LFD vs. LRFD — What’sUp With the Letter ‘R’Anyway?By Michael A. Grubb, P.E.

Over the past three decades, different disci-plines of structural engineering practice have beengradually following a trend toward design for max-imum strength under factored loads. In line withthis growing trend, two ultimate strength or limitstates design approaches have evolved to improvesteel-bridge design by providing more uniform lev-els of safety than are possible using the more tradi-tional allowable or working stress design approach.The first of these limit-states design approaches(LFD) was developed in the 1960s. The secondlimit-states approach was introduced to bridgedesign in the early 1990s (LRFD) and parallels areliability-based approach that has been availablefor the design of steel building frames since 1986.This article examines the basic philosophy of eachof these design approaches in an attempt to eluci-date the important differences and similaritiesbetween the two methods.

Load Factor Design (LFD)In the mid 1960s, an advisory committee was

formed by the American Iron and Steel Institute(AISI) to review bridge-design practices and devel-op new design recommendations that would yield amore consistent and effective use of steel in high-way bridges. The efforts of this committee resultedin the publication in 1969 of the “TentativeCriteria for Load Factor Design of Steel HighwayBridges” or AISI Bulletin No. 15. After a year ofstudy and some modifications, the tentative crite-ria were adopted by AASHTO in 1970 as an alter-nate method and published in the 1971 AASHTOInterim Specifications. Since that time, the use ofLoad Factor Design (LFD) for steel bridges hascontinued to increase; it is estimated that LFD isbeing used, either all or in part, by at least 40State DOTs.

In recognition of the inherent ductility andreserve strength of steel and an improved under-standing of the structural behavior of steel bridges,LFD was developed as a method for proportioningstructural members for multiples of the design

loads to satisfy specified structural performancerequirements. A structural performance require-ment indicates what is required from a bridge at agiven load level. With properly selected multiplesof the load, LFD can ensure a design allowing: 1. the expected number of passages of ordinary

vehicles during the life of the bridge, 2. occasional passages of overload vehicles without

permanent damage, and 3. in an extreme emergency, very few passages of

exceptionally heavy vehicles. The underlyingphilosophy is to ensure both safe and serviceableperformance, while at the same time providing aconsistent live-load carrying capacity for allbridges on the system. In Allowable StressDesign (ASD), attention is focused on perfor-mance under service conditions only. LFD con-siders performance in a broader context in thatit deals with serviceability and safety separate-ly.

LFD recognizes three basic and distinct load lev-els — Service Load, Overload, and Maximum Load.Service Load represents ordinary vehicles thatmay operate on the highways without special per-mit. For design purposes, Service Load is repre-sented in AASHTO as the sum of the dead loads Dand the standard live loads plus impact L+I. Theprimary structural performance requirements atService Load are to provide adequate fatigue lifeand to control live-load deflections and concretedeck cracking. If the design is adequate for fatigueand deflection under normal traffic loads, theabsolute maximum stress due to these loads —used for design in ASD — is of little concern.Overload is defined as the maximum live load thatcan be allowed on the structure on infrequent occa-sions. Infrequent implies that the stresses causedby these loads are not subject to fatigue require-ments. The single structural performance require-ment at Overload is control of permanent deforma-tions caused by localized yielding and connectionslip to ensure good riding quality. For design pur-poses, Overload is taken as the load factor βD timesthe dead load plus the load factor βL times the liveload plus impact. The load factor βD is to allow forpossible increases in the dead load and is usuallytaken as 1.0 on the assumption that the designerwill allow for future additions to the dead load.The load factor βL allows for possible overloads andis usually taken as 5/3 or 1.67 for live loadings

BRIDGECROSSINGSPractical Information For The Bridge Industry

No. 5, March 1997

Reprinted from Modern Steel Construction

greater than or equal to AASHTO H20 loading.

