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Single-Span Prestressed Girder Bridge: LRFD Designand ComparisonRichard J. Nielsen, M.ASCE,1and Edwin R. Schmeckpeper, M.ASCE2Abstract: This report summarizes the comparative design of a single-span AASHTO Type III girder bridge under the AASHTO StandardSpecification for Highway Bridges, 16th Edition, and the AASHTO LRFD Bridge Design Specification. The writers address the differencesin design philosophy, calculation procedures, and the resulting design. Foundation design and related geotechnical considerations are notconsidered. The LRFD design was similar in most respects to the Standard Specification design. The significant differences were: 1!increased shear reinforcement; 2! increased reinforcement in the deck overhang; and 3! increased reinforcement in the wing wall. Thecomparisons would likely change if the bridge were designed purely according to LRFD Specifications rather than as a comparativedesign. Design procedures under the LRFD Specification tend to be more calculation-intensive. However, the added complexity of theLRFD Specification is counterbalanced by the consistency of the design philosophy and its ability to consider a variety of bridges.DOI: 10.1061/ASCE!1084-07022002!7:122!CE Database keywords: Bridges, girder; Load and resistance factor design; Prestressing; Bridges, spans.IntroductionUntil the mid-1990s, the design of bridges in the United Stateswas governed by the AASHTO Standard Specification for High-way Bridges, 16th Edition Standard Specification! AASHTO1996!. The introduction of the AASHTO LRFD Bridge DesignSpecification LRFD Specification! in 1994 along with a secondedition in 1998 provided a new standard for bridge design thataddressed several of the perceived problems in the StandardSpecification AASHTO 1994a, 1998!. As stated in the forewordof the LRFD Specification, the first area of concern was the dis-cernable gaps, inconsistencies, and even some conflicts that hadexisted in the Standard Specification as a result of its evolutionover decades AASHTO 1994b!. The second concern was thedesire to incorporate the most recently developing design phi-losophy, load and resistance factor design AASHTO 1994b!. Itis also evident that the writers of the LRFD Specification at-tempted to include more up-to-date research along with the LRFDdesign philosophy.The change in design philosophy and the incorporation ofnewer analytical methodologies resulted in a design procedurethat is significantly different from the earlier procedure. However,the new code was intentionally calibrated to produce designs thatare similar to those produced by the Standard Specification, withsomeexceptionsassuggestedbymorecurrentresearchAASHTO 1994b!. Asward and Jacques 1992! performed a para-metric study of the impacts of the change from Standard Specifi-cation to LRFD Specification designs.The changes in design methodology are significant and repre-sent a significant challenge to engineers accustomed to workingwith the Standard Specification. In an effort to lead a transition tothe newer code, the Idaho Transportation Department ITD! hadthe first writer check the Standard Specification design of thesingle-span prestressed concrete girder bridge shown in Figs. 1and 2 and then redesign that bridge using the LRFD Specificationincluding the 1997 interim revisions AASHTO 1994b!.This paper summarizes the significant changes in the designprocedures by the LRFD Specification and compares the resultswith the Standard Specification. However, the conclusions givenin this report should be considered in light of the scope of work.First, the design experience is limited to a single span AASHTOType III girder bridge; these conclusions do not necessarily applyto multispan or steel girder bridges. Second, some design param-eters were selected to facilitate comparison between the StandardSpecification and LRFD design. A design based solely on LRFDconsiderations might be somewhat different. For example, thedeck overhang and girder spacing were the same in the StandardSpecification and LRFD designs. If direct comparisons were notneeded, it might be advantageous to reduce the overhangs for theLRFD design and adjust the resulting girder spacings.The comparisons are presented in the order they were encoun-tered in the design: general design considerations, followed byflexural design of the girder, shear design of the girder, deckdesign, and abutment design. Foundation design and related geo-technical considerations are not included in this paper.General Design ConsiderationsThe LRFD design philosophy provides a common framework forthe design of structures made of steel, concrete, and other mate-rials. However, the