Journal of Bridge Engineering

The American Association of State Highway and Transportation Officials (AASHTO) first published the Load and Resistance Factor Design Bridge Design Specifications (LRFD Code) in 1994 after several years of development. Each year since its inception, the reliability-based LRFD Code has been refined and improved. At present, the LRFD Code has achieved a level of stability and general acceptance by the bridge engineering community. However, the LRFD Code was initiated with a guiding principle that it could and should continually evolve. Because of this principle, it will always be a work in progress. Provided herein is a brief synopsis of the evolution of the LRFD Code that includes topics and research that are being considered at present and several possible future topics that could or should be addressed. Because the LRFD Code is the centerpiece of AASHTO’s reliability-based specifications, it is the primary focus. However, other reliability-based AASHTO manuals and guide specifications are also discussed along with the processes by which researchers and practitioners can affect future refinements for most structural AASHTO publications. The point of view is primarily that from one AASHTO member state, Illinois, from both a local and national perspective.

Statistical data from past terrorist attacks show that transportation infrastructure has been widely targeted, and a significant percentage of the attacks against transportation structures have been directed towards bridges. Recent threats to bridges in the United States validate this concern and have attracted the attention of the bridge engineering community. To address these concerns, the National Cooperative Highway Research Program sponsored a research project to investigate the response of critical bridge components subjected to blast loads. This paper includes a description of an experimental research program on ten different half-scale column designs in which the design parameters that have the greatest impact on the performance of blast-loaded bridge columns were evaluated. Interpretation of the test results and guidelines for the blast-resistant design of reinforced concrete bridge columns are provided in the companion paper written by the writers.

Guidelines for the design of critical bridge components subjected to blast loads are currently not available to the general bridge engineering community. Historically, however, transportation assets have proven to be attractive targets for terrorists because of their open access, utilization by large numbers of people, symbolic importance, and significance to commerce, in addition to a host of other reasons. To improve the current state of practice, the National Cooperative Highway Research Program sponsored a research project to investigate the response of reinforced concrete bridge columns subjected to blast loads. Part I of this manuscript details the unique experimental program carried out to assess the effects of different design parameters on overall performance under these types of loads. In the current paper, results from the test program are analyzed to identify the design parameters that most significantly influence the performance of blast-loaded reinforced concrete bridge columns. Using the scaled standoff distance as the primary variable to assess threat severity, three separate blast design categories are recommended.

One of the parameters that directly affects the seismic demand on a bridge is the excitation angle of the ground motion. Since analyzing a bridge with all possible excitation angles is impractical, combination rules have been used for computation of seismic demands. Provisions and specifications recommend the use of combination rules for computation of displacements and elastic forces, but they do not clearly suggest any combination rules for nonlinear time history analysis of bridges. This paper evaluates the $100/30$, $100/40$, and SRSS combination rules for nonlinear time history analysis of bridges. The probability of underestimation is computed for each combination rule, assuming a uniform distribution for the excitation angle. Two cases are considered for the combination rules: In the first case, only the major components of the earthquake records are used; the second case consists of using paired acceleration time histories. Results show that in the first case, the probability of underestimation is more than the second case, but using the second case produces conservative results on average, which are not economical to use in the design. Among the combination rules in the first case, $100/40$ rule has the smallest probability of underestimation of demands. Therefore, this paper suggests the use of the $100/40$ rule with the major component of earthquakes for the nonlinear time history analysis of bridges.

In the United States, barge impact-resistant bridge design typically involves static application of code-prescribed impact loads. However, the existing static analysis procedure neglects crucial dynamic effects in the impacted bridge. Recent experimental and analytical studies have uncovered important impact-related dynamic amplification of pier member demands, primarily stemming from superstructure inertial effects. These studies have focused on the use of dynamic structural analysis as a means of accounting for dynamic amplification. Although time-domain dynamic analysis techniques are capable of accurately predicting amplified member design forces, such techniques may not be warranted during preliminary design iterations when detailed structural parameters have not yet been established. In this paper, a static analysis procedure is developed that emulates pier response modes that arise during dynamic barge impact events. The proposed method provides a simplified means of approximating dynamic amplification effects and is shown to produce conservative predictions (in relation to dynamic analysis) of both pier and foundation design forces.

