Development of State Legal and Overweight Live Load Models

Live load models are essential to assess the safety of highway bridges. To determine the maximum permissible load, Rhode Island currently uses legal live load models developed for a national level application based on federal weight restrictions. However, the state has allowable limits higher than those mandated federally, therefore, the models are not entirely representative of the truck traffic in the state. Furthermore, the state’s transportation agencies may issue permits for the operation of trucks in excess of the weight restrictions. To assist in permitting decisions, permit live load models developed from previous applications are introduced in the evaluation of bridges. Changes in the characteristics of permit applications diminishes the effectiveness of the permit live load models. A database of approved permit applications was utilized to analyze the models through their ability to exceed, or envelope, the structural responses due to the applicant trucks. As a result, state-specific 3and 5-axle legal live load models were developed. A validation of the permit live load models was also performed and revealed that they did not perform adequately. New permit live load models were developed to further assist and expedite the state’s transportation agencies permit reviewing process.

Bridges may be deemed structurally deficient given its state of deterioration or functionally obsolete as being incapable of fulfilling its intended purpose. Structurally deficient bridges have one of its three elements (i.e., deck, superstructure, and substructure) found to be in poor condition or if it has insufficient carrying capacity . Functionally obsolete bridges have a geometric design not in compliance with current specifications or presents constraints to normal traffic operations . Approximately 10% of bridges are structurally deficient, and 14% are functionally obsolete in the U.S. ("Bridges & Structures," 2014). Rhode Island faces a severe problem with structurally deficient bridges having the worst rate in the country with 174 out of 766 (23%) deemed as such and 255 (33%) as functionally obsolete ("Bridges & Structures," 2014).
A contributor to the deterioration of the structural integrity of highway bridges is the exposure to increasing traffic volume and load spectra. Stresses on bridge elements beyond those expected develop from repetitive overweight loading undermining a bridge's load carrying capacity. To protect bridges and prevent such occurrences, weight restrictions set at a national level are imposed on trucks. State-specific restrictions in excess of national standards is allowable under "grandfather clauses," such as the case in Rhode Island.
Trucks meeting all limitations are classified as legal and may travel unrestrictedly in the jurisdiction it is in compliance. Different live load (LL) models, defined as moving loads, are used in the analysis of bridges to ensure it has sufficient capacity for the anticipated traffic. There are LL models used for design purposes that generates effects that exceeds, or envelopes, those of normal national truck traffic. Other LL models representative of the legal trucks are used to calculate the responses of an existing bridge to the maximum permissible load.
Trucking accounts for about 80% of the expenditure on freight transportation in the U.S. . To provide a more economical and efficient manner or due to inability to reduce a load, there are occasions in which a truck must operate with a total weight exceeding the restrictions. Under a state's transportation agency review, such trucks may apply for a permit to ensure the bridges on the intended route have sufficient resistance. Evaluating each bridge along the route with the permit truck can be a time consuming task. However, many states like Rhode Island incorporate another set of LL models developed from characteristics of previous permit applications during the evaluation of existing bridges. In this manner, the effects generated by the permit truck can 3 be compared to the effects of the corresponding model. If the model has an effect greater than the permit truck and a particular bridge performs well with the model, the permit truck is also safe to travel.

Problem Statement
Rhode Island currently uses legal LL models developed for a national level application based of federal weight restrictions. However, these models may not be representative of the truck traffic in the state as it has restrictions in excess of those federally mandated, particularly for 3-and 5-axle trucks. Also, the permit LL models used by the state may be outdated due to possible changes in the characteristics of trucks in recent applications.

Objectives of this Study
This study had the objective of using a database of approved permit applications by Rhode Island's transportation agencies for the development of state-specific 3-and 5-axle legal LL models and compare its performance with the currently used legal LL models for bridge load rating. Furthermore, this study analyzed the performance of the Rhode Island permit LL models and developed or made alterations to existing ones to assist transportation officials in the permit reviewing process by being sufficiently representative of expected applications.

CHAPTER 2. LITERATURE REVIEW
The expected truck traffic is of great concern in the design and evaluation of existing bridges. Due to the irregular and evolving truck traffic characteristics to sustain an evergrowing demand to efficiently transport products, numerous research have been dedicated to develop LL models in an effort to reduce the uncertainties.
Bridges are effected by load effects rather than a truck's gross vehicle weight (GVW). The calculation of load effects is dependent on several parameters including axle weight (AXW), axle configuration, the transverse and longitudinal position of the truck, multiple truck presence, span length, stiffness of structural members, and future growth . However, the parameters associated with the static effects (i.e., AXW, axle configuration, and span length) are analyzed separately from the remaining due to the complexity of their interaction. Four types of load effects are considered in an analysis as they are required by specifications: end shear force and mid-span moment of a simplysupported beam; and the shear force and negative moment at the interior support of a twoequal span continuous beam.
To protect the structural integrity of our national bridge inventory, weight and size restrictions are enforced on trucks at a national and state level. As a result, those meeting restrictions are considered legal and allowed unrestricted operations. The load effects of such trucks are typically enveloped by LL models used in the analysis of bridges. Trucks exceeding restrictions are classified as oversize/overweight (OSOW), and may be granted permission to travel a specific route with an approved permit application reviewed by a state's transportation agency. However, the load effects developed by an OSOW truck may not be properly represented by existing LL models. Therefore, an analysis must be performed using the information provided by the applicant truck to determine the bridge's capacity to support its passage.

