New AASHTO Guide Manual for Load and Resistance Factor Rating of Highway Bridges

This paper introduces the American Association of State Highway Officials’ (AASHTO) new Guide Manual for Condition Evaluation and Load and Resistance Factor Rating of Highway Bridges that was completed in March 2000 under a National Cooperative Highway Research Program research project and adopted as a Guide Manual by the AASHTO Subcommittee on Bridges and Structures at the 2002 AASHTO Bridge Conference. The new Manual is a companion document to the AASHTO Load and Resistance Factor Design (LRFD) Bridge Design Specifications in the same manner that the current Manual for Condition Evaluation of Bridges is to the AASHTO Standard Specifications. The new Manual is consistent with the LRFD Specifications in using a reliability based limit states philosophy and extends the provisions of the LRFD Specifications to the areas of inspection, load rating, posting and permit rules, fatigue evaluation, and load testing of existing bridges. This paper presents an overview of the manual; specifically, the new Load and Resistance Factor rating procedures are explained and the basis for their calibration is discussed.     

Effects of State Legal Loads on Bridge Rating Results Using the LRFR Procedure

The main objective of this research was to study the effects of different specified trucks on bridge rating with the load and resistance and factor rating (LRFR) procedure. Twelve specified trucks were selected for this study, which include one AASHTO design truck, three AASHTO legal trucks, and eight state legal trucks. These rating trucks were applied on 16 selected Tennessee Dept. of Transportation bridges to obtain the LRFR ratings. The selected bridges covered four commonly used bridge types, including prestressed I-beam bridges; prestressed box beam bridges; cast-in-place T-beam bridges; and steel I-beam bridges. The research results revealed that (1) LRFR AASHTO legal load ratings factors were enveloped by the LRFR HL-93 truck ratings factors, thereby confirming the validity of the LRFR tiered approach with regard to AASHTO legal loads; (2) the lighter state legal trucks were enveloped by the HL-93 loads, whereas the heavier state trucks with closer axle spacing typically resulted in load ratings that governed over the HL-93 loads; and (3) the bridges with both high average daily truck traffic and short spans were more likely to be governed by state legal load ratings instead of HL-93 load ratings.     

Steel Girder Design per AASHTO LRFD Specifications (Part 2)

This is the second of two companion papers discussing and illustrating the AASHTO LRFD Bridge Design Specifications for the design of steel girders subject to flexure and shear. In the first paper, notation was introduced that allows reformulation of the AASHTO design equations in a more convenient format and the design of steel I-girders in flexure was presented. The second paper addresses design of box girders for flexure and design of box and I-girders for shear. The design approach is illustrated by two detailed example problems.     

Steel Girder Design per AASHTO LRFD Specifications (Part 1)

The primary objective of this paper and its companion is to give the practicing engineer tools for quick design of steel and composite girders in flexure and shear and to provide a reference to aid with the transition to the AASHTO LRFD Specifications. The AASHTO equations are presented in a modified form, using newly introduced notation that allows formulation of most of the equations without explicit dependency on the steel strength. Based on these modified equations, charts are developed that help to visualize the sometimes complex design equations and which also may be found useful as design aids for preliminary designs. For noncompact sections the AASHTO equations are expressed consistently in a dual form that emphasizes the distinction between slender and nonslender elements. This is the first of two papers and addresses the design of I-girders for flexure.     

Assessment of AASHTO LRFD Specifications for Hybrid HPS 690W Steel I-Girders

This paper details research conducted to determine the applicability of the 2nd and 3rd editions of the AASHTO LRFD Specifications to hybrid I-girders fabricated from high-performance steel (HPS) 690W (100?ksi) flanges and HPS 480W (70?ksi) webs. Specifically, the scope of this paper is to evaluate the applicability of the negative moment capacity prediction equations for noncomposite I-girders subjected to moment gradient. This evaluation is carried out using three-dimensional nonlinear finite-element analysis to determine the ultimate bending capacity of a comprehensive suite of representative hybrid girders. In addition, a design study was conducted to assess the economical feasibility of incorporating HPS 690W (100?ksi) in traditional bridge applications. This was accomplished by designing a series of I-girders with varying ratios of span length to girder depth (L/D ratios) for a representative three-span continuous bridge. Results of this study indicate that both the 2nd and 3rd editions of the specifications may be used to conservatively predict the negative bending capacity of hybrid HPS 690W (100?ksi) girders, however increased accuracy results from use of the 3rd edition of the AASHTO LRFD Specifications. Thus, it is concluded that the restriction placed on girders fabricated from steel with a nominal yield strength greater than 480?MPa (70?ksi) can be safely removed. Additionally, results of the design study demonstrate that significant weight saving can result from the use of hybrid HPS 100W girders in negative bending regions, and that hybrid HPS 690W/HPS 480W girders may be ideally suited to sites with superstructure depth restrictions.     

