Protocols for Collecting and Using Traffic Data in Bridge Design (2011)

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26 Background to Development of Draft Recommended Protocols LRFD Background The HL93 live-load model was initially developed as a notional representation of shears and moments produced by a group of vehicles routinely permitted on highways of various states under “grandfather” exclusions to weight laws. The notional load model was subsequently compared to the results of truck weight studies, selected WIM data (Ontario), and the 1991 OHBDC (Ontario Code) live-load model. These com- parisons showed that the notional load could be scaled by appropriate load factors to be representative of these other load spectra. The calibration of the AASHTO LRFD specifications is based on the top 20% of trucks in an Ontario truck weight database assembled in 1975 from a single site over only a 2-week period. In the past 30 years, truck traffic has seen significant increases in volume and weight. The goal of this project is to develop a set of protocols and methodologies for using available current truck traffic data collected at different U.S. sites and recommend a step-by-step procedure that can be followed to obtain live-load models for bridge design. The protocols are geared to address the use of national WIM data to develop and calibrate vehicular loads for LRFD superstructure design, fatigue design, deck design, and design for overload permits. Various levels of complexity are available for utilizing the site-specific truck weight and traffic data to calibrate live-load models for bridge design. A simplified calibration approach is proposed that focuses on the maximum live-load variable, Lmax for updating the live-load model or the load factor for current traffic conditions, in a manner consistent with the LRFD calibration. A more robust reliability-based approach also is presented to consider the site-to-site variations in WIM data in the calibration of live loads. Some key issues and traffic parameters that influence the estimation of traffic statistics and the maximum load effect are summarized below. Use of High-Speed WIM Sites The first condition that any set of traffic data should meet before being used for the development of load models is the elimination of bias. Truck data surveys collected at truck weigh stations and publicized locations are not accurate because they are normally avoided by illegal overweight vehicles that could control the maximum loads applied on bridge structures. Furthermore, an important parameter that controls the load imposed on the structure is related to the number of simul- taneous vehicles on the bridge, which is determined through data on truck headways under operating conditions. Accurate headway information cannot be obtained from fixed weigh stations or from truck data collected at highway bypasses. For these reasons, it is determined that truck traffic data should be collected through WIM systems that can collect simulta- neously headway information as well as truck weights and axle weights and axle configurations while remaining hidden from view and unnoticed by truck drivers. WIM Data Quality WIM data collection should not sacrifice quality for quantity. The selection of WIM system sites should focus on sites where the owners maintain a quality assurance program that regu- larly checks the data for quality and requires system repair or recalibration when suspect data are identified. Weighing accuracy is sensitive to roadway conditions. Roadway con- ditions at a WIM site can deteriorate after a system is installed and calibrated. Regular maintenance and recalibrations are essential for reliable WIM system performance. Vehicle dynam- ics plays a significant role in the force actually applied by any given axle at any given point on the roadway. Site-specific calibration is the only way that the dynamic effects of the C H A P T E R 3 Findings and Applications

pavement leading to the scale can be accounted for in the WIM scale calibration. The dynamic motion of trucks is also influenced by the vehicle design, gross weight, and suspension systems. The calibration approach should account for the vehicle dynamics and the truck traffic characteristics of each data collection site. Physical and software-related failures of equipment and transmission failures are common sources of traffic data qual- ity problems. Transmission problems can lead to gaps in the data (i.e., missing data) even though data may be continuously collected in the field. Data quality checks should be imple- mented to detect and fix “bad data” before processing. WIM Scale Calibration Heavy emphasis is placed on the calibration of WIM data collection equipment. Quality information is more important than the quantity of data collected. It is far better to collect small amounts of well-calibrated data than to collect large amounts of data from poorly calibrated scales. Even small errors in vehicle weight measurements caused by poorly calibrated sensors could result in significant errors in measured loads. Key issues con- cerning the use of WIM equipment are (1.) the calibration of WIM equipment and (2.) the monitoring of the data reported by WIM systems as a means of detecting drift in the calibration of weight sensors. Recommendations for WIM sensor cali- bration and monitoring of data are given in Appendix 5-A of the Traffic Monitoring Guide (U.S.DOT 2001). Auto-calibration is the practice by which software calculates and applies an adjustment to the scale calibration factor based on a comparison of the average of a number of measurements of front axle weights against its expected value. There are drawbacks to auto-calibration techniques currently used by some states to offset calibration errors, and it is recommended that direct WIM scale calibration be implemented. Only direct calibration of a WIM scale after it has been installed at a site ensures that it is measuring axle weights correctly. This includes a comparison of static axle weights with axle weights that are estimated from multiple vehicle passes with more than one vehicle. Comparison of static weights and dynamic weights will provide an effective check of system accuracy with regard to sensor errors and errors due to vehicle dynamic effects. For long duration counts, the scale should be calibrated initially, the traffic characteristics at that site should be recorded, and the scale’s performance should be monitored over time. The state should also perform additional, periodic, on-site calibration checks (at least two per year). These steps will ensure that the data being collected are accurate and reliable. WIM data scatter for axles is different from gross weight scatter and is usually much larger. This axle scatter should be assembled separately from the equipment calibration and should be used to modify the measured axle loads. Filtration of WIM Measurement Errors Sensitivity analyses have shown that the most important parameters affecting maximum bridge loads are those param- eters that describe the shape of the tail end of the truck load effects histogram. Current WIM technology is known to have certain levels of random measurement errors that may affect the accuracy of the load modeling results. These errors are due to the inherent inaccuracies of the WIM system itself, the difference between the dynamic weight measured and the actual static scale weight, as well as the effect of tire pressure, size, and configuration on the WIM results. Hence, it is advisable to use a statistical algorithm to filter out these errors. A standardized approach to executing the error filtering procedure will bring uniformity in the load modeling process that will utilize WIM data from various sites. To execute the filtering process, a calibration of the results of the WIM system should be made by comparing the results of the WIM to those of a static scale. This calibration process should be executed for a whole range of truck and axle weight types and configurations. The ratio of the measured weight to the actual weight (bias) for a large sample of readings is the calibration statistics that should be assembled into a histogram. A procedure for error filtering utilizing the scale calibration data is recommended as part of the load modeling protocols. Site-to-Site Variability One of the largest variability in truck traffic is site-to-site variability. Site-to-site variability of truckloads should be incorporated since the calibration of the AASHTO LRFD specifications used data from only one site in Ontario, Canada (U.S. sites were not considered). Dividing truck routes into three functional classifications will allow a systematic assess- ment of truck load spectra within a state. Each route within a functional classification group is taken to experience truck weights per vehicle type that are similar to those of other routes within that group. The classification groups routes into Interstate and non-Interstate highways. Many states allow heavier loads on non-Interstate routes under grandfather exemptions to weight laws. Interstates are further divided into urban versus rural because many urban areas have been known to experience heavier truck loads and volume due to increased commercial activity, lack of alternate modes of freight movement, and a general lack of truck weight enforcement. Truck data will be collected from WIM sites on principal arterials. The routes on the principal arterial system are sub- classified as Interstate and other principal arterials (Table 8). Urban and rural areas could have fundamentally different traffic characteristics. Consequently, this workplan provides for separate classification of urban and rural functional systems. 27

Seasonal Variability in the Traffic Stream Traffic varies over time. Traffic varies over a number of different time scales, including: • Time of day, • Day of week, and • Season (month) of the year. Most trucks follow a traditional urban pattern where week- day truck volumes are fairly constant, but on weekends, truck volumes decline considerably. Long-haul trucks are not con- cerned with the “business day”; they travel equally on all seven days of the week. WIM sites should operate continuously throughout the year to measure temporal changes in the loads carried by trucks. Where possible, more than one site within a functional group should be monitored continuously to provide a more reliable measure of seasonal change. Track- ing of seasonal changes in truck traffic is necessary to obtain representative truck weight histograms needed for various analyses. Directional Variation Most roads exhibit differences in flow by direction. Truck weights, volumes, and characteristics can also change by direc- tion. One classic example of directional differences in trucks is the movement of loaded trucks in one direction along a road, with a return movement of empty trucks. This is often the case in regions where mineral resources are extracted or near port facilities. Tracking these directional movements is impor- tant to obtain the load spectra for bridge load modeling. Lane-by-Lane Variation The vast majority of trucks (80% or more) travel in the right (drive) lane. The expected maximum gross vehicle weight (GVW) and, therefore, the expected maximum moments and shears of the trucks in the drive lane are different than those of the trucks in the passing lane. The degree of this difference seems to be dependent on the site and travel direction. The max- imum lifetime loading requires as an input the percentage of trucks that cross the bridge side by side and the lane-by-lane distribution of truck weights. Assuming that the trucks in each lane have identical distribution (as in past simplified approaches) can introduce unnecessary conservatism. Using WIM data could easily improve past estimates or assumptions of various load uncertainties for trucks in each lane. Knowing the truck weight distribution in each lane, including mean, COV, and distribution type, can improve the input parameters needed for the load modeling process. Permit Traffic versus Non-Permit Traffic In most states permit records are either not specific enough or detailed enough to allow separation of permit loads from non-permit loads in a large WIM database. Routine permits are not route-specific and are allowed unlimited trips. For LRFD bridge design it is not necessary to separate legal loads from routine permits because both are classified as unanalyzed truck loads that should be enveloped by the HL93 design loading. Protocols require that legal loads and routine permits be grouped under Strength I and heavy special permits be grouped under Strength II. The following approach was developed for grouping trucks that would be consistent from site to site: • Do not attempt to classify trucks as permit or non-permit because customarily the permit records are not reliable enough or readily accessible to do this. • Group all trucks with six or fewer axles in the Strength I calibration. These vehicles include legal trucks and routine permits or divisible load permits. These vehicles are con- sidered to be enveloped by the HL93 load model. • Group all trucks with seven or more axles in the Strength II calibration. These vehicles should include the heavy special permit loads, typically in the 150-kip GVW and above category. For a state that maintains easily accessible permit records with a well established and enforced overweight permits program it would be possible to obtain the records for authorized permits or permit vehicles for a route for a specific data collection period and separate out these heavy vehicles (Strength II) from 28 Protocols Functional Class Description FHWA Functional Class(es) A Rural Interstate Principal Arterial 1 B Urban Interstate Principal Arterial 11 C Other Principal Arterial 2, 12, 14 Table 8. Proposed classification scheme for truck weight data collection.

the illegal overloads (Strength I), both of which populate the upper tail of the histogram. With many states moving to online and Web-based permits processing, electronic records for permits should become more readily available in the future. Multiple-Presence Probabilities In many spans, the maximum lifetime truck-loading event is the result of more than one vehicle on the bridge at a time. An important step in defining nominal design load models is the modeling of multiple-presence probabilities. Many modern WIM data loggers currently in use in the United States have the capability to record and report sufficiently accurate truck arrival times for estimating multiple-presence proba- bilities. Many traffic counters routinely record data to 1/100 of a second or even a millisecond in their binary files. These time stamps allow the determination of headway separation of trucks in adjacent lanes or in the same lane and the occurrence of simultaneous or near-simultaneous load events in each lane. The sensitivity analysis has demonstrated that small changes in the number of multiple-presence events do not have a significant effect on the estimated maximum load effect over the 75-year design life. Studies done using New York WIM data during this project show that there is a strong correlation between multiple- presence and ADTT. From Figure 12 it is evident that the number of multiple presences sees a sharp drop-off on days when the ADTT is low (such as weekends). Though not linear, the graph demonstrates that multiple-presence statistics are related to the site traffic conditions. A recent study of truck multiple-presence at 25 sites across New Jersey over a period of 11 years has also provided valuable data on the relationship between truck volume and truck multiple presence (Gindy and Nassif 2006). Obtaining reliable multiple-presence statistics requires large quantities of continuous WIM data with refined time stamps, which may not be available at every site. The site ADTT could serve as one key variable for establishing a site multiple-presence value. A single WIM site can provide multiple-presence data for varying ADTT values due to daily variation in ADTT. Multiple-Presence Probabilities for Permit Loads The multiple-presence probabilities for permit trucks are significantly different from those used for normal traffic. In the LRFD, the Strength II limit state is specified for checking an owner-specified permit vehicle during the design process with a reduced load factor of 1.35. Although no guidance is given in the LRFD specifications on how this load factor was derived, a reduced load factor is considered appropriate due to the reduced likelihood of permit trucks exceeding the authorized 29 0 5 10 15 20 25 30 35 40 45 0 500 1000 1500 2000 2500 3000 ADTT M P EV EN TS MP Count Figure 12. Side-by-side events vs. ADTT—I-81 NB New York.

weight, the reduced multiple-presence likelihood, and the reduced exposure period of 1 year. The permit live-load factors are derived to account for the possibility of simultaneous presence of non-permit heavy trucks on the bridge when the permit vehicle crosses the span. Information on loads and multiple-presence probabilities for permits needs to be obtained locally or regionally through WIM measurements and considered in the Strength II design process since the data used for calibration of national codes are unlikely to be rep- resentative of all jurisdictions. LRFD Fatigue Design Since fatigue is defined in terms of accumulated stress- range cycles over the anticipated service life of the bridge, fatigue design is based on typical conditions that occur as many cycles are needed to cause a fatigue failure. The present AASHTO fatigue truck, which is based on reliability analyses, was developed using truck traffic load data taken for some 30 WIM sites in about eight states collected in the 1980s. Over 20,000 trucks were used to calculate the stress ranges and then the fatigue damage averaged according to the fatigue damage law (cubic power). The number of cycles to failure was compared with lab test data for various welded details. The fatigue truck developed (54-kip, 5-axle truck) from these studies has been incorporated into the AASHTO LRFD speci- fications and the AASHTO LRFR manual. As truck weight and volume increase and bridges are maintained in service for increasingly longer periods of time, the fatigue design and assessment issues become even more important. The AASHTO fatigue load is used to represent the variety of trucks of different types and weights in actual traffic. Applying a single truck model that may not be repre- sentative of current traffic as a standard for all fatigue design may be inaccurate or potentially unsafe. Code-based load models based on past WIM data may not adequately represent modern traffic conditions in many jurisdictions. Draft Recommended Protocols for Using Traffic Data in Bridge Design Protocols recommended for collecting and using traffic data in bridge design can be categorized into the following steps: • Step 1: Define WIM data requirements for live-load modeling; • Step 2: Selection of WIM sites for collecting traffic data for bridge design; • Step 3: Quantities of WIM data required for load modeling; • Step 4: WIM calibration and verification tests; • Step 5: Protocols for data scrubbing, data quality checks, and statistical adequacy of traffic data; • Step 6: Generalized multiple-presence statistics for trucks as a function of traffic volume; • Step 7: Protocols for WIM data analysis for one-lane load effects for superstructure design; • Step 8: Protocols for WIM data analysis for two-lane load effects for superstructure design; • Step 9: Assemble axle load histograms for deck design; • Step 10: Filtering of WIM sensor errors/WIM scatter from Measured WIM histograms; • Step 11: Accumulated fatigue damage and effective gross weight from WIM data; • Step 12: Lifetime maximum load effect Lmax for super- structure design; and • Step 13: Develop and calibrate vehicular load models for bridge design. The steps to be followed are described in detail in the remainder of this chapter. Step 1. Define WIM Data Requirements for Live-Load Modeling An aim of these processes is to capture weight data appro- priate for national use or data specific to a state or local juris- diction where the truck weight regulations and/or traffic conditions may be significantly different from national stan- dards. The objective is to use data from existing WIM sites to develop live-load models for bridge design. The models will be applicable for the strength and fatigue design of bridge mem- bers, including bridge decks and design vehicles for overload permitting. The traffic data needs for live-load modeling are summarized as follows. • Data needed for calibration of superstructure (Strength I) design load models include – Lane-by-lane truck type distribution, total weights, and axle weights and spacings with particular emphasis on the tails of the weight histograms; – Headways and multi-presence for single, two, or more lanes including side by side, staggered and following trucks, which are of particular interest for multi-span or longer single-span bridges (how headways are affected by truck volumes is important for developing models that take into consideration local or regional traffic patterns); and – Calibration statistics for the WIM scale to filter out sensor errors. • Data needed for overload permitting (Strength II) include – State permit policies and routine permit types authorized for a specific route; – Where available, record of special permits authorized for a specific route during the data collection period, 30

including truck descriptions, axle weights, and axle spacings; – Information on multiple-presence for permit loads— two permit trucks side by side or a permit truck with a non-permit truck; and – WIM calibration data using overloaded test trucks, if available (if not, utilize same calibration data as for Strength I). • Data needed for calibration of deck design load models include – Common axle configurations and axle weight distribu- tions of legal trucks and permit trucks; – Frequencies of occurrences of common axle configura- tions; – Other multi-axle configurations with fixed and variable axles; – Headway information for side-by-side effects of axle groups or single axles; and – WIM scale calibration statistics for axle loads. • Data needed for calibration of fatigue load models (FATIGUE) include – Truck type distribution, total weights, and axle weights and spacings with emphasis on the most common vehi- cles rather than on the tails (this is because the fatigue process is due to the accumulation of damage from every truck crossing and is less dependent on the extreme loading events); – Frequencies of occurrences of common truck configu- rations; and – WIM scale calibration statistics. Step 2. Selection of WIM Sites for Collecting Traffic Data for Bridge Design • Select remote WIM sites away from weigh stations. This is very important for obtaining unbiased data. Traffic monitoring unknown to the truck drivers is key. • Select sites that do not experience significant breakdowns and provide reliable year-round operation. Select sites that can provide a year’s worth of continuous data. • Select WIM sites that have been recently calibrated and are subject to a regular maintenance and quality assurance program. A review of recent WIM data will indicate if there is an obvious problem with the calibration. Perform a calibration check of the system. Accuracy of the weight data and the time stamps should be verified. Request a manual recalibration using a group of trucks of known weight and configuration if the system does not meet specified toler- ances. Calibration data must be available for filtering out measurement errors. The project will recommend data quality requirements for WIM sites used for data collection. • Select WIM sites with free-flowing traffic, where trucks usually maintain their lanes and travel speed (>10 mph), and that do not experience any significant stop-and-go traffic or traffic backups. The sites should be away from exits, on level grade, with smooth roadway surfaces near the WIM installation. Avoid sites with numerous traffic stoppages. • Select sites with WIM sensors in right lane and passing lanes, in both directions. Some sites have sensors only in the drive lane. • The user should have a good understanding of the state’s overweight permit policies that apply to the specific routes. It would be difficult to identify continuous or routine permits in the traffic stream in most states. These permits are not route-specific and are allowed unlimited trips within the period of duration for the permit. Special permits that are issued for very heavy loads are subject to restrictions on the route taken and the number of crossings made. Use records of special permits (usually available from the permit office) to identify and remove those vehicles that populate the extreme end of the load data prior to statistical processing of “random” traffic. • Select sites equipped with current sensor and equipment technologies. Regular maintenance and periodic recali- bration of any WIM system is critical for obtaining reliable traffic data. It is also important to filter out WIM data measurement errors so that they do not affect the accuracy of the load modeling results. The calibration of the WIM system will provide information on the calibration factor, , for use in the filtering process. • Preferably, the WIM system should be able to capture and record truck arrival times to the nearest 1/100th of a second, or better, to allow the determination of truck headway separations. In general, the selection of WIM sites for bridge load model- ing will depend on the geographic spread of the truck load data represented by the model. Step 2.1 Sites for National Design Live-Load Modeling • Study of truck loads can be conveniently handled by dividing the country into five regions as shown in Figure 13 (FHWA 2001). • Ten states with the highest truck populations are California, Illinois, Texas, Ohio, Florida, Pennsylvania, Oklahoma, New York, North Carolina, and Indiana (Table 9). • Select one representative state from each region. The state should have a well-established and maintained WIM program that has been in place for a number of years that could provide the data needed for load modeling. The five recommended states, one from each region, are California, Florida, Indiana, New York, and Texas (Table 10). 31

32 Figure 13. U.S. regions for truck loads. State State Ranking Based on Truck Population Region (see map, Figure 14) How Long has the WIM Program been in Operation? Total Number of High- Speed WIM Sites Number of WIM Sites on Interstates WIM Data Available for a Whole Year? California 1 WE 15 years 137 58 Yes Florida 5 SA 32 years 40 14 Yes Indiana 10 NC 15 years 52 24 Yes Michigan 11 NC 14 years 41 21 Yes Missouri 15 NC 10 years 13 7 Yes New Jersey 19 NE 13 years 64 14 Yes New York 8 NE 10+ years 21 11 Yes Ohio 4 NC 15 years 44 21 Yes Oregon 23 WE 8 years 22 18 Yes Texas 3 SG 21 years 18 6 Yes Table 9. Candidate states for national data collection for live-load modeling. State State Ranking Based on Truck Population Region How Long has the WIM Program been in Operation? Total Number of High- Speed WIM Sites Number of WIM Sites on Interstates WIM Data Available for a Whole Year? California 1 WE 15 years 137 58 Yes Florida 5 SA 32 years 40 14 Yes Indiana 10 NC 15 years 52 24 Yes New York 8 NE 10+ years 21 11 Yes Texas 3 SG 21 years 18 6 Yes Table 10. Recommended states from each of the five regions. • For each representative state, select the sites and routes for WIM data collection based on functional classifications defined in Table 8. For each functional classification, select two WIM sites, guided by the following considerations, as applicable: • Heavy freight routes or routes known to have significant permit traffic; • Bulk cargo shipping routes; • Logging routes; • Specialized equipment shipping routes; • WIM sites near ports, railroad terminals, or other truck origination points; • WIM sites near industrial facilities or mining operations; • WIM sites near landfills or waste transfer sites; • WIM sites near military installations;

• WIM sites should preferably be geographically dispersed within a state; and • WIM sites should preferably have varied truck volumes. Step 2.2 Sites for State-Specific Design Live-Load Modeling It is important to recognize that there can be significant variations in traffic conditions within a state that should be accounted for in truck weight studies. For calibrating design load models for a specific state, some broad guidelines may be given as follows: • Select two sites from each of the three highway functional classes. Where WIM sites exist, verify that WIM data from all major truck routes within a state are included (Table 11). • Each site in a functional class should preferably be from a different region of the state. • The guidelines for selecting individual WIM sites should be as discussed above under Step 2.1, Sites for National Design Live-Load Modeling. Step 2.3 Sites for Design Live-Load Modeling for a Metro Area or Transportation Hub • For calibrating load models for a city or a transportation hub within a state, select at least six WIM sites from within a 25-mile radius of the city or region. Where WIM sites exist, verify that WIM data from all major truck routes within the area of interest are included. • The guidelines for selecting individual WIM sites should be as discussed above under Step 2.1. • Where enough permanent WIM sites are not in operation, temporary WIM sites for short-term data collection may be employed. Data should be collected to capture likely seasonal variability in truck traffic. Step 2.4 Sites for Route-Specific Design Live-Load Modeling • For calibrating live-load models for a designated hauling route, select a minimum of three WIM sites on that route or on feeder routes. • The guidelines for selecting individual WIM sites should be as discussed above in Step 2.1. • Where enough permanent WIM sites are not in operation, temporary WIM sites for short-term data collection may be employed. Data should be collected to capture likely seasonal variability in truck traffic. Step 2.5. Sites for Site-Specific Design Live-Load Modeling • This sub-step would be particularly relevant to major bridge design and/or evaluation. • For calibrating site-specific load models for a specific bridge, select three WIM sites on that route or feeder routes, preferably within a distance of 25 miles of the bridge. • If permanent WIM sites are not available, a temporary WIM site may be deployed at the approaches to the bridge. Data should be collected to capture likely seasonal variability in truck traffic. WIM data shall be gathered in both travel directions. For the purposes of picking WIM data collection sites for the demonstration of the protocols for this project, one site for each functional classification in two states is proposed. In this regard, the resources available on this project were also a consideration. Step 3. Quantities of WIM Data Required for Load Modeling Some recommendations for the quantity of WIM data to be collected from each site to capture the variability in traffic loads include the following: • A year’s worth of recent continuous data at each site to observe seasonal changes of vehicle weights and volumes is preferable. • If continuous data for a year is unavailable, seek a minimum of 1 month of data for each season for each site. • Use data from all lanes in both directions of travel. Step 4. WIM Calibration and Verification Tests To ensure that high-quality data will be collected for use in bridge live-load modeling, all WIM devices used for this purpose should be required to meet performance specifications for data accuracy and reliability. Because collection of accurate 33 Functional Class FHWA Functional Classes Description WIM Sites A 1 Rural Interstate Principal Arterial 2 B 11 Urban Interstate Principal Arterial 2 C 2, 12, 14 Other Principal Arterial 2 Table 11. Sites by functional classification for WIM data collection.

traffic loading rates throughout the year is necessary to pro- vide the load data needed, the WIM systems used in this effort must meet the ASTM criteria all year long. Histori- cally, many WIM systems have had problems accurately weighing vehicles when environmental conditions have changed from those that were present when the equipment was last calibrated. Changes in pavement condition at the scale location are also known to cause problems with WIM system sensor accuracy. Pavement design procedures compute equivalent single- axle loads (ESALs) from measured axle weights using a math- ematical formula developed by AASHTO. The fourth-order relationship in this formula heavily magnifies the effects of poor scale calibration, which can lead to significant errors in determining the load experienced by a pavement and thus computing the expected pavement life. Bridge design, however, is controlled by shear and moment effects that bear a linear relationship to axle loads and axle spacings. Therefore, errors in scale calibration are not magnified to the same extent as in pavement design. Many states attempt to work around the cost of scale cali- bration by relying on a variety of auto-calibration techniques provided by WIM equipment vendors. Auto-calibration is the practice by which software calculates and applies an adjustment to the scale calibration factor. This is a com- mon technique utilized on piezo systems to account for changing sensitivity of the scale sensors to changing environ- mental conditions. It is based on a comparison of the aver- age of a number of measurements of some specific variable against its expected value. Some of these techniques adjust scale-calibration factors to known sensitivities in axle sensors for changing environmental conditions, “known” truck conditions, and equipment limitations. Although these techniques have considerable value, they are only useful after the conditions being monitored at the study site have been confirmed. A state must determine whether the auto-calibration procedure used is based on assumptions that are true for a particular site and whether enough test trucks are crossing the sensor during a given period to allow the calibration technique to function as intended. Auto-calibration may not be particularly suited to low truck volume sites. Field tests to verify that a WIM system is performing within the accuracy required is an important component of data quality assurance for bridge load mod- eling applications. Steps to ensure that the data being collected are accurate and reliable follow. Step 4.1 Initial Calibration Initial calibration of WIM equipment should follow LTPP calibration procedures or ASTM 1318 standards. Step 4.2 Periodic Monitoring Periodic monitoring of the data reported by WIM systems should be performed as a means of detecting drift in the calibration of weight sensors. Step 4.3 Periodic On-Site Calibration Checks For long duration counts, the scale should be calibrated initially, the traffic characteristics at that site should be recorded, and the scale’s performance should be monitored over time. The state should also perform additional, periodic on-site calibration checks (at least two per year). Only direct calibra- tion of a WIM scale after it has been installed at a site ensures that it is measuring axle weights correctly. This includes a comparison of static axle weights with axle weights that are estimated from multiple vehicle passes with more than one vehicle. Assemble calibration statistics for a WIM site for filtration of sensor errors during the load modeling process (see Step 11). This calibration process should be executed for a range of truck and axle weight types and configurations operating at normal highway speeds. The ratio of the measured weight to the actual weight for a large sample of readings is the calibration factor that should be assembled into a histogram. WIM data scatter for axles is different from gross weight scatter and is usually much larger. This axle scatter should be assembled separately from the equipment calibration and should be used to modify the measured axle loads. Step 5. Protocols for Data Scrubbing, Data Quality Checks, and Statistical Adequacy of Traffic Data Step 5.1 Data Scrubbing The key to developing and calibrating bridge live-load models is quality of WIM data and not quantity. High-speed WIM is prone to various errors that need to be recognized and considered in the data review process. It is important to review the WIM data to edit out “bad or unreliable data” containing unlikely trucks to ensure that only quality data is made part of the load modeling process. It is also important to recognize that unusual data are not all bad data as truck configurations are becoming increasingly more complex and truck weights are getting heavier. Slow moving traffic (<10 mph) and stop- and-go traffic could cause difficulty in separating vehicles. Two or more trucks may be read as one truck. It is there- fore important to check speed data. Trucks with very large axle spacings and excessive total wheelbase may be combin- ing separate trucks. Maximum likely axle spacing must be specified. This could be done by importing the WIM text files into a database. The filters can be used to screen the 34

database for bad data or unlikely trucks during the data transfer process. The WIM survey data should be scrubbed to include only the data that meet the quality checks. The following is a filtering protocol that was applied for screening the WIM data used in this project. Truck records that meet the following filters were eliminated: • Speed <10 mph, • Speed >100 mph, • Truck length >120 ft, • Total number of axles <3, • Record where the sum of axle spacing is greater than the length of truck, • GVW <12 kips (and max as required), • Record where an individual axle is >70 kips, • Record where the steer axle is >25 kips, • Record where the steer axle is <6 kips, • Record where the first axle spacing is <5 ft, • Record where any axle spacing is <3.4 ft, • Record where any axle is <2 kips, and • Record which has GVW +/− sum of the axle weights by more than 10% (this may indicate that the axle records provided may not be complete or accurate). The data scrubbing rules have been refined and updated as WIM data from typical sites were processed during the course of this study. Adjustments to the data scrubbing rules may need to be made to accommodate differences in traffic char- acteristics, truck configurations and weight limit compli- ance from state to state. Some newer trucks with complex axle configurations may need rules specifically tailored to fit their use. The rules do not propose a maximum GVW limit. This ensures that trucks are not excluded just because they are very heavy. The test is to see if a truck configura- tion is “realistic” based upon an understanding of feasible axle configurations. Step 5.1.1 Review of Eliminated Suspect Data Reviewing a sampling of trucks that were eliminated dur- ing the data scrubbing process is recommended to check if the process is performing as intended and that real trucks have not been inadvertently removed from the dataset. This is a valuable quality assurance check of the data scrubbing process. Comparing WIM data with permit data or data from any nearby weigh station would provide an additional check. Where feasible, short-duration monitoring of trucks using real-time WIM data could be helpful to verify scale perfor- mance and the accuracy of truck classifications. Stopping of trucks for static weighing is not recommended during such monitoring because it may bias the WIM data if the heavy overweight trucks find an alternate route to avoid detection. Step 5.2 Quality Control Checks for Scrubbed WIM Data This section describes simple quality checks performed on WIM data to quickly confirm that a properly calibrated data collection device is working as intended. It should not be confused with calibration tests. Perform the following quality control checks for each WIM site for each lane, for each month of data collection: 1. Check vehicle classification statistics (truck percentages by class) and compare results with historical values or manual counts where available for the site/route. Large deviations from expected values could indicate sensor problems. 2. Produce a GVW histogram of Class 9 trucks (5-axle semi- trailer trucks) using a 4-kip increment. Most sites will have two peaks in the GVW distribution (unloaded peak usu- ally falls between 28 kips and 32 kips; the loaded peak falls somewhere between 72 kips and 80 kips). A shift in the peaks could indicate that the scale calibration may be changing or the scale may be malfunctioning. If both peaks have shifted, the scale is probably out of calibration. 3. Compute the number and percentage of Class 9 trucks over 100 kips. If the percentage of Class 9 trucks over 100 kips is high, the scale calibration may be questionable, un- less such readings could be explained by a state’s weight and permitting laws or by known movement of heavy commodities on a route. Such readings may indicate op- erational problems with the sensor. 4. Produce a histogram of steer axle weights for Class 9 trucks. The average front axle weight for Class 9 trucks is fairly constant for most sites. It ranges between 9 kips and 11 kips. Some variations are possible due to truck character- istics and GVW. Significant deviation of steer axle weights is a sign of scale operational problems. 5. Produce a histogram of Class 9 drive tandem axle weights. Compare with mean drive axle weight for Class 9 trucks given in NCHRP Report 495 (Fu et al. 2003) (estimates wheel weights as a function of truck GVW). 6. Produce a histogram of spacing between front axles and drive tandem axles. Check mean spacing between drive tandem axles. Compare results to historical values avail- able for Class 9 trucks. Step 5.3 Assess the Statistical Adequacy of Traffic Data The proposed protocols for calculating the maximum 75-year live-load effect, Lmax, is based on the WIM truck weight and truck traffic database assembled at various sites within the jurisdiction for which the Lmax estimates are required. The protocols are based on collecting truck weight and truck traffic 35