flexibility of this approach also increases thecomplexity of the process.1Associate Professor, Dept. of Civil Engineering, Univ. of Idaho,Moscow, ID 83844-1022.2Associate Professor, Dept. of Civil Engineering, Univ. of Idaho,Moscow, ID 83844-1022.Note. Discussion open until June 1, 2002. Separate discussions mustbe submitted for individual papers. To extend the closing date by onemonth, a written request must be filed with the ASCE Managing Editor.The manuscript for this paper was submitted for review and possiblepublication on February 22, 2000; approved on February 22, 2001. Thispaper is part of the Journal of Bridge Engineering, Vol. 7, No. 1, Janu-ary 1, 2002. ASCE, ISSN 1084-0702/2002/1-2230/$8.001$.50 perpage.22 / JOURNAL OF BRIDGE ENGINEERING / JANUARY/FEBRUARY 2002LRFD PhilosophyIn general, load and resistance design codes base their designs onultimate load and ultimate failure modes, i.e., conditions in thestructure under rare failure conditions. Although this is philo-sophically consistent with the stated purpose of providing a con-sistent reliability against failure, it is not as readily applied toother design considerations such as deflections, serviceability, fa-tigue, or creep, where behavior is often governed by serviceloads, i.e., day-to-day loads and deflections. Because of this dif-ference, there are limit states established specifically for pre-stressed girder design, e.g., the Service III limit state, which re-lates to tension in prestressed concrete structures with theobjective of crack control AASHTO 1998!. Fortunately, the for-mulation of the LRFD Specification allows the flexibility to ac-commodate these specific cases. However, the resulting load andresistance factors may seem to be much less conservative thanthose used for the strength limit states. The designer should rec-ognize that they were selected to provide designs that are consis-tent with the Standard Specification.Complexity Versus ConsistencyBecause the LRFD Specification attempts to unify the design ofall the bridge components under one design approach, the com-plexity of the process increases substantially. As mentionedabove, the number of limit states has increased. In the case ofreinforced and prestressed concrete, kips per square inch havereplaced pounds per square inch as units of stress. As a result,some of the design equations appear to have changed substan-tially when, in fact, they have not.To some extent, the consistency of the LRFD Specificationtends to counterbalance its complexity. As mentioned, the Stan-dard Specification is the result of evolving standards and proce-dures over decades. The patchwork nature of the StandardSpecification is, in a sense, compounded by the existence of in-ternal design standards adopted by state departments of transpor-tation that addressed perceived inadequacies in the StandardSpecification. In order to provide a true comparison between theStandard Specification and the LRFD Specification, no supple-mental internal design standards were added to the LRFD design.Fig. 1. Bridge plan viewFig. 2. Bridge cross sectionJOURNAL OF BRIDGE ENGINEERING / JANUARY/FEBRUARY 2002 / 23This approach avoids introducing inconsistencies in the LRFDphilosophy.TerminologyAnalysis of the collision case described below led to an exami-nation of the terminology used in the LRFD Specification. TheLRFD Specification uses the word extreme to describe twodifferent items. Article 3.4.1 refers to Extreme Events, i.e.,extreme loading events AASHTO 1998!. For example, ExtremeEvent II is a loading event that includes collision by vehicles.On the other hand, Article .1 refers to extreme forceeffects.A careful reading of this article indicates that the discus-sion of extreme force effects refers to the arrangement of loadsto produce the maximum or minimum i.e., extreme! moment orshear AASHTO 1998!. Thus, the discussion of the possibilitythat vehicles can mount the sidewalk in the last paragraph ofArticle C.1 refers to the positioning of the load to obtainthe maximum force effect. It does not necessarily imply that theplacement of the vehicle on the curb or sidewalk is an extremeloading event per Article 3.4.1 AASHTO 1998!.Thus, it is up to the engineers judgment to decide whether theplacement of the load on the curb or sidewalk should be includedin Extreme Event II Article 3.4.1! or whether it should be in-cluded in the service and strength limit states e.g., Service I,Service III, or Strength I!. Inclusion in Extreme Event II is ap-propriate if the recurrence interval associated with the event isthought to exceed the design life Article C3.4.1; AASHTO1998!. Inclusion in Service I, Service III, or Strength I is appro-priate if the load event