Vehicular Overloads: Load Model, Bridge Safety, and Permit Checking

All states in the United States issue special permits for nondivisible and∕or divisible truck overloads exceeding the weight limit of the highway jurisdiction. This causes stress levels higher than those induced by normal truck traffic. The rationality of such overstress levels has not been documented. This paper addresses several aspects of this issue. It presents (1) a method to develop live load models including overload trucks; (2) associated reliability models for assessing structural safety of highway bridges; and (3) proposed permit-load factors for overload checking in the load and resistance factor format. It shows that the proposed overload checking procedure leads to relatively uniform reliability of bridge structures. A sensitivity analysis is also presented here to assure that possible variations of the input data used to prescribe the proposed load factors will not adversely affect bridge safety. The proposed procedure is intended to be used by engineers responsible for checking overload permits. It may be included in evaluation specifications for highway bridges.     

Effect of Changing Truck Weight Regulations on U.S. Bridge Network

Historically, truck weight regulations have maintained controls on axle and gross weights with legal load formulas based on limiting allowable stresses in certain types of bridges. These stress limitations do not usually lead to consistent or defensible reliability levels and also ignore the impact of the weight regulation on the existing highway bridge network. This paper is the second part of a two-paper series. The companion paper by the first writer illustrated how new truck weight regulations can be developed to provide an acceptable reliability level. The target reliability level was derived from bridge structures designed to satisfy AASHTO standard design specifications that showed safe and adequate performance levels under current truck loading conditions. In this part of the two-paper series, a deterministic load capacity evaluation as well as a reliability assessment are performed to review the consequences of adapting such regulations on the existing U.S. bridge network. A sensitivity analysis shows how changes in the safety criteria used to develop the truck weight regulations would affect the existing bridge network. Detailed load capacity evaluations and reliability analyses also are performed on a representative sample of bridges to provide specific examples of expected changes in rating and safety levels if the proposed truck weight regulation is to be adopted.     

Live-Load Distribution Factors for Concrete Box-Girder Bridges

The current American Association of State Highway and Transportation Officials (AASHTO) Load and Resistance Factor Design (LRFD) Specifications impose fairly strict limits on the use of its live-load distribution factor for design of highway bridges. These limits include requirements for a prismatic cross section, a large span-length-to-width ratio, and a small plan curvature. Refined analyses using 3D models are required for bridges outside of these limits. These limits place severe restrictions on the routine design of bridges in California, as box-girder bridges outside of these limits are frequently constructed. This paper presents the results of a study investigating the live-load distribution characteristics of box-girder bridges and the limits imposed by the LRFD specifications. Distribution factors determined from a set of bridges with parameters outside of the LRFD limits are compared with the distribution factors suggested by the LRFD specifications. For the range of parameters investigated, results indicated that the current LRFD distribution factor formulas generally provide a conservative estimate of the design bending moment and shear force.     

Model Validation for Bridge-Road-Vehicle Dynamic Interaction System

The dynamic response of highway bridges subjected to moving truckloads has been observed to be dependent on (1) dynamic characteristics of the bridge; (2) truck configuration, speed, and lane position on the bridge; and (3) road surface roughness profile of the bridge and its approach. Historically, truckloads were measured to determine the load spectra for girder bridges. However, truckload measurements are either made for a short period of time [for example, weigh-in-motion (WIM) data] or are statistically biased (for example, weigh stations) and cost prohibitive. The objective of this paper is to present results of a 3D computer-based model for the simulation of multiple trucks on girder bridges. The model is based on the grillage approach and is applied to four steel girder bridges tested under normal truck traffic. Actual truckload data collected using a discrete bridge WIM system are used in the model. The data include axle loads, truck gross weight, axle configuration, and statistical data on multiple presence (side by side or following). The results are presented as a function of the static and dynamic stresses in each girder and compared with code provisions for dynamic load factor. The study provides an alternate method for the development of live-load models for bridge design and evaluation.     

