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.     

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.     

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.     

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.     

Predicting Truck Load Spectra under Weight Limit Changes and Its Application to Steel Bridge Fatigue Assessment

Truck weight-limit regulations have significant influence on truck operating weights. These regulations directly influence loads applied to highway facilities, such as bridges and pavements. “Truck weight” herein collectively refers to a vehicle’s gross weight, axle weights, and axle configuration. Truck load spectra as a result of truck weight limits are important to bridge engineering in many respects, such as that of determining requirements for evaluation and design of bridges for both strength and fatigue. This paper’s objective is to present a new method for predicting truck weight spectra resulting from a change in truck weight limits. This method is needed to estimate impacts of the change on highway bridges such as accelerated fatigue accumulation. Historical and recent truck weight data are used to test and illustrate the proposed method, and the results show its good prediction capability. This method is also applied here to an example of estimating the impact on steel bridge fatigue due to a possible increase in the gross-vehicle-weight limit from 356 kN (80 kips) on five axles to 431 kN (97 kips) on six axles. Also included is an investigation of the AASHTO fatigue truck model for steel bridge evaluation. Results show that the current fatigue truck model may become invalid under the studied scenario of truck weight-limit increase.     

Impact of Posted Load Limits on Highway Bridge Reliability

The effectiveness of posted load limits in reducing annual maximum live load effects, thus enhancing bridge reliability, is investigated for 12 and 40 m simple span highway bridges. Novel analytical expressions are derived for event gross vehicle weight (GVW) distributions that account for violation of posted load restrictions, and the corresponding annual maximum GVW distributions are presented. Annual reliability indices associated with load restrictions computed using typical bridge posting criteria and different compliance levels are compared to the target reliability index. For the case of perfect compliance, a posted load restriction can significantly reduce maximum annual live load effects and so enhance the reliability. Under imperfect compliance, however, a violation rate as low as 2.5% (i.e., one illegal truck in 40 ignores the posting) causes the mean value and variability of the annual maximum live load effect distribution to increase significantly, resulting in a significant loss in reliability. Thus, unless posted loads are strictly enforced, the effectiveness of enhancing existing bridge reliability with a posted load restriction is questionable.     

Live Load Distribution in Girder Bridges Subject to Oversized Trucks

A significant challenge facing motor carriers and engineers in this nation is the limitation of vehicle size and weight based on pavement and bridge capacity. However, the current demands of society and industry occasionally require a truck to carry a load that exceeds the size and weight of the legal limit. In these cases, engineering analysis is required before a permit is issued to ensure the safety of the structures and roadways on the vehicle's route. A truck with a wheel gauge larger than the standard 1.83 m (6 ft) gauge requires additional engineering effort because the wheel load girder distribution factors (GDFs) established by AASHTO cannot be used to accurately estimate the live load in the girders. In this study, the finite-element method is used to develop modification factors for the AASHTO flexure and shear GDFs to account for oversized trucks. The results of the analysis showed that the use of the proposed modification factors with the specification-based GDFs can help increase the allowable loads on slab-on-girder bridges.     

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.     

Balancing Connectivity of Deteriorating Bridge Networks and Long-Term Maintenance Cost through Optimization

Due to aggressive environmental stressors and increasing traffic loads, highway bridges are undergoing significant deterioration in both condition and safety. Timely and adequate maintenance interventions are therefore crucial to ensure the functionality of existing bridges in a network. Under budget constraints, it is important to prioritize maintenance needs to bridges that are most significant to the functionality of the entire network. In this paper, the network-level bridge maintenance planning problem is posed as a combinatorial optimization and is automated by a genetic algorithm (GA) to select and allocate maintenance interventions of different types among networked bridges as well as over a specified time horizon. Two conflicting objective functions are considered simultaneously: (1) The overall performance of a bridge network expressed by the time-dependent reliability of connectivity between the origin and the destination locations and (2) the present value of total maintenance cost over the specified time horizon. A variety of maintenance types, which differ in unit costs as well as in effects on bridge performance in terms of improvement in structural reliability levels, are used in the optimization. An event tree analysis is carried out to obtain a closed-form expression for the network connectivity reliability. As an illustration example, the GA-based procedure is applied to deteriorating deck slabs of an existing 13-bridge network located in Colorado. It is shown that the proposed maintenance planning procedure has the capability of both prioritizing scarce maintenance needs to deteriorating bridges that are most crucial to the network performance and cost-effectively distributing maintenance interventions over the time horizon.     

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.     