WIM data over a period of a year in order to cover all possible seasonal variations and other short-term fluctuations in truck traffic patterns. The models used in this study assume that the WIM data is stationary in the sense that the 1-year data is representative of all subsequent years within the 75-year design life of a bridge site. Possible growth in truck weights and traffic intensities must be considered using an economic projection analysis, which is beyond the scope of this study. Furthermore, the proposed protocols assume that the tail end of the truckload effect histogram for a bridge span follows a normal distribution, the statistical properties of which are obtained from a regression analysis of the upper 5% of the data plotted on a normal probability curve. Normal probability plots of truckload effects obtained from WIM data collected at several different sites have confirmed that the upper 5% of the data approaches a straight line with a regression coefficient R2 on the order of 0.97 to 0.99 indicating that the normal distri- bution does reasonably well model the upper tail of the truck load effect histograms. The slope and intercept of the regression fit of the upper tail on the normal probability plot can then be used to find the mean and standard deviation of the normal distribution. However, the values of the slope and intercept depend on the estimates of the frequency of trucks in each bin of the histogram. In particular, the normal probability plot uses the cumulative frequencies as the basis for the calculation of the slope and intercept of the regression line and thus the mean and standard deviation of the equivalent normal distribution. The calculated values for the mean and standard deviation provide “best estimates” of these parameters. However, the process does not provide any information about the accuracy of these estimates except our understanding that these estimates will improve as the sample size increases. In order to provide some quantitative measure of the accuracy of these estimates, it is herein proposed to use statistical confidence intervals. A confidence interval of a parameter defines a range with lower and upper limits within which the true value of the parameter will lie with a prescribed probability. These confidence intervals will reflect the effect of the sample size and the number of samples that are found to lie within a bin of the truck load effect. Obviously the more data is collected, the more confidence the engineer will have in the estimated truck load effect frequencies in each category and the higher will be the accuracy of the calculated mean and standard deviations of the equivalent normal distribution. Confidence Intervals on the Cumulative Frequencies. Assume that the percent cumulative frequency in a particular bin of the load effect histogram at a given site is given as “pi” which is calculated as the total number of trucks that produced moments within the bin “i” divided by the total number of trucks, n. It can be proven that statistically speaking, this pi is an unbiased estimate of the true value pi. Thus, according to Ang and Tang (2007), the (1 − α) lower and upper confidence intervals of pi can be obtained from the following: Where kα/2 = −Φ−1(1 − α /2) and k(1−α/2) = Φ−1(1 − α/2), Φ−1(. . .) is the inverse cumulative function of the normal stan- dard distribution. If the 95% confidence limits are desired, then 1 − α = 95% leading to kα/2 = −1.96 and k(1−α/2) = +1.96. To get the 95% confidence interval on the projected maximum live-load effect Lmax, follow Step 12.2.1 but use the upper and lower limits of the cumulative frequency pi rather than the value obtained directly from the WIM data. The evaluating engineer should decide whether the resulting con- fidence intervals Lmax are sufficiently narrow. If the intervals are not adequate, more WIM data should be collected to further narrow the intervals. Step 6. Generalized Multiple-Presence Statistics for Trucks as a Function of Traffic Volume In many spans, the maximum lifetime truck-loading event is the result of more than one vehicle on the bridge at a time. Refined time stamps are critical to the accuracy of multiple- presence statistics. Accurate multiple-presence data requires time stamps of truck arrival times to the hundredth of a second. Many states typically report arrival times to the nearest second. A time stamp that records to the nearest second could result in an error of over a truck length for trucks traveling at highway speeds. With time stamps recorded to the nearest hundredth of a second, headway separations will be accurate to within a foot. As noted, multiple-presence statistics need not be developed for each site because there is a correlation between multiple presence and ADTT. There also may be a correlation between multiple presence and the functional class of the highway. Higher multiple-presence probabilities may be more likely at urban WIM sites due to slower traffic speeds and increased congestion. Multiple-presence statistics are mostly transportable from site to site with similar truck traffic volumes and traffic flow. A single WIM site can provide multiple-presence data for varying ADTT values due to daily variation in ADTT. In this study, few sites with large quantities of continuous WIM data that include refined time stamps to a resolution of 0.01 second or better were investigated. A relationship between multiple Upper limit: p p k p p n i i i i − −( )= + −( ) α α2 1 2 1 15ˆ ˆ ˆ ( ) Lower limit: p p k p p n i i i i − = + −( ) α α2 2 1 14ˆ ˆ ˆ ( ) 36

presence and traffic volume was developed to utilize the multiple-presence values from national data to any given site without performing a site-specific analysis. Where ac- curate time stamps are not available multiple-presence events may be evaluated using multiple-presence statistics from other sites with similar traffic conditions and functional classifications. Multiple-presence statistics are obtained as a function of headway separation for side-by-side and fol- lowing trucks. Definitions • Headway: The distance between front axles of side-by-side trucks. • Gap: the distance between the rear axle of the first truck and the first axle of the following truck. If the gap exceeds the span length, then there is no multiple-presence on the bridge span. • Light Volume: ADTT ≤ 1000 • Average Volume: 1000 < ADTT ≤ 2500 • Heavy Volume: 2500 < ADTT ≤ 5000 • Very Heavy Volume: ADTT > 5000 Trucks can occur on a bridge in many different arrangements. Five loading patterns are defined as follows: • Single: Only one truck is present on the bridge in any lane. • Following: Two trucks in the same lane, with varying headway distances, with a gap less than the span length. • Side by Side: Two trucks in adjacent lanes with an overlap of more than one-half the truck length of the first truck. • Staggered: Two trucks in adjacent lanes with an overlap of less than one-half the truck length of the first truck and a gap less than the span length (Figure 14). • Multiple: Simultaneous presence of trucks in adjacent lanes and in same lane. For each WIM site with refined time stamp data, the cumu- lative frequencies for side-by-side, staggered, and following events are obtained for headway separation from 0 ft to 300 ft in 20-ft increments. Report multiple-presence probabilities for each day for each site as a function of daily truck count and headway separations or gap. For each site, the daily truck count will vary by day of week and by season. The study needs to be repeated for multiple WIM sites in several states with varying ADTTs (including very high ADTT > 5000) and on routes with a variety of functional classes. With a large dataset of multiple-presence statistics as a function of ADTT and highway class, guidelines for appropriate multiple-presence values for systemwide use may be developed. To calculate and report multiple-presence percentages, use the following procedure: • For each site, each direction, lump all days with light volume (daily truck counts ≤ 1000) into one bin. Find the average MP for each gap increment. • For each site, each direction, lump all days with Average volume (daily truck counts > 1000 but ≤ 2500) into one bin. Find the average multiple presence for each gap increment. • For each site, each direction, lump all days with heavy volume (daily truck counts > 2500 but ≤ 5000) into one bin. Find the average multiple presence for each gap increment. • For each site, each direction, lump all days with very heavy volume (daily truck counts > 5000) into one bin. Find the average multiple presence for each gap increment. Tabulate and chart the variation of multiple presence as a func- tion of gap and traffic volume (light, average, heavy, and very heavy). Multiple-Presence Data from Published Literature (New Jersey WIM Sites). Multiple truck presence statistics based on actual truck load data from New Jersey highways is 37 TRUCK 1 TRUCK 2 Headway Separation Figure 14. Staggered truck event with overlap less than one-half truck length.

available in the published literature (Gindy and Nassif 2006). The data consist of WIM measurements from various sites located throughout New Jersey and recorded over a 10-year period, between 1993 and 2003 (with some gaps). The data- base included 25 sites that are geographically dispersed across New Jersey and constitute a variety of functional classes including rural and urban principal and minor arterials. The sites represent a variety of site-specific conditions including truck volume, road and area type, and number of lanes. The study did not include heavy truck traffic sites with ADTT > 5000. Timestamps of truck arrivals to the hundredth of a second were recorded. Statistics for various truck loading cases including single, following, side by side, and staggered are presented (see Figure 15). Multiple truck presence statistics depend on factors such as truck volume and bridge span length. The position of all trucks in the near vicinity were checked to determine whether multiple trucks simultaneously occur on the bridge The statistics shown in Table 12 for multiple truck occurrences were extracted from Figure 15 for various truck volumes and span lengths. Since the paper did not provide a tabulation of multiple-presence statistics, the values are close approximations scaled from the charts. Use a linear interpolation for other spans. Multiple-Presence Data from Current Research (New York WIM Sites). By studying the occurrence of multiple trucks within a given headway separation at WIM sites with accu- rate time stamps, the effects of multiple trucks on a span can be simulated for WIM sites without accurate time stamps. Five WIM sites (10 directional sites) with free-flowing traffic in New York State were studied by the 12-76 research team to determine the maximum multiple-presence probabilities for various truck traffic volumes. The sites chosen were Route 12 eastbound and westbound (WIM Site 2680), a rural state route, I-84 eastbound and westbound (WIM Sites 8280 and 8382), a rural Interstate, I-81 northbound and southbound (WIM Site 9121), a rural Interstate, and Route 17 northbound and southbound (WIM Site 9631), a rural state route. Two WIM sites on urban interstates (I-95 and I-495) were studied, but not included in the results due to frequent traffic congestion, which precludes free-flowing traffic. Daily truck traffic volume was classified as light (less than 1,000 trucks per day), average (more than 1,000 trucks but less than 2,500 trucks per day), heavy (more than 2,500 trucks but less than 5,000 trucks per day), and very heavy (more than 5,000 trucks per day). When considering multiple trucks on a given span, a multiple-presence event is said to have occurred if the gap 38 Figure 15. Variation of multiple-presence with span length—NJ WIM sites.

between two trucks (i.e., the distance between the last axle of the leading truck and the first axle of the trailing truck) is less than the span length. For instance, two trucks with a head- way separation H ≤ 100 ft will be simultaneously on span of length = 100′ − truck length. Multiple-presence probabilities were compiled for two trucks in adjacent lanes side-by-side, two trucks in adjacent lanes staggered, and two trucks in the same lane. For the purpose of simulating a multiple-presence event, only the headway separation (i.e., the distance from the front axle of the lead truck to the front axle of the trailing truck) is important. Multiple-presence probabilities were compiled for headway separations up to 300 ft, in 20-ft increments (Table 13). For each day that truck data were captured at a WIM site, the number of multiple-presence events that occurred in that day was recorded as a percentage of the total truck count for that day. The average multiple-presence percentage is then calculated for all days with light truck volume, average truck volume, heavy truck volume, and very heavy truck volume, respectively. Each direction of traffic was considered separately. The maximum multiple-presence percentages are summarized in Tables 13 and 14. Multiple-presence data at New York WIM sites were cal- culated in NCHRP Project 12-76 using the same approach as the New Jersey statistics, to allow a direct comparison. The findings from the two states for side-by-side and staggered truck occurrences are quite comparable across most span lengths. The New Jersey values for following trucks are generally higher. The New York findings, defined in terms of head- way separation intervals (Table 14), will be used in the in- terim to simulate multiple-presence events for sites where accurate time stamps are not available. This is achieved by categorizing the likelihood of trucks occupying various slots or headway intervals on the bridge either in the adja- cent lane or in the same lane. Step 7. Protocols for WIM Data Analysis for One-Lane Load Effects for Superstructure Design (Single Events and Following Events) Step 7.1 Load Effects for Single Events for Superstructure Design • Group data into bins by travel lane. Generate GVW relative and cumulative histograms for all trucks. Use 4-kip bins. • Run the trucks (FHWA Class 6 and above—three or more axles) through moment and shear influence lines (or struc- tural analysis program) for simple and two-span continuous 39 Maximum Side-by-Side Trucks Percent Probabilities Site Truck Traffic Span Light:ADTT ≤ 1000 Average: 1000 < ADTT ≤ 2500 Heavy: 2500 < ADTT ≤ 5000 Very Heavy ADTT > 5000 All Spans 0.30 0.90 1.00 Maximum Staggered Trucks Percent Probabilities Site Truck Traffic Span Light:ADTT ≤ 1000 Average: 1000 < ADTT ≤ 2500 Heavy: 2500 < ADTT ≤ 5000 Very Heavy ADTT > 5000 20 0.40 1.20 1.90 Not Available 40 0.60 1.60 2.30 Not Available 60 0.70 1.80 3.20 Not Available 80 0.80 2.00 3.80 Not Available 100 0.90 2.40 4.20 Not Available 120 1.00 2.60 4.60 Not Available 160 1.20 3.20 5.20 Not Available 200 1.40 3.60 5.90 Not Available Maximum Following Trucks Percent Probabilities Site Truck Traffic Span Light:ADTT ≤ 1000 Average: 1000 < ADTT ≤ 2500 Heavy: 2500 < ADTT ≤ 5000 Very Heavy ADTT > 5000 20 0.00 0.00 0.00 Not Available 40 0.00 0.00 0.10 Not Available 60 0.10 0.50 0.60 Not Available 80 0.60 1.00 1.20 Not Available 100 1.20 1.80 2.20 Not Available 120 1.80 2.40 3.40 Not Available 160 3.40 4.00 4.80 Not Available 200 4.40 5.40 7.80 Not Available Table 12. Maximum observed multiple-presence probabilities as a function of ADTT and bridge span length—New Jersey sites.

spans. Use span lengths of: 20 ft, 40 ft, 60 ft, 80 ft, 100 ft, 120 ft, 160 ft, and 200 ft. • Normalize maximum moment and shear values by dividing by the corresponding load effects for HL93. Generate a database table of normalized load effects. Make sure that each record contains GVW, class, number of axles, date, arrival time, and travel lane, in addition to load effects. The date, GVW, and arrival time will serve as a truck record indicator. Step 7.2 Following Truck Events for Superstructure Design When Accurate Truck Arrival Time Stamps are Available Load effects for following trucks may be obtained directly from the WIM data where accurate time arrival stamps are collected together with truck weight data. The load effects analysis is performed with the following trucks in their proper relative positions. Estimate the maximum daily load effects for two random following trucks crossing the bridge as follows: • Combine the two trucks by superimposing the second truck on the first truck with the axles offset by the measured headway separation. • Run the combined truck through moment and shear in- fluence lines for simple and two-span continuous spans. Use span lengths of 20 ft, 40 ft, 60 ft, 80 ft, 100 ft, 120 ft, 160 ft, and 200 ft. • Repeat the process for each following truck event. • Normalize the results by dividing by the effects of HL93. Step 7.3 Simulation of Following Truck Events When Accurate Truck Arrival Time Stamps are not Available Load effects for following trucks may be obtained directly from the WIM data where accurate time arrival stamps are 40 Headway Light: Average: Heavy: Very Heavy: H (ft) ADTT < 1k 1k < ADTT < 2.5k 2.5k < ADTT < 5k ADTT > 5k H < 20 0.19 0.41 0.61 0.00 H < 40 0.33 0.84 1.27 0.00 H < 60 0.54 1.25 1.95 0.00 H < 80 0.80 1.60 2.57 0.00 H < 100 1.00 2.13 3.33 0.00 H < 120 1.21 2.54 4.14 0.00 H < 140 1.45 2.88 4.80 0.00 H < 160 1.62 3.18 5.41 0.00 H < 180 1.80 3.47 5.97 0.00 H < 200 1.99 3.73 6.49 0.00 H < 220 2.09 3.97 6.97 0.00 H < 240 2.23 4.21 7.42 0.00 H < 260 2.35 4.43 7.85 0.00 H < 280 2.49 4.64 8.26 0.00 H < 300 2.60 4.84 8.66 0.00 Headway Light: Average: Heavy: Very Heavy: H (ft) ADTT < 1k 1k < ADTT < 2.5k 2.5k < ADTT < 5k ADTT > 5k H < 20 0.00 0.00 0.00 0.00 H < 40 0.00 0.00 0.00 0.00 H < 60 0.01 0.00 0.00 0.00 H < 80 0.02 0.00 0.00 0.00 H < 100 0.08 0.04 0.03 0.00 H < 120 0.20 0.19 0.19 0.00 H < 140 0.41 0.52 0.64 0.00 H < 160 0.77 1.09 1.37 0.00 H < 180 1.25 1.76 2.28 0.00 H < 200 1.71 2.51 3.26 0.00 H < 220 2.22 3.19 4.20 0.00 H < 240 2.70 3.86 5.11 0.00 H < 260 3.12 4.51 5.98 0.00 H < 280 3.53 5.11 6.83 0.00 H < 300 3.92 5.70 7.63 0.00 Maximum Side-by-Side Truck Multiple Presence Cumulative Probabilities Site Truck Traffic Maximum Following Truck Multiple Presence Cumulative Probabilities Site Truck Traffic Table 13. Maximum observed multiple-presence cumulative probabilities as a function of headway separation and ADTT—NY sites.

collected together with truck weight data. The load effects analysis is performed with the following trucks in their proper relative positions. Where accurate truck arrival time stamps are not available, generalized multiple-presence statistics obtained in Step 6 may be used to simulate following trucks in their likely relative positions as follow: 1. From Step 6, obtain the probabilities for following trucks in the same lane with varying headway separations (given in 20-ft increments) as a function of ADTT in each direction (see Table 14). 2. The number of expected multiple-presence (MP) events in each direction for each headway separation interval, H, can be determined from the following equation: Number of MP Events MP Probability AADT= × 3. Randomly select two trucks from the entire population of trucks in the desired direction. Being that there is no correlation between the truck population and travel lane, any two randomly selected trucks can be considered, regard- less of lane, as long as the trucks are traveling in the desired direction. 4. Randomly select a headway separation within the desired headway separation interval. 5. With the randomly selected truck pair separated by the randomly selected headway separation, maximum load effects can be calculated in the same manner as for trucks with accurate time stamps and measured headway separation (Step 7.2). 6. Repeat Steps 3 through 5 for each headway separation inter- val and each direction of travel until the expected number of multiple-presence events has been generated for each headway separation and each direction of travel. 41 Maximum MP Probabilities based on 5 WIM sites (10 directional sites) in New York State Headway H (ft) ADTT < 1k 1k < ADTT < 2.5k 2.5k < ADTT < 5k ADTT > 5k H (ft) ADTT < 1k 1k < ADTT < 2.5k 2.5k < ADTT < 5k ADTT > 5k H < 20 0.19 0.41 0.61 0.00 20 < H < 40 0.14 0.43 0.66 0.00 40 < H < 60 0.21 0.41 0.68 0.00 60 < H < 80 0.26 0.35 0.62 0.00 80 < H < 100 0.20 0.53 0.76 0.00 100 < H < 120 0.21 0.41 0.81 0.00 120 < H < 140 0.24 0.34 0.66 0.00 140 < H < 160 0.17 0.30 0.61 0.00 160 < H < 180 0.18 0.29 0.56 0.00 180 < H < 200 0.19 0.26 0.52 0.00 200 < H < 220 0.10 0.24 0.48 0.00 220 < H < 240 0.14 0.24 0.45 0.00 240 < H < 260 0.12 0.22 0.43 0.00 260 < H < 280 0.14 0.21 0.41 0.00 280 < H < 300 0.11 0.20 0.40 0.00 H < 20 0.00 0.00 0.00 0.00 20 < H < 40 0.00 0.00 0.00 0.00 40 < H < 60 0.01 0.00 0.00 0.00 60 < H < 80 0.01 0.00 0.00 0.00 80 < H < 100 0.06 0.04 0.03 0.00 100 < H < 120 0.12 0.15 0.16 0.00 120 < H < 140 0.21 0.33 0.45 0.00 140 < H < 160 0.36 0.57 0.73 0.00 160 < H < 180 0.48 0.67 0.91 0.00 180 < H < 200 0.46 0.75 0.98 0.00 200 < H < 220 0.51 0.68 0.94 0.00 220 < H < 240 0.48 0.67 0.91 0.00 240 < H < 260 0.42 0.65 0.87 0.00 260 < H < 280 0.41 0.60 0.85 0.00 280 < H < 300 0.39 0.59 0.80 0.00 Maximum Side-by-Side Truck Multiple Presence Probabilities Site Truck Traffic Maximum Following Truck Multiple Presence Probabilities Site Truck Traffic Light: Average: Heavy: Very Heavy: Headway Light: Average: Heavy: Very Heavy: Table 14. Maximum observed multiple-presence probabilities by headway interval as a function of ADTT—NY sites.

7. Normalize by dividing the results by the effects of HL93 loading. Step 7.4 Group Load Effects into Strength I and Strength II (One Lane) Overloaded trucks seen in the WIM data could be either illegal overloads or authorized permit loads. It should be noted that separating permits from non-permit overloads in the WIM data is only viable where accurate permit records are available. In most jurisdictions only the special permit or single-trip permit moves are tracked in terms of their actual load configurations and travel routes. These heavy loads populate the upper tails of the load spectra and it would be beneficial to know which vehicles are authorized and which are illegal. Separating routine permits may not be possible due to the lack of necessary permit records at the state level and the sheer volume of permits in operation in most states. This is not considered a necessary requirement for live-load modeling since routine permits can be taken as variations of the exclusion loads allowed under state law. Legal loads, routine permits, and illegal overloads are grouped under Strength I. Heavy special permits are grouped under Strength II. For following events, if one of the trucks is a heavy special permit truck, group that loading event under Strength II. Step 7.5 Assemble Single-Lane Load Effects Histograms for Strength I and Strength II • Combine the normalized load responses of single truck events and following truck events into a single histogram for each load effect (M, V) and assemble in narrow bins of 0.02 increments for Strength I and Strength II. These combined histograms will represent the single-lane load effects from a single truck or multiple trucks in the same lane. • These will constitute the single-lane measured load effects histograms without any filtering for WIM sensor errors (see Step 10). Step 8. Protocols for WIM Data Analysis for Two-Lane Load Effects for Superstructure Design (Side by Side and Staggered Events) Step 8.1 Truck Load Effects from Trucks in Adjacent Lanes Using Accurate Truck Arrival Time Stamps to the 1/100th of a Second • Determine the number of truck multiple-presence (MP) events where trucks are in adjacent lanes in each direction for each day. During an MP event there could be more than one truck in a lane. • For each MP event, obtain the headway separation between trucks in adjacent lanes and in the same lane using the WIM data. • For estimating the maximum daily load effects for two random trucks simultaneously crossing the bridge, pro- ceed as follows: 1. Combine the two trucks by superimposing the second truck in the adjacent lane on the first truck with the axles offset by the headway separation. 2. Run the combined truck through moment and shear influence lines for simple and two-span continuous spans. Use span lengths of 20 ft, 40 ft, 60 ft, 80 ft, 100 ft, 120 ft, 160 ft, and 200 ft. 3. Keep track of the normalized M and V. 4. For each MP event, repeat the process. Step 8.2 Simulation of Load Effects of Trucks in Adjacent Lanes Using Generalized MP Statistics 1. From Step 6, obtain the probabilities for side-by-side/ staggered trucks in adjacent lanes with varying headway separations (given in 20-ft increments) as a function of ADTT in each direction (see Table 14). 2. The number of expected multiple-presence events in each direction for each headway separation interval, H, can be determined from the equation 3. Randomly select two trucks from the entire population of trucks in the desired direction. Since there is no correlation between the truck population and travel lane, any two randomly selected trucks can be considered, regardless of lane, as long as the trucks are traveling in the desired direction. 4. Randomly select a headway separation within the desired headway separation interval. 5. With the randomly selected truck pair separated by the randomly selected headway separation, maximum load effects can be calculated in the same manner as for trucks with accurate time stamps and measured headway separa- tion (Step 8.1). 6. Repeat Steps 3 through 5 for each headway separation inter- val and each direction of travel until the expected number of MP events has been generated for each headway sepa- ration and each direction of travel. Step 8.3 Group Load Effects into Strength I and Strength II (Two-Lane) Overloaded trucks seen in the WIM data could be either illegal overloads or authorized permit loads. It should be noted Number of MP Events MP Probability AADT= × 42

that separating permits from non-permit overloads in the WIM data is only viable where accurate permit records are available. In most jurisdictions only the special permit or single-trip permit moves are tracked in terms of their actual load configurations and travel routes. These heavy loads populate the upper tails of the load spectra and it would be beneficial to know which vehicles are authorized and which are illegal. Separating routine permits may not be possible due to the lack of necessary permit records at the state level and the sheer volume of permits in operation in most states. This is not considered a necessary requirement for live-load modeling since routine permits can be taken as variations of the exclusion loads allowed under state law. Legal loads, routine permits, and illegal overloads are grouped under Strength I. Heavy special permits are grouped under Strength II. For MP events, if one of the trucks is a heavy special permit truck, group that loading event under Strength II. Step 8.4 Assemble Two-Lane Load Effects Histograms for Strength I and Strength II • Assemble normalized load effects frequency histograms for two-lane load effects for Strength I and Strength II in narrow bins of 0.02 increments. • These will constitute the two-lane measured load effects histograms without any filtering for WIM sensor errors (see Step 10). Step 9. Assemble Axle Load Histograms for Deck Design Step 9.1 One-Lane Axle Loads for Deck Design • Separate trucks into Strength I and Strength II groups. • For each group, generate axle weight relative frequencies histograms for single, tandem, tridem, and quad axle types. Use a 2-kip interval for the bins. Axles spaced at less than 6 ft are to be considered as part of the same axle group. • This will constitute the measured axle load histogram with- out any filtering for WIM sensor errors (see Step 10). • Assuming normal distribution models for axle weight data for the filtered histogram, determine the mean and standard deviation for all axles, top 20% axles, top 5% axles. For each axle type, report the 99th percentile statistic W99. Step 9.2 Side-by-Side Axle Events for Two Lanes Multiple-presence studies specifically for axles loads are performed for the two-lane loaded case. There will be a greater probability of side-by-side axle events than side-by-side truck events, because each truck has two or more axles. However, an axle with a headway separation greater than the effective strip width for the slab as defined in the LRFD specifications would not have an influence on the load effect of the axle in the adjacent lane and may be neglected, if using the strip method. With these key differences recognized, the process for MP computations for axle loads will follow an approach similar to that used for truck MP studies. Determine the number of side-by-side axle events in each direction for the following combinations: • Single–single, • Single–tandem, • Tandem–tandem, and • Other. Step 10. Filtering of WIM Sensor Errors/ WIM Scatter from Measured WIM Histograms The live-load modeling protocols presented in this project rely on the weight histograms and the histograms of the cor- responding load effects as collected from WIM stations at various highway sites. Current WIM systems are known to have certain levels of random measurement errors that may affect the accuracy of the load modeling results. This section proposes an approach to filter out WIM measurement errors from the collected WIM data histograms. To execute the filtering process, a calibration of the results of the WIM system should be made by comparing the results of the WIM system to those of a static scale. The calibration process should be repeated several times within the WIM data collection timeframe. The results of this calibration will be the basis for filtering out WIM measurement errors for each WIM data site. Step 10.1 WIM System Calibration Typical WIM calibration procedures consist of taking several WIM measurements from representative calibration trucks and comparing the WIM measurements to those obtained from a certified static scale. Traditionally, it has been common to use a single truck for the calibration process, although it would be advisable to use different trucks having different characteristics to ensure that the accuracy of the results remain consistent independent of the truck character- istics. For example, Table 15 gives a summary sheet of the calibration data assembled for the northbound lane of Site No. 7100 on I-87 in New York. The table shows the actual axle weight along with the weights estimated from the piezo- loop WIM system installed at the site. The WIM data were collected for 10 different crossings of the same calibration truck. The truck’s speeds were approximately 40 mph. Table 16 shows the ratio of the WIM weight divided by the actual weight for each of the 5 axles for the 10 crossings. The average of the 43

ratios from all of the 50 measurements is 0.97 with a standard deviation of 10%. The plot of WIM error versus axle weight in Figure 16 demonstrates that the correlation between the bias value and the axle weight is practically negligible. There appears to be a difference in the standard deviations as the axle weights change. However, more data is needed to analyze this trend more accurately. Similarly, it is not clear why the readings for Axles 2 and 3 (or Axles 4 and 5), which respectively have somewhat similar weights, are leading to large differences in their standard deviations. Axle weight histograms are needed for modeling the live loads for deck design, while the design of main bridge members requires the maximum bending moment and shear force effect. Thus, for main bridge members, it is more important to study the influence of WIM errors on the load effect rather than on the axle weights. Because main member load effects are influenced by the weight and spacing of several axles, some of the axle weight errors will cancel out and thus the overall error may have a lower standard deviation than that for individual axles. For example, for the calibration data of the same I-87 site studied above, the maximum moment effect of the cali- bration truck for a 60-ft simple span beam would be equal to 275.4 kip-ft, if the actual axle weights and axle spacings were used. The maximum moment effect for the values obtained from the eighth pass would be 303.8 kip-ft. The maximum moments from the 10 different passes are provided in Table 16 showing an overall average error ratio of 1.04 and a standard deviation of 7.8%. These are compared to an average error of 0.97 and a standard deviation of 10% for the axle weights. The information provided in Table 16 can be used to filter out the errors from the axle weight and moment effect histograms as described in the next section. 44 Pass 1st Axle 2nd Axle 3rd Axle 4th Axle 5th Axle Moment on 60-ft span 1 0.92 1.07 0.90 1.07 1.03 1.04 2 0.94 0.88 0.91 0.88 0.98 0.92 3 0.81 0.88 0.95 1.38 1.01 1.21 4 0.91 0.98 0.90 1.06 0.94 1.00 5 0.99 1.13 0.98 0.84 1.03 1.05 6 1.01 0.86 0.98 1.05 1.02 1.03 7 1.02 1.18 1.07 0.89 0.93 1.06 8 0.89 1.01 0.87 1.14 1.08 1.10 9 0.94 0.99 0.91 1.04 1.02 1.02 10 0.97 0.86 0.97 0.96 0.97 0.96 Overall Axle Moment Average 0.94 0.98 0.94 1.03 1.00 1.04 Average 0.97 1.04 Stdev 0.062 0.116 0.059 0.157 0.046 0.078 Stdev 0.100 0.078 Table 16. WIM errors expressed as a ratio of measured values over actual values. 12.61 16.10 15.85 31.95 20.28 18.75 39.03 83.58 275.37 12.83 4.50 37.25 4.13 58.71 SITE: 7100 DATE: Sensor conf iguration Piezo-Loop_Piezo Contract#/Sales Order Drive 60-ft Steer 2nd Axle 3rd Axle Total 5th Axle Total Moment Axle 1-2 Axle 2-3 Axle 3-4 Axle 4-5 Length Actual Pass 1st Axle 1 11.60 17.20 14.20 31.40 21.70 19.30 41.00 84.0 287.2 12.3 4.6 37.3 4.10 58.30 2 11.90 14.10 14.40 28.50 17.90 18.40 36.30 76.7 254.3 12.3 4.6 37.2 4.00 58.10 3 10.20 14.20 15.00 29.20 28.00 19.00 47.00 86.4 332.2 12.8 4.5 37.1 4.00 58.40 4 11.50 15.70 14.30 30.00 21.50 17.60 39.10 80.6 275.2 12.80 4.50 37.20 4.00 58.50 5 12.50 18.20 15.50 33.70 17.00 19.30 36.30 82.5 288.3 12.8 4.5 37.2 4.00 58.50 6 12.70 13.90 15.60 29.50 21.20 19.20 40.40 82.6 283.7 12.8 4.6 37.3 4.00 58.70 7 12.80 19.00 17.00 36.00 18.00 17.50 35.50 84.3 292.8 16.7 4.4 33.2 4.10 58.40 8 11.20 16.20 13.80 30.00 23.10 20.20 43.30 84.5 303.8 12.8 4.6 37.2 4.10 58.70 9 11.80 15.90 14.40 30.30 21.00 19.20 40.20 82.3 281.6 12.8 4.5 37.2 4.10 58.60 LOCATION: I87 Champlain Exit 42 Rt 11 (BIN 1009070) - Acc Rt 9 5/25/2006 Lane: 1 Northbound Trailer 4th Axle GVW 2nd Axle 3rd Axle Total 5th Axle Total Moment Axle 1-2 Axle 2-3 Axle 3-4 Axle 4-5 Length4th Axle GVW Table 15. Typical WIM calibration results for NY State DOT installations.

The variation of the ratio with each truck crossing indicates that the measured axle weight to actual axle weight ratio is a random variable designated as  with a mean value of 0.97 and a standard deviation of 10% for this particular site. Figure 17 shows a plot of the axle error ratio data on a normal proba- bility plot. With only one exception, all of the data lies within the 95% confidence levels, indicating that the data can be reasonably well represented by a normal probability distribu- tion function. This information will be required to execute the WIM error filtration as will be discussed in the next section. In the following, the research team assumed that these results are valid for all of the trucks collected at the WIM sites independent of truck type, vehicle speed, and time at which the WIM measurements were taken. A sensitivity analysis is performed in Appendix E to study how the standard deviation of the error would affect the results. Step 10.2 WIM Error Filtration Procedure Assume that the actual weight of an axle, or the actual moment effect of a truck, is denoted by xr, while the measured value using the WIM system is xm. Because of WIM system measurement errors, the difference between the measured value and the actual value can be represented by a calibration factor or an error ratio, . Because the error may depend on various random factors related to the WIM system’s characteristics and truck/structure/WIM system dynamic interaction as well as some truck features including tire size and pressure, the calibration factor  is a random variable that relates the measured WIM data results to the “true” weight through the following equation: x xm r=  ( )16 45 y = 0.0121x + 0.777 R2 = 0.1048 1.6 1.4 1.2 1 0.8 W IM B ia s (m ea su re d w eig ht /ac tu al we igh t) 0.6 0.4 0.2 0 0 5 10 Axle weight in kips 15 20 25 Figure 16. Plot of WIM error ratio versus axle weight for I-84 site. 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1 5 10 20 30 40 50 60 70 80 90 95 99 Data Pe rc en t ML Estimates Mean: StDev: 0.979369 0.0986870 Figure 17. Plot of WIM axle error ratio on normal probability plot.

