Calibration of AASHTO LRFD Concrete Bridge Design Specifications for Serviceability (2014)

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4 LIVE LOAD FOR CALIBRATION 4.1 Development of Live Load Models for Service Limit States 4.1.1 Introduction The consideration of limit states, both ultimate (strength) and serviceability, requires the knowledge of loads. The objective of this task is to determine the statistical parameters of live load for the limit states considered in AASHTO LRFD (2012). For Strength Limit States, the live load statistics were determined in NCHRP 12-33 and documented in the Calibration Report (NCHRP Report 368) (Nowak, 1999). The emphasis was placed on prediction of the extreme expected live load effects in the 75 year lifetime of a bridge. The database at that time was a truck survey carried out by the Ontario Ministry of Transportation in Canada. The basic statistical parameters of the maximum 75 live load effect (moment and shear force) were determined by extrapolation of the truck survey data. It was assumed that the survey represented two weeks of heavy traffic. The procedure is described in NCHRP Report 368 (Nowak, 1999). The Serviceability Limit States require additional statistical parameters, not only the maximum values but also load spectra, i.e. frequency of occurrence of loads. The maximum values are needed for shorter time periods, such as day, week, month, or year. At present, a considerable amount of WIM truck data is available and the research team had access to two sources: NCHRP Project 12-76 (NCHRP Report 683) (Sivakumar, et al., 2011) and FHWA files. This chapter provides documentation on the development of the statistical parameters of live load for service limit states and fatigue. The analysis includes consideration of the WIM database from NCHRP 12-76 and FHWA. The obtained data included over 65 million vehicles. Out of that number, about 10 million were deleted/filtered because of obvious errors in the WIM records, leaving about 55 million. Then, data from New York (about 7.8 million records) and Indiana other than site SPS-6 (about 13 million records) were also removed. The New York data was not considered because it included a considerable number of extremely heavy vehicles. It was decided that this data would have a strong effect on the statistical parameters and the remaining states would be unnecessarily penalized. Indiana data could not be considered because the format was not compatible with the other states. Therefore, the considered database included about 35 million vehicles. The obtained WIM data includes the following information for each location and each recorded vehicle: number of axles, spacing between axles, axle loads, gross vehicle weight, vehicle speed, and exact time of measurement. Statistical parameters are determined for the GVW and moment caused by the vehicles, including a CDF, bias factor, λ, that is equal to the mean-to-nominal ratio, i.e. the ratio of the mean value and the nominal (or design) value, and coefficient of variation, COV, equal to the ratio of standard deviation to the mean. The CDFs for the WIM data for each site were plotted on normal probability paper which was described in Section 3.2.1. 22

4.1.2 WIM Database The truck survey includes WIM truck measurements from 52 sites obtained from NCHRP 12-76 and FHWA. The data obtained from FHWA is summarized herein and includes trucks recorded from: • Arizona (SPS 1 – Special Pavement Study, Location 1) – data recorded continuously from January 2008 until December 2008 • Arizona (SPS 2 – Special Pavement Study, Location 2) – data recorded continuously from January 2008 until December 2008 • Arkansas (SPS 2 – Special Pavement Study, Location 2) – data recorded continuously from January 2008 until December 2008 • Colorado (SPS 2 – Special Pavement Study, Location 2) – data recorded continuously from January 2008 until December 2008 • Delaware (SPS 1 – Special Pavement Study, Location 1) – data recorded continuously from January 2008 until December 2008 • Illinois (SPS 6 – Special Pavement Study, Location 6) – data recorded continuously from January 2008 until December 2008 • Indiana (SPS 6 – Special Pavement Study, Location 6) – data recorded continuously from July 2008 until December 2008 • Kansas (SPS 2 – Special Pavement Study, Location 2) – data recorded continuously from January 2008 until December 2008 • Louisiana (SPS 1 – Special Pavement Study, Location 1) – data recorded continuously from January 2008 until December 2008 • Maine (SPS 5 – Special Pavement Study, Location 5) – data recorded continuously from January 2008 until December 2008 • Maryland (SPS 5 – Special Pavement Study, Location 5) – data recorded continuously from January 2008 until December 2008 • Minnesota (SPS 5 – Special Pavement Study, Location 5) – data recorded continuously from January 2008 until December 2008 • New Mexico (SPS 1 – Special Pavement Study, Location 1) – data recorded continuously from May 2008 until December 2008 • New Mexico (SPS 5 – Special Pavement Study, Location 5) – data recorded continuously from May 2008 until December 2008 • Pennsylvania (SPS 6 – Special Pavement Study, Location 6) – data recorded continuously from January 2008 until December 2008 • Tennessee (SPS 6 – Special Pavement Study, Location 6) – data recorded continuously from January 2008 until December 2008 • Virginia (SPS 1 – Special Pavement Study, Location 1) – data recorded continuously from January 2008 until December 2008 • Wisconsin (SPS 1 – Special Pavement Study, Location 1) – data recorded continuously from January 2008 until December 2008 Data obtained from NCHRP projects is also summarized herein, and includes trucks recorded from: California: • Lodi – Site 003 – data recorded continuously from June 2006 until March 2007 23

• Antelope East Bound – Site 003 – data recorded almost continuously from April 2006 until March 2007 (107 days missing) • Antelope West Bound – Site 003 – data recorded almost continuously from April 2006 until March 2007 (109 days missing) • LA 710 South Bound – Site 059 – data recorded continuously from April 2006 until March 2007 • LA 710 North Bound – Site 060 – data recorded almost continuously from April 2006 until March 2007 (32 days missing) • Bowman – Site 072 – data recorded almost continuously from April 2006 until February 2007 (139 days missing) Florida: • US29 – Site 9916 – data recorded continuously from January 2005 until December 2005 (11 days missing) • I-95 – Site 9919 – data recorded continuously from January 2005 until December 2005 (16 days missing) • I-75 – Site 9926 – data recorded almost continuously from January 2005 until December 2005 (100 days missing) • I-10 – Site 9936 – data recorded almost continuously from January 2005 until December 2005 (100 days missing) • State Route – Site 9927 – data recorded almost continuously from January 2004 until December 2004 (5 days missing) Indiana: • Site 9511 – data recorded continuously from January 2006 until December 2006 • Site 9512 – data recorded continuously from January 2006 until December 2006 • Site 9532 – data recorded continuously from January 2006 until December 2006 • Site 9534 – data recorded continuously from January 2006 until December 2006 • Site 9552 – data recorded continuously from January 2006 until December 2006 Mississippi: • I-10 – Site 3015 – data recorded continuously from January 2006 until December 2006 (28 days missing) • I-55 – Site 2606 – data recorded continuously from January 2006 until December 2006 (16 days missing) • I-55 – Site 4506 – data recorded almost continuously from March 2006 until December 2006 (39 days missing) • US49 – Site 6104 – data recorded continuously from January 2006 until December 2006 (5 days missing) • US61 – Site 7900 – data recorded almost continuously from January 2006 until December 2006 (49 days missing) New York: • I-95 North Bound – Site 0199 – data recorded continuously from March 2006 until December 2006 • I-95 South Bound – Site 0199 – data recorded continuously from July 2006 until November 2006 • I-495 West Bound – Site 0580 – data recorded continuously from January 2006 until December 2006 24

• I-495 East Bound – Site 0580 – data recorded continuously from January 2006 until December 2006 • Highway 12 – Site 2680 – data recorded continuously from January 2005 until December 2005 • I-84 (East Bound and West Bound) – Site 8280 – data recorded continuously from January 2006 until December 2006 • I-84 (East Bound and West Bound) – Site 8382 – data recorded continuously from January 2005 until December 2005 • I-81 (North Bound and South Bound) – Site 9121 – data recorded continuously from January 2005 until December 2005 • Highway 17 (East Bound and West Bound) – Site 9631 – data recorded continuously from February 2006 until December 2006 4.1.3 WIM Data Filtering It was observed that the WIM data both from NCHRP 12-76 and FHWA include a number of vehicle records that appear to be incorrect. There are various reasons for questioning the data, for example GVW is too low, unrealistic geometry, and so on. Therefore, the data was filtered first to eliminate questionable vehicles using the following criteria: • Weight per axle <2 kips or >70 kips, based upon NCHRP 12-76 • Record where the first axle spacing is less than 5 feet, based upon NCHRP 12-76 • Record where any axle spacing is less than 3.4 feet, based upon NCHRP 12-76 • Record where GVW varies from the sum of the axle weights by more than 10%, based upon NCHRP 12-76 • Record where the length of the truck varies from the sum of the axle spacings by more than 1ft, based upon NCHRP 12-76 • Record which has a GVW less than a threshold. At various times the threshold was 10 kips or 12 kips • Record where the steering axle is less than 6 kips, based upon NCHRP 12-76 • Record where the sum of the axle spacing lengths is less than 7 ft., based upon Pelphrey, et al. (2008) • Record where the sum of axle spacing is greater than the length of truck by more than 1 ft • Class of the vehicle according to FHWA – 3 – 14, to filter out passenger vehicles, motorcycles, etc. • Speed – 10 mph – 100 mph, based upon NCHRP 12-76 The filtering process is illustrated in the flowchart in Figure 4-1. A heavy vehicle meeting all of the conditional filters involving GVW would pass the filters. Therefore, the research team reviewed exceptionally heavy vehicles to check if their configuration resembled permit vehicles, such as cranes and garbage trucks. The data was divided into two sets. The first set contains regular truck traffic. This data is used for the live load model for Service Limit States. The remaining set of data includes permit vehicles and illegally overloaded vehicles that occur relatively infrequently. The latter data is used along with the regular truck traffic for live load analysis including effect of heavy vehicles. The heavy vehicles are assumed to be permit vehicles or illegally loaded vehicles. The GVW criteria of 20 kips in Step 3 is a traditional, albeit arbitrary cutoff used in virtually all previous fatigue studies to reduce the calculation effort by not considering light traffic which will not contribute significantly to cumulative damage. 25

Vehicles considered to be permit vehicles and illegally loaded trucks were filtered using the following criteria: • Total number of axles less than 3 and GVW is more than 50 kips • Steering axle weight is more than 35 kips • Individual axle weight is more than 45 kips Vehicles used to calibrate for the fatigue limit state were determined by filtering out trucks with GVW less than 20 kips from the trucks used for the service limit states. This follows the process historically used to perform fatigue analysis. The filtering process is illustrated in the flowchart below shown as Figure 4-1. Figure 4-1 Flowchart of the Filtering Process. The CDFs of GVWs were plotted on the probability paper and examples are shown in Figure 4-2 through Figure 4-5. The live load model used in calibration for strength limit states based on the Ontario truck survey is also shown. Trucks included in the Ontario study were selected by observing traffic and stopping trucks that appeared to be heavy. This is the reason 26

for the position of the Ontario curve relative to the other curves. At the upper tail of the curve, the Ontario data does not indicate that the heaviest vehicles in the Ontario study are heavier that those represented by other curves. Figure 4-3 represents CDF of the GVW of trucks from the FHWA sites plotted on probability paper. Data collected from fourteen sites represent one year of traffic, data from Indiana sites represents six months of traffic and data from New Mexico sites represent eight months of traffic. The maximum truck GVW is 220 kips. Mean values range from 20 to 65 kips. Figure 4-2 CDF of GVW - FHWA Data and Ontario. Figure 4-2 through Figure 4-5 represent CDFs of the GVWs for Oregon, Florida, Indiana, Mississippi, California and New York, respectively, i.e. the NCHRP 12-76 data. The corresponding traffic data from these figures is given in Table 4-1. Table 4-1 Summary of State Sites and Their Traffic Data for Figure 4-2 through Figure 4-5 Figure Number State Number of Sites Months of Data Maximum GVW (kips) Mean-Value Range (kips) Figure 4-2 Oregon 4 4 200 43 - 52 Florida 5 12 250 20 - 50 Figure 4-3 Indiana 5 12 250 25 - 57 Mississippi 5 12 260 38 - 57 Figure 4-4 California 2 8.7 250 40 - 50 1 7 New York 7 12 380 35 - 50 27

Figure 4-3 CDF of GVW – Oregon, Florida and Ontario. Figure 4-4 CDF of GVW – Indiana, Mississippi and Ontario. Figure 4-5 CDF of GVW – California, New York and Ontario. 28

As an initial observation, the data shown in Figure 4-2 through Figure 4-5 is generally consistent for the majority of the sites (The word “consistent” refers to the similarity of the general shape of the curves, i.e., the CDFs.). Exceptions are the heavily loaded sites from New York identified below: • Site 9121 – on I-81 by Whitney Point • Site 8382 – on I-84 by Port Jervis • Site 8280 – on I-84 by Fishkill • Site 0580 – on I-495 – Queens New York City Since these sites were so exceptional, it was decided not to include the New York WIM data in developing a national, notional SLS live load. Additionally, several sites for which the recording format differed or had considerably less than one tier of data were eliminated from consideration. A summary of the remaining 32 sites and filtered data including the WIM locations, number of records and ADTT is shown in Table 4-2. Approximately 35 million records are represented by these sites. 29