Live-Load Distribution Factors in Prestressed Concrete Girder Bridges

This paper presents an evaluation of flexural live-load distribution factors for a series of three-span prestressed concrete girder bridges. The response of one bridge, measured during a static live-load test, was used to evaluate the reliability of a finite-element model scheme. Twenty-four variations of this model were then used to evaluate the procedures for computing flexural live-load distribution factors that are embodied in three bridge design codes. The finite-element models were also used to investigate the effects that lifts, intermediate diaphragms, end diaphragms, continuity, skew angle, and load type have on distribution factors. For geometries similar to those considered in the development of the American Association of State Highway and Transportation Officials Load and Resistance Factor Design Specifications, the distribution factors computed with the finite-element models were within 6% of the code values. However, for the geometry of the bridge that was tested, the discrepancy was 28%. Lifts, end diaphragms, skew angle, and load type significantly decreased the distribution factors, while continuity and intermediate diaphragms had the least effect. If the bridge had been designed using the distribution factors calculated with the finite-element model rather than the code values, the required concrete release strength could have been reduced by 6.9 MPa (1,000 psi) or the live load could have been increased by 39%.     

Equivalent Wheel Load Approach for Slender Cable-Stayed Bridge Fatigue Assessment under Traffic and Wind: Feasibility Study

In the current AASHTO LRFD specifications, the fatigue design considers only one design truck per bridge with 15% dynamic allowance. While this empirical approach may be practical for regular short and medium span bridges, it may not be rational for long-span bridges (e.g., span length >152.4?m or 500?ft) that may carry many heavy trucks simultaneously. Some existent studies suggested that fatigue may not control the design for many small and medium bridges. However, little research on the fatigue performance of long-span bridges subjected to both wind and traffic has been reported and if fatigue could become a dominant issue for such a long-span bridge design is still not clear. Regardless if the current fatigue design specifications are sufficient or not, a real understanding of the traffic effects on bridge performance including fatigue is desirable since the one truck per bridge for fatigue design does not represent the actual traffic condition. As the first step toward the study of fatigue performance of long-span cable-stayed bridges under both busy traffic and wind, the equivalent dynamic wheel load approach is proposed in the current study to simplify the analysis procedure. Based on full interaction analyses of a single-vehicle–bridge–wind system, the dynamic wheel load of the vehicle acting on the bridge can be obtained for a given vehicle type, wind, and driving condition. As a result, the dimension of the coupled equations is independent of the number of vehicles, through which the analyses can be significantly simplified. Such simplification is the key step toward the future fatigue analysis of long-span bridges under a combined action of wind and actual traffic conditions.     

Development of Live-Load Distribution Factors for Glued-Laminated Timber Girder Bridges

This paper presents simple relationships for calculating live-load distribution factors for glued-laminated timber girder bridges with glued-laminated timber deck panels. Analytical models were developed using the Ansys 113 finite-element program, and the results were validated using recorded data from four in-service timber bridges. The effects of the bridge span length, the spacing between girders, and the bridge width on the distribution of the live load were investigated by using the validated models. The live-load distribution factors obtained from the field test and the analytical models were compared with those obtained using the AASHTO LRFD Bridge Design Specifications2 live-load distribution relations. The comparison showed that the live-load distribution factors obtained by using the AASHTO LRFD Bridge Design Specifications2 were conservative. For this reason, statistical methods were used to develop accurate relationships that can be used to calculate the live-load distribution factors in the design of glued-laminated girder bridges.     

Comparative Study of Fatigue Provisions for the AASHTO Fatigue Guide Specifications and LRFR Manual for Evaluation

The recently developed Manual for condition evaluation and load and resistance factor rating (LRFR) of highway bridges in 2003 provides an alternative procedure for practicing engineers to evaluate the fatigue life of steel bridge structures. Although the evaluation manual maintains several aspects used in the AASHTO fatigue guide specification in 1990, it also utilizes formulas and values specified in the AASHTO LRFD bridge design specifications in 1998. A comparative study of the fatigue lives provided by the procedures in the Evaluation manual and the Guide specifications was performed using a life prediction of 14 steel bridges with different structural configurations and various fatigue details. It has been shown that longer predicted fatigue lives are typically obtained when using the Evaluation manual. The ratio of the finite evaluation fatigue lives for the two procedures was found to be in a range of 0.99–2.14.     

