Development of LRFD Specifications for Horizontally Curved Steel Girder Bridges (2006)

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62.1 Literature Search The scope and intent of the literature search was to continue the exhaustive literature survey conducted as Phase I of the FHWA-funded project,“Curved Steel Bridge Research Project” (DTFH61-93-C-00136) and published as Interim Report I: Synthesis (17). Although the report date of the synthesis is December 1994, the cut-off date of the literature survey activity is assumed to be June 1993. Therefore, the literature collected and included in the updated literature search (12) are those published after June 1993 and up to January 2000, the dates the original and updated searches were conducted, respectively. A copy of the literature search report is included as Appendix A. 2.2 Design Specifications The results of the FHWA-sponsored research indicated that resistance formulations applicable to both straight and curved systems could be developed. This led to a decision by the technical panel directing the work of the NCHRP 12-52 project to archive the curved girder design provisions devel- oped under Phase I of the project and to develop a new set of design provisions based on the FHWA-sponsored work. The latter set of provisions was determined to be applicable to both straight and curved bridges. These provisions were incorporated into the AASHTO LRFD specification by ballot of the AASHTO Highway Subcommittee on Bridges and Structures (HSCOBS) in 2003 for straight girders. These pro- visions were revised by ballot of HSCOBS in 2004 to incor- porate the curved girder requirements. The straight girder provisions were published in the third edition of the AASHTO LRFD specifications in 2004, and the curved bridge requirements were published in AASHTO’s 2006 interim specifications. The theoretical developments behind the design provisions balloted by HSCOBS in 2004 for curved bridges were done by others as documented in the references. The role of the NCHRP 12-52 project was to implement that work in the AASHTO LRFD specifications. 2.3 Calibration 2.3.1 Scope The objective of this section is to document the calibration of the design code for steel curved girder bridges, consistent with the AASHTO LRFD specifications. It is assumed that load factors for curved girders remain the same as for straight gird- ers. Therefore, the focus is on the determination of resistance factors. The calibration study was conducted by the University of Michigan (UMich) and was supervised by Professor Andrzej Nowak. Following is a brief description of the calibration study. More detailed information is included in Appendix C, which is available online at http://trb.org/news/blurb_detail. asp?id=5965. The relationship between the resistance factor, φ, and reli- ability index, β, is a complex function that includes nominal (design) values of load and resistance, and statistical param- eters of load and resistance such as bias factors, λ, and coeffi- cients of variation, V. The bias factor is defined as the ratio of mean-to-nominal value, and coefficient of variation is the ratio of standard-deviation-to-mean value.The statistical parameters were derived for straight girders (18, 19). An important part of this calibration is to determine values of these parameters for curved girders. The statistical load model developed for straight bridges (19) includes the maximum expected effects of dead load and live load and dynamic load. The maximum truck weights corresponding to various periods of time up to 75 years were determined by extrapolation of truck survey results. The multiple-truck presence in a lane and in adjacent lanes was considered based on field observations and by Monte Carlo simulations.The statistical parameters of truck weights, includ- ing extrapolations for longer periods of time, do not depend on bridge curvature. C H A P T E R 2 Findings

7– Number of girders: 4 spaced at 9 feet – Roadway width: 30 feet (two lanes) • Bridge B: – Location: Minnesota – Length: ∼105 feet – Number of spans: 1 simply supported – Radius of curvature: 106 feet – Number of girders: 4 spaced at 8 feet, 4 inches – Roadway width: 28 feet (two lanes) • Bridge C: – Location: Portland, Maine – Name: Fore River Bridge No. 2 – Length: 273 feet – Number of spans: 3 continuous – Radius of curvature: 175 feet – Number of girders: 4 (spaced at 8 feet) – Roadway width: 28 feet (two lanes) 2.3.3 Calibration Procedure The calibration procedure used in the development of the AASHTO LRFD specifications (18, 19) was used to cali- brate the curved bridge design provisions. The major steps of the calibration include the following: 1. Selection of representative structures: Existing and planned structures were considered. The data on the bridges were provided by various state DOTs. Several parameters—such as span, curvature, number of girders, and spacing between the girders—were considered. From the population of curved girder steel bridges, three repre- sentative structures were selected to be used as a reference in this study. Bridge A, which was field tested by the Uni- versity of Minnesota (UMinn), was included in this set. The bridge provided an opportunity to compare analyti- cal and experimental (test) results. 2. Identification of the load and resistance parameters and formulation of the limit state functions: The load param- eters include dead load, live load, dynamic load, and load effects (including bending, torsion, and shear). It is impor- tant to determine the absolute value of load effects in var- ious combinations. The behavior of a girder was assumed to follow the trends observed during testing of curved girder bridges (20). 3. Development of load and resistance models: This step involved gathering the available statistical data and calcu- lating missing and/or additional parameters by simulations. For Bridge A, the work on resistance models included the analysis of results of testing conducted by UMinn and advanced FEM computations to develop a reference for comparisons. For Bridges B and C, the FEM analysis was performed by the UMich, and the results were compared However, the live load effect in a girder (moment and shear) depends on load distribution. In particular, girder dis- tribution factor (GDF) represents the fraction of the lane moment (or shear) per girder. In calibration of the code for straight girders, it was assumed that the bias factor for GDF was 1.0. This means that, on average, the code-specified GDF is equal to the actual GDF. Because of geometry, the load distribution strongly depends on the degree of curva- ture. Therefore, an important task in this study is calculation of the bias factors and coefficients of variation for the load distribution method used in the design. It is assumed that the design analysis is performed using the commercial program developed by Bridge Software Development International, Ltd. (BSDI). To determine the statistical parameters for load distribution, the results of design analysis are compared with field measurements and with results of an advanced finite ele- ment analysis. The bridge resistance model depends on the statistical parameters of materials and geometry. Therefore, the latest available material test data are reviewed and used in derivation of the bias factors and coefficients of variation for moment and shear capacity of curved girders. The statistical parameters of load, load distribution, and resistance are derived for selected structures. The structural and reliability analysis is performed for three representative structures: • Bridge A: Minnesota Bridge No. 27998 • Bridge B: Minnesota Bridge No. 62705 • Bridge C: Fore River Bridge, Portland Maine The calibration work involved the development of load and resistance models, analysis of reliability, selection of the target reliability index, and calculation of load and resistance factors. Three bridges were analyzed using the finite element method (FEM) as part of the calibration. The analytical boundary conditions in the FEM analysis were calibrated using the actual field test data for one bridge (referred to as Bridge A). The objective of FEM analysis for Bridges B and C was to validate the statistical model developed for Bridge A. 2.3.2 Study Bridges The basic parameters for the three bridges considered in this study are as follows: • Bridge A: – Location: Minnesota – Length: 295 feet – Number of spans: 2 continuous – Radius of curvature: 285 feet