Weight and Size Restrictions
Vehicles traveling on bridges must comply with weight and size restrictions developed to maintain the integrity of the national highway system. The first federal regulation on size and weight of vehicles operating on the Interstate System was enacted in the Federal-Aid Highway Act (1956) to protect the substantial federal investment in its construction . The Act established a maximum GVW of 73.28 kips, tandemaxle weight of 32 kips, single-axle weight of 18 kips and a maximum width of 96 inches (Federal-Aid Highway Act, 1956). Prior to the adoption of the federal limits, states had their own restrictions. Provided in the act was a "grandfather right" provision allowing states to continue applying their own limits even if they exceeded those mandated federally to not disrupt the operation of heavier trucks accustomed to the region.
The Federal-Aid Highway Amendments (1975) increased the GVW and AXW limits in part to provide additional cargo carrying capacity to truckers faced with large fuel cost increases at the time, but Congress balanced this concession to productivity by enacting the Federal Bridge Formula B (FBF B) . The purpose of the concentrated. Load effect calculations is dependent on AXW and axle spacing (AXS) rather than the GVW. As shown by Figure 2.1, a truck with a short configuration (B) in comparison to a longer one with the same GVW will generate higher stresses on a bridge element. To reduce the effect, the load must be spread over additional axles or have an increase in AXS.

2015)
The FBF B determines the maximum allowable weight for a group of two or more axles along with compliance of the other weight restrictions on GVW, single-axle and tandemaxle ("Bridge Formula Weights," 2015). The FBF B is as following (Federal-Aid Highway Amendments, 1975): where: W is the overall gross weight on any group of two or more consecutive axles to the nearest 500 pounds; L is the distance in feet between the outer axles of any group of two or more consecutive axles; and N is the number of axles in the group under consideration.
An exception to the Bridge Formula is that two consecutive sets of tandem axles may carry 34 kips each if the overall distance between the first and last axle of these tandems is 36 ft.
The "grandfather right" continued in the 1975 amendments.  There is also limitations on the length of single and coupled vehicles as well as front and rear extensions of loads for maneuverability and safety purposes. These restrictions can be found in RI General Laws 31-25-5, 31-25-6, and 31-2-7.
Vehicles exceeding the limits may apply for a permit to operate a designated route. As of April 2, 2008, applications for OSOW permits in RI are submitted through an online application ("RI DMV/ DOT," n.d). In RI, OSOW permits are administered by the Rhode Island Division of Motor Vehicles (RIDMV) including processing applications, collecting fees, and issuing permits.
There are two types of permits issued to OSOW vehicles in RI. The first type of permit is a routine, or blanket permit (BP), approved for unlimited trips for a period no longer than a year over a specified route or within a restricted area (RIDOT, 2011). Limits for BP are found in Table 2.1. The other type of permit is for a single-trip, or overweight permit (OWP), issued for a one-way or round-trip movement of overweight (OW) vehicles valid only for a specific date, time, vehicle and route designated in the permit (RIDOT, 2011).
Also, restrictions on mixing with traffic and speed may apply. An OWP is issued to vehicles exceeding both legal and BP restrictions. Permits may be issued for divisible or non-divisible loads. Divisible loads consists of those that can be reduced in weight and dimension to comply with all restrictions. Non-divisible, on the contrary, cannot be reduced in weight or size, or they might be impractical to do so.

Design Live Load Model
Advances in bridge design specifications has further minimized the potential of detrimental effects developed by OW loads through improvements in the calculation of resistance as well as the expected demand. Adopted in 1994, the American Association of State Highway and Transportation Officials (AASHTO) Load and Resistance Factor Design (LRFD) of Highway Bridge Design Specifications introduced a limit state design philosophy, based on structural reliability methods, to achieve a more uniform level of safety in bridge design . Uncertainties associated with the design process are reduced in the specification by the application of factors developed from statistical variations of resistance and loads. ft. through 200 ft. . It was assumed that the economic life time for newly designed bridges to be 75 years . Therefore, the maximum load effects were calculated by extrapolations and simulations for the equivalent return period . The HL-93 model is referred to as a notional model, meaning it does not resemble an actual truck configuration but rather a combination of concentrated and distributed loads to produce maximum load effects that are greater than or equal to those produced by normal truck traffic. The HL-93 has three components: design truck; design tandem; and design lane. The design truck resembles a 3-axle 72 kips semitrailer truck, namely HS20, that has been used by AASHTO Standard Specifications since 1944  In the calculation of the strength limit state, referring to the bending and shear load effects, the calculated design demand values are multiplied by a factor of 1.75. This load factor was calibrated in the development of the LRFD to provide a reliability index, or β, of 3.5.
The β value gives a measurement to the structural reliability or, conversely, the risk that a design component has insufficient capacity and that some limit state will be reached ).