If the histogram and statistical information for  are obtained from the calibration of the WIM system, these statistics can be used to filter out the errors in the measured raw WIM truck weight histogram collected at a given site. The goal then is to obtain the histogram of xr given that the measured data give the histogram of xm and given the statistics of  using the following equation: Since the error  varies randomly, it will not be possible to ob- tain xr for each particular truck. Instead, an algorithm can be developed to obtain a histogram for all of the actual truck weights given the histogram of the measured weights and the probability distribution of the error ratio . The WIM data collected at a site will produce a histogram for xm which can be related to the probability distribution function of xm represented by fxm(. . .). Similarly, the calibration of the WIM system will provide information on the distribution function of  represented by f(. . .). For example, the WIM calibration of I-84 NB Lane 4 indicates that the error of the WIM system axle weights can be modeled as a normal probability distribution with a prob- ability function f() with mean value – = 0.97 and a standard deviation σ = 0.10. Since xr is the ratio of two random variables with known probability distribution functions, the probability distribution function of the actual weight xr, fxr(. . .) can be obtained using the following expression (Ang and Tang 2007): The analysis of the correlation of the error with the actual magnitude of the axle weight, as illustrated in Figure 16, has shown that they are practically independent (i.e., the per- cent error does not depend on the magnitude of the actual truck weight). It should be noted, however, that the number of readings is limited to those of a single truck. Actual statistics for  should be obtained from runs of different trucks at normal highway speeds. If one assumes that the measured truck weight xm and the error  are also independent random variables, then Equation 18 can be expanded as Step 10.3 WIM Error Filtration Algorithm The integration of Equation 19 can be executed numerically using a simple algorithm so that the integration is changed into a simple summation and the equation can be represented as f z y f zy f y dyx xr m( ) = ( ) ( ) −∞ ∞ ∫  ( )19 f z y f zy, y dyx xr m( ) = ( ) −∞ ∞ ∫ , ( ) 18 x x r m =  ( )17 Recalling that the probability distribution functions of , xr, and xm are related to the histograms by where Δ(. . .) is the bin size for each histogram. If the bin sizes for the histogram of the actual weight xr and that of the mea- sured weight xm are taken to be the same, so that Δz = Δ(zy), then Equation 20 can be expressed as Thus, given the histogram of the measured WIM data, xm, and the probability distribution of the calibration factor, , the integration of Equation 19 for all possible values of xr = z can be executed numerically using software tools. The protocols for calculating Lmax should then be executed using the filtered histogram Hxr(z). Implementation of the above WIM Error Filtration Algorithm, based on New York calibration data, is given in Appendix E. Step 11. Accumulated Fatigue Damage and Effective Gross Weight from WIM Data WIM data can be used to study the stress range produced by individual trucks on a bridge component. Damage accumu- lation laws such as Miner’s Rule can then be used to estimate the fatigue damage for the whole design period for the expected truck population at a site. Obtain cumulative fatigue damage from the WIM popula- tion and compare to LRFD fatigue truck (Figure 18, 54-kip gross weight) moments for each span. Use span lengths of 20 ft, 40 ft, 60 ft, 80 ft, 100 ft, 120 ft, 160 ft, and 200 ft. Determine fatigue damage adjustment factor K, defined as MFT = Moment from LRFD fatigue truck, includes 0.75 load factor; K M M FT i× = ( )⎡ ⎣⎢ ⎤ ⎦⎥ ∑ 3 1 3 24 # ( ) Trucks H z y H zy f y yx x y r m ( ) = ( ) ( )∑   Δ all values of = ( )23 f z z y f zy z f y yx xr m( ) ( ) = ( ) ( ) ( )Δ Δ Δ all values of =y ∑ ( )22 H y f y y H z f z z H zy f x x x x r r m m  ( ) = ( ) ( ) = ( ) ( ) = Δ Δ ( )21 zy zy( ) ( )Δ f z y f zy f y yx x y r m ( ) = ( ) ( ) = ∑   Δ all values of ( )20 46

K = Fatigue damage adjustment factor; Mi = Moment range of trucks measured; and # Trucks = Total number of trucks measured. Obtain K for each span. For varying spans, determine the effec- tive gross weight for trucks measured at the site using the fol- lowing equation: where: fi is the fraction of gross weights within interval i and Wi is the mid-width of interval i. In this calculation, use trucks only with three or more axles (Class 6 and above). Step 12. Lifetime Maximum Load Effect Lmax for Superstructure Design (Strength I) Step 12.1 Methods for Estimating Lmax To check the calibration of load models and/or load factors for a specification, it is necessary to estimate the mean maxi- mum loading or load effect Lmax. If further calibration of the specification is to be carried out, the corresponding COV also should be found. The estimation of the maximum load effect Lmax expected over a 75-year bridge design period can be executed through a variety of methods. Simplified analytical methods or simulations may be used to estimate the maximum loading over a longer period, from short-term WIM data. This has to be done from a limited set of data that is collected for truck weights and truck configurations as well as truck traffic headways over relatively short periods of time. These methods can be categorized as • Convolution or numerical integrations, • Monte Carlo simulations, and • Simplified statistical projections. W f Weq i i= ( )∑ 3 1 3 25( ) The models require as input the WIM data collected at a site after being scrubbed for data quality and filtered for WIM errors as described in the previous steps. The design of bridges requires the estimation of the maximum load effect over periods of 75 years. The convolution method uses numerical integrations of the collected WIM data histograms to obtain projections of the expected maximum load effect within a given return period (e.g., 75 years). The WIM data collected cannot reasonably be accurate enough in the tail of the dis- tributions to obtain good estimates of the parameters for such extended return periods. Hence, the only possible means to obtain the parameters of the distributions of the 75-year maximum load effect is by using statistical projections. The probability distribution of the maximum value of a random variable will asymptotically approach an extreme value distri- bution as the number of repetitions increases. Generally, a Gumbel fit can be executed on the tail of the short-term maximums for statistical projections. An alternative to the convolution approach consists of using a Monte Carlo simulation to obtain the maximum load effect. The Monte Carlo simulation uses random sampling from the collected data to obtain the maximum load effect. A Monte Carlo simulation requires the performance of an analysis a large number of times and then assembling the results of the analysis into a histogram that will describe the scatter in the final results. Each iteration is often referred to as a cycle. The process can be executed for the single-lane loading situation or the side-by-side loading. The Monte Carlo simulation may be performed to find Lmax in one of following two ways: • Use the empirical histogram to find Lmax by simulation for a short period and then project for a longer period (use an extreme value distribution such as Gumbel distribution). As mentioned earlier, the probability distribution of the maximum value of a normal random variable will asymp- totically approach the Gumbel distribution. • Alternatively, use a smoothed tail end of the WIM histogram by fitting the tail with a known probability distribution 47 14’ 30’ 6 k 24 k 24 k Figure 18. LRFD design fatigue truck (54 kips).

function (such as the normal distribution) and use that fitted distribution with the Monte Carlo simulation. This will require a very large number of repetitions. It should be emphasized however, that the Monte Carlo sim- ulation would be very inefficient for projections over long re- turn periods when the number of repetitions is very high. (Al- gorithms such as Markov Chain Monte Carlo modeling may allow improved performance in such cases.) Furthermore, one should make sure not to exceed the random number of generation limits of the software used, otherwise the gener- ated numbers will not be independent and the final results will be erroneous. Simplified statistical projections for estimating the maxi- mum load effect in a given return period can be developed based on the assumption that the tail end of the moment load effect for the original population of trucks as assembled from the WIM data approaches a normal distribution. The method uses the properties of the extreme value distribu- tion. Equations in closed form provide such a projection, requiring much less effort than the convolution approach. The estimation of the maximum load effect for two side- by-side trucks improves as the return period increases. This is again due to the asymptotic nature of the solution, which yields good results only as the number of load repetitions increases and as the sampling is made from the tail end of the raw WIM histogram. Step 12.2 Procedure for Calculating Lmax from WIM Data Using an Extreme Value Distribution for the Upper Tail There are several possible methods available to calculate the maximum load effect for a bridge design period from truck WIM data. The one implemented in these protocols is found to be one of the easiest methods that provide results comparable to many other methods including Monte Carlo simulations. This method is based on the assumption that the tail end of the histogram of the maximum load effect over a given return period approaches a Gumbel distribution as the return period increases. The method assumes that the WIM data are assembled over a sufficiently long period of time to ensure that the data are representative of the tail end of the truck weight histograms and to factor in seasonal variations and other fluctuations in the traffic pattern. The use of WIM data for a whole year will satisfy this requirement. In a separate analysis, this study will investigate how the confidence inter- vals in the projection results are affected by the number of samples collected and the number of days for which the WIM data are available, especially when only limited data are available at a site. Sensitivity analyses have shown that the most important parameters for load modeling are those that describe the shape of the tail end of the truck load-effects histogram. Cur- rent WIM technology has certain levels of random measure- ment errors that may affect the accuracy of the load model- ing results. To bring uniformity in the load modeling process, a standardized approach to executing the error filtering pro- cedure that utilizes calibration statistics for the WIM scale is described in Step 10. This procedure should be executed on the raw data prior to calculating Lmax. Step 12.2.1 Protocols for Calculating Maximum Load Effect Lmax The process begins by assembling the WIM truck weight data and load effects for single-lane events and two-lane events and filtering the data for WIM sensor errors. • Assemble the measured load effects histograms (moment effect or shear force effect) in narrow bins of 0.02 increments. • Execute a statistical algorithm to filter out WIM scatter/ sensor errors from the load effects histograms as described in Step 10. • Find the cumulative distribution function Fx (x) = cumulative distribution function value for each event x sample by divid- ing the number of samples in a bin by the total number of samples and adding the value to the value in the previous bin. • Calculate the standard deviate of the cumulative function for each bin. In MS Excel, this can be achieved by taking NORMSINV(F(x)). • Take the upper 5% of the values and plot the normal deviate versus X. • Take the trend line and find the slope, m, and the intercept, n, of the regression line. • Find the mean of normal that best fits the tail end of the distribution as μevent = −n/m. • Find the standard deviation of the best fit normal distri- bution to be σevent = (1-n)/m − μevent. • Take the number of events per day, nday. • Find, N, the total number of events for the return period of interest. For 75 years, take N = nday  365  75. • The most probable value, u, for the Gumbel distribution that models the maximum value in 75 years Lmax is given as • The dispersion coefficient for the Gumbel distribution that models the maximum load effect Lmax is given as α σ N N = ( )2 27 ln ( ) event u event eventN N N = + × ( ) − ( )( ) + ( )μ σ π2 4 2 2 ln ln ln ln ln ( ) N( ) ⎡ ⎣⎢ ⎤ ⎦⎥ 26 48

• The mean value of Lmax is given as • Calculate the standard deviation of the Gumbel distribution that best models the maximum daily effect as Step 12.3 Alternate Method for Calculating Maximum Load Effect Lmax Using Monte Carlo Simulation An alternative to the statistical projections approach described in Step 12.2 consists of using a Monte Carlo simu- lation to obtain the maximum load effect. If there are not enough multiple events recorded in the WIM data, one could utilize simulations to generate MP events that conform to the measured statistical MP probabilities. In this approach, results of WIM data observed over a short period can be used as a basis for projections over longer periods of time. It should be noted that the Monte Carlo method for single-lane events will not be able to give Lmax for 75 years directly. At best, a 1-week or a 1-month maximum single event could be obtained from a year’s worth of WIM data because the Monte Carlo simulation will not go beyond the maximum value measured at the site. A statistical projection technique must then be executed to ex- tend the single event results to 75 years. Alternatively, one can use the fitted normal distribution to represent the tail end of the histogram rather than use the raw data histogram and then the projection is automatically performed by the simulation. The same is not true for the two-lane loading cases because the Monte Carlo procedure will simulate more samples of side- by-side events based on the observed MP probabilities. A Monte Carlo simulation requires the performance of an analysis a large number of times and then assembling the results of the analysis into a histogram that will describe the scatter in the final results. The process can be executed for the single-lane loading situation or the side-by-side loading. Figure 19 gives a schematic representation of the Monte Carlo simulation, which follows the procedure described in the following steps: 1. Assemble the data representing the filtered load effects for the trucks in the drive lane into a histogram labeled Bin I. 2. Assemble the data representing the filtered load effects for the trucks in the passing lane into a histogram labeled Bin II. 3. Assemble the corresponding cumulative frequency curves for the two histograms. σ π α max ( )= 6 29 N L u N max max . ( )= = +μ α 0 577216 28 4. Determine a main return period, treturn, for which the expected maximum moment is desired. For example, a 1-week, 1-month, 2-year, or 75-year period may be selected. However, as noted earlier, it is unlikely that the sample size of the available WIM data will be sufficiently large to obtain results for the large return periods. Hence, it is expected that the process will be applicable for only short periods (e.g., a 1-week or 1-month period), the results of which can then be projected for longer periods using the extreme value projection. Alternatively, one can use the fitted normal distribution to represent the tail end of the histogram rather than use the raw data histogram and then the projection is automatically performed by the simulation. 5. Use a uniform distribution random generator to produce a pseudo random number varying between 0 and 1. Such random generator routines are provided in all general- purpose computer software and programming tools (such as Excel, MATLAB). 6. The pseudo-random number of Step 5 will serve to select a single value from Bin I representing the load effect of a truck arriving in the drive lane. The selection of the moment effect is executed by assuming that the pseudo-random number generated (call it ran1i) represents the cumulative frequency of the moment for this truck. Thus, to find the value of the moment, X1i, the cumulative distribution function needs to be inverted so that X1i = F −1 x1(ran1i) where F−1x1(. . .) is the inverse of the cumulative function for the effect of the trucks in the drive lane (Figure 20). 7. For estimating the maximum load effect for the trucks crossing the bridge in the drive lane, follow Sub-Steps A through E, otherwise skip this step and go to Step 8. 49 Truck in Lane 1 Truck in Lane 2 Bin I Bin II Figure 19. Schematic illustration of Monte Carlo simulation procedure.

A. Find the number of loading events in the drive lane, K1, corresponding to the pre-selected return period treturn. B. Repeat Steps 5 through 6 K1 times to generate K1 samples for the moments in the drive lane in the period treturn. C. Compare the K1 values and choose the largest one of these. This will give you one estimate of the maximum expected value in treturn, which is designated as X1mx K1. D. Repeat Sub-Steps A through C for several cycles to generate several estimates of the maximum value X1mx K1. E. Assemble the values collected in Step D in a histogram. Also, find their average value and standard deviations. 8. For estimating the maximum response for two side-by-side trucks, do the following: • Repeat Sub-Steps 5 and 6 by generating a pseudo num- ber ran2i, which represents the cumulative frequency of the moment for trucks in the passing lane. Find the value of the moment, X2i, by inverting the cumulative frequency, Fx2(. . .), for the load effects of the truck in the passing lane so that X2i = F x2 −1(ran2i). • Assuming that the maximum effect of the truck in the drive lane occurs at the same time as the maximum effect of the truck in the passing lane, add the moment effects of these two trucks to produce the moment effect of a single side-by-side event Xsi = X1i + X2i. • Repeat the process Ks times where Ks = number of side- by-side events expected in the basic return period treturn. • Compare all the Ks moment effects Xs1 . . . XsKs and take the maximum value out of these Ks values. This will produce a single estimate of the maximum response corresponding to the basic return Xs max Ks. • Repeat the whole simulation process m cycles to get m estimates of Xs max Ks. • Obtain the histogram of the m estimates of Xs max Ks and calculate the average value and standard deviation. Step 13. Develop and Calibrate Vehicular Load Models for Bridge Design Step 13.1 Superstructure Design Live-Load Calibration (Strength I) There are two calibration methods, as follows, that can be applied to calibrate a new live-load model based on recent changes in truck weights: • Method I: The first approach, which is relatively simple, is to focus on the mean or expected maximum live-load variable, Lmax. That is, assume that the present LRFD cali- bration and safety indices are adequate for the strength and load data then available, but update the load model or the load factor for current traffic conditions in a manner consistent with the LRFD calibration approach. One key assumption in this regard is that the site-to-site variability in Lmax as measured by the COV (COV = STDEV/Mean) is the same as that used during the AASHTO LRFD calibration. In the AASHTO LRFD calibration, the overall live-load COV was taken as 20%. • Method II: If the variability in the WIM data is much greater than that assumed in the calibration, then the entire LRFD 50 . . . . . . . Ran1 X1i Figure 20. Schematic illustration of the random generation of a sample X1i.

calibration to achieve the target 3.5 reliability index may no longer be valid for that state and a simple adjustment of the live-load factor as given above should not be done. The second approach, which is more robust, is to perform a reliability analysis using the new statistical data for live loads and determine the live-load factors needed to achieve the same reliability target adopted in the LRFD calibration. Method I: Simplified Adjustment of Strength I Live-Load Factor The process adjusts the loading model and/or the correspon- ding live-load factor by the following ratio: An increase in maximum expected live load based on current WIM data can be compensated in design by raising the live- load factor in a corresponding manner. The basic steps are summarized as follows: A. Obtain quality WIM data from a variety of jurisdictions and traffic conditions and compute the expected lifetime maximum load, Lmax, for each data set for one-lane and two-lane loadings. B. Compare Lmax for a suite of bridges to this expected 75-year maximum load for a similar suite of bridges given by NCHRP Report 368 (Nowak 1999). C. Compute the average ratio, r (Lmax WIM data, divided by Lmax Ontario data) for one lane and for two lanes. Compute also the corresponding COV for all sites examined. D. Adjust the design requirements by modifying the live-load factor by the average ratio, r, as given above. If r is relatively r L from WIM data projections for two-lmax 2 = anes L used in existing LRFD calibrationmax for two-lanes ( )31 r L from WIM data projections for one-lmax 1 = ane L used in existing LRFD calibrationmax for one-lane ( )30 uniform over the suite of bridges used to fix Lmax then the HL93 model can be maintained without adjustment. It is relatively easy to modify the live-load factor γL but this cannot be done unless it applies to every span. Lmax Used in Existing LRFD Calibration NCHRP Report 368 (Nowak 1999) provides mean maximum moments and shears for various periods of time from 1 day to 75 years for simple span moments, shears, and negative moments for continuous spans. Span lengths range from 10 ft to 200 ft (Table 17). Continuous spans are composed of two equal spans. Continuous span positive moments and shears at the center pier have not been provided in the report. The maximum one-lane load effect is caused either by a single truck or two or more trucks (with the weight smaller than that of the single truck) following behind each other. There was little data to verify statistical parameters for multiple presence. The maximum values of moments and shears were calculated by simulations. For two-lane moments and shears, simulations indicated that the load case with two fully correlated side-by- side trucks will govern, with each truck equal to the maximum 2-month truck. The ratio of the mean maximum 75-year moment (or shear) and a mean 2-month moment (or shear) is about 0.85 for all spans. Based on the above simple method, an increase in the maximum expected 75-year live-load as estimated from cur- rent WIM data can be accounted for in the design equation by raising the live-load factor in proportion to the ratio of the estimated live-load projection from WIM data to the value used during the calibration of the AASHTO LRFD specifications. Method II: Reliability Analysis and Adjustment of Strength I Live-Load Factor The simplified approach in Method I focuses on the max- imum live-load variable, Lmax, assuming that the overall LRFD calibration, multiple-presence factors, and target reliability indices are adequate. Hence, the approach only updates the load 51 One-Lane Two-Lane One-Lane Two-Lane One-Lane Two-Lane 20 1.30 2.12 1.23 2.12 1.27 2.28 40 1.35 2.34 1.23 2.18 1.30 2.40 60 1.32 2.30 1.23 2.22 1.25 2.30 80 1.32 2.28 1.27 2.26 1.21 2.24 100 1.31 2.26 1.28 2.28 1.20 2.22 120 1.29 2.24 1.22 2.20 1.20 2.22 160 1.24 2.18 1.20 2.14 1.20 2.22 200 1.23 2.16 1.17 2.08 1.20 2.22 Span (Ft) Simple Span Moment Simple Span Shear Negative moment 75-Year Lmax Table 17. Lmax used in existing LRFD calibration.

factors to better represent current truck traffic conditions. One key assumption in this regard is that the site-to-site vari- ability in Lmax as measured by the COV (COV = STDEV/Mean) is the same as that used during the AASHTO LRFD calibration. In the AASHTO LRFD calibration, the overall live-load COV was taken as 20%. This 20% includes site-to-site variability, uncertainties in estimating the load distribution factors, uncertainties in estimating the dynamic allowance factor, and uncertainties in estimating Lmax due to the randomness of the parameter and the limitations in the data. When implementing the draft protocols using recent WIM data in Task 8 from various states, it became evident that this procedure, although simple to understand and use, had certain limitations when applied to statewide WIM data. Using a single maximum or characteristic value for Lmax for a state would be acceptable if the scatter or variability in Lmax from site to site for the state was equal to (or less than, to be conservative) the COV assumed in the LRFD calibration. If the variability in the WIM data is much greater than that assumed in the calibration, then the entire LRFD calibration to achieve the target 3.5 reliability index may no longer be valid for that state and a simple adjustment of the live-load factor as given above should not be done. The site-to-site scatter in the Lmax values obtained from recent WIM data showed significant variability from span to span, state to state, and between one-lane and two-lane load effects as given in Table 18 for a sample set of states. For example, the data from Florida show a COV for the moments of simple span bridges under one-lane loadings that varies from 32.5% for the 20-ft simple spans to 22.3% for the 200-ft simple spans. These COVs for site to site must be augmented by the COVs for the other variables that control the maximum load including within site variability, the effect of the dynamic allowance factor, load distribution factor, and WIM data sample size, leading to much higher overall COV for the live load than the 20% used during the AASHTO LRFD calibration. For the same maximum moment of simple span bridges under one-lane loading, the site-to-site variability for the data collected in California shows a COV that ranges between 19.3% for the 20-ft simple span bridges down to 5.9% for the 200-ft simple span bridges. Overall, the results of Table 18 indicate that the Florida sites evidenced the highest variability in Lmax, whereas California data was a lot more uniform. As shown by the data in Table 18, the site-to-site COV statistics alone for FL are greater than the overall live-load COV used in the LRFD calibration. On the other hand, the site-to-site COV statistics for California are lower. It should also be noted that the one-lane COVs for Florida are higher than the two-lane COV, whereas in California the two-lane event has a higher site-to-site variability. The maximum Lmax values, site-to-site variability in Lmax, as well as the variability in one-lane vs. two-lane events are influenced by several factors that appear to be state specific. These factors include 1. The presence of exclusion vehicles that are state legal loads— these heavy hauling vehicles usually operate mostly on state truck routes. There is likely to be a greater variation in truck weights on different routes in states with exclusion vehicles such as Florida. These heavy exclusion vehicles (and routine permits) may also be resulting in high Lmax values for the one-lane loaded case. It should be noted that all trucks with six or fewer axles were grouped in the Strength I calibration. This group included legal loads, exclusion loads, and illegal overloads as well as routine permits. 52 State Event Type 20 40 60 80 100 120 160 200 M-simple 1-Lane FL COV 0.325 0.307 0.278 0.276 0.270 0.260 0.238 0.223 IN COV 0.185 0.137 0.122 0.135 0.147 0.142 0.122 0.132 CA COV 0.193 0.104 0.045 0.054 0.061 0.062 0.058 0.059 M-simple 2-Lane FL COV 0.201 0.187 0.213 0.213 0.207 0.207 0.206 0.212 IN COV 0.150 0.139 0.132 0.125 0.116 0.113 0.116 0.119 CA COV 0.112 0.125 0.136 0.146 0.133 0.126 0.121 0.113 V-simple 1-Lane FL COV 0.340 0.299 0.289 0.279 0.248 0.241 0.224 0.214 IN COV 0.188 0.129 0.108 0.113 0.105 0.103 0.115 0.131 CA COV 0.143 0.087 0.056 0.047 0.049 0.049 0.058 0.056 V-simple 2-Lane FL COV 0.203 0.204 0.205 0.183 0.174 0.175 0.180 0.189 IN COV 0.140 0.119 0.122 0.133 0.134 0.136 0.135 0.140 CA COV 0.109 0.127 0.137 0.120 0.113 0.112 0.107 0.109 SPAN (ft) Table 18. Site-to-site variability in Lmax measured by coefficient of variation (COV).

2. The load limit enforcement environment in a state will have an influence on the level of illegal overloading. For instance, California is known to have an effective truck weight monitoring (and enforcement) operation that effectively utilizes the network of WIM systems throughout the state. 3. Site-to-site variability in truck weight data is also impacted by the quality and reliability of WIM data collected at the remote WIM sites. WIM data quality is highly dependent on the WIM quality assurance programs implemented by the state DOTs. Quality assurance programs must regu- larly check data for quality and require system repair or recalibration when suspect data is identified. Weighing accuracy is also sensitive to roadway conditions. Less vari- ability in traffic data is expected when all WIM systems are maintained to the same standard of performance and data accuracy. To incorporate the site-to-site statistical variations in WIM data collected in a given state, a reliability-based approach to adjusting the live-load factors is proposed as described in this report. Reliability-Based Adjustment of Live-Load Factors AASHTO LRFD Background. The calculation of the Lmax values is meant for use to adjust the live-load factors in the LRFD design check equations. Since Lmax is a random variable with high levels of uncertainties including site-to-site variability, the most appropriate procedure for adjusting the live-load factor is by applying the principles of structural reliability. A reliability-based procedure for adjusting the live-load factors would explicitly account for the variations in the Lmax values as well as the other variables that control the loading of a bridge member and its capacity to resist the applied loads. The variability in the Lmax values is due to the random nature of Lmax including the projection to the 75-year design life, the limitation in the data sample size collected within each site, and site-to-site variability. For developing a new design code, the Lmax values for a wide range of nationally representative sites should be used as input. For adjusting the live-load factors to reflect state-specific truck weights and truck traffic patterns, Lmax values obtained from a representative sample of sites within the state should be used. This section illustrates how the reliability-based adjustment of the live-load factor can be executed given a set of Lmax values obtained from WIM data. The LRFD design equation takes the form Where φ and γ are the resistance and load factors, Rn is the nominal resistance, DW is the dead load effect for wearing φ γ γ γR Dn DW W DC C L n≥ + +D L ( )32 surface, DC is the dead load effect for the components and attachments and Ln is the live-load effect of the HL93 load including dynamic allowance and load distribution factor. According to the LRFD specifications φ =1.0 for the bending moment capacities of steel and prestressed concrete members, γDW = 1.50, γDC = 1.25. The current live-load factor is given as γL = 1.75. The dynamic allowance factor is 1.33 times the truck moment effect and the load distribution factor is calculated as a function of span length and beam spacing for different numbers of loaded lanes. If the WIM data in a particular state show large differences from the standard generic data used during the calibration of the AASHTO LRFD equations, it may be necessary to adjust the LRFD live-load factor to maintain the same safety levels. The adjustment requires the modeling of the live-load effects and the other random variables that control the safety of bridge members. Modeling of Live-Load Effect on a Single Beam. For bending of typical prestressed concrete and steel girder bridges loaded by one lane of traffic, the load distribution factor equa- tion is given as (AASHTO 2007) follows: Where S is the beam spacing, L is the span length, ts is the deck thickness, and Kg is a beam stiffness parameter. Note that Equation 33 already includes a multiple-presence factor m = 1.2, which accounts for the higher probability of having one heavy truck in one lane as compared to the probability of having two side-by-side heavy trucks in two adjacent lanes. For two lanes loaded, the load distribution factor equation for bending becomes (AASHTO 2007) Observing that the Lmax values are for the normalized total static load effects on a bridge and observing that the D.F. of Equation 33 for a single lane already includes a multiple- presence factor m = 1.2, the final mean value for maximum load effect on a single beam can be calculated for one lane and two lanes loaded as follows: For one lane max beam max −− = = × × ×LL L L HL IM D F93 . . .1 2 93 For two lanes max beam max −− = = × ×LL L L HL IM D F× . ( ). 2 35 D F S S L K Lt g s . . . . . . = + ⎛⎝⎜ ⎞⎠⎟ ⎛⎝⎜ ⎞⎠⎟0 075 9 5 12 0 6 0 2 3 ⎛ ⎝⎜ ⎞ ⎠⎟ 0 1 34 . ( ) D F S S L K Lt g s . . . . . = + ⎛⎝⎜ ⎞⎠⎟ ⎛⎝⎜ ⎞⎠⎟ ⎛ ⎝0 06 14 12 0 4 0 3 3⎜ ⎞ ⎠⎟ 0 1 33 . ( ) 53

Dividing D.F. of one lane by 1.2 is done to remove the multiple-presence factor, while dividing the D.F. of two lanes by 2 is done to account for the fact that the Lmax values for two lanes calculated in this report are normalized by dividing by the effect of one lane of HL93 loading. The COV of the maximum beam live-load effect should account for the site-to-site variability represented by Vsite-to-site, the variability within a site represented by Vprojection, the un- certainty associated with the limited WIM data sample size represented by Vdata, the variability in the dynamic amplification factor, VIM and the variability in the load distribution factor VDF. The final COV for the applied live-load effect on a single beam can be obtained from Vsite-to-site is obtained by comparing the Lmax values from different WIM sites within the state. An analysis of the results of Lmax projections shows that the uncertainties within a site are associated with a COV on the order of Vprojection = 3.5% for the projection of the one-lane maximum effect and a COV of Vprojection = 5% for the two side-by-side trucks’ load effect. Additional uncertainties are associated with Lmax due to the limited number of data points used in the projections and the confidence levels associated with the number of sample points. Using the +/−95% confidence limits, it is estimated that the COV associated with the use of 1 year’s worth of WIM data is on the order of Vdata = 2% for the one-lane case and about Vdata = 3% for the two-lane case. Nowak (1999) also observed that the dynamic amplification factors augmented the Lmax load effect by an average of 13% for one lane of traffic and by 9% for side-by-side trucks. The dynamic amplification also resulted in a COV of VIM = 9% on the one-lane load effect and VIM = 5.5% on the two-lane effect. In previous studies on live-load modeling, Ghosn and Moses (1985) included the uncertainties in estimating the lane distribution factor, which was associated with a COV equal to VDF = 8% based on field measurements on typical steel and prestressed concrete bridges. Modeling of Other Random Variables. In addition to the live loads, the random variables that control the safety of a bridge member include the actual resistance and the applied dead loads. Nowak (1999) provided models to rep- resent the mean values and the COVs or standard deviations of these random variables that can be summarized as follows for the dead loads: D D V D D V D C C DC C C DC W 1 1 1 2 2 2 = = = = = 1 03 8 1 05 10 1 0 . % . % . D VW DW = 25 37% ( ) V V V V VLL IM= + + +site-to-site projection data2 2 2 2 + VDF2 36( ) For the bending moment resistance the mean and COV are given as Calculation of Reliability Index and Adjustment of Live-Load Factor. In the LRFD specifications, safety is measured using the reliability index, β, which accounts for the uncertainties in estimating the effects of the applied loads and the resistance of bridge members. The reliability index, β, is related to the probability of failure, Pf, by Where Φ−1( ) is the inverse of the cumulative normal distri- bution function. If all the random variables representing the resistance, dead load, and live load follow Gaussian (normal) probability distributions, the reliability index, β, can be calculated as follows: Where the mean of the total dead load is given by the COV of the total dead load is and the standard deviations are obtained as The AASHTO LRFD was calibrated so that all bridge members designed using the specified load and resistance factors produce a uniform level of risk expressed in terms of a reliability index β equal to a preset target value βtarget. The AASHTO LRFD calibration was based on a standard set of Lmax values and live-load standard deviations. If the Lmax values or their COVs within a state are different than those used during the AASHTO LRFD calibration it may be necessary to adjust the live-load factors in order to maintain the same βtarget. The adjustment of the live-load factors requires the calculation of the reliability index for different values of the live-load σ σ σ R R DL DL LL LL R V DL V LL V = × = × = × ( )43 σ σ σ σDL DC DC DW= + +1 22 2 2 42( ) DL D D Dc c w= + +1 2 41, ( ) β σ σ σ = − − + + R DL LL R DL LL 2 2 2 40( ) β = −( )−Φ 1 39Pf ( ) R R V R R V n R n R = = = 1 12 10 1 05 . % . for composite beams = 7 5 38 . % ( ) for prestressed concrete beams 54

factor γL and adopting the γL that produces reliability index values as close to the target as possible for all material types, spans, and geometric configurations. During the calibration of the AASHTO LRFD, Nowak (1999) assumed that the resistance is Lognormal while the combined effect of the dead and live loads is normal. The reliability index calculations were then executed using a first-order reliability method (FORM) algorithm instead of using Equation 40. However, in order to illustrate the procedure and keep the calculations as simple as possible, it is herein assumed that all the random variables representing the resistance, dead load, and live load follow Gaussian (normal) probability distributions. In such a case, the reliability index, β, can be directly calculated from Equation 40. Note that the data and models used by Nowak (1999) led to a target reliability index βtarget = 3.5. Method II Reliability-Based Adjustment Procedure for Live-Load Factors 1. Assemble a set of representative bridge samples for the state comprising steel and concrete bridges of different span lengths, number of beams, and beam spacing. 2. Assume a value for γL. 3. Choose one bridge from the representative sample of bridges. 4. Find the nominal dead loads of components and wearing surface: DC1, DC2, and DW. 5. Find the nominal live-load effect for the HL93 loading. 6. Apply the new value of γL into Equation 32 to obtain the required nominal resistance value Rn. 7. Find the mean resistance R – using Equation 38. 8. Find the COV VR also using Equation 38. 9. Find the mean dead load effects using Equation 37. 10. Find the COV for the dead loads using Equation 37 and find the standard deviations σDC1 = VDC1D –– C1 –– σDC2 = VDC2D –– C 2 –– σDW = VDWDW –––– 11. Use the protocols for the WIM data analysis to get Lmax for 75 years for one-lane loadings and two-lane loadings for several sites within the state. 12. Take the average Lmax and find Vsite-to-site COV for one-lane loading and two-lane loading for site-to-site variability. 13. Find the mean value of the live-load effect for one lane and two lanes using Equation 35. 14. Find the COV of the live-load effect for one-lane loading and two-lane loading using Equation 36. The proposed adjustment of the live-load factor is based on the following assumptions: • The target reliability index βtarget = 3.50 is a satisfactory target and does not need to be modified. This target was estab- lished by the AASHTO LRFD code writers based on the generic live-load data available at the time. Future research could lead to selecting a different target. • Although the changes in γL would lead to different bridge member capacities Rn, it is assumed that these changes would not lead to changes in the dead loads applied on the bridge members. • Equation 40 is based on the assumption that the resist- ance, dead load effects, and live-load effects follow normal (Gaussian) probability functions. Otherwise one should use a first-order reliability method (FORM) algorithm as described by Nowak (1999). • The models used to obtain the statistical data on the mean values and COVs of the moment and shear capacity of steel composite and prestressed concrete members, as well as the dynamic amplification factors and load distri- bution factors used during the AASHTO LRFD calibra- tion, are still valid. • The goal of the calibration is to adjust the live-load factor only so that the representative sample of bridges would, on average, match the target reliability index. In general, the target reliability index should be matched as closely as possible for all representative span lengths and bridge configurations. However, this may not be always possible by changing the live-load factor only. Step 13.2 Deck Design Load Calibration (Strength I) The database upon which the present AASHTO LRFD deck provisions were fixed is less defined for bending and shear in longitudinal members. LRFD design loads for decks represented by a 32-kip axle or a pair of 25-kip axles (Figure 21) were not based on the Ontario WIM data. The design truck has the same weights and axle spacing as the HS20 load model, which was adopted in 1944 for bridge design, and has been carried over from the standard specifications. WIM data were not used to validate these axle load models during LRFD development. NCHRP Report 368 (Nowak 1999) on LRFD calibration is focused on bridge loads for superstructure design and does not specifically address calibration of load models for deck design, fatigue design, or overload permitting. 55 DECK DESIGN – LRFD CODE PROVISIONS 32 k DESIGN AXLE 25 k DESIGN TANDEM25 k 4’ Figure 21. LRFD deck design loads.

