Calibraion of Servie Limi Saes for Conree in AASHTO LRFD Bridge Design Speifiaions WAGDY WASSEF, AECOM, Mehanisburg, Pennsylvania, HANI NASSIF, Rugers Universiy, New Brunswik, New Jersey, JOHN KULICKI, Modjeski and Masers, In., Mehanisburg, Pennsylvania, and DENNIS MERTZ, Universiy of Delaware, Newark, Delaware IBC-16-50 KEYWORDS: Design Speifiaions, AASHTO, LRFD, Load Faors, Resisane Faor, Calibraion, Reliabiliy. ABSTRACT: The srengh, or ulimae, limi saes (ULS) of he AASHTO LRFD were alibraed hrough sruural-reliabiliy heory o ahieve a erain level of safey. In heory, exeeding he srengh limi sae resuls in a ollapse or failure of a omponen. Unlike srengh limi saes, he onsequenes of exeeding he servie limi saes are no well defined. In he pas, he servie limi saes were no saisially-alibraed. This paper presens he work performed o saisially alibrae he servie limi saes for onree. INTRODUCTION The noion of limi sae is fundamenal in he AASHTO LRFD Bridge Design Speifiaions (AASHTO LRFD) (AASHTO 2014). A limi sae is defined as he boundary beween aepable and unaepable performane of he sruure or is omponen. The srengh, or ulimae, limi saes (ULS) of he AASHTO LRFD were alibraed hrough sruuralreliabiliy heory o ahieve a erain level of safey. Theoreially, exeeding he srengh limi sae resuls in a ollapse or failure; an even ha should no our any ime during he lifeime of he sruure. Therefore, here is a need for an adequae safey margin expressed in he form of a arge reliabiliy index, β T. For bridge girders, he arge reliabiliy is aken as, β T = 3.5 (Nowak 1999; Kuliki e al., 2007). The srengh limi saes do no onsider he inegraion of he daily, seasonal, and long-erm servie sresses ha direly affe long-erm bridge performane and subsequen servie life. The urren servie limi saes (SLS) of he AASHTO LRFD are inended o ensure a servieable bridge for he design life; assumed o be 75 years in AASHTO LRFD. When he SLS is exeeded, repair or replaemen of omponens may be needed, and repeaedly exeeding SLS an lead o deerioraion and evenually ollapse or failure (ULS). In general, SLS an be exeeded, bu he frequeny and magniude have o be wihin aepable limis. Originally, he servie limi saes in AASHTO LRFD were based upon he radiional servieabiliy provisions of he Sandard Speifiaions for Highway Bridges (AASHTO 2002). They were formulaed o ahieve omponen proporions similar o hose of he Sandard Speifiaions. However, hese servie limi saes were no alibraed using reliabiliy heory o ruly ahieve uniform probabiliy of exeedane as he ools and daa neessary o aomplish his alibraion were no available o he ode wriers when AASHTO LRFD was developed.
Even wih he developmen of addiional informaion afer he original developmen of AASHTO LRFD, he developmen of alibraed servie limi saes remains a diffiul ask. The main soure of diffiuly is he lak of informaion on he relaionship beween he frequeny of exeeding a erain servie limi sae and he deerioraion of he sruure. The lak of his informaion does no allow he ode developers o sele he level of reliabiliy required o ahieve a level of performane ha orresponds o a erain servie life. The pioneering work performed under he Sraegi Highway Researh Program 2 (SHRP2), Proje R19B, and he Naional Cooperaive Highway Researh Program (NCHRP) Proje 12-83, developed a proess for he alibraion of he servie limi saes in AASHTO LRFD. This paper deails he hallenges in alibraing he servie limi saes and he proess proposed o alibrae he servie limi saes for onree sruures in he AASHTO LRFD bridge design speifiaions. SELECTION OF LIMIT STATES TO BE CALIBRATED Servie limi saes in he hen-urren AASHTO- LRFD were reviewed. I was deermined ha no all limi saes an be alibraed using available informaion. The limi saes were firs divided o non-load-driven and load-driven limi saes. Differene beween he wo groups is basially in he degree of involvemen of exernally-applied load omponens in he formulaion of he limi sae funion. In he non-load-driven SLS, he damage ours due o deerioraion or degradaion as a funion of ime and aggressive environmen or as inheren behavior due o erain maerial properies. Examples of non-load driven SLS inlude peneraion of hlorides leading o orrosion of reinforemen, leaking joins leading o orrosion of he sruural omponens under he joins, and raking of onree omponens due o shrinkage of he onree and due o hanges in emperaure. In hese examples, he exernal load ourrene plays a seondary role. The researh eam deermined ha he available informaion is no suffiien o perform a