8with the analysis carried out by Modjeski and Masters using software marketed by BSDI. 4. Selection of the reliability analysis procedure: There are numerical procedures available, but they were developed for specific limit state functions. Thus, it was most efficient to develop a customized procedure for this project.The reliabil- ity analysis is performed to determine the reliability indices. As in the original calibration, the procedure was performed for a 75-year service life and involved extrapolation. 5. Reliability analysis for the selected representative struc- tures: The reliability indices were calculated for the limit state functions identified in Step 2.The reliability index spec- trum was reviewed to identify the trends and discrepancies. 6. Selection of the target reliability index: The selected tar- get reliability index is consistent with the AASHTO LRFD specifications for straight bridges, as calculated in the Cali- bration Report (19). 7. Calculation of resistance factors: It is assumed that load factors remain the same as in the AASHTO LRFD specifi- cations. However, the load factors for some of the combi- nations that are specific for curved girders may require some special load combination factors. The resistance factors are determined by trial and error. Various possible resist- ance factors were tried (each rounded to the nearest 0.05). For each set of factors, the reliability indices were calculated, and the optimum resistance factors correspond to the closest fit to the target reliability index. 8. Final selection of the resistance factors: This step involves the verification of the calculated factors by additional reli- ability analysis, check of special cases (e.g., combinations with dominating dead load), and selection of load and resistance factors consistent with the rest of AASHTO LRFD specifications. Simplicity of the specifications was an important consideration. 2.3.4 Load Models 2.3.4.1 Load Components The major load components of highway bridges are dead load, live load (both static and dynamic), environmental loads (e.g., temperature, wind, and earthquake) and other loads (e.g., collision and emergency braking). Load components are random variables. Their variation is described by the cumu- lative distribution function (CDF) and/or by parameters such as the mean value, bias factor (i.e., mean-to-nominal ratio), and coefficient of variation. The relationship among various load parameters is described in terms of the coefficients of correlation. The basic load combination for highway bridges is a simul- taneous occurrence of dead load, live load, and dynamic load. Therefore, these three load components are considered in the present study. It is assumed that the economic service life for newly constructed bridges is 75 years. The extreme values of load are extrapolated from the available database. Nominal (i.e., design) values of load components are calcu- lated according to AASHTO’s Standard Specifications for High- way Bridges (hereafter referred to as “AASHTO Standard”) (21) and AASHTO LRFD specifications (10). 2.3.4.2 Dead Load Dead load is the gravity load due to self weight of the struc- tural and nonstructural elements permanently connected to a bridge. Because of different degrees of variation, it is con- venient to consider three components of dead load: weight of factory-made elements (i.e., steel, precast concrete members), weight of cast-in-place concrete members, and weight of the wearing surface (i.e., asphalt). All components of dead load are treated as normal random variables. The statistical param- eters were derived in conjunction with the development of the Ontario Highway Bridge Design Code (OHBDC) (22) and AASHTO LRFD specifications (10), and they are listed in Table 1. The bias factors are taken as used in the previous bridge code calibration work; however, the coefficients of variation are increased to include human error as recommended (23). In case of steel curved girder bridges, the critical load com- bination can occur during construction, prior to composite action with the concrete deck slab. The parameters of dead load during construction are also taken as given in Table 1. The calculation of dead load effects (i.e., moments and shear forces) for curved girders (using girder distribution factors) involves a considerable degree of variation. In this study, the statistical parameters were determined using the field mea- surements performed by UMinn, finite element analysis per- formed by UMich,and calculations performed by UMinn using grillage model for Bridge A. The cumulative distribution function of the stress ratio obtained by UMich and UMinn is plotted on normal probability paper in Figure 1. The average value is 0.95, and the coefficient of variation, V, is equal to 0.12. Therefore, in this study, the bias factor for dead load effect, λ, is equal to 1.00, and the coefficient of variation, V, is equal to 0.15. 2.3.4.3 Live Load Live load covers a range of forces produced by vehicles moving on a bridge. The effect of live load depends on many * Mean thickness equal to 3.5 in. (90 mm). Category of component Bias factor Coefficient of variation Factory-made (precast) 1.03 0.08 Cast-in-place 1.05 0.10 Asphalt surface 1.00* 0.25 Table 1. Statistical parameters of dead load.

parameters, including the span length, truck weight, axle loads, axle configuration, position of the vehicle on the bridge (trans- verse and longitudinal), number of vehicles on the bridge (multiple presence), girder spacing, and stiffness of structural members (slab and girders). The effect of these parameters is considered separately. The live load model was originally determined during the development of the AASHTO LRFD specifications. For curved girder bridges, the spans are mostly 60 to 150 feet (18 to 45 meters). For this span range, the bias factor is 1.25 to 1.35, with the larger value corresponding to shorter spans. The mean value is the 75-year maximum midspan moment, and nominal value is the AASHTO-specified HL-93 load effect in one lane. For two lanes, the maximum 75-year live load is the effect of two trucks side by side, with each truck being equal to the heaviest truck predicted in any 2-month period (19, 24). The ratio of the mean maximum 2-month moment and the mean maximum 75-year moment is 0.85. Therefore, the bias factor for two lanes is a product of 1.25 to 1.35 and 0.85, resulting in 1.05 to 1.15. The girder distribution factors (GDFs) used in the analy- ses were determined using the straight GDF included in the AASHTO LRFD specifications. Both field measurements and FEM analysis were considered when the bias factor for GDFs for curved girders was determined. The CDF of the ratio of stress obtained by UMich and UMinn is shown in Figure 2 on the normal probability paper. For the most loaded components (i.e., girders), the bias factor for GDF is 0.75, with the coefficient of variation being 0.12. The overall bias factor for live load moment in a curved girder is 0.80 to 0.85, and the coefficient of variation is 0.215, including dynamic load. 2.3.4.4 Dynamic Load The dynamic load model was previously developed and was verified by field measurements (25, 26, 27). Dynamic load is a function of three major parameters: road surface roughness, bridge dynamics (i.e., frequency of vibration), and vehicle dynamics (i.e., suspension system). It was observed that dynamic strain and deflection are almost constant and 9 Dead Load -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 Assumed CDF of dead load Stress Ratio in UMich/UMinn Test Inverse Normal Distribution Figure 1. Cumulative distribution function of the stress ratio due to dead load determined for Bridge A.

