Development of Truck Weight Regulations Using Bridge Reliability Model

Historically, truck 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 safety levels and also ignore the cost impact of the weight regulation on the national bridge network. This paper illustrates how new truck weight regulations can be developed to provide acceptable safety levels. Target safety levels are derived from existing AASHTO bridge evaluation and rating procedures applied to structures showing adequate performance levels. Reliability indices are used to relate the statistics of bridge load effects, based on either existing or proposed truck weight regulations, to the dynamic behavior and resistance variables of existing bridges. The sensitivity of the results to various assumptions and errors in the database is also analyzed. An accompanying paper reviews the consequences of adapting such a formula on the safety of existing bridges. The deterministic analysis as well as a reliability assessment are performed in the accompanying paper to review the consequences of adapting such regulations on the U.S. bridge network using the National Bridge Inventory files.     

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.     

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.     

The beta-adrenomimetic effect of human and animal blood serum

The conventional analysis and design of highway bridges ignore the contribution of sidewalks and∕or railings in a bridge deck when calculating the flexural strength of superstructures. The presence of sidewalks and railings or parapets acting integrally with the bridge deck have the effect of stiffening the outside girders and attracting more load while reducing the load effects in the interior girders. This paper presents the results of a parametric study showing the influence of typical sidewalks and railings on wheel load distribution as well as on the load-carrying capacity of highway bridges. A typical one-span, two-lane, simply supported, composite steel girder bridge was selected in order to investigate the influence of various parameters such as: span length, girder spacing, sidewalks, and railings. A total of 120 bridges were analyzed using three-dimensional finite-element analysis. American Association of State Highway and Transportation Officials (AASHTO) HS20 design trucks were positioned in both lanes to produce the maximum moments. The finite-element analysis results were also compared with AASHTO wheel load distribution factors. The AASHTO load and resistance factor design (LRFD) wheel load distribution formula correlated conservatively with the finite-element results and all were less than the typical empirical formula (S∕5.5). The presence of sidewalks and railings were shown to increase the load-carrying capacity by as much as 30% if they were included in the strength evaluation of highway bridges.     

Structural Behavior of FRP Composite Bridge Deck Panels

Fiber-reinforced polymer (FRP) composite bridge deck panels are high-strength, corrosion resistant, weather resistant, etc., making them attractive for use in new construction or retrofit of existing bridges. This study evaluated the force-deformation responses of FRP composite bridge deck panels under AASHTO MS 22.5 (HS25) truck wheel load and up to failure. Tests were conducted on 16 FRP composite deck panels and four reinforced concrete conventional deck panels. The test results of FRP composite deck panels were compared with the flexural, shear, and deflection performance criteria per Ohio Department of Transportation specifications, and with the test results of reinforced concrete deck panels. The flexural and shear rigidities of FRP composite deck panels were calculated. The response of all panels under service load, factored load, cyclic loading, and the mode of failure were reported. The tested bridge deck panels satisfied the performance criteria. The safety factor against failure varies from 3 to 8.     

Field Performance of FRP Bridge Repairs

Many reinforced concrete bridges throughout the United States on county and state highway systems are deteriorated and∕or distressed to such a degree that structural strengthening of the bridge or reducing the allowable truck loading on the bridge by load posting is necessary to extend the service life of the bridge. The structural performance of many of these bridges can be improved through external bonding of fiber-reinforced plastic (FRP) laminates or plates. This paper describes the rehabilitation of an existing concrete bridge in Alabama through external bonding of FRP plates to the bridge girders. Field load tests were conducted before and after application of the FRP plates, and the response of the bridge to test vehicle loadings was recorded. Results of the field tests are reported, and the effects of the FRP plates on the bridge response are identified. The repaired bridge structure exhibited a decrease in steel reinforcing bar stresses and vertical midspan deflections. These decreases ranged from 4 to 12% for various static and dynamic loading cases.     