occurs more frequently; i.e., it has a re-currence interval less than the service life of the structure.Girder DesignCompared with the Standard Specification, the LRFD Specifica-tion makes several significant changes in the way the dead andlive loads are distributed to the bridge girders.Permanent Deck LoadsLRFD Specification Article .1 states that where bridgesmeet the conditions specified herein, permanent loads of and onthe deck may be distributed uniformly among the beams and/orstringersAASHTO 1998; emphasis added!. This is a substantialchange from the Standard Specification design practice in con-junction with ITD standard design practice, both of which dictatethat railings, parapets, and sidewalk dead loads are applied onlyto the exterior girders, and deck self-weight is distributed in pro-portion to the tributary width ITD 1994!.The LRFD approach is reasonable for railings and sidewalksthat are installed after the deck is in place and can distribute loadsfrom the exterior to the interior girders. Although permitted, thisapproach may not be reasonable for the diaphragms and the deckitself. Before the deck concrete is set, the concrete is in the plasticstate and it cannot distribute these loads to the interior girders.For this reason, these loads were not distributed between the in-terior and exterior girders in the LRFD design of the examplebridge.A comparison on the dead loads for the Standard Specificationdesign and the LRFD design is shown in Table 1. The values inthis table assume that the diaphragm weight is replaced by auniform load, and that the stay-in-place forms are metallic, havingan equivalent load of 960 Pa 20 psf!. These results indicate that,compared with the Standard Specification design, the LRFD de-sign increases the noncomposite dead load on the exterior girderby 9%, and decreases the noncomposite dead load on the interiorgirder by 4%. Also, the LRFD design decreases the compositedead load on the exterior girder by 50% and increases the com-posite dead load on the interior girder by 97%. Although some ofthese individual changes are significant, they represent a smallportion of the total load, and they do not change the final design.Vehicular Live LoadFor the Standard Specification design, the bridge was to carry anHS-25 loading, which is 125% of the AASHTO HS-20 truck con-sisting of a 440.5 kN 45-ton! design truck or a design lane loadcomprised of a 11.7 kN/m 800 lb/ft! distributed load plus a 100kN 22.5 kip! or 145 kN 32.5 kip! point load for the flexure orshear design cases, respectively Fig. 3!. For the LRFD Specifi-cation design, the bridge was to carry an HL-93 load, which con-sists of a 325 kN 36 ton! design truck or design tandem and a 9.3kN/m 640 lb/ft! design lane load Fig. 4!. Furthermore, theHL-93 design lane load is not interrupted for the design truck ordesign tandem. Interruption is needed only where pattern loadingsare used to produce maximum load effects. For bridges of thisTable 1.Dead Load ComparisonLoad typeSectionExterior girderInterior girderStandard SpecificationLRFDStandard SpecificationLRFDNoncomposite dead load, kN/m kip/ft!Deck13.5a0.925a!14.0 0.958!14.2a0.975a!14.0 0.958!Camber strip0.12a0.008a!0.12 0.008!0.12a0.008a!0.12 0.008!Diaphragm0.19a0.013a!0.19a0.013a!0.38a0.026a!0.38a0.026a!Stay-in-placeforms1.2a0.084a!2.0 0.140!2.45a0.168a!2.0 0.140!Total15.0 1.030!16.33 1.119!17.18 1.177!16.52 1.132!Composite dead load kN/m kip/ft!Sidewalk7.39a0.506a!2.47 0.169!0.000a2.47 0.169!Rail3.93a0.269a!1.31 0.090!0.000a1.31 0.090!Futurewearingsurface1.12a0.077a!2.38 0.163!3.12a0.214a!2.38 0.163!Total12.4 0.852!6.16 0.422!3.12 0.214!6.16 0.422!aItems not distributed uniformly between girders.24 / JOURNAL OF BRIDGE ENGINEERING / JANUARY/FEBRUARY 2002span length, the resulting bending moment and shears after loaddistribution are roughly comparable for the two load specifica-tions.Impact FactorUnder the Standard Specification, the impact factor is expressedas a fraction of the live load and is a function of the span length:I550/(L1125), where I is the impact factor and L is the lengthof the span in feet. For the 70 ft span under consideration here,I50.26, i.e., causes a 26% increase in the live load effect.According to Article of the LRFD Specification, thedynamic load allowance or impact factor is a constant value de-pending on the components and limit states being considered. Forthe girder design other than fatigue or fracture limits states!, thisresults in an increase of 33% for the truck load only.Live Load Distribution FactorsUnder the Standard Specification, live loads are distributed to theexterior girders using some variation on the so-called lever ruleAASHTO 1996!. For interior girders, live