do not depend on truck weight. Therefore, the dynamic load, as a fraction of live load, decreases for heavier trucks. For the maximum 75-year values,the corresponding dynamic load factor (DLF) does not exceed 0.15 of live load for a single truck and 0.10 of live load for two trucks side by side. The coefficient of variation of dynamic load is about 0.80. The results of the simulations indicate that DLF values are almost equally dependent on road surface roughness,bridge dynamics, and vehicle dynamics. The actual contribution of these three parameters varies from site to site and is very difficult to predict. Therefore, it is recommended to specify DLF as a constant percentage of live load. 2.3.4.5 Load Ratios In the reliability analysis, the absolute values of load com- ponents are not important. However, the relative values of load components affect the statistical parameters of the total load effect. Therefore, load components are expressed in terms of relative values (i.e., load ratios). The ratios of load components are determined for the selected bridges. The cal- culations were performed for Bridge A, as listed in Table 2. For example, D1 equal to 4 and D2 equal to 9.5 means that the ratio of D1/D2 is equal to 4/9.5. The load ratios are different during construction, and these ratios are also shown in Table 2. Similarly, load ratios are calculated for Bridges B and C, and these load ratios are included in Appendix C. Bridges A, B, 10 Live Load -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 Inverse Normal Distribution Stress Ratio in UMich/UMinn Test Figure 2. Cumulative distribution function of the stress ratio due to live load determined for Bridge A. Stage Spans D1* D2* D3* LL* IL* operation 150 ft 4 9.5 0 4.5 0.75 construction 150 ft 4 7.5 0 0.25 0 * D1, D2, D3, LL and IL denote weight of factory-made components, weight of cast-in-place components, weight of wearing surface, live load allowance, and dynamic load allowance, respectively. Table 2. Load ratios considered for Bridge A.

and C are considered representative for the current trends in curved girder bridge design. 2.3.5 Resistance Models For straight girders, the resistance (i.e., load-carrying capac- ity), R, is considered a product of three factors, M, F, and P: where M represents the material properties (i.e., strength), F represents the dimensions or fabrication (i.e., area, cross- section properties such as section modulus, and moment of inertia), and P represents the professional factor (i.e., analysis). In curved girder bridges, there is an additional factor, S, representing system behavior. The statistical parameters of S are based on field tests and FEM analysis. The statistical parameters for materials, fabrication, and the professional factor are all detailed in Appendix C, which is available online at http://trb.org/news/blurb_detail.asp?id=5965. 2.3.6 Calibration Results It was assumed that the load factors remain the same as in the AASHTO LRFD specifications. The objective of the cali- bration was to determine the optimum value of the resistance factor for curved girder bridges. The major difference between a straight bridge and a curved bridge is in the girder distribu- R M F P= tion factors. This is the only major factor that can affect the reliability. The reliability analysis was performed to establish the rela- tionship between the resistance factor and reliability index for the three considered bridges. The results are shown in Fig- ures 3, 4, and 5 for Bridges A, B, and C, respectively. They are also summarized in Table 3. The results indicate that a resistance factor φ equal to 1.0, which is the same resistance factor previously specified for straight bridges for the design cases considered, resulted in an adequate reliability factor (3.70 to 4.51). The details of the analysis and tests of the calibration work are detailed in Appendix C, which is available online at http://trb.org/news/ blurb_detail.asp?id=5965. 2.4 Design Comparisons 2.4.1 Objective The purpose of the design comparisons was to perform a comparison among the three most recent curved girder design specifications: the 1993 Guide Specifications (2), the 2003 Guide Specifications (9), and the 2006 Interim AASHTO LRFD specifications that resulted from NCHRP Project 12-52. 2.4.2 Application of the NCHRP 12-50 Process The core concepts outlined in NCHRP Project 12-50 were used to formulate a subdomain of curved girder bridges 11 0.0 1.0 2.0 3.0 4.0 5.0 6.0 0.80 0.90 1.00 1.10 1.20 1.30 Resistance factor R el ia bi lit y in de x construction operation Figure 3. Reliability index as a function of resistance factor for Bridge A.

to be compared as part of the NCHRP 12-52 research. The NCHRP 12-50 methodology relates to the organization and manipulation of bridge data enough that the methodology can be effectively used as a tool for software testing. One of the other NCHRP 12-50 “use cases” that was documented in the 12-50 report was the use of similar techniques for the pur- pose of comparing the results obtained from different design specifications (or proposed changes to an existing set of design specifications).This particular application of the NCHRP 12-50 methodology fits in well with the curved girder bridge design comparisons outlined herein. The NCHRP 12-50 research team used spreadsheets and databases as tools for generating, storing, and manipulating the input and output data for the various bridge subdomains 12 0.0 1.0 2.0 3.0 4.0 5.0 6.0 0.80 0.90 1.00 1.10 1.20 1.30 Resistance factor R el ia bi lit y in de x construction operation Figure 4. Reliability index as a function of resistance factor for Bridge B. 0.0 1.0 2.0 3.0 4.0 5.0 6.0 0.80 0.90 1.00 1.10 1.20 1.30 Resistance factor R el ia bi lit y in de x construction operation Figure 5. Reliability index as a function of resistance factor for Bridge C.