The recently established and publicly available database for Pile-Load Tests (PILOT) is an amalgamated, electronic source of rich information comprising both static and dynamic data for driven piles (http://srg.cce.iastate.edu/lrfd/database%20downloads.html). The database, which includes quality-assured historical data on pile-load tests dating back to 1966, is intended for use in the establishment of resistance factors for load and resistance factor design (LRFD) and a reliable construction-control method for driven pile foundations and their future developments. Although a considerable amount of geotechnical and pile-load test data is available in literature as well as in various state department of transportation files, PILOT is one of the first regional databases to be exclusively used in the development of resistance factors for LRFD and a reliable construction-control method for pile foundations. Currently providing an electronically organized assimilation of geotechnical and pile-load test data for 274 piles of various types (e.g., steel H-shaped, timber, pipe, Monotube, and concrete) driven within the state of Iowa, PILOT is comparable in quality, if not superior, to such familiar national databases used in the calibration of LRFD resistance factors for pile foundations as the FHWA Deep Foundation Load Test Database. By narrowing geographical boundaries while maintaining a high number of pile-load tests, PILOT exemplifies a model for effective regional LRFD calibration procedures. Using the findings associated with a regional calibration of LRFD resistance factors for the construction control of driven piles in Iowa by means of dynamic pile-driving formulas, the economy gain realized with a regional database such as PILOT is demonstrated at the state and national/international levels.

The load and resistance factor design (LRFD) of piles embedded in layered soils that are commonly classified as sand, clay, and mixed soil sites is investigated using static analysis methods at the strength limit state. Unlike the current practice, the main emphasis of this study is to use a more clearly defined, less ambiguous classification for the sites based on the percentage of soil types present along the pile embedment length. Two different site classifications and the corresponding LRFD resistance factors are recommended for different static methods, used during the pile design stage, in accordance with the AASHTO-LRFD calibration framework. For this purpose, a total of 90 high-quality static load tests data obtained from steel $\mathrm{H}$-piles were used, including 10 load tests conducted recently on heavily instrumented steel $\mathrm{H}$-piles. The new group of data facilitated verification of the proposed methods, which were first developed based on the 80 load test data and then updated based on the entire 90 pile tests. In addition to a locally developed static method known as the Bluebook approach, several commonly adopted static analysis approaches, as well as combinations of methods, have been examined with due consideration to soil variation along the pile length. The investigation found that (1) the Bluebook method consistently provided higher resistance and efficiency factors, (2) using a 70% rule is an appropriate means to define the soil type at the site while maintaining simplicity in the design approach, and (3) utilizing a more refined site classification based on the percentage of cohesive versus cohesionless soils existing along the pile embedded length further enhanced the LRFD approach for pile foundations.

The design of deep foundations for bridge structures should ideally consider the interaction between the soil and the foundation element to properly model the side and tip resistance components. A soil-structure interaction model, such as the $t\mathrm{\text{-}}z$ model method, can be utilized to develop a load-displacement curve for a deep foundation subjected to axial loads. The load-displacement curve represents the behavior of the deep foundation over a range of applied axial loads. More importantly, however, the load-displacement curve can be analyzed by using performance-based design criteria, such as a tolerable displacement corresponding to the service limit state. The tolerable displacement of an individual deep foundation element can be selected to correspond to a movement that would cause adverse performance, excessive maintenance issues, or functionality problems with the bridge structure. In this paper, a performance-based soil-structure interaction design approach for the strength and service limit state axial design of drilled shafts using the AASHTO-LRFD approach is presented. The approach explicitly incorporates field load test data into the design to increase design efficiency while satisfying the limit states. A design example using drilled shaft load test data acquired via the O-cell technology has also been included to demonstrate the developed methodology for use in day-to-day bridge foundation design.