Bridge Rating Live Load Models
For the evaluation of existing bridges, the AASHTO Guide Manual for Condition A RF is calculated for several LL models at different load rating levels. It is undesirable to have a RF less than 1 as it implies there is insufficient structural capacity to support the analyzed model.
There are two main load rating levels, namely design and legal load rating. The design load rating composes of two evaluation levels, namely inventory and operating. Inventory is the first evaluation level performed at a design level of reliability of a new bridge for an inservice one taking into consideration the current condition of the structure. Therefore, it provides a direct comparison of an in-service bridge to a new design. The HL-93 shown on Figure 2.2 is used along with the appropriate LL factor shown in Table 2.2 to determine a bridge's capacity to carry normal truck traffic for an indefinite amount of time. Therefore, if a rating factor is acceptable, it can be assumed that the proceeding rating levels will also be satisfied. At the operating evaluation level the LL factor is calibrated for a lower β of 2.5 equivalent to the one used for the legal load rating. The legal load rating determines the maximum single safe load that can be placed on a bridge during the interval between routine inspections. Therefore, the LL factors are calibrated at a lower β of 2.5 due to the shorter exposure period compared to the 75-year assumed for design . Table 2.3 displays the factors used at the legal load rating level based on a bridge's traffic volume. Linear interpolation is permitted for other ADTT between 1000 and 5000 (MBE, 2013). At this rating level AASHTO legal LL models are introduced for their capability of assisting in management decisions as they resemble real commercial trucks commonly found on highways. AASHTO provides several legal LL models for rating and posting purposes. Although the models do not represent an actual truck configuration, they were developed to resemble and encompass the load effects of the various trucks each one describes. The first is the 2axle, 40 kips, H20 model having an AXS of 14 ft. AASHTO also developed the Family 3 Series (i.e. Type3, Type 3S2, and Type 3-3) in the 1970s to be sufficiently representative of commercial truck configurations at the time .   The AASHTO legal LL models were developed to be sufficiently representative of vehicles commonly found in the nation's highway that comply with federal weight restrictions.
However under the "grandfather rights," trucks exceeding federal restrictions are considered legal within the state's own limits. Therefore, the AASHTO legal LL models may not accurately envelope the load effects of the truck traffic of a particular state. The LRFR provides flexibility for states to implement their own legal LL models that satisfy their regulations. State-specific legal LL models are allowed by LRFR as long as they are load rated in the same manner as those provided by AASHTO .
Although RI has weight limits that exceed those federally mandated, it currently does not have state-specific legal LL models.

Permit Live Load Models
OSOW vehicles may operate with the approval of a permit application reviewed by a state's transportation agency. Permit application analysis can be a time consuming task.
Therefore, it is beneficial for a state to have OWP models, either notional or resembling real truck configurations, developed based on truck characteristics of previous applications to be evaluated during a bridge rating at a permit level. This procedure has the ability of there is sufficient carrying capacity. The models satisfy two types of permits issued to OW vehicles: BP and single-trip permits (OWP). There are four BP models, namely RI-BP1 through RI-BP4, and three OWP, namely RI-OP1 through RI-OP3.

Figure 2.6: RI permit LL models (RIDOT, 2011)
Similarly with the design and legal LL models, the permit models must also utilize load factors in the analysis. Permit load factors depend on the type of permit, traffic volume, weight and configuration of permit vehicle as shown in Table 2.4. The factors for routine permits were calibrated using a β of 2.5. Due to risk of structural damage and associated benefit/ cost considerations lead to a higher β of 3.5 for singleand multiple-trip special permits.

CHAPTER 3. METHODOLOGY
This chapter presents the approach adopted to achieve the study's objectives. A review of the research database is described and detailed information on the data analysis procedure is provided.

Characteristics of OSOW Truck Database
RIDMV maintains a log of approved single-trip permit applications reviewed by the agency as well as RIDOT. A database containing 44,507 records extending from April 2008 through June 2013 was obtained from RIDMV as an excel spreadsheet. Each row in the spreadsheet pertains to a specific application and the columns its details. Table 3.1 summarizes the information provided by each column of the database. Details on the truck's configuration and weights (i.e., NAX, AXS and AXW) are necessary for the calculation of load effects and the development of the LL models. Other data provided by the database such as the reviewing agency and number of submittals were used to analyze the characteristics of the applications.

Database Quality Analysis
A data quality analysis was the first procedure performed with the purpose of removing erroneous records. The latter was achieved by the use of data quality filters based on possible sources of error as well as observed discrepancies in the input values. Records failing one or more data quality filters were separated from the database. It is important to eliminate such records as they could impair the findings of this study.
The records meeting all quality filters were used for the progression of the study and its characteristics were evaluated. By incorporating the RI General Laws, the records were then categorized into groups based NAX and weight restrictions as legal, BP, or OWP loads (e.g., legal 5-axle, BP 5-axle, and OWP 5-axle). In this study of concern was the classification of trucks based on weight restrictions, therefore, the size restrictions were not taken into consideration to categorize the trucks.

Model Performance
For each record within the different groups, the maximum load effects (i.e., mid-span moment and end shear force of a simply-supported beam, and negative moment and shear force at the interior support of a two-equal span continuous beam) were calculated for 37 span lengths ranging from 20 ft. through 300 ft. with fixed intervals (i.e., 20-30 ft. every 1 ft., 30-60 ft. every 10 ft., 100-200 ft. every 20 ft., 250 ft., and 300 ft.). Therefore, each record had a total of 148 calculated load effects. No LL factors were applied to the calculations. A detailed explanation of the method taken to calculate the load effect can be found in the appendix. The selected method was incorporated into a MATLAB code due to the highly computational effort involved in calculating the load effects.
The performance of a LL model was assessed by its ability to exceed, or envelope, the load effects of the trucks in the group it represents. Load effect ratios were used for evaluating the latter, as shown in Equation 3.1. The model and records were compared for all types of load effects and span lengths. A target value of < 1 is desirable meaning the model sufficiently envelopes or is equivalent to the load effect of the record.