meaningful alibraion of he non-load-driven limi saes. On he oher hand, in load-driven limi saes, he damage ours due o aumulaed appliaions of exernal loads, usually live load (ruks). Examples of load-driven limi saes inlude: deompression and raking of presressed onree, raking of reinfored onree under applied loads, and, faigue of onree and reinforemen under repeaed appliaion of live load. The informaion available on hese limi saes in he lieraure, supplemened by addiional informaion developed in he researh, was deemed o be suffiien o perform he alibraion SELECTION OF THE RELIABILITY INDEX Due o he lak of orrelaion beween he frequeny of exeeding a erain servie limi sae and he deerioraion of he sruure, he inheren reliabiliy of sruures designed o pas speifiaions was used in deermining he arge reliabiliy level for he alibraion. As he inheren level of reliabiliy in exising sruures varied from one limi sae o anoher, he arge reliabiliy also varied. This is a fundamenal differene beween he alibraion of he srengh limi sae, where he same level of reliabiliy was used for all limi saes, and he alibraion of he servie limi saes. For eah servie limi sae, he ulimae goal of he alibraion beame o alibrae he limi sae o obain uniform reliabiliy level for he full range of appliaions and his reliabiliy level is similar o he average reliabiliy inheren in exising sruure. BASIC STEPS OF THE CALIBRATION PROCESS Regardless of he level of probabilisi design used o perform LRFD alibraion, he seps needed o ondu a alibraion are as follows: Develop he limi sae equaion o be evaluaed, so ha he orre random variables are onsidered. Eah limi sae equaion mus be developed based on a presribed failure mehanism. The limi sae equaion should inlude all he parameers ha desribe he failure mehanism and ha would normally be used o arry ou a deerminisi design of he sruure or sruural omponen. Saisially haraerize he daa upon whih he alibraion is based (i.e., he daa ha saisially represen eah random variable in
he limi sae equaion being alibraed). Key parameers inlude he mean, sandard deviaion, and oeffiien of variaion (COV) as well as he ype of disribuion ha bes fis he daa (i.e. ofen normal or lognormal). Sele a arge reliabiliy value based on he margin of safey implied in urren designs, onsidering he need for onsiseny wih reliabiliy values used in he developmen of oher AASHTO LRFD speifiaions, he onsequene of exeeding he limi sae, os and he levels of reliabiliy for design as repored in he lieraure for similar sruures. If he performane of exising sruures ha were designed using he urren ode provisions is aepable, hen here is no need o inrease safey margin in he newly developed ode. Furhermore, he aepable safey level an be aken as orresponding o he lower ail of disribuion of he reliabiliy indies. Deermine load and resisane faors using reliabiliy heory onsisen wih he seleed arge reliabiliy. Expanding on he four basi seps oulined above, he framework for alibraion of SLS using reliabiliy indies is summarized as follows: Sep 1: Formulae he Limi Sae Funion and Idenify Basi Variables. Idenify he load and resisane parameers and formulae he limi sae funion. For eah onsidered limi sae, he aepabiliy rieria were esablished. In mos ases, i was no possible o sele a deerminisi boundary beween wha is aepable and unaepable. Some of he ode-speified limi sae funions do no have a physial meaning (e.g. allowable ompression sress in onree). Sep 2: Idenify and Sele Represenaive Sruural Types and Design Cases. Sele he represenaive omponens and sruures o be onsidered in he developmen of ode provisions for he SLS. Sep 3: Deermine Load and Resisane Parameers for he Seleed Design Cases. Idenify he design parameers based on ypial sruural ypes, loads, and loaions (limae, exposure o harsh environmen). For eah onsidered elemen and sruure, values of ypial load omponens mus be deermined. Sep 4: Develop Saisial Models for Load and Resisane. Gaher saisial informaion abou he performane of he onsidered ypes and models, in seleed represenaive loaions and raffi. Gaher saisial informaion abou qualiy of workmanship. Ideally, for given loaion, and raffi, he required daa inludes: general assessmen of performane, assumed ime o iniiaion of deerioraion, assumed deerioraion rae as a funion of ime, mainenane, and repair (frequeny and exen). Develop saisial load and resisane models (as a minimum, deermine he bias faors and oeffiiens of variaion). The parameers of load and resisane are deermined no only by magniude, as is he ase wih srengh