-6. Hovr, thi improvmnt do not ontribt hr inraing k vg bond k vg ar btn matrial tl paramtr. onrt, From thi th improvmnt maximm amont inra atr rtraint pr nit volm pot-raking an onrt fill all por in th (both vrtial apillary dirtion por ithot gl altring por), on th intrloking an allat mhanim. K a on obtain Inraing onfinmnt in th vrtial dirtion improv har tranfr aro th horizontal rak ndr high-yl load. Th tnion tiffning/tning.88α +.22far α G i xplaind a fol- g α α lo; (6) K ( α, α ) = ε t g t = f α α () t ε t hr Th matrial t = avrag paramtr onrt k tr in tnion; f t = vg k vg g an niaxial b alibratd tnil by trngth fitting xprimntal onrt; data ε t rlvant = avrag onrt fr (vaporabl) train at hih atr rak ontnt or; in εonrt t = avrag at onrt vario ag train; (Di Lzio = & tnion Cati tiffning/tning 29b). far (Makaa t al. 23). Gnrally paking, =.4 i d for onrt ith dformd bar. 2.2 Th Tmpratr athor think voltion tnion tiffning/tning far Not, an b at arly improvd ag, in not only th ith hmial dformd ration bar or aoiatd bt alo ith mnt om amont hydration fibr SF matrial ration in prati. ar xothrmi, Abrihami th tmpratr Mithll fild (997) i not xprimntally for non-adiabati dmontratd ytm th improvmnt vn if th nvironmntal pot-raking niform bhavior tmpratr rinford i ontant. onrt Hat in ondtion niaxial tnion an by b ing dribd % fibr in onrt, by volm at lat onrt. for tmpratr not xding C (Bažant & Kaplan 996), by 4.2 Forir Fatig la, lif hih dk rad failr mod Figr q = λ T 8 ho progr th omptd mid-pan (7) dfltion vr nmbr moving load yl. Th maximm dfltion dring th firt yl i 2.7 mm hr q i th hat flx, T i th abolt for TS-6 i 2.8mm for I-6. Thi diffrn inra from. mm 3. mm (TS-6; 5.5mm, tmpratr, λ i th hat ondtivity; in thi I- Proding FraMCoS-7, May 23-28, 2

6 6; 8.6mm) aftr, yl. Thi man th pot-raking onrt trongly afft th longtrm trtral prforman, vn if it do not giv ignifiant infln on th trtral prforman th vry bginning. Mid-pan Dfltion (mm) F-6.E-.E+.E+3.E+5.E+7.E+9 Nmbr Cyl Figr 8. Progr mid-pan dfltion ndr moving load. Conrt Rib A B TS-6 A - A B - B I-6 Dip x 5 (a) Dformation at,, yl, a TS-6 (b) Dformation at,, yl, a F-6 Figr 9. Dformation at,, yl moving load. A B Obrvabl dformation J = D ( h, T ) onrt h a ll a th gap opning btn onrt rib an b larly n in Figr 9(b). Th maximm proportionality prinipal fiint train D(h,T) th botm plat i moitr 2289 µ. prmability Thi man onrt it i a nonlina th flat-plat rib th do rlativ not at hmidity gthr h ithot tmpratr loking ytm in & Najjar th vrtial 972). dirtion. Th moitr Thi ma in- balan d failr both th tl variation onrt. in tim Th th trtral onitny i volm damagd. onrt (atr ontnt ) b q atr ma Th maximm divrgn prinipal train th moitr botm flx plat J i 2289 µ. Thi man onrt flat-plat rib do not at gthr ithot loking ytm in vrtial dirtion. Thi ind = failr J both tl onrt. t Aording thi Th tdy, atr prforman ontnt an th b ompoit dk hold xprd a th b vaporabl valatd not atr only by th (apillary a mid-pan dfltion bt alo by damag onrt vapor, adorbd atr) th non- d high-yl fatig load. Fatig failr th (hmially bond) atr n (Mil ppr onrt fibr rally afft th rvi lif Pantazopolo & Mill 995). It i ra ompoit bridg dk. am th vaporabl atr i a f rlativ hmidity, h, dgr hydration dgr ilia fm ration, α 5 CONCLUSIONS, i.. = = ag-dpndnt orption/dorption (Norling Mjonll 997). Undr thi am Strtral prforman tl-onrt ompoit by btitting Eqation in Eqati dk i imlatd in ing a thr dimnional