Inclusion of Crawl Tests and Long-Term Health Monitoring in Bridge Serviceability Analysis

Due to limited resources, structural health monitoring (SHM) of highway bridges has to be integrated in structural performance assessment in a cost-effective manner. The instrumentation and the long-term SHM procedures are generally chosen with emphasis on most critical bridge components for a particular failure mode. However, global structural analysis is necessary to obtain useful structural performance information. It is then a major challenge to use monitoring data at some locations to perform a structural reliability analysis at other locations. In this paper, a methodology for lifetime serviceability analysis of existing steel girder bridges including crawl tests and long-term monitoring information is presented. The case where the initial goal of monitoring is to provide data for a fatigue analysis of some bridge components is considered. The monitoring results are used to perform a structural reliability analysis of different sections that are critical considering serviceability of the bridge. Limit state equations are used firstly by adhering to the load and strength formulas and requirements set forth in AASHTO specifications, and secondly by integrating monitoring information. Serviceability with respect to permanent deformation under overload is estimated for the girders with these two different methods and a time-dependent performance analysis is conducted by considering corrosion penetration. The proposed approach is applied to the I-39 Northbound Bridge over the Wisconsin River in Wisconsin. A monitoring program of that bridge was performed by the Advanced Technology for Large Structural Systems Center at Lehigh University.     

Locality of Truck Loads and Adequacy of Bridge Design Load

United States highway bridge design has advanced into the era of risk-based practice, milestoned by the American Association of State Highway and Transportation Officials Load and Resistance Factor Design Bridge Design Specifications. On the other hand, national and state design codes cannot specifically account for localized risk for each bridge site, which may have significantly different loading conditions from the national average. This issue is focused on here, as related to the adequacy of current bridge design loads for sites in the state of Michigan. The structural reliability indices are calculated for a randomly selected sample of new bridges from the Michigan inventory, including four major girder bridge types. Weigh-in-motion truck load data collected in Michigan are used to statistically characterize the truck load effect in the bridges’ primary members for moment and shear at critical cross sections. The reliability indices are found to vary significantly among the bridge sites and types investigated. Many of them indicate inadequate design load for the Detroit area.     

Shear Live-Load Distribution Factors for I-Girder Bridges

A full scale, single lane test bridge was used to evaluate a typical slab-on-girder bridge’s response to shear. The results of the shear load test provided the means to evaluate the level of detail for a finite element model that is required to accurately replicate the behavior of bridges subject to shear loads. This finite element modeling scheme was then used to evaluate more than 200 finite element bridge models. The bridge models investigated the effects of girder spacing, span length, overhang distance and skew angle on the shear live-load distribution factor. The finite element shear distribution factors were compared with those calculated according to the American Association of State Highway and Transportation Officials load and resistance factor design (AASHTO LRFD) specifications. It was found that the AASHTO LRFD procedure accurately predicted the shear distribution factor for changes in girder spacing and span length. However, the LRFD shear distribution factor for the exterior girder was found to be unconservative for certain overhang distances and overly conservative for the interior girder for higher skew angles. Alternative equations are provided for the single and multilane exterior girder correction factor.     

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.     