that were developed under that project. The large volume of data that needed to be manipulated necessitated the use of a large database. In the case of the NCHRP 12-52 research, the amount of data generated was comparatively modest, and it was convenient to use spreadsheets exclusively to accommo- date the input/output and comparative data for this project. Although the NCHRP 12-50 project involved subdomains of hundreds of computer-generated bridges, the majority of the bridges that were used as a basis for comparison in the NCHRP 12-52 research were existing bridges obtained from various state DOTs. These bridges were supplemented with variations to several additional bridges to form a set of bridges termed “simulated bridges.” A strict application of the NCHRP 12-50 method would require the assignment of database keys for the results of interest. However, since the data manipulation was limited to spreadsheets and the NCHRP 12-52 database is not being actively maintained, this part of the process was not carried out (the assignment of the database keys would have to be coor- dinated with the database administrator to avoid conflicts with any existing identifiers). Nonetheless, the input and output data that were generated as part of the NCHRP 12-52 research are tabulated and organized in such a way that does not preclude the addition of this information to an actively maintained NCHRP 12-50 database at a later time. 2.4.3 Methodology Sample information from 32 bridges was collected from various agencies and compiled by Modjeski and Masters, Inc. Bridges 1 through 21 were submitted by state DOTs and/or design agencies and represent real, in-service bridges using typical modern-day construction. Bridges 22 through 32, the “simulated bridges,” are examples that have been modified from existing structures for analysis purposes. The full report for this portion of the project, which contains additional information and further examination of the specifications, is outlined in Appendix D, which is available online at http://trb. org/news/blurb_detail.asp?id=5965. Basic geometric information about the bridges in the sample (e.g., span length and curvature radius) is included in Table 4. Several of the key aspects of the bridges in this sample are as follows: • Most of the bridges are multispan,continuous girder bridges, and 4 of the 32 bridges are single span. • For the greatest portion of the bridges, the critical positive moment section occurred in an end span and the critical negative moment section occurred over the first interior pier. • The critical shear section generally occurred at or near a pier. • The vast majority of the bridges used Grade 50 steel exclu- sively; only two had hybrid sections, both occurring in the negative moment region. Four bridges used Grade 36 steel throughout. • Two of the bridges had haunched girders. • Twenty of the 32 bridges in the sample were transversely stiffened, and none had longitudinal stiffeners. • Among the existing bridges, the longest span of the bridges in the sample was 190 feet, and the minimum radius was 239 feet. 13 Bridge A Bridge B Bridge C Bridge A Bridge B Bridge C 0.80 5.52 5.31 5.40 5.67 6.04 5.59 0.85 5.10 4.89 4.98 5.26 5.64 5.17 0.90 4.70 4.48 4.58 4.85 5.25 4.77 0.95 4.31 4.08 4.19 4.46 4.87 4.38 1.00 3.93 3.70 3.82 4.08 4.51 4.00 1.05 3.56 3.34 3.46 3.71 4.15 3.64 1.10 3.21 2.98 3.11 3.35 3.80 3.28 1.15 2.87 2.65 2.78 3.00 3.47 2.94 1.20 2.54 2.32 2.46 2.67 3.15 2.61 1.25 2.22 2.01 2.15 2.35 2.83 2.30 1.30 1.92 1.71 1.86 2.03 2.53 1.99 1.35 1.63 1.42 1.58 1.73 2.24 1.70 1.40 1.35 1.14 1.31 1.44 1.96 1.42 1.45 1.08 0.88 1.05 1.17 1.69 1.15 1.50 0.82 0.63 0.80 0.90 1.43 0.89 Reliability index, β Construction Operation Resistance factor, φ Table 3. Reliability indices for various values of φ for the considered bridges.

Table 4. General bridge information. G i r d e r 1 / A G i r d e r 2 / B G i r d e r 3 / C G i r d e r 4 / D G i r d e r 5 / E G i r d e r 6 / F G i r d e r 7 / G G i r d e r 8 / H 1 9 0 0 . 6 9 f t 1 9 0 9 . 8 6 f t 1 9 1 9 . 0 3 f t 1 9 2 8 . 1 9 f t 1 4 0 3 . 0 2 f t 2 6 4 1 . 0 8 f t 1 2 8 8 . 3 9 f t 1 1 8 1 . 3 6 f t 1 1 8 1 . 3 6 f t 1 1 8 1 . 3 6 f t 3 9 7 . 6 4 f t 3 8 9 . 7 6 f t 3 8 1 . 8 9 f t N A N A N A 5 6 2 . 0 9 f t 9 4 5 . 0 6 f t 9 5 3 . 8 1 f t 9 6 2 . 5 6 f t 9 3 6 . 3 1 f t 68 in Three-Span Continuous Composite Plate GirderMifflin County (PA) L.R. 470 5 5 4 . 2 5 f t 48 in Centre County (PA) S.R. 6026 CO5 Three-Span Continuous Composite Plate Girder 5 4 Chester & Montgomery Counties (PA) S.R. 0202 SEC. 404 One-Span Composite Plate Girder 2 9 3 . 9 4 f t 68 in6 2 6 3 . 3 1 f t 2 8 7 . 8 1 f t 2 8 1 . 6 9 f t 2 7 5 . 5 6 f t 2 6 9 . 4 4 f t 4 PENN DOT (Hard Copy) PENN DOT (Hard Copy) PENN DOT (Hard Copy) Wyoming DOT (Hard Copy) 3 1 2 2 6 1 4 . 8 3 f t 2 6 2 1 . 3 9 f t 2 6 2 7 . 9 5 f t 2 6 3 4 . 5 1 f t 2 6 0 8 . 2 7 f t UPRR Separation STA 7+084.075 Sweetwater County (WY) Three-Span Continuous Composite Plate Girder 6 17.0 ft40 ft 90 ft Wyoming DOT (Hard Copy)5 Bridge Over Tongue River Sheridan County (WY) Three-Span Continuous Composite Wide Flange Girder 4 0 5 . 5 1 f t 33 in (W 840 x 176)4 44 in 30 ft 6 Illinois DOT (Hard Copy) Illinois DOT (Hard Copy) 5 Wyoming DOT (Hard Copy) Wyoming DOT (Hard Copy) Bridge Over Gunbarrel Creek Park County (WY) Simple-Span Composite Haunched Plate Girder Illinois Route 3 Over Sexton Creek Alexander County (IL) 5 haunched 87 in to 61 in 36 in (W 920 x 271) 1 8 9 1 . 5 3 f t Three-Span Continuous Composite Plate Girder 22.5 ft44 ft 135 ft 1 3 9 7 . 2 4 f t 1 3 9 1 . 4 7 f t 1 3 8 5 . 7 0 f t 54 in Bridge Over North Fork Shoshone River Park County (WY) Three-Span Continuous Composite Haunched Plate Girder N A N A 1 2 9 7 . 2 4 f t 1 2 6 1 . 8 1 f t haunched 94 in to 55 in 7 8 Illinois Route 96 Over Burton Creek Adams County (IL) Three-Span Continuous Composite Wide Flange Girder 1 4 0 8 . 7 9 f t 1 2 7 0 . 6 6 f t 1 2 7 9 . 5 2 f t 5 6 10 Illinois DOT (Hard Copy) Illinois Route 408 Over Napoleon Hollow Draw STA 579+04 Pike County (IL) Three-Span Continuous Composite Plate Girder 5 9 42 in 3 8 4 1 . 7 2 f t 3 8 3 3 . 2 2 f t 3 8 2 4 . 7 2 f t 3 8 1 6 . 2 2 f t 34 in11 Illinois DOT (Hard Copy) Bowman Ave. Over F.A.I Route 74 Vermilion County (IL) 8 Two-Span Continuous Composite Plate Girder 66 ft 12 HDR Eng./Iowa DOT (Hard Copy) US 75 Over Ramp 11000 Woodbury County (IA) Five-Span Continuous Composite Plate Girder 84 in 1 1 8 1 . 3 6 f t 4 16.5 ft 17.0 ft 10.5 ft 3 8 5 0 . 2 2 f t 24.5 ft 12.5 ft 25.0 ft 12.0 ft 14.0 ft 7.0 ft 20.0 ft 38 ft 34 ft 36 ft 42 ft 42 ft 34 ft 44 ft 85 ft 130 ft 150 ft 44 ft 45 ft 130 ft 165 ft 90 ft 90 ft 90 ft 170 ft 4 7 1 . 3 7 f t 4 7 9 . 8 7 f t 4 8 8 . 3 7 f t 4 9 6 . 8 7 f t 5 0 5 . 3 7 f t 5 1 3 . 8 7 f t 5 2 2 . 3 7 f t 5 3 0 . 8 7 f t 1 3 7 9 . 9 2 f t 5 7 7 . 7 5 f t 5 6 9 . 9 2 f t 5 8 5 . 5 8 f t Submitted byBridge Number Depth of Web No. of GirdersTypeLocation Avg. Span (approx) Width of Bridge (approx) Unbraced Length (approx) Radius