Table 4-2 WIM Locations and Number of Recorded Vehicles Site Number of Days in Data Total Number of Truck Records, N Lane ADTT AZ SPS-1 365 35,572 97 AZ SPS-2 365 1,430,461 3919 AR SPS-2 365 1,675,349 4590 CO SPS-2 365 343,603 941 DE SPS-1 365 201,677 553 IL SPS-6 365 854,075 2340 IN SPS-6 214 185,267 508 KS SPS-2 365 477,922 1309 LA SPS-1 365 85,702 235 ME SPS-5 365 183,576 503 MD SPS-5 365 164,389 450 MN SPS-5 365 55,572 152 NM SPS-1 245 117,102 321 NM SPS-5 245 608,280 1667 PA SPS-6 365 1,495,741 4098 TN SPS-6 365 1,622,320 4445 VA SPS-1 365 259,190 710 WI SPS-1 365 226,943 622 CA Antelope EB 258 837,667 2192* CA Antelope WB 256 943,147 2258* CA Bowman 134 651,090 2018* CA LA-710 NB 333 4,092,484 6380* CA LA-710 SB 365 4,661,287 8366* CA Lodi 304 3,298,499 5186* FL I-10 354 1,641,480 2207* FL I-95 349 2,112,518 2558* FL US-29 354 389,164 606* MS I-10 337 1,965,022 2967* MS I-55UI 268 1,232,223 2054* MS I-55R 349 1,333,268 1790* MS US-49 359 1,225,138 1475* MS US-61 319 159,299 254* Total 35,856,898 * NCHRP data is for multilane cases, lane with maximum ADTT is listed. The CDFs of GVWs and moment are plotted as separate curves for each location. The legend for all CDFs is shown in Figure 4-6. 30

FHWA Data NCHRP Data Figure 4-6 Legend for All Graphs. 4.2 Initial Data Analysis 4.2.1 Gross Vehicle Weight (GVW) The CDFs for the GVWs from the remaining FHWA and NCHRP sites are plotted on probability paper in Figure 4-7. Each of the 32 curves represents a different location. The resulting curves indicate that the distribution of GVW is not normal. Irregularity of the CDFs is a result of different types of vehicles in the WIM data such as long and short, fully loaded and empty, or loaded by volume only, and so on. For the considered locations, the mean gross vehicle weights are between 25 and 65 kips. The upper tails of the CDF curves show a similar trend, but there is a considerable spread of the maximum values, from 150 to over 250 kips. 31

Figure 4-7 CDF of Gross Vehicle Weight (GVW). 4.2.2 Moments from the WIM Data The distribution of simple span moments due to WIM trucks was obtained by calculating the maximum bending moment for each vehicle in the database. Each vehicle was run over influence lines to determine the maximum moment using a specially developed computer program. The calculations were carried out for spans from 30 through 200 ft. For easier interpretation and comparison of results, the calculated WIM data moments were then divided by the corresponding HL-93 moment. Normalizing the data to a common reference makes the data easier to interpret. HL-93 was just a convenient reference and ties this work to the original strength limit state calibration and associated published information. The CDFs for the ratio of the WIM truck moment to HL-93 moment are plotted on normal probability paper in Figure 4-8 and Figure 4-12. The shape of the CDF curves is similar to that of GVW. The mean WIM moments are between 0.2 and 0.4 of the HL-93 moments, for all span lengths considered. The maximum values of the WIM moment are between 1.0 and 1.4 of HL- 93 moment in most cases. The obtained results served as basis for determining the statistical parameters of live load needed for the reliability analysis of the serviceability limit states. 32

Figure 4-8 CDFs of WIM Moment and HL- 93 Moment Ratio, Span = 30 ft. Figure 4-9 CDFs of WIM Moment and HL-93 Moment Ratio, Span = 60 ft. 33

Figure 4-10 CDFs of WIM Moment and HL- 93 Moment Ratio, Span = 90 ft. Figure 4-11 CDFs of WIM Moment and HL- 93 Moment Ratio, Span = 120 ft. Figure 4-12 CDFs of WIM Moment and HL-93 Moment Ratio, Span = 200 Ft. 34

4.2.3 Filtering of Presumed Illegal Overloads and Special Permit Loads The goal of this analysis was to observe the change in the very top tail of the distribution after removing a number of the heaviest vehicles from the database. These extremely heavy vehicles seem to be either permit vehicles which should either be included in the design process, as some states do, or reviewed for permit issuance using the Strength II limit state load combination, or they are illegal overloads. An example of the heaviest truck in the WIM data is presented in Figure 4-13. This truck was recorded at site 8382 located near Port Jervis, NY. The total length of the truck is 100.6 ft. The GVW is 391.4 kips. The position of the twelve axles, their weight and its length suggest that the vehicle should be categorized as a permit vehicle. WIM equipment captures each vehicle, including permit vehicles, as a string of axles and an FHWA designation is given based on the best FHWA category that fits the detected configuration. Heavy vehicles are assumed to be permit vehicles or illegally loaded vehicles. Figure 4-13 Configuration of Extremely Loaded Truck. The initial study indicated that the removal of a very small number of the heaviest vehicles drastically changes the upper tail of the CDF of moments and shears. It was decided to explore this by investigating the number of vehicles that exceed an upper value of 1.35, which corresponds to the maximum bias ratio obtained from the Ontario measurements. The results of the analysis for sites from New York and Mississippi were plotted on probability paper, in Figure 4-14 through Figure 4-16. It can be observed that, as expected, the very upper tail of the distribution changes drastically by removal of only a very small percentage of vehicles. For example in Figure 4-15 New York 8382, considering 90 ft spans if only the six largest moment ratios (corresponding to the six heaviest trucks including the 391-kip vehicle shown above) out of 1.55 million data records remaining after application of the additional filter to remove moments less than 15% of the corresponding HL-93 moment, the bias changes from approximately 2.35 to approximately 1.65. Even for the WIM sites which demonstrated very extreme tails, these extreme trucks constituted only the upper 0.01% to 0.22% of the truck population. For most of the locations reviewed, the percentage was lower (see Table 4-3). The heaviest loads may have an important impact on calibration of the ULSs, however, in the case of SLS, the upper tail of the CDF of the live load is not important, as it is the main body of CDF that affects the SLS performance. Therefore, for SLS calibration, it was decided to ignore the upper tip of the CDF of live load. 35

Table 4-3 Removal of the Heaviest Vehicles for 90 ft Spans Figure Number State Location Number of trucks before filtering Number of trucks after filtering Number of removed trucks Percent of removed trucks Figure 4-14 NY 0580 2,474,407 2,468,952 5455 0.22% Figure 4-14 NY 2680 89,286 89,250 36 0.04% Figure 4-15 NY 8280 1,717,972 1,717,428 544 0.03% Figure 4-15 NY 8382 1,551,454 1,550,914 540 0.03% Figure 4-16 NY 9121 1,235,963 1,235,886 77 0.01% Figure 4-16 MS I-10 2,103,302 2,103,300 2 0.00% Figure 4-14 Data Removal New York 0580 and 2680. Figure 4-15 Data Removal New York 8280 and 8382. 36

Figure 4-16 Data Removal New York 9121 and Mississippi I-10. 4.2.4 Multiple Presence Analysis Multiple presence was investigated by a correlation analysis of the WIM data sets. The objective of the correlation analysis was to select two trucks within the group of vehicles that simultaneously occurred on the bridge positioned as shown in Figure 4-17, and which satisfy the following requirements: Both trucks have the same number of axles GVWs of the trucks are within +/- 5% All corresponding spacings between axles are within +/- 10% The maximum load effect is often caused by a simultaneous occurrence of two or more trucks on the bridge. The statistical parameters of these effects are influenced by the degree of correlation. In calibration for the strength limit states, certain probabilities of occurrence of correlated trucks were assumed based on engineering judgment applied to limited observations of multiple presence of trucks of unknown weight. The available WIM data allows for verification of these assumptions. A special program was developed to filter the data using the time of a record and the speed of the truck to find instances when either of the events shown in Figure 4-17 occurred involving similar trucks. The filter resulted in selecting the observed cases of two trucks with the headway distance less than 200 ft in either the same lane or two adjacent lanes, as illustrated in Figure 4-17. 37

Figure 4-17 Two Cases of The Simultaneous Occurrence. Two Trucks – Side-by-Side The analysis of the degree of correlation was performed for Site 9936 in Florida along I- 10 and 8382 in New York with a total number of records equal to 1,654,004 and 1,594,674, respectively. The filtering of the data resulted in selection of 2518 fully correlated trucks in adjacent lanes in Florida and selection of 3748 fully correlated trucks in adjacent lanes in New York. Histograms of GVW of the fully correlated side-by-side trucks identified are shown in Figure 4-18. Florida I10 New York 8382 Figure 4-18 Histogram – Trucks Side-by-Side – Florida I-10 and New York 8382. The selected trucks were plotted on probability paper and compared with all recorded vehicles. The GVW of both of the correlated trucks were added together and divided by two to obtain the average GVW. (Note that the correlation criteria assure that the average is similar to the two selected trucks in each pair.) The comparison of the mean correlated GVW of the trucks recorded in adjacent lanes with the GVW of the whole population from Florida and New York are shown in Figure 4-19. T1 T2 Headway Distance max 200 ft T1 T2 Headway Distance max 200 ft 38

Florida I10 New York 8382 Figure 4-19 Comparison of the Mean GVW and GVW of the Whole Population – Florida and New York. Two Trucks – One After Another The filtering of the data resulted in selection of 8380 fully correlated trucks in one lane in Florida and 9868 fully correlated trucks in one lane in New York. Histograms of these trucks are shown in Figure 4-20. The comparison of the mean correlated GVW of the trucks recorded in one lane with the GVW of the whole data from Florida and New York are shown in Figure 4-21. Florida I-10 New York 8382 Figure 4-20 Histogram – Trucks One After Another – Florida I-10 and New York 8382. 39

Florida I10 New York 8382 Figure 4-21 Comparison of the Mean GVW and GVW of the Whole Population – Florida and New York. Implications for Specification Development This study of multiple presence based on WIM data indicated that the vehicles representing the extreme tails of the CDF need not be considered to occur simultaneously in multiple lanes. The implication is that, for the SLS, only a single-lane live-load model need be considered on the load side, Q, of limit state functions. The resistance side of limit state functions, R, should represent the requirements of the applicable design requirement, even if that is a multiple lane loading. The issue of multiple load lanes was considered in the development of HL-93 for AASHTO LRFD Strength Limit States, and the conclusion was that extreme truck load does not occur simultaneously with another, fully correlated, extreme truck, but was considered to occur simultaneously with a somewhat lighter truck—about 15% to 20% lighter truck. This 2-lane loading was correlated to the design loading of two lanes of HL-93 with a load factor of 1.75 and a multiple presence factor of 1.0. (Note that the multiple presence factor for a single lane loading is 1.20 to account for the occasional truck that creates more force effect than the family of configurations used to develop the HL-93 load configuration.) 4.2.5 Project Guidelines Regarding Live Load The following guidelines are based on live load bias factors and coefficients of variation determined from the preliminary analysis of WIM measurements and some previous work by the research team (Nowak, 1999). • It is recommended to use dynamic load as 10% of live load, with COV = 80% • Generally use a single loaded lane (no multiple loaded lanes) • The national load, i.e. notional load, should not try to encompass all WIM records. Some of the extremely heavy vehicles are permit loads and some are illegal overloads. A relatively small number of loads were excluded for most of the service limit state studies, but they were included for overload limit state. 40

• Different probabilities of exceedance may be used for various limit states based on consequences. Different probabilities of exceedance may also be used when calibrating the same limit state for components in different environment. • Some jurisdictions may need exceptions based on their legal loads and extent of enforcement, and • Basic HL-93 load model, scaled by calibrated load factors, is appropriate for SLS With these recommendations, the evaluation of numerical live load models continued. The processes used and results obtained are summarized herein. Further details and extensive graphical presentations are contained in Rakoczy (2011). 4.3 Statistical Parameters for Service Limit States Other Than Fatigue 4.3.1 Maximum Moments for Different Time Periods The maximum moment is a random variable. It depends on the period of time, ADTT and distribution of traffic (e.g. CDF of WIM moments). For a given CDF of WIM moments, F(x), period of time, T, and ADTT, the mean value of the maximum moment can be determined as follows. The total number of vehicles, N, expected during the considered time period, T (days), is T times ADTT. The expected or mean value of the maximum moment, Mmax(T) for time T is equal to the moment corresponding to probability {1 – F[1/N(T)]}, where F(x) is the CDF of WIM moments, which is F-1[1 - 1/N(T)] where F-1 is the inverse of CDF. The objective is to determine the mean maximum moment for different time periods, i.e. 1 day, 2 weeks, 1 month, 2 months, 6 months, 1 year, 5 years, 50 years, 75 years and 100 years. The number of recorded vehicles for each location is given in Table 4-2. The data was collected over different time periods, in most cases about one year, but the number of vehicles varies because of different ADTT. Each CDF in Figure 4-8 through Figure 4-12 includes the number of data points equal to the corresponding number of vehicles, N. For each CDF, the vertical coordinate of the maximum moment, zmax, is equal to, ( )1maxz Φ 1/ N−= − (4-1) where Φ-1 is the inverse standard normal distribution function. For example, if N = 1 million, then zmax = 4.75. In further analysis, five single lane ADTT’s are considered: 250, 1,000, 2,500, 5,000 and 10,000. The calculations were performed separately for each ADTT. To determine the mean maximum moments corresponding to the considered time periods, the vertical coordinates are found first. Starting with ADTT = 250, the vertical coordinate of the mean maximum 1 day moment, z, is ( )1z Φ 1/ 250 2.65−= − = (4-2) because the number of trucks per 1 day is 250. For the mean maximum 2 week moment, z, is 41