Service Load and Overload address serviceabili-ty requirements. To ensure adequate safety, theMaximum Load level is introduced. The singlestructural performance requirement at MaximumLoad is that the bridge be able to safely resist theload. In LFD, this performance requirement is sat-isfied at Maximum Load through the followingrelationship:

φ (Maximum strength) > γ [βDD + βL(L+I)]

The load factor γ recognizes uncertainties thatexist in the loads and load analysis. The resistancefactor φ represents several sources of uncertaintysuch as variations in materials and section size,variations in workmanship, and approximationsmade in strength calculations. In LFD, a value of φequal to 1.0 was selected for members in flexureand shear since the maximum strength equationsin LFD for flexure and shear represent the lowerbounds of the test data. Lower values of φ arespecified for column and connection design becauseof the greater consequences of failure of these ele-ments.

For flexure and shear design in LFD, φ is shiftedto the right-hand side of the preceding equation.The resulting γ/φ term, together with the load fac-tors βD and βL, establishes the margin of safetyinherent in LFD for flexural members. The valueof the γ/φ term was established based on past expe-rience using ASD practice as a guide. The safety ofthe ASD approach has been well established, butthe live-load margin of safety is known to varywith the span because a single safety factor of1/0.55 or 1.82 is applied to both dead and live loadsin ASD. The minimum margin of safety in ASD isassociated with short spans. Therefore, it wasdecided that in order to provide both safe and eco-nomical designs in LFD, a value of γ/φ would beselected that would yield the same steel section byASD and LFD for a short simple-span bridge. Itwas determined that a value of γ/φ equal to 1.3would yield about the same minimum level of safe-ty by ASD and LFD for an approximately 45-footlong noncomposite simple-span bridge. As thespan length increases, the live-load margin of safe-ty increases slightly in LFD since different loadfactors are applied to the dead and live loads, whilethe margin of safety remains nearly constant inASD. Since φ is equal to 1.0 for flexural members,φ does not explicitly appear in the strength equa-tions for flexural members in LFD.

Load and Resistance Factor Design(LRFD)

In 1993, AASHTO adopted the Load andResistance Factor Design (LRFD) specifications forbridge design, which were developed underNCHRP Project 12-33. The LRFD specifications

were approved by AASHTO for use as alternativespecifications to the AASHTO StandardSpecifications for Highway Bridges, which containboth the ASD and LFD provisions. The LRFDspecifications were developed in response to a highlevel of interest amongst the members of theAASHTO Subcommittee on Bridges and Structuresin developing updated bridge specifications alongwith an accompanying commentary. The goal wasto develop more comprehensive specifications thatwould eliminate any gaps and inconsistencies inthe Standard Specifications, incorporate the latestin bridge research, and achieve more uniform mar-gins of safety or reliability across a wide variety ofstructures. The decision was then made to developthese new specifications in a probability basedLRFD format.

In the LRFD method, load and resistance factorsare determined through statistical studies of thevariability of loads and resistances, which is con-sidered to be a more realistic approach than theapplication of judgment-based deterministic fac-tors. In the calibration process, load and resis-tance factors are calculated to provide a targetlevel of reliability for a wide variety of structuretypes and configurations.

The reliability theory on which the LRFDmethod is based has been well-documented else-where and will not be expanded on in depth here.Essentially, the level of reliability is measuredthrough the use of a reliability index. Althoughnot strictly correct, the reliability index can bethought of in simple terms as a statistical indicatorof the fraction of times that a particular design cri-teria will be met or exceeded over the design life ofthe structure. For example, according to this sim-ple definition, a reliability index of 3.5 indicatesthat a particular design criteria may be exceededin 2 out of 10,000 cases. The reliability index iscurrently based only on the design of individualcomponents of the bridge and does not represent asystem reliability, which will typically be higher.In the calibration, a target reliability index isselected to provide a minimum acceptable marginof safety. Following the lead of LFD, past practicewas used as a guide in establishing the target reli-ability index. The primary goal during the devel-opment of the LRFD specifications was not tocause a radical departure from the basic level ofsafety inherent in the current highway system.Rather, the primary objective was to increase theuniformity of the margin of safety across thevarious structure types that are utilized onthe system.