Axle groups with more than two axles (Figure 22) are cur- rently not considered for deck design in the LRFD. However, LRFD commentary C3.6.1.3.3 states the following: Individual owners may choose to develop other axle weights and configurations to capture the load effects of the actual loads in their jurisdiction based upon local legal load and permitting policies. Triple-axle configurations of single-unit vehicles have been observed to have load effects in excess of the HL-93 tandem- axle load. A relevant issue that is beyond the scope of this project is the conservative nature of the present checking rules on the resistance side. The simple strip flexural model is conservative with respect to the true capacity of a deck that actually fails in a punching shear mode. Introducing an accurate strength model would require a change in nominal strength formulas as well as the calibrated factors, which require research beyond the current scope. Resistance factors vary with design methods and are not constant. Rigorous calibration of load and resistance factors for deck design requires the availability of statistical data beyond live loads. The LRFD did not specifically address deck components in the calibration. It is important to note that there are no β calculations or database of loads/load effects used for the calibration of decks in the LRFD available for use in this project. One reasonable approach to calibration of deck design loads is to assume the present LRFD safety targets are adequate for the strength design of decks and establish new nominal loads for axles based on recent WIM data. The LRFD live-load factors will remain unchanged, but the axle loads and axle types will be updated to be representative of current traffic data. For instance, tri-axles and quad-axles that are currently not included in the LRFD loadings may need to be considered. Axle weight statistics from WIM data will first be assembled. The measured axle weights should be adjusted for WIM scatter and measurement errors as detailed in Step 10. This proce- dure will be repeated for multiple WIM sites to determine the governing nominal loads, taken as follows: • For single axles, 32 kips or the 99th percentile statistic W99, whichever is higher; • For tandem axles, 50 kips (2 × 25 kips) or the 99th percentile statistic W99, whichever is higher; • For tridem axles, the 99th percentile statistic W99; and • For quad axles, the 99th percentile statistic W99. The nominal axle loads derived using WIM data are used instead of the code specified values, where the W99 statistic is higher than the code values. W99 represents an axle load with a 1% probability of exceedance in a year. This approach provides realistic axle loads for deck design based on current WIM data while keeping all other factors (load factor, deck dynamic load allowance) unchanged (Table 19). It also allows the intro- duction of three- and four-axle configurations for deck design in a consistent manner. WIM data will also be applied to define nominal axle spacings for the multi-axle groups. Step 13.3 Repetitive Live-Load Calibration (FATIGUE) The LRFD fatigue truck configuration will be checked and updated to ensure that it produces fatigue damage similar to that obtained from actual trucks from the traffic data for typ- ical bridge configurations and fatigue details. Adjustments to the fatigue load model could include changes to • Effective gross weight and • Axle configuration and axle loads. Fatigue adjustment factor K for each span using site WIM data could provide the basis for calibrating fatigue design load models, as follows: 1. Use LRFD fatigue truck if K values are uniform and equal to 1.0. 2. LRFD fatigue truck should be modified using the effective gross weight if K values are uniform but not equal to 1.0. 56 W3 W3 W3 S3 S3 W4 W4 W4 S4 S4 W4 S4 TRIDEM QUAD Figure 22. Common axle group loads. AXLE TYPE DESIGN AXLE LOAD AXLE SPACING LOAD FACTOR Single W99 not less than 32 K N/A 1.75 Tandem W99 not less than 50 K 4 ft 1.75 Tridem W99 from WIM 4 ft 1.75 Quad W99 from WIM 4 ft 1.75 Table 19. Deck design load calibration using WIM.

3. Recommend site-specific fatigue trucks if K varies from 1.0 for varying spans. Step 13.4 Superstructure Design Overload Calibration (Strength II) Live-Load Modeling for Strength II The AASHTO LRFD Strength II limit state is used when checking the safety of bridge members under the effect of owner-specified special design vehicles or evaluation permit vehicles. The return period implicit in Strength II is equal to 1 year. To develop appropriate live-load factors for the AASHTO LRFD Strength II limit state, the following three loading scenarios must be considered: • Case I: permit vehicle alone; • Case II: permit vehicle alongside another permit; and • Case IIII: permit vehicle alongside random vehicle. Case I is exclusively used if the permit vehicle is escorted and traffic is controlled such that no other heavy vehicle is allowed to cross the bridge when the permit is on. Otherwise, Case I should be compared to Cases II and III and the most critical case would govern. Case II may control the loading if a high number of permits are allowed over a certain route or are allowed to travel freely within a jurisdiction. Case III may control depending on the relative weights of the permit as com- pared to the heavy legal and illegal vehicles that normally cross the bridge. Case I: Permit Vehicle Alone. In this case, assume that the axle weights and axle configuration of the permit truck are perfectly known so that the total maximum static live-load effect on the bridge of the permit truck, designated by P, is a deterministic value. However, this does not imply that the total live-load effect on a bridge member is deterministic due to the uncertainties in estimating the dynamic effect represented by the dynamic amplification factor, IM, and the uncertainties in the structural analysis process that allocates the fraction of the total load to the most critical member. For multi-girder bridges, the structural analysis is represented by the load dis- tribution factor, D.F. The equations for the D.F. of multi- girder bridges loaded by a single lane given in the AASHTO LRFD specifications already include a multiple-presence factor m = 1.2. Therefore, the expression for the maximum load effect on the most critical beam when a single vehicle is on the bridge can be calculated from Nowak (1999) observed that the dynamic amplification factor augments the load effect by an average of 13% for one lane of For Case I max beamLL L P IM D F= = × × . . . ( )1 2 44 traffic. Assuming that the weight and axle configuration of the permit vehicle are exactly known, the COVs of the maxi- mum beam live-load effect are obtained from the COV of IM and the COV of DF as follows: Using the data for VIM and VDF for one lane proposed by Nowak (1999) and Ghosn and Moses (1985), for the load- ing of a single permit vehicle, the live-load COV becomes Case II: Two Permits Side by Side. In this case, assume that the axle weights and axle configurations of the two permit trucks are the same and are perfectly known so that the total maximum static live-load effect on the bridge is a deter- ministic value equal to 2P. However, this does not imply that the total live-load effect on a bridge member is deterministic due to the uncertainties in estimating the dynamic effect rep- resented by the dynamic amplification factor, IM, and the uncertainties in the structural analysis process that allocates the fraction of the total load to the most critical member. The structural analysis is represented by the load distribution factor, D.F. The equations for the D.F. of multi-girder bridges loaded in two lanes given in the AASHTO LRFD specifications assume that the two lanes are loaded by the same vehicle and give the load on the most critical beam as a function of the load in one of the lanes. Thus, the live-load effect on one member can be given as: According to Nowak (1999), the dynamic amplification factor augments the load effect by an average of 9% for side- by-side trucks. The dynamic amplification also results in a COV of VIM = 5.5% on the two-lane effect. Also assume that the same COV for the lane distribution factor VDF = 8% ob- tained by Moses and Ghosn (1986) from field measurements on typical steel and prestressed concrete bridges is still valid. Therefore, for the loading of a single permit vehicle, the live-load COV becomes The reliability index conditional on the arrival of two side-by-side permits on the bridge can then be calculated using Equation 40 where R – is the mean resistance when the bridge member is designed for two side-by-side permits and LL –– is the live-load effect on the beam due to two side- by-side permits. The reliability index calculated from Equation 40 in this case is conditional on having two side-by-side trucks. The prob- ability that a bridge member would fail given that two permit vehicles are side by side can be calculated from the inverse of LL = ( ) + ( ) =5 5 8 9 712 2. % % . %. For Case II max beamLL L P IM D F= = × × . . ( )46 VLL = ( ) + ( ) =9 8 122 2% % %. V V VLL IM DF= +2 2 45( ) 57

Equation 39. However, the final unconditional probability of failure will depend on the conditional probability given two side-by-side events and the probability of having a situation with side-by-side permits. Thus The probability of having two-side-by-side permits depends on the number of permit trucks expected to cross the bridge within the return period within which the permits are granted. The percentage of these permits that will be side by side is related to the total number of permit crossings. Tables re- lating the percentage of side-by-side events, Pside-by-side, as a function of the number of truck crossings can be obtained from the WIM data. The final unconditional reliability index is then obtained by inserting the results of Equation 47 into Equation 39. Case III: Permit Truck Alongside a Random Truck. For Case III, the maximum live-load effect is due to the permit truck alongside the maximum truck expected to occur simul- taneously in the other lane. The maximum total load effect depends on the number of side-by-side events expected within the return period. To determine the number of side-by-side permit-random truck events that would occur within a 1-year period, assume that NP gives the number of permit truck crossings expected in a return period T. The final number of random trucks along- side a permit will be Where Pside-by-side is the percentage of side-by-side events that depend on the ADTT and Np is the number of permits within the return period of interest. The maximum live-load effect is obtained from Where P is the load effect of the permit truck, DFP is the distribution factor for the load P, Lmax NR is the maximum load effect of random trucks for NR events which correspond to the 1-year return period applicable for the Strength II case, DFR is the distribution factor for the random load, and IM is the impact factor for side-by-side events. The problem in this case is that the DF tables provided in the AASHTO LRFD for two lanes assume that the two side-by-side trucks are of equal weight, which is clearly not the case. Following the AASHTO LRFD approach for permit trucks alongside random trucks, Moses (2001) suggested that DFP be obtained from the AASHTO LRFD tables for single lane while DFR be obtained from the difference between the DF of two lanes and that of a single lane. LL P DF L DF IMP N RR= × + ×( )max ( )49 N P NR P= ×side-by-side ( )48 P P Pf f= ×side-by-side events side-by-side ( )47 The coefficient of variation for Lmax NR × DFR is estimated as: Where all of the values are taken for the single-lane case. Assuming the effect of the permit load is deterministic, the coefficient of variation for PxDFP is estimated as follows which is the COV for the load distribution factor, DFP. Hence, the standard deviation of LL without the impact factor is and the COV for the live-load effect on the critical beam including the effect of the impact factor is given by where LL = (P × DFP + Lmax NR × DFR) is the static live-load effect on the most critical bridge member. The mean live load obtained from Equation 49 and the COV obtained from Equation 53 are then used to find the reliability index from Equation 40. The calibration of the appropriate live-load factor would consist of finding the γL that will lead to reliability index values equal to the target value for Cases I, II, and III. Method II: Reliability-Based Adjustment Procedure for Overload Live-Load Factors 1. Assemble a set of representative bridge samples for the state comprising steel and concrete bridges of different span lengths, number of beams, and beam spacing. 2. Determine the permit vehicle configuration. 3. Assume a value for γL. 4. Choose one bridge from the representative sample of bridges. 5. Find the nominal dead loads of components and wearing surface: DC1, DC2, and DW. 6. Find the nominal live-load effect, P, for the permit vehicle. 7. Apply the new value of γL into Equation 32 to obtain the required nominal resistance value Rn. 8. Find the mean resistance R – using Equation 38. 9. Find the COV VR also using Equation 38. 10. Find the mean dead load effects using Equation 37, 11. Find the COV of the dead loads from Equation 37 and find the standard deviations σDC1 = VDC1D –– C1 –– σDC2 = VDC2D –– C 2 –– σDW = VDWDW –––– V LL VLL LL IM= ⎛ ⎝⎜ ⎞ ⎠⎟ + ∗ ∗ σ 2 532 ( ) σLL P P L N RV P DF V L DFR∗ ∗ ∗= × ×( ) + × ×( )2 2 52max max ( ) VP∗ = 8 51% ( ) V V V V VL max∗ = + + +site-to-site2 projection data2 2 DF2 ( )50 58

12. Use the protocols for the WIM data analysis to get Lmax NR for one-lane loadings for a 1-year return period. 13. Calculate LL ––– for Case I, Case II, and Case III from Equa- tions 44, 46, and 49. 14. Find the COV for LL for each case using Equations 45 or 53. 15. Find the standard deviations using Equations 42 and 43. 16. Apply the mean and standard deviation values of loads and resistance into Equation 40 to calculate the reliability index, β, for the bridge configuration selected in Step 4 for each of the three cases. • For Cases I and III the reliability index is obtained from Equation 40 directly. • For Case II, the conditional reliability index, βcond is obtained from Equation 40. The final unconditional reliability index, β, is obtained from β = Φ−1(−Pf) where Pf is obtained from Equation 47 and Pf/side-by-side = Φ(−βcond) where Φ is the standard normal cumulative distribution function. 17. Go to Step 4 to select another bridge and repeat Steps 4 to 16 until you exhaust all of the bridges in the represen- tative sample. 18. Find the average βave of each load case for the representative sample of bridges. 19. If βave = βtarget = 3.50, stop. Otherwise, go to Step 3 and start the process over. 20. Determine the value of γL that leads to βave = βtarget = 3.50 for each of the three cases. Demonstration of Recommended Protocols Using National WIM Data In this chapter, draft protocols including step-by-step procedures for collecting and using traffic data in bridge design were developed. They are geared to address the use of national WIM data to develop and calibrate vehicular loads for LRFD superstructure design, fatigue design, deck design, and design for overload permits. The aim of this section is to give practical examples of using these protocols with national WIM data drawn from sites around the country with different traffic exposures, load spectra, and truck configurations. This will give a good cross- section of WIM data for illustrative purposes. This step will allow the updating and/or refinement of the protocols based on its applicability to WIM databases of varying quality and data standards currently being collected by the states. This section of the report discusses the results of the demonstration studies in more detail. Selection of Sites for National WIM Data Collection The protocols established in this chapter were implemented using recent traffic data (either 2005 or 2006) from 26 WIM sites (47 directional sites) in five states across the country (Table 20). The sites were chosen to capture a variety of geo- graphic locations and functional classes, including urban interstates, rural interstates, and state routes. Requests for WIM data needed for the studies were sent out to certain selected states based on the national survey findings. The requirements for selection of WIM sites were for WIM data for a whole year (2006 or 2005) from the following high- way functional classifications: • Two WIM sites on rural interstates, • Two WIM sites on urban interstates, and • Two WIM sites on principal arterials (non-interstate routes). 59 State Site ID Route Dir # Truck Records ADTT CA 0001 Lodi E/N 1537613 5058 CA 0001 Lodi W/S 1470924 4839 CA 0003 Antelope E 719834 2790 CA 0004 Antelope W 806122 3149 CA 0059 LA710 S 4243780 11627 CA 0060 LA710 N 3806748 11432 CA 0072 Bowman E/N 310596 2318 CA 0072 Bowman W/S 289319 2159 FL 9916 US-29 N 175905 498 FL 9919 I-95 N 939637 2708 FL 9919 I-95 S 875766 2524 FL 9926 I-75 N 1096076 4136 FL 9926 I-75 S 1032680 3897 FL 9927 SR-546 E 204549 567 FL 9927 SR-546 W 168114 466 FL 9936 I-10 E 700774 1980 FL 9936 I-10 W 723512 2044 IN 9511 I-65 N 2119022 5919 IN 9511 I-65 S 2068073 5777 IN 9512 I-74 E 931971 2596 IN 9512 I-74 W 1003443 2795 IN 9532 US-31 N 224506 629 IN 9532 US-31 S 229532 643 IN 9534 I-65 N 2128577 5929 IN 9534 I-65 S 2162874 6025 IN 9544 I-80/I-94 E 3786127 11235 IN 9544 I-80/I-94 W 4032537 11966 IN 9552 US-50 E 95900 278 IN 9552 US-50 W 102212 296 MS 2606 I-55 N 564393 1622 MS 2606 I-55 S 604919 1733 MS 3015 I-10 E 750814 2248 MS MS MS MS TX TX 3015 I-10 W 667560 1999 4506 I-55 N 530517 2002 4506 I-55 S 477931 1804 MS 6104 US-49 N 462301 1288 MS 6104 US-49 S 498054 1387 7900 US-61 N 69996 220 MS 7900 US-61 S 68198 216 TX 0506 US-287 E/N 559663 1701 TX 0506 US-287 W/S 520092 1581 TX 0516 I-35 E/N 717666 2384 0516 I-35 W/S 707744 2449 0523 US-281 E/N 430227 1429 TX 0523 US-281 W/S 394804 1312 TX 0526 I-20 E/N 1330799 4070 TX 0526 I-20 W/S 1174954 3593 Table 20. WIM sites studied in Task 8.

Table 21 lists the sites studied along with their respective ADTTs. For consistency, lanes one and two are eastbound or northbound lanes; lanes three and four are westbound or southbound lanes. Data Filtering and Quality Control (Protocol Steps 5.1 and 5.2) The same data scrubbing criteria established in Steps 5.1 and 5.2 were employed. That is, truck records that met any one of the following criteria were eliminated as unlikely or unwanted trucks for the purposes of this study. The following filtering protocol was applied for screening the WIM data used in this project. Truck records that met the following filters were eliminated: • Speed < 10 mph • Speed > 100 mph • Truck length > 120 ft • Total number of axles > 12 • Total number of axles < 3 • Record where the sum of axle spacing is greater than the length of truck • GVW < 12 kips • Record where an individual axle > 70 kips • Record where the steer axle > 25 kips • Record where the steer axle < 6 kips • Record where the first axle spacing < 5 ft • Record where any axle spacing < 3.4 ft • Record where any axle < 2 kips • Record which has GVW +/− sum of the axle weights by more than 10% The two most common criteria used to eliminate records were “number of axles < 3” (2-axle light vehicles) and “steer axle < 6 kips.” Typically, one of these two criteria was respon- sible for 75% to 90% of all scrubbed records at a given WIM site. Furthermore, the gross vehicle weight of these trucks tends to be low. Therefore, their removal from the study has very little effect on the analysis, which tends to concentrate on the upper tail of the data. Table 21 shows the number of trucks, as well as the percentage of the total truck population, eliminated from each WIM site for meeting one or more of the above criteria. Also shown is the mean gross vehicle weight, in kips, of all of the eliminated trucks. The scrubbed WIM data were passed through various quality control checks. The quality control checks established in Step 5.2 were employed for each WIM site studied. The quality control checks look specifically at Class 9 trucks (5-axle semi-trailer trucks). Since Class 9 trucks are so prevalent in the population and their configurations are well defined, deviations from their expected characteristics can be noted and corrective measures taken. The quality control checks are described as follows: 1. Percentage of trucks by class. Class 9 trucks should be the most prevalent truck class in the population. 2. Class 9 truck GVW histogram. The characteristic bi-modal shape of the GVW histogram should show an “unloaded” peak between 28 kips and 32 kips, and a “loaded” peak between 72 kips and 80 kips. 3. Overweight Class 9 trucks. The percentage of Class 9 trucks over 100 kips should be small. 4. Class 9 truck steer axle weight histogram. The weight of the front axle of Class 9 trucks should be between 9 kips and 11 kips. There should not be a significant deviation from this range. 5. Class 9 drive tandem weight histogram. The weight of the drive tandem should not deviate significantly from the esti- mated values given in NCHRP Report 495 (Fu et al. 2003). 6. Class 9 axle spacing histogram. The spacing between the steer axle and the drive tandem axle as well as the spacing between the drive tandem axles should be fairly consistent. The traffic in each lane at a WIM site is recorded by its own sensor. If a sensor malfunctions or begins to lose its calibration it will manifest itself in one or more of the results of the quality control checks. By segregating the data of these quality control checks by lane and by month, deviations from the normal, 60 State Site Number % GVW CA 0001 1671347 35.7 12.0 IN 9511 984044 19.0 CA 0003 643461 47.2 11.2 IN 9512 17.9 CA 0004 771032 48.9 11.4 IN 9532 64.9 CA 0059 1242393 22.6 14.3 IN 9534 31.3 CA 0060 1366271 26.4 14.8 IN 9544 19.2 CA 0072 407724 40.5 10.9 IN 9552 45.0 FL 9916 533513 73.0 16.5 MS 2606 24.6 FL 9919 457426 20.1 22.5 MS 3015 53.4 FL 9926 1752902 45.2 13.7 MS 4506 31.3 FL 9927 276965 42.6 16.5 MS 6104 33.7 FL 9936 330745 18.8 26.3 MS 7900 38.6 TX 0506 35.1 TX 0516 38.2 TX 0523 36.1 TX 0526 421592 839445 1952426 1855062 162192 380794 1712866 458419 488899 86777 584553 881932 465556 1261244 33.5 14.6 13.2 10.9 10.9 12.9 11.0 27.8 25.9 19.1 24.3 13.6 10.9 9.6 10.7 11.4 Table 21. Trucks eliminated by data filtering.

expected values can be more easily identified and isolated. If a sensor appears to be malfunctioning or providing less reliable data, then the data collected by the offending sensor is elimi- nated from the population. Of all the sites studied, only two required additional data scrubbing due to non-conformance during the quality control checks. At WIM Site 3015 in Mississippi, all data from Lane 3 during the months of January through June were eliminated. This accounted for 74,351 trucks, or 5.0% of the filtered truck data. At WIM Site 9916 in Florida, all data from Lane 1 dur- ing the month of January were eliminated. This accounted for 14,521 trucks, or 7.6% of the filtered truck data. After this second round of data scrubbing due to sensor issues, all remaining data was considered reliable and ready for processing. Truck Multiple-Presence (Protocol Step 6) Accurate multiple-presence data requires time stamps of truck arrival times to the hundredth of a second. The research team requested this time stamp resolution, but the WIM data records were mostly to a second accuracy. Multiple-presence statistics need not be developed for each site. Multiple-presence statistics are mostly transportable from site to site with similar truck traffic volumes and traffic flow. A relationship between multiple presence and ADTT was developed in this study, which could be applied to any given site without performing a site-specific analysis (see Step 7). WIM Data Analysis for One-Lane Loading (Step 7) Grouping Trucks into Strength I. Protocols developed in Step 7 require that legal loads, illegal overloads, and routine permits be grouped under Strength I and heavy special permits be grouped under Strength II. The following approach to sorting trucks in the WIM databases was used initially: • Do not attempt to classify New York trucks as permit or non-permit based on permit records when using large-scale WIM databases. The permit data are unreliable, incomplete, or not easily accessed to allow this to be achieved. • Group all trucks with six or fewer axles in the Strength I calibration. These vehicles include legal trucks, illegal over- loads, and routine permits. These vehicles are considered to be enveloped by the HL93 load model. • Group all trucks with seven or more axles in the Strength II calibration. These vehicles should include the heavy special permit loads, typically in the 150-kip GVW and above cate- gory. An analysis of WIM data from several states indicates a big drop-off in truck population for vehicles with seven or greater axles. Only a very small percentage of trucks belong to this permit group. This simple approach to separating trucks into Strength I and Strength II was considered reasonable. There are other approaches with varying degrees of complexity that may also provide a satisfactory way to achieve the same objective and may even provide better accuracy in some cases. Under the initial 12-76 study, the demonstration of the protocols was based only on the above noted sorting methodology. A follow-on study, NCHRP 12-76 (01), to investigate the sensitivity of “r” values to truck sorting strategies was conducted by the NCHRP 12-76 research team from 2009 to 2010. The results of this study and key recommendations on sorting of trucks into Strength I and Strength II limit states are presented at the end of this chapter. Gross Vehicle Weight Histograms (Step 7.1) Gross vehicle weight (GVW) histograms were generated by direction of travel for each WIM site. Figure 23 shows, as a sample, the GVW histogram for WIM Site 9926 in Florida (I-75). Appendix C contains the GVW histograms for all other WIM sites studied in this task. 61 Figure 23. GVW histogram (WIM Site 9926 in Florida).

for a simple 60-ft span for WIM Site 9926. Appendix C contains the moment histograms for all other WIM sites studied in this task. As would be expected, the general shape of these histograms is similar to that of the GVW histogram; that is, bi-modal with the first major peak representing unloaded or lightly loaded trucks and the second major peak representing trucks loaded near the legal limit. WIM Data Analysis for Two-Lane Loading (Step 8) Simulation of Truck Events using Generalized Multiple-Presence Statistics (Step 8.2) All of the New York WIM sites studied captured accurate time stamps with each truck record. This allowed for the analysis of two trucks existing simultaneously on a span. Additional data also were available from several WIM sites in New Jersey. 62 Figure 24. Single truck simple-span moment histogram (WIM Site 9926 in Florida). Figure 25. Single truck simple-span shear histogram (WIM Site 9926 in Florida). The bi-modal shape of this histogram is typical of GVW histograms with the first major peak representing unloaded or lightly loaded trucks and the second major peak represent- ing trucks loaded near the legal limit of 80 kips. One-Lane Load Effects (Step 7.1) The load effects of each truck individually were calculated for eight span lengths from 20 ft to 200 ft for both simple spans and two-span continuous spans. The load effects calculated were maximum mid-span moment for a simple span, shear at a support for a simple span, maximum positive moment for a two-span continuous span, maximum negative moment for a two-span continuous span, and shear at the center support of a two-span continuous span. All load effects were normal- ized to those of HL93 loading. Figure 24 shows, as a sample, the single truck maximum mid-span moment histogram for a simple 60-ft span for WIM Site 9926 in Florida (I-75). Similarly, Figure 25 shows the single truck maximum shear histogram

None of the WIM sites included reported time stamps with sufficient precision (to the nearest 1/100th of a second) to accurately model the relative positions of two trucks on a span. However, the probabilities of two trucks existing within various headway separations were determined. These probabilities, shown in Table 22, were used to simulate the simultaneous presence of two trucks on a span. Note that the very heavy ADTT multiple presence was based only on one site in New York City and has some anomalies that should be addressed by additional studies at other U.S. sites. Based on a WIM site’s ADTT and the multiple-presence probabilities established as shown in Table 23, the number of expected multiple-presence events for the given WIM site were determined. For each expected multiple-presence event, two trucks traveling in the desired direction were chosen at random from the entire population of trucks traveling in that direction and positioned to achieve the required headway separation. The load effects of the simulated multiple-presence events were calculated as for the single truck events. For the purpose of design, in consideration of distribution factors, load effects were segregated into one-lane and two-lane; one-lane load effects are those due to a single truck as well as two trucks in the same lane, while two-lane load effects are those due to two trucks in adjacent lanes. Figure 26 shows, as a sample, the one-lane and two-lane moment histograms for a 60-ft simple span for lanes one and two of WIM Site 9926 in Florida (I-75). Figures 27 and 28 are similar, but show the histograms for simple-span shear and negative moment, 63 Headway (ft) Light Average Heavy Very Heavy Light Average Heavy Very Heavy 0 to 20 0.19 0.41 0.61 0.60 0.00 0.00 0.00 0.00 20 to 40 0.14 0.43 0.66 0.63 0.00 0.00 0.00 0.00 40 to 60 0.21 0.41 0.68 0.66 0.01 0.00 0.00 0.01 60 to 80 0.26 0.35 0.62 0.64 0.01 0.00 0.00 0.09 80 to 100 0.20 0.53 0.76 0.74 0.06 0.04 0.03 0.49 100 to 120 0.21 0.41 0.81 0.64 0.12 0.15 0.16 1.81 120 to 140 0.24 0.34 0.66 0.61 0.21 0.33 0.45 3.04 140 to 160 0.17 0.30 0.61 0.56 0.36 0.57 0.73 3.29 160 to 180 0.18 0.29 0.56 0.53 0.48 0.67 0.91 3.03 180 to 200 0.19 0.26 0.52 0.50 0.46 0.75 0.98 2.74 200 to 220 0.10 0.24 0.48 0.48 0.51 0.68 0.94 2.52 220 to 240 0.14 0.24 0.45 0.43 0.48 0.67 0.91 2.28 240 to 260 0.12 0.22 0.43 0.41 0.42 0.65 0.87 2.18 260 to 280 0.14 0.21 0.41 0.39 0.41 0.60 0.85 1.98 280 to 300 0.11 0.20 0.40 0.36 0.39 0.59 0.80 1.87 ** Light: ADTT < 1000 Average: 1000 < ADTT < 2500 Heavy: 2500 < ADTT < 5000 Very Heavy: ADTT > 5000 Multiple Presence Probabilities (%) Two-Lane Events (Side-by-Side) One-Lane Events (Following) Site Truck Traffic (ADTT)** Site Truck Traffic (ADTT)** Table 22. Multiple-presence probabilities. Figure 26. Simple-span moment histogram (WIM Site 9926 in Florida).

64 Figure 27. Simple-span shear histogram (WIM Site 9926 in Florida). Figure 28. Two-span continuous negative moment histogram (WIM Site 9926 in Florida). respectively. Appendix C contains the load effect histograms for all other WIM sites studied in this task. Since it is unlikely that two trucks traveling in the same lane will be separated by less than 60 ft, the load effects histograms for the one-lane events are very similar to the single-truck load effects histograms; that is, they display the typical bi-modal shape. The same cannot be said of the two-lane events. Here, the distinction between unloaded trucks and loaded trucks is blended, resulting in a unimodal distribution. Accumulated Fatigue Damage and Effective Gross Weight (Step 11) Damage accumulation laws such as Miner’s Rule can then be used to estimate the fatigue damage for the whole design period for the expected truck population at a site. For varying spans, the effective gross weight for trucks measured at the site was determined using the following equation: where: fi is the fraction of gross weights within interval i, and Wi is the mid-width of interval i. In this calculation, use trucks only with three or more axles (Class 6 and above). The LRFD fatigue truck has a 54-kip effective gross weight. Table 23 shows the effective gross weights calculated for the various WIM sites. Accumulated fatigue damage was studied, as in Step 11, by calculating the fatigue adjustment factor, K. The fatigue adjust- ment factor K was calculated relative to three reference trucks— the LRFD fatigue truck, the modified LRFD fatigue truck, and the site-specific fatigue truck. K M M FT i× = ( )⎡ ⎣⎢ ⎤ ⎦⎥ ∑ 3 1 3 55 # ( ) Trucks W f Wi ieq = ( )∑ 3 1 3 54( )

The modified LRFD fatigue truck has the same number of axles, the same axle spacing, and the same axle weight distribution as the LRFD fatigue truck, but a GVW equal to the effective gross weight of the truck population at the WIM site. For the site-specific fatigue truck, the most common axle spacings and axle weight distributions were determined for the 5-axle trucks (the most common truck type) and used to define an equivalent 3-axle fatigue truck. That is, the drive tandem axles were combined into an equivalent single axle (with an axle weight equal to the combined weight of the tandem, located mid-way between the two tandem axles), and the trailer tandem axles were combined into an equivalent single axle. This is a slight adjustment to the definition of the site-specific fatigue truck used. The effective gross weight of the truck population was still used for the GVW of this fatigue truck. Table 24 shows the effective gross vehicle weight, in kips, used in calculating K for each directional WIM site studied in this task. The most common axle configuration of the five-axle trucks was gathered from histograms of axle weights and axle spacing for each WIM site. This information was used to define a site-specific fatigue truck for each site. Figure 29 shows, as a sample, the typical configuration of 5-axle trucks and the equivalent 3-axle fatigue truck derived from it for WIM Site 9926 in Florida (I-75). Table 24 shows, as a sample, the values of the fatigue adjustment factor, K, for the northbound lanes of WIM Site 9926. Appendix C contains the fatigue adjustment factor values for all other WIM sites studied in this task. The more closely the reference truck represents the actual truck traffic at a site, the closer the value of the fatigue adjust- ment factor is to unity. Values of K greater than 1.0 indicate that the reference truck underestimates the accumulated fatigue damage of the traffic, while values of K less than 1.0 indicate that the reference truck overestimates the accumulated fatigue damage. As would be expected, the site-specific fatigue truck most closely represents the entire truck population in regard to accumulated fatigue damage. 65 State Site ID Route Dir Weff CA 0001 Lodi E/N 61.5 MS 2606 I-55 N 73.7 CA 0001 Lodi W/S 60.3 MS 2606 I-55 S 66.0 CA 0003 Antelope E 56.3 MS 3015 I-10 E 56.9 CA 0004 Antelope W 56.4 MS 3015 I-10 W 61.7 CA 0059 LA710 S 45.8 MS 4506 I-55 N 67.1 CA 0060 LA710 N 54.4 MS 4506 I-55 S 56.9 CA 0072 Bowman E/N 56.0 MS 6104 US-49 N 65.5 CA 0072 Bowman W/S 57.2 MS 6104 US-49 S 66.0 FL 9916 US-29 N 56.1 MS 7900 US-61 N 58.9 FL 9919 I-95 N 49.3 MS 7900 US-61 S 60.7 FL 9919 I-95 S 50.0 TX 0506 E/N 63.1 FL 9926 I-75 N 56.2 TX 0506 W/S 62.7 FL 9926 I-75 S 59.6 TX 0516 E/N 55.6 FL 9927 SR-546 E 52.9 TX 0516 W/S 58.4 FL 9927 SR-546 W 47.2 TX 0523 E/N 60.9 FL 9936 I-10 E 73.9 TX 0523 W/S 62.2 FL 9936 I-10 W 50.2 TX 0526 E/N 60.8 IN 9511 I-65 N 51.4 TX 0526 W/S 61.9 IN 9511 I-65 S 47.4 IN 9512 I-74 E 64.5 IN 9512 I-74 W 65.1 IN 9532 US-31 N 47.4 IN 9532 US-31 S 50.7 IN 9534 I-65 N 49.0 IN 9534 I-65 S 51.6 IN 9544 I-80/I-94 E 53.5 IN 9544 I-80/I-94 W 50.1 IN 9552 US-50 E 55.7 IN 9552 US-50 W 46.3 Table 23. Effective gross vehicle weight for all WIM sites studied in Task 8. 16.5 ft 4 ft 31.5 ft 4 ft 0.214 W 0.213 W 0.204 W 0.187 W 0.182 W Typical 5-Axle Truck Configuration 18.5 ft 35.5 ft 0.21 W 0.42 W 0.37 W Site-Specific Fatigue Truck Configuration Figure 29. Site-specific truck configurations (WIM Site 9926 in Florida on I-75.)