( )1z Φ 1/ 3500 3.44−= − = (4-3) because the number of trucks per 2 weeks is (250 trucks)(14 days) = 3500 trucks. Finally, for the mean maximum 100 year moment, z, is ( )1z Φ 1/ 9,125,000 5.18 −= − = (4-4) because the number of trucks per 100 years is (250 trucks)(365 days)(100 years) = 9,125,000 trucks. Similarly, for ADTT = 1000, the vertical coordinate of the mean maximum 1 day moment, z, is ( )1z Φ 1/1000 3.09−= − = (4-5) because the number of trucks per 1 day is 1000. For the mean maximum 2 week moment, z, is ( )1z Φ 1/14,000 3.8−= − = (4-6) because the number of trucks per 2 weeks is (1000 trucks)(14 days) = 14,000 trucks. Finally, for the mean maximum 100 year moment, z, is ( )1z Φ 1/ 36,500,000 5.67−= − = (4-7) because the number of trucks per 100 years is (1000 trucks)(365 days)(100 years) = 36,500,000 trucks. Values of z for the considered ADTTs and time periods from 1 day to 100 years are summarized in Table 4-4. 42

Table 4-4 Vertical Coordinates for the Mean Maximum Moment. ADTT 250 1,000 2,500 5,000 10,000 1 Day 2.65 3.09 3.35 3.54 3.72 2 Weeks 3.44 3.08 4.02 4.18 4.33 1 Month 3.65 4.00 4.20 4.35 4.50 2 Months 3.82 4.15 4.35 4.50 4.65 6 Months 4.09 4.39 4.59 4.73 4.87 1 Year 4.24 4.55 4.73 4.87 5.01 5 Years 4.59 4.87 5.05 5.18 5.31 50 Years 5.05 5.31 5.47 5.60 5.72 75 Years 5.13 5.38 5.55 5.67 5.78 100 Years 5.18 5.44 5.60 5.72 5.83 For example, for the WIM moments in Figure 4-11 (span 120 ft.), the vertical coordinates corresponding to different time periods are shown in Figure 4-22 for ADTT = 1000. There are 32 WIM locations and, therefore, 32 curves in each Figure 4-8 through Figure 4-12, representing CDFs of WIM moment. The mean maximum moment can be obtained directly from the graph by reading the moment ratio (horizontal axis) corresponding to the vertical coordinate representing the considered time period. For example, from Figure 4-22, the mean maximum 1 day moment ratio for FL-US29 is 0.95, and the mean maximum 1 year moment ratio is 1.39. Values for longer time periods were projected or interpolated as appropriate. 43

Figure 4-22 Vertical Coordinates for Different Time Periods, ADTT = 1000 and Span = 120 ft. In the results for each ADTT and span length, there are 32 values of the mean maximum 1 day moment, 32 values of the mean maximum 2 week moment, and so on. For easier review and comparison, cumulative distribution functions of these 32 values obtained from Figure 4-22, are plotted on the normal probability paper in Figure 4-23. There is one CDF for 1 day values, one for 2 weeks, and so on. These are CDFs of extreme variables, as each of the 32 values is the maximum moment for a WIM location. The obtained CDFs are almost parallel, in particular this applies to the upper part. Because of regularity, it is easier to determine the statistical parameters. Each data point represents the mean of maximum value for one of 32 WIM locations, therefore, the CDF’s in Figure 4-23 are extreme value distributions rather than hypothetical curves. 44

Figure 4-23 CDFs of Mean Maximum Moment Ratios for ADTT = 1000 and Span Length 120 ft. 4.3.2 Statistical Parameters of Live Load It is assumed that the considered 32 WIM locations are representative for the truck traffic in the United States. The statistical parameters (the mean maximum and coefficient of variation of the maximum live load) were determined for each WIM location. The cumulative distribution functions (CDF) of the mean maximum values were plotted on probability paper. This is an extreme value distribution. The mean of these mean maximum values can be considered as the mean maximum national live load. The standard deviation of the mean maximum values can be determined from the graphs (slope of the CDF). However, the WIM locations were not selected randomly, but the selection was based on availability of WIM stations with truck data and credibility of the measured data (truck records). If the considered WIM locations are biased (non-representative), then the processed database can underestimate or overestimate the statistical parameters of the national live load. Therefore, for the purpose of further reliability analysis, it is conservatively assumed that the calculated mean maximum live load is increased by 1.5 standard deviation. The probability of exceeding this value (mean plus 1.5 standard deviation) is about 5%, so that it will be exceeded by 5% out of 32 WIM locations (i.e. in one or two WIM locations). The upper parts of the CDFs are almost straight lines, therefore, the fitting by normal distributions is justified. The mean values can be read directly from the graph, as the intersection of CDFs (represented by straight lines) and the horizontal axis at zero on the vertical scale. This process is depicted in Figure 4-24. The visual comparison of how the actual CDF fits a straight line is much better than any curve fitting formula because we are mostly 45

interested in some parts of the CDF only. Different curves can have different slope and this is reflected in the standard deviations. Calculations were carried out for all considered cases of ADTT and span length. The results were extrapolated to 100 years and span length of 300 ft. and are summarized in Table 4-5 through Table 4-9. Statistical parameters were calculated for a variety of ADTT’s (500, 1000, 2500, 5000, 10,000) but AASHTO LRFD is based on 5000 (consistent with strength limit states). Live load data for other values of ADTT other than 5000 are tabulated so owners can repeat the calibration process with other data. For a given bridge, use of a lower ADTT should lead to a higher reliability index. Bias factors vary depending on ADTT for shorter time periods, however for longer time periods it is about 1.4. Figure 4-24 Determination of Mean Values at 1.5 σ. 4.3.3 Reactions Tables of statistics for reactions of simply supported spans were developed for the same spans, time periods and ADTTs as previously presented for bending moments using an analogous methodology as presented in Section 4.3.2. The results are shown in Table 4-10 to Table 4-14. Graphical representations are presented in Rakoczy (2011). 46

4.3.4 Axle Loads Decks are typically designed for axle loads, not truck loads. Therefore, statistical parameters for axle loads for various time periods and ADTTs are developed using methodology analogous to the methodology used for moments (see in Section 4.3.2) are presented in Table 4-15. 47

Table 4-5 Statistical Parameters of Live Load Moments for ADTT 250, λ = µ + 1.5σ ADTT 250 Span 30 ft 60 ft 90 ft 120 ft 200 ft 300 ft λ µ COV λ µ COV λ µ COV λ µ COV λ µ COV λ µ COV 1 Day 0.92 0.65 0.28 0.82 0.64 0.23 0.80 0.66 0.17 0.79 0.65 0.15 0.71 0.56 0.18 0.61 0.48 0.18 2 Weeks 1.06 0.80 0.21 1.05 0.80 0.16 1.01 0.80 0.18 1.02 0.80 0.16 0.93 0.73 0.16 0.84 0.67 0.16 1 Month 1.12 0.85 0.21 1.09 0.85 0.19 1.08 0.85 0.18 1.08 0.85 0.17 1.01 0.78 0.19 0.90 0.73 0.16 2 Months 1.14 0.90 0.18 1.15 0.91 0.17 1.14 0.90 0.18 1.14 0.90 0.17 1.05 0.85 0.15 0.95 0.77 0.15 6 Months 1.19 0.95 0.17 1.23 0.96 0.19 1.20 0.97 0.15 1.19 0.98 0.14 1.12 0.91 0.15 1.04 0.85 0.15 1 Year 1.23 1.00 0.15 1.27 0.98 0.19 1.24 1.00 0.16 1.22 1.04 0.12 1.15 0.94 0.15 1.08 0.88 0.15 5 Years 1.31 1.07 0.15 1.35 1.09 0.16 1.31 1.13 0.11 1.31 1.14 0.10 1.25 1.02 0.15 1.18 0.97 0.15 50 Years 1.37 1.17 0.11 1.39 1.16 0.13 1.39 1.25 0.07 1.37 1.19 0.10 1.32 1.06 0.16 1.25 1.02 0.15 75 Years 1.38 1.20 0.10 1.40 1.19 0.12 1.41 1.27 0.07 1.39 1.21 0.10 1.34 1.08 0.16 1.27 1.04 0.15 100 Years 1.39 1.22 0.09 1.43 1.21 0.12 1.42 1.28 0.07 1.41 1.22 0.10 1.35 1.09 0.16 1.29 1.05 0.15 Table 4-6 Statistical Parameters of Live Load Moments for ADTT 1,000, λ = µ + 1.5σ ADTT 1,000 Span 30 ft 60 ft 90 ft 120 ft 200 ft 300 ft λ µ COV λ µ COV λ µ COV λ µ COV λ µ COV λ µ COV 1 Day 0.99 0.72 0.28 0.89 0.71 0.20 0.90 0.72 0.17 0.89 0.71 0.17 0.81 0.63 0.19 0.71 0.55 0.19 2 Weeks 1.14 0.87 0.21 1.13 0.90 0.16 1.13 0.89 0.18 1.14 0.91 0.16 1.06 0.85 0.16 0.97 0.77 0.16 1 Month 1.18 0.95 0.16 1.19 0.95 0.16 1.19 0.95 0.17 1.19 0.96 0.16 1.11 0.91 0.14 1.01 0.83 0.14 2 Months 1.23 0.99 0.16 1.26 0.99 0.18 1.26 1.00 0.17 1.23 1.03 0.13 1.16 0.96 0.14 1.07 0.89 0.14 6 Months 1.27 1.04 0.14 1.31 1.05 0.16 1.30 1.10 0.12 1.27 1.09 0.11 1.22 0.99 0.15 1.15 0.93 0.15 1 Year 1.33 1.07 0.16 1.34 1.08 0.16 1.32 1.15 0.10 1.31 1.14 0.10 1.25 1.01 0.16 1.18 0.95 0.16 5 Years 1.37 1.11 0.15 1.37 1.14 0.13 1.36 1.21 0.08 1.35 1.17 0.10 1.30 1.06 0.15 1.24 1.01 0.15 50 Years 1.38 1.24 0.07 1.42 1.21 0.12 1.41 1.26 0.08 1.41 1.21 0.11 1.35 1.11 0.14 1.28 1.05 0.14 75 Years 1.40 1.26 0.07 1.42 1.23 0.11 1.42 1.28 0.07 1.41 1.23 0.10 1.36 1.13 0.13 1.29 1.07 0.13 100 Years 1.40 1.27 0.07 1.44 1.24 0.11 1.43 1.29 0.07 1.43 1.24 0.10 1.37 1.14 0.13 1.30 1.09 0.13 48