limi saes, bu also frequeny of ourrene (e.g. rak opening) and as a funion of ime (e.g. orrosion rae, hloride peneraion rae). The available saisial parameers were uilized. However, he daabase is raher limied, and for some servieabiliy limi saes, here is a need o assess, develop, and/or derive he saisial parameers. The parameers of ime-varying loads were deermined for various ime periods. The analyses were performed for various raffi parameers (average daily ruk raffi (ADTT), legal loads, muliple presene, raffi paerns). The load frequenies serve as a basis for deerminaion of aepabiliy rieria. Sep 5: Develop he Reliabiliy Analysis Proedure. The reliabiliy index for eah ase an be alulaed using losed-form formulas available for pariular ypes of probabiliy disribuion funions (PDF) in he lieraure or Mone Carlo mehod. In his sudy, all of he reliabiliy alulaions were based on Mone Carlo analysis. The Mone Carlo mehod is a sohasi ehnique ha is based on he use of random numbers and probabiliy saisis o simulae a large number of ompuerbased experimens. The ouome of he simulaion is a large number of soluions ha akes ino aoun all of he random variables in he resisane equaion. Sep 6: Calulae he Reliabiliy Indies for Designs Performed Using Curren Design Code and
Curren Praie. Calulae he reliabiliy indies for seleed represenaive bridge omponens orresponding o urren design and praie. Sep 7: Review he Resuls and Sele he Targe Reliabiliy Index, β T. Based on he alulaed reliabiliy indies, sele he arge reliabiliy index, β T. Sele he aepabiliy rieria, i.e., performane parameers, ha are aepable, and performane parameers ha are no aepable. Sep 8: Sele Poenial Load and Resisane Faors. Prepare a reommended se of load and resisane faors. The objeive is ha he design parameers (load and resisane faors) have o mee he aepabiliy rieria for he onsidered design siuaions (loaion and raffi). The design parameers should provide reliabiliy ha is onsisen, uniform, and oneivably lose o he arge level. Sep 9: Calulae Reliabiliy Indies. Calulae he reliabiliy indies orresponding o he reommended se of load and resisane faors for verifiaion. If he design parameers do no provide onsisen reliabiliy, modify he parameers and repea Sep 8. The annual probabiliy of exeedane was used in he saisial analysis of all limi saes exep for he alibraion of he faigue limi sae whih was performed based on infinie faigue life. For eah limi sae onsidered, he alibraion proess was revised o bes fi he limi sae. The live load used in his sudy was based on a large sudy of weigh-in-moion (WIM) daa. The dead load, live load and maerials resisane saisis may be found in Wassef e.al. (2014). CALIBRATION OF THE LIMIT STATE FOR TENSION IN PRESTRESSED CONCRETE BEAMS, SERVICE III LIMIT STATE The design of presressed beams is ypially onrolled by he ensile sress limis for he onree under Servie III limi sae. As suh, he alibraion for presressed onree supersruures was performed for Servie III limi sae. An aepable design will resul in maximum ensile sress below he limi se in he speifiaions when he sress is alulaed based on unraked seion under he full design live load for Servie III load ombinaion. For ypial preas, preensioned beams, he ensile sress limis, f, are f = 0.0948 f and f = 0.19 f for bridges in severe orrosion ondiions and in no worse han moderae orrosion ondiions, respeively. Even hough hese limis are below he modulus of rupure for onree ( f = 0.24 f for normal densiy onree), his does no mean ha raks will no open under he Servie III design load. This an be explained as follows: When he girder is subjeed o heavy loads, suh as heavy permi or illegal overweigh vehiles, he ensile sress in he onree may exeed he modulus of rupure ausing he beam o rak. Subsequen o he formaion of he raks, every ime he load on he bridge resuls in ensile sress in he onree, i.e. resuls in deompression, he rak will open. The widh of he rak opening depends on he differene beween he deompression momen and he aual momen applied. Afer he load passes, he rak loses again. Opening of he raks allows a pah for onaminans o reah he presressing seel. I is expeed ha he vulnerabiliy of presressing srands o orrosion inreases wih he inrease of rak widh and wih he inrease in he frequeny of rak opening. Basis of he load faor in AASHTO LRFD: During he early sages of he developmen of he AASHTO LRFD Speifiaions in he early 1990s, only Servie I load ombinaion was onsidered for alulaing all sresses in presressed onree omponens. The load faor for live load was 1.0 whih is he same load faor used for servie loads under he AASHTO Sandard Speifiaions; he predeessor o he AASHTO LRFD Speifiaions. The design live load speified in he AASHTO LRFD Speifiaions produes higher unfaored, undisribued load effes han ha speified in he AASHTO Sandard Speifiaions. The girder disribuion faors, pariularly for