Wheel Load Distribution in Simply Supported Concrete Slab Bridges

This paper presents the results of a parametric study related to the wheel load distribution in one-span, simply supported, multilane, reinforced concrete slab bridges. The finite-element method was used to investigate the effect of span length, slab width with and without shoulders, and wheel load conditions on typical bridges. A total of 112 highway bridge case studies were analyzed. It was assumed that the bridges were stand-alone structures carrying one-way traffic. The finite-element analysis (FEA) results of one-, two-, three-, and four-lane bridges are presented in combination with four typical span lengths. Bridges were loaded with highway design truck HS20 placed at critical locations in the longitudinal direction of each lane. Two possible transverse truck positions were considered: (1) Centered loading condition where design trucks are assumed to be traveling in the center of each lane; and (2) edge loading condition where the design trucks are placed close to one edge of the slab with the absolute minimum spacing between adjacent trucks. FEA results for bridges subjected to edge loading showed that the AASHTO standard specifications procedure overestimates the bending moment by 30% for one lane and a span length less than 7.5 m (25 ft) but agrees with FEA bending moments for longer spans. The AASHTO bending moment gave results similar to those of the FEA when considering two or more lanes and a span length less than 10.5 m (35 ft). However, as the span length increases, AASHTO underestimates the FEA bending moment by 15 to 30%. It was shown that the presence of shoulders on both sides of the bridge increases the load-carrying capacity of the bridge due to the increase in slab width. An extreme loading scenario was created by introducing a disabled truck near the edge in addition to design trucks in other lanes placed as close as possible to the disabled truck. For this extreme loading condition, AASHTO procedure gave similar results to the FEA longitudinal bending moments for spans up to 7.5 m (25 ft) and underestimated the FEA (20 to 40%) for spans between 9 and 16.5 m (30 and 55 ft), regardless of the number of lanes. The new AASHTO load and resistance factor design (LRFD) bridge design specifications overestimate the bending moments for normal traffic on bridges. However, LRFD procedure gives results similar to those of the FEA edge+truck loading condition. Furthermore, the FEA results showed that edge beams must be considered in multilane slab bridges with a span length ranging between 6 and 16.5 m (20 and 55 ft). This paper will assist bridge engineers in performing realistic designs of simply supported, multilane, reinforced concrete slab bridges as well as evaluating the load-carrying capacity of existing highway bridges.     

Impact Factors for Horizontally Curved Composite Box Girder Bridges

This paper presents a method for determining the dynamic impact factors for horizontally curved composite single- or multicell box girder bridges under AASHTO truck loading. The bridges are modeled as three-dimensional structures using commercially available software. The vehicle is idealized as a pair of concentrated forces, with no mass, traveling in two circumferential paths parallel to the curved centerline of bridges. An extensive parametric study is conducted, in which over 215 curved composite box girder bridge prototypes are analyzed. The key parameters considered in this study are: Number of cells, number of lanes, degree of curvature, arc span length, slope of the outer steel webs, number and area of bracing and top chord systems, and truck(s) speed and truck(s) positioning. Based on the data generated from the parametric study, expressions for dynamic impact factors for longitudinal moment, reaction, and deflection are proposed as function of the ratio of the arc span length to the radius of curvature. The results from this study would enable bridge engineers to design horizontally curved composite box girder bridges more reliably and economically. Furthermore, the results can be used to potentially increase the live-load capacity of existing bridges to prevent posting or closing of the bridge.     

Live-Load Distribution Factors for Prestressed Concrete, Spread Box-Girder Bridge

This study presents an evaluation of shear and moment live-load distribution factors for a new, prestressed concrete, spread box-girder bridge. The shear and moment distribution factors were measured under a live-load test using embedded fiber-optic sensors and used to verify a finite element model. The model was then loaded with the American Association of State Highway and Transportation (AASHTO) design truck. The resulting maximum girder distribution factors were compared to those calculated from both the AASHTO standard specifications and the AASHTO LRFD bridge design specifications. The LRFD specifications predictions of girder distribution factors were accurate to conservative when compared to the finite element model for all distribution factors. The standard specifications predictions of girder distribution factors ranged from highly unconservative to highly conservative when compared to the finite element model. For the study bridge, the LRFD specifications would result in a safe design, though exterior girders would be overdesigned. The standard Specifications, however, would result in an unsafe design for interior girders and overdesigned exterior girders.     