Lifetime Maximum Load Effect Lmax for Strength I (Step 12.2) Statistical projections with a Gumbel distribution fit to the upper tail of the load effects histograms were used to determine the lifetime maximum load effects, Lmax, for Strength I super- structure design. Lmax was calculated for all 5 load effects, 8 span lengths, and 47 directional WIM sites, and segregated by one-lane and two-lane events. The results of the calculation of Lmax based on the data assembled from several WIM sites are provided in Tables 25 through 29 for different span lengths. The results show a slight decrease in the value of Lmax with span length. The average value of Lmax tends to be more closely related to its minimum value than to its maximum value, indicating a bias to less heavily loaded spans. Where the information is available, the 75-year Lmax values used in the LRFD calibration also are shown. With the exception of negative moment in a two-span continuous span, the Lmax values used in the LRFD calibration are unconservative, being less than the maximum values observed in this study. The degree to which these values are unconservative is more pronounced in the one-lane events where the Lmax values used in the LRFD calibration are less than the average values observed 66 Lanes 1 and 2 LRFD Fatigue Truck GVW = 54 kips Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kips Axle Spacing: 14 ft 30 ft Span (ft) 20 40 60 80 100 120 160 200 K (simple) 0.8965 0.9933 1.0718 0.9749 0.9846 0.9944 1.0069 1.0142 K (pos.) 0.875 0.9761 0.9988 0.967 0.9789 0.9885 1.0014 1.0094 K (neg.) 1.1614 0.9462 1.0834 1.0868 0.9887 1.0004 1.0175 1.0257 Modified LRFD Fatigue Truck GVW = 56.203 kips (effective gross weight) Axle Weight: Steer = 6.245 kips Drive = 24.979 kips Trailer = 24.979 kips Axle Spacing: 14 ft 30 ft Span (ft) 20 40 60 80 100 120 160 200 K (simple) 0.8613 0.9544 1.0298 0.9367 0.946 0.9554 0.9675 0.9745 K (pos.) 0.8407 0.9378 0.9596 0.9291 0.9406 0.9498 0.9622 0.9698 K (neg.) 1.1158 0.9091 1.0409 1.0442 0.95 0.9612 0.9777 0.9855 Site-Specific Fatigue Truck GVW = 56.203 kips (effective gross weight) Axle Weight: Steer = 11.803 kips Drive = 23.605 kips Trailer = 20.795 kips Axle Spacing: 18.5 ft 35.5 ft Span (ft) 20 40 60 80 100 120 160 200 K (simple) 0.9115 1.0464 1.0364 1.0236 1.0072 1.0028 1.0002 0.9995 K (pos.) 0.8896 1.0024 1.0203 1.0128 1.0051 1.0021 1 0.9994 K (neg.) 0.9749 1.0111 0.9887 1.0052 1.029 1.0147 1.0073 1.0045 Lanes 3 and 4 LRFD Fatigue Truck GVW = 54 kips Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kips Axle Spacing: 14 ft 30 ft Span (ft) 20 40 60 80 100 120 160 200 K (simple) 0.9928 1.1091 1.1941 1.0721 1.0701 1.0739 1.0804 1.0848 K (pos.) 0.9649 1.0879 1.1129 1.0638 1.0657 1.0695 1.0763 1.0811 K (neg.) 1.2809 1.0062 1.149 1.1622 1.0599 1.0688 1.0831 1.0901 Modified LRFD Fatigue Truck GVW = 59.573 kips (effective gross weight) Axle Weight: Steer = 6.619 kips Drive = 26.477 kips Trailer = 26.477 kips Axle Spacing: 14 ft 30 ft Span (ft) 20 40 60 80 100 120 160 200 K (simple) 0.8999 1.0054 1.0824 0.9718 0.97 0.9734 0.9794 0.9833 K (pos.) 0.8746 0.9861 1.0088 0.9643 0.966 0.9695 0.9756 0.9799 K (neg.) 1.1611 0.9121 1.0415 1.0535 0.9607 0.9688 0.9818 0.9881 Site-Specific Fatigue Truck GVW = 59.573 kips (effective gross weight) Axle Weight: Steer = 12.51 kips Drive = 25.021 kips Trailer = 22.042 kips Axle Spacing: 18.5 ft 35.5 ft Span (ft) 20 40 60 80 100 120 160 200 K (simple) 0.9523 1.1023 1.0894 1.0619 1.0327 1.0217 1.0125 1.0086 K (pos.) 0.9255 1.0541 1.0726 1.0512 1.0323 1.0229 1.014 1.0099 K (neg.) 1.0144 1.0143 0.9893 1.0142 1.0406 1.0228 1.0115 1.0071 Table 24. Fatigue adjustment factor, K (WIM Site 9926 in Florida on I-75).

Load Effect 20 40 60 80 100 120 160 200 1-Lane 1.989 1.635 1.413 1.392 1.351 1.311 1.227 1.168 2-Lane 1.955 1.823 1.844 1.891 1.859 1.783 1.676 1.544 1-Lane 1.861 1.526 1.483 1.427 1.391 1.349 1.258 1.175 2-Lane 1.930 1.843 1.904 1.870 1.842 1.796 1.662 1.549 1-Lane 1.861 1.526 1.483 1.427 1.391 1.349 1.258 1.175 2-Lane 1.867 1.859 1.859 1.894 1.854 1.806 1.697 1.564 1-Lane 1.599 1.557 1.364 1.346 1.250 1.078 0.939 0.846 2-Lane 2.017 2.013 1.446 1.086 1.020 0.973 0.895 0.812 1-Lane 1.752 1.508 1.506 1.439 1.344 1.208 1.020 0.915 2-Lane 1.906 1.846 1.896 1.848 1.757 1.520 1.356 1.200 Maximum Lmax Values of 8 Directional WIM Sites in California Span (ft) M-simple V-simple M-positive M-negative V-center Table 25. Maximum Lmax values for California. Load Effect 20 40 60 80 100 120 160 200 1-Lane 2.860 2.571 2.234 2.240 2.178 2.112 1.939 1.800 2-Lane 2.511 2.478 2.471 2.451 2.405 2.365 2.244 2.141 1-Lane 2.955 2.515 2.456 2.395 2.290 2.193 2.008 1.854 2-Lane 2.444 2.467 2.493 2.380 2.297 2.273 2.199 2.101 1-Lane 2.880 2.586 2.273 2.230 2.220 2.145 2.003 1.829 2-Lane 2.407 2.423 2.496 2.497 2.429 2.361 2.260 2.151 1-Lane 2.640 2.336 1.807 1.582 1.396 1.195 1.025 0.958 2-Lane 2.480 2.577 1.814 1.615 1.489 1.361 1.279 1.128 1-Lane 2.851 2.436 2.404 2.306 2.204 1.903 1.588 1.421 2-Lane 2.506 2.270 2.288 2.371 2.280 2.074 1.821 1.649 Maximum Lmax Values of 9 Directional WIM Sites in Florida Span (ft) M-simple V-simple M-positive M-negative V-center Table 26. Maximum Lmax values for Florida. Load Effect 20 40 60 80 100 120 160 200 1-Lane 2.302 2.207 1.932 1.896 1.859 1.806 1.702 1.636 2-Lane 2.219 1.958 1.814 1.765 1.706 1.749 1.740 1.669 1-Lane 2.422 2.079 1.899 1.883 1.839 1.789 1.687 1.618 2-Lane 2.134 1.820 1.885 2.019 2.057 2.034 1.914 1.798 1-Lane 2.352 2.175 1.961 1.891 1.858 1.807 1.736 1.636 2-Lane 2.278 1.952 1.800 1.735 1.739 1.768 1.742 1.672 1-Lane 1.861 1.917 1.608 1.505 1.302 1.153 1.009 0.939 2-Lane 1.841 2.335 1.853 1.324 1.076 1.073 1.017 0.934 1-Lane 2.392 2.024 1.831 1.810 1.764 1.581 1.395 1.302 2-Lane 2.100 1.791 1.837 1.971 1.991 1.799 1.555 1.416 Maximum Lmax Values of 12 Directional WIM Sites in Indiana Span (ft) M-simple V-simple M-positive M-negative V-center Table 27. Maximum Lmax values for Indiana. Load Effect 20 40 60 80 100 120 160 200 1-Lane 1.687 1.679 1.666 1.674 1.678 1.796 1.989 2.010 2-Lane 2.255 2.156 1.930 1.935 2.025 2.031 1.954 1.856 1-Lane 1.683 1.689 1.790 1.781 1.957 2.083 2.158 2.133 2-Lane 2.309 2.135 2.054 2.097 2.104 2.093 1.981 1.861 1-Lane 1.618 1.659 1.660 1.646 1.626 1.791 1.955 2.012 2-Lane 2.237 2.182 1.979 1.989 2.034 2.035 1.973 1.873 1-Lane 1.905 1.816 2.164 1.972 1.733 1.466 1.240 1.186 2-Lane 2.059 2.490 1.911 1.353 1.228 1.193 1.118 1.015 1-Lane 1.711 1.702 1.853 1.839 1.940 1.920 1.824 1.764 2-Lane 2.260 2.086 2.054 2.069 2.071 1.864 1.635 1.467 Maximum Lmax Values of 10 Directional WIM Sites in Mississippi Span (ft) M-simple V-simple M-positive M-negative V-center Table 28. Maximum Lmax values for Mississippi.

in this study. Appendix B contains the Lmax results for all the WIM sites studied in this task. Table 25 through Table 29 show, for each state studied in this task respectively, the maximum values of Lmax calculated for each load effect and span length. (The maximum value shown in a cell in the table is the maximum for all WIM sites in that state.) Although in many cases the maximum Lmax value for a two-lane event is larger than that of the equivalent one-lane event, this is not a generality that holds true for all load effects, all span lengths, or even all states. It is, however, evident that the truck traffic is state-dependent, resulting in a broad range of Lmax values among the states. Table 30 shows the 75-year Lmax values used in the LRFD calibration. Here the Lmax values remain fairly constant with span length and even with load effect. One apparent trend is for the Lmax value of the two-lane event to be nearly 2 × 0.85 that of the equivalent one-lane event. Discussion and Analysis of Lmax Results • The ratio of two-lane Lmax divided by one-lane Lmax is reasonably constant for shear and moments within a range of 1.05 to 1.13 (Figure 30). • The ratio of Lmax 2-lane/Lmax 1-lane for moments and shear of simple spans is relatively small, compared with the LRFD calibration data. This would indicate that in many cases the single event may govern design load effects. This would also depend on the LRFD live-load distribution factors for one- and two-lane loaded conditions. • Average Lmax seems to decrease with span length (Figure 31) indicating that HL93 loading is not entirely consistent with current truck weight data. • The spread in Lmax is very high with a coefficient of variation (COV) 0.36 to 0.24 with a tendency to go lower with span length. This COV expresses the site-to-site variability. Also, the COV accounts for the extreme distribution property (obtained from the projections protocols). The one-lane COV is lower and decreases faster with span length than the two-lane COV. • There seems to be no correlation between Lmax and ADTT. R2 is approximately zero for all the cases (Figures 32 through 36). Calibrate Vehicular Load Factors for Bridge Design Strength I (Step 13.1) Method I An increase in maximum expected live load based on current WIM data can be compensated in design by raising the live-load factor in a corresponding manner. The calibration process adjusts the corresponding live-load factor by the ratios r1 and r2 of Equations 30 and 31, as shown in Equation 56. 68 Load Effect 20 40 60 80 100 120 160 200 1-Lane 1.718 1.844 1.793 1.647 1.524 1.463 1.313 1.190 2-Lane 1.966 1.763 1.598 1.557 1.600 1.611 1.559 1.462 1-Lane 1.742 1.694 1.648 1.578 1.515 1.454 1.345 1.260 2-Lane 1.996 1.655 1.706 1.776 1.785 1.759 1.666 1.554 1-Lane 1.688 1.741 1.798 1.674 1.570 1.479 1.331 1.233 2-Lane 1.937 1.698 1.579 1.561 1.609 1.612 1.575 1.490 1-Lane 1.642 1.605 1.206 0.864 0.941 0.966 0.906 0.850 2-Lane 1.567 2.028 1.536 1.098 0.978 0.993 0.952 0.838 1-Lane 1.666 1.706 1.670 1.569 1.447 1.242 1.057 0.966 2-Lane 1.951 1.605 1.682 1.732 1.733 1.560 1.356 1.224 Maximum Lmax Values of 8 Directional WIM Sites in Texas Span (ft) M-simple V-simple M-positive M-negative V-center Table 29. Maximum Lmax values for Texas. Load Effect 20 40 60 80 100 120 160 200 1-Lane 1.300 1.350 1.320 1.320 1.310 1.290 1.240 1.230 2-Lane 2.120 2.340 2.300 2.280 2.260 2.240 2.180 2.160 1-Lane 1.230 1.230 1.230 1.270 1.280 1.220 1.200 1.170 2-Lane 2.120 2.180 2.220 2.260 2.280 2.200 2.140 2.080 1-Lane 1.270 1.300 1.250 1.210 1.200 1.200 1.200 1.200 2-Lane 2.280 2.400 2.300 2.240 2.220 2.220 2.220 2.220 75-year Lmax Values Used in LRFD Calibration Span (ft) M-simple V-simple M-negative Table 30. Seventy-five-year Lmax values used in LRFD calibration.

69 2 lane VS 2.500 2.000 1.500 Lm ax 1.000 0.500 0.000 2 lane MS 1 lane VS 1 lane MS 0 50 100 Span in Ft 150 200 250 Figure 31. Average Lmax vs. span length. 1.2 1 0.8 0.6 R at io 0.4 0.2 0 0 50 100 Span Length 150 200 250 MS VS Figure 30. Lmax for 2-lane/Lmax for one-lane for moments and shear of simple spans.

70 0 0 0.05 0.1 0.15 0.2 CO V of L m ax 0.25 0.3 0.35 0.4 50 100 Span Length 150 200 250 2 lane VS 2 lane MS 1 lane VS 1 lane MS Figure 32. COV of Lmax vs. span length. Series1 y = 7E-06x + 1.5401 R2 = 0.00201 Linear (Series1) 2.500 3.000 2.000 1.500 Lm ax 1.000 0.500 0.000 0 2000 800060004000 1200010000 14000 ADTT Figure 33. Lmax vs. ADTT for one-lane simple span moment.

71 Series1 y = -4E-06x + 1.6447 R2 = 5.1E-08 Linear (Series1) 2.500 3.000 2.000 1.500 Lm ax 1.000 0.500 0.000 0 2000 800060004000 1200010000 14000 ADTT Figure 34. Lmax vs. ADTT for one-lane simple span shear. Series1 y = -5E-07x + 1.6725 R2 = 6.9E-06 Linear (Series1) 2.500 4.000 3.500 3.000 2.000 1.500 Lm ax 1.000 0.500 0.000 0 2000 800060004000 1200010000 14000 ADTT Figure 35. Lmax vs. ADTT for two-lane simple span moment.

The value r is taken to be the ratio of the Lmax value as calculated from WIM data to the Lmax value used in the LRFD calibration. It can be used to determine the effectiveness of HL93 for lifetime maximum loading. One key assumption with regard to this simplified procedure for adjusting live-load factors is that the site-to-site variability in Lmax as measured by the COV is the same as that used during the AASHTO LRFD γ L StrengthI StrengthIr, . ( )= ×1 75 56 calibration. In the AASHTO LRFD calibration, the overall live-load COV was taken as 20%. Table 31 through Table 35 show, for each state studied in this task respectively, the maximum values of r calculated for each load effect and span length. Summary of Method I Results. As with Lmax, the value of r is state dependent. Unlike Lmax, however, there is a significant— and consistent—difference between the r-values for one-lane 72 Series1 y = -9E-06x + 1.8324 R2 = 0.00208 Linear (Series1) 2.500 4.000 3.500 3.000 2.000 1.500 Lm ax 1.000 0.500 0.000 0 2000 800060004000 1200010000 14000 ADTT Figure 36. Lmax vs. ADTT for two-lane simple span shear. Load Effect 20 40 60 80 100 120 160 200 1-Lane 1.530 1.211 1.070 1.055 1.031 1.016 0.990 0.950 2-Lane 0.922 0.779 0.802 0.829 0.823 0.796 0.769 0.715 1-Lane 1.513 1.241 1.206 1.124 1.087 1.106 1.048 1.004 2-Lane 0.910 0.845 0.858 0.827 0.808 0.816 0.777 0.745 1-Lane 1.259 1.198 1.091 1.112 1.042 0.898 0.783 0.705 2-Lane 0.885 0.839 0.629 0.485 0.459 0.438 0.403 0.366 Maximum r Values of 8 Directional WIM Sites in California Span (ft) M-simple V-simple M-negative Table 31. Maximum r values for California. Load Effect 20 40 60 80 100 120 160 200 1-Lane 2.200 1.904 1.692 1.697 1.663 1.637 1.564 1.463 2-Lane 1.184 1.059 1.074 1.075 1.064 1.056 1.029 0.991 1-Lane 2.402 2.045 1.997 1.886 1.789 1.798 1.673 1.585 2-Lane 1.153 1.132 1.123 1.053 1.007 1.033 1.028 1.010 1-Lane 2.079 1.797 1.446 1.307 1.163 0.996 0.854 0.798 2-Lane 1.088 1.074 0.789 0.721 0.671 0.613 0.576 0.508 Maximum r Values of 9 Directional WIM Sites in Florida Span (ft) M-simple V-simple M-negative Table 32. Maximum r values for Florida.

events and two-lane events. The r-values for one-lane events are significantly greater than those for two-lane events. Whereas the maximum r-values for two-lane events exceed 1.0 in some cases, its maximum value among all WIM sites is 1.184. This indicates that the HL93 loading defined in the LRFD specifi- cation is fairly adequate in modeling the lifetime maximum loading on a span with two lanes loaded. For one-lane events, the maximum r-values are often greater than 1.5 with a max- imum value among all WIM sites of 2.402. This indicates that the HL93 loading defined in the LRFD specification under- estimates the lifetime maximum loading on a span with only one lane loaded. It should be noted that HL93 load effects are being compared with routine truck traffic at a site, defined as all trucks with six or fewer axles that will include legal loads, illegal overloads, and routine permits. These unanalyzed rou- tine permits are a form of exclusion traffic for a particular state and should be enveloped by the HL93 design live-load model. This simplified procedure for adjusting live-load factors assumes that the site-to-site variability in Lmax is within the AASHTO LRFD calibration limits. This needs to be verified as a precondition for the use of Method I. Adjustment of Live-Load Factors Using Method II An example illustrating the application of the protocols for adjusting the load factors for Strength I using the reliability- based approach is presented. The illustration is provided for a set of bridges varying in span length between 60 ft to 200 ft with beam spacing varying between 4 ft and 12 ft. Composite steel and prestressed concrete simple span bridges are selected. The procedure follows the protocols provided in Step 13.1, Method II, using the equations of Chapter 2, and the results are given in Tables 40 through 45. For example, using the data provided by Nowak (1999) for a typical 60-ft simple span composite steel bridge with beams at 4-ft spacing, the wearing surface dead load is estimated to be DW = 49 kip-ft (referred to as D3 in Tables 36 and 37), the other dead loads are combined into DC = 284 kip-ft (with DC1=39 kip-ft for factory-made mem- bers, referred to as D1 in Tables 36 and 37, and DC2 = 245 kip-ft for cast in place members referred to as D2 in Tables 36 and 37). Assuming that as suggested by the AASHTO LRFD (2007) for the cases when the detailed design is not K Lt g s12 1 0 3 ⎛ ⎝⎜ ⎞ ⎠⎟ = . 73 Load Effect 20 40 60 80 100 120 160 200 1-Lane 1.771 1.635 1.464 1.436 1.419 1.400 1.373 1.330 2-Lane 1.047 0.837 0.789 0.774 0.755 0.781 0.798 0.773 1-Lane 1.969 1.690 1.544 1.483 1.437 1.466 1.406 1.383 2-Lane 1.007 0.835 0.849 0.893 0.902 0.925 0.894 0.864 1-Lane 1.465 1.475 1.286 1.244 1.085 0.961 0.841 0.783 2-Lane 0.807 0.973 0.806 0.591 0.485 0.483 0.458 0.421 Maximum r Values of 12 Directional WIM Sites in Indiana Span (ft) M-simple V-simple M-negative Table 33. Maximum r values for Indiana. Load Effect 20 40 60 80 100 120 160 200 1-Lane 1.298 1.244 1.262 1.268 1.281 1.392 1.604 1.634 2-Lane 1.064 0.921 0.839 0.849 0.896 0.907 0.896 0.859 1-Lane 1.368 1.373 1.455 1.402 1.529 1.707 1.798 1.823 2-Lane 1.089 0.979 0.925 0.928 0.923 0.951 0.926 0.895 1-Lane 1.500 1.397 1.731 1.630 1.444 1.222 1.033 0.988 2-Lane 0.903 1.038 0.831 0.604 0.553 0.537 0.504 0.457 Maximum r Values of 10 Directional WIM Sites in Mississippi Span (ft) M-simple V-simple M-negative Table 34. Maximum r values for Mississippi. Load Effect 20 40 60 80 100 120 160 200 1-Lane 1.322 1.366 1.358 1.248 1.163 1.134 1.059 0.967 2-Lane 0.927 0.753 0.695 0.683 0.708 0.719 0.715 0.677 1-Lane 1.416 1.377 1.340 1.243 1.184 1.192 1.121 1.077 2-Lane 0.942 0.759 0.768 0.786 0.783 0.800 0.779 0.747 1-Lane 1.293 1.235 0.965 0.714 0.784 0.805 0.755 0.708 2-Lane 0.687 0.845 0.668 0.490 0.441 0.447 0.429 0.377 Maximum r Values of 8 Directional WIM Sites in Texas Span (ft) M-simple V-simple M-negative Table 35. Maximum r values for Texas.

74 Composite steel Dead Loads HL-93 Required Nominal Resist. Span Spacing D1 D2 D3 Truck load lane load two lanes one lane ft ft kip-ft kip-ft kip-ft kip-ft kip-ft kip-ft kip-ft 60 4 39 245 49 805 288 1430.07 1210.44 60 6 48 335 73 805 288 1905.25 1580.00 60 8 70 414 97 805 288 2362.18 1931.67 60 10 84 521 122 805 288 2831.06 2295.99 60 12 103 639 146 805 288 3307.38 2668.51 Composite steel Dead Loads HL-93 Required Nominal Resist. Span Spacing D1 D2 D3 Truck load lane load one lane two lanes ft ft kip-ft kip-ft kip-ft kip-ft kip-ft kip-ft kip-ft 120 4 502 981 194 1882 1152 4552.49 3925.44 120 6 607 1341 292 1882 1152 6019.48 5112.16 120 8 650 1656 389 1882 1152 7302.59 6119.07 120 10 681 2083 486 1882 1152 8676.66 7220.72 120 12 773 2556 583 1882 1152 10158.57 8433.60 Composite steel Dead Loads HL-93 Required Nominal Resist. Span Spacing D1 D2 D3 Truck load lane load one lane two lanes ft ft kip-ft kip-ft kip-ft kip-ft kip-ft kip-ft kip-ft 200 4 2780 2725 540 3320 3200 12317.82 10987.92 200 6 3303 3725 810 3320 3200 16016.30 14116.20 200 8 3790 4600 1080 3320 3200 19422.06 16963.58 200 10 4190 5788 1350 3320 3200 23046.27 20039.36 200 12 4875 7100 1620 3320 3200 27132.98 23586.16 Table 36. Calculation of nominal resistance, Rn, using current LRFD for a sample of typical composite steel bridges. Prestressed Concrete Dead Loads HL-93 Required Nominal Resist. Span Spacing D1 D2 D3 Truck load lane load two lanes one lane ft ft kip-ft kip-ft kip-ft kip-ft kip-ft kip-ft kip-ft 60 4 262 245 49 805 288 1708.82 1489.19 60 6 262 335 73 805 288 2172.75 1847.50 60 8 262 414 97 805 288 2602.18 2171.67 60 10 262 521 122 805 288 3053.56 2518.49 60 12 262 639 146 805 288 3506.13 2867.26 Prestressed Concrete Dead Loads HL-93 Required Nominal Resist. Span Spacing D1 D2 D3 Truck load lane load one lane two lanes ft ft kip-ft kip-ft kip-ft kip-ft kip-ft kip-ft kip-ft 120 4 1899 981 194 1882 1152 6298.74 5671.69 120 6 1899 1341 292 1882 1152 7634.48 6727.16 120 8 1899 1656 389 1882 1152 8863.84 7680.32 120 10 1899 2083 486 1882 1152 10199.16 8743.22 120 12 1899 2556 583 1882 1152 11566.07 9841.10 Prestressed Concrete Dead Loads HL-93 Required Nominal Resist. Span Spacing D1 D2 D3 Truck load lane load one lane two lanes ft ft kip-ft kip-ft kip-ft kip-ft kip-ft kip-ft kip-ft 200 4 5650 2725 540 3320 3200 15905.32 14575.42 200 6 5650 3725 810 3320 3200 18950.05 17049.95 200 8 5650 4600 1080 3320 3200 21747.06 19288.58 200 10 5650 5788 1350 3320 3200 24871.27 21864.36 200 12 5650 7100 1620 3320 3200 28101.73 24554.91 Table 37. Calculation of nominal resistance, Rn, using current LRFD for a sample of typical prestressed concrete bridges.

available, Equation 34 will yield a distribution factor D.F. = 0.42 for two lanes loaded and Equation 33 gives D.F. = 0.33 for one lane loaded. Given that the AASHTO HL93 lane load moment for a 60-ft simple span is 288 kip-ft and the HL93 truck load is 805 kip-ft, and applying the dynamic allowance factor IM = 1.33 on the truck load, Equation 32 would lead to a nominal required resistance for a single beam Rn=1430 kip-ft for the two-lane case and Rn=1210 kip-ft for the one lane case. Since in this case the Rn value for two lanes is higher than that obtained for one-lane loading, the two-lane case governs the design. Similar calculations can be executed to find the required nominal bending moment capacity of steel and prestressed concrete bridges having different span lengths and beam spacings. For example, Tables 36 and 37 show the nominal bending moment resistances obtained using Equation 32 with the AASHTO LRFD-specified live-load factor γL = 1.75 for a sampleofsimple-spanbridgeconfigurations.Theconfigurations selected and the corresponding values for the dead weights are adopted from the report of the AASHTO LRFD calibration study (Nowak 1999). Live-Load Effect Modeling The work performed as part of NCHRP 12-76 consisted of collecting WIM truck traffic data on a variety of sites within the United States and using these data to project for the maximum expected live-load effects, Lmax, over the 75-year design life of a new bridge. For example, Table 38 provides a set of Lmax values obtained for the maximum bending moments of 60-ft, 120-ft, and 200-ft simple-span bridges from eight sites in California. The Lmax values were calculated for one lane of traffic and two lanes of traffic, and they are normalized with respect to the effect of one lane of HL93 loading. For example, the results of Table 38 for the 60-ft span show that, on average, the 75-year maximum load effect will be equal to 1.321 times the static load effect of the HL93 design load. The values vary from site to site, showing a standard deviation for site-to-site variability of 0.060 or as expressed in terms of a coefficient of variation Vsite-to-site = 4.5%. Table 39 gives the calculated Lmax values for the same sites for the cases when two lanes are loaded simultaneously. Note that the 60-ft span for the two-lane Lmax is, on average, equal to 1.44 times the effect of one lane of 75 Max State Site ID Direction ADTT 20 40 60 80 100 120 160 200 Value CA 0001 E/N 5058 1.370 1.278 1.239 1.206 1.173 1.164 1.137 1.086 1.370 CA 0001 W/S 4839 1.400 1.354 1.305 1.237 1.174 1.161 1.124 1.069 1.400 CA 0003 E 2790 1.190 1.216 1.293 1.268 1.219 1.191 1.149 1.106 1.293 CA 0004 W 3149 1.365 1.354 1.382 1.337 1.253 1.189 1.114 1.051 1.382 CA 0059 S 11627 1.340 1.291 1.368 1.358 1.338 1.293 1.212 1.127 1.368 CA 0060 N 11432 1.989 1.635 1.413 1.392 1.351 1.311 1.227 1.168 1.989 CA 0072 E/N 2318 1.138 1.228 1.297 1.255 1.221 1.140 1.052 1.003 1.297 CA 0072 W/S 2159 1.217 1.227 1.272 1.213 1.149 1.094 1.046 0.976 1.272 Min Value 1.138 1.216 1.239 1.206 1.149 1.094 1.046 0.976 Avg Value 1.376 1.323 1.321 1.283 1.235 1.193 1.132 1.073 Max Value 1.989 1.635 1.413 1.392 1.351 1.311 1.227 1.168 stand. Dev. 0.266 0.137 0.060 0.070 0.076 0.074 0.065 0.063 0.101 COV 0.193 0.104 0.045 0.054 0.061 0.062 0.058 0.059 0.057 1-Lane Event Lmax for Simple Span Moment Span Length (ft) Table 38. Lmax values for one lane for the moment effect of simple-span beams. Max State Site ID Direction ADTT 20 40 60 80 100 120 160 200 Value CA 0001 E/N 5058 1.663 1.706 1.515 1.412 1.456 1.450 1.386 1.299 1.706 CA 0001 W/S 4839 1.592 1.475 1.324 1.382 1.445 1.460 1.410 1.341 1.592 CA 0003 E 2790 1.447 1.421 1.429 1.392 1.374 1.332 1.281 1.213 1.447 CA 0004 W 3149 1.575 1.441 1.440 1.460 1.515 1.529 1.479 1.388 1.575 CA 0059 S 11627 1.678 1.665 1.490 1.553 1.562 1.578 1.506 1.419 1.678 CA 0060 N 11432 1.955 1.823 1.844 1.891 1.859 1.783 1.676 1.544 1.955 CA 0072 E/N 2318 1.368 1.235 1.172 1.199 1.224 1.233 1.177 1.122 1.368 CA 0072 W/S 2159 1.499 1.428 1.335 1.265 1.286 1.247 1.198 1.125 1.499 Min Value 1.368 1.235 1.172 1.199 1.224 1.233 1.177 1.122 Avg Value 1.597 1.524 1.444 1.444 1.465 1.452 1.389 1.306 Max Value 1.955 1.823 1.844 1.891 1.859 1.783 1.676 1.544 stand. Dev. 0.179 0.191 0.196 0.211 0.195 0.183 0.168 0.148 COV 0.112 0.125 0.136 0.146 0.133 0.126 0.121 0.113 0.127 2-Lane Event Lmax for Simple Span Moment Span Length (ft) Table 39. Lmax values for two lanes for the moment effect of simple-span beams.