loads are distributed asa function of the girder spacing s. Both the lever rule and theStandard Specification distribution factors make very simple as-sumptions about the structural behavior of the deck and girder todistribute the loads. The LRFD Specification allows the designerto use more refined analysis methods, including finite-elementmodels of the bridge deck and girder system, to determine the liveload distribution AASHTO 1998!. In general, the finite-elementor grillage analysis procedures result in smaller distribution fac-tors Chen and Aswad 1996!.In order to simplify the process for common bridge types, theLRFD Specification includes an approximate method based onparametric analyses of selected bridge geometries that provideequations for the distribution factors based on the results of theseanalyses AASHTO 1994a, 1998!. In order to make use of theLRFD distribution factors, the designer must select a geometrythat falls within the limits of the parametric analysis on which theequations are based, i.e., the range of applicability AASHTO1998!. Some bridge geometries girder spacing and overhang dis-tances! that were acceptable under the Standard Specification maynot be within the range of applicabilityof the LRFD equations,requiring changes in bridge layout or bridge analysis using moredetailed models. The parameters considered in the calculation oftheLRFDdistributionfactorsforthisbridgewereA5360,000mm2(559 in.2); I5523109mm4(125,000in.4); yt5627mm (24.7in.); ts5203mm (8 in.); Kg51.9131012mm4(4.603106in.4); and Eprecast/Eslab51.25.As a conservative assumption for exterior girders with rigiddiaphragms, the LRFD specification for distribution factors alsoconsiders a rigid body rotation mechanism that is not consideredin the Standard Specification AASHTO 1998!. Given the factthat the diaphragms are relatively slender and discontinuous be-cause of the skew, this conservatism may be unnecessary for thisbridge.SkewThe LRFD Specification includes factors that modify the shearand moment distribution factors to account for the skew of thebridge AASHTO 1998!. For certain angles, the moment factorTable .2e-1! decreases the moment distribution factor andapparently applies to both interior and exterior girders, since thetable does not distinguish between those two cases. The shearfactor Table .3c-1! increases the shear at the obtuse cor-ners AASHTO 1998!. The skew factor is applied to both interiorand exterior beams.The Standard Specification does not include a shear factor.However, the Standard Specification design shown here used askew factor suggested by the California Department of Transpor-tation ITD 1994!. The skew factor decreased linearly from amaximum at the support to unity at the center of the girder. Onthe other hand, the LRFD skew factor does not vary with length.The constant skew factors were used as prescribed by the LRFDSpecification AASHTO 1998!.Overhang DistanceTheoverhangdistancedemustsatisfy Articles.1,.2, and C..1 of the LRFD Specification. Accordingto Section .1, deis the distance from the exterior web ofthe exterior beam and the interior edge of the curb or trafficbarrier Fig. 5!. Measuring from the sidewalk curb to the centerof the exterior web of the exterior girder of the bridge, the dis-tance de520.533m 21 ft 8 in.!.However, when considering extreme loading events, ArticleC.1 suggests that where a sidewalk is not separated fromthe roadway by a crash-worthy traffic barrier, considerationshould be given to the possibility that vehicles can mount thesidewalk AASHTO 1998!. For consistency between the vehicleFig. 3. HS-25 vehicle live loadFig. 4. HL-93 vehicle live loadJOURNAL OF BRIDGE ENGINEERING / JANUARY/FEBRUARY 2002 / 25loading, pedestrian loading, and the collision event, it was pref-erable to treat the sidewalk as part of a vehicle lane.If a vehicle is allowed on the sidewalk, then the distance mea-sured from the inside edge of the bicycle/pedestrian rail to theexterior web of the exterior girder, de51.02m 3 ft 4 in.!. Sincethe range of applicability for deis 20.305mde1.68m(21 ft 0 in.de5 ft 6 in.), it was possible to use the distribu-tion factors from Table .2d-1 AASHTO 1998!.For purposes of comparison, girders were designed once usingde520.533m 21 ft 8 in.! no vehicles on the sidewalk! andagain with de51.02m 3 ft 4 in.! vehicle on the sidewalk!. Thetwo values of the overhang represent a substantial variation in de;in fact, the lower value is slightly below the range of applicabilityfor de. Therefore, it is not surprising that there was a substantialvariation in the behavior between these two cases. For the nega-tive overhang, the largest distribution factor was obtained whenconsidering the rotation of the bridge as