inerior girders, for many ypial girder sysems in he AASHTO LRFD Speifiaions are lower han hose in he Sandard Speifiaions hus reduing he differene beween he unfaored disribued load effes in he wo speifiaions. Even wih he smaller disribuion faor, he unfaored disribued load effes from he AASHTO LRFD Speifiaions were higher for mos girder sysems. Using he same load faor for he servie limi sae (1.0) resuled in higher design faored load effes for he AASHTO LRFD designs han for hose designed o he AASHTO Sandard Speifiaions. The resuls from he rial designs ondued during he developmen of he AASHTO LRFD Speifiaions indiaed he need for a larger number of srands han required by he AASHTO Sandard Speifiaions. This would sugges ha designs performed under he AASHTO Sandard Speifiaions resuled in underdesigned omponens ha should have shown signs of raking. In he absene of widespread raking, he load faor for live load was dereased o 0.8 and he Servie III load ombinaion was reaed and was speified for ension in presressed onree omponens. This resuled in a similar number of srands for he designs ondued using boh AASHTO Sandard and AASHTO LRFD Speifiaions. Mehod of Calulaing Presressing Losses: The AASHTO LRFD Speifiaions (2014) inludes hree mehods for deermining he imedependen presressing losses. These hree mehods are: Approximae mehod: Currenly, his mehod is ermed: Approximae Esimae of Time-Dependen Losses and is he leasdeailed. I requires limied alulaions o esimae he ime-dependen losses. Prior o 2005, he speifiaions inluded a simpler approximae mehod whih was ermed: Approximae Lump Sum Esimae of Time-Dependen Losses. The lump-sum mehod allowed seleing a value for he imedependen losses from a able. The value varied based on he ype of girders and he ype and grade of presressing seel. Some onree ompressive srengh requiremens were required o be allowed o use his mehod. Time-Sep mehod: This mehod is highly deailed and is based on raking he hanges in he maerial properies wih ime. The loss alulaions are based on he ime of he appliaion of loads and he maerial properies a he ime of he load appliaion. This mehod is required o be used in he design of pos-ensioned segmenal bridges. I may also be used for oher ypes of bridges; however, due o he level of effor required, i is ypially limied o segmenal bridges. Refined Esimaes of Time-Dependen Losses: This mehod is more deailed han he approximae mehod bu less deailed han he ime sep mehod. This mehod is he mos used among all hree mehods. Originally, he mehod of alulaing presressing fore losses in AASHTO LRFD Speifiaions (he pre-2005 mehod) was he same mehod used in AASHTO Sandard Speifiaions. A new mehod of loss alulaions (he pos-2005 mehod) firs appeared in he 2005 Inerim o he Third Ediion of AASHTO LRFD Speifiaions. The pos-2005 mehod is hough o produe a more aurae esimae of he losses. The pos-2005 mehod has new equaions for alulaing he ime-dependen presressing losses and i also inrodued he onep of elasi gain. Afer he iniial presressing loss a ransfer, when load omponens ha produe ensile sresses in he onree a he srand loaions are applied o he girder, he srands are subjeed o an addiional ensile srain equal o he srain in he surrounding onree due o he appliaion of he loads. This resuls in an inrease in he fore in he srands. The inrease in he fore in he srands was ermed elasi gain and he pos- 2005 presressing loss mehod allows inluding he elasi gain o be used o offse some of he losses. When he elasi gain was onsidered, he pos-2005 presressing loss mehod produed lower presressing fore losses han he earlier mehod. The reduion in presressing losses resuled in fewer srands han wha was required under he AASHTO Sandard Speifiaions and under earlier ediions of