HL93 with a site-to-site variability expressed through a COV, Vsite-to-site = 13.6%. The higher COV for the two-lane effects is partially due to the differences in the number of two-lane events collected at each site over the 1-year WIM data collection period as compared to the number of data samples collected for single-truck events in the main traffic lane. Other factors that influence the differences in the COVs include the ADTT at the sites, the frequency of heavy legal and overloaded vehicles (illegal, exclusion, or permit) in the truck traffic stream, and the probability of having two lanes loaded by such vehicles. In addition to the site-to-site variability, the uncertainties associated with the estimated values for Lmax include the un- certainties within a site due to the random nature of Lmax and the fact that the WIM data histograms do not necessarily include all of the extreme load events that may occur within the 75-year design period of the bridge. An analysis of the results of the projections shows that the uncertainties within a site are associated with a COV on Lmax on the order of Vprojection = 3.5% for the projection of the one-lane maximum effect and a COV of Vprojection=5% for the two side-by-side load effect. Vprojection was obtained from the analysis of the WIM data described in the draft protocols, by taking the ratio of the standard deviation σmax obtained from Equation 29 divided by the mean Lmax = μmax = of Equation 28. Additional uncertainties are associated with Lmax due to the limited number of data points used in the projections and the confidence levels associated with the number of sample points. Using the +/−95% confidence limits, it is estimated that the COV is on the order of Vdata = 2% for the one-lane case and about Vdata = 3% for the two-lane case. Vdata is an estimate obtained from the upper and lower 95% confidence intervals calculated as presented earlier in Step 5.3, Assess the Statistical Adequacy of Traffic Data. The research team took the upper and lower 95% values and assumed that they fall within +/− 1.96 standard deviations from the mean. So, by dividing the differ- ence between the mean value and the upper and lower 95% val- ues by 1.96 estimates of the standard deviation were obtained that, when divided by the mean value, gave estimates of the COV. For example, the upper and lower 95% limits for the WIM data collected at the I-81 site in New York State for Lmax of the one lane loading for the moment at the midpoint of a 60-ft simple span are 1.964 and 1.839. The mean Lmax for the one lane loading case is obtained as 1.906. Thus, one estimate of the stan- dard deviation is obtained as (1.906 − 1.839)/1.96 = 0.034. The estimate of the COV, Vdata, becomes 0.034/1.906 = 0.018 or about 1.8%. Another estimate is obtained as (1.964 − 1.906)/ 1.96/1.906 = 1.6%. The final Vdata used is rounded up to 2%. Similarly for the two-lane loading, the mean is Lmax =3.276, the lower 95% limit is 3.058, and the upper 95% limit is 3.462. One estimate for the standard deviation is (3.276 − 3.058)/ 1.96 = 0.111 and the estimate for the COV is 0.111/3.276 = 3.40%. Another estimate is obtained as (3.462 − 3.276)/1.96/ 3.276 = 2.90% and the final Vdata used is 3%. Strictly speaking, the approach followed for finding Vdata is not exact, but the Vdata calculated gives some measure of the uncertainty related to the size of the data sample. Nowak (1999) also observed that the dynamic amplifica- tion factors augmented the Lmax load effect by an average of 13% for one lane of traffic and by 9% for side-by-side trucks. The dynamic amplification also resulted in a COV of VIM = 9% on the one-lane load effect and VIM= 5.5% on the two-lane effect. In previous studies on live-load modeling, Ghosn and Moses (1985) included the uncertainties in estimating the lane distribution factor, which was associated with a COV equal to VDF = 8% based on field measurements on typical steel and prestressed concrete bridges. This information is used in Equations 35 and 36 to find the mean value of the live load and the COV. For example, the application of Equation 35 for the aver- age load effect on a 60-ft simple-span bridge from the Cali- fornia sites with beams at 4 ft would lead to the following: For one lane: For two lanes: For the one-lane case, Lmax=1.32 is obtained from Table 38 as the average value for the California sites for 60-ft spans. Lmax = 1.44 for two lanes is obtained from Table 39 as the average value for the 60-ft spans from all of the sites. Note that the mean live-load effect for the one-lane case is higher than that of the two-lane case. This is due to the fact that the number of side-by-side events is generally low compared to the number of single-lane events, thus the projection to the 75-year maximum for one lane of traffic would lead to the possibility of having a very heavy single truck load (1.32 times the effect of the HL93 load) as compared to having two very heavy side-by-side trucks, the maximum for each one being on the order of 0.72 (1.44/2) times the effect of the HL93 live load. Also, the load distribution factor D.F. indicates that the effect of a single truck would more likely load a single beam by 27% of the weight of one truck (D.F. = 0.33/1.2 =0.27) as compared to the weights of two trucks side-by-side, which would be more evenly spread over all the beams of the bridge such that the most loaded beam would carry 21% of the lane load (D.F = 0.42/2 = 0.21). Furthermore, the dynamic ampli- fication peaks of two trucks are not likely to coincide due to the different natural frequencies, which would lead to a lower LL L HL= × = × +( ) × × = max . . .bean 93 1 44 288 805 1 09 0 42 2 360 kip-ft LL L HL= × = × +( ) × ×max . . . .bean 93 1 32 288 805 1 13 0 33 1 2 448= kip-ft 76

overall dynamic allowance factor for the two-lane case (1.09) as compared to the one-lane case (1.13). Note that in these calculations and following the procedure of Nowak (1999), it has been assumed that the load distribution factors provided by AASHTO LRFD are the expected (mean) values. It should also be mentioned that the data for the dynamic allowance and for the load distribution factors as used by Nowak (1999) are based on very limited data and much more research is needed on these topics to study how these factors change from site to site and how they relate to the truck weights and traffic data. However, these issues are beyond the scope of this study and in this case, this study uses the same data applied during the AASHTO LRFD calibration. The application of Equation 36 for the 60-ft Lmax yields the following: For two lanes: For one lane: Vsite-to-site values of 4.5% and 13.5% for one-lane and two-lane cases are respectively obtained from Tables 39 and 40 for the 60-ft spans. The standard deviation for the two-lane case be- comes σLL = VLL  LL ––– = 65 kip-ft and for the one-lane case it is σLL = 58 kip-ft. Thus, the COV of the two-lane effect for the California sites is comparable to the VLL=19% to 20% obtained by Ghosn and Moses (1985) and subsequently used by Nowak (1999) during the calibration of the AASHTO LRFD specifications. Note that the COV for the single-lane effect is lower than that of the two-lane effect, indicating that the estimation of the maximum load effect for one lane is associated with lower levels of uncertainty. The difference in the two VLL COVs is primarily due to the site-to-site variability, which is much higher for the two-lane loading as compared to that for the one-lane loading. Modeling of Other Random Variables The application of Equations 37 and 38 for the beams of the 60-ft composite steel bridge at 4-ft spacing will yield mean dead loads as follows: The standard deviations are σDC1 = 3.2 kip-ft, σDC2 = 25.7 kip- ft, and σDW = 12.3 kip-ft. The mean of the total dead load be- D D DC C W1 2kip-ft, kip-ft and kip-= = =40 257 49 ft. VLL = ( ) + ( ) + ( ) + ( ) + ( ) =4 5 3 5 2 9 8 132 2 2 2 2. % . % % % % % VLL = ( ) + ( ) + ( ) + ( ) + ( ) =13 5 5 3 5 5 8 182 2 2 2 2. % % % . % % % comes DL ––– = 346 kip-ft and, using the square root of the sum of the square, the standard deviation for the total dead load is σDL = 29 kip-ft. The mean nominal resistance is as follows: For a two-lane bridge: R – = 1602 kip-ft and For a one-lane bridge: R – = 1355 kip-ft. The standard deviation for the resistance for the two-lane bridge is σR = 160 kip-ft and for the one-lane bridge, σR = 136 kip-ft. For the maximum moment of the sample of simple- span bridges studied in this report, Equations 37 and 38 will yield the mean and standard deviation values provided in Tables 36 and 37 for the bending moment of simple-span composite steel and prestressed concrete bridges. Calculation of Reliability Index and Calibration of Live-Load Factor The adjustment of the live-load factors requires the cal- culation of the reliability index for different values of the live-load factor γL. The γL that produces reliability index values as close to the target as possible for all material types, spans, and geometric configurations will be adopted as the final γL. Using γL = 1.75 for the one-lane 60-ft bridge with beams at 4-ft spacing, the reliability index is calculated from Equation 40 as For the two-lane 60-ft bridge with beams at 4-ft spacing, the reliability index is calculated as The results for this example indicate that, based on the WIM data collected at the California sites, the use of the AASHTO LRFD strength design equation with a live-load factor γL = 1.75 and the HL93 loading leads to a reliability index of β = 3.72 for the 75-year design life of a 60-ft simple-span steel bridge with beams at 4-ft spacing. In this case, the one-lane load governs the safety of the bridge beams, producing a reliability index value of β = 3.72, which is higher than the target β = 3.50 set during the calibration of the AASHTO LRFD specifications. It should be emphasized that the target β = 3.50 was set during the AASHTO LRFD code calibration based on the observation made at the time that, under the generic live-loading data, typical bridge configurations that were designed to satisfy the AASHTO LRFD specifications produced an average reliability index β= 3.50. Thus, the new LRFD code was developed in order for new designs to match this β = 3.50 as closely as possible for all bridge spans, configurations, and material types. Two lanes: β = − − + + = 1602 346 360 160 29 65 5 12 2 2 2 . One lane: L L β = − − + + = 1355 346 448 136 29 58 3 72 2 2 2 . 77

The two-lane loading leads to a much higher reliability index value of β = 5.12. This indicates that for the two-lane case, the AASHTO LRFD is conservative. It is noted that for the sake of simplicity this report assumed that the resistance, dead load and live load follow normal (Gaussian) distributions. The work of Nowak (1999) assumed that the resistance is lognormal while the combination of all the loads is normal. A preliminary sensitivity analysis was performed indicating that the normal model produces lower reliability index values than the lognormal model. The calcula- tion of the reliability index can be executed using Monte Carlo simulations (or other simulation techniques) if the probability distributions of all of the random variables are available. Previous sensitivity analyses performed by this research team have demonstrated that the calibration of LRFD design equa- tions is not sensitive to the probability distribution type used as long as the new equations are designed to match an aver- age reliability index calculated using the same models and probability distributions (Ghosn and Moses 1985, 1986). California Data. Tables 40 and 41 show the reliability index values obtained for the maximum bending moment of a sample of simple-span steel composite and prestressed bridge configurations. The results show that for the California truck traffic conditions, the reliability index for one lane is on the average equal to β = 3.55 which is close to the target β = 3.50. For two lanes of truck traffic, the average reliability index is β = 4.63. This indicates that for the two-lane loading of California bridges, the current AASHTO LRFD is conserva- tive producing higher reliability index values than the target β = 3.50 set by the AASHTO LRFD code writers. The range of the β’s however is large varying between a β = 5.32 for short span prestressed concrete bridges with closely spaced beams to β = 4.0 for long span prestressed concrete bridges with closely spaced beams. The fact that the loading of the short-span bridges is dominated by the live loads while the long span bridges’ loading is dominated by the dead load indicates that for California bridges, the HL93 nominal design live load is conservative. If one wishes to reduce the reliability index for the two-lane cases and achieve an average reliability index for the two-lane cases equal to the target β=3.50, then a live-load factor γL = 1.20 should be used. This would mean that the HL93 loading should be associated with a multiple lane reduction factor of 1.46 (1.75/1.20) when checking the design for two lanes of traffic. Alternatively, for the California WIM data, one could keep the current AASHTO LRFD live-load factor γL = 1.75 and accept the fact that the design will yield the target reliability index for one lane of traffic with the understanding that the design would be conservative for multiple lanes. The adjusted γL = 1.20 for the two-lane loading conditions is obtained by trial and error using the steps provided in 13.1, Method II. These steps are based on having established a representative sample of bridge configurations that represent the most common bridge spans, types, and configurations in the state and having predetermined an appropriate reliability index target βtarget, that bridges evaluated using the adjusted live-load factor should meet. In usual reliability-based adjustments of design and evalua- tion equations, the reliability index after adjusting the live-load factor should match the target reliability, βtarget, as closely as possible for all representative span ranges, bridge types, loading cases, etc. Given the large spread in the calculated reliability index values observed in Tables 40 and 41, this may not be possible to achieve by only adjusting the live-load factor. Furthermore, the sample of bridges selected for analysis may not actually be representative of the California bridges. However, to illustrate the process, the steps provided in 13.1 outline a reliability-based live-load adjustment procedure that assumes that the target reliability index has already been established as βtarget = 3.5 for the sample of bridges analyzed in the previous section, and the goal of the trial and error analysis process is to adjust the live-load factor γL so that the average reliability index of the bridges analyzed after adjusting the live-load fac- tor will produce the target index. Florida Data. The results presented above for the Califor- nia WIM data may not be consistent with the data from other states or jurisdictions. The differences are mainly due to the legal truck weight limits or exemptions and the permit overload frequencies and weight regulations that may vary from state to state. For example, if the Lmax values generated from the Florida WIM data sites are used as input for the live-load modeling, the reliability index values shown in Tables 42 and 43 are obtained. These tables show that the reliability index for one lane of load- ing drops to an average of β = 2.58. The two-lane Lmax would lead to an average reliability index β = 3.96. The latter value is still higher than the target β = 3.50 while the one-lane reli- ability is lower than the target. It is noted that the Florida data shows high variations from the results of different sites leading to a high COV for Lmax and subsequently lower reliability index values than those observed from the California data. It is noted that if the live-load factor is raised to γL = 2.37 the reliability indexes for the Florida sites would increase to β = 3.50 for the one-lane cases, and β = 4.95 for the two-lane cases, bringing the reliability indexes more in line with the California results. Indiana Data. Using the Lmax values generated from the Indiana WIM data sites, the reliability index values shown in Tables 44 and 45 are obtained. These tables show that the reliability index for one lane of loading is, on average, equal to β = 3.16 for one-lane loading. The two-lane Lmax would lead to an average reliability index of β = 4.71. The latter value is higher than the target β = 3.5 while the one-lane reliability is 78

Span Spacing Ave. Res. 1 Av. Res. 2 σ Res. 1 σ Res. 2 Mean DL σ DL Mean LL 1 Mean LL 2 σ LL 1 σ LL 2 beta 1-lane beta 2-lane 60 4 1356 1602 136 160 346 28 447 362 60 64 3.73 5.11 60 6 1770 2134 177 213 474 38 567 476 76 84 3.71 5.09 60 8 2163 2646 216 265 604 48 675 583 91 103 3.69 5.07 60 10 2572 3171 257 317 756 61 776 684 105 121 3.66 5.02 60 12 2989 3704 299 370 923 74 870 782 117 138 3.63 4.97 120 4 4396 5099 440 510 1741 117 949 904 134 153 3.60 4.50 120 6 5726 6742 573 674 2325 160 1193 1181 169 200 3.57 4.49 120 8 6853 8179 685 818 2797 199 1414 1440 200 244 3.57 4.50 120 10 8087 9718 809 972 3375 247 1618 1686 229 286 3.53 4.47 120 12 9446 11378 945 1138 4063 301 1811 1923 256 326 3.49 4.42 200 4 12306 13796 1231 1380 6265 377 1630 1611 228 258 3.38 4.07 200 6 15810 17938 1581 1794 8123 500 2035 2095 285 335 3.36 4.08 200 8 18999 21753 1900 2175 9814 614 2401 2547 336 408 3.35 4.09 200 10 22444 25812 2244 2581 11743 749 2740 2977 384 476 3.32 4.06 200 12 26416 30389 2642 3039 14096 906 3059 3390 428 542 3.28 4.01 Table 40. Reliability index calculation for bending moment of simple span composite steel bridges based on California WIM data. 60 4 1564 1794 125 144 576 34 447 362 60 64 3.78 5.32 60 6 1940 2281 155 183 695 44 567 476 76 84 3.80 5.40 60 8 2280 2732 182 219 802 52 675 583 91 103 3.82 5.45 60 10 2644 3206 212 256 939 64 776 684 105 121 3.80 5.45 60 12 3011 3681 241 295 1087 77 870 782 117 138 3.78 5.43 120 4 5955 6614 476 529 3180 187 949 904 134 153 3.45 4.35 120 6 7064 8016 565 641 3656 215 1193 1181 169 200 3.53 4.51 120 8 8064 9307 645 745 4084 245 1414 1440 200 244 3.57 4.61 120 10 9180 10709 734 857 4629 285 1618 1686 229 286 3.58 4.64 120 12 10333 12144 827 972 5223 331 1811 1923 256 326 3.56 4.64 200 4 15304 16701 1224 1336 9221 545 1630 1611 228 258 3.28 4.00 200 6 17902 19898 1432 1592 10541 620 2035 2095 285 335 3.36 4.17 200 8 20253 22834 1620 1827 11730 699 2401 2547 336 408 3.41 4.28 200 10 22958 26115 1837 2089 13247 808 2740 2977 384 476 3.41 4.32 200 12 25783 29507 2063 2361 14895 934 3059 3390 428 542 3.40 4.32 Span Spacing Ave. Res. 1 Av. Res. 2 σ Res. 1 σ Res. 2 Mean DL σ DL Mean LL 1 Mean LL 2 σ LL 1 σ LL 2 beta 1-lane beta 2-lane Table 41. Reliability index calculation for bending moment of simple span prestressed concrete bridges based on California WIM data.

60 4 1564 1794 125 144 576 34 1201 1036 151 134 2.21 4.07 60 6 1940 2281 155 183 695 44 1510 1354 192 177 2.20 4.09 60 8 2280 2732 182 219 802 52 1789 1651 229 216 2.19 4.10 60 10 2644 3206 212 256 939 64 2048 1934 263 254 2.20 4.10 60 12 3011 3681 241 295 1087 77 2292 2205 295 290 2.21 4.09 120 4 5955 6614 476 529 3180 187 2120 1851 315 269 2.67 3.91 120 6 7064 8016 565 641 3656 215 2648 2407 397 351 2.68 4.01 120 8 8064 9307 645 745 4084 245 3123 2926 470 429 2.69 4.07 120 10 9180 10709 734 857 4629 285 3565 3420 538 502 2.69 4.09 120 12 10333 12144 827 972 5223 331 3980 3894 602 572 2.68 4.09 200 4 15304 16701 1224 1336 9221 545 1630 1611 565 498 2.75 3.71 200 6 17902 19898 1432 1592 10541 620 2035 2095 706 648 2.79 3.84 200 8 20253 22834 1620 1827 11730 699 2401 2547 833 788 2.80 3.92 200 10 22958 26115 1837 2089 13247 808 2740 2977 950 921 2.80 3.94 200 12 25783 29507 2063 2361 14895 934 3059 3390 1061 1049 2.80 3.94 Span Spacing Ave. Res. 1 Av. Res. 2 σ Res. 1 σ Res. 2 Mean DL σ DL Mean LL 1 Mean LL 2 σ LL 1 σ LL 2 beta 1-lane beta 2-lane Table 43. Reliability index calculation for bending moment of simple span prestressed concrete bridges based on Florida WIM data. 60 4 1356 1602 136 160 346 28 566 425 151 134 2.25 4.02 60 6 1770 2134 177 213 474 38 718 558 192 177 2.27 4.02 60 8 2163 2646 216 265 604 48 855 683 229 216 2.30 4.02 60 10 2572 3171 257 317 756 61 982 802 263 254 2.32 4.01 60 12 2989 3704 299 370 923 74 1102 916 295 290 2.34 3.99 120 4 4396 5099 440 510 1741 117 1201 1036 315 269 2.69 4.01 120 6 5726 6742 573 674 2325 160 1510 1354 397 351 2.71 4.00 120 8 6853 8179 685 818 2797 199 1789 1651 470 429 2.71 4.01 120 10 8087 9718 809 972 3375 247 2048 1934 538 502 2.72 3.99 120 12 9446 11378 945 1138 4063 301 2292 2205 602 572 2.72 3.96 200 4 12306 13796 1231 1380 6265 377 2120 1851 565 498 2.82 3.78 200 6 15810 17938 1581 1794 8123 500 2648 2407 706 648 2.83 3.79 200 8 18999 21753 1900 2175 9814 614 3123 2926 833 788 2.83 3.79 200 10 22444 25812 2244 2581 11743 749 3565 3420 950 921 2.83 3.78 200 12 26416 30389 2642 3039 14096 906 3980 3894 1061 1049 2.82 3.74 Span Spacing Ave. Res. 1 Av. Res. 2 σ Res. 1 σ Res. 2 Mean DL σ DL Mean LL 1 Mean LL 2 σ LL 1 σ LL 2 beta 1-lane beta 2-lane Table 42. Reliability index calculation for bending moment of simple span composite steel bridges based on Florida WIM data.

60 4 1356 1602 136 160 346 28 508 376 62 50 3.31 5.17 60 6 1770 2134 177 213 474 38 644 495 79 65 3.30 5.14 60 8 2163 2646 216 265 604 48 767 606 94 80 3.29 5.12 60 10 2572 3171 257 317 756 61 881 711 107 94 3.28 5.07 60 12 2989 3704 299 370 923 74 988 812 121 107 3.26 5.01 120 4 4396 5099 440 510 1741 117 1137 888 162 100 3.15 4.64 120 6 5726 6742 573 674 2325 160 1430 1161 203 131 3.14 4.62 120 8 6853 8179 685 818 2797 199 1695 1415 241 160 3.14 4.63 120 10 8087 9718 809 972 3375 247 1940 1657 275 187 3.12 4.59 120 12 9446 11378 945 1138 4063 301 2170 1890 308 214 3.09 4.54 200 4 12306 13796 1231 1380 6265 377 1999 1598 264 190 3.08 4.11 200 6 15810 17938 1581 1794 8123 500 2496 2078 329 247 3.07 4.12 200 8 18999 21753 1900 2175 9814 614 2944 2526 389 301 3.07 4.13 200 10 22444 25812 2244 2581 11743 749 3360 2952 444 351 3.05 4.10 200 12 26416 30389 2642 3039 14096 906 3752 3362 495 400 3.02 4.05 Span Spacing Ave. Res. 1 Av. Res. 2 σ Res. 1 σ Res. 2 Mean DL σ DL Mean LL 1 Mean LL 2 σ LL 1 σ LL 2 beta 1-lane beta 2-lane Table 44. Reliability index calculation for bending moment of simple span composite steel bridges based on Indiana WIM data. 60 4 1564 1794 125 144 576 34 508 376 62 50 3.34 5.40 60 6 1940 2281 155 183 695 44 644 495 79 65 3.35 5.50 60 8 2280 2732 182 219 802 52 767 606 94 80 3.36 5.55 60 10 2644 3206 212 256 939 64 881 711 107 94 3.36 5.55 60 12 3011 3681 241 295 1087 77 988 812 121 107 3.34 5.53 120 4 5955 6614 476 529 3180 187 1137 888 162 100 3.05 4.46 120 6 7064 8016 565 641 3656 215 1430 1161 203 131 3.10 4.64 120 8 8064 9307 645 745 4084 245 1695 1415 241 160 3.13 4.76 120 10 9180 10709 734 857 4629 285 1940 1657 275 187 3.13 4.80 120 12 10333 12144 827 972 5223 331 2170 1890 308 214 3.12 4.80 200 4 15304 16701 1224 1336 9221 545 1999 1598 264 190 2.99 4.04 200 6 17902 19898 1432 1592 10541 620 2496 2078 329 247 3.05 4.22 200 8 20253 22834 1620 1827 11730 699 2944 2526 389 301 3.09 4.34 200 10 22958 26115 1837 2089 13247 808 3360 2952 444 351 3.09 4.37 200 12 25783 29507 2063 2361 14895 934 3752 3362 495 400 3.08 4.38 Span Spacing Ave. Res. 1 Av. Res. 2 σ Res. 1 σ Res. 2 Mean DL σ DL Mean LL 1 Mean LL 2 σ LL 1 σ LL 2 beta 1-lane beta 2-lane Table 45. Reliability index calculation for bending moment of simple span prestressed concrete bridges based on Indiana WIM data.

slightly lower than the target. The Indiana data show a site- to-site variability in COVs on the order of 11% to 15% for both one-lane and two-lane loadings. This is compared to the California data that show low site-to-site variability in the one-lane loading cases (typically less than 10% for spans greater than 40 ft) and the Florida data that show high COVs for both the one-lane and two-lane cases (typically greater than 20%). Summary. Using a single maximum or characteristic value for Lmax for a state would be acceptable if the scatter or variability in Lmax from site-to-site for the state was equal to (or less than, to be conservative) the COV assumed in the LRFD calibration. If the variability in the WIM data is much greater than that assumed in the calibration, then the entire LRFD calibration to achieve the target 3.5 reliability index may no longer be valid for that state and a simple adjustment of the live-load factor as given in the Method I, Step 13.1 protocols, should not be done. This example presented a reliability-based procedure to adjust the live-load factors based on the Lmax values assembled for each state. The results show that the average reliability index values vary considerably from state to state as a function of the average Lmax values, the live- load case that governs, and the site-to-site variability expressed in terms of the COV of Lmax. Also, the results reflect that current WIM data indicate that one-lane loadings are often dominating the safety of bridge members due to the lower number of side- by-side events and the lower load effects produced by these events when compared to the data used during the calibration of the AASHTO LRFD. The Method II procedure outlined provides a more robust method for updating live-load factors for LRFD design using recent WIM data. Calibrate Overload Load Factors for Strength II (Step 13.4) Reliability Analysis and Adjustment of Live-Load Factor for Case I—Permit Vehicle Alone To execute the reliability calculations, the research team used a set of typical permit vehicle configurations as shown in Figure 37. These configurations are for typical special hauling vehicles (SHV) and are adopted from the work performed for NCHRP 12-63 (Sivakumar et al. 2007). The weights of these SHVs are increased by 150% from the legal limits to be con- sidered as special permit loads. For 60-ft, 120-ft, and 200-ft simple spans, these hypothetical permit vehicles produce the maximum moments of Table 46. The nominal resistance that would be required for a set of multi-beam simple-span steel bridges can be calculated by applying Equation 32 with γD = 1.25 for component dead 82 T4A T5A T6A T7A T8 Bridge Formula Truck (BFT) 10' 4' 4' 10' 4' 4' 4' 10' 4' 4' 4' 4' 10' 4' 4' 4' 4' 4' 6' 4' 4' 4' 4' 4' 4' 6' to 14' 4' 4' 4' 4' 4' 4' 12 8 17 17 12 8 8 8 8 17 17 11.5 11.5 17 17 8 8171788 8 6.5 6 10.5 8 10.5 8 10.5 17 17 10.5 10.5 8 10.5 8 10.5 8 GVW=54Kips GVW=62Kips GVW=69.5Kips GVW=77.5Kips GVW=80Kips GVW=80Kips Legal Limit Permit Weight GVW=120Kips GVW=120Kips GVW=116.3Kips GVW=104.3Kips GVW=93Kips GVW=81Kips Figure 37. Examples of permit truck configurations. Moments in kip-ft Span length T4A T5A T6A T7A T8 BFT 60 ft 1016 1116 1240 1346 1336 1405 120 ft 2230 2508 2802 3090 3134 3205 200 ft 3850 4366 4887 5415 5534 5604 Table 46. Moment effect for a set of permit trucks.

weights and γD = 1.50 for the wearing surface. In Equation 32, the effect of the permit trucks is multiplied by a load factor γL = 1.35 after applying the D.F. of Equation 33 and the impact factor specified in the AASHTO LRFD as IM = 1.33. The required nominal resistance values for the cases con- sidered in this example are provided in Table 47. In these calculations the research team assumed that the dead loads of the components remain essentially unchanged when the applied live loads are changed. The application of Equa- tion 40 leads to the reliability index values provided in Table 48. The results of Table 48 illustrate the following points: • For a given span length and beam spacing, the different vehicle configurations produce little change in the reliability index. The largest difference in β is on the order of 0.11 when the range is between β = 3.22 to β = 3.33 for the 60-ft span with beams at 12 ft. • Increasing the beam spacing leads to slightly lower reliability index values. • Increasing span length leads to lower reliability index values. • The average reliability index for the span lengths and beam spacings considered is on the order of βave = 3.07 with a min- imum value of β = 2.74 and a maximum value of β = 3.40. • Using a live-load factor γL = 1.35 for Strength II produces an average reliability index of βave = 3.07 for a single permit on the bridge. This average value is lower than the βtarget = 3.50 used for the calibration of the AASHTO LRFD equa- tions. If an average reliability βave = 3.50 is desired for the bridge configurations considered in this example, then a γL = 1.62 should be used when considering the case of a per- mit load alone on the bridge. The γL = 1.62 is obtained using a trial-and-error procedure. The process is repeated until a βave = 3.5 is obtained. • An average reliability index βave = 2.5 was used for the cali- bration of the operating rating live-load factor in the LRFR 83 Composite steel Dead weight effect (kip-ft) RN Nominal resistance (kip-ft) Span (ft) Space (ft) DC1 DC2 DW T4A T5A T6A T7A T8 BFT 60 4 39 245 49 928 978 1038 1091 1086 1120 60 6 48 335 73 1222 1285 1362 1428 1422 1465 60 8 70 414 97 1506 1580 1672 1751 1743 1795 60 10 84 521 122 1806 1892 1998 2089 2080 2139 60 12 103 639 146 2119 2215 2334 2436 2426 2492 120 4 502 981 194 3074 3190 3312 3432 3450 3480 120 6 607 1341 292 4041 4187 4341 4491 4515 4552 120 8 650 1656 389 4850 5023 5205 5384 5411 5455 120 10 681 2083 486 5768 5966 6175 6379 6411 6461 120 12 773 2556 583 6808 7029 7263 7492 7527 7583 200 4 2780 2725 540 9116 9307 9500 9695 9740 9765 200 6 3303 3725 810 11779 12018 12259 12502 12558 12590 200 8 3790 4600 1080 14206 14488 14772 15060 15125 15163 200 10 4190 5788 1350 16893 17214 17538 17867 17941 17984 200 12 4875 7100 1620 20073 20432 20794 21160 21243 21292 Table 47. Nominal resistance for beams of simple-span bridges under a single permit. Composite steel Reliability index, β Span (ft) Space (ft) T4A T5A T6A T7A T8 BFT 60 4 3.31 3.34 3.37 3.39 3.39 3.40 60 6 3.30 3.33 3.36 3.38 3.38 3.39 60 8 3.28 3.31 3.34 3.37 3.37 3.38 60 10 3.25 3.29 3.32 3.34 3.34 3.36 60 12 3.22 3.26 3.29 3.32 3.31 3.33 120 4 3.01 3.05 3.08 3.12 3.12 3.13 120 6 2.99 3.03 3.07 3.10 3.11 3.11 120 8 2.99 3.03 3.07 3.10 3.10 3.11 120 10 2.96 3.00 3.04 3.07 3.08 3.09 120 12 2.93 2.97 3.01 3.04 3.05 3.06 200 4 2.78 2.81 2.84 2.86 2.87 2.87 200 6 2.77 2.80 2.83 2.86 2.87 2.87 200 8 2.78 2.81 2.83 2.86 2.87 2.87 200 10 2.76 2.79 2.82 2.84 2.85 2.85 200 12 2.74 2.77 2.80 2.82 2.83 2.83 Table 48. Reliability index for a single permit with L = 1.35.

code. If an average reliability βave = 2.5 is desired for the bridge configurations considered in this example, then a γL = 1.04 should be used when considering the case of a permit load alone on the bridge. Reliability Analysis and Adjustment of Live-Load Factor for Case II—Two Permits Side by Side In this case, assume that the axle weights and axle configu- rations of the two permit trucks are the same and are perfectly known so that the total maximum static live-load effect on the bridge, Lmax, is a deterministic value. However, this does not imply that the total live-load effect on a bridge member is deterministic due to the uncertainties in estimating the dynamic effect represented by the dynamic amplification factor, IM, and the uncertainties in the structural analysis process that allocates the fraction of the total load to the most critical member. The structural analysis is represented by the load distribution factor, D.F. The equations for the D.F. of multi- girder bridges loaded in two lanes given in the AASHTO LRFD specifications assume that the two lanes are loaded by the same vehicle and give the load on the most critical beam as a function of the load in one of the lanes. Thus, the live-load effect on one member can be given from Equation 46. According to Nowak (1999), the dynamic amplification factor augments the load effect by an average of 9% for side-by-side trucks. The dynamic amplification also resulted in a COV of VIM = 5.5% on the two-lane effect. Also assume that the same COV for the lane distribution factor VDF = 8%, obtained by Ghosn and Moses (1986) from field measurements on typical steel and prestressed concrete bridges, is still valid. Therefore, for the loading of a single permit vehicle, the live-load COV becomes The reliability index, conditional on the arrival of two side-by-side permits on the bridge, can then be calculated using Equation 40 where R – is the mean resistance when the bridge member is designed for two side-by-side permits and LL ––– is the live-load effect on the beam due to two side- by-side permits. The reliability index calculated from Equation 40 in this case is conditional on having two side-by-side trucks. The proba- bility that a bridge member would fail given that two permit vehicles are side by side can be calculated from Pf/side–by–side = Φ(−βcond). However, the final unconditional probability of failure will depend on the conditional probability given two side-by-side events and the probability of having a situation with side-by-side permits as shown in Equation 47. The prob- ability of having two side-by-side permits depends on the number of permit trucks expected to cross the bridge within the return period within which the permits are granted. In this example, assume that all of the permits will likely cross the same bridges so that the number of permits crossing a certain bridge within a 1-year period is equal to the number of permits granted. The percentage of these permits that will be side by side is related to the total number of crossings as provided in Table 49. For example, assuming that the number of permit- vehicles expected on a bridge during the return period when the permits are in effect will be on the order of 1,000 vehicles then, according to Table 49, the probability of having side-by-side events is 0.54% (= 0.19 + 0.14 + 0.21). This value is obtained by conservatively assuming that trucks within a headway dis- tance H < 60 ft are actually side by side. VLL = ( ) + ( ) =5 5 8 9 712 2. % % . % 84 Table 49. Multiple-presence probabilities for side-by-side events as a function of headway distance.