The orthotropic steel deck bridge is a structural system that has the potential to provide an extended service life and standardized modular design as compared to more conventional bridge construction. This paper summarizes proposed changes to the fifth edition of the AASHTO LRFD Bridge Design Specifications related to orthotropic deck bridges. The current version of AASHTO-LRFD contains provisions that provide limited guidance to complete the fatigue design. Contained within these proposed changes is a new framework for design verification, which may be based on different levels of design or physical testing. Criteria related to loads, load factors, limit states including fatigue in particular, resistance, and analysis requirements are covered in detail. Designs made according to these new provisions can be expected to perform very well and meet the design service life as per AASHTO-LRFD.

The focus of this study is to assess the performance of empirically designed reinforced concrete bridge decks versus those designed using traditional analytical design methods and to check the adequacy of both design methods by correlating the theoretical results with field observations. A case study of Buffalo Creek Bridge was selected for this study, because it was originally constructed with an empirical deck that developed severe cracking and required demolition, and was reconstructed again with a traditional deck. Three-dimensional finite-element modeling of the Buffalo Creek bridge superstructure was developed, taking into consideration real-life loading configurations of environmental loads. Both the empirical deck and the current traditionally designed deck were modeled and the state-of-stress developed in each design was identified. The connections between the steel main girders and the concrete deck were identified as the primary constraints for deck expansion and contraction in the transverse direction; hence, high tensile stresses were developed over the girders in the transverse direction. Additionally, the sharp edge of the clip angle protruding into the concrete deck, in addition to the top of the slope of the stay-in-place forms, were identified as stress risers that contribute to the longitudinal cracking problem. Therefore, additional reinforcement is needed in these areas to control the occurrence of such cracks.

The live load distribution-factor (LLDF) equations in the AASHTO-LRFD specifications were developed under National Cooperative Highway Research Program (NCHRP) Project 12-26. These equations include limited ranges of applicability, and when these ranges are exceeded, a refined analysis must be used. Additionally, the multiple-presence factors, bias, and variability with respect to the rigorous estimates are obscurely embedded. Herein, a simplified LLDF framework is provided. The effects of analysis uncertainty, variability, and multiple presence are separated and distinctly defined. This separation provides specification writers with the opportunity to use different multiple-presence and variability models. LLDFs were calculated using several simplified methods and grillage analyses for over 1,500 bridges. Based on the comparison, two simplified methods were further studied: adjusted uniform distribution and adjusted lever rule methods. Calibration factors were used to their improve accuracy. Seventy-four “test-the-limits” bridges (11 steel) were designed to test wide ranges of girder spacing, relative transverse to longitudinal stiffness, and bridge flexural-to-torsional stiffness. The focus of this paper is on the framework. The procedure and results are similar for other bridge types.

This paper presents the results of a three-dimensional (3D) finite-element study that investigated the effect of the multipresence factor of the load-reduction factors used in the AASHTO Bridge Design Specifications. Typical one-span, two-equal-span continuous, simply supported, three- and four-lane reinforced concrete slab highway bridges were selected for this study. AASHTO HS20 design truck loads are first placed transversally in all lanes, positioned side-by-side and close to one edge of the bridge slab; this fully loaded condition served as a reference case. Reduced loading patterns are then investigated using 3D finite-element analysis (FEA), with design loads in two out of three lanes (reduced 2/3), three out of four lanes (reduced 3/4), and two out of four lanes (reduced 2/4). The longitudinal bending moments and deflection results obtained for the FEA for reduced and fully loaded bridges are directly compared. Furthermore, a correlation between the reduced-load cases and AASHTO reduction factors or multiple-presence factors is made for concrete slab bridges. For the three- and four-lane bridge cases, AASHTO Standard Specifications generally correlate well with or overestimate the FEA-reduced maximum moments and edge-beam moments by up to 15% and 30%, respectively. This overestimation is more pronounced in short-span bridges. It is recommended that a reduction factor of 25% be applied only for reinforced concrete slabs with span lengths greater than 12 m (40 ft) and a reduction factor of 10% be applied for spans less than 12 m (40 ft). The AASHTO-LRFD overestimated the maximum longitudinal moments and edge-beam moments by up to 15% and 40%, respectively. This overestimation by AASHTO-LRFD, which is larger for longer spans, is increased to 40% and 55% when compared to the FEA results because of reduced moments. This research supports the current AASHTO-LRFD multiple-presence factors of 0.85 for three lanes and 0.65 for four lanes in estimating longitudinal bending moments in concrete slab bridges. The FEA results highlight the importance of considering span length in determining the multipresence factors when designing three-lane or more concrete slab bridges. This paper will assist bridge engineers in quantifying the adjustment factors used in analyzing and designing multilane reinforced concrete slab bridges.