AASHTO LRFD Speifiaions. This raised some onern as some praiioners and researhers hough ha he higher presressing losses alulaed using he pre-2005 loss mehod ompensaed for he lower live load effes aused by he lower design live load used in he AASHTO Sandard Speifiaions or he lower load faor used for Servie III load ombinaion of AASHTO LRFD Speifiaions. The effe of he presressing loss mehod on he design and on he reliabiliy index of presressed beams was invesigaed. Live Load Model Live load used in he design of sudy bridges: Tradiionally, presressed onree omponens are designed for he number of raffi lanes, inluding muliple presene faors, ha produes he highes load effes. This was assumed o oninue in he fuure and all beams used in he alibraion were designed uilizing his approah. Live load used in deermining he reliabiliy indies: As he limi sae funion, or he physial phenomena, is relaed o he rak opening, he load used in he alibraion had o refle he load bridges are expeed o be subjeed o on regular basis; no he maximum design load. The sudy of WIM daa indiaed ha he presene of heavy ruks simulaneously in adjaen raffi lanes simulaneously is no likely. As suh, he load side of he limi sae funion in he reliabiliy analysis was alulaed assuming he live load exised in only one lane and no muliple presene faor was inluded. The design ruk, andem, and uniform lane load speified in he AASHTO LRFD Speifiaions were used unless oherwise noed. The live load disribuion faors speified in he AASHTO LRFD Speifiaions were used in disribuing he design loads. The dynami load allowane used in he original alibraion of he srengh limi sae in AASHTO LRFD (10%) was applied o he load side. The reurn period onsidered in he alibraion of he Servie III limi sae was one year. This reurn period was seleed due o he fa ha he live load saisis were developed based on 1 year of reliable WIM daa from various WIM sies. Furhermore, an ADTT of 5000 was used for he bulk of he alibraion. This ADTT is higher han ha for he majoriy of he WIM sies used in he sudy and, as suh, represens a onservaive ADTT for mos sies. Mehods of Analysis for Sudy Bridges Sudy bridges were analyzed wie. Exep for he mehod used in deermining he presressing losses, boh analyses were performed using AASHTO LRFD. The presressing losses were deermined as follows: For he firs analysis, he presressing losses were deermined using he mehod ermed Refined Esimaes of Time-Dependen Losses in urren AASHTO LRFD and he elasi gain was onsidered. In he seond analysis, he bridges were analyzed using he mehod ermed Refined Esimaes of Time-Dependen Losses, in AASHTO LRFD prior o 2005. In his ase, he elasi gain was no allowed Performing he analysis wie allowed he invesigaion of he effe of he presressing loss mehod on he required number of srands and on he reliabiliy index. Limi Sae Funions Invesigaed The following hree differen limi sae funions were invesigaed: Deompression Limi Sae: This limi sae assumes ha he failure ours when he sress in he onree on he ension fae alulaed based on he unraked seion under he ombined effe of faored dead load and live load eases o be ompression. Sress Limi Sae: This limi sae assumes ha he failure ours when he ensile sress in he onree on he ension fae under he ombined effe of faored dead load and live load exeeds a erain ensile sress limi alulaed based on he unraked seion properies regardless of wheher he seion has been previously raked or no. Sress limis of f = 0.0948 f, f = 0.19 f and f = 0.25 f were iniially onsidered in he reliabiliy analysis, however, a sress limi of f = 0.19 f was used for he final alibraion.
Crak Widh Limi Sae: This limi sae assumes ha he failure ours when he previously formed rak in he onree opens and he rak widh reahes a erain prespeified rak widh. Crak widhs of 0.008, 0.012, and 0.016 inhes were iniially onsidered in he reliabiliy analysis, however, none produed uniform reliabiliy. The bulk of he alibraion was performed using a rak widh of 0.016 inhes. The differeniaion beween differen environmens is aouned for in he alibraion hrough he use of differen reliabiliy indies in assoiaion wih he same rak widh. For eah girder, he design was performed based on erain sress limis as is onvenionally done and he girder seion and number of srands were deermined. The reliabiliy index was deermined for eah of he hree limi sae funions desribed above using he same girder design, i.e. he same girder seion and same number of srands. Eah of he limi sae funions requires a differen level of loading before he rieria is violaed. As suh, he frequeny a whih any of he hree limi saes is violaed and he orresponding reliabiliy index depend on he level of loading required o ause he limi sae o be violaed. For a speifi ross seion wih a speifi presressing seel area and fore, reahing he deompression limi sae requires less applied load han reahing a speified ensile sress whih in urn requires less load han ha required o reah a speifi wider rak widh. For