Behavior of RCC T-Beam Bridges with Cross Diaphragms in Nonlinear Range

Behavior of reinforced cement concrete (RCC) T-beam bridges with cross diaphragms is studied for a realistic range of values of three parameters, such as span, type of loading (specified by Indian Roads Congress), and type of bridge deck layout. The method used for this study is based on the grillage idealization of RCC T-beam bridge superstructures. Material nonlinearity is considered through elastoplastic idealization of moment curvature and torque-twist relationships of the cross section. Geometrical nonlinearity has been neglected. The important conclusions which have emerged from this study are as follows: The behavior of RCC T-beam bridge superstructures can be broadly classified into two categories depending on the type and location of formation of the first plastic hinge. Category I is identified with the formation of first plastic hinge, which is a torsional hinge in the mid outer cross girders. Category II is identified with the formation of the first plastic hinge, which is a flexural hinge in the exterior longitudinal girder under the maximum loading. Bridge superstructures falling under Category I are associated with a greater degree of redistribution and more ductility as compared to those under Category II.     

Rating and Reliability of Existing Bridges in a Network

Currently, the load rating is the method used by State DOTs for evaluating the safety and serviceability of existing bridges in the United States. In general, load rating of a bridge is evaluated when a maintenance, improvement work, change in strength of members, or addition of dead load alters the condition or capacity of the structure. The AASHTO LRFD specifications provide code provisions for prescribing an acceptable and uniform safety level for the design of bridge components. Once a bridge is designed and placed in service, the AASHTO Manual for Condition Evaluation of Bridges provides provisions for determination of the safety and serviceability of existing bridge components. Rating for the bridge system is taken as the minimum of the component ratings. If viewed from a broad perspective, methods used in the state-of-the-practice condition evaluation of bridges at discrete time intervals and in the state-of-the-art probability-based life prediction share common goals and principles. This paper briefly describes a study conducted on the rating and system reliability-based lifetime evaluation of a number of existing bridges within a bridge network, including prestressed concrete, reinforced concrete, steel rolled beam, and steel plate girder bridges. The approach is explained using a representative prestressed concrete girder bridge. Emphasis is placed on the interaction between rating and reliability results in order to relate the developed approach to current practice in bridge rating and evaluation. The results presented provide a sound basis for further improvement of bridge management systems based on system performance requirements.     

Predicted and Measured Performance of Prestressed Concrete Bridges

Testing results of six existing prestressed concrete bridges are used to evaluate analytical methodologies. These bridges cover different span lengths, number of lanes, and skew angles. Strains, load distribution factors, and ratings predicted by finite-element analyses and AASHTO code specifications are compared with those from measurements. The comparison reveals a significant difference between the analytical and test results due to the effects of many field factors. Factors that exist in reality but whose effects on bridge performance cannot easily be quantified are defined as field factors. Due to these field factors, existing bridges are different from idealized calculation models and are thus defined as field bridges. To examine this difference and to quantify their effects, some field factors are modeled in a more refined finite-element analysis. It is found that the field factors have a larger effect on the maximum strain than on the load distribution factor. Parametric studies of the effects of diaphragms, bearing stiffness, and skew angles on the load distribution and maximum strain are conducted.     

Probability-Based Bridge Network Performance Evaluation

This paper presents a comprehensive mathematical model for evaluating the overall performance of a bridge network based on probability analyses of network connectivity, user satisfaction, and structural reliability of the critical bridges in the network. A bridge network consists of all nodes of interest in a geographical region. These nodes of interest are connected to each other through multiple paths. The network performance evaluation in terms of connectivity is formulated by using an event tree technique. The network performance measure of user satisfaction deals with traffic demand and capacity of each link in the network. Moreover, the shortest paths in terms of total traffic costs are identified by network optimization algorithms for each pair of the origin and destination nodes of interest under the specified traffic demands. Using this information, the minimum-weight spanning tree (MST) that consists of the identified shortest paths is constructed. The bridges associated with MST are defined as the critical bridges in the network. The network performance in terms of structural reliability of the critical bridges can be computed from system reliabilities of the critical bridges by using a series-parallel system model. Finally, by combining the above three criteria, a single numerical measure is proposed to evaluate the overall performance of the bridge network. This novel approach is illustrated on a group of fourteen existing bridges with different reliability profiles located in Colorado. This study provides the basis of a network-level bridge management system where lifetime reliability and life-cycle costs are the key considerations for optimal bridge maintenance strategies.     

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.     