To execute the reliability calculations, a set of typical permit vehicle configurations is used, as shown in Figure 37. These configurations were adopted from the work performed for NCHRP 12-63 (Sivakumar et al. 2007) and multiplying the legal weights of each SHV by 150%. For 60-ft, 120-ft, and 200-ft simple spans, these vehicles produce maximum moments as shown in Table 47. The nominal resistance that would be required for a set of multi-beam simple-span steel bridges can be calculated by applying Equation 32 with γD = 1.25 for component dead weights and γD = 1.50 for the wearing surface. In Equation 32, the effect of the permit trucks is multiplied by a load factor of γL = 1.35 after applying the D.F. of Equation 34 and the impact factor specified in the AASHTO LRFD as IM = 1.33. These calculations assume that the dead loads of the components remain essentially unchanged when the applied live loads are changed. The conditional reliability index is given in Table 50. Equation 46 is then used to find the unconditional probability of failure that is then inverted using Equation 39 to find the unconditional reliability index β. The final (unconditional) reliability index values are provided in Table 51 for the bridge configurations analyzed in this example. The results of Tables 50 and 51 illustrate the following points: • For a given span length and beam spacing, the different vehicle configurations produce little change in the reliability index. The largest difference in the unconditional β is on the order of 0.12 for the 120-ft span bridges. • Increasing the beam spacing leads to small changes of less than 0.06 in the reliability index values. • Increasing the span length leads to lower reliability index values. • The average unconditional reliability index for the span lengths and beam spacings considered is on the order of βave = 4.62 with a minimum value of β = 4.30 and a maximum value β = 4.91 • The higher reliability index obtained for the two side-by-side permits as compared to the single permit is primarily due to 85 Composite steel Reliability index, Span (ft) space (ft) T4A T5A T6A T7A T8 BFT 60 4 4.83 4.85 4.88 4.90 4.89 4.91 60 6 4.82 4.84 4.87 4.89 4.89 4.90 60 8 4.81 4.84 4.86 4.88 4.88 4.89 60 10 4.79 4.82 4.85 4.87 4.87 4.88 60 12 4.77 4.80 4.83 4.85 4.85 4.86 120 4 4.55 4.59 4.62 4.66 4.66 4.67 120 6 4.55 4.58 4.62 4.65 4.66 4.66 120 8 4.55 4.59 4.63 4.66 4.66 4.67 120 10 4.54 4.58 4.61 4.65 4.65 4.66 120 12 4.52 4.55 4.59 4.62 4.63 4.64 200 4 4.32 4.35 4.38 4.41 4.42 4.42 200 6 4.32 4.35 4.39 4.42 4.42 4.43 200 8 4.33 4.36 4.39 4.42 4.43 4.43 200 10 4.32 4.35 4.38 4.41 4.42 4.42 200 12 4.30 4.34 4.37 4.40 4.40 4.41 Table 51. Final (Unconditional) Reliability Index for Case II. Composite steel Conditional Reliability index, Span (ft) space (ft) T4A T5A T6A T7A T8 BFT 60 4 3.65 3.69 3.72 3.74 3.74 3.76 60 6 3.64 3.68 3.71 3.74 3.73 3.75 60 8 3.64 3.67 3.70 3.73 3.73 3.74 60 10 3.61 3.65 3.68 3.71 3.71 3.72 60 12 3.59 3.62 3.66 3.69 3.68 3.70 120 4 3.29 3.34 3.39 3.43 3.44 3.45 120 6 3.29 3.34 3.39 3.43 3.43 3.44 120 8 3.29 3.35 3.39 3.44 3.44 3.45 120 10 3.27 3.33 3.38 3.42 3.42 3.43 120 12 3.25 3.30 3.35 3.39 3.40 3.41 200 4 2.97 3.02 3.06 3.10 3.11 3.12 200 6 2.98 3.03 3.07 3.11 3.12 3.13 200 8 2.99 3.04 3.08 3.12 3.13 3.13 200 10 2.98 3.02 3.07 3.11 3.12 3.12 200 12 2.96 3.00 3.04 3.08 3.09 3.10 Table 50. Conditional Reliability Index for Case II.

the low probability of having side-by-side events. If one looks at the conditional reliability index, then the average βconditional = 3.38 is closer to, but still higher than, the βave = 3.07 obtained for a single permit truck. In this case, the still higher conditional reliability index value is partially due to the lower mean impact factor (IM ––– = 1.09 versus 1.13) and the lower corresponding COV (VIM = 5.5% versus 9%) for side-by-side events, which are justified by the low likelihood of having the peaks of the dynamic oscillations of the two side-by-side vehicles occur simultaneously. Reliability Analysis and Adjustment of Live-Load Factor for Case III—Permit Truck Alongside a Random Truck For Case III, the maximum live-load effect is due to the permit truck alongside the maximum truck expected to occur simultaneously in the other lane. The maximum total load effect depends on the number of side-by-side events expected within the return period. To determine the number of side-by-side permit-random truck events that would occur within a 1-year period, assume that the number of side-by-side events involving one random truck is obtained from Table 43 based on the ADTT. For example, assume that NP gives the number of permit truck crossings expected in a return period T. The average number of random trucks in 1 day is given by the ADTT. For ADTT between 1,000 and 2,500 trucks per day, the percentage of side-by-side events involving a random truck (assumed to be those within a headway H≤60 ft) is taken from Table 43 to be 1.25% (= 0.41% + 0.43% + 0.41%). Thus, within a 1-year return period, there will be 4.56 × ADTT (= 1.25% × 365 × ADTT) random trucks alongside another truck. Assuming that there will be 1,000 permits on this route within this 1-year period, the percentage of permits in the total truck population will be . This indicates that the num- ber of random trucks alongside a permit truck will be, on average, NR = 12.5 (=4.56 × 2.74) events within a 1-year return period. The maximum live-load effect expected within this 1-year period will be due to the heaviest of these 12.5 random trucks combined with the effect of the permit. Table 52 gives the LmaxNR values for the maximum moment effect on simple spans obtained for the maximum of 12.5 events for single lanes for WIM data collected at six California sites. These are obtained by applying the protocols Step 12.2.1 with N = Nr = 12.5 in Equations 26 and 27. The values in Table 52 are normalized as a function of the effect of the HL93 vehicle. The maximum live-load effect is obtained from Equation 49 where P is the load effect of the permit truck, DFP is the dis- tribution factor for the load P, LmaxNR is the maximum load effect of random trucks for NR events, DFR is the distribution 2 74 1000 365 . ADTT ADTT = × ⎛⎝⎜ ⎞⎠⎟ factor for the random load, and IM is the impact factor for side-by-side events. The coefficient of variation for LmaxNR × DFR is estimated using Equation 50 as follows: where: 5.6% is the COV for site-to-site variability, 3.5% is due to randomness in the WIM data, 2% is due to the limitation in the WIM sample size, and 8% is due to the uncertainties in estimating DFR. Assuming the effect of the permit load is deterministic, the coefficient of variation for PxDFP is estimated as VP = 8%, which is the COV for the load distribution factor, DFP. Hence, the standard deviation of LL without the impact factor is obtained using Equation 52 as follows: The COV for the live-load effect on the critical beam includ- ing the effect of the impact IM is given by Equation 53. The live-load mean obtained from Equation 49 and the COV obtained from Equation 53 are then used to find the reliability index from Equation 40. In these example calculations, the same bridge configurations used for Case II are assumed and the nominal Rn values are obtained from two side-by-side permit loads as traditionally done. The reliability calculations produce the results shown in Table 53. The results in Table 53 show a large range for β varying between 2.93 and 4.51 with an average β = 3.72. To reduce the average to βtarget = 3.5, the live-load factor would need to be reduced from γL = 1.35 to 1.25. σLL P N RP DF L DFR = × ×( ) + × ×( )8 10 62 2% . % max VLmax∗ = ( ) + ( ) + ( ) + ( ) =5 6 3 5 2 8 10 62 2 2 2. % . % % % . % 86 LmaxNR for NR=12.5 events Site 60-ft 120-ft 200-ft Lodi 1 0.67 0.70 0.67 Lodi 2 0.69 0.71 0.63 Antelope 1 0.67 0.66 0.59 Antelope 2 0.72 0.70 0.62 LA 710 1 0.70 0.68 0.63 LA 710 2 0.74 0.71 0.66 Bowman 1 0.64 0.62 0.56 Bowman 2 0.63 0.64 0.58 Average 0.68 0.68 0.62 Std. Dev. 0.04 0.03 0.04 Table 52. Lmax values for the maximum moment effect on simple spans obtained for the maximum of 12.5 events for single lanes.

Summary. The reliability analysis executed in this re- port for the limit state of Strength II with a live-load factor γL=1.35 shows large variations in the reliability index de- pending on whether the permit load crosses the bridge with no other trucks alongside of it, the permit is alongside another permit, or the permit is alongside a random truck. When the permit crossing is controlled such that no other trucks are alongside, the average reliability index for the span lengths and beam spacings considered in this report is on the order of βave = 3.07. The average reliability index for two permits side by side is on the order of βave = 4.62. The results for a permit alongside a random truck is, on aver- age, β = 3.72. A high average reliability index for two side- by-side permits is due to the low probability of the occur- rence of such cases. If the number of permits is such that the chances of their side-by-side occurrences is close to 100%, then the average reliability index becomes β = 3.38 which is lower than the random-permit reliability index of 3.72. In this latter case, the reliability index β = 3.38 is lower than the 3.72 because in the random-permit case it is un- likely that the random truck will be as heavy as the permit truck. Adjustments to the live-load factor γL = 1.35 can be made to match a target reliability index. It should be noted that the determination of the target reliability index and the sample of bridge configurations for which the adjustment of the live-load factor need to be made should be based on the experience of bridge owners with the performance of the bridges in their jurisdiction. The calculations per- formed as part of this report assume that the resistance, dead loads, and live loads follow normal (Gaussian) prob- ability distributions. This assumption was made to illus- trate the procedure and can be adjusted as more informa- tion on these variables is assembled from ongoing and recent research studies. Axle Loads for Deck Design from WIM Data (Step 9) Axle Group Weight (Steps 9.1 and 9.2) One-lane (single truck) and two-lane (side-by-side trucks) axle events were analyzed for the purpose of calibrating deck design loads. For the one-lane events, single, tandem, tridem, and quad axle groups were considered. For the two-lane events, single-single, single-tandem, and tandem-tandem axle group combinations were considered. All other axle group combinations were consolidated into one group. Single axles and tandem axles are, by far, the most common axle groups. Figure 38 shows, as a sample, the one-lane axle group weight histograms for WIM Site 9926 in Florida (I-75). Table 54 shows summary statistics for the data. Figure 39 shows the two-lane axle group weight histograms for the same site and Table 55 shows summary statistics for these data. In addition to the mean and standard deviation of the entire population, top 20% of the population, and top 5% of the population, the 99th percentile is shown. This upper extreme is taken in this project as the maximum anticipated load for design. Table 56 shows the 99th percentile of the one- lane axle group weights for all the WIM sites studied in this task. Table 57 shows the 99th percentile of the two-lane axle group weights for all the WIM sites studied in this task. As expected, the combined load of the two-lane events is less than sum of the constituent one-lane events, indicating that the heaviest axle loads are not, necessarily, involved in side- by-side events. Appendix C contains axle group weight his- tograms for all other WIM sites studied in this task. Rigorous calibration of load and resistance factors for deck design requires the availability of statistical data beyond live loads. LRFD did not specifically address deck components in the calibration. In the protocols developed in this study, the nominal axle loads derived using WIM data are used instead 87 Composite steel Reliability index, Span (ft) space (ft) T4A T5A T6A T7A T8 BFT 60 4 4.03 4.16 4.30 4.41 4.40 4.47 60 6 4.04 4.17 4.32 4.44 4.43 4.49 60 8 4.04 4.18 4.33 4.45 4.44 4.51 60 10 4.01 4.16 4.32 4.43 4.42 4.49 60 12 3.98 4.13 4.29 4.41 4.40 4.47 120 4 3.37 3.52 3.67 3.80 3.82 3.85 120 6 3.37 3.53 3.68 3.81 3.83 3.86 120 8 3.38 3.54 3.70 3.84 3.86 3.89 120 10 3.36 3.52 3.68 3.82 3.84 3.87 120 12 3.33 3.49 3.65 3.79 3.81 3.84 200 4 2.95 3.07 3.18 3.28 3.30 3.31 200 6 2.96 3.08 3.19 3.30 3.32 3.33 200 8 2.97 3.09 3.20 3.31 3.34 3.35 200 10 2.95 3.08 3.19 3.30 3.32 3.34 200 12 2.93 3.05 3.16 3.27 3.30 3.31 Table 53. Reliability Index for Case III.

of the code specified values, where the W99 statistic is higher than the code values. All other factors are kept unchanged (load factor, deck dynamic load allowance). The governing nominal axle loads for LRFD deck design are taken as follows: • For single axles, 32-kip load given in LRFD or the 99th per- centile statistic W99, whichever is higher; • For tandem axles, 50 kips (2 × 25 kips given in LRFD) or the 99th percentile statistic W99, whichever is higher; • For tridem axles, the 99th percentile statistic W99; and • For quad axles, the 99th percentile statistic W99. The 99th percentile axle weights are as given in the tables for each axle type at each WIM site. Additional Studies on Truck Sorting Strategies—NCHRP 12-76 (01) The original NCHRP 12-76 study addressed the issue of separating traffic data into Strength I and Strength II limit states by recommending that all uncontrolled traffic that con- stitutes normal traffic or service loads at a site be grouped into Strength I and all controlled or analyzed overload permits be grouped into Strength II. NCHRP 12-76 protocols for classi- fying trucks into Strength I and Strength II limit states may be summarized as follows: 1. All legal trucks, illegal overloads and un-analyzed permits (all routine permits) were grouped into Strength I because they were considered to represent normal service traffic at bridge sites. 2. All controlled or analyzed overload permits were grouped into Strength II. 3. Due to the difficulty in separating permit vs. non-permit traffic using permit records, it was decided to group all trucks with six or fewer axles in the Strength I calibration. The high r values (r is defined as Lmax WIM data/Lmax LRFD calibration data) obtained for Strength I in the NCHRP 12-76 study for one-lane loaded conditions may have been influenced by the truck sorting methodology (based on number of axles) used in the study. This additional study was conducted to fur- ther investigate the truck sorting methodology and the sensitiv- ity of r values to how the trucks are sorted into Strength I. The two-lane loaded condition is governed by the presence of two heavy trucks side by side and is less sensitive to the weight and configuration of an individual truck than it is for the one-lane loaded condition. That is, truck sorting into Strength I and Strength II is more of a factor for the single-lane loading. Issues investigated in this phase of the research are as follows: 1. Strategies for sorting trucks into non permit (state legal loads and illegal loads), routine or annual permits, and special permits (superloads); 2. Strategies for grouping the various trucks defined in Step 1 into Strength I and Strength II for design load calibration; and 88 Figure 38. One-lane axle group weight histogram (WIM Site 9926 in Florida). Statistics Single Tandem Tridem Quad Axle Count 2986536 3293111 94115 1077 Mean All Axles 10.831 21.773 46.649 43.899 Std Dev All Axles 3.494 9.847 13.955 22.070 COV All Axles 0.323 0.452 0.299 0.503 Mean Top 20% Axles 16.039 36.285 63.111 70.777 Std Dev Top 20% Axles 2.932 3.763 3.976 6.282 COV Top 20% Axles 0.183 0.104 0.063 0.089 Mean Top 5% Axles 20.152 41.357 68.343 79.444 Std Dev Top 5% Axles 2.008 3.913 3.817 6.380 COV Top 5% Axles 0.100 0.095 0.056 0.080 99th Percentile 20 42 68 82 Table 54. One-lane axle group weight statistics (WIM Site 9926 in Florida).

89 Figure 39. Two-lane axle group weight histogram (WIM Site 9926 in Florida). State Site ID Route Single- Single Single- Tandem Tandem- Tandem Other CA 0001 Lodi 34 50 66 76 CA 0003 Antelope 30 46 62 82 CA 0004 Antelope 32 48 64 78 CA 0059 LA710 26 44 62 72 CA 0060 LA710 30 48 66 74 CA 0072 Bowman 30 46 62 80 FL 9916 US-29 36 60 78 90 FL 9919 I-95 26 42 58 74 FL 9926 I-75 32 58 74 120 FL 9927 SR-546 30 50 70 76 FL 9936 I-10 38 60 84 106 IN 9511 I-65 26 40 54 78 IN 9512 I-74 34 52 72 90 IN 9532 US-31 28 46 64 84 IN 9534 I-65 28 44 58 86 IN 9544 I-80/I-94 28 46 60 80 IN 9552 US-50 28 46 64 70 MS 2606 I-55 36 62 86 92 MS 3015 I-10 28 46 66 78 MS 4506 I-55 34 54 72 84 MS 6104 US-49 32 50 68 90 MS 7900 US-61 32 52 68 76 TX 0506 32 50 68 84 TX 0516 30 48 66 82 TX 0523 30 50 70 96 TX 0526 32 50 68 96 Table 57. Two-lane axle group weight (99th percentile). State Site ID Route Single Tandem Tridem Quad CA 0001 Lodi 18 36 50 40 CA 0003 Antelope 16 32 52 62 CA 0004 Antelope 18 34 56 64 CA 0059 LA 710 16 34 46 54 CA 0060 LA 710 18 36 46 60 CA 0072 Bowman 16 32 50 54 FL 9916 US-29 20 46 78 88 FL 9919 I-95 14 32 50 62 FL 9926 I-75 20 42 68 82 FL 9927 SR-546 18 38 58 64 FL 9936 I-10 22 44 74 94 IN 9511 I-65 14 30 52 62 IN 9512 I-74 18 38 58 68 IN 9532 US-31 16 34 58 72 IN 9534 I-65 16 34 56 66 IN 9544 I-80/I-94 16 34 54 64 IN 9552 US-50 16 34 56 62 MS 2606 I-55 20 48 76 78 MS 3015 I-10 16 36 52 68 MS 4506 I-55 18 40 60 78 MS 6104 US-49 16 36 52 74 MS 7900 US-61 16 40 56 78 TX 0506 18 36 56 -- TX 0516 18 36 56 -- TX 0523 18 36 62 -- TX 0526 18 36 60 -- Table 56. One-lane axle group weight (99th percentile). Statistics Single- Single Single- Tandem Tandem- Tandem All Others Event Count 13124 29735 16306 1801 Mean All Events 21.585 32.535 43.445 63.314 Std Dev All Events 4.994 10.486 14.111 17.759 COV All Events 0.231 0.322 0.325 0.280 Mean Top 20% Events 29.141 47.916 64.044 87.483 Std Dev Top 20% Events 3.345 4.509 6.522 8.462 COV Top 20% Events 0.115 0.094 0.102 0.097 Mean Top 5% Events 33.655 54.181 72.988 99.089 Std Dev Top 5% Events 3.003 4.094 5.088 7.489 COV Top 5% Events 0.089 0.076 0.070 0.076 99th Percentile 34 54 74 102 Table 55. Two-lane axle group weight statistics (WIM Site 9926 in Florida).

3. The influence of the various truck sorting strategies on r values. Truck Definitions To further refine the truck sorting criteria, the following truck definitions were utilized based on state vehicle weight and permit regulations: • State highway agencies have established processes for per- mitting overweight non-divisible loads on state highways. Some states also have “grandfather rights” to authorize per- mits for divisible loads that exceed 80,000 lbs. A “divisible load” is any vehicle or combination of vehicles transporting cargo of legal dimensions that can be separated into units of legal weight without affecting the physical integrity of the load. Examples of divisible loads include: aggregate (sand, top soil, gravel, stone), logs, scrap metal, fuel, milk, trash/ refuse/garbage, etc. • State legal trucks are trucks that meet state vehicle weight regulations for legal loads. Typically specified are axle weight limits or single and axle groups, gross weight limit, and requirements for axle configuration and spacing based on Federal Bridge Formula B. • Annual (or blanket) overweight permits are usually valid for unlimited trips within a state over a period of time, not to exceed 1 year, for vehicles of a given configuration within specified gross and axle weight limits. • Trip (or superload) overweight permits are usually valid for a single trip only, a limited number of trips, a vehicle of specified configuration, axle weights, and gross weight. Spe- cial permit vehicles are usually heavier than those vehicles issued annual permits. • Illegal trucks do not meet state vehicle weight regulations for legal loads or for permit loads. Sorting Variations Variation P12:All vehicles in Strength I. The sorting variations investigated in this study can be placed into the following groups: • Group I: Sorting based on number of axles – Baseline: Strength I = 6 axles or less (same as NCHRP 12-76 protocols) – Variation P1: Strength I = 7 axles or less – Variation P2: Strength I = 8 axles or less – Variation P3: Strength I = 5 axles or less • Group II: Sorting based on GVW – Variation P4: Strength I = GVW ≤ 84 – Variation P5: Strength I = GVW ≤ 100 – Variation P6: Strength I = GVW ≤ 120 – Variation P7: Strength I = GVW ≤ 150 • Group III: Sorting based on state permit regulations – Variation P8: Strength I = state legal trucks only – Variation P9: Strength I = state legal trucks, annual (routine) permits – Variation P10: Strength I = state legal trucks, illegal trucks – Variation P11: Strength I = state legal trucks, illegal trucks, annual permits (only trip permits in Strength II) • Group IV: Non Sorted NCHRP 12-76 protocols for classifying trucks into Strength I and Strength II limit states (defined as the baseline case in this study) included all legal trucks, illegal overloads, and un- analyzed permits (all routine permits) into Strength I; trip per- mits were grouped into Strength II as shown in Table 58. Sort- ing Variation P11 is aimed at achieving the same classification of trucks into Strength I and Strength II, but using the state’s permit regulations as the criteria, not the number of axles. Both the baseline case and Sorting Variation 11 have the same objective but take different approaches to sorting trucks into Strength I and Strength II. WIM Sites for Testing Sorting Variations This phase of the NCHRP 12-76 study considered three WIM sites each from Indiana, California, and Florida that were taken from the original NCHRP 12-76 research for studying how changing the definition of classification of loads into Strengths I and II changes the results of the study (especially in terms of the r value, which is a measure of how each site com- pares to the HL93 design basis). As shown in Table 59, the states and sites were chosen to capture a variety of geographic locations and functional classes. Truck Sorting Strategies Based on State Permit Regulations The previously noted sorting strategies were implemented using permit rules and recent WIM data. For each state with the selected WIM sites (Indiana, California, and Florida), the permit variations were customized to incorporate state-specific vehicle weight laws and permit regulations as described below. Indiana Permit Regulations. Indiana generally uses the federal definition of overweight vehicles. The following is from the Indiana Oversize/Overweight Vehicle Permitting Handbook (Indiana ND): Once your load is non-divisible, you must determine if your truck and load are over the legal dimensions and/or legal weight for Indiana. To travel legally on any Indiana roads, you cannot exceed the following weights: 80,000 lbs gross vehicle weight; or 12,000 lbs on the steering axle; or 90

91 Sorting Variation Strength I Strength II Comment Baseline Trucks with 6 or fewer axles Trucks with 7 or more axles Same as NCHRP 12- 76 protocols. Provides a basis for comparison. 12 All trucks Provides a basis for comparison and for sensitivity studies. Generalized Sorting Methods Applicable to All States 1 Trucks with 7 or fewer axles Trucks with 8 or more axles 2 Trucks with 8 or fewer axles Trucks with 9 or more axles 3 Trucks with 5 or fewer axles Trucks with 6 or more axles 4 GVW > 84 kips Includes a 5% scale allowance over 80 kips. 5 GVW > 100 kips 6 GVW > 120 kips 7 GVW > 150 kips State-Specific Sorting Methods Based on State Weight Regulations and Permit Rules 8 State Legal Trucks Illegal Trucks Annual (Routine) Permits Trip Permits Only State legal trucks in Strength I. 9 State Legal Trucks Annual (Routine) Permits Illegal Trucks Trip Permits Only used for comparison purposes. 10 State Legal Trucks Illegal Trucks Annual (Routine) Permits Trip Permits All valid permit trucks grouped in Strength II. 11 State Legal Trucks Illegal Trucks Annual (Routine) Permits Trip Permits Truck sorting goal intended in 12-76 protocols. Useful to compare with baseline case. Table 58. Sorting variations used for including trucks into Strength I/Strength II. State Site ID Route Direction No. of Truck Records ADTT IN 9512 I-74 E 931971 2596 IN 9512 I-74 W 1003443 2795 IN 9532 US-31 N 224506 629 IN 9532 US-31 S 229532 643 IN 9544 I-80/I-94 E 3786127 11235 IN 9544 I-80/I-94 W 4032537 11966 CA 0003 Antelope E 719834 2790 CA 0059 LA710 S 4243780 11627 CA 0072 Bowman E/N 310596 2318 CA 0072 Bowman W/S 289319 2159 FL 9919 I-95 N 939637 2708 FL 9919 I-95 S 875766 2524 FL 9926 I-75 N 1096076 4136 FL 9926 I-75 S 1032680 3897 FL 9936 I-10 E 700774 1980 FL 9936 I-10 W 723512 2044 Table 59. WIM sites used in the current research.

20,000 lbs on a single axle; or 34,000 lbs on a tandem axle; or 800 lbs per inch of rim width and subject to the above axle weights. An overweight vehicle is generally any vehicle whose over- all weight exceeds 80,000 lbs. However, road and bridge stress levels are determined by the distribution of the weight, so it is important that the weight per axle, or sets of tandem axles, be observed. Weight per tire also is considered. The total gross weight may be calculated by the following federal bridge for- mula and then compared to the established weight limits listed above. where: W = The overall gross weight on any group of two or more consecutive axles, to the nearest 500 lbs, L = The distance between the extreme of any group of two or more consecutive axles, and N = The number of axles in the group under considera- tion, except that two consecutive sets of tandem axles may carry a gross load of 34,000 lbs each, providing the first and last axles of the consecutive sets of tan- dem axles are at least 36 ft or more apart. Like most states, Indiana has some exceptions to their stan- dard rules, however the gross vehicle weight, axle weight, tan- dem axle weight, and compliance with Formula B form the basis of the Indiana regulations. Indiana considers permits exceeding the legal limits as “overweight” for loads up to a GVW of 120 kip. Permits ex- ceeding 120 kip are given an extra designation as “superload” permits. California Permit Regulations. California follows the federal weight laws for legal limits. Federal Bridge Formula B is enforced for axle weight and spacing combinations. The single-axle weight limit is 20,000 lbs. Tandem axle group weights are limited to 34,000 lbs. Gross vehicle weights are limited to 80,000 lbs. One exception route (Port of Long Beach, Route 41) is present but it was not considered in this study. California issues annual permits for vehicle weights exceed- ing 80,000 lbs. and less than 300,000 lbs. Permits for more than 300,000 lbs are only issued as single-trip permits. Cali- fornia requires that annual permits satisfy the Purple Weight Table that lists the maximum allowable permit weight on groups of axles as a function of axle spacing, without the gross vehicle weight limit. The maximum allowable weight on groups of axles is given as 1.50 × 700 (L + 40) lbs, where L is the distance from first to last axle in feet. The Purple Weight W LN N N= ( ) ÷ −( )[ ]+ +{ }500 1 12 36 Table also limits the maximum tandem axle combination to 60,000 lbs. (Special, heavier, tandem axles with 8 tires per axle and 8 or 10 ft wide are allowed a bonus weight but this allowance is not considered in this study.) California also limits the number of axles in tractor-trailer configurations with annual permits to six. Crane trucks are also issued annual permits and are allowed up to eight axles. However the maximum number of axles that can exceed per- mit weight is five. Florida Permit Regulations. The Florida Commercial Motor Vehicle Manual, 6th edition (FDOT 2006), defines legal and permit loads for the State of Florida. Florida regulations mostly follow the federal legal load def- initions. The legal single-axle weight is set at 22,000 lbs and the legal tandem-axle weight is 44,000 lbs. One difference between the typical federal legal load definitions and the Florida regulations is a grandfather exemption for short single-unit trucks. Florida allows short single-unit trucks as legal loads up to 70,000 lbs with the 22,000-lb axle weight require- ment; these vehicles do not meet the Federal Bridge For- mula B requirement. The Florida manual specifies legal loads using both the outer-bridge and inner-bridge distances. The inner-bridge distances allow the same checking as is done using Federal Bridge Formula B for tractor trailers. Tractor trailers meet the Federal Bridge Formula B requirements and have a maximum legal gross vehicle weight of 80,000 lbs. Florida requires an overload permit for any vehicle that exceeds 80,000 lbs. Florida issues blanket (annual) permits based upon predefined routes shown on maps. These blanket permits are issued based on weight restriction charts matched to the maps for truck cranes and tractor trailers. The weight restriction charts use number of axles, minimum outer-bridge distance, and maximum axle group weights. Minimum dis- tances between axle groups are also dictated. The outer-bridge distance is the length of the vehicle from front to rear axle. From the Axle Weight Limitations Table, Florida also places a limit on special permit vehicles of 40,000 lbs for an axle with eight tires. For the typical blanket permits of greatest interest, the highest single-axle limit is 27,500 lbs and the highest gross vehicle weight limit is 199,000 lbs. Review of Results General Trends in Strength I Maximum r Values Additional insight into the influence of truck sorting strate- gies on r values was gained by investigating the variations in r values based on the following: 1. Force effects such as simple-span moment, simple-span shear, and negative bending; and 2. Span length (20 ft, 60 ft, 120 ft). 92

The maximum moment or shear values of r for all span lengths considered (from 20-ft to 200-ft) have been tabulated in Table 60 for sorting variations P1 through P12 and the baseline sorting strategy. 1. As can be seen in the variations of r for Strength I in Table 60, the variation in number of axles does not have a large impact upon r values. 2. Increasing GVW for trucks in Strength I leads to a small increase in r values. 3. Configurations of the trucks as governed by state permit regulations (and weight regulations) have the greatest influence on r values when compared to either GVW or the number of axles. 4. Compared with P12 where all trucks are in Strength I, P8 and P9 see a big drop in Strength I r values. In P8 and P9, all illegal trucks and trip permits are moved to Strength II. 5. Comparing P8, P9, and P10 is instructive. The inclusion of annual permits in with legal trucks in P9 only resulted in a small increase in r values. However, when illegal trucks are added to legal trucks in P10, there is a signifi- cant increase in r values. 6. Comparing P11 to P12, the only difference is that trip permits are added to Strength I in P12. It is evident that adding trip permits causes no noticeable change in max- imum r values. This shows that heavy permits, when they are legal and comply with permit regulations, do not in- duce significant load effects. 7. In P10 and P11 overloaded trucks not complying with permit or weight regulations were grouped into Strength I, which led to high r values. 8. Florida Site 9919 did not show a jump in r values between P9 and P10 as did the other sites. This may be explained by the low number of illegal trucks (only 24) at this site (see Table 63). With the exception of these 24 trucks, this site has only legal loads and annual permits that comply with all permit regulations. With this high level of com- pliance, the r values are predictably low. As the number of illegal loads increases for the other two Florida sites, the r values also show a big increase. 9. Most Strength II trucks in Indiana were classified as illegal (P9–P11). Most Strength II trucks in Florida were classified as annual permits (P10–P11). In California, the Strength II trucks were equally divided between illegal trucks and annual permits (P9 and P10). 10. There is a big drop in number of Strength II trucks with axles > 7 (baseline) and GVW > 100. 11. Baseline and P11 results provide a useful comparison. Both sorting cases seek to include all legal trucks, illegal overloads, and unanalyzed permits (all annual/routine permits) into Strength I, but execute this by different approaches as previously discussed. For Florida, the results are comparable. For Indiana, P11 is slightly higher. For California, it is about 30% higher. This means that California has more annual permits or illegal loads with number of axles greater than seven, which were being 93 Maximum r Values, Strength I IN WIM Sites CA WIM Sites FL WIM Sites Sorting Variation 9544 9532 9512 Site 0003 Site 0059 Site 0072 9919 9926 9936 Str. I: # Axles 5 P3 1.97 1.41 1.07 1.08 1.07 1.08 0.92 2.19 2.18 Str. I: # Axles 6 (Baseline) 1.97 1.41 1.12 1.11 1.10 1.08 0.94 2.21 2.17 Str. I: # Axles 7 P1 1.98 1.42 1.21 1.13 1.13 1.08 0.94 2.21 2.15 # Axles Str. I: # Axles 8 P2 2.11 1.42 1.21 1.43 1.16 1.08 0.94 2.21 2.15 Str. I: GVW 84 P4 1.34 1.13 1.06 0.90 0.94 0.85 0.92 1.21 1.11 Str. I: GVW 100 P5 1.51 1.29 1.07 1.08 0.96 0.89 0.93 1.35 1.22 Str. I: GVW 120 P6 1.59 1.40 1.07 1.10 1.02 1.02 0.94 1.47 1.49 GVW Str. I: GVW 150 P7 1.82 1.41 1.18 1.13 1.11 1.08 0.95 1.87 2.03 Str I: Legal P8 0.76 0.71 0.68 0.64 0.71 0.67 0.83 0.92 0.80 Str I: Legal & Annual P9 0.85 0.71 0.72 0.99 0.95 0.95 0.95 1.33 1.42 Str I: Legal & Illegal P10 2.11 1.45 1.38 1.52 1.42 1.61 0.89 2.32 2.24 State Permit Regulations Str I: All but Trip P11 2.11 1.45 1.38 1.46 1.36 1.54 0.95 2.21 2.15 Non Sorted All Trucks in Str I P12 2.11 1.45 1.38 1.46 1.36 1.54 0.95 2.21 2.15 Table 60. Summary of maximum Strength I r values for all WIM sites.