Table 4-7 Statistical Parameters of Live Load Moments for ADTT 2,500, λ = µ + 1.5σ ADTT 2,500 Span 30 ft 60 ft 90 ft 120 ft 200 ft 300 ft λ µ COV λ µ COV λ µ COV λ µ COV λ µ COV λ µ COV 1 Day 1.03 0.80 0.19 0.97 0.79 0.18 0.97 0.77 0.17 0.98 0.78 0.17 0.90 0.70 0.19 0.80 0.62 0.19 2 Weeks 1.20 0.93 0.19 1.20 0.96 0.17 1.20 0.96 0.17 1.20 0.97 0.15 1.12 0.92 0.14 1.02 0.84 0.14 1 Month 1.23 0.99 0.16 1.25 0.99 0.17 1.26 1.00 0.17 1.22 1.04 0.12 1.16 0.95 0.15 1.09 0.89 0.15 2 Months 1.28 1.04 0.15 1.31 1.04 0.17 1.29 1.11 0.11 1.27 1.12 0.09 1.21 0.98 0.15 1.12 0.91 0.15 6 Months 1.31 1.07 0.15 1.34 1.07 0.17 1.32 1.15 0.10 1.31 1.14 0.10 1.25 1.01 0.16 1.18 0.95 0.16 1 Year 1.34 1.11 0.14 1.35 1.11 0.14 1.36 1.19 0.09 1.34 1.17 0.09 1.28 1.04 0.15 1.21 0.98 0.15 5 Years 1.36 1.15 0.12 1.39 1.18 0.12 1.39 1.24 0.08 1.38 1.20 0.10 1.33 1.07 0.16 1.26 1.01 0.16 50 Years 1.40 1.25 0.08 1.42 1.22 0.11 1.43 1.29 0.07 1.43 1.23 0.11 1.37 1.11 0.15 1.29 1.05 0.15 75 Years 1.40 1.26 0.07 1.43 1.24 0.10 1.43 1.30 0.07 1.44 1.24 0.10 1.37 1.13 0.14 1.29 1.06 0.14 100 Years 1.40 1.27 0.07 1.44 1.25 0.10 1.44 1.31 0.07 1.44 1.25 0.10 1.39 1.14 0.14 1.32 1.09 0.14 Table 4-8 Statistical Parameters of Live Load Moments for ADTT 5,000, λ = µ + 1.5σ ADTT 5,000 Span 30 ft 60 ft 90 ft 120 ft 200 ft 300 ft λ µ COV λ µ COV λ µ COV λ µ COV λ µ COV λ µ COV 1 Day 1.08 0.85 0.18 1.02 0.82 0.17 1.03 0.82 0.17 1.03 0.82 0.17 0.95 0.75 0.17 0.84 0.67 0.17 2 Weeks 1.24 0.98 0.17 1.26 1.00 0.17 1.24 1.00 0.16 1.24 1.04 0.13 1.16 0.96 0.14 1.06 0.88 0.14 1 Month 1.28 1.04 0.15 1.32 1.03 0.18 1.30 1.12 0.11 1.26 1.11 0.09 1.20 0.99 0.14 1.13 0.93 0.14 2 Months 1.31 1.07 0.15 1.34 1.07 0.17 1.32 1.15 0.10 1.31 1.14 0.10 1.23 1.02 0.14 1.16 0.96 0.14 6 Months 1.34 1.11 0.14 1.35 1.11 0.14 1.34 1.19 0.08 1.32 1.17 0.09 1.28 1.04 0.15 1.23 1.00 0.15 1 Year 1.35 1.14 0.12 1.38 1.14 0.14 1.38 1.21 0.09 1.36 1.19 0.09 1.31 1.07 0.15 1.25 1.02 0.15 5 Years 1.39 1.16 0.13 1.40 1.19 0.12 1.40 1.25 0.08 1.41 1.21 0.11 1.34 1.10 0.15 1.28 1.05 0.15 50 Years 1.41 1.21 0.11 1.44 1.24 0.10 1.44 1.27 0.09 1.46 1.23 0.12 1.39 1.13 0.15 1.30 1.06 0.15 75 Years 1.42 1.22 0.11 1.45 1.25 0.10 1.45 1.29 0.08 1.46 1.25 0.11 1.40 1.14 0.15 1.31 1.07 0.15 100 Years 1.42 1.23 0.11 1.45 1.26 0.10 1.47 1.30 0.08 1.47 1.26 0.11 1.40 1.15 0.15 1.33 1.08 0.15 49

Table 4-9 Statistical Parameters of Live Load Moments for ADTT 10,000, λ = µ + 1.5σ ADTT 10,000 Span 30 ft 60 ft 90 ft 120 ft 200 ft 300 ft λ µ COV λ µ COV λ µ COV λ µ COV λ µ COV λ µ COV 1 Day 1.17 0.88 0.22 1.09 0.89 0.16 1.11 0.87 0.18 1.13 0.87 0.20 1.02 0.81 0.17 0.91 0.75 0.17 2 Weeks 1.29 1.02 0.18 1.31 1.04 0.17 1.29 1.11 0.11 1.27 1.12 0.09 1.22 0.98 0.16 1.16 0.93 0.16 1 Month 1.32 1.06 0.16 1.34 1.08 0.16 1.32 1.15 0.10 1.29 1.14 0.09 1.25 1.01 0.16 1.20 0.97 0.16 2 Months 1.35 1.09 0.16 1.35 1.11 0.14 1.35 1.18 0.09 1.32 1.17 0.09 1.28 1.04 0.15 1.23 1.00 0.15 6 Months 1.35 1.12 0.13 1.37 1.14 0.13 1.37 1.20 0.09 1.34 1.19 0.08 1.30 1.06 0.15 1.25 1.02 0.15 1 Year 1.37 1.17 0.11 1.39 1.16 0.13 1.39 1.24 0.08 1.38 1.20 0.10 1.32 1.08 0.15 1.27 1.04 0.15 5 Years 1.39 1.24 0.08 1.41 1.21 0.11 1.42 1.27 0.08 1.42 1.22 0.11 1.37 1.11 0.15 1.30 1.06 0.15 50 Years 1.40 1.28 0.06 1.45 1.24 0.11 1.45 1.30 0.08 1.46 1.25 0.11 1.40 1.14 0.15 1.31 1.07 0.15 75 Years 1.41 1.29 0.06 1.46 1.26 0.10 1.47 1.32 0.08 1.47 1.26 0.11 1.40 1.16 0.14 1.32 1.09 0.14 100 Years 1.42 1.30 0.06 1.47 1.27 0.10 1.49 1.33 0.08 1.48 1.27 0.11 1.42 1.17 0.14 1.33 1.10 0.14 Table 4-10 Statistical Parameters of Live Load Reactions for ADTT 250, λ = µ + 1.5σ ADTT 250 Span 30 ft 60 ft 90 ft 120 ft 200 ft 300 ft µ+1.5σ µ COV µ+1.5σ µ COV µ+1.5σ µ COV µ+1.5σ µ COV µ+1.5σ µ COV µ+1.5σ µ COV 1 Day 1.02 0.85 0.13 0.88 0.74 0.12 0.88 0.74 0.12 0.86 0.72 0.13 0.73 0.61 0.13 0.57 0.48 0.13 2 Weeks 1.22 1.02 0.13 1.08 0.91 0.12 1.11 0.94 0.12 1.08 0.90 0.13 0.97 0.80 0.14 0.82 0.68 0.14 1 Month 1.28 1.07 0.13 1.14 0.96 0.13 1.17 0.99 0.12 1.15 0.97 0.12 1.06 0.88 0.14 0.93 0.77 0.14 2 Months 1.32 1.11 0.13 1.19 1.01 0.12 1.22 1.04 0.12 1.20 1.02 0.12 1.12 0.92 0.14 0.98 0.81 0.14 6 Months 1.37 1.16 0.12 1.27 1.07 0.12 1.32 1.11 0.13 1.30 1.10 0.12 1.18 0.97 0.14 1.08 0.89 0.14 1 Year 1.41 1.20 0.12 1.31 1.10 0.13 1.37 1.14 0.13 1.35 1.12 0.13 1.22 1.01 0.14 1.12 0.93 0.14 5 Years 1.49 1.26 0.12 1.38 1.15 0.13 1.46 1.22 0.13 1.44 1.20 0.13 1.35 1.11 0.14 1.24 1.02 0.14 50 Years 1.54 1.30 0.12 1.49 1.23 0.14 1.52 1.28 0.13 1.52 1.28 0.13 1.45 1.18 0.15 1.36 1.11 0.15 75 Years 1.55 1.31 0.12 1.50 1.24 0.14 1.55 1.29 0.13 1.55 1.29 0.13 1.46 1.19 0.15 1.37 1.12 0.15 100 Years 1.56 1.32 0.12 1.50 1.25 0.14 1.55 1.30 0.13 1.55 1.30 0.13 1.47 1.20 0.15 1.38 1.12 0.15 50

Table 4-11 Statistical Parameters of Live Load Reactions for ADTT 1,000, λ = µ + 1.5σ ADTT 1000 Span 30 ft 60 ft 90 ft 120 ft 200 ft 300 ft µ+1.5σ µ COV µ+1.5σ µ COV µ+1.5σ µ COV µ+1.5σ µ COV µ+1.5σ µ COV µ+1.5σ µ COV 1 Day 1.14 0.94 0.14 0.95 0.80 0.13 0.94 0.80 0.11 0.91 0.79 0.10 0.84 0.70 0.13 0.74 0.62 0.13 2 Weeks 1.31 1.10 0.13 1.17 0.99 0.12 1.19 1.02 0.11 1.19 1.02 0.11 1.09 0.91 0.13 0.97 0.81 0.13 1 Month 1.35 1.15 0.12 1.23 1.03 0.13 1.26 1.08 0.11 1.25 1.07 0.11 1.17 0.97 0.13 1.06 0.88 0.13 2 Months 1.38 1.18 0.11 1.26 1.08 0.11 1.31 1.11 0.12 1.31 1.11 0.12 1.22 1.01 0.14 1.11 0.92 0.14 6 Months 1.42 1.22 0.11 1.29 1.11 0.11 1.38 1.15 0.13 1.37 1.16 0.12 1.28 1.05 0.14 1.18 0.97 0.14 1 Year 1.45 1.25 0.11 1.32 1.14 0.11 1.40 1.19 0.12 1.40 1.19 0.12 1.32 1.09 0.14 1.21 1.00 0.14 5 Years 1.50 1.29 0.11 1.40 1.20 0.11 1.49 1.26 0.12 1.50 1.26 0.13 1.38 1.14 0.14 1.28 1.06 0.14 50 Years 1.56 1.33 0.11 1.46 1.25 0.11 1.56 1.30 0.13 1.57 1.30 0.14 1.47 1.20 0.15 1.35 1.10 0.15 75 Years 1.57 1.34 0.11 1.47 1.26 0.11 1.57 1.31 0.13 1.58 1.31 0.14 1.48 1.21 0.15 1.36 1.11 0.15 100 Years 1.57 1.35 0.11 1.48 1.27 0.11 1.57 1.32 0.13 1.59 1.32 0.14 1.49 1.22 0.15 1.36 1.12 0.15 Table 4-12 Statistical Parameters of Live Load Reactions for ADTT 2,500, λ = µ + 1.5σ ADTT 2500 Span 30 ft 60 ft 90 ft 120 ft 200 ft 300 ft µ+1.5σ µ COV µ+1.5σ µ COV µ+1.5σ µ COV µ+1.5σ µ COV µ+1.5σ µ COV µ+1.5σ µ COV 1 Day 1.18 1.00 0.12 1.02 0.88 0.10 1.07 0.90 0.12 1.04 0.89 0.11 0.93 0.78 0.13 0.79 0.66 0.13 2 Weeks 1.35 1.14 0.12 1.23 1.05 0.11 1.29 1.09 0.12 1.29 1.09 0.12 1.19 0.99 0.13 1.06 0.89 0.13 1 Month 1.38 1.17 0.12 1.26 1.08 0.11 1.35 1.14 0.12 1.34 1.13 0.12 1.23 1.02 0.14 1.12 0.93 0.14 2 Months 1.41 1.20 0.12 1.29 1.11 0.11 1.40 1.17 0.13 1.38 1.17 0.12 1.29 1.06 0.14 1.17 0.96 0.14 6 Months 1.47 1.24 0.12 1.34 1.14 0.11 1.44 1.20 0.13 1.44 1.20 0.13 1.33 1.09 0.15 1.22 1.00 0.15 1 Year 1.49 1.25 0.13 1.36 1.16 0.11 1.47 1.23 0.13 1.48 1.24 0.13 1.38 1.12 0.15 1.25 1.02 0.15 5 Years 1.55 1.29 0.13 1.44 1.21 0.12 1.55 1.29 0.13 1.54 1.28 0.13 1.43 1.17 0.15 1.31 1.08 0.15 50 Years 1.59 1.33 0.13 1.53 1.27 0.13 1.58 1.32 0.13 1.59 1.32 0.14 1.50 1.21 0.16 1.38 1.11 0.16 75 Years 1.60 1.34 0.13 1.54 1.28 0.13 1.59 1.33 0.13 1.60 1.33 0.14 1.51 1.22 0.16 1.39 1.12 0.16 100 Years 1.60 1.35 0.13 1.54 1.29 0.13 1.59 1.34 0.13 1.61 1.34 0.14 1.51 1.23 0.16 1.40 1.13 0.16 51