Truck Models for Improved Fatigue Life Predictions of Steel Bridges

A new fatigue load model has been developed based on weigh-in-motion (WIM) data collected from three different sites in Indiana. The recorded truck traffic was simulated over analytical bridge models to investigate moment range responses of bridge structures under truck traffic loadings. The bridge models included simple and two?equally continuous spans. Based on Miner’s hypothesis, fatigue damage accumulations were computed for details at various locations on the bridge models and compared with the damage predicted for the 240-kN (54-kip) American Association of State Highway and Transportation Officials (AASHTO) fatigue truck, a modified AASHTO fatigue truck with an equivalent effective gross weight, and other fatigue truck models. The results indicate that fatigue damage can be notably overestimated in short-span girders. Accordingly, two new fatigue trucks are developed in the present study. A new three-axle fatigue truck can be used to represent truck traffic on typical highways, while a four-axle fatigue truck can better represent truck traffic on heavy duty highways with a significant percentage of the fatigue damage dominated by eight- to 11-axle trucks.     

Truck Loads and Bridge Capacity Evaluation in China

Over the past 2–3 decades, the economic development in China has natured the establishment of a highway network with a large number of bridges. However, there are still no nationwide specification provisions for assessing their safe load carrying capacity. The research work reported herein focuses on developing reliability based requirements for this purpose. In this study, weigh-in-motion data for more than 7.3 million trucks were gathered from highways in three provinces of China, continuously over 1–16 months in 2006 and 2007. The data were processed and projected to model the live-load spectrum over 3-year and 100-year periods, respectively. The former is the required bridge inspection interval and the latter the bridge design life span, according to current Chinese maintenance and design specifications. The proposed projection method is shown to be more reliable compared with those reported. The resulting load spectra are used to assess the structural reliability of typical Chinese highway bridges at the component level. Based on the accordingly selected target reliability index, the live-load factors for bridge evaluation are developed in this study, proposed to be included in the Chinese national specifications.     

Recommended Procedures for Simplified Inelastic Design of Steel I-Girder Bridges

This paper presents summary recommendations pertaining to new AASHTO procedures for simplified inelastic design of steel I-girder bridges. First, key developments are summarized that lead to the proposed inelastic design approach. The paper then outlines a set of equations that provide an improved characterization of the inelastic moment-rotation response for a wide range of I-beams and plate girders. Effective plastic moment predictions based on these equations are combined with the recently proposed design method, resulting in greater accuracy and simplicity of the proposed approach. The ease of use of the resulting procedure is illustrated by a design example.     

Importance of Lower-Bound Capacities in the Design of Deep Foundations

There is generally a physical limit to the smallest possible capacity for a deep foundation. However, a lower bound on the capacity has rarely been accounted for in performing reliability analyses and developing reliability-based design codes. The objectives of this paper are to investigate the effect of having a lower-bound capacity on the reliability of a geotechnical engineering system and to propose a load and resistance factor design (LRFD) checking format that includes information on the lower-bound capacity in design. It is concluded that a lower-bound capacity can cause a significant increase in the calculated reliability for a geotechnical design even if it is an uncertain estimate. Two alternative LRFD formats that incorporate lower-bound capacities and that would not require substantive changes to existing codes are proposed. Real-world examples dealing with the design of onshore and offshore foundations indicate that the incorporation of a lower-bound capacity into design is expected to provide a more realistic quantification of reliability for decision-making purposes and therefore a more rational and efficient basis for design.     