Load Effect Ratio = Load Effect of Record
Load Effect of Model (3.1) A visual representation of the load effect ratios assists in determining the models performance. The number of times the model is exceeded for a specific span length divided by the number of records in the group is plotted as a percentage against the span lengths.
Based on the percent exceeding graphs, an observation of the span lengths in which the model is exceeded can be made. A uniform percent exceedance is desirable for the application of a single LL factor for all span lengths and type of load effects.
There were many records in the database not eliminated by the quality analysis that displayed information raising concerns. These records have configurations that appear unlikely, or rare, while others could have a user input error. It is difficult to decipher the distinction between the two possibilities due to the database's nature of uncommon trucks.
A specific concern is with the low value of the summation of AXS compared to the truck's total length. These trucks can generate extremely high load effects due to the proximity of the axles. Under RIDOT advisement, characteristics of such records were identified and deemed rare or with a potential user input error. Furthermore, applications are submitted in advance to the truck being loaded, which can cause applicants to input higher weights to avoid fines if the truck surpasses what is specified on the permit. Given the presented uncertainties and the inability to eliminate records through a coherent manner, an assumption was made that a maximum exceedance of 10% would be acceptable. Therefore, at least 90% of the records are well represented by the model without being excessively conservative.

Live Load Model Development
Models that represent a group composed of trucks having the same NAX were developed using an actual truck configuration found within that group. A better understanding of the characteristics of trucks traveling on the state's bridges and the ones that can generate the maximum load effects are beneficial aspects of such models that assists in management decisions such as closure and posting.
A systematic procedure was adopted to create actual truck configuration LL models. Since one of the configurations within the group would be used to develop the model, only the AXWs had to be determined. "Trial models" were developed using a MATLAB code that used all the configurations of trucks within the group with replaced AXWs from several predetermined cases. The maximum percent exceedance of all "trial models" for each load effect were calculated by the code that then ranked them based on performance.
AXWs for the "trial models" were selected using the group's database characteristics. To be sufficiently representative of the database and develop suitable models, it was determined to use the 90 th and 95 th percentile of the GVW and AXWs. Also, the division of GVW among the axles was another parameter investigated. For all records in the group, the percent of the GVW each axle supports was calculated. Then, statistical parameters the development of a notional model in this study follows the same systematic procedure of the actual configuration model except with different GVW and AXW cases.
Furthermore, the notional model has the same NAX as the trucks with the most NAX in the group's database. Therefore, the "trial models" and the GVW division among axles for the model development only uses such trucks. The best case is then used as the starting point for the alterations to fabricate the model in a trial and error approach to enhance its performance. The following are the cases evaluated: 1. a. Highest 90 th percentile GVW of the trucks in the group, and the mean division among the axles.
b. Highest 90 th percentile GVW of the trucks in the group, and the mode division among the axles. In this study, actual configuration models were developed for all legal and BP groups as the restrictions are specific to a trucks NAX. A combination of notional and actual truck configuration models were developed for OWP groups depending on the number of records.

CHAPTER 4. DATABASE ANALYSIS
In this chapter the findings of the database analysis is presented. Initially a data quality analysis was performed to eliminate erroneous records found in the provided spreadsheet by RIDMV of approved single-trip OSOW permits. Figure 4.1 displays the distribution based on NAX of the database and Table 4.1 summarizes the findings. The classification of trucks into groups using the RI General Laws is also presented. Then, the characteristics of the applications within these groups were investigated.

Data Quality Analysis
The quality analysis was completed by using filters selected from expected sources of error and observed discrepancies in the input values. MATLAB was used to assign flags to records failing filters. Records meeting all filters were compiled into a database named "Good Data," and those eliminated into a database named "Bad Data." There were six filters used to perform the quality analysis, as shown in the flowchart on an assumption made that any AXS < 24 inches is extremely short and unlikely to occur given the characteristics of the remaining trucks in the database. As a result, filter 2 was responsible for flagging the most trucks (6.10%) followed by filter 3 (0.96%).  This can be due to missing a significant figure in the GVW input (e.g., actual GVW of 80,000 entered as 8,000 pounds).
Filter 3 and 6 evaluated the configuration of the trucks. A possible explanation to errors flagged by these filters could have originated from the manner in which the information is requested in the application process, as shown on Figure 4.4. The AXS necessary to fill in the application does not specify that the measurement must be taken from center-to-center of axles. Therefore, an applicant could have measured the gap between the tires instead.

Truck Classification by RI General Laws
The progression of the study utilized the records found in the "Good Data." To develop the LL models, these records had to be categorized and separated based on the weight restrictions specified in the RI General Laws. Table 4.2 summarizes the possible classification of each truck depending on the NAX. Shown on Figure 4.5 is a flowchart with the results of applying the information found in Table 4.2 to classify the trucks. Trucks classified as legal under the weight restrictions applied for permits due to a size violation.       done by compiling all records by month of approval and dividing by 5, the number of years the data was collected. June is the month with the highest average of legal (11.95%) and OWP (11.55%) applications reviewed by the agencies combined, and May for BP (24.57%). These calculations used the "Good Data" composed of approved permits, therefore, the total number of reviewed applications can be higher if the statistics on the rejected ones were known.      As previously stated, an application may be rejected if the truck cannot be accommodated in the requested route or necessary information is not provided. However, applications may be re-submitted with the necessary corrections. Tables 4.9-4.11 shows the number of application submittals required until approval. The OWP reviewing process had the lowest first time submittal approval rate of 88.97% in comparison to legal and BP. However, the legal applications required the most number of re-submittals, up to seven.  The percent of applications reviewed by each agency separated into NAX is summarized in Tables 4.12-4.14. RIDMV reviews the most applications for all types of trucks based on NAX for both legal and BP. However for OWP, as the NAX increases RIDOT reviews more applications than RIDMV.