17 7 . 0 0 f t 1 8 5 . 0 0 f t 1 9 3 . 0 0 f t 1 2 5 6 . 2 2 f t 82 in 1 1 9 5 . 8 9 f t 1 2 1 0 . 9 7 f t 1 2 2 6 . 0 5 f t 1 2 4 1 . 1 4 f t Four-Span Continuous Plate Girder 6 23.5 ft86 ft 180 ft25 Modjeski and Masters, Inc. Fore River Bridges, Portland, ME Main Span Unit Between Piers 95 and 135 - Simulated Bridge 60 in Two-Span Continuous Composite Plate Girders 3 4 7 5 . 2 1 f t 63 in 15 TNDOT (Electronic) Ramp "D" Over Interstate 40 Davidson County (TN) Three-Span Continuous Composite Plate Girder 5 3 6 8 . 1 4 f t 1 5 4 2 . 8 9 f t 1 5 5 1 . 8 9 f t 1 5 6 0 . 8 9 f t Three-Span Continuous Composite Plate Girder 5 1 5 2 4 . 8 9 f t 1 5 3 3 . 8 9 f t 20.0 ft44 ft 185 ft14 TNDOT (Electronic) Interstate 65 North Bound Ramp "B" Davidson County (TN) 54 in 2 3 9 . 0 0 f t 2 2 9 . 6 7 f t 2 2 0 . 3 3 f t 2 1 1 . 0 0 f t 13 PENN DOT (Hard Copy) Wabash Tunnel HOV Facility Bridge No. 29 Wabash HOV Ramp Allegheny County (PA) Two-Span Continuous Plate Girders, One Simple Span Plate Girder, One Simple Span Precast Box Beam 4 16 TNDOT (Electronic) Ramp "M" Over State Route 1 Rutherford County (TN) 72 in 17 NCDOT (Hard Copy) Slater Road Over I-540 Wake- Durham Counties (NC) Three-Span Continuous Plate Girder 4 9 6 6 . 7 0 f t 9 7 6 . 8 7 f t 74.8 in 9 8 7 . 0 4 f t 9 9 7 . 2 1 f t 18 NCDOT (Electronic) Fox Road Over I-540 Wake County (NC) Two-Span Continuous Plate Girder 4? 17.0 ftunknown 120 ft 72 in 2 2 8 0 . 4 4 f t 2 2 8 0 . 4 4 f t 19 NYDOT (Hard Copy) NYS Route 30 Over Schoharie Creek Schoharie County (NY) Four-Span Continuous Composite Plate Girder 4 23.0 ft30 ft 140 ft 56 in 8 2 4 . 3 5 f t 8 3 2 . 6 2 f t 2 2 8 0 . 4 4 f t 2 2 8 0 . 4 4 f t 150 ft20 Modjeski and Masters, Inc. Lincoln Highway (SR 3070) in Chester County, PA crossing four sets of Amtrak rails {9} One-Span Continuous Plate Girder 6 5 2 0 . 1 3 f t 5 2 8 . 3 8 f t 17.5 ft 20.0 ft varies 62 in to 84.5 in 21.0 ft 21 NYSDOT Cold Springs Road over Erie Barge Canal Three-Span Continuous Plate Girder 5 17.5 ft 24.0 ft 10.0 ft 38 ft 50 ft 51 in 1 8 9 4 . 3 3 f t 1 9 0 2 . 1 7 f t 1 9 1 0 . 0 0 f t 1 9 1 7 . 8 3 f t 4 27.0 ft22 BSDI Example Problem Three-Span Continuous Plate Girder 69 in 4 14.0 ft 23 Modjeski and Masters, Inc. Harper's Ferry Bridge, WV - Simulated Bridge Three-Span Continuous Plate Girder 5 20.0 ft 1 1 3 4 . 0 4 f t 24 Modjeski and Masters, Inc. Fore River Bridges, Portland, ME Beach Street Ramp - Simulated Bridge Three-Span Continuous Plate Girder 85 in 1 6 9 . 0 0 f t 1 1 2 2 . 8 9 f t 48 in 1 1 4 5 . 1 9 f t 1 1 5 6 . 3 4 f t 1 1 6 7 . 4 9 f t 44 ft 32 ft 36 ft 44 ft 52 ft 32 ft 36 ft 110 ft 175 ft 170 ft 115 ft 105 ft 150 ft 190 ft 90 ft 1 1 8 0 . 8 0 f t N A 1 9 2 5 . 6 7 f t 5 6 1 . 3 8 f t 5 5 3 . 1 3 f t 5 4 4 . 8 8 f t 5 3 6 . 6 3 f t 8 1 6 . 0 7 f t 8 0 7 . 8 0 f t 4 8 6 . 4 6 f t 4 9 7 . 7 1 f t 4 0 4 . 1 4 f t 3 9 5 . 1 4 f t 3 8 6 . 1 4 f t 3 7 7 . 1 4 f t (continued on next page)