Table 4-13 Statistical Parameters of Live Load Reactions for ADTT 5,000,  λ = µ + 1.5σ ADTT 5000 Span 30 ft 60 ft 90 ft 120 ft 200 ft 300 ft µ+1.5σ µ COV µ+1.5σ µ COV µ+1.5σ µ COV µ+1.5σ µ COV µ+1.5σ µ COV µ+1.5σ µ COV 1 Day 1.25 1.05 0.12 1.09 0.94 0.11 1.14 0.96 0.13 1.12 0.94 0.13 1.02 0.84 0.14 0.90 0.74 0.14 2 Weeks 1.42 1.19 0.13 1.30 1.10 0.12 1.36 1.13 0.13 1.36 1.13 0.13 1.26 1.03 0.15 1.13 0.93 0.15 1 Month 1.46 1.22 0.13 1.34 1.13 0.12 1.39 1.16 0.13 1.40 1.17 0.13 1.30 1.06 0.15 1.18 0.96 0.15 2 Months 1.48 1.24 0.13 1.36 1.15 0.12 1.43 1.20 0.13 1.44 1.20 0.13 1.33 1.09 0.15 1.21 0.99 0.15 6 Months 1.51 1.27 0.13 1.39 1.18 0.12 1.47 1.23 0.13 1.48 1.24 0.13 1.39 1.13 0.15 1.27 1.03 0.15 1 Year 1.54 1.28 0.13 1.41 1.20 0.12 1.50 1.26 0.13 1.51 1.27 0.13 1.41 1.15 0.15 1.29 1.06 0.15 5 Years 1.58 1.32 0.13 1.48 1.25 0.12 1.54 1.30 0.12 1.56 1.30 0.13 1.46 1.19 0.15 1.34 1.09 0.15 50 Years 1.62 1.36 0.13 1.53 1.29 0.12 1.59 1.35 0.12 1.61 1.35 0.13 1.52 1.23 0.15 1.40 1.14 0.15 75 Years 1.63 1.37 0.12 1.54 1.30 0.12 1.60 1.36 0.12 1.62 1.36 0.13 1.53 1.24 0.15 1.41 1.15 0.15 100 Years 1.63 1.38 0.12 1.55 1.31 0.12 1.61 1.37 0.12 1.62 1.37 0.13 1.53 1.25 0.15 1.42 1.15 0.15 Table 4-14 Statistical Parameters of Live Load Reactions for ADTT 10,000, λ = µ + 1.5σ ADTT 10000 Span 30 ft 60 ft 90 ft 120 ft 200 ft 300 ft µ+1.5σ µ COV µ+1.5σ µ COV µ+1.5σ µ COV µ+1.5σ µ COV µ+1.5σ µ COV µ+1.5σ µ COV 1 Day 1.31 1.10 0.13 1.20 1.00 0.13 1.23 1.03 0.13 1.21 1.01 0.13 1.11 0.91 0.14 0.98 0.81 0.14 2 Weeks 1.45 1.21 0.13 1.35 1.12 0.13 1.40 1.17 0.13 1.41 1.18 0.13 1.31 1.07 0.15 1.19 0.97 0.15 1 Month 1.48 1.24 0.13 1.39 1.16 0.13 1.43 1.20 0.13 1.45 1.21 0.13 1.36 1.10 0.15 1.24 1.00 0.15 2 Months 1.50 1.26 0.13 1.42 1.19 0.13 1.46 1.23 0.12 1.48 1.24 0.13 1.39 1.13 0.15 1.27 1.03 0.15 6 Months 1.52 1.28 0.13 1.45 1.21 0.13 1.48 1.25 0.12 1.52 1.26 0.13 1.41 1.15 0.15 1.31 1.07 0.15 1 Year 1.55 1.29 0.13 1.46 1.22 0.13 1.51 1.28 0.12 1.54 1.28 0.13 1.44 1.17 0.15 1.33 1.08 0.15 5 Years 1.60 1.34 0.13 1.50 1.26 0.13 1.55 1.31 0.12 1.59 1.33 0.13 1.49 1.22 0.15 1.37 1.12 0.15 50 Years 1.64 1.37 0.13 1.56 1.30 0.13 1.62 1.36 0.13 1.62 1.35 0.13 1.54 1.25 0.15 1.43 1.16 0.15 75 Years 1.65 1.38 0.13 1.57 1.31 0.13 1.63 1.37 0.12 1.63 1.36 0.13 1.55 1.26 0.15 1.44 1.17 0.15 100 Years 1.66 1.39 0.13 1.57 1.32 0.13 1.63 1.38 0.12 1.64 1.37 0.13 1.55 1.27 0.15 1.45 1.18 0.15 52

Table 4-15 Statistical Parameters for Axle Loads, λ = µ + 1.5σ Time period ADTT=250 ADTT=1000 ADTT=2500 ADTT=5000 ADTT=10 000 λ COV [%] λ COV [%] λ COV [%] λ COV [%] λ COV [%] 1 day 0.91 0.17 1.00 0.17 1.07 0.16 1.11 0.16 1.15 0.16 2 weeks 1.09 0.16 1.17 0.16 1.24 0.15 1.29 0.15 1.32 0.15 1 month 1.14 0.16 1.23 0.15 1.28 0.15 1.32 0.14 1.36 0.14 2 months 1.18 0.15 1.27 0.15 1.32 0.14 1.36 0.14 1.38 0.14 6 months 1.24 0.15 1.32 0.14 1.37 0.14 1.40 0.14 1.42 0.13 1 year 1.30 0.14 1.37 0.14 1.41 0.13 1.42 0.13 1.45 0.13 5 years 1.38 0.14 1.43 0.13 1.46 0.13 1.47 0.13 1.49 0.13 50 years 1.45 0.13 1.48 0.13 1.50 0.13 1.51 0.13 1.53 0.12 75 years 1.45 0.13 1.48 0.12 1.50 0.12 1.51 0.12 1.53 0.12 100 years 1.46 0.13 1.49 0.12 1.51 0.12 1.52 0.12 1.53 0.12 53

4.4 Development of Statistical Parameters of Fatigue Load 4.4.1 Objective Fatigue is one of the major causes of distress in steel highway bridges. Cracking or rupture of components and connections calls for costly repairs or replacements. The durability of affected structures can be enhanced by applying reliability theory to this limit state. The limit state of fatigue is reached when accumulated load spectra exceed the fatigue resistance of material. Therefore, a rational approach to evaluation of existing bridges and design for new bridges requires the knowledge of the load carrying capacity and accumulated loads as shown on Figure 4-25. A considerable effort was directed toward tests of materials under cyclic loading, to establish the so called S-N curves, where S is the applied stress and N is number of load applications to failure. However knowledge about the real fatigue stress caused by the current truck traffic was limited and outdated, based on research done in the 1980's. Figure 4-25 Fatigue Failure on S-N Curve. The current AASHTO LRFD (2012) has two different Fatigue Limit States. Fatigue Limit State I is related to infinite load-induced fatigue life. The fatigue load in this limit state reflects the load levels found to be representative of the maximum stress range of the truck population for infinite fatigue-life design. Fatigue Limit State II is related to finite load-induced fatigue life. The fatigue load in this limit state is intended to reflect a load level found to be representative of the effective stress range of the truck population with respect to the induced number of load cycles and their cumulative damage effects on the bridge components. Only Fatigue I applies to fatigue of concrete and the considered types of reinforcement. The focus of this section is to develop statistical models of fatigue load based on the WIM truck survey data. The fatigue load is intended to be used in calibration of the design provisions in the AASHTO LRFD (2012). The WIM measurements provide an unbiased data set. The 15 WIM sites provided by the Federal Highway Administration are considered as representative for the United States for this analysis. Only sites with one full year of constant reading were used for fatigue analysis. 54

Three cases are considered: mid-span moment for a simply supported bridge, moment at the interior support of a two span continuous bridge and moment at 0.4 span of a continuous bridge. The surveyed vehicles were run over influence lines as traffic streams to determine the number and magnitude of moment cycles for a wide range of span lengths for each case. The fatigue load time history was then developed for the bending moment as shown in Kulicki et. al (2013). The Fatigue II (finite life) load was calculated as an equivalent moment using the linear damage rule first proposed by A. Palmgren (1924) and later popularized by Miner (1945) as the Palmgren-Miner rule. The Fatigue I (infinite life) load for each location was determined by finding the highest 0.01% of the load cycles and using the smallest of them as the fatigue load for the considered location. The obtained results combined with fatigue resistance models served as the basis for the development of calibrated criteria for service limit state in AASHTO LRFD. 4.4.2 WIM Data Used for Fatigue Calculation To be consistent with previous research done by Fisher (1977), in addition to filters used for live load, filter 3 was used to remove light trucks with GVW under 20 kips because light vehicles cause relatively low fatigue damage. A summary of the data used for fatigue analysis including WIM locations, number of records and ADTT is shown in Table 4-16. Table 4-16 WIM Locations and Number of Vehicles Used for Fatigue Analysis Site Number of Days in Data Total Number of Truck Records, N Lane ADTT AZ SPS-1 365 26,501 97 AZ SPS-2 365 1,391,098 3919 AR SPS-2 365 1,642,334 4590 CO SPS-2 365 326,017 941 DE SPS-1 365 175,889 553 IL SPS-6 365 821,809 2340 KS SPS-2 365 456,881 1309 LA SPS-1 365 70,831 235 ME SPS-5 365 172,333 503 MD SPS-5 365 124,474 450 MN SPS-5 365 47,794 152 PA SPS-6 365 1,458,818 4098 TN SPS-6 365 1,583,151 4445 VA SPS-1 365 237,804 710 WI SPS-1 365 209,239 622 55

4.4.3 Fatigue Limit State II – Finite Fatigue Life Live load on bridges is caused mainly by moving trucks. As a truck moves across a bridge, the stress at any point varies. Determining the accumulated fatigue damage due to traffic loads involves the conversion of the live load effects to an equivalent constant stress amplitude and an associated number of cycles. This is done using the rain flow method and the Palmgren-Miner's formula for equivalent load. This process is used to determine the accumulated fatigue damage and how it compares to the fatigue damage observed in similar details during laboratory testing. Based on the comparison, the remaining fatigue life of a certain detail can be determined. The development of the design load for the Fatigue Limit State II is documented in Kulicki et. al. (2013) (SHRP R19B Report). For concrete and reinforcement fatigue, Fatigue Limit State II is not used. 4.4.4 Fatigue Limit State I – The Maximum Moment Range Ratio Fatigue limit state I is related to an infinite load-induced fatigue life. The fatigue load in this limit state reflects the load levels found to be representative of the maximum stress range of the truck population for an infinite fatigue-life design (AASHTO LRFD, 2012). In other words, if the majority of stress cycles is below a threshold magnitude, ( )THF∆ , failure will require so many load cycles that the considered detail will have an infinite fatigue life. The threshold stress, ( )THF∆ , is a boundary between the finite and infinite fatigue life, as shown in Figure 4-26. Figure 4-26 The Threshold Stress ( )THF∆ on S-N Curve. Fatigue limit state I refers to the stress value that has 1/10,000 probability of being exceeded. It is assumed that the distribution of stress has the same shape of the CDF as that of the corresponding moments. Therefore, the fatigue load analysis is performed using the developed CDFs for moments for various considered sites, cases and spans from 30 to 200 ft. The moment corresponding to the upper 0.01% is determined as a percentile corresponding to the probability of 0.9999 or 3.8 on the vertical axis in Figure 4-27. This moment represents the maximum stress range corresponding to an unlimited fatigue life. For example, for the WIM data from Arkansas (SPS-1) the moment for span of 120 ft corresponding to the upper 0.01% is 2505.5 k- ft, as shown in Figure 4-27. 56

Figure 4-27 Moment Corresponding to the Upper 0.01%, Span = 120 ft. The calculations were performed for the considered locations, cases and span lengths. The obtained values of moment were divided by the corresponding AASHTO fatigue truck moment. The results are summarized in Table 4-17 through Table 4-19. 57

Table 4-17 The Maximum Moment Range for Simply Supported Bridges at the Mid-Span Simple Support - mid-span # of Vehicles "1/10000 Moment Cycle" "1/10000 Moment" / HS20 Fatigue Moment 30 60 90 120 200 30 60 90 120 200 Arizona (SPS-1) 26501 424 1003 1761 2754 5640 1.74 1.84 1.63 1.70 1.84 Arizona (SPS-2) 1391098 308 765 1416 2246 4711 1.26 1.41 1.31 1.38 1.54 Arkansas (SPS-2) 1642334 352 860 1526 2460 5066 1.44 1.58 1.41 1.52 1.65 Colorado (SPS-2) 326017 336 814 1497 2409 4854 1.38 1.50 1.38 1.48 1.58 Delaware (SPS-1) 175889 454 1257 2302 3212 5735 1.86 2.31 2.12 1.98 1.87 Illinois (SPS-6) 821809 350 844 1480 2408 5033 1.43 1.55 1.37 1.48 1.64 Kansas (SPS-2) 456881 411 1018 1989 3112 6083 1.69 1.87 1.84 1.92 1.99 Louisiana (SPS-1) 70831 460 1237 2126 3332 6616 1.89 2.27 1.96 2.05 2.16 Maine (SPS-5) 172333 397 964 1722 2726 5549 1.63 1.77 1.59 1.68 1.81 Maryland (SPS-5) 124474 412 1038 1802 2599 5061 1.69 1.91 1.66 1.60 1.65 Minnesota (SPS-5) 47794 392 1111 2220 3316 6225 1.61 2.04 2.05 2.04 2.03 Pennsylvania(SPS-6) 1458818 402 1003 1730 2623 5291 1.65 1.84 1.60 1.62 1.73 Tennessee (SPS-6) 1583151 419 1020 1652 2387 4906 1.72 1.88 1.52 1.47 1.60 Virginia (SPS-1) 237804 369 946 1709 2562 5055 1.51 1.74 1.58 1.58 1.65 Wisconsin (SPS-1) 209239 393 968 1712 2717 5396 1.61 1.78 1.58 1.67 1.76 58

