A METHODOLOGY FOR DEVELOPMENT OF DESIGN PERMIT VEHICLES

Transcription

1 The Pennsylvania State University The Graduate School College of Engineering A METHODOOGY FOR DEVEOPMENT OF DESIGN PERMIT VEHICES A Thesis in Civil Engineering by Meet Shah 06 Meet M. Shah Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science December 06

2 The thesis of Meet Shah was reviewed and approved* by the following: Jeffrey A. aman Professor of Civil Engineering Thesis Advisor Ali. M. Memari Professor of Civil Engineering Konstantinos Papakonstantinou Assistant Professor of Civil Engineering Patrick Fox Department head of Civil & Environment Engineering * Signatures are on file in the Graduate School ii

3 Abstract This study proposes a methodology for the establishment of a design permit vehicle that will predict loading effects (shear and moment) caused by a population of special hauling permit vehicles, specifically from the heaviest state-issued superload permits. This methodology utilizes databases obtained from the Pennsylvania Department of Transportation and a forecasting of vehicle loads. A fundamental objective of this study was to develop analytical tools to evaluate vehicle data files, both weigh in motion (WIM) and superloads. Primary analytical tools were developed to enable an automated procedure to simulate the passage of large numbers of vehicles, including WIM database vehicles, and permit database vehicles, over several bridge configurations to obtain the maximum moments and shears. The main objective was to construct a permit design vehicle model that envelopes 98% of WIM and superload vehicles. WIM and superload vehicles were processed by characterizing the population by vehicle width, number of axles, axle spacings, axle loads, axle group loads, and gross vehicle weight (GVW). Characterization for a given vehicle class includes averages, standard deviations, 95th percentiles, and maximums. Additionaly, a procedure to forecast the maximum vehicle effects on highway bridge for AASHTO specified design life is proposed. This procedure required processing of the WIM and superload vehicles by modelling individual and group axle weight as Generalized Extreme Value Distribution. A permit design vehicle was developed demonstrating the proposed methodology. Individual axle loads and axle groups were observed to follow the generalized extreme value distribution. iii

4 Table of Contents Acknowledgements...vi.0 Introduction...0. Problem Statement Research Objective Scope of Research Tasks iterature Review State Permit Design Vehicles Vehicle oad Model Development Vehicle Development based on WIM Data Vehicle Development based on Permit Vehicle Data Statistical Modeling of Experimental Data Forecasting of Vehicle oad and oad effects Summary Analytical Tool Development Simple Span Simple-Span Moment Influence ine Simple-Span Shear Influence ine Two Span Continuous, Two-Span, Positive Moment Influence ine Continuous, Two-Span, Negative Moment Influence ine Continuous, Two-Span, Shear Influence ine Three Span Continuous, Three-Span, Negative Moment Influence ine Continuous, Three-Span, Positive Moment Influence ine Continuous, Three-Span, Shear Influence ine Simulation and Presentation of Results Comparison to Pennsylvania Design Permit Vehicle Comparison to AASHTO ive oad Model HS Development of Permit Design Vehicle Model Objectives and Methodology WIM Database Permit Design Vehicles Superload Database Permit Design Vehicles Proposed Vehicle Comparison to Superload Statistical Evaluation of Vehicles Introduction Discussion of Method Results...75 iv

5 7.0 Summary and Conclusions Summary Conclusions Recommendations for Future Research...8 References...8 Appendix Weigh-In-Motion Database Format...85 v

6 Acknowledgement First I thank my thesis advisor, Dr. Jeffrey A. aman, for his continuous support of my study and related research, for his patience, motivation, and immense knowledge. His guidance helped me during research and writing of this thesis. I could not have imagined having better advisor and mentor for my thesis. I am also grateful to my thesis advising committee that showed me direction when required and enriched my work with their viewpoints. I also thank my friends Jigisha, Rahul, Harshil, Priyan, Amal, Manav, Jaskanwal, and Neel, for their support. It would not have been possible without them. ast but not the least, I thank my parents, Milan Shah and Sonal Shah, for always supporting me in all my endeavors and for having faith in me. vi

7 Chapter Introduction Trucking accounts for a large percentage of expenditures on freight transportation in the United States and is vital to the US economy. There are, however, gross vehicle weight (GVW), axle weight, and axle spacing legal limits that vary by state. Where loads must be transported that exceed the legal limit, vehicle haulers must seek special exception to the legal limit in the form of a permit. Permit vehicles are overweight vehicles which, in order to travel a state s highways, must apply for a permit from that state. They are usually heavy vehicles (e.g., combination vehicles, construction vehicles, or cranes) that have a range of axle weights and spacing depending upon the design of the individual vehicle. To ensure that these vehicles can safely operate on existing highways and bridges, states require that bridges be designed for a permit vehicle or that the bridge be evaluated to determine if it can support a specific type of vehicle. For safe and legal operation, agencies issue permits upon requests that identify the approved GVW, number of axles, axle spacing, and maximum axle weights for a designated route. There are several types of permits. Single trip permits are valid for one trip over a defined time period to move vehicles that exceed maximum legal size or weight over state highways. Annual permits are issued for one year for overweight and oversized vehicles with some travel restrictions. Escort vehicles are required to accompany permitted vehicles under written guidelines. Permitting heavy vehicles to operate on highways will advance the productivity of the highway system and benefit the economy. All state departments of transportation issue significant numbers of permits every day. As the GVW of vehicles increases and number of permits increase it will become necessary for each state department of transportation to assess their live load model. It is

8 necessary to accommodate overweight loads on highways and their influences on bridges in order to achieve safe and economical freight transportation. Each state department of transportation has either developed or adopted vehicle load models for highway bridge design. The vehicle models are typically based on statistical analysis of vehicle load and configuration. A design vehicle is a vehicle used as a representation of vehicular loads on highway bridges. In some states the current vehicle load models and their corresponding effects do not envelope the overload vehicle effects, recommendation for an enveloping vehicle model is made. A methodology is proposed for the establishment of a design permit vehicle that will predict loading effects (shear and moment) caused by a population of special hauling permit vehicles, specifically from the heaviest state-issued superload permits. This study will demonstrate using databases obtained from a department of transportation and a forecasting of future vehicle loads. A review of the available published literature directly relating to the relevant issues of the present study will be incorporated, including vehicle load model development processes, particularly special permit load models for slab-on-girder bridges. The present study develops a methodology to establish a new live load model.