nonlinar finit lmnt analyi flly tra m- obtain hanial damag platiity onrt ndr high yl rptition load in logarithmi al-ratd tim intgration. Intrfa h modl i d o α + ( D h) + rprod th Mohr-Colomb frition btn tl onrt. hr Th athor invtigatd / i th lop th orption/ th ompoit mhanim ith rgard th mhanial intrlok th iothrm (alo alld moitr apa govrning qation (Eqation 3) mt b intrfaial frition xamind thir ontribtion by appropriat bondary initial onditi th hol prforman by ing th tati analyi. Th rlation btn th amont Firt, th fft intrfa frition i addrd. atr rlativ hmidity i alld Sond, th pro intrnal rak onrt i iothrm if mard ith inraing xplaind bad on th mhanial intrlok by onidring diffrnt rib hap. Finally, th fft hmidity dorption iothrm in th a. Nglting thir diffrn (Xi t al. pot-raking bhavior i xamind in ing highyl fatig analyi. Th main onlion ar litd th folloing, orption iothrm ill b rfrn both orption dorption a; By th ay, if th hytri th Compoit dk ith amd intrfa fritional iothrm old b takn in aont, fiint µ =. ho mor than % lor rlation, vaporabl atr v rlativ hmi tati apaity than th protyp ( µ =.6) for b d aording th ign th varia th a I-hap tl rib. rlativity hmidity. Th hap th Th ompoit dk, hih ha th amd intrfa fritional fiint iothrm for µ =., HPC ho i inflnd mor than by many p 3% lor tiffn pially than tho th infln protyp xtnt ( µ =.6) for th a hmial I-hap ration tl rib., in trn, dtrm Th rtanglar trtr rib, hih por i dignd iz ditribtion hav (atrratio, qivalnt momnt inrtia mnt a hmial th ompoition, I-hapd SF rib, ho abot ring % lor tim tati mthod, apaity tmpratr, than mix th protyp (I-hapd t.). In th rib). litratr vario formlatio Th rtanglar fond rib a drib tr th orption loalization iothrm arond it tip, onrt thi loalization (Xi t al. 994). a Hovr, intrnal in th raking onrt. papr th mi-mpirial xprion pro Norling Mjornll (997) i adoptd b Proding FraMCoS-7, May 23-28, 2

7 J = In D ( th h, T ) abn h vrtial rtraint d mhanial intrloking, th vrtial opning at th in- () trfa Th btn proportionality tl fiint onrt i D(h,T) obrvd i alld omptationally. moitr prmability it i a nonlinar fntion Inraing th rlativ onfinmnt hmidity h onrt tmpratr in th T (Bažant vrtial dirtion & Najjar improv 972). Th th moitr long-trm ma trtral balan prforman th ndr variation high-yl in tim moving th load. atr ma pr nit rqir volm A th flat-plat onrt rib (atr do ontnt not provid ) b th qal mhanial divrgn lok in th th vrtial moitr dirtion, flx J onrt tl th rib do not mov gthr a a onitnt mannr. Th high-yl moving load a rio damag not only = Jonrt btn tl rib bt alo (2) th t tl itlf. Th atr ontnt an b xprd a th m th vaporabl atr (apillary atr, atr 6 ACKNOWLEDGEMENT vapor, adorbd atr) th non-vaporabl (hmially bond) atr n (Mill 966, Th athor xpr thir gratitd Dr. Bnny Pantazopolo & Mill 995). It i raonabl Sryan Th Univrity Tokyo for hi valabl am th vaporabl atr i a fntion diion. Th athor dp appriation i xtndd th finanial pport from Global rlativ hmidity, h, dgr hydration, α, COE dgr ilia fm ration, α projt on Urban Rgnration in, i.. Th Univrity = (h,α,α ) = ag-dpndnt orption/dorption iothrm Tokyo. Thi ork a pportd by JSPS Grant-in- (Norling Mjonll 997). Undr thi amption Aid for intifi rarh (A) No by btitting Eqation in Eqation 2 on JSPS Grant in Aid for rarh fllohip for yong obtain intit No ( D h) + & n (3) REFERENCES Abrihami, H., H. & Mithll, D Infln Stl Fibr Tnion / i th Stiffning. lop ACI th Strtral