Table 4-18 The Maximum Moment Range for Continuous Bridges at the Middle Support Continuous - Middle Support # of Vehicles "1/10000 Moment Cycle" "1/10000 Moment" / HS20 Fatigue Moment 30 60 90 120 200 30 60 90 120 200 Arizona (SPS-1) 26501 -266 -701 -1026 -1608 -3089 1.45 1.95 1.94 2.11 2.30 Arizona (SPS-2) 1391098 -211 -549 -968 -1526 -3019 1.15 1.52 1.83 2.00 2.25 Arkansas (SPS-2) 1642334 -213 -643 -995 -1522 -3187 1.16 1.78 1.88 2.00 2.38 Colorado (SPS-2) 326017 -231 -579 -877 -1312 -2813 1.25 1.61 1.66 1.72 2.10 Delaware (SPS-1) 175889 -248 -650 -1173 -1643 -3303 1.35 1.80 2.21 2.16 2.46 Illinois (SPS-6) 821809 -207 -640 -1005 -1506 -3093 1.13 1.78 1.90 1.98 2.31 Kansas (SPS-2) 456881 -294 -755 -1015 -1469 -2937 1.60 2.10 1.92 1.93 2.19 Louisiana (SPS-1) 70831 -278 -815 -1128 -1539 -3255 1.51 2.26 2.13 2.02 2.43 Maine (SPS-5) 172333 -251 -694 -970 -1418 -2967 1.37 1.93 1.83 1.86 2.21 Maryland (SPS-5) 124474 -240 -592 -1049 -1564 -3281 1.31 1.64 1.98 2.05 2.45 Minnesota (SPS-5) 47794 -292 -695 -1034 -1487 -2753 1.59 1.93 1.95 1.95 2.05 Pennsylvania(SPS-6) 1458818 -245 -638 -1067 -1588 -3131 1.33 1.77 2.01 2.09 2.33 Tennessee (SPS-6) 1583151 -222 -628 -1025 -1559 -2977 1.21 1.74 1.93 2.05 2.22 Virginia (SPS-1) 237804 -223 -603 -973 -1477 -3010 1.21 1.67 1.84 1.94 2.24 Wisconsin (SPS-1) 209239 -250 -671 -953 -1394 -2892 1.36 1.86 1.80 1.83 2.16 59

Table 4-19 The Maximum Moment Range for Continuous Bridges at 0.4 of the Span Length Continuous - 0.4L # of Vehicles "1/10000 Moment Cycle" "1/10000 Moment" / HS20 Fatigue Moment 30 60 90 120 200 30 60 90 120 200 Arizona (SPS-1) 26501 399 976 1764 2769 5542 1.62 1.67 1.61 1.71 1.83 Arizona (SPS-2) 1391098 293 761 1431 2228 4636 1.19 1.30 1.30 1.37 1.53 Arkansas (SPS-2) 1642334 338 849 1527 2416 4914 1.37 1.45 1.39 1.49 1.62 Colorado (SPS-2) 326017 319 805 1528 2428 4857 1.30 1.38 1.39 1.50 1.60 Delaware (SPS-1) 175889 439 1279 2243 3141 5635 1.78 2.19 2.04 1.94 1.86 Illinois (SPS-6) 821809 334 814 1508 2399 4893 1.36 1.39 1.37 1.48 1.61 Kansas (SPS-2) 456881 394 1049 1983 3088 5988 1.60 1.79 1.81 1.90 1.98 Louisiana (SPS-1) 70831 458 1126 2174 3349 6486 1.86 1.92 1.98 2.06 2.14 Maine (SPS-5) 172333 377 937 1811 2768 5525 1.53 1.60 1.65 1.71 1.82 Maryland (SPS-5) 124474 406 1036 1817 2618 4941 1.65 1.77 1.65 1.61 1.63 Minnesota (SPS-5) 47794 382 1142 2134 3223 6065 1.55 1.95 1.94 1.99 2.00 Pennsylvania(SPS-6) 1458818 395 1020 1726 2608 5243 1.61 1.74 1.57 1.61 1.73 Tennessee (SPS-6) 1583151 416 1012 1636 2379 4868 1.69 1.73 1.49 1.47 1.61 Virginia (SPS-1) 237804 356 955 1704 2509 4947 1.45 1.63 1.55 1.55 1.63 Wisconsin (SPS-1) 209239 375 958 1705 2662 5326 1.53 1.64 1.55 1.64 1.76 60

4.4.5 Statistical Parameters of Fatigue Live Load The objective was to determine the statistical parameters of fatigue load for the Fatigue I limit state (LS) that can be considered as representative for a national load. The ratios of "1/10000 Moment" to “HL-93 Fatigue Moment” were plotted on normal probability paper in Figure 4-28 through Figure 4-30. Each point on the graphs represents one of 15 sites considered. Figure 4-28 The Maximum Moment Range Ratio (Fatigue LS I) for Simple Supported Bridges at the Mid-Span. Figure 4-29 The Maximum Moment Range Ratio (Fatigue LS I) for Continuous Bridges at the Middle Support. 61

Figure 4-30 The Maximum Moment Range Ratio (Fatigue LS I) for Continuous Bridges at 0.4 of the Span Length. To determine the statistical parameters from the graphs, a straight line was fitted for each distribution. A straight line corresponds to the normal distribution on the normal probability paper. The intersection of the straight line with the horizontal axis is at the mean value. The standard deviation is determined from the slope of the straight line. The statistical parameters of fatigue load based on 15 considered sites, i.e. mean, µ, and COV, calculated as the ratio of standard deviation, σ to the mean, µ, are listed in Table 4-20. It is assumed that the considered 15 WIM locations are representative for truck traffic in the United States. For the purpose of further reliability analysis, it is recommended to assume that the mean fatigue load is equal to the mean for 15 WIM locations plus 1.5 standard deviations, 1.5 σ. The probability of exceeding this value is about 5%; 95% of sites in the United States are below this value as is shown on Figure 4-31. The moment ratios corresponding to the mean plus 1.5 standard deviations for Fatigue I limit state are also listed in Table 4-20. 62

Figure 4-31 Probability Density Function of the National Fatigue Load. The statistical parameters were calculated for all considered cases and span length. Table 4-20 The Maximum Moment Range Ratio for Fatigue I LS The Maximum Moment Range Ratio for Fatigue I LS Span Mean Mean+1.5 σ COV Simple Supported Mid-span 30 ft 1.6 1.90 0.13 60 ft 1.83 2.24 0.15 90 ft 1.6 1.96 0.15 120 ft 1.64 1.88 0.10 200 ft 1.7 2.15 0.18 Continuous Middle Support 30 ft 1.35 1.61 0.13 60 ft 1.81 2.13 0.12 90 ft 1.92 2.18 0.09 120 ft 1.97 2.17 0.07 200 ft 2.27 2.47 0.06 Continuous 0.4 L 30 ft 1.54 1.86 0.14 60 ft 1.67 2.06 0.16 90 ft 1.6 1.92 0.13 120 ft 1.65 1.97 0.13 200 ft 1.72 2.11 0.15 The values at the middle support are expected to be lower than shown in Table 4-20 due to fanning of the reaction force through the height of the beams and because the actual support is not a knife edge support. This was taken into account when recommending a revised load factor for Fatigue I limit state. 4.4.6 Recommendations The analysis resulted in the relatively tightly clustered moment range ratios shown in Table 4-20 for the Fatigue I limit state. As with previous live load recommendations herein, the values to be considered for calibration are the moment ratios at the “mean plus 1.5 standard deviations” and the COVs. Therefore, for simplicity, the recommended values for the calibration of the fatigue limit states are further simplified into single values independent of span length. For Fatigue I limit state, it is recommended to use stress ranges (loads) based on 2.0 HL-93 and a COV=0.12. 63

The calibration of the fatigue limit state for concrete and reinforcement is detailed in Chapter 5. 4.5 Development of Overload and Permit Load Parameters 4.5.1 Based on WIM Data 4.5.1.1 Load Model Heavy vehicles in the WIM data are assumed to be either permit vehicles or illegally overloaded vehicles. WIM data was used as the basis for estimating how often a given design moment (or shear) is exceeded. Table 4-21 shows the number of times the live load moment exceeded 100% of HL-93, 110% of HL-93, 120% of HL-93 and 130% of HL-93 for 32 WIM sites. One of the sites clearly has a unique traffic pattern – Florida Route 29. The Florida Department of Transportation was contacted about this site and it was determined that truck traffic from several other highways were being directed onto this road and that undoubtedly accounted for the relatively large number of times the HL-93 was exceeded for the various percents indicated. Additionally, the total number of times the various ratios of HL-93 were exceeded, excluding Florida Route 29, are shown in the table, as well as the average number per site. Notice that data was collected for most, but not all, sites for a full year. The data was scaled to one year and the scaled data is shown in Table 4-22. The average rate of exceedance in Table 4-23 is higher than Table 4-22 because the data was collected for less than one year at a number of sites. These sites are those showing increased number incidents in Table 4-23 than in Table 4-22. Figure 4-32 shows the average accumulative rate of exceedance for the 31 remaining WIM sites by HL-93 ratio for each span length considered. Figure 4-33 shows the same information by span for each HL-93 ratio considered. The reduction in the rate of exceedance with increasing HL-93 ratio is clear. 64

Table 4-21 Number of Times WIM Moments Exceeded a Factored HL-93 Loadings MOMENT Ratio Truck/HL-93 >= 1.1 Ratio Truck/HL-93 >= 1.2 Ratio Truck/HL-93 >= 1.3 Site 30 ft 60 ft 90 ft 120 ft 200 ft 30 ft 60 ft 90 ft 120 ft 200 ft 30 ft 60 ft 90 ft 120 ft 200 ft AZ SPS-1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 AZ SPS-2 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 AR SPS-2 2 7 3 0 0 0 3 0 0 0 0 0 0 0 0 CO SPS-2 0 2 5 4 0 0 0 2 0 0 0 0 0 0 0 DE SPS-1 36 33 22 11 0 10 22 10 1 0 1 11 1 0 0 IL SPS-6 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 IN SPS-6 3 11 11 10 2 2 4 5 4 0 0 0 1 0 0 KS SPS-2 16 33 35 31 2 7 16 17 7 0 6 7 6 0 0 LA SPS-1 44 6 12 14 7 26 6 7 7 0 6 6 5 4 0 ME SPS-5 4 4 5 2 0 0 4 2 0 0 0 2 0 0 0 MD SPS-5 5 6 2 2 0 0 1 1 0 0 0 1 0 0 0 MN SPS-5 7 5 6 5 0 4 2 2 1 0 2 1 1 0 0 NM SPS-1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 NM SPS-5 3 1 1 2 0 2 0 0 0 0 0 0 0 0 0 PA SPS-6 32 22 17 14 1 13 17 13 1 0 3 13 2 0 0 TN SPS-6 53 4 4 0 0 5 1 0 0 0 1 0 0 0 0 VA SPS- 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 WI SPS-1 1 0 3 3 1 0 0 1 1 0 0 0 0 0 0 CA Antelope EB 0 1 0 0 5 0 0 0 0 0 0 0 0 0 0 CA Antelope WB 0 5 4 13 28 0 0 0 1 9 0 0 0 0 1 CA Bowman 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 CA LA-710 NB 1 31 50 51 15 0 6 24 19 0 0 0 4 1 0 CA LA-710 SB 1 17 45 48 14 0 3 18 19 0 0 0 1 1 0 CA Lodi 0 4 16 46 140 0 0 1 2 32 0 0 0 0 2 FL I-10 79 40 46 75 37 22 16 14 17 5 10 5 4 5 2 FL I-95 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 FL US-29 653 495 322 245 106 360 266 174 119 51 177 160 82 59 21 MS I-10 24 22 31 33 22 7 2 10 19 2 2 2 2 2 1 MS I-55UI 0 0 0 1 2 0 0 0 0 0 0 0 0 0 0 MS I-55R 19 30 48 58 32 7 8 16 21 19 2 3 5 8 9 MS US-49 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 MS US-61 0 0 1 2 1 0 0 1 1 0 0 0 0 0 0 Ratio Truck/HL-93 >= 1.1 Ratio Truck/HL-93 >= 1.2 Ratio Truck/HL-93 >= 1.3 30 ft 60 ft 90 ft 120 ft 200 ft 30 ft 60 ft 90 ft 120 ft 200 ft 30 ft 60 ft 90 ft 120 ft 200 ft Total W/O FL 29 331 285 373 430 310 105 111 144 121 68 33 51 32 21 15 Average per site 10.7 9.2 12.0 13.9 10.0 3.4 3.6 4.6 3.9 2.2 1.1 1.6 1.0 0.7 0.5 65