9 . Problem Statement Overloaded vehicles, either GVW, axle weight or both, can be allowed to cross bridges with careful analysis and in cases where the overweight vehicles were considered in the original design. States dictate different design permit vehicles. However, previously established design permit vehicles may not sufficiently represent the load effects of current of future overweight loads on state highway bridges. Significant number of permits are issued every day by state departments. As total weight of vehicle increases and number of permit increases it becomes necessary to reconsider bridge design vehicle models to achieve harmless and viable freight transportation. Hence, the effects of the design permit vehicle needs to be evaluated and compared with the effects of the existing overloaded vehicles on state highways. AASHTO specified bridge design life is 75 years. It is very difficult, without knowing future load demands, to design a bridge for heavy vehicle loads. Extrapolation of CDFs of shears, moments and axle loads can be used to predict future vehicle load requirements. Construction of a vehicle model anticipating future loads can be a key factor in ensuring the design life of the bridge. Very little information has been published regarding the study and development of design vehicles on the basis of a permit vehicle database. The present study will develop a methodology to establish a new permit design vehicle model. The study will also propose forecasting techniques for development of vehicle models based on forecasting loads. 3

10 . Research Objectives: A primary objective is to propose, through demonstration of analytical and statistical analysis of a sample WIM and superloads vehicle database, a design permit vehicle development process. The objective is to provide a step-by-step methodology to develop a new permit design vehicle from a standard format vehicular database. This research will present a generalized method to develop bridge design vehicle models that account for permitted overload vehicles..3 Scope of Research The scope of present studies is limited WIM and superloads database as inputs. WIM and superload vehicles have number of axles varying from -axle to 9-axle. Vehicle considered from both databases are single lane (width < ft) vehicle. Analysis of data will be done assuming one, two and three-span hypothetical bridges. Numerical analysis of vehicles will be completed for the following spans: Simple span Girder Bridges: 8, 6, 4, 40, 60, 80, 00, 44, 00, and 50 ft. Two-span Girder Bridges: 00 ft total length with 00-ft and 00-ft spans 303 ft total length with 88-ft and 5-ft spans Three-span Girder Bridges: 355 ft total length with 00-ft, 55-ft and 00-ft spans 80 ft total length with 40-ft, 00-ft and 40-ft spans Bridge details required to evaluate transverse distribution are not available the 4 bridges considered for analysis are described on the basis of span only computation of transverse distribution is not possible. Selection of partial load factors and dynamic load allowance is not covered in this study. 4

11 .4 Tasks Present study requires the following tasks to accomplish the objectives: Gather and evaluate information on overloaded vehicles operating on highways. Develop analytical tools to calculate maximum responses for gathered vehicular database. Run analysis to utilize the procedures and tools developed to evaluate maximum bridge moments and maximum bridge shears for all bridges of interest under the filtered superload database and WIM database. Process analytical data to identify vehicle configurations that best envelope the overloaded vehicles effects. Propose one or more new permit vehicle classified according to the bridge spans or other pertinent factors. Establish a methodology to validate the axle load distributions and develop a load model for heavy future loads. 5

12 Chapter iterature Review The objective of this literature review is to conduct a review of the available published literature directly relating to the relevant issues of the present study. The primary topics of the literature review are: Vehicle load model development processes, particularly special permit load models; Statistical modelling of data for forecasting Studies pursuing the development of vehicle design models on the basis of both WIM vehicle databases and permit vehicle databases have been reviewed. Since the early 990s, the use of WIM equipment has advanced significantly with the consequence of databases collected in nearly every state in the United States. These databases are extremely large and useful to an extent; however, there are biases and limits to conclusions that can be derived from WIM databases. There are limited published studies of WIM data characteristics and the development of design vehicles; however, very little published information is available regarding the study and development of design vehicles on the basis of permit vehicle databases. The statistical approaches and slight variations in each study have been reviewed here.. State Permit Design Vehicles Each state has different design permit vehicle depending upon the vehicular traffic and load requirements of individual state. Figure. to Figure.6 represents state design vehicle for Pennsylvania, California, New York, Oregon, and Connecticut. Figure. represents Three California design permit vehicles. Figure. is one New York design permit vehicle. Figure. and Figure.4 are two Oregon design permit vehicles. Figure.5 and Figure.6 are two Connecticut design permit vehicles. Figure.7 is Pennsylvania state design permit vehicle. 6

13 6K 48K 48K 48K 48K 48K 48K 4'-6" '-3" 8'-0" 8'-0" 8'-0" 8'-0" 8'-0" 8'-0" P9 6K 48K 48K 48K 48K - - P 6K 48K 48K 48K 48K 48K - P3 6K 48K 48K 48K 48K 48K 48K Figure., California Permit Design Vehicle. 0K 8K 8K 3K 3K 3K K K K K K 9' 4' 4' 4' 4' 0' 4' 4' 4' 4' Figure., New York Permit Design Vehicle. K 4K 4K 4K 4K 4K 4K 4K 4K 8' 4.5' 4' 5' 3' 5' 6' 4.5' Figure.3, Oregon Design Permit Vehicle (OR-STP-5BW). 8K 0K 0K 0K 0K 0K 0K 0K 0K 0K 0K 0K 0K 5.5' 4.5' 5' 5' 5' 43' 5' 5' 6' 5' 5' Figure.4, Oregon Design Permit Vehicle (OR-STP-4E). 7