Development and Implementation of a Continuous Strain Monitoring System on a Multi-Girder Composite Steel Bridge

This paper describes the implementation and evaluation of a long-term strain monitoring system on a three-span, multisteel girder composite bridge located on the interstate system. The bridge is part of a network of bridges that are currently being monitored in Connecticut. The three steel girders are simply supported, whereas the concrete slab is continuous over the interior supports. The bridge has been analyzed using the standard AASHTO Specifications and the analytical predictions have been compared with the field monitoring results. The study has included determination of the location of the neutral axes and the evaluation of the load distributions to the different girders when large trucks cross the bridge. A finite-element analysis of the bridge has been carried out to further study the distribution of live load stresses in the steel girders and to study how continuity of the slabs at the interior joints would influence the overall behavior. The results of the continuous data collection are being used to evaluate the influence of truck traffic on the bridge and to establish a baseline for long-term monitoring.     

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.     

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.     

Design and Construction of Modern Bamboo Bridges

The writers are conducting a comprehensive research program, with the goal to develop modern bamboo structures for buildings and bridges. This paper reports the design, construction, and testing of modern bamboo bridges. Laminated bamboo girders or glubam were developed and verified for satisfactory mechanical performance through full-scale testing. It was demonstrated that the laminated bamboo girders have satisfactory stiffness and load carrying capacity. The use of carbon fiber-reinforced plastics can further enhance the stiffness and capacity of the bamboo girders. Based on the test results and analysis, a 10-m long single lane roadway bridge was designed and constructed, which was the first of its kind in the world. The field tests were carried out using an over loaded two-axel truck with a total weight of 8.6 t which exceeded the given design truckload of 8.0 t. The bridge performed satisfactorily with the midspan deflection corresponding to the critical service loading condition being much smaller than the code required limit. Computer simulation of the field tests shows that the trend of the measured midspan deflection can be reasonably well captured. Examples of other bridge applications are also reported in this paper.     

Reliability-Based Assessment of Suspension Bridges: Application to the Innoshima Bridge

Many suspension and cable-stayed bridges were designed and constructed between Honshu Island and Shikoku Island in Japan. All these bridges were designed according to the allowable stress design method. In the allowable stress design method, it is not possible to quantify the reliabilities of both bridge components and the entire bridge system. Therefore, in light of current reliability-based design philosophy, there is an urgent need to assess the safety of suspension bridges from a probabilistic viewpoint. To develop cost-effective design and maintenance strategies, it is necessary to assess the condition of suspension bridges using a reliability-based approach. This is accomplished by a probabilistic finite-element geometrically nonlinear analysis. This study describes an investigation into the reliability assessment of suspension bridges. The combination of reliability analysis and geometrically nonlinear elastic analysis allows the determination of reliabilities of suspension bridges. A probabilistic finite-element geometrically nonlinear elastic code, created by interfacing a system reliability analysis program with a finite-element program, is used for reliability assessment of suspension bridges. An existing suspension bridge in Japan, the Innoshima Bridge, is assessed using the proposed code. The assessment is based on static load effects. Reliabilities of the bridge are obtained by using 2D and 3D geometrically nonlinear models. Furthermore, damage scenarios are considered to assess the effects of failure of various elements on the reliability of undamaged components and on the reliability of the bridge. Finally, sensitivity information is obtained to evaluate the dominant effects on bridge reliability.     

Dynamic Load Allowance for Through-Truss Bridges

The objective of the present study was to experimentally evaluate the statistics of dynamically induced stress levels in steel through-truss bridges as a function of bridge component type, component peak static stress, vehicle type, and vehicle speed. Better understanding of critical bridge rating parameters will enable more accurate bridge evaluations of this type of structure. Three 60-year-old, steel through-truss bridges with similar characteristics were investigated in the present study. Several bridge components on each of the three bridges were instrumented (truss members, stringers, and floor beams), and dynamic strain data were collected under controlled and normal traffic conditions. The dynamic strain histories were processed to obtain bridge component peak static response and peak dynamic response, resulting in the determination of the dynamic load allowance (DLA) for each of the instrumented bridge components for each of several truck crossings. The calculated DLA value are plotted as a function of member peak static stress for each bridge member instrumented. The DLA data are examined as a function of component type, component location, truck type, number of axles, truck speed, and truck direction. This study has demonstrated that the DLA is dependent on truck location, component location, component type, and component peak static stress but appears to be nearly independent of vehicle speed.     

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.     

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.     

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.     

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.