Strength Evaluation of Deteriorated RC Bridge Columns

Condition-rating methods followed by load rating calculations are used for evaluating existing bridges in the United States. Ratings are assessed visually based on engineering expertise and experience, and in some cases supplemented by nondestructive tests. Good understanding of the effects of deterioration on the structural performance leads to better inspection procedures, planning, and cost-effective rehabilitation methods. This paper presents a bridge pier column strength evaluation method that can be adapted into a currently used bridge condition evaluation method. This method uses damaged material properties, and accounts for amount of corrosion and exposed bar length for each reinforcement, concrete loss, bond failure, and type of stresses in the corroding reinforcement. The proposed evaluation method provides a good estimate of the condition and load-carrying capacity of bridge piers that currently cannot be obtained by normal visual surveys. In addition, the proposed evaluation approach will help reduce repair costs, avoid overconservative condition ratings, and result in a more uniform level of safety of concrete bridge substructure in the United States.     

Distribution Factors for Curved Continuous Composite Box-Girder Bridges

The use of horizontally curved composite box-girder bridges in modern highway systems has become increasingly popular for economic as well as for aesthetic considerations. Based on a recent literature review on the design of box-girder bridges, it was observed that a simple design method for curved bridges, based on load distribution factors for stresses and shears, is as yet unavailable. This paper presents the results of an extensive parametric study, using a finite element method, in which the structural responses of 240 two-equal-span continuous curved box-girder bridges of various geometries were investigated. The parameters considered in this study included span-to-radius of curvature ratio, span length, number of lanes, number of boxes, web slope, number of bracings, and truck loading type. Based on the data generated from this study, empirical formulas for load distribution factors for maximum longitudinal flexural stresses and maximum deflection due to dead load as well as AASHTO live loading were deduced. An illustrative design example is presented.     

Probabilistic Strength Estimates and Reliability of Damaged Parallel Wire Cables

Cable reliability analysis involves the combined evaluation of cable capacity and cable load in a probabilistic manner. Assessment of cable capacity is only possible through visual inspections of the wires, field sampling, laboratory analysis of the degraded wire populations, and analytical techniques. In addition to a brief presentation of cable mechanics and deterministic models that approximate cable strength, this paper discusses inspection methodologies and statistical methods of estimation of the sizes of the degraded wire populations, and wire properties, leading to cable capacities. These capacities are described by probability distributions. The paper also discusses fundamentals of reliability analysis as they apply to bridge cables. Load criteria of present standard specifications (such as AASHTO or other international codes) are not applicable to long-span suspension bridges. The paper discusses criteria of bridge loading and reliability indices for bridge cables. More work is needed in the evaluation of loading for long-span bridges.     

Dynamic Performance Simulation of Long-Span Bridge under Combined Loads of Stochastic Traffic and Wind

Slender long-span bridges exhibit unique features which are not present in short and medium-span bridges such as higher traffic volume, simultaneous presence of multiple vehicles, and sensitivity to wind load. For typical buffeting studies of long-span bridges under wind turbulence, no traffic load was typically considered simultaneously with wind. Recent bridge/vehicle/wind interaction studies highlighted the importance of predicting the bridge dynamic behavior by considering the bridge, the actual traffic load, and wind as a whole coupled system. Existent studies of bridge/vehicle/wind interaction analysis, however, considered only one or several vehicles distributed in an assumed (usually uniform) pattern on the bridge. For long-span bridges which have a high probability of the presence of multiple vehicles including several heavy trucks at a time, such an assumption differs significantly from reality. A new “semideterministic” bridge dynamic analytical model is proposed which considers dynamic interactions between the bridge, wind, and stochastic “real” traffic by integrating the equivalent dynamic wheel load (EDWL) approach and the cellular automaton (CA) traffic flow simulation. As a result of adopting the new analytical model, the long-span bridge dynamic behavior can be statistically predicted with a more realistic and adaptive consideration of combined loads of traffic and wind. A prototype slender cable-stayed bridge is numerically studied with the proposed model. In addition to slender long-span bridges which are sensitive to wind, the proposed model also offers a general approach for other conventional long-span bridges as well as roadway pavements to achieve a more realistic understanding of the structural performance under probabilistic traffic and dynamic interactions.     