14 0.3K.8K 0.3K 0.3K K K K 0.3K 0.3K 0.3K 0.55K 0.55K 0.55K 9.7K 9.7K 9.7K 0.55K 0.55K 0.55K 4.08' 5' 5' 4.08' 5' 5' 4.08' 5' 5' 47' 5' 5' 4.08' 5' 5' 4.08' 5' 5' Figure.5, Connecticut Design Permit Vehicle (CT-P380). 3.5K 8K.5K.5K 63.7K 64.9K 8K 8K 38.5K 9.6' 4.' 4.5' 8' 4.33' 4.75' 3' 6.5' Figure.6, Connecticut Permit Design Vehicle (CT-TC). 5K 7K 7K 7K 7K 7K 7K 7K ' 4' 4' 4' 5' 5' 5' Figure.7, Pennsylvania Permit Design Vehicle (P-8). 8

15 . Vehicle oad Model Development Published literature describing the development of bridge design load models on the basis of WIM data and permit vehicle database as well as the statistical analysis methodologies employed in the process are discussed herein. WIM data collection has become prevalent throughout the United States. Also, databases of vehicles receiving permits for legal travel above legal load limits are collected by many jurisdictions and provide a useful source for evaluation of current design vehicles as well as a source for development of new design vehicles. Design vehicle models are typically developed by performing statistical analysis of database information including evaluation of GVW, axle spacing, and individual axle weights. To better understand and identify the critical vehicle configuration, vehicles are typically categorized into classes for further analysis. The process to identify the particulars of a design vehicle are fundamentally the same for both WIM and permit vehicle databases. Articles relevant to this process are reviewed in this section... Vehicle Development based on WIM Data In order to understand the vehicle characteristics on highways, WIM data can be very useful. WIM data, when collected over long periods in locations unknown to the public, can offer a substantially unbiased sample of vehicle parameters, including GVW, individual axle loads, and axle spacing. WIM data file vehicles can then be used to numerically determine bridge response over a range of spans and configurations to enable comparison with established design and rating vehicles. Vehicle records have been used to evaluate and develop vehicle models for bridge design and evaluation. Vehicle traffic is constantly monitored at WIM stations, that results in extremely large data files that can be statistically analyzed and predictions well into the future can confidently be made. Because WIM data files often contain millions of vehicle records, most of which are not of 9

16 interest for the development of model vehicles, the WIM data must be filtered and reduced. There are a number of filtering or data reduction approaches that have been employed. Zhao and Tabatabai (0) filtered and reduced a 6-million-vehicle Wisconsin WIM data file to extract vehicles of a particular classification and then identify vehicle groups in terms of axle configuration with particular interest in 5-axle vehicles. Zhao and Tabatabai examined vehicle records that were separated into 3 classes based on configuration according to the Federal Highway Administration (FHWA) Traffic Monitoring Guide (995) as described in Table.. Table. FHWA Vehicle Classes FHWA Vehicle Class No. FHWA Vehicle Class Name Class Motorcycles Class Passenger Cars Class 3 Other Two-Axle, Four-Tire Single Unit Vehicle Class 4 Buses Class 5 Two-Axle, Six-Tire, Single-Unit Trucks Class 6 Three-Axle, Single-Unit Trucks Class 7 Four or More Axle Single-Unit Trucks Class 8 Four or Fewer Axle Single-Unit Trucks Class 9 Five-Axle Single-Trailer Trucks Class 0 Six or More Axle Single-Trailer Trucks Class Five or Fewer Axle Multi-Trailer Trucks Class Six-Axle Multi-Trailer Trucks Class 3 Seven or More Axle Multi-Trailer Trucks FHWA vehicle classes 4 or less represent smaller vehicles and were excluded from analysis. FHWA classes 5 through 5 were retained. In order to manage the large quantity of vehicle data, a statistical analysis of each vehicle class was completed to determine the vehicle distribution in 0

17 each class. To accurately represent analysis and simulations it was determined that 5% of the heaviest gross vehicle weight vehicles in each class/group (i.e., vehicles that weigh more than the 95 th percentile) would be used to evaluate bridge response and identify the critical vehicle. Bridge moments and shears due to the heaviest 5% of vehicles were calculated in three types of bridges, single span, -span and 3-span continuous girder bridges, and compared to the bridge response induced by the Wisconsin design vehicle, the Wisconsin Standard Permit Vehicle (Wis-SPV), as presented in Figure.. Figure.8, Wisconsin Standard Permit Vehicle Wis-SPV (Zhao and Tabatabai, 0). The analysis of all other vehicle classes indicated that 5-axle, short-length vehicles cause larger moments than the Wis-SPV. The moment and shear ratios were combined and plotted to simplify data presentation, though the distribution of maximum negative moment ratios showed a somewhat different pattern. A generalized extreme value distribution was used to best fit the distribution of moment and shear ratios, though a log-normal distribution fit the ratios equally well. Zhao and Tabatabai found that conducting a moving load analysis for all WIM vehicles of an entire vehicle class was computationally expensive. To test the hypothesis that the heaviest 5% of vehicles in a vehicle group was sufficient for developing a design vehicle model, 50 vehicles were randomly selected from the heaviest 5%. These 50 vehicles were simulated on all three bridge configurations with two randomly selected span lengths. An extreme value distribution was found