Reliability indices were calculated for a numberof sample bridge designs extracted from plans sup-plied by State DOTs using: 1. the AASHTO HS live loading and lateral distri-

bution factors given in the Standard

Specifications in conjunction with the currentload and resistance factors specified in LFD, and

2. a new HL live-load model and new lateral distri-bution factors introduced in the AASHTO LRFDspecifications in conjunction with new load andresistance factors determined from the calibra-tion process.

The LFD designs were clustered around a relia-bility index of 3.5 with a large amount of scatter.The use of the selected LRFD load and resistancefactors in conjunction with the new live-load modeland distribution factors again resulted in a cluster-ing of the indices around the target value of 3.5,but with a greatly reduced amount of scatter indi-cating the attainment of a more uniform reliabilitythan provided by LFD procedures.

Similarities and DifferencesBoth LFD and LRFD are limit-states design

approaches that strive to achieve more uniformlive-load margins of safety for steel bridges, whilestill meeting established structural performancecriteria for serviceability and safety. While tradi-tional ASD considers performance under serviceconditions only, LFD and LRFD treat serviceabilityand safety separately. In LFD, limit-state criteriaare specified to satisfy performance criteria atthree distinct load levels: Service Load, Overloadand Maximum Load. In LRFD, similar limit-statecriteria are specified to satisfy similar performanceobjectives at four distinct limit states: the ServiceLimit State, the Fatigue and Fracture Limit State,the Strength Limit State and the Extreme EventLimit State.

Load and resistance factors are specified in eachmethod to account for various sources of uncertain-ty. In each method, lower load factors are appliedto the dead loads. The values of the load and resis-tance factors are different in the two methods.Also, in LRFD, a single load factor is applied toeach load component rather than applying sepa-rate βD and βL factors. The resistance factors arealways explicitly applied in LRFD, while the resis-tance factor of 1.0 for flexural members is implicit-ly applied in LFD. In the LRFD specifications, anattempt is also made to treat redundancy, ductilityand importance more explicitly in the design byapplying subjective modifiers to the load side of theequation.

In the LRFD specifications, the load and resis-tance factors are determined from a probability-based calibration process to achieve a more uni-form reliability index for the various components ofthe system than LFD. In the LFD specifications,the load and resistance factors are determinedusing a simpler calibration process based on judg-ment and experience to achieve a more uniformlive-load carrying capacity than is possible usingASD.

While more specific differences between theAASHTO LRFD and LFD specifications — such asdifferences in the live-load models, impact factors,lateral distribution factors, load combinations andthe design for fatigue — and their effects on theoverall design could be discussed and debated atsome length, the purpose of this discussion is toemphasize that the differences in the basic under-lying philosophies of the two methods are not allthat great. The primary difference in philosophyboils down to the procedures used to perform thecalibration in order to provide the minimumdesired level of safety. LRFD calibration proce-dures allow for an improvement in the uniformityof the margin of safety across the system and alsoprovide a more realistic and rational framework forperforming future calibrations as more is learnedabout loads and material resistances. While proba-bilistic theories are employed in the LRFD calibra-tion process, it should be kept in mind that theuser of the LRFD specification provisions need notbe well-grounded in probability theory in order toapply the provisions. Most of the LRFD resistanceequations for the design of steel-bridge componentsare in fact very similar to the resistance equationsgiven in the current LFD provisions. Thus, design-ers who are proficient with LFD procedures forsteel bridges should have little trouble convertingto LRFD, once some level of familiarity is attainedwith the revisions to the load side of the basicdesign equation that are presented in the LRFDspecifications.

Michael A. Grubb, P.E., is a Senior Steel BridgeDesign Specialist in the Pittsburgh office of HDREngineering, Inc. Prior to 1994, he served as theAssistant Manager of Bridge Engineering for AISCMarketing, Inc.

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