a rigid body with threelanes loaded, which may be overly conservative, as mentionedearlier see Article .2d; AASHTO 1998!. For the positiveoverhang with only one lane loaded, the LRFD Specification usesthe lever rule to calculate the live load distribution factor formoments in the exterior girder see Table .2d-1; AASHTO1998!. If a vehicle is allowed on the sidewalk, the overhang dis-tance becomes relatively large and the distribution factor in-creases nearly 27% over the interior girder. Reducing the over-hang distance and adjusting the girder spacing would reduce thiseffect. A comparison of the maximum live load distribution fac-tors for the Standard Specification design and the LRFD design isgiven in Table 2.Prestressing LossesThe LRFD Specification provides several options for calculatingprestressing losses. The simplest involves a lump-sum approxi-mation of the long-term losses, as given in Table -1AASHTO 1998!. More accurate estimates of losses are given inArticle AASHTO 1998!. As described in Barker andPuckett 1997!, the lump-sum estimates in Article are de-rived from yet more detailed methods outlined in Article AASHTO 1998!. Since all these methods depend on the pre-stressing force and since the prestressing force changes with time,Lwin et al. 1997! developed a time-step methodology for deter-mining the total prestressing losses. The losses were calculatedfor the exterior girder of this bridge using three methods. Theresults are summarized in Table 3.The prestressing losses are somewhat sensitive to the modulusof elasticity of the concrete at release. Typically, the girders arereleased from the forms after one to one-and-one-half days. How-ever, the equations in Article predict a strength at one-and-one-half days for exterior girders that is substantially less than thespecified strength at release, fci8. In order to force fci8used in theequationstomatchthespecifiedstrengthatrelease,fci8543MPa 6.3 ksi!, the time at transfer used in the equations wasfictitiously increased to six days, as suggested by Lwin et al.1997!. If the calculations assume that transfer takes place at arealistic value of one day, the modulus at release decreases andthe losses increase by nearly 69 MPa 10 ksi!.Since the bridge in this study is fairly short, the final designdid not change as the prestressing losses were decreased from 393MPa 57.5 ksi! to 353 MPa 51.2 ksi!. This is due in part to thelower loads imposed on the exterior girder by the LRFD assump-tions described previously.When the bridge was designed according to the StandardSpecification, the strength at release was specified to be fci8543MPa 6.3 ksi!. The final release strength was also assumed tobe fc8543MPa 6.3 ksi!, conservatively recognizing that it shouldactually be higher. In the Standard Specification design, the loadson the exterior girder were higher than the LRFD design loads.When nonstandard time-step! losses were considered, theFig. 5. Overhang dimensionsTable 2.Maximum Live Load Distribution Factors per Lane for MomentsSpecificationInterior girderExterior girderStandard Specification0.8860.859LRFD Specification including skew!0.7750.994Table .1b-1; 2 or more lanes loadedTable .2d-1; 1 lane loaded26 / JOURNAL OF BRIDGE ENGINEERING / JANUARY/FEBRUARY 2002losses were reduced and the girder required a compressivestrength fc8that was greater than 43 MPa 6.3 ksi!.Service Limit StatesThe LRFD Specification checks the compressive stresses in theprestressed concrete girder using the Service I limit stateAASHTO 1998!. The live load factor for the Service I limit stateis gLL51.0. Tensile stresses in the prestressed concrete girder arechecked using the Service III limit state AASHTO 1998!. TheService III limit state is included in the LRFD code explicitly andexclusively for the calculation of tensile stresses in prestressedgirders. The live load factor for the Service III limit state is gLL50.8. The reduced live load factor is justified in the commentaryArticle C3.4.1! by noting that this factor corresponds to a liveload that is expected to occur about once a year for bridges withtwo traffic lanes, less often for bridges with more than two trafficlanes, and about once a day for bridges with a single traffic laneAASHTO 1998!.Since the live load factor for the Service III limit state is lessthan one, it is possible to perceive this as unconservative. How-ever, the LRFD Specification was calibrated to the StandardSpecification, and in this case the LRFD Specification Strength Ilimit state produced a design that is slightly more conservativethan the Standard Specification design in terms of number ofstrands and required concrete strength.Flexural Design SummaryA comparison of the various load combinations