18 to be appropriate for fitting the obtained moment and shear response ratios because the 50 vehicles were selected from the heaviest group of vehicles. In order to investigate the vehicle data used by Nowak (999) in calibrating the AASHTO RFD Bridge Design Specifications, Kozikowski (009) plotted cumulative distribution functions (CDFs) of WIM vehicle moment to H-93 moment ratio and WIM vehicle shear to H-93 shear. Filters were introduced to remove the bias for lightly loaded vehicles that had no effect on the comparison. Kozikowski s analysis of the WIM data suggested that live load is strongly site specific. Kozikowski developed three types of load models: heavy, medium and light, after analyzing WIM data that included 47 million vehicles. Cumulative distribution functions of load effects were extrapolated assuming a 75-year bridge design life. After comparing maximum bridge moment due to Ontario design vehicles from Ontario Highway Design Code (OHBC 979), it was demonstrated that on average, Ontario vehicles are heavier than WIM vehicles obtained for the study recorded from New York WIM GVW exceeds Ontario design vehicle GVW. A sensitivity analysis of New York WIM revealed that there were extremely heavy vehicles in the file, which resulted in the conclusion that permit vehicles must have been present. Miao and Chan (00) used a repeatable methodology to obtain daily moments and shears using 0 years of WIM data collected in Hong Kong rather than the more widely used method of extending the tails of data through the use of normal probability functions. Based on WIM data collected at five different sites, moments and shears induced by extreme daily vehicles were calculated to develop a vehicle model. Vehicles were classified into three categories short vehicles (vehicle length less than 40 ft), medium combined vehicles (vehicle length between 40 ft and 50 ft) and long combined vehicles (vehicle length greater than 50 ft). For each category, maximum moments and shears were calculated. From these response results, a Hong Kong bridge design vehicle model was developed, with the goal that bridge moments and shears induced by the

19 proposed Hong Kong bridge design vehicle model will be similar to those induced by the WIM database vehicles... Vehicle Development Based on Permit Vehicle Data Generally, vehicles operating on the highway system in a particular state will conform to standard sizes and weights in order to comply with legal load limits of that state. Frequently, legal axle loads and configurations must be exceeded to transport large loads such as heavy construction equipment, industrial equipment, or other materials or objects. To allow for these heavy loads, permits are requested of, and issued by, the governing bridge authority. This process results in the accumulation of permit vehicle configurations over time. NCHRP Report 368 (999) describes the calculation of load and resistance factors for the AASHTO RFD bridge design code by evaluation load model specified by AASTHO. oad and resistance models are described by cumulative distribution functions. CDFs for live loads and dead loads were derived using available statistical data and then extrapolated to predict the effects of load models for 75 years. ive-load parameters were derived with an assumption of no increase in vehicle weight; if weight increases, then load factors should be recalculated. Zhao and Tabatabai (009) compared the moment and shear load effects due to the Wis-SPV with single-trip permit vehicles. In reviewing distributions of permit vehicle GVW, it was observed that the data is widely scattered with a peak GVW equal to 90 kips. Almost all permit vehicles were longer than 50 ft and more than 50% of the permit vehicles were longer than 75 ft. The distribution of number of axles for permit vehicles indicates that the majority of vehicles were between 3 axles and 5 axles. Vehicles were separated into classes with the purpose of identifying a representative vehicle for each class based on configuration characteristics. The characteristics were quantified by evaluating maximum, minimum, mean, and standard deviation of the relevant configuration parameters. Axle weights for each of the representative vehicles are the 95 th 3

20 percentile value of the corresponding distribution of each class. Axle spacings corresponding to the 5 th percentile and the 95 th percentile define the range of a variable spacing per vehicle. Comparison of this representative permit vehicle of each class with Wis-SPV demonstrated that the Wis-SPV is reasonably representative within the permit vehicle database to reflect the load effects on simply supported, -span and 3-span continuous bridges for most vehicles with less than nine axles. Representative vehicles with seven and eight axles caused larger bridge responses than the Wis-SPV. Vehicles causing larger effects were predominantly short overall length vehicles configured with several axles. Permit vehicles with greater than nine axles, which were about 0% of permit records, may have caused a larger bridge response than the Wis-SPV, as they were heavier than Wis-SPV. Comparison of permit vehicles with neighboring state permit vehicles indicated that longer vehicles cause larger negative moments for two and three-span continuous bridges. It was observed that vehicles with short axle spacing caused severe positive moments and long-spaced vehicles caused large negative moments...3 Statistical Modeling of Experimental Data Recently an increase has been observed in the number of permitted and illegal overweight vehicles travelling over U.S. highways. This has raised concerns over the cost of maintaining and repairing or replacing the highway infrastructure system as well as the adequacy of the current design vehicle models. Fiorillo and Ghosn (04) developed a data mining process to identify and classify overweight vehicles into different permit and illegal categories. WIM data of The New York State Department of Transportation (NYSDOT) was categorized including illegal and permit vehicles. A typical histogram of GVW showed two different peaks, as presented in Figure.. 4

21 Figure.9, WIM GVW distribution (Fiorillo and Ghosn, 04). The peak at 40 kip GVW represents light vehicles or empty larger vehicles. The peak just less than 80 kip GVW represents the loaded, legal vehicles as the GVW legal limit is 80 kips. The long, upper tail represents a significant number of vehicles exceeding the legal weight limit and/or permit vehicles. Unfortunately, most WIM stations are not equipped to identify whether an overweight vehicle is permitted. High GVW vehicles were separated into 3 classes based on FHWA vehicle type classifications. Axle configurations, axle weights, and all other data required for the issue of permits was the basis for developing data mining rules and a technique for an algorithm to execute the mining. The first step of the data mining estimated percentages of permit and illegal vehicles from WIM data, which was completed by classifying vehicles based on the legal weight limits exceeded. The data mining process consisted of two procedures pattern recognition and Bayesian updating. 5