64 in 1 0 5 . 8 3 f t 1 1 0 . 0 0 f t 1 1 4 . 1 7 f t 1 2 2 . 5 0 f t 32 Modjeski and Masters, Inc. Minnesota Bridge No. 62705 - Simulated Bridge One-Span Composite Plate Girder 4 12.0 ft 9 7 . 5 0 f t 50 in 1 6 9 . 6 3 f t 1 7 6 . 0 0 f t 1 8 2 . 3 8 f t 1 8 8 . 7 5 f t 31 Modjeski and Masters, Inc. Minnesota Bridge No. 62707 - Simulated Bridge Two-Span Continuous Plate Girder 5 11.0 ft 1 6 3 . 2 5 f t 47 in 2 5 7 . 8 0 f t 2 6 6 . 6 3 f t 2 7 5 . 4 5 f t 30 Modjeski and Masters, Inc. Missouri Bridge A5682 - Unit 4 - Simulated Bridge Four-Span Continuous Plate Girder 4 15.5 ft 2 4 8 . 9 8 f t 48 in 1 5 3 . 2 5 f t 1 6 0 . 7 5 f t 1 6 8 . 2 5 f t 29 Modjeski and Masters, Inc. Missouri Bridge A5658 - Unit A1 - Simulated Bridge Three-Span Continuous Plate Girder 4 10.5 ft 1 4 5 . 7 5 f t 82 in 3 5 7 . 0 0 f t 3 6 8 . 0 0 f t 28 Modjeski and Masters, Inc. Washington State SR405 - Simulated Bridge Four-Span Continuous Plate Girder 3 15.0 ft 3 4 6 . 0 0 f t 54 in 5 2 4 . 9 3 f t 5 3 4 . 4 4 f t 27 Modjeski and Masters, Inc. Washington State SR405/SR167 - Simulated Bridge Four-Span Continuous Plate Girder 3 20.0 ft 5 1 5 . 4 2 f t 81 in 5 0 4 . 0 0 f t 5 1 6 . 0 0 f t 5 2 8 . 0 0 f t 26 Modjeski and Masters, Inc. Washington State Bridge No. 530/120 - Simulated Bridge Three-Span Continuous Plate Girder 4 14.5 ft 4 9 2 . 0 0 f t 32 ft 32 ft 46 ft 28 ft 32 ft 30 ft 32 ft 70 ft 130 ft 105 ft 150 ft 125 ft 170 ft 65 ft G i r d e r 1 / A G i r d e r 2 / B G i r d e r 3 / C G i r d e r 4 / D G i r d e r 5 / E G i r d e r 6 / F G i r d e r 7 / G G i r d e r 8 / H Submitted byBridge Number Depth of Web No. of GirdersTypeLocation Avg. Span (approx) Width of Bridge (approx) Unbraced Length (approx) Radius Table 4. General bridge information (Continued).

• Among the simulated bridges, the minimum radius was approximately 120 feet. • The webs varied in depth from 33 inches to 94 inches. • Lateral bending stresses were not submitted for some of the bridges in the study. For one of these bridges, the orig- inal design ignored the lateral stresses. Another bridge consisted of straight girders with a curved deck. The lat- eral stresses of the other bridges were estimated using the V-load method. For each bridge, the critical positive flexure, critical negative flexure, and critical shear locations were either submitted by the agency or determined by Modjeski and Masters, Inc., from the documentation submitted. The critical-to-applied stress ratios according to each spec- ification were plotted for each bridge. Submitted load effects (e.g., moments and shears) were assumed to be service loads, and the applied stress calculations used the load factors for the LRFD Strength I combination as a basis for comparison.An attempt to remove the effects of the load factors was made by also plotting the critical stress calculated by each specification normalized to the critical stress calculated by the 1993 Guide Specifications. These comparisons of normalized stress are the primary focus of the analyses outlined in this section. Addi- tional analyses, which are outlined in Appendix D (available online at http://trb.org/news/blurb_detail.asp?id=5965), were performed to compare the LRFD Service II load provisions with the corresponding provisions in both the 1993 Guide Specifications and the 2003 Guide Specifications. It should be noted that when a reference to an equation number is made in this section (i.e., Section 2.4), the equation number is that used in the specifications. 2.4.4 Shear Design Appendix D contains a series of flowcharts that outline the shear design protocols and variables according to each of the three specifications—the 1993 Guide Specifications, the 2003 Guide Specifications, and the 12-52 recommended specifica- tions (which have subsequently been adopted by AASHTO and published in the 2006 interim specifications). The reader is encouraged to consult the appropriate specification for clarifi- cation and further information regarding the design protocols. In general, the shear design protocols for the three analysis specifications are very similar. This is true for both transversely stiffened and unstiffened members. The main differences among the three specifications are as follows: • The maximum transverse stiffener spacing has been progres- sively increased from D, the depth of the web, in the 1993 Guide Specifications to 3D in the 12-52 recommended specifications. • The 12-52 recommended specifications allow for the con- sideration of the additional post-buckling strength from tension-field action in the shear critical stress calculations. Figure 6 shows the shear critical-to-applied stress ratio for the sample of bridges according to the three specifications, while 17 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 Bridge ID Cr iti ca l-t o- Ap pl ie d St re ss R at io LFD 12-38 12-52 Existing Bridges Simulated Bridges Note: Stiffened bridges are denoted with a box around the number identifier. Figure 6. Shear critical-to-applied stress ratio.

Figure 7 shows the shear critical stress normalized to that cal- culated using the 1993 Guide Specifications. In these figures, as in the shear-related figures in Appendix D, the stiffened bridges are denoted with a box around the number identifier. The fig- ures also differentiate the existing bridges from the simulated bridges. In general, the critical-to-applied stress ratios for the three analysis specifications are relatively consistent among specifications and within the sample. All bridges except for Bridges 4 and 22 exhibited equal or slightly higher shear critical stress according to the 1993 Guide Specifications than according to the 2003 Guide Specifications. The change in maximum transverse stiffener spacing among the three specifications is evident in the critical stress values for Bridges 4 and 22. These two bridges are the only ones that have a transverse stiffener spacing value greater than the depth of the web and are the only ones that exhibit a higher critical stress according to the 2003 Guide Specifications than according to the 1993 Guide Specifications. This is because the sections are analyzed as unstiffened according to the 1993 Guide Specifications when the transverse stiffener spacing exceeds the maximum value of D. The analysis of transversely stiffened members with the 1993 Guide Specifications and the 2003 Guide Specifications is more conservative than with the 12-52 recommended spec- ifications in several instances, as evidenced by the lower nor- malized critical stress values. These cases are for Bridges 2, 4, 7, 12–14, 16, and 22–28. For these bridges, the 12-52 rec- ommended specifications allow the additional post-buckling strength from tension-field action to be considered. This post-buckling strength is also recognized in the 1993 Guide Specifications andAASHTO LRFD specifications straight girder provisions. According to the 12-52 recommended specifications, Eq. 6.10.9.2-1, which is identical to Eq. 6-4 in the 2003 Guide Specifications, is used for both stiffened and unstiffened webs to account for the shear-yielding or shear-buckling strength of the web. Note that this equation is unnumbered in the 1993 Guide Specifications. The 12-52 recommended specifications use an additional equation, Eq. 6.10.9.3.2-2, to account for the post-buckling strength of the interior panels of stiffened webs that satisfy certain geometric requirements. The use of this equation pro- duces a higher multiplier on Vp for these webs. Eq. 6.10.9.3.2-2 is used in the 12-52 recommended specifications for both straight and curved steel girders and is applicable for Bridges 2, 4,12–14,16,and 22–31.Among the bridges with stiffened webs, only Bridge 7 does not meet the geometric requirements for the use of this equation and, subsequently, uses a more conser- vative variation, identified as Eq. 6.10.9.3.2-8. The flowcharts in Appendix D (available online at http://trb.org/news/blurb_ detail.asp?id=5965) outline the number of bridges in the sam- ple that meet the requirements for each classification according to each of the specifications for the stiffened and unstiffened critical stress equations. V CVcr p= Eq. . . .6 10 9 2 1- 18 0.00 0.50 1.00 1.50 2.00 2.50 1 2 3 4 5 6 7 8 9 10 1112 13 1415 16 17 18 19 20 2122 23 24 25 26 27 28 29 30 31 32 Bridge ID Cr iti ca l S tre ss /L FD C rit ic al S tre ss 12-38 12-52 Existing Bridges Simulated Bridges Note: Stiffened bridges are denoted with a box around the number identifier. Figure 7. Shear critical stress divided by 1993 Guide Specifications shear critical stress.