and limit statesindicates that the exterior girders are the most heavily loadedgirders for both the Standard Specification and LRFD designs. Acomparison of the exterior girders designs shown in Table 4 indi-cates that the LRFD design requires the same number of pre-stressing strands and a slightly higher concrete strength. The in-creased strength requirements for the LRFD design are a result ofthe changes in live loads, load distribution factors, impact factors,skew factors, and prestressing losses. For example, a reduction inthe overhang distance and increase in girder spacing would tendto reduce the strength requirements for the exterior girder andequalize the strands and camber between all the girders.Shear ReinforcementFor this bridge, the LRFD Specification design requires substan-tially more shear reinforcement than the Standard Specificationdesign. As shown in Fig. 6, the LRFD-based design requires 119#16 #5! stirrups per girder, whereas the Standard Specificationdesign requires 89 #16 #5! stirrups per girder. This assumes thesame design for interior and exterior girders and also uses thesame shear reinforcement for both the obtuse and the acute endsof the girders.! The increased reinforcement was due in part to theincreased live load distribution factor for shear given in Table 5.In addition, the skew factor applied to the Standard Specificationdesign of the exterior girder varied from 1.30 at the abutmenttapering linearly to unity at midspan, whereas the skew factor forthe LRFD design is a constant along the length. The skew factorapplied to the Standard Specification design of the interior girdervaried linearly from 1.05 to unity. It is also significant to note thatthe increased live load distribution factor for skew makes it im-possible to satisfy Article -2 Eq. 5.8.3-2! in the LRFDdesign without increasing the concrete strength to fc8549 MPa7.1 ksi! AASHTO 1998!.Slab DesignFor the interior spans, the LRFD Specification specifies that theslab can be analyzed approximately by assuming it behaves as aTable 3.Prestressing LossesMethodTotal lossesMPa ksi!#Approximate lump sum Table -1!393 57.0!Article 396 57.5!Time-step353 51.2!Table 4.Girder Flexural Design SummarySpecificationNumber of strands: 12.7 mm f 1,860 MPa12in. f 270 ksi!, low-relaxationfci8Mpa ksi!#Standard3843 6.3!LRFD3845 6.5!Fig. 6. Shear reinforcement comparisonJOURNAL OF BRIDGE ENGINEERING / JANUARY/FEBRUARY 2002 / 27series of strips which shall be treated as continuous beams orsimply supported beams, as appropriate. Span length shall betaken as the center-to-center distance between the supportingcomponents. For the purpose of determining force effects in thestrip, the supporting components shall be assumed to be infinitelyrigid Article .6, emphasis added, AASHTO 1998!.The commentary notes that this is a deviation from the tra-ditional approach based on a continuity correction applied to re-sults obtained for simply supported spans AASHTO 1998!. Itdeviates from typical Standard Specification designs in that it usescenter-to-center distances rather than flange-to-flange distance tocalculate the bending moment. The deck slab was not designedempirically because the slab was supported by stay-in-place form-work, which is excluded in Article AASHTO 1998!.Therefore, the LRFD design is more complicated analytically.However, the influence coefficients provided by Barker and Puck-ett 1997! reduced the computational effort. As a result of thedifferences in their procedures, the LRFD design requires lesssteel than the Standard Specification design Table 6!.Temperature and Distribution ReinforcementThe LRFD equation for temperature reinforcement has changedas compared with the Standard Specification AASHTO 1996,1998!. However for this bridge, the amount of temperature steel isthe same for both designs.The LRFD distribution steel specification Article !uses the same equation as the Standard Specification AASHTO1996, 1998!. However, the LRFD Specification defines the effec-tive span as the distance between the webs of the girders. TheStandard Specification design considered the distance between theflanges of the girders. The Standard Specification also reduced thedistribution steel by one-half in the outer quarters of each span;the LRFD Specification does not. The Standard Specification de-sign of this bridge did not take advantage of the reduced steelrequirement in the outer quarters of each span; therefore, nomodification was required in the LRFD design. Since the LRFDSpecification increases the effective span, two additional barswere added to the distribution steel to provide steel closer to theweb face of each girder. Otherwise, the longitudinal reinforce-ment is the same