22 Pattern recognition identified vehicle configurations from vehicle data based on certain specified conditions. Bayesian updating subsequent to pattern recognition improved the results by statistically accounting for vehicles that may have been suspected of being illegal but were configured similarly to permit vehicles. The validity of this algorithm was established by comparing the results to those obtained from a survey conducted by NYSDOT using a WIM system equipped with a camera. A NYSDOT survey manually checked the percentage of vehicles that were illegally overweight and those to which permits were issued. The NYSDOT survey results were consistent with the results obtained through the data mining process. Mohammadi and Shah (99) studied the statistics of vehicle weights and configurations on highways. The ability to statistically model vehicle overloads is useful in determining to what extent these overloads will cause damage. The probability of occurrence of specific vehicle axles and corresponding weights from databases permits the determination of the frequency of occurrence of more damaging and heavy postulated loads. This is useful to relevant state agencies during issuance of vehicle load permits. Mohammadi and Shah studied the frequency distributions of 5-axle and 6-axle vehicles to observe that the frequency of loads exceeding 80 kips was relatively high. A mixed probability distribution was used to represent the entire data set, because 5-axle and 6-axle load data presented a different load distribution both above and below the 80-kip legal load. The vehicle load distribution models developed for different vehicles classes provided the information required to predict load intensity and frequency of overloads. Nowak and Ferrand (004) also studied the statistics of bridge WIM vehicle weight data utilizing cumulative distribution functions to compare critical and extreme GVW values. For the data considered in the study, a summary of the number of vehicles for each of several axle counts 6

23 is provided. It was observed that majority of the vehicles were -axle followed by 5-axle vehicles, with the heaviest being -axle vehicles. The maximum GVW ranged from 78 kips to 47 kips, for which CDFs were plotted on normal probability paper. The CDFs permitted the observation that vehicles on certain studied bridges were heavier than on other bridges considered in the study. CDFs were compared with Michigan State Police Motor Carrier Division citation data to validate the results. CDFs of lane moment and shear to H93 moment and shear for a 90-ft span indicated that the statistics of moment and shear are similar with mean approximately 0.9 to 0.35 for each bridge WIM site. The maximum WIM vehicle moment and shear to H93 ratio ranged from 0.6 to.0. Miao and Chan (00) conducted a statistical analysis of WIM data to obtain representative vehicles with distinct numbers of axles. To obtain the necessary statistical parameters, an expected value, standard deviation, and maximum likelihood approach was used. To represent the recorded WIM data through a statistical model, the Kolmogorov-Simnorv (K-S) method was adopted. To simulate the complex random stochastic process, a Monte Carlo Simulation was employed. From the statistical analysis of WIM data, five vehicle configurations were obtained. The five vehicle configurations were able to represent all combinations and occurred with a probability of 98%. These configurations were representative of the maximum permissible vehicle weights within the shortest possible base length..3 Forecasting of Vehicle oad and oad effects Obrien, Enright, and Getachew (00) performed a statistical analysis of GVW for a very large WIM database. The analysis was intended to predict characteristic extreme vehicle load effects. GVWs were mathematically modelled using three different methods parametric, non-parametric, and semiparametric fitting. Daily maximum mid-span bending moments were calculated for a 5-ft, simply supported span subject to a single vehicle load for all three types of mathematical 7

24 modelling methods. Extrapolation of the resulting bridge responses was then performed to obtain a,000-year return value of the same. Extrapolation was performed by fitting a Weibull extreme value distribution to top the n values as presented in Figure.3. Figure.0, CDF of Daily Maximum Design Bending Moments (Obrien et al., 00). Correia and Branco (006) presented a methodology for utilizing permit vehicle databases to check overloads based on an initial statistical study performed to characterize the overload vehicles. The characterization of vehicular overloads included a definition, analysis of transported materials, analysis of origins and destinations, analysis of transportation companies, analysis of loads, and a tentative definition of vehicular overload design loads for each vehicle type by ranges of total weight. Correa and Branco (006) recognized that live load is time varying and can be extrapolated to determine the maximum expected load effects for a particular future date. Vehicle occurrence and GVW are random variables that are required to predict extreme values for a given time interval. Selection of the H93 by the RFD Bridge Design Specifications (004) writers was based in part on force effects caused by a -week heavy-vehicle dataset Novak (999). The force effects 8

25 were assumed to be normally distributed, and simple-span positive bending, simple-span shear, and two-equal-span negative bending for 30ft - to 00-ft span lengths were extrapolated to those expected in 75 years. The implied design load was approximately 5% greater than that shown to occur in two weeks. Kozikowski (009) also extrapolated cumulative distributive functions of shear to predict maximum live load effect that will occur in 75 years for different highways of different states. Hida (007) showed that the vehicle load is a time varying process, which can be modeled as a Poisson process, the intensities of which are also time-dependent variables where the average occurrence can be calculated using a Poisson distribution. In probability and statistics, The Generalized Extreme Value (GEV) distribution is a flexible three-parameter model that combines the Gumbel, Fréchet and Weibull maximum extreme value distributions. It has following PDF: f ( x) / k / k exp( ( kz) )( kz) k 0 (.) f ( x) exp( z exp( z)) k = 0 (.) where z=(x-µ)/σ, and k, σ, µ are the shape, scale, and location parameters respectively. The scale must be positive (sigma>0), the shape and location can take on any real value. The extreme value distributions can be easily fitted to your data using either automated fitting capability of matlab. To compare the fit of the extreme value distribution and select the best fitting model, the goodness of fit tests and distribution graphs are used. 9

26 .4 Summary Studies examining WIM vehicle databases, permit vehicle databases, and the statistical analyses employed for determining a statewide design vehicle have been reviewed. There is very limited available, published information regarding permit databases employed for the purpose of developing a design vehicle to encompass anticipated permit vehicle effects; however, there is broad consensus on the methodology to be used in developing design vehicles on the basis of a database. Other studies peripherally related to the present study were briefly reviewed; however, the contribution of these studies to the present work is of interest but of very limited value. 0