Bridges 29, 30, and 31 also qualified for the use of the post- buckling strength provision. However, no additional strength is realized for cases when the ratio of the shear-buckling resist- ance to the shear yield strength, C, is equal to unity; in this situation, Eq. 6.10.9.3.2-2 becomes Eq. 6.10.9.2-1 and only the buckling strength is considered. The equations used to determine C for each of the three specifications are listed in Appendix D and are essentially equivalent. Although also stiffened, Bridges 3, 20, and 32 were analyzed at the end panels and are therefore not able to rely on the for- mation of a tension field or to account for any additional post- buckling strength. These observations are evident in Figure 7. 2.4.5 Flexural Design The flowcharts in Appendix D outline the number of bridges in the sample that met the requirements for each classifica- tion according to each of the specifications for the composite positive flexure (C+), composite negative flexure (C−), non- composite positive flexure (NC+), and noncomposite nega- tive flexure (NC−), respectively. Furthermore, they outline the design protocols and variables used for each of the three spec- ifications. The reader is encouraged to reference the appro- priate specification for clarification and further information regarding the design protocols. Table 5 outlines the width-to-thickness (i.e., slenderness) ratio limits for the various classifications of the flanges accord- ing to the three specifications. For a yield strength of 50 ksi, the limits for compact and slender flanges are lower with the 1993 Guide than with the 2003 Guide, but only marginally so. V V C + - C d D d D n p O O = ( ) ⎛⎝⎜ ⎞⎠⎟ + ⎡ ⎣ ⎢⎢⎢ ⎤ ⎦ ⎥⎥⎥ 0.87 1 1+ 2 Eq. . . . .6 10 9 3 2 8- V V C + - C d D n p O = ( ) ⎛⎝⎜ ⎞⎠⎟ ⎡ ⎣ ⎢⎢⎢ ⎤ ⎦ ⎥⎥⎥ 0.87 1 1+ 2 6Eq. .10 9 3 2 2. . . - For the 12-52 recommended specifications, the ratios are slightly higher than for the 2003 Guide Specifications. The following trends, as they relate to the studied bridges, are worth noting from the flowcharts: • For the 12-52 recommended specifications related to com- posite sections in positive flexure (Section 6.10.7), there are two bridges in the sample for which the section is regarded as noncompact; it should be noted, however, that because plastic design is not permitted, all composite curved steel girders in positive flexure must be analyzed as noncompact according to 12-52 Section 6.10.6.2.2. • According to the 12-52 recommended specifications, the majority of the bridges in the sample were classified as com- pact for flange local buckling (FLB) considerations and as noncompact for lateral-torsional buckling (LTB) consider- ations for all design conditions. • For the composite negative flexure and noncomposite section recommended specifications of 12-52 (Section 6.10.8), the case where the compression flange is continuously braced is not represented in the sample because such a case would be atypical. The bottom flange is usually braced at discrete points where the cross-frames exist. • Generally, the LTB considerations controlled the critical stress of the bridges in the sample, which is logical given the classifications pertaining to their buckling behavior. • None of the specifications reduce the capacity of a contin- uously braced flange below the yield strength, Fy. • In a sense, the magnification factor in the 12-52 recom- mended specifications, defined in Section 6.10.1.6, replaces the ρ factors from the 1993 Guide Specifications and the 2003 Guide Specifications. A comparison reveals that both factors increase the tendency of the section to deform because of secondary effects. • Hybrid sections are not allowed by the 2003 Guide Specifi- cations, but are allowed by the 1993 Guide Specifications and the 12-52 recommended specifications, which have similar provisions for the consideration of stresses in hybrid sections. The provisions for hybrid sections in the 1993 Guide Spec- ifications consider only yielding of the tension flange in positive bending regions or only yielding of the compres- sion flange in negative bending regions, while the 12-52 19 Specifications Compact Flange Noncompact Flange Slender Flange 1993 Guide Specifications f f t b ≤ 14.31 14.31 < f f t b ≤ 19.68 f f t b > 19.68 2003 Guide Specifications f f t b ≤ 18 18 < f f t b ≤ 23 f f t b > 23 12-52 Recommended Specifications f f t b ≤ 18.3 18.3 < f f t b ≤ 24 f f t b > 24 Table 5. Flange classifications by slenderness ratio.