Current AASHTO-LRFD specifications use many disparate design provisions to establish live load demands in bridge decks. As an example, approximately 17% of Chapter 4 addresses the analysis of decks. One of the AASHTO-LRFD analysis methods for decks uses an orthotropic plate model. The present AASHTO-LRFD orthotropic plate model has a single formulation for the plate torsional stiffness, and this is not generally applicable to all deck types. In this paper, new analytical expressions are developed for moment in bridge decks subjected to arbitrary patch loading considering each of the three cases of orthotropy: (1) relatively torsionally stiff, flexurally soft decks; (2) relatively uniformly thick decks (such as a reinforced concrete deck); and (3) relatively torsionally soft, flexurally stiff decks. Using these newly developed expressions, the AASHTO-LRFD notional live load models were combined with impact, multiple presence, and live load factors to determine maximum strong direction live load moments for the Strength I design limit state. Design equations were developed to estimate the maximum strong direction live load moments without performing cumbersome moving load analysis for common deck orientations. Using the proposed formulations, bridge deck strength design demands can now be treated in a unified way across different deck types using only four equations. Application of these methods can significantly reduce and simplify the analysis of decks and allow bridge engineers to make comparisons across different deck design alternatives.

In this paper, the live load factor in the Strength I Limit State in the AASHTO LRFD Bridge Design Specifications is calibrated based on state-specific traffic environments and bridge configurations. As the initial development of the live load factor in the LRFD specifications was intended to be applied at the national level, state-specific traffic conditions, such as traffic volume, truck load, or bridge configurations, were not considered in the development process. In addition, due to the lack of reliable U.S. truck weight data in the early 1990s, truck data from Ontario, Canada, collected in the 1970s were used for the initial AASHTO calibration. Hence, the application of the live load factor in the LRFD specifications may result in over- or under-designed bridges for a specific state. Through reliability analysis of bridges based on state-specific traffic and bridge conditions, the live load factor can be recalibrated to achieve both reliable and economical bridge design. In this study, the traffic data collected for 5 years at weigh-in-motion stations in Missouri are used to simulate realistic truck loads. In addition, typical bridge configurations identified from statistical analyses of 2007 National Bridge Inventory are used to define representative bridges in Missouri. Reliability analysis results using the weigh-in-motion data and the representative bridge configurations show that most bridges have reliability indexes higher than 3.5. Live load calibration factors for the design of new bridges in Missouri are proposed as a function of the bridge’s average daily truck traffic.

Anchorage zones of posttensioned structures are prone to splitting cracks, necessitating rational reinforcement design methods for anticracking in such regions. This paper presents a generalized method to calculate bursting forces in posttensioned anchorage zones. Compression-dispersion models are individually formulated for anchorage zones with single concentric, eccentric, and inclined tendons, and a unified equation for calculating bursting forces is developed accordingly. In these models, the load paths of the anchor force are mathematically visualized by infinite isostatic lines with their own geometric and physical boundary conditions. The models are demonstrated to be capable of reflecting the nature of anchorage zones with regard to the distribution of bursting stresses. Finite-element evaluation and experimental verification show that the proposed equation provides accurate and safe predictions for different loading conditions, while the AASHTO equation is found to be overly conservative in most cases. For this reason, a suggested revision to the AASHTO-LRFD Bridge Design Specifications is presented.