any limi sae funion, requiring higher load o violae a speifi limi sae means ha he seion resisane is higher and his resuls in higher reliabiliy index alulaed. Daabase of Exising Bridges: To deermine he inheren reliabiliy index of exising bridges, a daabase of exising presressed onree girder bridges was exraed from he daabase of bridges used in he NCHRP 12-78 proje (Mlynarski, e al. 2011). The daabase used in his sudy inluded 30 I- and bulb-t girder bridges, 31 adjaen box girder bridges, and 36 spread box girder bridges. The reliabiliy index was alulaed for he girders of hese bridges for he hree limi sae funions lised above. The alulaed reliabiliy indies were used o esablish he arge reliabiliy index for he alibraion. Daabase of Simulaed Bridges A daabase of simulaed simple span bridges was designed using AASHTO I-girder seions for four differen ases. The simulaed bridges have span lenghs of 30, 60, 80, 100, and 140 f and girder spaing of 6, 8, 10, and 12 f. This daabase was analyzed o deermine he effe of he hange in he mehod of esimaing presressing losses (pre-2005 and pos-2005 mehods) and he design environmen ( severe orrosive ondiions and normal or no worse han moderae orrosion ondiions ). The wo environmenal ondiions are signified by he maximum onree ensile sress limi ( f = 0.0948 f or f = 0.19 f ) used in he design. The four ases of design onsidered were: Case 1: AASHTO LRFD wih maximum onree ensile sress of f = 0.0948 f and pre- 2005 presress loss mehod Case 2: AASHTO LRFD wih maximum onree ensile sress of f = 0.0948 f and pos-2005 presress loss mehod Case 3: AASHTO LRFD wih maximum onree ensile sress of f = 0.19 f and pre- 2005 presress loss mehod Case 4: AASHTO LRFD wih maximum onree ensile sress of f = 0.19 f and pos- 2005 presress loss mehod The average reliabiliy indies for he exising bridges and he simulaed bridges for differen assumpions of design and for differen limi sae funions are shown in Table 1. Calibraion Resuls: The reliabiliy indies for differen limi sae funions for bridges designed in aordane wih he hen-urren AASHTO LRFD (2012) were alulaed and ploed. The graphs for he deompression limi saes are shown below for bridges designed for ensile sress limi in onree
of f = 0.0948 f and f = 0.19 f. The graphs for oher limi sae funions and oher sress limis may be found in Wassef e.al. (2014). Figures 1 and 2 show he resuls when he girders were designed for a load faor for Servie III limi sae of 0.8 as was speified in AASHTO LRFD (2012). As shown in Figures 1 and 2, he reliabiliy index is no uniform for he full range of span lengh. In addiion, he reliabiliy index is generally lower han he inheren reliabiliy of bridges designed based on he presressing loss mehod used before 2005. Wih he majoriy of bridges designed using he pre-2005 loss mehod, he inheren reliabiliy of he sysem is ha of he bridges designed o pre-2005 loss mehod. Therefore, he simulaed bridges were redesigned using a load faor of 1.0 insead of he 0.8 exised in he AASHTO LRFD (2012). Figures 3 and 4 show he reliabiliy index for he redesigned bridges. Figures 3 and 4 show ha he designs using a load faor of 1.0 for live load in Servie III limi sae exhibi more uniform reliabiliy level aross he full range of span lenghs inluded in he sudy. The average reliabiliy indies also loser o he arge reliabiliy indies of 1.2 and 1.0 for bridges designed for onree ensile sress limis of 0.0948 f and 0.19 f, respeively. Figure 1. Reliabiliy indies for bridges a deompression limi sae (ADTT=5000), γ LL =0.8, ( f = 0.0948 f ) Figure 2. Reliabiliy indies for bridges a deompression limi sae (ADTT=5000), γ LL =0.8 ( f = 0.19 f ). Table 1. Reliabiliy Indies for Exising and Simulaed Bridges (Reurn Period of 1 Year and ADTT 5000) Performane Level Average β for Exising Bridges in he NCHRP 12-78 Average β for Simulaed bridges designed for f = 0.0948 f an Reliabiliy Index Average β for Simulaed bridges designed for f = 0.19 f and Proposed Targe β for bridges in severe environmen Proposed Targe β for bridges in normal environmen d pre-2005 loss mehod pre-2005 loss mehod Deompression 0.74 1.44 1.07 1.20 1.00 Maximum Allowable Tensile Sress of f = 0.19 f Max. Allowable Crak Widh of 0.016 in. 1.05 1.80 1.43 1.50 1.25 2.69 3.68 3.15 3.30 3.10