Live-Load Analysis of a Curved I-Girder Bridge

Horizontally curved, steel girder bridges are often used in our modern infrastructural system. The curve in the bridge allows for a smother transition for traffic, which creates better road travel. However, some of the disadvantages of horizontally curved bridges are that they are more difficult to analyze, design, and sometimes construct in comparison to conventional straight bridges. This study focuses on a three-span, curved steel I-girder bridge which was tested under three boundary condition states to determine it’s response to live load. The measured live-load strains were used to calibrate a finite-element model. The finite-element design moments and distribution factors for the three condition states were then compared with the results based on the V-load method. These different boundary conditions provided the researchers a unique opportunity to evaluate the impact that these changes had on the bridges behavior. It was found that while the V-load method produced positive bending moments that were close to the finite-element moments for some of the girders, this was a result of the V-load moment being unconservative and the distribution factor being conservative.     

Full-Scale Test and Analysis of a Curved Steel-Box Girder Bridge

Since the first edition of the AASHTO Guide Specifications for Horizontally Curved Steel Girder Highway Bridges was published in 1980, there have been two more editions including many revisions to the specifications. Some changes were based on valid research results and others were based on limited or uncertain research results and information. The current edition of the specifications contains provisions that may result in unreasonably conservative load capacity ratings. In this paper, the results of field tests and analyses conducted on the Veterans’ Memorial curved steel-box girder bridge are discussed. Test and analytical results show: (1) current AASHTO guide specifications regarding the first transverse stiffener spacing at the simple end support of a curved girder may be too conservative for bridge load capacity ratings; (2) current AASHTO guide specifications may greatly overestimate the dynamic loadings of curved box girder bridges with long span lengths; and (3) a plane grid finite-element model of about 20 elements per span in the longitudinal direction can be used to analyze curved multigirder bridges with external bracings located only over supports. The research results are instructive and applicable to bridge design and bridge load-rating activities.     

Assessment of Bridge Remaining Fatigue Life through Field Strain Measurement

With the aging of existing steel bridges and the accumulated stress cycles under traffic loads, assessment of remaining fatigue life for continuing service has become more important than ever, especially for decisions on structure replacement, deck replacement, or other major retrofits. Experience from engineering practice indicates that fatigue analysis based on specification loads and distribution factors usually underestimates the remaining fatigue life of existing bridges by overestimating the live load stress ranges. Fatigue evaluation based on field-measured stress range histograms under actual traffic load proves to be a more accurate and efficient method for existing bridges. This paper describes the application of such a method in assessing the remaining fatigue life of bridge structures. Current AASHTO specifications for fatigue evaluation of existing bridges are reviewed and compared. Case studies of three major highway bridges are discussed. Finally, a procedure is proposed for evaluating fatigue life of existing bridges through field strain measurement.     

Seismic Effect on Highway Bridges in Chi Chi Earthquake

This paper reports the bridge damage in the Chi Chi earthquake. Damage to bridge structures may occur in the superstructure, the substructure, or the approaches. Typical types of damage are discussed and illustrated in this paper. A review of the design specifications in Taiwan is also presented to give the background on the seismic design of highway bridges in Taiwan.     

Load Distribution for a Highly Skewed Bridge: Testing and Analysis

The American Association of State Highway and Transportation Officials (AASHTO) specifications provide formulas for determining live load distribution factors for bridges. For load distribution factors to be accurate, the behavior of the bridge must be understood. While the behavior of right-angle bridges and bridges with limited skews is relatively well understood, that of highly skewed bridges is not. This paper presents a study aimed at developing a better understanding of the transverse load distribution for highly skewed slab-on-steel girder bridges. The study involved both a diagnostic field test of a recently constructed bridge and an extensive numerical analysis. The bridge tested and analyzed is a two-span, continuous, slab-on-steel composite highway bridge with a skew angle of 60°. The bridge behavior is defined based on the field test data. Finite-element analyses of the bridge were conducted to investigate the influence of model mesh, transverse stiffness, diaphragms, and modeling of the supports. The resulting test and analytical results are compared with AASHTO’s Load and Resistance Factor Design formulas for live load distribution to assess the accuracy of the current empirical formulas.