In 1998, AASHTO-LRFD adopted a new equation for evaluating the stress $f_{ps}$ in unbonded tendons at ultimate. In explaining the development and applicability of the new AASHTO-LRFD equation, some investigators concluded that the new equation is conservative and more rational when compared with the ACI building code approach for computing $f_{ps}$. However, in a comprehensive study carried out by the writer, it was found that while the AASHTO-LRFD equation is indeed more rational than the ACI building code approach because it accounts for continuous members, it still encounters significant scatter in predicting test data. Also, using conservative collapse mechanisms that involve loading a single span in a multispan member for all loading cases as proposed in AASHTO-LRFD leads to design inconsistencies. Based on the results of this assessment, supported by a large body of test data, an expression for evaluating the equivalent plastic-hinge length in unbonded members at ultimate was developed. The corresponding expression can be used in conjunction with the concept of a collapse mechanism for developing a general strain-compatibility model and a direct equation for evaluating $f_{ps}$ in unbonded externally or internally posttensioned continuous members. This paper illustrates the development of the strain-compatibility model and the direct-design expression and proposes that they replace Eq. 5.7.3.1.2-1 of AASHTO-LRFD for computing $f_{ps}$. A design example is provided to illustrate the use of the proposed approach.

Deterioration of concrete structures caused by corrosion of steel reinforcement requires large capital investments in order to repair or replace existing structures which may or may not be nearing the end of their expected service lives. Fiber-reinforced polymer (FRP) reinforcement has emerged as a viable alternative to conventional reinforcement with lower life cycle costs. Serviceability typically governs the design of FRP structures because of the inherent low stiffness of FRP materials. As a result, concrete members tend to exhibit high deflections, large crack widths, and a reduction in shear capacity compared to similar steel-reinforced members. This study focuses on glass fiber–reinforced polymer (GFRP) reinforced slab strips cast with self-consolidating concrete (SCC) and posttensioned with carbon fiber–reinforced polymer (CFRP) tendons to improve the serviceability, shear capacity, and deformability of slab bridges. The flexural performance of five FRP slabs and one steel-reinforced control slab are compared to the design provisions of the AASHTO Load and Resistance Factor Design (LRFD) Bridge Design Specifications.

The flexural and shear behavior of three full-scale pretensioned high-strength concrete (HSC) bridge girders, which were designed to a modified bulb tee (BT) section according to AASHTO specifications, were investigated experimentally to evaluate the applicability of high-strength concrete and a higher percentage of debonding ratio to pretensioned bridge girders. The test results indicated that performance in terms of load-carrying capacities, ductility, and crack patterns was improved by using high-strength concrete compared to predictions of AASHTO specifications. In addition, the prestressed concrete (PSC) specimen, in which higher percentages of debonded strands were used, showed superior load-carrying capacities, stiffness, and ductility compared to the specimen in which the number of partially debonded strands did not exceed 25% of the total number of strands. A parametric study on the relationship between concrete strength, debonding ratio, and maximum girder length was conducted. Cracking angle analysis was carried out and compared with the AASHTO specifications and RESPONSE 2000 program.

Condition assessment and safety verification of existing bridges and decisions as to whether a bridge requires posting currently are addressed through analysis, load testing, or a combination of these methods. The rating process is described in AASHTO’s Manual for Bridge Evaluation, which permits ratings to be determined by allowable stress, load factor, or load and resistance factor methods, the latter of which is keyed to AASHTO LRFD Bridge Design Specifications. These three rating methods may lead to differently rated capacities and posting limits for the same bridge, a situation that has serious implications with regard to public safety and the economic well-being of communities that may be affected by bridge postings or closures. This paper is the first of two papers that summarize a research program to develop improvements to the current bridge rating process using structural reliability methods. This paper appraises current bridge rating methods and summarizes a coordinated program of analysis and load testing of several bridges to support recommended improvements to the bridge rating process. The second paper presents the reliability basis for the recommended load rating and recommends specific improvements to current bridge rating methods in a format that is consistent with the load and resistance factor rating (LRFR) option in the Manual for Bridge Evaluation.