27 Chapter 3 Analytical Programs Analytical tools were developed to evaluate the vehicle data files for moment and shear created in several hypothetical bridges. A filtering tool is also developed to remove vehicles from the file that are of low GVW. Primary analytical tools will enable an automated procedure to simulate passage of a large number of vehicles over the selected bridge spans & configurations to obtain the maximum moment and shears. The analytical tools are designed to simulate the passage of a vehicle across a bridge and compute the maximum shear response at any location, maximum positive moment response at any location, and maximum negative moment at any location (if appropriate). This requires the development of general influence line functions capable of describing an infinite number of influence lines shear or moment at any location for any span or combination of spans. Influence line functions were developed considering specified bridge geometries. These influence line functions are presented in equations 3. to 3.6. Notation for the functions is as follows: x = the position of the unit load a = the location of the effect (moment or shear) of interest P = unit load in first span, P = unit load in second span, = + Simple span influence line functions were derived for shear and moment for any bridge length. Two-span influence line functions were derived for shear and moment for any bridge length for

28 any combination of equal or unequal length. Three-span influence lines functions were derived for shear and moment with one restriction that the exterior spans must be of equal length. MATAB codes were developed to analyze vehicle database. The algorithm of simulating the driving of each vehicle across the bridge to obtain maximum shear and moment induced by each vehicle is described below:. Describe the bridge geometry.. Beginning from the left support, calculate the influence line for either shear or moment depending on the analysis being conducted. 3. Position the vehicle on the influence line as it enters the bridge from left to right, steering axle starting at the support. 4. Compute the shear or moment at the first location of interest (a), beginning at the left support. 5. Increment the vehicle position by a - 0 to the right. 6. Compute the shear or moment at the same location of interest (a) again. 7. Continue incrementing the vehicle position until it has driven across the entire bridge. 8. Discard all but the maximum shear or moment, and save the result. 9. Increment the location of the influence line - 0 to the right to consider a new location of interest (a). 0. Drive the same vehicle across the bridge again in the same - 0 increment process as described in (5), discard all but the maximum shear or moment and save the result.. This process continues until every location on the bridge ( - 0 ) is evaluated for shear and moment and the maximum is determined anywhere for that particular vehicle.. The process begins over again starting at step for the next vehicle in the file. 3. Then the entire process is repeated, but with the vehicles traveling right to left.

29 A flowchart describing matlab steps is presented in Figure 3.: Input File (WIM/Superloads) Initialize Matrices for Axle oad and Spacing Yes Filtering (w.r.t GVW of Vehicle) If GVW > 08 Kips No Discard Data No Z= to n Analysis for Each filtered truck (Z) If z > total trucks Yes a= to End Select Point for maximum response (a) No Z = Z+ Xi = to (+length of truck) If a > Yes Save Maximum response for previous truck x a Check if the axle is on bridge (x) x > x > a Calculate response of axle M/S Calculate response of axle M/S Axle not on bridge M/S = 0 a = a+ Maximum response for selected truck position M+M+M3 x = x+ If last axle has crossed the bridge Saved in matrix max response for selected (a) Yes Figure 3., Flowchart describing Matlab Steps. 3

30 3. Simple Span 3.. Simple Span Moment Influence ine For 0 x a: M a Figure 3., Simple-Span Moment Influence line = 50 ft, a = 00 ft. P a x (3.) For a x : a M a P x a (3.) 3.. Simple Span Shear Influence ine Figure 3.3, Simple-Span Shear Influence line = 50 ft. x R A P (3.3) 4

31 x P R B (3.4) 3. Two-Span 3.. Continuous, Two Span, Positive Moment Influence ine Figure 3.4, Two-Span Moment Influence line = 88 ft, = 5 ft, a = 5 ft. For x<: 3 ) ( x x P x P R A (3.5) If x < a : ) ( x a P a R M A a (3.6) If x > a : a R M A a (3.7) For >x > : 3. ) ( x x P R A (3.8) a R M A a (3.7) 5

32 3.. Continuous, Two Span, Negative Moment Influence ine Figure 3.5, Two-Span Negative Moment Influence line = 80 ft, = 0 ft, a = 80 ft. For 0 x : 3 ) ( x x P M B (3.9) For x : 3. ) ( x x P M B (3.0) 3..3 Continuous, Two Span, Shear Influence ine at Support Figure 3.6, Two-Span Shear Influence line = 88 ft, = 5 ft, a = 0 ft. 6

33 For 0 x : 3 ) ( x x P x P R A (3.5) For x : 3 ) ( x x P R A (3.8) 3.3 Three-Span 3.3. Continuous, Three Span, Negative Moment Influence ine Figure 3.7, Three-Span Negative Moment Infl line = 3 = 00 ft, = 55 ft, a = 00 ft. For 0 x : ) ( ) ( 3 x x P M B (3.) ) ( ) ( ) ( 3 x x P M C (3.) 7

34 For x : 4 K K P M B (3.3) 4 K K K P M C (3.4) For x : ) ( K K ap M B (3.5) a M M B a 3.3. Continuous, Three Span, Positive Moment Influence ine Figure 3.8, Three-Span, Moment Influence line = 3 = 00 ft, = 55 ft, a = 70 ft. For a < : If x < : ) ( ) ( 3 x x P M B (3.) ) ( x P M R B A (3.5) 8

35 If x < a: ) ( x a P a R M A a (3.6) If x > a: a R M A a (3.7) If < x < 4 K K P M B (3.) a M M B a For x : ) ( K K ap M B (3.5) a M M B a Figure 3.9, Three-Span, Moment Influence line = 3 = 00 ft, = 55 ft, a = 50 ft. 9