for both the Standard Specification and theLRFD designs Table 7!.Deck OverhangThe LRFD design of the overhang or cantilever portion of theslab differs significantly from the Standard Specification design.According to Article , the overhang must now be designedto resist the bending moment generated by a collision of a vehiclewith the rail AASHTO 1998!. Experimental values for the colli-sion force were not available, so the force was based on a yieldline analysis as described in Article A13.3 AASHTO 1998!.Even with the decreased load factors for the Extreme Event IIlimit state, the total bending moment for the Extreme Event IIlimit state 2213 kN m/m 247.9 k ft/ft! is substantially higherthan the total moment for the LRFD Strength I limit state, result-ing from the placement of a wheel load on the sidewalk 2105 kNm/m 223.6 k ft/ft!, or that considered in the Standard Specifica-tion load factor design, 270.3 kN m/m 215.8 k ft/ft!.It was not possible to create a practical design that could carrythe increased moment with a 203 mm 8 in.! slab depth. A bridgedesigned purely to LRFD Specifications would probably have asmaller overhang and adjusted girder spacings. However, it wouldbe very difficult to compare such a bridge with the StandardSpecification design. For purposes of comparison, a hypotheticaldesign was considered that doubled the slab depth in the over-hang. The additional depth made it possible to carry this increasedmoment, but it still requires a substantial increase in reinforce-ment in the top of the slab Table 8!. A variety of issues related toslab depth transition and reinforcement anchorage make this farless practical than adjusting the overhang distance and girderspacing.Abutment DesignVertical ForcesThe LRFD design for vertical loads in the abutment differs sig-nificantly from the Standard Specification design. Given the depthof the abutment and the spans between the pile caps, Article 5.6.3requires that the abutment be designed using a strut-and-tie modelAASHTO 1998!. In general, a strut-and-tie model can be some-what problematic, since the geometry of the truss must be visu-alized perhaps somewhat arbitrarily by the designer. For this abut-ment, the geometry of the truss was assumed to be as shown inFig. 7.The forces in the struts and ties can be determined from staticsincluding the customary shear and moment diagrams. For ex-ample, the maximum moment in the moment diagram will corre-spond to the maximum force in the tension tie. The force in theTable 5.Maximum Live Load Distribution Factors for ShearSpecificationInterior girderExterior girderStandardincluding skew!0.9301.27LRFDincluding skew!1.56: Table .3a-1;2 lanes loaded1.53: Table .3b-1;1 lane loadedTable 6.Transverse Slab ReinforcementSpecificationTopBottomStandard#19 140 mm#6 512in. O.C.!#19 140 mm#6 512in. O.C.!LRFD#19 190 mm#6 712in. O.C.!#19 190 mm#6 712in. O.C.!Table 7.Longitudinal Slab ReinforcementSpecificationTopBottomStandard#13 381 mm#4 15 in. O.C.!#16 152 mm#5 6 in. O.C.!LRFD#13 381 mm#4 15 in. O.C.!#16 152 mm#5 6 in. O.C.!Table 8.Transverse Reinforcement in OverhangSpecificationTop of SlabStandard, 203 mm 8 in.! slab#13 280 mm #4 11 in. O.C.!LRFD, 406 mm 16 in.! slab#19 114 mm #6 412in. O.C.!28 / JOURNAL OF BRIDGE ENGINEERING / JANUARY/FEBRUARY 2002tension tie can be calculated by taking a free-body section thoughthe truss at this point and determining the horizontal force re-quired to equilibrate the moment. The force in the diagonal strutscan be calculated by selecting a value of shear from the sheardiagram adjacent to but not at a reaction point. A free-body dia-gram is drawn at that point. Since the vertical component of thediagonal strut force is the only means of equilibrating the verticalforces, it can be calculated and resolved into the axial force in thestrut.The stress in the tension-tie members is simply the tensileforce divided by the area of the reinforcing steel. The compres-sive stresses in the struts depend on their cross-section dimen-sions. These dimensions are determined using rules specified inArticle 5.6.3 AASHTO 1998!. The allowable stresses also de-pend on the interaction of compressive and tensile stresses fromMohrs circle, as specified in Eqs. .3-1 and .3-2AASHTO 1998!. The interaction of stresses is further compli-cated at the nodal regions where the forces in the struts and tiesintersect. The interaction is handled approximately by reductionfactors that are applied to the allowable stresses in the nodalregions.The tension-tie forces can be carried using the same steel re-quired for the Standard Specification design. The compressivestresses are also adequately resisted by the Standard Specificationdesign. A significant difference