Theoretical Evaluation of Flange Local Buckling for Horizontally Curved I-Girders

Curvature greatly complicates the behavior of horizontally curved steel plate girders used in bridge superstructures. The warping stress gradient across the width of I-girder flange plates reduces the vertical bending stress at which the flange plate buckles. The 2007 AASHTO Load and Resistance Factor Design Specifications eliminate the shortcomings of the 2003 AASHTO Guide Specifications for Horizontally Curved Bridges by unifying the flexural design of tangent and curved I-girder bridges. This paper evaluates flange local buckling resistance based upon theoretical and analytical models that consider the effect of stress gradient across the flange coupled with the influence of rotational resistance provided by the web. The developed equations are verified using the finite element method, and the potential impact is demonstrated using the design example presented in the Guide Specifications.     

Effect of Live-Load Deflections on Steel Bridge Performance

This paper presents an evaluation of the influence of AASHTO live-load deflection criteria on the performance of steel I-girder bridges. Background information is provided regarding previous research studies focused at understanding the role and suitability of live-load deflection limits on steel bridge design. Further, the results of an extensive survey of state transportation departments regarding the use of these limitations is provided. The results of a computer analysis package developed to evaluate the variability of these survey results are also presented. Last, a series of analyses of existing steel bridges conducted to examine the effects of the live-load deflection limits on typical and damaged bridges to determine the role that these limits play in overall superstructure performance is provided.     

Uncertainty Analysis of Micropile Pullout Based upon Load Test Results

Micropiles are applied in foundation rehabilitation projects to enhance the pullout capacity of the existing foundation system and minimize the vertical deflection of the structures. Consequently, the methods to calculate the pullout load–displacement behavior are important for the design of micropiles used for such rehabilitation projects. Production pullout load tests were performed on approximately 120 micropiles used for seismic retrofitting of the 580/980/24 freeway interchange in Oakland, Calif. These micropiles were required to satisfy the serviceability design capacity at a maximum deflection of 1.27?cm (0.5?in.), in addition to the ultimate design capacity. Because the existing structures varied in height and loading, micropiles of different pullout capacities were designed. In this paper, the measured data are using a closed-form “t–z” method to develop probability distribution functions for the model parameters. As the back-calculated model parameters are assumed to be random variables, the Monte Carlo simulation process is employed to develop a series of load–displacement curves. A method for determining the probability of micropile failure at the service limit state is developed using the results of the simulations. The method is utilized to obtain resistance factors that can be applied to LRFD based service limit- state design.     

Multiple Resistance Factor Design for Shallow Transmission Line Structure Foundations

This paper presents the development of simplified reliability-based design (RBD) equations that are suitable for spread foundations subjected to uplift. Emphasis is placed on the loading and foundation characteristics relevant to the electric utility industry. A general reliability calibration procedure is used to derive robust resistance/deformation factors for load and resistance factor design (LRFD) and multiple resistance factor design (MRFD) formats. Two target reliability indices of 3.2 and 2.6 are proposed based on an extensive study of existing designs for ultimate and serviceability limit state, respectively. The main advantage of using these RBD factors is that a known level of reliability can be consistently achieved over a wide range of design conditions. Simple design calculations using the MRFD format are shown to demonstrate their ability to account for parametric uncertainties in a rational manner.     

Relaxing the Stud Spacing Limit for Full-Depth Precast Concrete Deck Panels Supported on Steel Girders (Phase I)

The AASHTO LRFD Bridge Design Specifications state that the spacing between the shear connectors for steel girders should not exceed 610 mm (24 in.). This decision was made based on research conducted more than three decades ago. The goal of this research is to investigate the possibility of extending this limit to 1,220 mm (48 in.) for stud clusters used with full-depth precast concrete deck panels installed on steel girders. This paper presents the history of the 610 mm (24 in.) limit, various formulas developed to calculate fatigue and design capacity for stud clusters and concerns about extending the current LRFD limit. This paper also presents information on the first phase of the experimental investigation, which is conducted on push-off specimens to validate extending the limit to 1,220 mm (48 in.).     