36 For a >: If x < : ) ( ) ( 3 x x P M B (3.) a a M M B a (3.6) If < x < : 4 K K P M B (3.) 4 K K K P M C (3.4) ) ( x P M M V C B C (3.7) BR V C P V (3.8) If x > a: ( ) a V M M BR B a (3.9) If x < a: ) ( ) ( x a P a V M M BR B a (3.0) 30

37 3.3.3 Continuous, Three Span, Shear Influence ine at Support Figure 3.0, Three-Span Shear Influence line = 3 = 00 ft, = 55 ft, a = 0 ft. For x < : ) ( ) ( 3 x x P M B (3.) ) ( x P M R B A (3.5) For < x < : 4 K K P M B (3.) M R B A (3.) ) ( x P M M V C B C (3.7) BR V C P V (3.8) 3

38 For x > : ) ( K K P R A (3.) where: 3 x x K (3.3) 3 x x K (3.4) 3 x K (3.5) (3.6) On the basis of the above Equations 3. through 3.4 that are the influence lines for moment and shear, the analytical tools have been developed to place the vehicles at -ft increments across the several bridge spans, collect the results, and evaluate the maximum effect. The simulations were performed to utilize the procedures and tools developed to evaluate maximum bridge moments and maximum bridge shears for all bridges of interest and results of simulations are presented in the following chapter. 3

39 Chapter 4 Simulation and Presentation of Results The objective of the simulations is to utilize the procedures and tools developed to evaluate maximum bridge moments and maximum bridge shears for all bridges of interest due to the filtered WIM vehicles and Superload. Simulations were conducted for following bridge geometries: Simple span girder bridges: 8, 6, 4, 40, 60, 80, 00, 44, 00, and 50 ft Two-span girder bridges: - 00 ft total length with 00-ft and 00-ft spans ft total length with 88-ft and 5-ft spans Three-span girder bridges: ft total length with 00-ft, 55-ft, and 00-ft spans - 80 ft total length with 40-ft, 00-ft, and 40-ft spans The WIM data files utilized were collected during each month of 04. The superloads database consists of,508 combined permit vehicle configurations and axle weights collected from February 03 to March 05 as described in Appendix A. The superloads database includes individual axle weights, axle spacing, and track width. The analytical tools were developed to read vehicle configurations from the database and compute maximum moments and shears for each vehicle in the database. Based on the results of the simulations and subsequent comparisons presented in Figures 4. through 4.6, further processing of vehicle data was initiated in anticipation of developing a proposed permit design vehicle. Identification of vehicle configurations (WIM and superload) that cause bridge responses (shear and moment) greater than the current design live load vehicle was completed. 33

40 4. Comparison with State Design Permit Vehicle A direct, one-to-one comparison of WIM and superload vehicles is performed. This one-toone comparison is accomplished through ratios of:. Positive bridge moment caused by WIM or superload vehicles to the same caused by the P-8;. Negative bridge moment caused by WIM or superload vehicles to the same caused by the P-8; and 3. Bridge shear caused by WIM or superload vehicles to the same caused by the P-8. For single-span bridges, maximum shears and moments, normalized to P-8 shear and moment, for each vehicle are presented in Figures 4. and 4. for WIM database and Figures 4.5 and 4.6 for superload database for spans ranging from 8 ft to 50 ft. For two-span and three-span bridges, normalized maximum positive moment, maximum negative moment, and maximum shear of each vehicle are represented in Figures 4.3 and 4.4 for WIM database and Figures 4.7 and 4.8 for superloads database for each of the two-span geometries defined. All data points lying above.0 represent vehicles that cause shear and moment effects in excess of P-8. These WIM and superload vehicles were forwarded into the process of developing the permit design vehicle, heretofore referred to as Extra-Design-Effect vehicles. It is important to recognize that WIM vehicle databases contain vehicles traveling within normal traffic and cannot be identified as not being permit vehicles; therefore, the WIM data presentation must be viewed and considered in that context. 34

41 .4..0 M veh /M P Span (ft.) Figure 4., All WIM Vehicles, MWIM/MP8 vs. Simple Span ength V veh /V P Span (ft.) Figure 4., All WIM Vehicles, VWIM/VP8 vs Simple Span ength. 35

42 M veh /M P M veh /M P Bridge Bridge Bridge Bridge (a) Positive MWIM/MP8 vs. Two-Span (b) Negative MWIM/MP8 vs. Two-Span.6.4. V veh /V P Bridge Bridge (c) VWIM/VP8 vs. Two-Span Figure 4.3, All WIM Vehicles vs. Two-Span Bridges (Bridge = 5ʹ - 88ʹ, Bridge = 00ʹ - 00ʹ) 36

43 M veh /M P M veh /M P Bridge Bridge Bridge Bridge (a) Positive MWIM/MP8 vs. Three-Span (b) Negative MWIM/MP8 vs. Three-Span V veh /V P Bridge Bridge (c) VWIM/VP8 vs. Three-Span Figure 4.4, All WIM Vehicles vs. Three-Span Bridges. (Bridge = 00ʹ - 55ʹ - 00ʹ, Bridge = 40ʹ - 00ʹ - 40ʹ) 37

44 M SUPEROAD /M P Span (ft.) Figure 4.5, Superload Vehicles, MSuper/MP8 vs. Simple Span ength. V SUPEROAD /V P Span (ft.) Figure 4.6, All Superload Vehicles, VSuper/VP8 vs. Simple Span ength 38

45 M SUPEROAD /M P M SUPEROAD /M P Bridge Bridge Bridge Bridge (a) Positive MSuper/MP8 vs. Two-Span (b) Negative MSuper/MP8 vs. Two-Span V SUPEROAD /V P Bridge Bridge (c) VSuper/VP8 vs. Two-Span Figure 4.7, All Superload Vehicles vs. Two-Span Bridges. (Bridge = 5ʹ - 88ʹ, Bridge = 00ʹ - 00ʹ) 39