orption/dorption Jornal 94(6): hr iothrm (alo alld moitr apaity). Th Collin, govrning M. P. qation & Vhio, (Eqation F Th 3) mt rpon b ompltd rinford by onrt appropriat in-plan bondary har initial normal ondition. tr. Univrity Toron.Hakin, M. N. & Mithll, D Simi Th rlation btn th amont vaporabl rpon ompoit har onnr. Jornal Strtral Enginring rlativ (9): hmidity i alld adorption atr Fjiyama, iothrm C. if & Makaa, mard K. ith 29. A inraing nmrial analyi rlativity hmidity damag mhanim dorption bridg iothrm dk lab in ndr th high oppoit yl a. moving Nglting load. Proding thir diffrn Sond (Xi Intrnational t al. 994), Confrn folloing, on Fatig orption Fratr iothrm in Infratrtr ill b d 29. ith in th Mada, Y. Mati, S Fatig rinford onrt rfrn lab ndr both trking orption hl load. dorption Proding ondition. JCI 6: By th ay, if th hytri th moitr Mati, iothrm S. old 987. Fatig b takn trngth in aont, RC-lab diffrnt highay rlation, bridg by vaporabl hl rnning atr mahin v rlativ infln hmidity, atr mt b on d fatig. aording Proding th JCI ign 9(2): th variation th Makaa,K., rlativity hmidity. Toongonthong, Th K., hap Gbryohann, th orption E. Kihi, T. 26a. Dirt path-intgral hm for fatig iothrm imlation for HPC rinford i inflnd onrt in by har. many Jornal paramtr, Adv Conrt tho Thnology infln 4(): xtnt rat th pially Makaa, hmial K., ration Gbryohann,, in E., trn, Mihima, dtrmin T. An, por X. trtr 26b. Thr-dimnional por iz ditribtion fatig imlation (atr--mnt RC lab ratio, ndr mnt travling hmial hl-typ ompoition, load. Jornal SF Adv ontnt, Conrt Thnology 4(3): ring tim mthod, tmpratr, mix additiv, Makaa, K., Fkra, N. Soltani, M. 28. Patht.). Dpndnt In th High litratr Cyl Fatig vario Modling formlation Joint an Intrfa in drib Strtral th Conrt. orption Jornal iothrm Adv normal Con- b fond onrt rt Thnology (Xi t al. 6(): 994) Hovr, in th prnt Pdikari, papr th P. C. mi-mpirial & Bim, S. R xprion RC bridg propod dk ndr by Norling plating Mjornll moving (997) load. Jornal i adoptd Strtral ba Engnring 4(3): it Rabbat, xpliitly B. G. aont & Rll, for H. th G voltion Frition Cfiint hydration ration Stl on Conrt SF or ontnt. Gorot. Thi Jornal orption Strtral iothrm Enginring (3): rad Sakrai, N., Fjikaa, K., Mizkami, S., Mati, S. Nagai, M. 25. A tdy on rationalization th hap tl bridg. Jornal JSCE 794: ( h, α, α ) = G ( α, α ) + ( g α α ) h (4) ( g α α ) h K ( α, α ) hr th firt trm (gl iothrm) rprnt th phyially bond (adorbd) atr th ond trm (apillary iothrm) rprnt th apillary atr. Thi xprion i valid only for lo ontnt SF. Th fiint G rprnt th amont atr pr nit volm hld in th gl por at % rlativ hmidity, it an b xprd (Norling Mjornll 997) a G ( α, α ) = k α + k α vg vg (5) hr k vg k vg ar matrial paramtr. From th maximm amont atr pr nit volm an fill all por (both apillary por gl por), on an allat K a on obtain α α K (, ) = g α α.88α +.22α G g α α (6) Th matrial paramtr k vg k vg g an b alibratd by fitting xprimntal data rlvant fr (vaporabl) atr ontnt in onrt at vario ag (Di Lzio & Cati 29b). 2.2 Tmpratr voltion Not, at arly ag, in th hmial ration aoiatd ith mnt hydration SF ration ar xothrmi, th tmpratr fild i not niform for non-adiabati ytm vn if th nvironmntal tmpratr i ontant. Hat ondtion an b dribd in onrt, at lat for tmpratr not xding C (Bažant & Kaplan 996), by Forir la, hih rad q = λ T (7) hr q i th hat flx, T i th abolt tmpratr, λ i th hat ondtivity; in thi Proding FraMCoS-7, May 23-28, 2