grouped into Strength II in the baseline case. Using a state’s permit and weight regulations as in P11 to group trucks into Strength I and Strength II is considered more rational, whereas the axles-based approach used in the 12-76 protocols is considered simpler, yet less precise, when using national WIM data. Sensitivity Analysis of Strength I Maximum r Values The previous sections compared the maximum r values for the baseline and sorting variations P1 thru P12 by grouping them into the following: Group I: Baseline, P1, P2, and P3 sorting based on number of axles; Group II: P4, P5, P6 and P7 sorting based on GVW; Group III: P8, P9, P10, and P11 sorting based on state permit regulations; and Group IV: Non sorted—P12 used as a reference for sensitiv- ity analysis. Sensitivity Analysis Using r Differentials for Strength I The key objective of this analysis is to investigate how sen- sitive the r values are to how the trucks are sorted. This section is comprised of the findings of a sensitivity analysis performed on r values by defining a new metric for Strength I termed the “r differential.” This metric is defined as Where: r12 = r value for reference case P12, which includes all trucks in Strength I rx = r value for sorting variation Px (could be any one of P1 through P11 or baseline) It provides a quantification of how the r value changes in percentage terms as various trucks are removed from P12 (the reference case that was not sorted) and includes all trucks in Strength I. For example, to understand how sensitive the r values are when trucks that weigh more than 120 kips are ex- cluded from Strength I, the following r differential is executed: To understand how sensitive the r values are when trip per- mits are excluded from Strength I, the following r differential is executed: r differential for P11 r12 r11 r12= −( )[ ]×100% r differential for P6 r12 r6 r12= −( )[ ]×100% r differential r12 rx r12= −( )[ ]×100% Similarly, to understand how sensitive the r values are when all trucks but state legal loads are excluded from Strength I, the following r differential is executed: General Trends in Strength I r Differential Results The results of r differentials are summarized in Table 61. The average r differentials for the three WIM sites in each state are shown for the following force effects and span lengths: • Force effects such as simple-span moment, simple-span shear, and negative bending; and • Span lengths (20 ft, 60 ft, 120 ft). The last three columns of Table 61 show the averages for all WIM sites by span length and load effect for easy compar- ison. A detailed review of r differential results for selected sites is included later in this chapter. Complete results for each WIM site are included in Appendix F. The findings from Table 61 may be stated as follows: 1. Group III results (based on state permit regulations), par- ticularly P8 and P9, are the most sensitive, followed by Group II (based on GVW), and then Group III (based on number of axles). 2. The r differential results for P8 were the highest. This signi- fies the biggest difference in r values occurs when only state legal loads are included in Strength I or when illegal loads, trip permits, and annual permits are excluded. The average drop was between 44% and 64%. 3. The r differential results for P10 and P11 were negligible. This indicates the minimal influence of removing annual permits or trip permits from Strength I. 4. The r differential results for P9 were the second highest in Group III. The average drop was between 32% and 40%. This signifies the sensitivity of the results to removing illegal loads and trip permits. P10 and P11 show that trip permits exert minimal influence on r values, which means that illegal trucks were essentially responsible for the drop in r values. 5. The Group III r differential results were not significantly sensitive to span length or load effect and remained rela- tively consistent for each state. Similar findings were iden- tified in the previous discussions on r values for Group III. 6. P4 r differential results were the highest within Group II (based on GVW) and decrease gradually to the lowest val- ues obtained for P7. This shows that as heavier trucks were included in Strength I the r differential is minimized as expected. This is in line with the previous discussions on Group II r values. r differential for P8 r12 r8 r12= −( )[ ]×100% 94

20 ft 60 ft 120 ft 20 ft 60 ft 120 ft 20 ft 60 ft 120 ft 20 ft 60 ft 120 ft Based on # Axles Baseline M-simple 18 18 14 21 5 10 28 0 1 0 6 8 17 # Axles 6 or less V-simple 13 29 4 16 29 0 0 3 5 10 20 M-negative 40 44 11 29 37 1 15 9 8 28 30 P1 M-simple 15 11 11 3 6 20 0 0 0 5 6 11 # Axles 7 or less V-simple 15 10 20 2 11 20 0 0 2 4 7 14 M-negative 31 36 10 19 30 0 7 8 6 19 25 P2 M-simple 12 8 10 0 1 4 0 0 0 4 3 5 # Axles 8 or less V-simple 12 8 17 0 2 6 0 0 0 4 3 8 M-negative 15 24 33 3 7 14 0 0 4 3 10 17 P3 M-simple 22 28 33 5 13 32 4 1 6 7 14 24 # Axles 5 or less V-simple 21 20 32 4 21 34 1 4 9 5 15 25 M-negative 32 40 48 14 35 41 2 23 14 11 33 35 Based on GVW P4 40 38 49 19 30 53 34 28 42 26 32 48 GVW 84 or less 44 37 55 22 39 57 32 36 48 27 37 53 52 63 65 31 62 64 29 59 54 30 61 61 P5 35 31 40 12 23 45 30 25 35 22 27 40 GVW 100 or less 39 27 45 14 32 50 29 32 41 23 30 45 45 55 58 24 53 57 25 49 46 24 52 54 P6 27 19 26 9 18 37 20 21 26 16 19 30 GVW 120 or less 28 17 35 11 24 39 22 24 29 17 22 34 34 44 49 16 40 47 18 35 33 16 40 43 P7 18 11 13 6 10 26 9 6 14 10 9 18 GVW 150 or less 20 11 22 6 15 28 7 11 18 8 12 22 25 33 35 11 25 36 9 20 20 11 26 30 Based on State Permit Regulations P8 52 53 55 50 52 62 46 40 52 47 48 56 Legal 54 48 59 51 56 63 45 47 54 48 50 58 57 63 67 49 63 67 40 59 58 44 62 64 P9 38 41 38 47 51 56 23 26 27 32 39 40 Legal & Annual 37 1 1 33 35 49 54 55 25 29 23 34 39 38 34 33 30 49 51 55 23 17 14 35 34 33 P10 0 -3 0 0 0 3 1 0 1 0 0 Legal & Illegal 0 -4 0 0 1 1 0 2 0 0 0 -4 -3 0 0 0 2 12 7 0 3 1 P11 0 0 0 0 0 0 0 3 0 0 1 All but Trip Permits 1 0 0 0 0 0 2 4 0 1 1 0 0 0 0 0 1 7 6 0 2 2 P12 0 0 0 0 0 0 0 0 0 0 0 All Trucks 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Average for CA Average for IN Average for FL Strength I Definition Load Effect Average r Differential Values (percentage) for Strength I Average for CA, IN,FL 26 21 M-simple V-simple M-negative M-simple V-simple M-negative M-simple V-simple M-negative M-simple V-simple M-negative M-simple V-simple M-negative M-simple V-simple M-negative M-simple V-simple M-negative M-simple V-simple M-negative M-simple V-simple M-negative 0 0 0 0 0 0 0 Table 61. Summary average r differentials.

7. The r Differential results for Group II vary from under 10% for P7 to over 60% for P4. The r differential shows an in- crease with increasing span lengths, and generally the high- est values were for the negative moments. This is likely due to the fact that the longer and heavier trucks could be dom- inating both the longer spans and the negative bending. The trends were similar for all three states, with the exception that Florida had a very low r differential for P7. 8. Group I r differential results were the lowest, particu- larly for Florida, where the results mostly were less than 10%. This shows that sorting trucks based on number of axles for Florida WIM sites is not particularly effective— at least when compared with Group II and Group III sorting strategies. 9. For California and Indiana, the Group I r differential re- sults increase with increasing span lengths. The r differen- tial also increases as trucks with a higher number of axles are removed from Strength I. The highest values were obtained for P3 and the lowest for P2. The general trends were similar for all load effects. Sensitivity analysis of r values shows that Group III results (based on state permit regulations), particularly P8 and P9, are the most sensitive, followed by Group II (based on GVW), and then Group III (based on number of axles). In P10, when illegal trucks are added to state legal loads, the r differential disappears, which indicates that illegal trucks—not the permits that follow state permit regulations—are likely the biggest drivers of high r values. Baseline and P11 results provide a useful comparison. Both sorting cases seek to include all legal trucks, illegal overloads, and unanalyzed permits (all annual/routine permits) into Strength I, but execute this by different approaches. For Florida, the results are comparable. But for Indiana and California P11 will give higher r values than the baseline case of using trucks with six or fewer axles to define all trucks other than heavy trip permits. Using a state’s permit and weight regulations (as in P11) to group trucks into Strength I and Strength II is considered more rational, and more precise, when using national WIM data. The r differentials for a 60-ft span moment are given in Table 62. Another helpful sensitivity index is the change in r values from P8 to P9 where annual permits are added to state legal loads and from P8 to P10 where illegal loads are added to state legal loads. Table 63 also illustrates the influence of illegal trucks in driving high r values. For Indiana, adding annual permits to state legal loads did not result in a significant increase in r val- ues. But this was very different when the illegal loads were in- cluded. To travel legally on any Indiana roads, trucks cannot exceed the federal weight limits and must comply with Fed- eral Bridge Formula B. An overweight vehicle is generally any vehicle whose overall weight exceeds 80,000 lbs. However, the overweight truck must comply with Federal Bridge Formula B. Indiana considers permits exceeding the legal limits as an- nual permits for loads up to a GVW of 120 kips. The illegal trucks exceed the federal weight limits, and particularly the Formula B limits, resulting in high r values. 96 Sorting Variation Trucks in Strength I r Differential for 60-Ft Span Moment (CA, IN, FL) P12 All trucks (0,0,0) GROUP I (Based on Number of Axles) P3 Trucks with 5 or fewer axles (28, 13, 1) Baseline Trucks with 6 or fewer axles (14, 10, 1) P1 Trucks with 7 or fewer axles (11, 6, 0) P2 Trucks with 8 or fewer axles (8, 1, 0) GROUP II (Based on GVW) P4 Trucks with GVW 84 kips (38, 30, 28) P5 Trucks with GVW 100 kips (31, 23, 25) P6 Trucks with GVW 120 kips (19, 18, 21) P7 Trucks with GVW 150 kips (11, 10, 6) GROUP III (Based on State Permit Regulations) P8 State legal trucks only (53, 52, 40) P9 State legal trucks, annual (routine) permits (41, 51, 26) P10 State legal trucks, illegal trucks (0, 0, 1) P11 State legal trucks, illegal trucks, annual (routine) permits (0, 0, 0) Table 62. Sorting variations showing r differential.

Unlike the Indiana results, California and Florida show bigger increases when annual permits are added to state legal loads. California issues annual permits for vehicle weights up to 300,000 lbs. Florida requires an overload permit for any vehicle that exceeds 80,000 lbs. For the typical blanket per- mits, the highest gross vehicle weight limit is 199,000 lbs. Another difference between the typical federal legal load def- initions and the Florida regulations is a grandfather exemp- tion for short single-unit trucks. Florida allows short single- unit trucks as legal loads up to 70,000 lbs that do not meet the Federal Bridge Formula B requirement. For both California and Florida, the influence of illegal trucks on r values was far more significant than that of annual permits. Detailed Review of Strength I r Differential Results One WIM site from each state has been selected for a more in-depth review and discussion and will serve as representa- tive examples of the other sites for each state. The sites to be discussed are Indiana Site 9544, California Site 0059, and Florida Site 9936. A discussion of r differential results is provided following the sorting groups previously defined. Group I: Sorting Variation Based on Number of Axles. The following sorting variations will be discussed under Group I: • Baseline: Strength I = 6 axles or less, • P1: Strength I = 7 axles or less, • P2: Strength I = 8 axles or less, and • P3: Strength I = 5 axles or less. From Table 64 and Figure 40, sorting case P2 where trucks with nine axles or more are excluded from Strength I shows no noticeable r differential values. However, baseline, P1 and P2 show increasing r differential values with increasing span length. The trucks excluded in baseline, P1, and P3 are • Baseline: 7 axles or more, • P1: 8 axles or more, and • P3: 6 axles or more. 97 WIM Site % Change in r values from P8 to P9 (number of added annual permits) % Change in r values from P8 to P10 (number of added illegal trucks) IN 9544 10.6 % (6685) 178 % (110,774) IN 9532 0 % (433) 104 % (17,378) IN 9512 0 % (17599) 103 % (140,098) CA 0003 55 % (1118) 138 % (1576) CA 0059 34 % (22,525) 100 % (26,487) CA 0072 42 % (1411) 140 % (1200) FL 9919 15 % (4389) 7 % (24) FL 9926 45 % (219,378) 152 % (3259) FL 9936 78 % (234,938) 180 % (2989) Table 63. Percentage change in r values. Strength I r Values r Differential = (r12 - rx) / r12 x 100% Span Length (ft) Span Length (ft) Sorting Variation Load Effect 20 60 120 20 60 120 Baseline M-simple 1.77 1.45 1.28 7.22 12.86 30.99 V-simple 1.97 1.54 1.38 5.56 27.14 34.27 M-negative 1.45 1.12 0.74 21.24 29.24 35.18 P1 M-simple 1.78 1.50 1.34 6.52 9.94 27.72 V-simple 1.98 1.64 1.46 4.77 21.96 30.21 M-negative 1.47 1.15 0.78 20.39 27.92 31.66 P2 M-simple 1.91 1.66 1.86 -0.01 0.03 -0.04 V-simple 2.08 2.11 2.10 0.00 -0.04 -0.07 M-negative 1.84 1.58 1.14 -0.03 0.54 0.35 P3 M-simple 1.77 1.45 1.26 7.20 13.21 31.99 V-simple 1.97 1.52 1.35 5.62 27.88 35.50 M-negative 1.44 1.07 0.72 21.67 32.51 37.44 P12 M-simple 1.91 1.67 1.86 0.00 0.00 0.00 V-simple 2.08 2.11 2.10 0.00 0.00 0.00 M-negative 1.84 1.59 1.15 0.00 0.00 0.00 Table 64. Indiana Site 9544 r differentials for Group I.

P3, where trucks with six or more axles are excluded, has the highest r differential. From Table 65 and Figure 41, all sorting cases show increas- ing r differential values with increasing span length. The trucks excluded in baseline, P1, P2, and P3 are • Baseline: 7 axles or more, • P1: 8 axles or more, • P2: 9 axles or more, and • P3: 6 axles or more. P3, where trucks with six or more axles are excluded, has the highest r differential. Unlike the Indiana site, P2 values do vary with span length indicating that the California site has a population of trucks with 9 or more axles. From Table 66 and Figure 42, all sorting cases show mini- mal r differential values with increasing span length for the Florida site. Group II: Sorting Variation Based on GVW. The follow- ing sorting variations will be discussed under Group II: • P4: Strength I = GVW ≤ 84, • P5: Strength I = GVW ≤ 100, • P6: Strength I = GVW ≤ 120, and • P7: Strength I = GVW ≤ 150. In Table 67 and Figure 43 all sorting cases show increasing r differential values with increasing span length for the Indi- ana site. This shows that as increasingly heavier trucks are 98 Figure 40. Strength I moment r differentials for Group I vs. span lengths (Indiana Site 9544). Strength I r Values r Differential = (r12 - rx) / r12 x 100% Span Length (ft) Span Length (ft) Sorting Variation Load Effect 20 60 120 20 60 120 Baseline M-simple 0.94 1.03 0.97 5.61 9.88 25.49 V-simple 1.07 1.10 1.01 4.56 12.81 23.76 M-negative 1.05 0.82 0.55 8.50 30.75 37.88 P1 M-simple 0.99 1.06 1.09 0.65 7.70 16.57 V-simple 1.09 1.13 1.13 3.30 10.69 14.14 M-negative 1.12 0.97 0.63 1.95 17.92 28.59 P2 M-simple 0.99 1.08 1.12 0.58 5.90 13.89 V-simple 1.09 1.14 1.16 3.21 9.69 12.08 M-negative 1.13 1.04 0.66 1.56 12.15 25.04 P3 M-simple 0.94 0.90 0.81 5.94 21.05 37.70 V-simple 1.07 0.97 0.93 4.72 22.78 29.61 M-negative 1.02 0.81 0.48 10.49 31.15 45.09 P12 M-simple 1.00 1.14 1.30 0.00 0.00 0.00 V-simple 1.13 1.26 1.32 0.00 0.00 0.00 M-negative 1.14 1.18 0.88 0.00 0.00 0.00 Table 65. California Site 0059 r differentials for Group I.

Figure 41. Strength I moment r differentials for Group I vs. span lengths (California Site 0059). Figure 42. Strength I moment r differentials, Group I vs. span lengths (Florida Site 9936). Load Effect Strength I r Values r Differential = (r12 - rx) / r12 x 100% Span Length (ft) Span Length (ft) Sorting Variation 20 60 120 20 60 120 Baseline M-simple 2.02 1.51 1.31 -0.97 -0.42 0.42 V-simple 2.17 1.66 1.43 -0.91 -0.40 5.48 M-negative 1.46 1.13 0.74 0.24 22.03 13.03 P1 M-simple 2.00 1.51 1.31 -0.30 -0.14 0.44 V-simple 2.15 1.65 1.46 -0.31 -0.16 3.71 M-negative 1.46 1.26 0.76 0.24 12.46 11.24 P2 M-simple 2.00 1.51 1.32 -0.02 -0.07 0.09 V-simple 2.15 1.65 1.51 -0.02 -0.04 0.22 M-negative 1.46 1.44 0.80 0.24 0.29 5.69 P3 M-simple 2.03 1.52 1.31 -1.63 -1.05 0.30 V-simple 2.18 1.66 1.43 -1.50 -0.93 5.61 M-negative 1.47 1.12 0.74 0.01 22.69 13.54 P12 M-simple 2.00 1.51 1.32 0.00 0.00 0.00 V-simple 2.15 1.65 1.51 0.00 0.00 0.00 M-negative 1.47 1.44 0.85 0.00 0.00 0.00 Table 66. Florida Site 9936 r differentials for Group I.

included in Strength I, going from P4 to P7, the r differential is minimized as expected. In Table 68 and Figure 44, all sorting cases show increasing r differential values with increasing span length for the Cali- fornia site. This shows that as increasingly heavier trucks are included in Strength I, going from P4 to P7, the r differential is minimized as expected. In Table 69 and Figure 45, all sorting cases generally show increasing r differential values with increasing span length for the Florida site. This shows that as increasingly heavier trucks are included in Strength I, going from P4 to P7, the r differ- ential is minimized as expected. Group III: Sorting Variation Based on State Permit Regulations. The following sorting variations will be dis- cussed under Group III: • P8: Strength I = state legal trucks, • P9: Strength I = state legal trucks and annual permits, • P10: Strength I = state legal trucks and illegal trucks, and • P11: Strength I = state legal trucks, illegal trucks, and annual permits. In Table 70 and Figure 46, Group III results (based on state permit regulations), particularly P8 and P9, are the most sen- sitive. The r differential results for P8 were the highest. This sig- nifies the biggest difference in r values occurs when only state legal loads are included in Strength I or illegal loads, trip permits, and annual permits are excluded. The r differential results for P10 and P11 were negligible. This indicates the minimal influence of removing annual permits or trip permits from Strength I. The Group III r differential results were not significantly sensitive to span length or load effect. 100 Strength I r Values r Differential = (r12 - rx) / r12 x 100% Span Length (ft) Span Length (ft) Sorting Variation Load Effect 20 60 120 20 60 120 P4 M-simple 1.34 0.92 0.67 29.56 44.80 63.93 V-simple 1.31 0.91 0.68 37.06 56.86 67.48 M-negative 0.92 0.51 0.35 50.10 67.76 69.51 P5 M-simple 1.51 1.08 0.81 21.14 35.38 56.55 V-simple 1.50 1.08 0.84 27.93 48.97 60.00 M-negative 1.09 0.65 0.43 40.74 59.25 62.42 P6 M-simple 1.59 1.13 0.92 16.88 32.13 50.48 V-simple 1.59 1.19 1.00 23.76 43.59 52.20 M-negative 1.24 0.80 0.53 32.53 49.53 54.14 P7 M-simple 1.64 1.37 1.14 14.25 17.43 38.71 V-simple 1.82 1.46 1.23 12.80 30.85 41.49 M-negative 1.43 0.97 0.65 22.30 38.72 43.60 P12 M-simple 1.91 1.67 1.86 0.00 0.00 0.00 V-simple 2.08 2.11 2.10 0.00 0.00 0.00 M-negative 1.84 1.59 1.15 0.00 0.00 0.00 Table 67. Indiana Site 9544 r differentials, Group II. Figure 43. Strength I moment r differentials for Group II vs. span lengths (Indiana Site 9544).

101 Figure 44. Strength I moment r differentials for Group II vs. span lengths (California Site 0059). Strength I r Values r Differential = (r12 - rx) / r12 x 100% Span Length (ft) Span Length (ft) Sorting Variation Load Effect 20 60 120 20 60 120 P4 M-simple 0.88 0.75 0.59 11.64 34.77 54.34 V-simple 0.94 0.78 0.63 16.23 37.91 52.46 M-negative 0.84 0.49 0.33 26.69 58.64 62.79 P5 M-simple 0.89 0.79 0.69 11.09 31.11 46.84 V-simple 0.95 0.88 0.74 15.72 30.23 43.77 M-negative 0.96 0.59 0.40 15.67 50.44 54.85 P6 M-simple 0.92 0.91 0.83 8.17 20.47 35.92 V-simple 1.02 0.98 0.88 9.60 22.61 33.67 M-negative 1.02 0.72 0.47 10.43 38.77 46.18 P7 M-simple 0.94 1.05 1.05 5.47 8.09 19.21 V-simple 1.08 1.11 1.08 4.45 11.78 18.40 M-negative 1.06 0.86 0.60 7.53 27.58 31.38 P12 M-simple 1.00 1.14 1.30 0.00 0.00 0.00 V-simple 1.13 1.26 1.32 0.00 0.00 0.00 M-negative 1.14 1.18 0.88 0.00 0.00 0.00 Table 68. California Site 0059 r differentials for Group II. Sorting Variation Load Effect Strength I r Values r Differential = (r12 - rx) / r12 x 100% Span Length (ft) Span Length (ft) 20 60 120 20 60 120 P4 M-simple 1.11 0.90 0.65 44 40.18 50.73 V-simple 1.11 0.90 0.66 48 45.60 56.08 M-negative 0.99 0.49 0.33 32.86 66.05 61.32 P5 M-simple 1.22 0.95 0.71 38.97 37.14 46.00 V-simple 1.18 0.96 0.75 44.96 41.97 50.24 M-negative 1.04 0.58 0.39 29.14 59.89 53.87 P6 M-simple 1.49 1.05 0.86 25.39 30.51 34.71 V-simple 1.43 1.10 0.92 33.22 33.35 39.31 M-negative 1.16 0.74 0.49 20.75 48.98 42.66 P7 M-simple 1.86 1.48 1.15 7.01 1.90 13.10 V-simple 2.03 1.52 1.21 5.52 7.87 19.92 M-negative 1.39 1.00 0.63 5.33 31.10 26.46 P12 M-simple 2.00 1.51 1.32 0.00 0.00 0.00 V-simple 2.15 1.65 1.51 0.00 0.00 0.00 M-negative 1.47 1.44 0.85 0.00 0.00 0.00 Table 69. Florida Site 9936 r differentials, Group II.

102 Figure 45. Strength I moment r differentials for Group II vs. span lengths (Florida Site 9936). Strength I r Values r Differential = (r12 - rx) / r12 x 100% Span Length (ft) Span Length (ft) SortingVariation Load Effect 20 60 120 20 60 120 P8 M-simple 0.74 0.65 0.58 61.38 60.76 69.05 V-simple 0.76 0.70 0.62 63.42 66.70 70.39 M-negative 0.72 0.51 0.33 60.89 68.00 71.18 P9 M-simple 0.80 0.74 0.76 58.27 55.65 59.12 V-simple 0.85 0.79 0.78 59.37 62.64 62.67 M-negative 0.73 0.67 0.46 60.20 58.14 59.73 P10 M-simple 1.91 1.67 1.86 -0.04 -0.06 -0.07 V-simple 2.09 2.11 2.10 -0.04 -0.04 -0.06 M-negative 1.85 1.59 1.15 -0.04 -0.07 -0.07 P11 M-simple 1.91 1.67 1.86 0.00 0.00 0.00 V-simple 2.08 2.11 2.10 0.00 0.00 0.00 M-negative 1.84 1.59 1.15 0.00 0.00 0.00 P12 M-simple 1.91 1.67 1.86 0.00 0.00 0.00 V-simple 2.08 2.11 2.10 0.00 0.00 0.00 M-negative 1.84 1.59 1.15 0.00 0.00 0.00 Table 70. Indiana Site 9544 r differentials for Group III. Figure 46. Strength I moment r differentials for Group III vs. span lengths (Indiana Site 9544).

In Table 71 and Figure 47, Group III results (based on state permit regulations) for the California site, particularly P8 and P9, are the most sensitive. The r differential results for P8 were the highest. This signifies that the biggest difference in r values occurs when only state legal loads are included in Strength I or illegal loads, trip permits, and annual permits are excluded. The r differential results for P10 and P11 were negligible. This indicates the minimal influence of removing annual per- mits or trip permits from Strength I. The Group III r differ- ential results for P8 and P9 were sensitive to span length. From Table 72 and Figure 48, Group III results (based on state permit regulations) for the Florida site, particularly P8 and P9, are the most sensitive. The r differential results for P8 were the highest. This signifies that the biggest difference in r values occurs when only state legal loads are included in Strength I or illegal loads, trip permits, and annual permits are excluded. The r differential results for P10 and P11 were negligible. This indicates the minimal influence of removing annual per- mits or trip permits from Strength I. The Group III r differen- tial results are not particularly sensitive to span length. Findings and Recommendations Some important findings from this study are • Sorting based on the number of axles does not have a large impact upon r values. 103 Strength I r Values r Differential = (r12 - rx) / r12 x 100% Span Length (ft) Span Length (ft) Sorting Variation Load Effect 20 60 120 20 60 120 P8 M-simple 0.65 0.57 0.52 35.09 50.16 60.07 V-simple 0.69 0.66 0.59 38.83 48.03 55.40 M-negative 0.71 0.48 0.31 38.03 59.14 64.58 P9 M-simple 0.87 0.70 0.68 12.92 39.22 48.06 V-simple 0.95 0.79 0.86 15.52 37.26 34.89 M-negative 0.81 0.85 0.62 29.31 28.24 29.84 P10 M-simple 1.00 1.14 1.34 -0.77 0.74 -3.02 V-simple 1.14 1.26 1.37 -1.00 -0.13 -3.55 M-negative 1.15 1.22 0.90 -0.32 -3.27 -2.73 P11 M-simple 1.00 1.14 1.30 0.00 0.00 0.00 V-simple 1.13 1.26 1.32 0.00 0.00 0.00 M-negative 1.14 1.18 0.88 0.00 0.00 0.00 P12 M-simple 1.00 1.14 1.30 0.00 0.00 0.00 V-simple 1.13 1.26 1.32 0.00 0.00 0.00 M-negative 1.14 1.18 0.88 0.00 0.00 0.00 Table 71. California Site 0059 r differentials for Group III. Figure 47. Strength I moment r differentials for Group III vs. span lengths (California Site 0059).

104 Sorting Variation Load Effect Strength I r Values r Differential = (r12 - rx) / r12 x 100% Span Length (ft) Span Length (ft) 20 60 120 20 60 120 P8 M-simple 0.76 0.68 0.52 61.70 54.83 60.19 V-simple 0.80 0.68 0.59 62.70 58.74 61.24 M-negative 0.71 0.48 0.31 51.61 66.53 64.18 P9 M-simple 1.42 0.95 0.90 28.61 37.02 31.95 V-simple 1.37 1.03 1.08 36.27 37.44 28.50 M-negative 1.07 1.08 0.73 27.33 25.43 14.47 P10 M-simple 2.09 1.58 1.38 -4.75 -4.59 -5.01 V-simple 2.24 1.74 1.55 -4.32 -5.37 -2.50 M-negative 1.55 1.48 0.83 -5.64 -2.29 2.23 P11 M-simple 2.00 1.51 1.31 -0.02 0.11 0.62 V-simple 2.15 1.65 1.45 -0.01 0.06 3.79 M-negative 1.46 1.33 0.78 0.21 8.08 8.39 P12 M-simple 2.00 1.51 1.32 0.00 0.00 0.00 V-simple 2.15 1.65 1.51 0.00 0.00 0.00 M-negative 1.47 1.44 0.85 0.00 0.00 0.00 Table 72. Florida Site 9936 r Differentials for Group III. Figure 48. Strength I moment r differentials for Group III vs. span lengths (Florida Site 9936). • Increasing GVW for trucks in Strength I leads to a small increase in r values. • Configurations of trucks as governed by state permit regu- lations (and weight regulations) have the greatest influence on r values than either GVW or the number of axles. • The inclusion of annual permits in Strength I, along with legal trucks, only resulted in a small increase in r values. However, when illegal trucks are added to legal trucks, a significant increase in r values was observed. Adding trip permits to the vehicle mix causes no noticeable change in max r values. • This shows that heavy permits, when they are legal and com- ply with permit regulations, do not significantly impact r val- ues. However, overloaded trucks not complying with permit or weight regulations (illegal trucks), led to high r values. • Baseline and P11 results provide a useful comparison. Both sorting cases seek to include all legal trucks, illegal overloads, and unanalyzed permits (all annual/routine permits) into Strength I, but execute this by different approaches. For Florida, the results are comparable. For Indiana, P11 is slightly higher. For California, P11 is about 30% higher. Using a state’s permit and weight regulations as in P11 to group trucks into Strength I and Strength II is considered more rational, and more precise, when using national WIM data. • A sensitivity analysis of r values shows that Group III re- sults (based on state permit regulations), particularly P8 and P9, are the most sensitive, followed by Group II (based on GVW), and then Group III (based on number of axles). • The biggest difference in r values occurs when only state legal loads are included in Strength I (P8). This highlights the influence of sorting trucks based on a state’s weight and per- mit regulations (as opposed to an axle or GVW criterion).

Recommendations for Sorting Traffic in the WIM Database into Strength I and Strength II The NCHRP 12-76 study addressed the criteria for separat- ing traffic data into Strength I and Strength II limit states by recommending that all uncontrolled traffic that constitutes normal traffic or service loads at a site be grouped into Strength I and all controlled or analyzed overload permits be grouped into Strength II. Strength I vehicles were taken to include state legal trucks, illegal overloads, and routine permits because they were considered to represent normal service traffic at bridge sites. Only the controlled trip permits or superloads were in- cluded in Strength II. Some questions on how to best imple- ment this sorting criteria when using large WIM databases did arise in the 12-76 study. In the 12-76 study it was decided to use a simplified approach and group all trucks with six or fewer axles in the Strength I calibration as a reasonable though approx- imate way to capture all legal trucks, illegal overloads, and annual permits. Thus, trucks with seven or more axles were con- sidered as controlled or trip permits. More detailed recommendations for grouping trucks into Strength I and II, based on the additional research conducted in this phase on truck sorting strategies, are as follows: 1. Using a state’s permit and weight regulations (as in varia- tion P11) to group trucks into Strength I and Strength II is considered the most precise and rational approach, when using national WIM data. Variation P11 includes state legal trucks, illegal trucks, and annual (routine) per- mits in Strength I. P11 is best implemented using state permit and weight regulations as in Group III. Sensitivity analysis of r values shows that Group III results are the most sensitive. This demonstrates the effectiveness of this sorting approach for classifying trucks into Strength I and Strength II. 2. Using the number of axles as a means to separate the trip permits from the rest of the traffic is an approximate alternate sorting approach that may be easier to imple- ment. Trucks with seven or more axles (or another suit- able cutoff) could be grouped into Strength II as trip permits. It would be important that when setting the cutoff for the number of axles, the typical axle configu- rations for routine permits in a state are taken into ac- count. In some states that have high GVW limits for routine permits, a cut off limit higher than seven axles for separating routine permits from trip permits would be appropriate. 3. Using GVW as a means to separate the trip permits from the rest of the traffic is also an approximate alternate sort- ing approach that can be implemented easily. Trucks with GVW = 150 kips or more could be grouped into Strength II as trip permits. For certain states this may need to be in- creased to 200 kips or higher depending on state permit regulations. 105