. LEGAL LIVE LOAD MODELS
This chapter presents the development of the legal LL models: RI-3 and RI-5, for 3-and 5-axle trucks, respectively. Currently, there are no state-specific legal LL models.
However, the 3-axle RI-BP1 and 5-axle RI-BP3 models used for BP purposes have characteristics that resemble the limitations of legal trucks imposed by the RI General Laws. Therefore, the two BP models were evaluated in this chapter as the existing legal LL models.

Proposed RI-3
A total of 419 records in the "Good Data" were classified as legal 3-axle trucks having a GVW < 76.65 kips. These records were further used to develop the RI-3 model and to evaluate its performance.

Figure 5.3: Legal 3-axle records AXW NPP
All statistical parameters discussed so far is summarized in Table 5.1 with the inclusion of other necessary information. This data was used to create the "trial model" cases accordingly to the adopted procedure for an actual truck configuration model development, explained in Chapter 3. The distribution of GVW among the axles of the legal 3-axle records was also calculated as it is required to develop certain "trial model" cases. For each record, the percent of GVW each axle supports was calculated and from those values statistical parameters were determined with results shown in Table 5.2. Once all the necessary information was obtained, the "trial model" cases were selected, as presented in Table 5.3. The maximum percent exceeding for each load effect and the corresponding configuration for all analyzed cases are shown in Tables 5.4-5.5. Case 5a and case 6 both had the best and equivalent performances only having CSMomNeg exceeded by 0.7%.  Although both cases 5a and 6 performed equally well, the latter is selected as the proposed RI-3 given its current functional application in bridge rating purposes as the RI-BP1. Figure   5.4 displays the proposed RI-3 configuration.

Proposed RI-5
There were 17,881 records in the "Good Data" classified as legal 5-axle trucks having a GVW < 104.8 kips. These records were utilized to develop the RI-5 model and to evaluate its performance. Figure 5.13 demonstrates the distribution of GVW with a maximum of 104.75 kips, minimum of 8.5 kips, and mode of 80 kips. The database has a mean GVW of 78.5 kips and standard deviation of 14.8 kips.

Figure 5.14: Legal 5-axle records yearly variation of GVW statistics
Shown on Figure 5.15 is the NPP of the AXWs. It was observed that for lighter weights, the distribution of the AXWs are relatively similar for all axles. However, as the weights increase the AXW1 distribution deviates from the others. This observation was considered in the model development.

Figure 5.15: Legal 5-axle records AXW NPP
other necessary information. This data was used to create the "trial model" cases accordingly to the adopted procedure for an actual truck configuration model development, explained in Chapter 3. The statistics on the distribution of GVW among the axles of the legal 5-axle records was also analyzed as it is required to develop certain "trial model" cases. Table 5.9 displays the calculation results. Once all the necessary information was obtained, the "trial model" cases were selected as presented in Table 5.10. The maximum percent exceeding for each load effect and the corresponding configuration for all analyzed cases are shown in Tables 5.11-5.12. Cases 1, 3 and 6 (existing model) did not perform well for CSMomNeg with a maximum exceeding as high as 14.43%. The target maximum percent exceeding for cases 2, 4 and 5 is satisfactory for all load effects, therefore, any could be selected as the proposed model.  Although cases 2, 4, and 5 performed well, case 4 was selected as the proposed RI-5. The    However, in RI such trucks with 5-axles to be considered legal must only comply with the maximum GVW of 104.8 kips regardless of the other weight restrictions. Therefore, an increase in the AXWs generates higher load effects of trucks with similar configurations.

Figure 5.24: Proposed RI-5 vs. HL-93
Tables 5.13-5.14 summarizes the ratios calculated used to develop the plots displayed in

CHAPTER 6. BLANKET PERMIT LIVE LOAD MODELS
In this chapter the development of BP LL models is presented: RI-BP4 and RI-BP5, for 4and 5-axle trucks, respectively. Any truck with NAX less than six above legal restrictions and with a GVW < 130 kips and any axle < 25 kips classifies as a BP in the RI General Laws. Therefore, 2-and 3-axle trucks may also fall within this category. However, models for these trucks were not developed as there was insufficient or no records available. The existing 4-axle RI-BP2 was evaluated for the development of the proposed RI-BP4, while the existing 5-axle RI-BP3 was not analyzed in this chapter as it was used in the development of the proposed RI-5 for having legal restrictions characteristics.