Figure 3. Reliabiliy indies for bridges a deompression limi sae (ADTT=5000), γ LL =1.0 ( f = 0.0948 f ). Two exposure lassifiaions exis in AASHTO LRFD: Class 1 exposure ondiion and Class 2 exposure ondiion. Class 1 relaes o an esimaed maximum rak widh of 0.017 in. while Class 2 relaes o an esimaed maximum rak widh of 0.01275 in. Class 2 is ypially used for siuaions where he onree is subjeed o severe orrosion ondiions suh as bridge deks exposed o deiing sals and subsruures exposed o waer. Class 1 is used for less orrosive ondiions and ould be hough of as an upper bound in regards o rak widh for appearane and orrosion. Previous researh indiaes ha here appears o be lile or no orrelaion beween rak widh and orrosion. However, he differen lasses of exposure ondiions have been so defined in he design speifiaions in order o provide flexibiliy in he appliaion of hese provisions o mee he needs of he bridge owner. The available informaion allowed he alibraion of deks. Oher ypes of omponens were no inluded in he alibraion. Figure 4. Reliabiliy indies for bridges a deompression limi sae (ADTT=5000), γ LL =1.0 ( f = 0.19 f ). Based on he sudy, i was proposed ha he load faor for live load in he Servie III limi sae be inreased from 0.8 o 1.0. AASHTO aeped he reommendaion and i was inorporaed in he AASHTO LRFD Design Speifiaions. CALIBRATION OF THE LIMIT STATE FOR CONTROLE OF CRACKING IN REINFORCED CONCRETE, SERVICE I LIMIT STATE The disribuion of reinforemen is used o onrol of reinfored onree in AASHTO LRFD. Tigher spaing of reinforemen resuls in larger numbers of narrow raks. The narrow raks resul in beer resisane o onaminan peneraion hus reduing he reinforemen exposure o orrosive agens. Reinfored onree deks designed using he onvenional mehod are designed for he heavy axles of he design ruk. This required developing he saisial parameers of he axle loads of he ruks in he WIM daa. (Wassef e. al. 2014). Saisial parameers orresponding o a one year reurn period were assumed in he reliabiliy analysis. ADTTs of 1000, 2500, 5000, and 10,000 were onsidered, however, an ADTT of 5000 was used as he basis for he alibraion. Due o he lak of lear onsequenes for violaing he limiing rak widh, here was no basis for hanging he naure or he limiing values of he limi sae funion, i.e. he rak widh rieria. The work was based on mainaining he urren rak widh values and alibraing he limi sae o produe a uniform reliabiliy index similar o he average reliabiliy index produed by he urren designs. A daabase of deks represening ommonly used proporions was developed and used in he alibraion. The haraerisis of he deks are shown in Table 2.
Table 2. Summary Informaion of 15 Bridge Deks Designed using AASHTO LRFD Convenional Dek Design Mehod Dek Group # Girder Spaing (f.) 1 6 2 8 3 10 4 12 Dek Thikness (in.) 7.0 7.5 8.0 7.5 8.0 8.5 8.0 8.5 9.0 9.5 8.0 8.5 9.0 9.5 10.0 The reliabiliy indies are dependen on he ADTT and hey derease as he ADTT inreases. The ase of ADTT of 5000 was used as he base ase. For his ADTT, he reliabiliy index inheren in urren designs for he negaive momen region and 1-year reurn period was alulaed as 1.61 and 1.05 for Class 1 and Class 2, respeively. Based on hese values, arge reliabiliy indies of 1.6 and 1.0 were seleed for Class 1 and Class 2, respeively. Figure 5. Reliabiliy Indies of Various Bridge Deks Over A 1 Year Reurn Period (ADTT=5000), Posiive Momen Region, Class 1 Exposure Figure 6. Reliabiliy Indies Of Various Bridge Deks Over A 1 Year Reurn Period (ADTT=5000), Negaive Momen Region, Class 1 Exposure Figures 5 hrough 8 show he reliabiliy indies deermined for he dek in he daabase. In all ases, he load faor for live load for he Servie I limi sae was aken as 1.0. The resuls showed ha he variaion in he reliabiliy indies is relaively small and ha urren designs give uniform reliabiliy indies for he range of girder spaing onsidered. As suh, i was onluded ha urren design provisions do no need o be revised. Figure 7. Reliabiliy Indies Of Various Bridge Deks Over A 1 Year Reurn Period (ADTT=5000), Posiive Momen Region, Class 2 Exposure
For welded-wire reinforemen wih a ross weld in he high-sress region, he faigue resisane is speified as: ( F) Δ = 16-0.33 f min TH Where f min is he minimum sress. Figure 8. Reliabiliy Indies Of Various Bridge Deks Over A 1 Year Reurn Period (ADTT=5000), Negaive Momen Region, Class 2 Exposure CALIBRATION OF THE FATIGUE LIMIT STATE FOR REINFORCEMENT AND CONCRETE IN COMPRESSION The limi on he ompressive sress in presressed onree is aually inended o onrol faigue of onree in ompression. Faigue of reinforemen and onree in ompression are boh heked assuming infinie faigue life. The sudy of WIM daa deermined he appropriae load faor for urren raffi for boh finie and infinie faigue life (Kuliki e. al. 