46 3.5 M SUPEROAD /M P M SUPEROAD /M P Bridge Bridge Bridge Bridge (a) Positive MSuper/MP8 vs. Three-Span (b) Negative MSuper/MP8 vs. Three-Span V SUPEROAD /V P Bridge Bridge (c) VSuper/VP8 vs. Three-Span Figure 4.8, All Superload Vehicles vs. Three-Span Bridges. (Bridge = 00ʹ - 55ʹ - 00ʹ, Bridge = 40ʹ - 00ʹ - 40ʹ) 40

47 4. Comparison to AASHTO ive oad Model HS0 All WIM and superload vehicle maximum shears and moments are compared to HS0 maximum shears and moments for all 4 span configurations, as presented through Figures 4.9 to 4.6. For single-span bridges, normalized maximum shears and moments for each vehicle are presented in Figures 4.9 and 4.0 for WIM database and Figures 4.3 and 4.4 for superload database for spans ranging from 8 ft to 50 ft. For two-span and three-span bridges, the normalized maximum positive moment, maximum negative moment, and maximum shear of each vehicle are represented in Figures 4. and 4. for WIM database and Figures 4.5 and 4.6 for superload database for each of the two-span geometries defined. Many vehicles were observed to produce more effect than P-8 from WIM and Superload vehicles database. All the vehicles falling above black highlighted line from Figure 4. to Figure 4.8, producing effect more than the state permit design vehicle, are processed in Chapter 5 for the purpose of developing a permit design vehicle. 4

48 M veh /M HS Span (ft.) Figure 4.9, All WIM Vehicles, MWIM/MHS0 vs. Simple Span ength V veh /V HS Span (ft.) Figure 4.0, All WIM Vehicles, VWIM/VHS0 vs. Simple Span ength 4

49 M veh /M HS M veh /M HS Bridge Bridge Bridge Bridge (a) Positive MWIM/MHS0 vs. Two-Span (b) Negative MWIM/MHS0 vs. Two-Span V veh /V HS Bridge Bridge (c) VWIM/VHS0 vs. Two-Span Figure 4., All WIM Vehicles vs. Two-Span Bridges (Bridge = 5ʹ - 88ʹ, Bridge = 00ʹ - 00ʹ) 43

50 M veh /M HS M veh /M HS Bridge Bridge Bridge Bridge (a) Positive MWIM/MHS0 vs. Two-Span (b) Negative MWIM/MHS0 vs. Two-Span V veh /V HS Bridge Bridge (c) VWIM/VHS0 vs. Two-Span Figure 4., All WIM Vehicles vs. Three-Span Bridges. (Bridge = 00ʹ - 55ʹ - 00ʹ, Bridge = 40ʹ - 00ʹ - 40ʹ) 44

51 M SUPEROAD /M HS Span (ft.) Figure 4.3, Simple Span Bridges Msuperload/MPH93/P8 vs Span V SUPEROAD /V HS Span (ft.) Figure 4.4, Simple Span Bridges Vsuperload/VPH93/P8 vs Span 45

52 M SUPEROAD /M HS M SUPEROAD /M HS Bridge Bridge Bridge Bridge (a)+msuper/mhs0 vs Two-Span (b) -Msuper/MHS0 vs Two-Span V SUPEROAD /V HS Bridge Bridge (c) Vsuper/VHS0 vs Two-Span Figure 4.5, All Superload Vehicles vs. Two-Span Bridges. (Bridge = 5ʹ - 88ʹ, Bridge = 00ʹ - 00ʹ) 46

53 M SUPEROAD /M HS M SUPEROAD /M HS Bridge Bridge Bridge Bridge (a) +Msuper/MHS0 vs Three-Span (b) -Msuper/MHS0 vs Three-Span V SUPEROAD /V HS Bridge Bridge (c) Vsuper/VHS0 vs Three-Span Figure 4.6, All Superload Vehicles vs. Three-Span Bridges. (Bridge = 00ʹ - 55ʹ - 00ʹ, Bridge = 40ʹ - 00ʹ - 40ʹ) 47

54 Chapter 5 Development of Permit Design Vehicle Model Data processing of the previous section indicated that certain WIM vehicles (a total of 36) and superload vehicles (a total of,879) cause shear and moment effects in excess of the P-8. These WIM and superload vehicles that exceed P-8 effects are referred as Extra-Design-Effect vehicles. Extra-Design-Effect vehicles are processed for the purpose of developing a permit design vehicle. Extra-Design-Effect vehicles are analyzed to identify new vehicle configurations that envelope the load effects of both the WIM database and the superload database, leading to a permit vehicle design model. This chapter describes and demonstrates the methodology used to construct a permit design vehicle using WIM and Superload vehicle database. 5. Objective and Methodology The objective is to construct a permit design vehicle model that envelopes all Extra-Design- Effect vehicles. Permit design vehicle construction requires processing of the Extra-Design-Effect vehicles by characterizing the population by vehicle width, number of axles, axle spacing, axle loads, axle group loads, and GVW. Axle were Characterization for a given vehicle class includes averages, standard deviations, 95 th percentiles, and maximums, as is described in this section.. Axle groups were defined keeping in mind the common configurations in vehicular database. Commonly all vehicle configurations had group of three axles. WIM measurements have discrepancy while measuring individual axle load values which are closely spaced. Grouping of axles will reduce the discrepancy while measuring axle loads. The evaluation and characterization of the Extra-Design-Effect vehicles to construct a permit design vehicle is a multi-step process. The methodology of the characterization and eventual construction of the prototype permit design vehicle is as follows: 48