The current bridge-rating process described in AASHTO Manual for Bridge Evaluation, First Edition permits ratings to be determined by allowable stress, load factor, or load and resistance factor methods. These three rating methods may lead to different rated capacities and posting limits for the same bridge, a situation that has serious implications with regard to public safety and the economic well-being of communities that may be affected by bridge postings or closures. This paper is the second of two papers that summarize a research program to develop improvements to the bridge-rating process by using structural reliability methods. The first paper provided background on the research program and summarized a coordinated program of load testing and analysis to support the reliability assessment leading to the recommended improvements. This second paper presents the reliability basis for the recommended load rating, develops methods that closely couple the rating process to the results of in situ inspection and evaluation, and recommends specific improvements to current bridge-rating methods in a format that is consistent with the load and resistance factor rating (LRFR) option in the AASHTO Manual for Bridge Evaluation.

The current highway bridge design in the United States follows the AASHTO-LRFD specifications, which prescribe a dynamic load allowance, $IM$, of 0.33 for the dynamic effect of truck/tandem loading. Studies have shown that the $IM$ value prescribed by the LRFD code may underestimate this dynamic effect under poor road surface conditions (RSCs). One reason for this underestimation is that the $IM$ value employed in the AASHTO specifications was obtained from the statistical properties of the $IM$ relative to average RSC, as defined by the ISO 1995 standards. In addition, the $IM$, which is a random variable with certain statistical properties, was modeled as a deterministic constant in the code calibration process. In this paper, the reliability indexes of a selected group of prestressed concrete girder bridges, designed following the AASHTO-LRFD code, are calculated by modeling the $IM$ explicitly as a random variable for different RSCs. It is found that although the calculated bridge reliability indexes are usually above the target reliability index value of 3.5 under above-average RSCs, they can be significantly below the target value of 3.5 when the RSCs are below average. Following the load rating procedure proposed by the AASHTO load and resistance factor rating (LRFR) manual, it is also found that the code-employed $IM$ value may overestimate the rating factors when RSCs are below average. Based on these results, appropriate $IM$ values are suggested for different RSCs to achieve a consistent target reliability index and a reliable load rating. The results presented in this paper are particularly valuable for the rating of existing prestressed concrete girder bridges, for which the actual RSCs can be directly evaluated. The RSCs must be properly taken into account to accurately estimate the actual safety of the considered bridge.

The nonuniform normal stress distribution along the flange of thin-walled flexural members, such as box girders, is recognized as shear lag effects. Effective flange width is widely used to consider shear lag effects in bridge design. The existing provisions for effective flange width in AASHTO LRFD Specifications can be unconservative compared with this study and other design regulations worldwide. An energy-based variation analysis was used in the study to evaluate the AASHTO provisions. With extensive parametric studies, equations were proposed to calculate the effective flange width for box girders. The new provisions consider the critical factors for the shear lag behavior: geometry of the girder, loading pattern, material properties, and the existence of longitudinal stiffeners.

The design of reinforced concrete fixed-flexible twin-walled bridge piers for lateral loads is an ambiguously defined task for bridge engineers. As the bridge experiences lateral loads, primarily from temperature fluctuations and time-dependent effects, the walls undergo cracking, requiring designers to consider sectional stiffness reductions. Two types of finite-element models were generated of the recently constructed Wakota Bridge in South St. Paul, Minnesota, one using a design-level program (SAP2000) and the other using a research-level program (ABAQUS). For an arbitrary temperature load, a commonly used refined design method, implemented in the design-level program, was evaluated for accuracy of reduced section properties relative to a more descriptive progressive cracking solution provided by the research model. The refined design method with four stiffness update segments was found to provide a balance between accuracy and analysis effort. A staged construction model of the Wakota Bridge, defined in SAP2000 to incorporate time-dependent effects of the construction sequence, indicated that pier forces for the design options in the AASHTO-LRFD Specifications for simulating reduced section properties (i.e., refined analysis with stiffness updates versus gross sections with reduced load factors) correlated to within approximately 10%. Additionally, of the two temperature change procedures in the AASHTO-LRFD Specifications, Procedure B produced moments for the Wakota Bridge that were as much as 25% larger than those from Procedure A.