2015). The proess for alibraing he faigue limi sae for sruural seel was also developed by Kuliki. e. al. (2015) and was used o alibrae he faigue limi sae for reinforemen and in onree. Tes resuls of faigue in reinforemen and onree in ompression were olleed and used in he alibraion. The lis of ess and he resuls may be found in Wassef e. al. (2014) Faigue of Seel Reinforemen in Tension in AASHTO LRFD The infinie faigue life hreshold in AASHTO LRFD for sraigh reinforing bars and welded-wire reinforemen wihou a ross weld in he highsress region (defined as one-hird of he span on eah side of he seion of maximum momen) is speified as: ( ) Δ F = 24-20 f / f TH min y Resuls from pas sudies used o define he faigue resisane of seel reinforemen were reanalyzed o esimae onsan-ampliude faigue hresholds for every ase ha an be idenified in he researh o deermine heir unerainy, in erms of bias, mean, and oeffiien of variaion (COV). The various hresholds were grouped ogeher o make design praial. The alibraion resuled in revising he faigue resisane equaions as follows: For sraigh reinforing bars and welded-wire reinforemen wihou a ross weld in he highsress region (defined as one-hird of he span on eah side of he seion of maximum momen): ( ) Δ F = 26-22 f / f TH For welded-wire reinforemen wih a ross weld in he high-sress region, he faigue resisane is speified as: ( F) min Δ = 18-0.36 f min TH The revised equaions resuls in higher faigue resisane in all ases for sraigh reinforing bars and welded-wire reinforemen wihou a ross weld in he high-sress region. The revised equaions also resul in higher faigue resisane for all praial ases for welded-wire reinforemen wih ross welds (all ases wih f 50ksi). min Conree in Compression The ompressive sress limi of 0.40 f for fully presressed omponens in oher han segmenally onsrued bridges of AASHTO LRFD Arile 5.5.3.1 applies o a ombinaion of he live load speified in he Faigue I limi sae load y
ombinaion plus one-half he sum of he effeive presress and permanen loads afer losses, i.e. a load ombinaion derived from a modified Goodman diagram. This suggess ha i represens an infinie-life hek as he Faigue I limi sae load ombinaion orresponds wih infinie faigue life. For his sudy, he researh used o define hese S-N urves, Hilsdorf and Kesler (1966) was reevaluaed o esimae he onsan-ampliude faigue hreshold, he infinie-life faigue resisane. The unerainy of he faigue resisane was quanified in erms of bias, mean, and oeffiien of variaion. The reliabiliy index alulaed for designs performed using urren design praies was 0.9. This value was lose o he arge reliabiliy index of 1.0. Therefore, no revisions o he urren design speifiaions were reommended. ACKNOWLEDGEMENTS The researh was ondued under he Naional Cooperaive Highway researh Program (NCHRP) Proje 12-83. Signifian informaion on he servie limi sae alibraion was originaed in he Sraegi Highway Researh Program (SHRP) Proje R19B. The views presened by he auhors are no neessarily hose of he funding agenies. A he ime he work was performed, his paper s primary auhor, Dr. Wagdy Wassef, was an employee of Modjeski and Masers, In.; he onraor of he proje. REFERENCES AASHTO LRFD Bridge Design Speifiaions, 7h ed. 2014. AASHTO, Washingon, DC. AASHTO Sandard Speifiaions for Highway bridges, 17h ed. 2002. AASHTO, Washingon, DC. Hilsdorf, H., and C. Kesler. 1966. Faigue Srengh of Conree under Varying Flexural Sresses. Journal Proeedings, Amerian Conree Insiue, Vol. 63, No. 10, pp. 1059 1076. Kuliki, J., W. Wassef, D. Merz, A. Nowak, N. Samani, and H. Nassif. 2013. Servie Load Design for 100-Year Life. SHRP 2, R19B. Transporaion Researh Board of he Naional Aademies, Washingon, DC (Under Preparaion). Kuliki, J., Z. Pruz, C. Clany, D. Merz, and A. Nowak. 2007. Updaing he Calibraion Repor for AASHTO LRFD Code. Repor on NCHRP 20-7/186. Transporaion Researh Board of he Naional Aademies, Washingon, DC. Mlynarski, M., W. Wassef, and A. Nowak. 2011. NCHRP Repor 700: A Comparison of AASHTO Bridge Load Raing Mehods. Transporaion Researh Board of he Naional Aademies, Washingon, DC. Nowak, A. 1999. NCHRP Repor 368: Calibraion of LRFD Bridge Design Code. TRB, Naional Researh Counil, Washingon, DC. Wassef, W. G., J. M. Kuliki, H. A. Nassif, D. R. Merz, and A. S. Nowak. 2014. Calibraion of LRFD Conree Bridge Design Speifiaions for Servieabiliy, NCHRP Web-Only Doumen 201, Transporaion Researh Board, Naional Researh Counil, Washingon, DC. AASHTO LRFD Bridge Design Speifiaions, 6h ed. 2012. AASHTO, Washingon, DC.