Table 4-22 Exceedances Per Year Site MOMENT – Exceedances Per Year Ratio Truck/HL-93 >= 1.0 Ratio Truck/HL-93 >= 1.1 Ratio Truck/HL-93 >= 1.2 Ratio Truck/HL-93 >= 1.3 30 ft 60 ft 90 ft 120 ft 200 ft 30 ft 60 ft 90 ft 120 ft 200 ft 30 ft 60 ft 90 ft 120 ft 200 ft 30 ft 60 ft 90 ft 120 ft 200 ft AZ SPS-1 4 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 AS SPS-2 0 2 6 5 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 AR SPS-2 14 10 17 10 0 2 7 3 0 0 0 3 0 0 0 0 0 0 0 0 CO SPS-2 0 5 6 6 2 0 2 5 4 0 0 0 2 0 0 0 0 0 0 0 DE SPS-1 140 48 33 27 1 36 33 22 11 0 10 22 10 1 0 1 11 1 0 0 IL SPS-6 1 3 4 4 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 IN SPS-6 27 32 24 19 14 5 19 19 17 3 3 7 9 7 0 0 0 2 0 0 KS SPS-2 42 47 80 96 10 16 33 35 31 2 7 16 17 7 0 6 7 6 0 0 LA SPS-1 76 16 25 30 13 44 6 12 14 7 26 6 7 7 0 6 6 5 4 0 ME SPS-5 6 7 8 7 1 4 4 5 2 0 0 4 2 0 0 0 2 0 0 0 MD SPS-5 25 8 8 2 1 5 6 2 2 0 0 1 1 0 0 0 1 0 0 0 MN SPS-5 9 8 18 19 2 7 5 6 5 0 4 2 2 1 0 2 1 1 0 0 NM SPS-1 1 1 1 3 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 NM SPS-5 12 7 7 9 4 4 1 1 3 0 3 0 0 0 0 0 0 0 0 0 PA SPS-6 155 45 22 21 1 32 22 17 14 1 13 17 13 1 0 3 13 2 0 0 TN SPS-6 2085 29 8 7 0 53 4 4 0 0 5 1 0 0 0 1 0 0 0 0 VA SPS-1 7 10 1 2 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 WI SPS-1 6 3 5 4 2 1 0 3 3 1 0 0 1 1 0 0 0 0 0 0 CA Antelope EB 0 13 25 31 25 0 1 0 0 7 0 0 0 0 0 0 0 0 0 0 CA Antelope WB 0 30 71 100 84 0 7 6 19 40 0 0 0 1 13 0 0 0 0 1 CA Bowman 0 3 3 8 16 0 0 0 3 3 0 0 0 0 3 0 0 0 0 0 CA LA-710 NB 10 99 150 153 85 1 34 55 56 16 0 7 26 21 0 0 0 4 1 0 CA LA-710 SB 3 62 105 111 54 1 17 45 48 14 0 3 18 19 0 0 0 1 1 0 CA Lodi 0 110 137 281 417 0 5 19 55 168 0 0 1 2 38 0 0 0 0 2 FL I-10 279 141 159 264 152 81 41 47 77 38 23 16 14 18 5 10 5 4 5 2 FL I-95 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 MS I-10 41 48 53 53 44 26 24 34 36 24 8 2 11 21 2 2 2 2 2 1 MS I-55UI 0 4 5 11 8 0 0 0 1 3 0 0 0 0 0 0 0 0 0 0 MS I-55R 142 100 255 349 89 20 31 50 61 33 7 8 17 22 20 2 3 5 8 9 MS US-49 0 3 11 13 7 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 MS US-61 0 1 5 8 6 0 0 1 2 1 0 0 1 1 0 0 0 0 0 0 FL US-29 1291 995 651 496 204 673 510 332 253 109 371 274 179 123 53 183 165 85 61 22 Annual Average 99.6 28.9 40.4 53.4 33.6 11.0 9.8 12.8 15.1 11.7 3.5 3.7 4.9 4.2 2.6 1.1 1.7 1.1 0.7 0.5 66

Figure 4-32 Annual Average Exceedances Versus Span. Figure 4-33 Annual Average Exceedances Versus Ratio Truck/HL-93. A more meaningful assessment of the exceedance rate is presented in Table 4-23 and Figure 4-34 and Figure 4-35. In this case, the exceedance data has been scaled for a number of vehicles based on a single lane ADTT of 2500 at each site assuming that the distribution of trucks is the same, i.e. the data is scalable. The average rate of exceedance in Table 4-23 is higher than Table 4-22 because many of the WIM sites were on roads with single lane ADTTs less than 2500. Nevertheless, the rate at which 1.3 HL-93 is exceeded is quite low. The values in Table 4-23 can be scaled for locations with a single lane ADTT other than 2500 with the same assumption of scalability. 0 20 40 60 80 100 120 30 ft 60 ft 90 ft 120 ft 200 ft An nu al A ve ra ge Span (ft.) > 1.0HL93 > 1.1HL93 > 1.2HL93 > 1.3HL93 0 20 40 60 80 100 120 > 1.0HL93 > 1.1HL93 > 1.2HL93 > 1.3HL93 An nu al A ve ra ge Ratio Truck/HL93 30 ft 60 ft 90 ft 120 ft 200 ft 67

Table 4-23 Events Per Year Scaled to ADTT = 2500 Site MOMENT – Events Per Year Scaled to ADTT = 2500 Ratio Truck/HL-93 >= 1.0 Ratio Truck/HL-93 >= 1.1 Ratio Truck/HL-93 >= 1.2 Ratio Truck/HL-93 >= 1.3 30 ft 60 ft 90 ft 120 ft 200 ft 30 ft 60 ft 90 ft 120 ft 200 ft 30 ft 60 ft 90 ft 120 ft 200 ft 30 ft 60 ft 90 ft 120 ft 200 ft AZ SPS-1 103 0 0 26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 AS SPS-2 0 1 4 3 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 AR SPS-2 8 5 9 5 0 1 4 2 0 0 0 2 0 0 0 0 0 0 0 0 CO SPS-2 0 13 16 16 5 0 5 13 11 0 0 0 5 0 0 0 0 0 0 0 DE SPS-1 633 217 149 122 5 163 149 100 50 0 45 100 45 5 0 5 50 5 0 0 IL SPS-6 1 3 4 4 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 IN SPS-6 79 94 69 54 39 15 54 54 49 10 10 20 25 20 0 0 0 5 0 0 KS SPS-2 80 90 153 183 19 31 63 67 59 4 13 31 32 13 0 11 13 11 0 0 LA SPS-1 808 170 266 319 138 468 64 128 149 74 277 64 74 74 0 64 64 53 43 0 ME SPS-5 30 35 40 35 5 20 20 25 10 0 0 20 10 0 0 0 10 0 0 0 MD SPS-5 139 44 44 11 6 28 33 11 11 0 0 6 6 0 0 0 6 0 0 0 MN SPS-5 148 131 296 312 33 115 82 99 82 0 66 33 33 16 0 33 16 16 0 0 NM SPS-1 8 8 8 16 0 0 8 8 8 0 0 0 0 0 0 0 0 0 0 0 NM SPS-5 45 / / * 8 8 2 2 3 0 3 0 0 0 0 0 0 0 0 0 PA SPS-6 95 27 13 13 1 20 13 10 9 1 8 10 8 1 0 2 8 1 0 0 TN SPS-6 1173 16 4 4 0 30 2 2 0 0 3 1 0 0 0 1 0 0 0 0 VA SPS-1 25 35 4 7 4 0 0 4 4 0 0 0 0 0 0 0 0 0 0 0 WI SPS-1 24 12 20 16 8 4 0 12 12 4 0 0 4 4 0 0 0 0 0 0 CA Antelope EB 0 10 20 24 20 0 1 0 0 5 0 0 0 0 0 0 0 0 0 0 CA Antelope WB 0 20 48 68 57 0 5 4 13 27 0 0 0 1 9 0 0 0 0 1 CA Bowman 0 1 1 4 8 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 CA LA-710 NB 2 20 31 31 17 0 7 11 11 3 0 1 5 4 0 0 0 1 0 0 CA LA-710 SB 1 12 21 22 11 0 3 9 9 3 0 1 4 4 0 0 0 0 0 0 CA Lodi 0 25 32 65 96 0 1 4 13 39 0 0 0 1 9 0 0 0 0 1 FL I-10 151 76 86 142 82 44 22 26 42 21 12 9 8 9 3 6 3 2 3 1 FL I-95 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 MS I-10 0 2 3 6 4 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 MS I-55UI 0 2 3 6 4 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 MS I-55R 93 66 167 229 58 13 21 33 40 22 5 5 11 14 13 1 2 3 5 6 MS US-49 0 2 8 10 5 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 MS US-61 0 6 23 40 29 0 0 6 11 6 0 0 6 6 0 0 0 0 0 0 FL US-29 2922 2252 1473 1122 462 1524 1155 751 572 247 840 621 406 278 119 413 373 191 138 49 Annual Average 117.0 37.8 50.6 58.7 21.7 32.0 18.4 20.8 19.8 7.5 14.3 9.7 9.1 5.8 1.2 4.0 5.6 3.2 1.7 0.3 68

Figure 4-34 Annual Average Events Scaled to ADTT = 2500 Versus Span. Figure 4-35 Annual Average Events Scaled to ADTT = 2500 Versus Ratio Truck/HL-93. The issue of number of loaded lanes was discussed in Section 4.2.4. For the WIM sites where data was recorded in two lanes, and given the definition of correlated events in that discussion, it was shown that the number of events of multiple lanes loaded with correlated trucks was quite small, and the histograms of GVW showed that the number of events of two heavy trucks was even smaller. It was concluded that multiple lanes of heavy trucks need not be considered for the service limit states. Thus it is concluded that in most cases design for multiple lanes of overload is not necessary. Furthermore, no MPF needs to be applied on the load side of the limit state function when calibrating for overloads. 0 20 40 60 80 100 120 30 ft 60 ft 90 ft 120 ft 200 ft An nu al A ve ra ge Span (ft.) > 1.0HL93 > 1.1HL93 > 1.2HL93 > 1.3HL93 0 20 40 60 80 100 120 > 1.0HL93 > 1.1HL93 > 1.2HL93 > 1.3HL93 An nu al A ve ra ge Ratio Truck/HL93 30 ft 60 ft 90 ft 120 ft 200 ft 69

To summarize, based on a review of the WIM data: • Site-specific consideration of sites with unusually high volumes of heavy trucks is warranted • Design for a single lane loading is justified by this study • Elimination of the single lane MPF of 1.20 when investigating service limit states under overload vehicles is justified by this study 4.5.2 Based on Louisiana Permit Load Citations Louisiana DOTD provided a compilation of truck citations issued in the state in 2009. Due to missing needed information, the data was not sufficient for calibration. Nevertheless, the data was analyzed to provide insight into the nature of permit vehicles. The data includes information about the vehicle class according to the Louisiana Regulations for Trucks, actual and permitted GVW, number of axle sets, number of axles for each axle set, axle set scale weight and axle set legal weight. Vehicles classified as Type 9999 are considered to be permit vehicles. It was observed that most of the violations were due to incorrect load distribution resulting in violation of the allowable axle set weight rather than exceeding of the gross vehicle weight. The data did not include the weight of individual axles or axle spacing. This limited the value of the data to investigating the statistical parameters of the vehicle GVW and precluded determining the statistical parameters of the load effects by running the trucks across spans of different length. It is also important to note that while the vehicles stopped represent a sample of the entire population of legal and permit vehicles; the vehicles in the database only represent those that were cited. The original data included 50,257 records. A number of records were eliminated from the set as they included no axle set loads (1456) or included obvious errors, e.g. two records included axle loads below 100 pounds. The remaining number of records was 48,799. These records included both permit and legal loads. Out of these, 869 records were designated as Type 9999 which indicates they were permit vehicles. Each vehicle had two different permitted GVWs listed; one for interstate highways and one for non-interstate routes. For all vehicles, the non-interstate GVW was equal to or higher than the interstate GVW. The permitted individual axle set weight was the same for both the interstate and non-interstate roads. For many trucks, the sum of the permitted individual axle weights exceeded the permitted GVW which indicated that when the truck reaches its permitted GVW, some axle sets will have to be lower than their permitted weight. Table 4-24 gives a statistics of the violations when all permit vehicles are considered (869 records). 70