Proposed RI-BP4
There were 851 records in the "Good Data" classified as BP 4-axle trucks. These records were further used to develop the RI-BP4 model and to evaluate its performance. Shown on

Figure 6.3: BP 4-axle records AXW NPP
All statistical parameters discussed so far is summarized in Table 6.1 with the inclusion of other necessary information. This data was used to create the "trial model" cases accordingly to the adopted procedure for an actual truck configuration model development, explained in Chapter 3. The statistics on the distribution of GVW among the axles of the BP 4-axle records was also analyzed as it is required to formulate certain "trial model" cases.  Once all the necessary information was obtained, the "trial model" cases were selected as presented in Table 6.3. In cases where the division of GVW among the axles resulted in AXWs exceeding the limit imposed by the RI General Laws, the AXW was set at the maximum allowable value of 25 kips. This was done to develop a model that is both representative of the BP 4-axle database and of the restrictions imposed on such trucks.

Proposed RI-BP5
In the "Good Data" there were 611 records classified as BP 5-axle trucks. These records were further used to develop the RI-BP4 model and to evaluate its performance. Shown on Figure 6.11 is the distribution of GVW with a maximum of 125 kips, minimum of 105 kips, and mode of 110 kips. The database has a mean GVW of 111.64 kips and standard deviation of 4.93 kips.

Figure 6.11: BP 5-axle records GVW distribution
The yearly variation of GVW statistics of the BP 5-axle records is shown on Figure 6.12.   other necessary information. This data was used to create the "trial model" cases accordingly to the adopted procedure for an actual truck configuration model development, explained in Chapter 3. The statistics on the distribution of GVW among the axles of the BP 5-axle records was also analyzed as it is required to formulate certain "trial model" cases. Table 6.8 displays the calculation results. presented in Table 6.9. In cases where the division of GVW among the axles resulted in AXWs exceeding the limit imposed by the RI General Laws, the AXW was set at the maximum allowable value of 25 kips. This was done to develop a model that is both representative of the BP 5-axle database and of the restrictions imposed on such trucks.   Case 4 resulted in the best performance and was selected as the proposed RI-BP5 model.
The AXWs all match the maximum permissible value of 25 kips, therefore, it also matches the maximum GVW of 125 kips. Figure 6.14 displays the proposed RI-BP5 configuration.  The distribution of ratios displayed as box plots and the statistical parameters for all span lengths are shown on Figures 6.16-6.19. The simple span load effects and CSShear ratios mean and mode values start off high for short spans, then decreases before increasing with longer span lengths. For CSMomNeg, the statistical parameters of the ratios peak at short spans and then lowers before following the same pattern as the other load effects.

CHAPTER 7. OVERWEIGHT PERMIT LIVE LOAD MODELS
This chapter presents the development of OWP LL models. Currently, RI has three notional OWP models, namely 5-axle RI-OP1, 8-axle RI-OP2, and 13-axle RI-OP3. Each model was developed to envelope the load effects of OWP trucks having the same NAX or less: RI-OP1 for 2-5-axle, RI-OP2 for 6-8-axle, and RI-OP3 for 9-13-axle. By grouping the trucks based on the NAX limits the necessary amount of models to be sufficiently representative of the expected OWP trucks to travel across RI's bridges.
The records in the OWP database were grouped in the same manner as the existing model's intended purpose. However, due to the high number of 6-axle OWP records, a model for such truck type was developed based on an actual truck configuration. Therefore, a total of four models were developed: three notional (i.e. RI-OP5 for 2-5-axle, RI-OP8 for 7/8-axle, and RI-OP13 for 9-13-axle) and one actual truck configuration model (i.e. RI-OP6 for 6axle).

Proposed RI-OP5
There were 3,319 records in the "Good Data" classified as OWP 2-5-axle. Of the 3,319 records there were no trucks with 2-axle, 126 3-axle, 597 4-axle, and 2,596 5-axle. These records were further used to develop the RI-OP5 and to evaluate its performance. Figure   7.1 demonstrates the distribution of GVW with a maximum of 150 kips, minimum of 54 deviation of 8.98 kips. Table 7.1 summarizes the GVW statistics.  The variation of the GVW statistics by year is shown on Figure 7  The data was compiled by separating the database by NAX. The latter was necessary to create the "trial model" cases accordingly to the adopted procedure for notional models, explained in Chapter 3. The statistics on the distribution of GVW among the axles of the 5-axle records was also analyzed as it is required to formulate the "trial model" cases.  Once all the necessary information was obtained, the "trial model" cases were selected as presented in Table 7.5. Case 4 AXW1 was modified to 22 kips from 25.57 kips to have the summation of AXWs be the same as the 95 th percentile of the 5-axle records GVW.  Case 8 had the best performance, therefore, it was selected as the proposed RI-OP5 model.

Proposed RI-OP6
In the "Good Data" there were 7,397 records classified as OWP 6-axle trucks. These records were further used to develop the RI-OP6 model and evaluate its performance.
Shown on Figure 7.10 is the distribution of GVW with a maximum of 159 kips, minimum of 52.1 kips, and mode of 120 kips. The database has a mean GVW of 111.8 kips and standard deviation of 14.58 kips.   other necessary information. This data was used to create the "trial model" cases accordingly to the adopted procedure for an actual truck configuration model development, explained in Chapter 3. The statistics on the distribution of GVW among the axles of the OWP 6-axle records was also analyzed as it is required to formulate certain "trial model" cases. Table 7.10 displays the calculation results. It can be seen that the sum of the mode distribution is above 100%.
These percentages were still used although they increase the model's GVW in comparison to the GVW used to calculate the AXW. presented in Table 7.11. Cases 1 and 2 are the same as the 90 th and 95 th GVW percentile are equal. The last two cases, 5 and 6, are not evaluated as there is no maximum limit for an OWP truck nor an existing model.
The maximum percent exceeding for each load effect and the corresponding configuration for all analyzed cases are shown in Tables 7.12-7.13. For all cases trucks with equally spaced axles at 33" and others with AXS ranging from 29" to 36" outperformed the other configurations. However, such trucks are considered rare or might have a user input error due to the low sum of AXS compared to the total tuck length. Therefore, they were not considered among the cases as a suitable configuration for the model.