recommended specifications, in Eq. 6.10.1.10.1-1, have been adapted to include all positions of the neutral axis and all combinations of yield strengths for the various portions of the girder. One noticeable difference among the three specifications is the fact that while the 1993 Guide Specifications and the 2003 Guide Specifications consider the lateral bending stress to reduce the critical stress, the 12-52 recommended specifications consider the lateral bending stress as a load. In order to alleviate this difference, the appropriate portion of the lateral bending stress was deducted from the critical stress calculated accord- ing to the 12-52 recommended specifications to obtain the bending resistance, Fbu. The flexural capacity figures in Appendix D (which is avail- able online at http://trb.org/news/blurb_detail.asp?id=5965) use the bending resistance values, with the exception of the critical-to-applied stress plots, which consider the flange crit- ical stress, Fn, as outlined in the recommended specifications directly. Note that the gaps occurring in the negative flexure figures for Bridges 3, 6, 20, and 32 are because those bridges are simple-span structures.Furthermore,Bridges 24,25,29,and 30 use Grade 36 steel throughout and Bridges 1 and 22 have hybrid sections in the negative moment regions. In spite of the differences between the flexural design spec- ifications, the calculated capacity values are, for the most part, very similar. The main causes of major differences in capacity among the three specifications are as follows: • Changes in the classification of the flange (e.g., compact, noncompact, and slender) among the three specifications; • Lateral stress consideration (including magnification) according to the 12-52 recommended specifications as compared with the reductions due to the r factors used in the 1993 Guide Specifications and the 2003 Guide Specifi- cations; and • Noncomposite design as a temporary condition. Again, specific information regarding the capacity of the bridges for each of the design conditions is outlined in Appendix D. Although the proportion varies based on the design speci- fication selected, most composite positive flexure sections are controlled by the tension flange, while most negative flexure sections are controlled by the compression flange. For the non- composite section design checks, the compression flange con- trols both positive and negative flexural sections. This control F F fbu f n l= −φ 1 3 indicates that the compression flange is the critical flange in unbraced or discretely braced conditions. 2.4.6 Summary of Comparison Results Based on the analyses, the following observations and con- clusions can be made regarding the shear design protocols in the 1993 Guide Specifications, the 2003 Guide Specifications, and the 12-52 recommended specifications (which have sub- sequently been adopted by AASHTO and published in the 2006 interim specifications): Strength I load case, shear design: • The maximum transverse stiffener spacing has been progres- sively increased from D, the depth of the web, in the 1993 Guide Specifications to 3D in the 12-52 recommended specifications. • All three specifications use the ratio of the shear-buckling resistance to the shear yield strength, C. A comparison of the equations used to calculate C in each of the specifications reveals that the constants for the equations are equivalent. • In general, the critical stress values for the three specifica- tions are consistent except that the 12-52 recommended specifications allow for the consideration of the additional post-buckling strength from tension-field action in the shear critical stress calculations. This post-buckling strength is also recognized in the 1993 Guide Specifications and AASHTO LRFD specifications straight girder provisions and results in a higher critical stress for the majority of the stiffened bridges in the sample. Strength I load case, flexural design: • Flexural analysis, according to all of the specifications, is divided between composite and noncomposite sections, positive and negative flexure, and compression and tension flanges. • Only modest changes are made to the slenderness limits for the various classifications of the flanges (e.g., compact, noncompact, and slender) according to the three specifica- tions. These changes, however, are often enough to change the classification of a flange and, therefore, the critical stress of the section. • All three of the specifications account for an increased ten- dency of the curved girders to deform due to secondary bending effects. The 1993 Guide Specifications and the 2003 Guide Specifications consider ρ factors, and the 12-52 recommended specifications consider a magnification factor for the lateral bending stress. For the 1993 Guide Specifica- tions and the 2003 Guide Specifications, the ρ factors act to reduce the critical stress of the section based on lateral bending stress and geometry resulting in Fcr1. The magni- 20

fier on the lateral bending stress for the 12-52 recommended specifications focuses on the magnitude of the longitudi- nal bending stress, resulting in a final combined reduction in the stress limit due to the effects of geometry (i.e., either FLB or LTB considerations) and bending. • The 1993 Guide Specifications and the 2003 Guide Speci- fications consider the lateral bending stress to reduce the critical stress, while the 12-52 recommended specifications consider the lateral bending stress as a load. The final effect of including the lateral bending stress in all of the specifi- cations is to reduce the useable stress limit for gravity loads. • For the bridges considered, the noncomposite design was a temporary condition, and the noncomposite dead loads that were provided for the final structure were used to analyze the noncomposite structure. Information was not provided regarding any temporary support points or the construction sequence for a more inclusive analysis. • Hybrid sections are not allowed by the 2003 Guide Specifi- cations, but are allowed by the 1993 Guide Specifications and the 12-52 recommended specifications, which have similar provisions for the consideration of stresses in hybrid sec- tions. Minor reductions in the critical stress occur when the yield strength of the web is less than the yield strength of one or both of the flanges. • In spite of the differences between the flexural design spec- ifications, the calculated critical stress values are largely very similar. 2.5 Design Examples Two design examples, one for an I-girder bridge and one for a box-girder bridge, were developed in the NCHRP 12-38 project. As part of Phase I of the NCHRP 12-52 project, these design examples were updated to conform to Phase I recom- mended specifications. The work plan for Phase II called for updating the two design examples to conform to the design provisions approved by AASHTO. This work was conducted, and the two design examples are available online at http:// www.transportation.org/sites/bridges/docs/Box%20Girder. pdf and http://www.transportation.org/sites/bridges/docs/ I-Girder.pdf. Following is a brief description of the bridges used for the two examples. I-Girder bridge example: • Three continuous spans: 160 feet, 210 feet, and 160 feet. • Centerline radius: 700 feet. • Girder spacing: 11 feet, 0 inches. • Overhang width: 3 feet, 9 inches. • Out-to-out deck width: 40 feet, 6 inches. • Three 12-foot design lanes. • Total deck thickness: 9.5 inches (includes a 1/2-inch inte- gral wearing thickness). Figure 8 shows a cross-section of the I-girder example bridge. 21 Roadway = 37'-6" Out to Out = 40'-6" 4 Girders total = 33'-0" 3'-9" 11'-0" 11'-0" 11'-0" 3'-9" At SimpleIntermediate Cross Frame Supportand Interior Supports Slope = 5% Structural t = 9"Single Angles 3 Lanes @ 12'-0" G4 G3 G2 G1 Deck concrete – f’c = 4,000 psi E = 3.6x106 psi Haunch – 20 in. wide, 4 in. deep measured from top of web Permanent deck forms are present Total deck thickness = 9.5 in., structural thickness = 9.0 in. Figure 8. I-girder bridge example, cross-section.

Box-girder bridge example: • Three continuous spans: 160 feet, 210 feet, and 160 feet. • Centerline radius: 700 feet. • Individual tub girder web spacing: 10 feet, 0 inches. • Interior web spacing: 12 feet, 6 inches. • Out-to-out deck width: 40 feet, 6 inches. • Three 12-foot design lanes. • Total deck thickness: 9.5 inches (no provision for integral wearing thickness). Figure 9 shows a cross-section of the box-girder example bridge. 22 Figure 9. Box-girder bridge example, cross-section. Roadway = 37'-6" Out to Out = 40'-6" Slope = 5% 3 Lanes @ 12'-0" t = 9 1/2" 4'-0" 10'-0" 12'-6" 10'-0" 4'-0" Angles at Bearings Typ. Plate DiaphragmTyp. Section at Interior Cross-frame Deck concrete – f’c = 4,000 psi E = 3.6x106 psi Haunch – 20 in. wide, 4 in. deep measured from top of web Permanent deck forms are present Total deck thickness = 9.5 in.