Table 4-25 shows the statistics when only permit vehicles with a legal load above 80,000 lbs are considered (680 records). As the data did not classify the type of road, the analyses were performed once assuming all vehicles were on interstate roads and then were repeated assuming all vehicles were on non-interstate roads. When all records are considered: • About 39.9% and 40.7% of the citations considering interstate and non-interstate roads, respectively, were for reasons other than GVW or axle group weights. No reason was given for non-load-related citations but it is assumed that the citations are related to the geometric characteristics of the trucks including axle spacing and tire width. • The GVW exceeded the permitted in 31.1% and 30.0% of the records for interstate and non-interstate roads, respectively • For both interstate and non-interstate roads, one or more axle group exceeded the permitted axle group weight in 46.4% of the records, while the GVW was not exceeded • About 13.7% and 12.9% of the citations considering interstate and non-interstate roads, respectively, indicated the permitted GVW was exceeded while none of the permitted axle group weights were exceeded Table 4-24 Statistics of Cited Vehicles When All Permit Vehicles are Considered Total Number of Records No of violators (Interstate) No of violators (Non-Interstate) No of violations not related to axle group weight or GVW 869 347 354 Steering axle (axle set 1)(*) 869 85 85 Axle set 2 (*) 864 233 233 Axle set 3 (*) 816 183 183 Axle set 4 (*) 168 33 33 Axle set 5 (*) 54 7 7 GVW exceeding permitted 869 270 261 GVW exceeding permitted with no axle group exceeding permitted 869 119 112 One or more axle group exceeding permitted with GVW exceeding permitted 869 151 149 Vehicles with one or more axle groups exceeding permitted 869 403 403 Vehicles with one or more axle groups exceeding permitted with GVW less than permitted 869 252 254 Axle groups exceeding permitted 2771 axle groups 541 541 (*) Number of axle groups in each record varied from 1 to 5. Five records represented one-axle- group dollies. These records showed one axle group instead of a steering axle. 71

Table 4-25 Statistics of Cited Permit Vehicles When Only Vehicles with GVW Greater Than 80,000 lbs are Considered Interstate Non-Interstate Total Number of Records No of violators Total Number of Records No of violators Steering axle (axle set 1) 680 78 681 78 Axle set 2 (*) 676 180 677 180 Axle set 3 (*) 640 165 641 165 Axle set 4 (*) 141 31 142 31 Axle set 5 (*) 49 7 49 7 GVW exceeding permitted 680 162 681 154 GVW exceeding permitted with no axle group exceeding permitted 680 42 681 36 One or more axle group exceeding permitted with GVW exceeding permitted 680 120 681 118 Vehicles with one or more axle groups exceeding permitted 680 336 681 336 Vehicles with one or more axle groups exceeding permitted with GVW less than permitted 680 216 681 218 Axle groups exceeding permitted 2186 axle groups 461 2190 axle groups 461 (*) Number of axle groups in each record varied from 1 to 5. Four records represented one- axle-group dollies. These records showed that the vehicle contain one axle group instead of listing a steering axle followed by other axle groups. When only records with permitted GVW greater than 80,000 lbs are considered: • About 44.4% and 45.4% of the citations considering interstate and non-interstate roads, respectively, were for reasons other than GVW or axle group weights. • The GVW exceeded the permitted in 23.8% and 22.6 of the records for interstate and non-interstate roads, respectively • One or more axle group exceeded the permitted axle group weight 31.7% and 32.0% of the records for interstate and non-interstate roads, respectively, while the GVW was not exceeded • The permitted GVW was exceeded while none of the permitted axle group weights were exceeded in 6.2% and 5.3% of the records for interstate and non-interstate roads, respectively Comparing the results for all the records to those for records of vehicles with permitted GVW greater than 80,000 lbs indicates that the latter are slightly more likely to be cited for reasons other than weight-related issues. In other words, heavier vehicles are less likely to violate the permitted axle group weights and GVW. The gross vehicle weight (GVW) of Louisiana permit trucks (Type 9999) from citation data was plotted on normal probability paper. For comparison, the CDF’s of the GVW of the vehicles in the WIM data from Louisiana (LA SPS-1) and GVW of the permit vehicles were 72

plotted in Figure 4-36. The shape of CDF of permit vehicles is similar to the upper tail of the WIM data from Louisiana; the part representing heavier vehicles. Ratio of axle set scale weight and allowable axle set weight for axle sets with different number of axles was calculated and plotted on the normal probability paper as shown on Figure 4-37. Ratio of GVW and allowable GVW for all permit vehicles was calculated and plotted on the normal probability paper as shown on Figure 4-38. The relationship between GVW and the ratio of GVW and allowable GVW is shown in Figure 4-39. The Louisiana violation data did not include any information about the axle spacing, therefore, the load effect (moment or shear) due to a permit truck passage cannot be calculated. However, Laman and Nowak (Laman 1993) observed that the GVW and load effect due to a truck passage (moment) are highly correlated as shown in Figure 4-40. For longer spans, such as 120 and 200 ft, the correlation is almost perfectly linear. For shorter spans, the correlation is also linear for a significant range of truck weights but with a higher degree of variation for heavier vehicles. For shorter spans, the maximum moment due to a truck passage is often caused by a group of axles rather than the GVW of the truck. Therefore, the shape of the cumulative distribution function of the load effect (moment) is very similar to the CDF of GVW due to the correlation between the two. The statistical parameters of permit vehicles in the database are determined by considering the distribution of ratio of actual GVW and allowable GVW, as shown on Figure 4-38. From this figure, the bias factor is taken as 1.0 and the coefficient of variation is 10%. However, for shorter span lengths, below 90 ft, where axle set weight governs, the coefficient of variation is taken as 20% due to a higher variation in ratio of axle set scale weight and permitted axle set weight. These values are based on analyzing the curves in Figure 4-37. Figure 4-39 shows the relationship between the permitted GVW and the actual GVW. Out of 869 vehicles, 162 had a permitted GVW between 70 kips and 80 kips, inclusive, and 133 vehicles had a permitted GVW between 80.01 kips and 85 kips. Figure 4-39 indicates that the worst violators are concentrated in these two groups. When the GVW is violated, heavier vehicles tend to exceed the permitted value by a smaller percentage than lighter vehicles. Table 4-26 shows the total number of vehicles and the number of vehicles with scale GVW exceeding the permitted GVW. A breakdown of the ratio of scale GVW to permitted GVW is also included. The results in Table 4-26 and in Figure 4-37 indicate that the worst violators are the vehicles with permitted GVW between 70 kips and 85 kips, inclusive. The heavier the permitted GVW, the lower the percentage of vehicles with scale GVW exceeding the permitted GVW. In addition, when in violation, the maximum ratio of scale GVW to permitted GVW is typically lower for heavier vehicles. For example: • For the 295 vehicles with permitted GVW between 70 kips to 85 kips, inclusive, 47 vehicles (15.9%) has a ratio greater than 1.25. • For the 105 vehicles with permitted GVW between 85.01 kips to 100 kips, inclusive, two vehicles (1.9%) has a ratio greater than 1.25 (1.55 and 1.27). The next highest ratio is 1.14. 73

• For the 147 vehicles with permitted GVW between 100.01 kips to 125 kips, inclusive, one vehicle (0.68%) has a ratio greater than 1.25 (1.257). The next highest ratio is 1.16. • For the 295 vehicles with permitted GVW above 125 kips the highest ratio is 1.07 with no ratio above 1.02 for vehicles with permitted GVW above 150 kips. The tendency of haulers to violate the permitted weights is dependent on the level of enforcement, the amount of the fine for the violation and the availability of a permit legally covering the load they need to move, i.e. the maximum loads allowed by the issuing state. Therefore, the analysis of the Louisiana violations data can only be generalized to other states with similar level of enforcement, level of fines and similar collection of permit vehicles. In addition, the total number of vehicles that were stopped but were found in conformance with the permits is not known. Therefore, the statistics of the entire population of permit vehicles, in conformance and in violation of the permits, could not be determined using the available information. 74

Table 4-26 Number of GVW Violations Per Weight Class for Louisiana Permit Vehicles Total No. of Records No. of GVW violations Ratio of actual GVW/Permitted GVW R < 1.0 1.0 < R ≤ 1.25 1.25 < R ≤ 1.5 1.5 < R ≤ 1.75 1.75 < R ≤ 2.0 R>2.0 Permitted GVW < 70 27 8 19 6 0 1 0 1 70 ≤ Permitted GVW ≤ 80 162 100 62 80 9 4 4 3 80 < Permitted GVW ≤ 85 133 96 37 69 10 9 7 1 85 < Permitted GVW ≤ 100 105 14 91 12 1 1 0 0 100 < Permitted GVW ≤ 125 147 24 123 23 1 0 0 0 125 < Permitted GVW ≤ 150 159 14 145 14 0 0 0 0 150 < Permitted GVW ≤ 175 92 13 79 13 0 0 0 0 175 < Permitted GVW ≤ 200 24 0 24 0 0 0 0 0 200 < Permitted GVW ≤ 250 19 0 19 0 0 0 0 0 Permitted GVW >250 1 1 0 1 0 0 0 0 Total 869 270 75

Figure 4-36 Gross Vehicle Weight of Louisiana Permit and WIM Trucks 76

Figure 4-37 Ratio of Axle Group Scale Weight and Permitted Axle Set Weight for Axle Sets with Different Number of Axles 77

Figure 4-38 Ratio of GVW and Permitted GVW for Permit Vehicles 78

Figure 4-39 Correlation of GVW to Ratio of GVW and Permitted GVW 0 50 100 150 200 250 300 0 50 100 150 200 250 300 S ca le G V W Permitted GVW Louisiana Permit Vehicles (Type 9999) 79

Figure 4-40 Correlation of GVW and Lane Moment for Various Span Lengths. (Laman 1993) The research team also obtained a database of the permits issued by New Jersey Department of Transportation from 8/16/10 through 11/30/2011. No information about the actual trucks or violations was available which diminished the value of this database. Nevertheless, the statistics of the NJ permits were compared to those of Louisiana violations. 80

Table 4-27 shows the distribution of the New Jersey Permitted GVW’s and Louisiana permitted and actual GVW’s is shown in Table 4-27 and Figure 4-41. The analysis of the data indicates that the majority of permits in New Jersey (83%) are for permitted GVW between 85 and 150 kips. This compares to 47 % for the same GVW group in Louisiana. On the other hand, vehicles permitted for GVW up to 85 kips represent 6% of the permits in New Jersey and 37% of the permits in Louisiana. The percentage is comparable for the vehicles permitted for GVW higher than 150 kips is also higher in Louisiana, 11% for New Jersey Verses 16% in Louisiana. The statistics of the actual GVW are closer to New Jersey Permit data. With no information available on New Jersey actual GVW’s, it is not possible to extend the statistics of Louisiana actual GVW’s to New Jersey Permit data. Table 4-27 Statistics for Different GVW Categories GVW Category (kips) NJ Permit Data Louisiana (Permitted GVW) Louisiana (Actual GVW) Count of Trucks Percentage Count of Trucks Percentage Count of Trucks Percentage <70 284 0.60% 27 3.11% 69 7.94% 70~80 902 1.90% 162 18.64% 54 6.21% 80~85 1610 3.39% 133 15.30% 114 13.12% 85~100 11136 23.46% 105 12.08% 179 20.60% 100~125 15544 32.75% 147 16.92% 174 20.02% 125~150 12858 27.09% 159 18.30% 172 19.79% 150~175 3267 6.88% 92 10.59% 74 8.52% 175~200 990 2.09% 24 2.76% 18 2.07% 200~250 592 1.25% 19 2.19% 14 1.61% >250 282 0.59% 1 0.12% 1 0.12% Total 47465 869 869 81

Figure 4-41 Histograms for NJ Permit Data and Louisiana Violation Records The significant difference between the distribution of the vehicles in different load categories in New Jersey permits as compared to the vehicles in Louisiana’s permit vehicles violations indicated that generalizing the relationship between the permitted and scale weights in Louisiana’s permit vehicle violations to New Jersey data is unjustifiable. 4.5.3 Conclusions Regarding Overloads and Permit Loads The analyses of WIM data led to the following conclusions: • Site-specific consideration of sites with unusually high volumes of heavy trucks is warranted • Design for a single lane loading is justified by this study • Elimination of the single lane MPF of 1.20 on the HL-93 loading when considering the effects of overload and permit vehicles for service limit state is justifiable The analyses of Louisiana permit load citations and comparing the data to New Jersey Permit data led to the following conclusions: • Heavier permit vehicles are less likely to violate the permitted axle group weights and GVW • When the GVW is violated, heavier vehicles tend to exceed the permitted value by a smaller percentage than lighter vehicles. • Due to difference in permit weight limits in different states, the weight and geometry characteristics of permit vehicles are state-specific or at best regional Generally, it is expected that the tendency of haulers to violate the permitted weights is dependent on the level of enforcement, the amount of the fine for the violation and the availability of a permit legally covering the load they need to move, i.e. the maximum loads allowed by the issuing state. Therefore, the analysis of permit vehicles will tend to be jurisdiction-specific or at best regional. 82