Influence of Spatially Variable Side Friction on Single Drilled Shaft Resistance and LRFD Resistance Factors

Load and resistance factor design (LRFD) is a method that aims at meeting specified target reliabilities (probabilities of failure) of engineered systems. The present work focuses on ultimate side friction resistance for axial loads on single cylindrical drilled shaft foundations in the presence of spatially variable rock/soil strength. Core sample data are assumed to provide reliable information about local strength in terms of mean, coefficient of variation and spatial correlation structure (variogram) at a site. The geostatistical principle of support up-scaling is applied to quantify the reduction in variability between local strength and the average ultimate shaft side friction resistance without having to recur to lengthy stochastic finite difference/element simulations. Site and shaft specific LRFD resistance factors (Φ values) are given based on the assumption of lognormal load and resistance distributions and existing formulas recommended by the Federal Highway Administration. Results are efficiently represented in dimensionless charts for a wide range of target reliabilities, shaft dimensions, and geostatistical parameters including nested variograms of different types with geometric and/or zonal anisotropies. Field data of local rock strength is used to demonstrate the method and to evaluate the sensitivity of obtained resistance factors to potentially uncertain variogram parameters.     

Analytical and Experimental Investigation of Bridge Girder Shear Distribution Factors

Tests on twelve bridges (six along Interstate 55 and six along Interstate 70/270 in Illinois) were performed to determine the validity of certain provisions for calculating bearing forces in the load and resistance factor design (LRFD) and the load factor design bridge specifications. The bridges were selected to be typical of Illinois interstate highway bridges and maintain a range of parameters to study. These bridges were instrumented on their beam webs with three strain gauge rosettes installed on each beam to measure shear stresses caused by loads. Static tests and slow moving 8 km/h (5?mi/h) tests with a loaded truck in specified locations were performed. Dynamic tests at highway speeds were also completed. Finite-element models were developed and compared to the test results. The study shows that the LRFD specification procedures closely approximate the shear distribution factors determined by finite-element analysis and testing.     

Assessment of Current Load Factors for Use in Geotechnical Load and Resistance Factor Design

Load and resistance factor design (LRFD) is the standard structural design practice. In order for foundation design to be consistent with current structural design practice, the use of the same loads, load factors, and load combinations would be required. In this paper, we review the load factors presented in various LRFD codes from the United States, Canada, and Europe. A simple first-order second-moment (FOSM) reliability analysis is presented to determine appropriate ranges for the values of the load factors. These values are compared with those proposed in the codes. The comparisons between the analysis and the codes show that the values of load factors given in the codes generally fall within ranges consistent with the results of the FOSM analysis. However, it would be desirable for the successful development and adoption of the geotechnical component of LRFD codes to have uniformity of load-factor values across different codes for the loads that are common for virtually all civil structures.     

Assessment of Variable Uncertainties for Reliability-Based Design of Foundations

LRFD shows promise as a viable alternative to the present working stress design (WSD) approach to shallow foundation design. The key improvements of LRFD over the traditional WSD are the ability to provide a more consistent level of reliability and the possibility of accounting for load and resistance uncertainties separately. For LRFD to gain acceptance in geotechnical engineering, a framework for the objective assessment of resistance factors is needed. Such a framework, based on reliability analysis, is proposed in this paper. Probability density functions (PDFs), representing design variable uncertainties, are required for analysis. A systematic approach to the selection of PDFs is presented. A procedure such as that proposed provides a rational probabilistic basis for the development of LRFD methods in geotechnical engineering.     

Mechanisms Governing Fatigue, Damage, and Fracture of Commercially Pure Titanium for Viable Aerospace Applications

In this paper, the cyclic stress amplitude controlled high-cycle fatigue properties and final fracture behavior of commercially pure titanium (Grade 2) are presented and discussed. The material characterization was developed and put forth for selection and use in a spectrum of applications spanning the industries of aerospace, defense, chemical, marine, and commercial products. Test specimens were prepared from the as-received plate stock of the material with the stress axis both parallel (longitudinal) and perpendicular (transverse) to the rolling direction of the plate. The test specimens were cyclically deformed at a constant load ratio of 0.1, at different values of maximum stress, and the corresponding cycles-to-failure is presented. The cyclic fatigue fracture surfaces were examined in a scanning electron microscope to establish the macroscopic fracture mode, the intrinsic features on the fatigue fracture surface, and the role of applied stress-microstructural feature interactions in governing failure. The intrinsic features on the fracture surface as a function of maximum stress and resultant cyclic fatigue life are discussed.