between the traditional beambending analysis and the strut-and-tie model arises when the ver-tical shear in the girder bending is transformed into diagonal com-pression in the girder. In this model, the shear forces can beresisted by the concrete alone. However, the LRFD Specificationdoes require a minimum amount of both vertical and horizontalreinforcement based on gross area of concrete Article ;AASHTO 1998!. The vertical and horizontal steel is required toresist cracking, which in turn is required to provide the allowablestress levels assumed in the strut-and-tie model. The horizontaland vertical steel provided by the Standard Specification designsatisfies the LRFD requirements of Article AASHTO1998!.Horizontal ForcesThe horizontal forces specified by the LRFD Specification aresimilar to those specified by the Standard Specification, namely,earth pressures, live load surcharge, andsince this is an integralabutmenttemperature displacements from the girder. There isnot universal agreement on the levels of earth pressures to beconsidered in an integral abutment. However, with the exceptionof new load factors, the approaches are very similar. The biggestdifference lies in the calculation of the live load surcharge. TheLRFD live load surcharge is now a uniform pressure that dependson the coefficient of earth pressure k, the unit weight of the soilgs, the presence of an approach slab, and the equivalent height ofthe wall supporting the backfill AASHTO 1998!. The equivalentheight depends, in turn, on the actual height.The LRFD live load surcharge is significantly higher than theStandard Specification surcharge. Assuming the at-rest soil coef-ficient as used in the Standard Specification design, the unfac-tored LRFD live load surcharge is 11.3 kPa 237 psf!, whereas theStandard Specification live load surcharge is 6.61 kPa 138 psf!Table 9!. The difference would be much smaller if the active soilcoefficient were used. In this case, the LRFD live load surchargewould be 7.23 kPa 151 psf!. Even with the higher live loadsurcharge, the steel on the fill side of the abutment provided bythe Standard Specification design is adequate to handle the bend-ing moment.Temperature-induced contraction of the girders causes tensionin the stream side of the abutment. The LRFD temperature rangenow considers both the base temperature temperature duringconstruction! and the minimum temperatures expected at the sitebased on climatic considerations. The climatic considerations arestill very simple moderate versus cold climates!, and the tem-perature range is still the same, 21827C 080F!. However,the temperature range may increase if the bridge is assumed to bebuilt when the temperature is at the maximum for the climaticrange. As a result, the LRFD thermal displacements may be largerthan the Standard Specification displacements. However, for thisabutment, the resulting thermal forces are limited by the capacityof the piles to resist horizontal loads, and the bending moments inthe abutment do not change significantly. The steel provided inthe stream side of the abutment for the Standard Specificationdesign is adequate for the LRFD design.Wing Wall DesignThe change in the live load surcharge discussed above also ap-plies to the wing wall design. However, the most significantchange results from the loads applied to the rail. In the StandardSpecification design using ITD Office Standards, a 44.5 kN 10kip! horizontal load is applied at a specified location to determinethe bending moment the rail could impose on the wing wall ITD1994!. For the Standard Specification design, this causes a bend-ing moment of 75 kN m 55 kip ft! in the wing wall. For theLRFD design, a vehicle collision at the end of the rail was con-sidered as an extreme loading event and the maximum collisionforce was determined from a yield-line analysis of the rail. Evenwith the reduced load factors for the Extreme Event load, thecollision force increases to 269 kN 60.5 kips! and the bendingmoment increases to 545 kN m 402 kip ft!. This is a substantialincrease in bending moment, requiring a substantial increase insteel in the wing wall see Table 10!.Summary and ConclusionsThe resulting bridge design was similar in most respects to theStandard Specification design. This is expected, since the LRFDSpecification was calibrated to the Standard Specification. Thesignificant differences were: 1! the shear design where the skewFig. 7. Strut-and-tie modelTable 9.Live-Load SurchargeSpecificationAt-rest conditionkPa psf!#Standard6.61 138!LRFD11.3 237!JOURNAL OF BRIDGE ENGINEERING / JANUARY/FEBRUARY 2002 / 29factor and reinforcement requirements required an increased
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