Proposed RI-OP8
Of the 4,148 records in the "Good Data" classified as OWP 7/8-axle, 2,640 have 7-axle and 1,508 have 8-axle. These records were further used to develop the RI-OP8 and to evaluate its performance. Figure 7.20 demonstrates the distribution of GVW with a maximum of 193 kips, minimum of 54.9 kips, and mode of 130 kips. The database has a mean GVW of 135.25 kips and standard deviation of 19.12 kips.   The variation of GVW statistics by year is shown on Figure 7.21. In 2009 the maximum GVW of 193 kips occurred and the minimum of 54.9 kips in 2011.

Figure 7.21: OWP 7/8-axle records yearly variation of GVW statistics
Shown in Tables 7.16-7.17 is the summarized statistical parameters of the records weight.
The data was compiled by separating the database by NAX. The latter was necessary to create the "trial model" cases accordingly to the adopted procedure for notional models, explained in Chapter 3. The statistics on the distribution of GVW among the axles of the 8-axle records was also analyzed as it is required to formulate the "trial model" cases. Table 7.18 displays the calculation results. Once all the necessary information was obtained, the "trial model" cases were selected as presented in Table 7  percentile of the database GVW. Case 8 was selected over these cases given the current use of the configuration in permit application evaluation and the updated AXWs resulted in a satisfactory performance. Figure 7.22 displays the model's configuration.

Proposed RI-OP13
There were 645 records in the "Good Data" classified as OWP 9-13-axle. The OWP 9-13axle database is composed of 203 9-axle, 278 10-axle, 62 11-axle, 50 12-axle, and 52 13axle records. These records were further used to develop the RI-OP13 and to evaluate its performance. Figure 7.29 demonstrates the distribution of GVW with a maximum of 360.3 kips, minimum of 68 kips, and mode of 199 kips. The database has a mean GVW of 167.56 kips and standard deviation of 35.98 kips. Table 7.23 summarizes the GVW statistics.

Figure 7.30: OWP 9-13-axle records yearly variation of GVW statistics
Shown in Tables 7.24-7.26 is the summarized statistical parameters of the records weight.
The data was compiled by separating the database by NAX. The latter was necessary to create the "trial model" cases accordingly to the adopted procedure for notional models, explained in Chapter 3.  The statistics on the distribution of GVW among the axles of the 13-axle records was also analyzed as it is required to formulate the "trial model" cases. Table 7.27 displays the calculation results.  Table 7.28.  The maximum percent exceeding for each load effect and the corresponding configuration for all analyzed cases are shown in Tables 7.29-7.30. In all analyzed cases, the maximum percent exceeding for all types of load effects were above the acceptable value. The best performance was by case 5, the existing RI-OP3 model. Therefore, the model was used in case 8 as the starting point for the necessary modifications to enhance its performance. To capture higher influence ordinates with higher AXWs, the last two groups of rear axles were altered by exchanging AXS11 with AXS12. As a result, axle 8 through 11 are evenly spaced at 4'-4" and AXS10 becomes 10'-6". Lastly, AXWs 8 through 10 were changed to the 90 th percentile of the OWP 10-axle records, and AXWs 11 through 13 to correspond to the 90 th percentile of the OWP 13-axle records. These adjustments improved all types of load effects maximum percent exceeding.  Based on the performance of case 8, it was selected as the proposed RI-OP13 model.

CHAPTER 8. CONCLUSIONS
This study had the purpose of validating the OWP LL models currently used by RI's transportation agencies to assist in reviewing permit applications. Furthermore, this study also sought out to develop state-specific legal LL models representative of such defined in the RI General Laws. The study was accomplished by utilizing a database of approved single-trip permit applications by RIDMV and RIDOT expanding from April 2008 through June 2013. Incorporating the state's truck traffic characteristics in the LL models promotes more reliable bridges by protecting their structural integrity and reduces the potential of expenditures in repairs or replacements.
The proposed RI-3 and RI-5 legal LL models are shown on Figure 8.1. These models are based on an actual truck configuration beneficial in the legal rating of bridges to identify the maximum permissible load. The existing BP models resembling the characteristics of legal trucks were analyzed as potential legal models. As a result, the proposed RI-3 is the same RI-BP1 as it sufficiently envelopes the load effects of the legal 3-axle database.
However, the RI-BP3 did not perform well for the legal 5-axle database. Therefore, the proposed RI-5 was developed using the characteristics of the database. Further research of state-specific legal LL models is encouraged with the application of weight-in-motion (WIM) sensors, an automated data collection system embedded in the road surface. Data collected by WIM includes AXWs and configuration at normal highway traffic speeds. In this manner, a broader understanding of the truck traffic is possible compared to the utilized database of permit applications. The protocols developed by Sivakumar et al. (2011) along years, the interval between routine bridge inspections.