Bridge Structural Condition Assessment Based on Vibration and Traffic Monitoring

A stochastic model of traffic excitation on bridges is developed assuming that the arrival of vehicles traversing a bridge (modeled as an elastic beam) follows a Poisson process, and that the contact force of a vehicle on the bridge deck can be converted to equivalent dynamic loads at the nodes of the beam elements. The parameters in this model, such as the Poisson arrival rate and the stochastic distribution of vehicle speeds, are obtained by image processing of traffic video data. The model reveals that traffic excitations on bridges are spatially correlated. This important characteristic is usually incorrectly ignored in most output-only methods for the identification of bridge structural properties using traffic-induced vibration measurement data. In this study, the stochastic traffic excitation model with partial traffic information is incorporated in a Bayesian framework, to evaluate the structural properties and update their uncertainty for condition assessment of the bridge superstructure. The vehicle weights are also estimated simultaneously in this procedure. The proposed structural assessment methodology is validated on an instrumented highway bridge.     

Impact of Commercial Vehicle Weight Change on Highway Bridge Infrastructure

Heavy trucks represent a major load to highway bridges in the transportation infrastructure system. These loads are directly related to the truck weight limits of the jurisdiction, and largely determine the standard loads for bridge design and evaluation. Thus, truck weight limit is one of the major factors affecting bridge deterioration and expenditure for maintenance, repair, and/or replacement. Truck weight in this paper not only refers to the truck gross weight but also to the axle weights and spacings that affect load effects. This paper presents the concepts of a new methodology for estimating cost effects of truck weight limit changes on bridges in a transportation infrastructure network. The methodology can serve as a tool for studying impacts of such changes. The resulting knowledge is needed when examining new truck weight limits, several of which have been and are still being debated at both the state and federal levels in the United States. The development of this estimation method has considered maximizing the use of available data (such as the bridge inventory) at the state infrastructure system level. In application examples completed (but not reported herein), the costs for relatively inadequate strength of existing bridges and for increased design requirement for new bridges were found dominant in the total impact cost.     

Seismic Performance Assessment of Damage-Controlled FRP-Retrofitted RC Bridge Columns Using Residual Deformations

Despite the improved performance of fiber-reinforced plastic (FRP)-retrofitted bridges, residual deformations in the event of an earthquake are inevitable. Little consideration is currently given to these deformations when assessing seismic performance. Moreover, important structures are currently required not only to have high strength and high ductility but also to be usable and repairable after high intensity earthquakes. This paper presents a definition of an FRP-RC damage-controllable structure. An intensive study of 109 bridge columns, extracted from recent research literature on the inelastic performance of FRP retrofitted columns with lap-splice deficiencies, flexural deficiencies, or shear deficiencies, is used to evaluate the recoverability of such retrofitted columns. The residual deformation, as a seismic performance measure, is used to evaluate the performance of 39 FRP-retrofitted RC columns from the available database. Based on this evaluation, a requirement for the recoverable and irrecoverable states of FRP-RC bridges is specified. Finally, the Seismic Design Specifications of Highway Bridges for RC piers is adapted to predict the residual deformations of FRP-RC columns.     

Sensitivity of Live Load Distribution Factors to Vehicle Spacing

Two slab-on-girder bridge superstructures are analyzed using grillage models. Different live load placement configurations are investigated to determine the sensitivity of live load shear and moment to vehicle spacing. Results from both bridges show that the distribution factors are relatively insensitive to vehicle spacing. Therefore significant computational speedups are available when applying vehicle loads on an influence surface with a fixed spacing.     

Bridge Safety Evaluation Based on Monitored Live Load Effects

A novel approach to evaluating safety of existing bridges based on monitored structural responses and component conditions is presented in this paper. A limit state equation is developed for the measured strain data from structural health monitoring (SHM). The new concepts of the condition function, α(s,t), and prediction function, ζ(s,t), are introduced. The condition function is utilized to estimate the strains at locations other than the strain gauge locations. This function is related to the structural condition assessment results, strain gauge locations, and failure modes under consideration. The prediction function is used to predict the extreme values of the SHM data in the future. An illustration of the proposed approach is provided on an existing highway bridge in Pennsylvania, which had been monitored from 2001 to 2005 by the Advanced Technology for Large Structural Systems Center, a National Engineering Research Center at Lehigh University, Bethlehem, Pa. This study provides the basis for integrating achievable SHM data into structural safety evaluation, and establishes a valid platform for life-cycle, cost-oriented, and reliability-based infrastructure management systems using structural health monitoring.