Load Effects Calculations
The maximum structural responses to an applied load, or load effects, are necessary in bridge analysis to determine its carrying capacity. There are four load effects generally considered: end shear force and mid-span moment of a simply-supported beam; and the shear force and negative moment at the interior support of a two-equal span continuous beam.
To establish the maximum load effects, loads must be positioned in the most critical manner. However, for a truck such placement is frequently not evident as the structural responses vary as it moves along a beam. A systematic procedure called influence lines is commonly used to determine the maximum load effects. An influence line is a diagram whose ordinates, which are plotted as a function of the distance along a beam, give the value of an internal force, a reaction, or a displacement at a particular point in a structure as a unit load of 1 moves across the structure . As the truck moves along the beam, the influence ordinate at the location of each axle is multiplied by the corresponding AXW. The load effect is the summation of the influence ordinate multiplied by the AXW. This computation is only valid for linear behavior, as the forces created in an elastic structure are directly proportional to the magnitude of the applied load . Load effects due to a distributed load can also be obtained by multiplying the magnitude of the force by the area under the influence line.
The functions are then utilized to develop codes in the computer software MATLAB to simulate the trucks in the database crossing over bridges of various span lengths.

Simple Span End Shear Force
The maximum shear force in a simply-supported beam typically occurs adjacent to a support. Therefore, the maximum shear force is equal to the highest support reaction.
Placement of a concentrated load directly over a support produces the highest reaction, therefore, the maximum shear force. To capture each axle over a support, the MATLAB code for simple span shear force (SSShear) positions the first axle over a support and moves the truck along the beam accordingly to the truck's AXS.
Summing the forces about the y-axis, the function for By is solved: Equations 1 and 2 are the influence functions of the support reactions Ay and By, respectively, as the unit load varies in position along the span. Figure 2 displays the influence lines for the calculated functions.

Simple Span Mid-Span Moment
Bending moment increases as a concentrated load approaches mid-span of a simplysupported beam. The MATLAB code for simply-support mid-span moment (SSMomMid) positions the first axle over the center of the beam and moves the truck accordingly to the AXS to capture all axles at that location and maximize the load effect. Figure 3 shows the cut section of a beam used to calculate the SSMomMid influence function as the unit load moves closer to mid-span. the section used to calculate the mid-span moment influence function as the unit load moves always from mid-span.

Figure 4: Unit load moving away from mid-span
The influence function is determined for the above condition by taking the moment about mid-span:

Continuous Span Interior Support Shear Force
In a continuous beam the shear force of interest is equivalent to the interior support reaction. Similarly to SSShear, the MATLAB code for the shear force at the interior support of two-equal span continuous beam (CSShear) positions the first axle over the interior support and moves the truck along the beam accordingly to the AXS. A continuous beam is an indeterminate structure and cannot be solved directly using the equations of equilibrium. Therefore, other methods must be applied to solve for the reactions. The flexibility method, or the method of superposition, was chosen for this analysis. Figure 6 displays the procedure to superimpose the indeterminate structure with determinate release structures in order to formulate the compatibility equation. The first structure is analyzed with a moving unit load. The second has a unit load applied to the released support and is multiplied by the actual magnitude of the redundant reaction.

Figure 6: Formulation of the compatibility equation
The deflections of the released structures are summed at the location of the interior support and set equal to the deflection of the indeterminate structure, which is zero as it is fixed against translation in the y-direction. Equation 5 formulates the latter statement: ∆B + δ BB (1)R B = 0 Calculating ΔB is accomplished through the same manner as δBB by the application of the Maxwell-Betti law of reciprocal deflections. The law states that a linear deflection ΔB due to a unit load at "x" of the first release structure is equal to the displacement at "x" (i.e., δxB) of the second release structure due to a unit load at the location of ΔB (Megson, 2005).
Since the deflections of the release structures are assumed in opposite direction, -ΔB = δxB.
By making the appropriate substitutions and rearranging equation 5 results in: The deflection equations for a simply supported beam with a concentrated unit load at midspan is expressed as: υ = 1 48EI (4x 3 − 3L 2 x) 0 < x < L/2 (7) υ = 1 48EI (4(L − x) 3 − 3L 2 (L − x)) L/2 < x < L To solve for δBB, the distance to mid-span (L/2) is plugged into equation 7 and results in: Because the interior reaction will increase as the unit load approaches its location and decreases as it moves away, the influence function is solved for two intervals. The deflection δxB is equal to equation 7 and 8 as it varies with the location of the applied unit load.
By substituting equations 7 and 9 into 6, the influence function for the interior support is calculated and results in: By substituting equations 8 and 9 into 6, the influence function for the interior support is calculated and results in:

Continuous Span Negative Moment
Continuous beams are subjected to both positive and negative bending moments.
Maximum negative bending moment at the interior support of a two-equal span beam is generally considered for evaluation purposes. A concentrated load maximizes the negative bending moment when placed at a location of about 0.577L. Therefore, the MATLAB code for continuous span negative moment at the interior support of a two-equal span beam (CSMomNeg) positions the first axle at 0.577L and moves the truck along the length of the beam accordingly to the truck's AXS.
The influence function for the interior support reaction, By, was calculated in section 3. By applying the equations of equilibrium, the influence functions for the outer supports, Ay and Cy, are as shown: Solving for the moment at the interior support, the negative moment influence function is: Once the unit load moves past the center support, the influence functions become: