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

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

APPENDIX A – CURRENT STATE OF THE ART A-1

Table of Contents A.1 Approach ................................................................................................................. A-4 A.2 Questionnaire of Bridge Owners............................................................................ A-4 A.2.1 Introduction ...................................................................................................... A-4 A.2.2 Analysis of Questionnaire Responses .............................................................. A-5 A.2.3 Lessons Learned from the Questionnaire .................................................. A-2020 A.3 Concrete Serviceability Requirements in Several Modern Bridge Design Specifications ........................................................................................................ A-20 A.3.1 AASHTO LRFD .............................................................................................. A-20 A.3.1.1 Limitations on the Live Load Deflection of Bridge Structures ...... A-25 A.3.1.2 Fatigue-and-fracture Limit States .................................................... A-28 A.3.1.2.1 General......................................................................................... A-28 A.3.1.2.2 Loads ........................................................................................... A-28 A.3.1.2.3 Fatigue Resistance of Concrete Structures ................................... A-29 A.3.1.3 Cracking of Reinforced Concrete Structures ................................. A-32 A.3.1.3.1 Crack Control Reinforcement ........................................................ A-32 A.3.1.3.2 Control of Cracks in Current Specifications Provisions ................. A-39 A.3.1.4 Principal Stresses in Webs of Segmental Concrete Bridges ........ A-41 A.3.1.5 Stress Limitations for Prestressing Tendons ................................. A-42 A.3.1.6 Concrete Tension Stresses ............................................................. A-43 A.3.1.7 Existing Limit States that are Deterministic or Represent Detailing Requirements ................................................................... A-45 A.3.2 Eurocode ....................................................................................................... A-47 A.3.2.1 Definition of SLS .............................................................................. A-47 A.3.2.2 Background on the Eurocode’s Reliability Basis .......................... A-48 A.3.2.3 Serviceability Design Basic Approach............................................ A-51 A.3.2.3.1 Basic Equation.............................................................................. A-51 A.3.2.3.2 Serviceability Criteria .................................................................... A-52 A.3.2.3.3 Combination of Actions (Load Combinations) ............................... A-52 A.3.2.4 Existing Limit State .......................................................................... A-55 A.3.3 Canadian Highway Bridge Design Code (CHBDC) ........................................ A-55 A.3.3.1 Background ...................................................................................... A-55 A.3.3.2 Existing Limit States ........................................................................ A-55 A.4 Search for SLSs Not Yet Implemented ................................................................ A-56 A.5 References ............................................................................................................. A-57 A-2

List of Tables Table A-1 Existing Service Limit States in AASHTO LRFD ................................................... A-21 Table A-2 Recommended Minimum Depth of Concrete Structures in 1989 AASHTO ........... A-26 Table A-3 Fatigue Live-Load Load Factors ........................................................................... A-28 Table A-4 Prestressing-Tendon Fatigue Resistance ............................................................. A-31 Table A-5 Constant-Amplitude Fatigue Threshold of Splices from AASHTO LRFD Table 5.5.3.4-1................................................................................................................................ A-32 Table A-6 Stress Limits for Prestressing Tendons (AASHTO LRFD, 2012) ........................... A-43 Table A-7 Tensile Stress Limits in Prestressed Concrete at SLS after Losses, Fully Prestressed Components (AASHTO LRFD, 2012, Table 5.9.4.2.2-1) ................................... A-45 Table A-8 Design Working Lives (EN 1990, 2002, adapted from Table (2.1)) ....................... A-48 Table A-9 Eurocode Consequence Classes (EN 1990, 2002, adapted from Table (B1)) ....... A-49 Table A-10 Multiplication Factor, KF1, for Reliability Differentiation ....................................... A-49 Table A-11 Target Probabilities of Failure (pF) and Reliability Indices (βT) ............................ A-50 Table A-12 Irreversible SLS Target Probabilities of Failure and Corresponding Reliability Indices (EN 1990, 2002, adapted from Table (C2)) ............................................................... A-50 Table A-13 SLS Combinations .............................................................................................. A-51 Table A-14 Recommended Values of Ψ Factors for Highway Bridges in the Eurocode (EN 1990, 2002, adapted from Table A2.1) .................................................................................. A-54 List of Figures Figure A-1 Deflection provisions in 2006 edition of CHBDC. ................................................. A-27 A-3

A. A.1 Approach As part of Phase I of the project an assessment of the current state of the art related to service limit states was conducted as follows: • A survey of Bridge owners was conducted and is presented in Section A2. • A review of technical literature is summarized in Section A.3. • A survey was made of the requirements for SLSs in several modern bridge design specifications including AASHTO LRFD. The requirements of the Eurocode and the Canadian Highway Bridge Design Code (CHBDC) (2006) were also reviewed and significant clauses are summarized herein. A.2 Questionnaire of Bridge Owners A.2.1 Introduction To determine the current state of practice of design for the Service Limit State, a questionnaire was developed and sent to major bridge owners across North America. In addition to the 50 US states and the District of Columbia, the questionnaire was also sent to the following bridge owners: Alberta Transportation Delaware River and Bay Authority Delaware River Joint Toll Bridge Commission Delaware River Port Authority Kansas Turnpike Maryland Transportation Authority - FSK Bridge New Brunswick Department of Transportation New Jersey Transit Authority New Jersey Turnpike Authority New Jersey Turnpike Authority New York City Transit Authority - New York New York State Bridge Authority New York State Thruway Authority Nova Scotia Department of Transportation and Infrastructure Renewal Ohio Turnpike Oklahoma Turnpike Authority Ontario Ministry of Transportation Pennsylvania Turnpike Commission Port Authority of New York and New Jersey Rhode Island Turnpike and Bridge Authority Saskatchewan Ministry of Highways and Infrastructure The questionnaire included 20 questions covering design loads, design provisions and general questions related to the performance of bridge structures. A-4

Twenty nine responses were received. These responses came from: Alabama Department of Transportation Alaska Department of Transportation Arizona Department of Transportation Arkansas Department of Transportation California Department of Transportation Florida Department of Transportation Hawaii Department of Transportation Kansas Department of Transportation Kentucky Department of Transportation Louisiana Department of Transportation Michigan Department of Transportation Minnesota Department of Transportation Mississippi Department of Transportation Missouri Department of Transportation Montana Department of Transportation New Mexico Department of Transportation New York Department of Transportation North Carolina Department of Transportation Oklahoma Department of Transportation Pennsylvania Department of Transportation South Carolina Department of Transportation South Dakota Department of Transportation Texas Department of Transportation Virginia Department of Transportation Washington Department of Transportation Wisconsin Department of Transportation Wyoming Department of Transportation Kansas Turnpike Authority Ontario Ministry of Transport Most responses included answering all questions. However, as some respondents skipped one or more questions, the total number of responses cited in some of the following sections is less than the total number of questionnaires returned to us. A.2.2 Analysis of Questionnaire Responses Shown below is a copy of the questionnaire questions with the number of responses and comments and explanations received. Shown also are the research team’s analysis of the responses. 1. Some agencies modify the HL93 loading. Please specify what load your agency use for the design of concrete structures: _23_ Unmodified HL93 loading __4_ Modified HL93 Loading: (please specify): __1_ Other (please specify): A-5

The modifications to the HL 93 loading included: California: The application of the tandem load for negative moment near, and reaction of, interior supports is modified. 100% of two tandems spaced 26 to 40 ft. in the same lane is used. Kentucky: The HL93 load is increased by 25% Michigan: The HL93 load is increased by 20% and the load case involving two tandems in the same lane was revised to replace the two axles (25 kips each) with one 60 kip load. A load factor of 1.2 is applied to the 60 kip load. Minnesota: MNDOT load rating is currently done by LFR. Because there have been some low ratings for continuous steel superstructures designed by LRFD, the double truck plus lane load is increased for all continuous superstructures (including concrete) when the longest span is greater than 100 ft. MNDOT Bridge Office Memo to Designers (2005-01) states: • For bridges with longest span below 100 feet: 90% of the HL-93 double truck with DLA plus lane load (same as in LRFD 3.6.1.3) • For bridges with longest span between 100 and 200 feet:(90 + (span - 100) x 0.2)% of the HL-93 double truck with DLA plus lane load • For bridges with longest span above 200 feet: 110% of the HL-93 double truck with DLA plus lane load Ontario: Canadian Highway Bridge Design Code loading Pennsylvania: The tandem load increased by 25%. The dynamic load allowance for deck design was increased from 33% to 50% It is clear that revisions to the HL93 by bridge owners are kept to a minimum. These revisions appear to address issues related to state-specific weight limits and vehicle configurations. 2. In addition to the HL93 loading (or its replacement as indicated in the answer to question 1 above), does your agency routinely check bridge structures for the effects of legal permit loads as part of the normal design procedure? Yes 13 No 15 If Yes, does your agency check concrete components for the service limit states under these legal loads? Yes 5 No 6 If Yes: Please provide the configuration of the legal loads used Only New York and Pennsylvania provided the configuration of their permit vehicles used for service limit state. Following is the description of the two vehicles and their use: A-6

New York: The New York Permit Vehicle is an eleven-axle vehicle. The total weight of the vehicle is 220 kips and the distance between the front and rear axles is 51 ft. (axle weights are: 10, 18, 18, 23, 23, 23, 21, 21, 21, 21, 21 and axle spacings, in ft., are 9, 4, 4, 4, 4, 10, 4, 4, 4, 4). The permit vehicle is used in checking the Strength II limit state and in checking prestressed components under Service III Limit State. Pennsylvania: The Pennsylvania P-82 vehicle is an eight-axle vehicle. The total weight of the vehicle is 204 kips and the distance between the front and rear axles is 55 ft. The truck consists of a front axle weighing 15 kips followed by seven axles weighing 27 kips each. The axle spacings are: 11, 4, 4, 24, 4, 4, 4 (ft). The permit vehicle is used in checking the Strength II limit state and in checking prestressed components under two state-specific revised Service III limit states. The load for both limit states is 100% of the dead load plus 100% of the live load. Service IIIA is used for checking that the stress in the reinforcement does not exceed 0.9 the yield strength under the specified load combination and Service IIIB is used to ensure that prestressed concrete members do not reach the cracking moment under the specified loads. Indicate whether the same service stress limits are used for both the HL93 and the legal loads Four respondents answered Yes and another one answered No. Other respondents skipped this question. Indicate whether the permit vehicle is applied to: __3_ Multiple lane __5__ Single lane with normal traffic in other lanes __1__ Single lane with no traffic in other lanes Owners are nearly equally split on the issue of checking new designs for legal loads as part of the design procedures. Furthermore, the owners who check new designs for legal loads are split on whether these legal loads should be used in conjunction with service limit states. 3. Did your agency revise the stress limits for prestressed concrete components under Service limit states as shown in Articles 5.9.4 of the AASHTO LRFD bridge design specifications? (for example: design for no tension under all loads) Yes 12 No 16 The responses indicate that revisions to the specifications’ stress limits under service load combinations are not widely used. Revisions pointed out by respondents include: Alaska: No tensile stresses in concrete under Service I Load combination. Arizona: Tensile stress limit of 0.0948√f′c (ksi) in the precompressed tension zone. California: No tensile stresses in concrete under final conditions in areas with bonded reinforcement under service loads A-7

Hawaii: No tensile stresses allowed in precompressed tensile zone after all losses have occurred except when computing load capacity ratings at the operating level and for Legal and permit loads Kansas: Allowed tensile stress in concrete is 0.0948√f′c (ksi) for inventory rating and 0.19√f′c (ksi) for operating rating Minnesota: Zero tension in post-tensioned slabs and in top slabs of post-tensioned boxes. North Carolina: Article 5.9.4.2 Allowable Stresses: Stress at Service Limit State After Losses Tension in the Precompressed Tensile Zone, • Box beams and cored slabs at all sites: no tension at mid span • Girders at corrosive sites: no tension • For other girders and panels, the tension is limited to 0.19√f′c (ksi) Pennsylvania: A table with stress limits for different situations is included in the design specifications South Dakota: No tensile stresses in concrete after losses and under full service loading for Interstate and high truck traffic routes and one-half the allowable tensile stress for all other state route structures. Washington: Differences include: • Temporary tension in areas with bonded reinforcement sufficient to resist the tensile force in the concrete Limit is 0.19 instead of 0.24 √f′c except during shipping where the 0.24√e′c applies • Final tensile stress in precompressed tensile zone: No tension • Final compression under LL + ½ DL + Effective P/S = 0.4f’c 4. With the exception of issues covered under Question 3 above, did your agency revise any other service limit states (design requirements specified to be checked under service load combinations)? Yes 12 No 16 The responses indicate that the majority of jurisdictions do not apply any revisions to the service limit states in the AASHTO LRFD specifications. Revisions pointed out by respondents include: Arizona: The steel stress is limited to 0.6fy and for bridge deck design steel stress is limited to 0.4fy Kansas: Deflection limits were revised Louisiana: Design for 1.0 LL factor (rather than 0.80) under Service III Michigan: Check cantilevers for reinforcement dead load service stress < 22 ksi Minnesota: Use a maximum value of 2 inches for concrete cover Pennsylvania: LL Load Factor for Service III revised to 0.65 for load cases containing both pedestrian live loads and vehicular load together. Texas: Limit dead load stress in main reinforcement of pier caps to 22 ksi. 5. What method of Control of Cracking by Distribution of Reinforcement (AASHTO LRFD Article 5.7.3.4) is used by your jurisdiction: _15__ Current requirements without modifications A-8

__7__ Current requirements with modifications (Please specify revisions below) __2__ Pre-2005 Interim requirements (the Z equation) without modifications 0 Pre-2005 Interim requirements (the Z equation) with modifications (please specify revisions below) __7__ Other, please specify below The responses indicate that the great majority of jurisdictions are using the provisions included in AASHTO LRFD for Control of Cracking by Distribution of Reinforcement. The revisions applied by some jurisdictions mostly relate to the application of the provisions to certain components. Respondents indicating using “other methods” indicated the following revisions: Alaska: The computer program Response 2000 is used to check the design of some members Florida: Tensile stresses in longitudinal reinforcing steel for all mildly reinforced pier columns, pier caps and bent caps under construction loading and Service III Loading are limited to 24 ksi for Grade 60 reinforcement Kansas: Use maximum cover of 2” for deck design Minnesota: Use maximum cover of 2” Missouri: Use Pre-2005 Interims for crack control reinforcement in decks; current provisions used for all other components New York: Crack control requirements are not applied to footings Ontario: Use CHBDC CAN/CSA S6-06, Clause 8.12 Virginia: Crack control not applied to concrete decks on prestressed concrete or steel stringers Washington: Only Exposure Class 2 is used 6. Do you check concrete structures, including concrete substructures, for any additional service load combinations beyond that in the LRFD Specifications? Yes 3 No 23 If Yes, please provide the additional load combinations below or provide relevant pages of your agency’s design manual Michigan: Check cantilevers for reinforcement dead load service stress < 22 ksi. Missouri: Gross concrete section of beams in multi-column bents, without contribution from reinforcement, shall not rupture under service dead loads (1.0DC + 1.0DW). Pennsylvania: A table of load factors is provided in the design manual 7. When analyzing structures for overloads (i.e. trucks with special permits), do you check concrete components for the service limit state under these trucks? Yes 6 No 20 If Yes, are the same service stress limits used for both the HL93 and the overloads. Yes 3 No 3 A-9

If Yes, please specify: Among the six responses indicating checking bridges under overloads for the service limit state, only one response indicated which limit states the bridges are checked for: In Kansas, bridges are checked for fatigue and crack control under overloads. 8. Have you observed cracking of pretensioned concrete beams immediately after prestressing force release and before removing the beam from the precasting bed? Yes 17 No 12 If Yes, please state typical locations: __16_ Near the end of the beams ( __5__ Vertical cracks ___15__ Inclined cracks) ___1_ Near midspan of the beam ( _____ Vertical cracks ____1__ Inclined cracks) Among the 17 responses indicating observing early-age cracking of prestressed concrete beams in service, two responses did not indicate the location and type of cracking while the remaining 16 responses indicated cracking near the ends of the beams. Among the latter 16 responses, one response indicated only vertical cracking, 11 responses indicated only inclined cracking, four responses indicated both vertical and inclined cracking and one response did not indicate the orientation of cracking. The frequency of cracking was cited by only two responses. One response indicated the frequency is “rare” and the other indicated that cracking is not routinely observed and indicated that is mostly related to precasting yard procedures. The responses to this question suggest that a study of the cause of cracking should be considered by the bridge community. 9. Have you observed cracking of prestressed concrete beams in service? Yes 21 No 7 If Yes: Approximately, what is the percentage of prestressed beams in your inventory in which you observed cracking? __8__ Less than 1% __7__ 1 to 5% __5__ 5 to 10% __1_ More than 10%, Please state __15______%_ When are the cracks typically first observed? A-10

__1__ Immediately after construction __5__ Within 1 year of construction __3__ 2 to 5 years after construction _____ More than 5 years after construction _13__ Not sure What type of cracks and in bridges of what age group (e.g. bridges constructed before 1970’s)? (please mark all applicable): _14__ Shear cracks (typically inclined cracks near the end of the girders) Age group this was observed in: _________ __2__ Flexural cracks (typically vertical cracks near max. moment regions) Age group this was observed in: _________ __6__ Vertical cracks near the end of pretensioned girders Age group this was observed in: _________ __2__ Anchorage zone of post-tensioned girders Age group this was observed in: _________ __5__ Other, Please describe: Age group this was observed in: _________ The responses to this question suggest the following: Even though approximately 75% of the respondents to this question indicated that they observed cracking of prestressed concrete beams in service, it appears that the percentage of bridges where cracking is observed is typically small. Among 21 jurisdictions indicating that cracks have been observed, eight (38%) indicated cracking observed in less than 1% of bridges, seven (33%) indicated cracking observed in 1% to 5% of bridges, and, five (24%) indicated cracking observed in 5% to 10% of bridges. Most of the cracking occurs at a relatively young age. Out of 22 respondents answering the question related to the time cracking was observed six respondents (27%) indicated cracking observed within two years of construction, three respondents (14%) indicated cracking observed 2 to 5 years from construction and the remaining thirteen respondents (59%) were not sure of the time of cracking. The most common form of cracking is shear cracking (48% of responses indicating cracking observed) followed by vertical cracking (21%). Only Florida and Wisconsin indicated anchorage zone cracking (this is probably because Florida uses post-tensioning more extensively than most other owners and, thus, are more likely to observe problems related to post-tensioning) Most reported cracking took place in older bridges (pre-1970’s). in only one case cracking was reported in bridges in the 2 to 5 year age group. A-11

Other types of reported cracking included: Arkansas: Vertical cracks over piers of simple spans made continuous for bridges from between 1973 and 2005. Florida: Insignificant longitudinal cracks in upper/lower flanges predominately over bearing areas, Hairline diagonal cracks in the web, running from the top of the web near beam end diagonally 3 to 4 feet in length. In all age groups Michigan: Cracking observed in beams of bridges on highly skewed alignments Missouri: Diagonal cracking observed but in opposing orientation to shear cracks; occurs in all age groups. Pennsylvania: Cracking in adjacent non-composite P/S box beams under open joints in parapets Texas: Anchorage zone of pretensioned girders. The responses to this question indicate that newer bridges designed under the current specifications did not show wide spread cracking. However, it is not clear whether more cracking will start appearing once these bridges continue to age. 10. Have you observed end of prestressed beam damage under expansion joints? Yes 12 No 16 If Yes, Did it affect serviceability? Yes 6 No 5 Have you tried to repair the damage? Yes 9 No 2 If repaired, what repair technique was used? Even though 40% of the respondents to this question indicated observing damage to ends of prestressed concrete beams under expansion joints, none of the responses indicated that it was a significant concern. Methods of repair indicated are: patching, chipping and over-casting, fiber wrap, mortar repair and expansion of the beam seat to provide support further from the beam end. 11. Is the deck empirical design method used in your jurisdiction? Yes 5 No 23 If Yes, What percentage of new decks (defined as decks designed in the last 5 years) are designed using the empirical method A-12

0% 23 Responses 1%-20% 1 Response 20% to 40% 1 Response 40% to 60% 60% to 80% 80% to 99% 2 Response 100% Did decks designed using the empirical design method perform as good as traditionally designed decks? Yes 4 No 1 If No, please explain in what way: More cracking than conventional decks was cited as the reason for the negative answer above. Are the minimum reinforcement ratios specified in AASHTO LRFD for empirical deck design used? Yes 2 No 3 If No, Please indicate the limits used: The revisions to reinforcement requirements include using the following reinforcement: Michigan: #4 @ 12” top mat longitudinal and transverse, #4 @ 8” bottom mat longitudinal and transverse, and, extra bars under barrier and at corners of bridges with skew angle greater than 25 deg Louisiana: Use #5@12 each direction at top and bot. Later the spacing was reduced to 7” (Notice that Louisiana’s response indicated that currently they do not construct decks using the empirical method) Is the maximum reinforcement spacing of 18” specified in AASHTO LRFD for empirical deck design used? Yes 1 No 4 If No, Please indicate the maximum spacing used: If a tighter spacing is used, what is the reason? __2_ Maximum reinforcement spacing accepted by your jurisdiction is generally <18” ____ Spacing dictated by crack control requirements is used __1_ Other, please specify A-13

Generally, it appears that the 12” maximum reinforcement spacing allowed by most jurisdictions for a wide range of concrete components is enforced for decks designed using the empirical method. It also appears that tighter reinforcement spacing is sometimes used in an attempt to minimize deck cracking problems. 12. Has deck cracking been widely observed in bridges under your agency’s jurisdiction? Yes 21 No 7 If Yes, What types of deck cracks have you observed in bridges under your agency’s jurisdiction? _10__ Longitudinal cracking _20_ Transverse cracking _10_ Map cracking When cracking was first observed? __9__ After exposure to service traffic __8__ After exposure to construction live loads _19__ During/Immediately after curing. If the latter, was there a correlation between ambient conditions and early cracking: Yes 3 No. 6 If Yes, please explain: Minnesota indicated that a significant temperature differential between the girder and deck during curing may cause early cracking. Mississippi indicated that while cracking of the deck was not widely observed, shrinkage cracking was observed in decks when concrete was cast during hot weather. New York reported correlation between deck cracking and low air and beam temperature at the time the deck is cast. Was there any correlation between deck cracking and traffic (traffic counts and percentage of trucks)? Yes 4 No 17 If Yes, please explain below. Positive responses to this question indicated higher tendency of deck cracking for bridges with high ADTT and for more flexible steel girders. A-14

Is the deck cracking type and extent in decks designed using the empirical design method different from cracking in decks designed using the traditional method? Yes 1 No 3 Not Applicable 23 (Empirical deck design not used) If yes, how does the performance of decks designed using the empirical compare to that of standard decks? One respondent indicated that decks designed using the empirical method tends to develop more cracks than conventionally designed deck. The response also indicated that the empirically designed decks tend to develop more cracks parallel to the girders while conventionally designed decks tend to develop cracks transverse to the girders. 13. What type of reinforcement do you use in newer (designed in the last 5 years) concrete decks? _14_ Epoxy-coated rebar (used in approximately _see (a) below_ % of newer decks) __9_ Black rebar (used in approximately _see (b) below_ % of newer decks) __3_ Galvanized rebar (used in approximately _see (c) below_ % of newer decks) ____ Stainless steel rebar (used in approximately _____________ % of newer decks) ____ Stainless steel clad rebar (used in approximately ___________ % of newer decks) __2__ Other (see (d) below) (a) Out of the 14 relevant responses, 12 responses indicated using epoxy-coated bars almost exclusively. One response gave the percentage to be 70% another 80%. (b) Out of the 9 relevant responses, 6 responses indicated using black bars almost exclusively. 20%, 75% and 80% were given by one respondent each. (c) All three relevant responses indicated use in 5% of decks with the balance being epoxy-coated rebar in New York and Pennsylvania and black rebar in South Carolina. (d) New Mexico reported using MMFX rebar in 5% of new decks. Virginia started using the MMFX rebar in 2008 and was planning on using it in all new decks starting January 2010. Generally, epoxy-coated rebar is the most-used type of deck reinforcement. The use of black bars is limited to southern states where the use of deicing chemicals is limited or nonexistent (California, Hawaii, Louisiana, Mississippi and South Carolina). 14. What is the average life span of concrete decks under your agency’s jurisdiction ____ Years A-15

Range of deck life span from 25 years to full bridge life was given. No general trend could be deduced. Some northern states indicated deck life span longer than that given by some southern states. And, What is the main reason decks are replaced _19_ Deterioration of the concrete itself _15_ Corrosion of reinforcement __9_ Extensive cracking __4_ Other, Please state:________________________________________ There was no clear correlation between the reason for deck replacement and the climate (use of deicing chemicals). 15. What type of new concrete superstructures (bridges designed in the last five years) typically used in your jurisdiction and what is the approximate percentage of each type of the total number of concrete bridges? ___% Prestressed I-beam and bulb tees ___% Prestressed adjacent prestressed box beams ___% Prestressed spread prestressed box beams ___% Slab bridges ___% Segmental concrete ___% Reinforced concrete ___% Others, Please specify Out of 27 responses to this question, 21 responses indicated that prestressed I and Bulb Tees are the most-used types varying in percentage from 100% to 40%. Respondents showing different types of construction to be the dominant types are as follows: Arkansas: Reinforced concrete accounts for 75% of bridges California: Cast-in-Place post-tensioned box-girders account for 69% of bridges (85% of bridge area) Louisiana: Bridges are split equally between reinforced concrete slab bridges and prestressed precast beams (I beams and bulb tees combined) Michigan: Prestressed precast spread box beams account for 50% of concrete bridges while prestressed precast beams account for 40% New York: Prestressed precast adjacent box beams account for 45% of concrete bridges while prestressed precast beams account for 20% North Carolina: Prestressed precast adjacent box beams account for 40% of concrete bridges while prestressed precast I and Bulb Tees account for 35%. Virginia: The response stated that reinforced concrete bridges account for 38% of concrete bridges while prestressed precast beams account for 26%. It is not A-16

clear whether culverts are counted in determining reinforced concrete bridges causing them to appear the dominant type.. It appears that the type of construction is mostly a function of past practice and the sections produced by local/regional precasters. 16. Have you observed problems with bearings in concrete bridges? Yes 13 No 15 If Yes: What type of problems? Types of problems cited include: Hawaii: Bulging elastomeric bearing pads. Unseated roller bearings. Louisiana: Lack of anchor bolt cover (riser concrete), resulting in loss of restraint. Bolt shear, resulting in lateral movement of bearing pads. Excessive movement resulting in shear or distortion of bearing pads. Bad detailing, corrosion. North Carolina: Freezing of steel bearings; tearing, deformation, and “walking” of elastomeric bearings Michigan: Bulging, splitting of neoprene Minnesota: Locking of sliding plate type bearings, "walking" of elastomeric bearings, and leaking of elastomer in pot bearings. Mississippi: Older steel sliding bearings tend to lock-up over time Missouri: “Walking” of elastomeric bearings Pennsylvania: Uneven bearing South Dakota: Shifting of neoprene/rubber bearings and hardness inconsistency. Texas: Occasional pad slippage. Washington: Steel-reinforced elastomeric bearings have “walked” Did the problems cause significant unintended forces to develop? Yes 4 No 9 Did the problems result in damage to the concrete beams? Yes 2 No 11 If Yes, please state what type of damage In two responses, the locking of steel sliding bearings tend to cause cracks or spalling in the bottom flange at the beam end or cracking and spalling of substructures. Another response cited cracking near the ends of reinforced concrete T-beams without specifying the type of bearings, if any, used. A-17

Generally, it appears that problems with bearings on concrete bridges are not wide spread. Except for the steel sliding bearings cited above, when bearing problems arise, they do not seem to cause significant damage to the girders. 17. Have you observed cracking of abutments and piers? Yes 20 No 8 If Yes, please state what type of cracks Substructure cracking problems cited include: Alaska: Problems appear to be related to providing too much heat during cold weather concrete construction. Arkansas: Cracking and deflection of abutment backwalls at top of cap Florida: Typically due to time effects, shrinkage or creep. Kansas: Tension cracks Louisiana: Longitudinal, vertical and inclined cracks and spalling Michigan: On rare occasions - Various Causes - settlement, pull out from bearing anchors, corroded steel, shear cracking in hammerhead piers etc. Minnesota: Settlement or shrinkage cracks, shear cracks, diagonal cracks in abutment wingwalls. Missouri: Horizontal cracks along beam edge due to inadequate cover and water ponding, vertical cracks due to thermal movement of superstructure, and diagonal shear cracks New Mexico: Problems mostly observed with the steel expansion bearing devices that locked up and caused spalling of the vertical faces of the pier caps. Replacing the steel expansion bearing devices with elastomeric bearing pads and patching the pier caps appear to have eliminated the problems. New York: Vertical cracking in abutments, corrosion related cracking in piers North Carolina: Horizontal cracks where deicing salt has reached horizontal reinforcing steel. Spalling of pier caps when steel bearings are frozen. Oklahoma: Cracks between wingwalls and backwalls Pennsylvania: Shrinkage cracks. South Dakota: There has been some minor spalling of integral backwall/diaphragm concrete around the embedded ends of concrete beams (mostly on skewed structures). Also, cracks developed on local road double tee structures where the beam ends were welded to anchor plates embedded into the abutment/pier caps. Texas: Flexural, shear and corrosion related. Virginia: Flexural cracks in concrete pier caps. Settlement cracks in abutments Temperature and shrinkage cracks. Wisconsin: Wingwall body cracks Wyoming: Cracks of different orientation in 53% of abutments (including pedestals on abutments), 34% of bent caps and 20% of concrete columns.. The lack of a pattern of the observed problems indicate that these problems are associated more with workmanship and detailing practice more than the design provisions. A-18

18. What is the average service life span of the concrete substructures under your agency’s jurisdiction ____ Years One respondent cited a life span of 40 years for substructures in salt water. Other responses indicated a range of substructure life span from 45 years to bridge life span. One respondent indicated that the goal for new substructures is 100 years. 19. Have you observed problems that you think are related to fatigue in: Rebar Yes 0 No 28 Prestressing strand Yes 0 No 28 Concrete Yes 2 No 25 It does not appear that fatigue of concrete and reinforcement represents a concern to most bridge owners. The only two responses indicating problems with concrete fatigue were those from California and Hawaii. The latter indicated that they are speculating that observed spalling deck problems may be related to fatigue of concrete in addition to cover issues rather than corrosion of rebar. 20. Does your agency specify coatings for concrete substructures? Yes 9 No 19 If Yes, please state what type Types of coatings cited include: Kansas: Mastic system below grade and epoxy above grade Michigan: When specified in the special provisions: acrylic based concrete surface coating. Minnesota: A gray colored cementitious based surface finish or acrylic paint is applied for aesthetic reasons but it also supplies some level of sealing protection. Missouri: Epoxy or urethane protective coating on substructures under deck joints New Mexico: Penetrating Water Repellent Treatment. Other coatings used on exposed concrete surfaces include: special surface finish (color) and permanent anti- graffiti protective coatings New York: Occasionally silane or epoxy coating Oklahoma: Water repellant on pier caps and beam seats Pennsylvania: Penetrating sealer at expansion joints & substructure within 14' of traffic lanes Washington: Pigmented sealer for architectural reasons. Generally, the responses indicate that the use of concrete coatings does not follow any trend. A-19

A.2.3 Lessons Learned from the Questionnaire The responses to the questionnaire indicated that most bridge owners apply the service limit states included in AASHTO LRFD with no, or with few, revisions. The additional limit states used by bridge owners appeared to be related either to owner-specified vehicles, or to address a specific issue that does not seem to be shared by other bridge owner as evident by the lack of use of these additional limit states by other owners. It is expected that some of the other agencies that have not responded to the questionnaire also use permit vehicles in checking some aspects of the design under service loads. The use of permit vehicles to check some service conditions, the desire expressed by some bridge designers to have guidance on applying permit vehicles to service conditions, and, the requirements of the Request For Proposals (RFP) of the NCHRP 12-83 project which included a requirement to consider the treatment of owner-specified vehicles, suggest a need exists for a service load combination for concrete structures that is akin to the Service II limit state used for steel structures. The load factors for live load for such load combination can be determined using the same principles that will be used for calibrating limit states under other service limit states. However, the statistical parameters to be used for permit vehicles will be different from those for random traffic. More detailed discussions on the statistical parameters for permit vehicles are presented in Section 4. A.3 Concrete Serviceability Requirements in Several Modern Bridge Design Specifications A.3.1 AASHTO LRFD The existing AASHTO LRFD Bridge Design Specifications (AASHTO LRFD) was reviewed to identify the service limit states in the specifications. In addition, these limit states were compared to those in the Canadian Highway Bridge Design Code (CHBDC) and the Eurocode to identify any service limit states that does not have an equivalent in AASHTO LRFD; which would represent a potential additional limit states. Table A-1 lists the existing limit states in AASHTO LRFD specifications and the relevant specifications articles. A-20

Table A-1 Existing Service Limit States in AASHTO LRFD AASHTO LRFD Article Basic Provision 2.5.2.6.2 Criteria for Deflection In the absence of other criteria, the following deflection limits may be considered for steel, aluminum, and/or concrete construction: Vehicular load, general - Span/800, Vehicular and/or pedestrian loads - Span/1000, Vehicular load on cantilever arms - Span/300, and Vehicular and/or pedestrian loads on cantilever arms - Span/375. 3.4.1 and 3.6.1.4 Fatigue Fatigue truck and load factors in Table 3.4.1-1. 5.5.3.1 General “Fatigue need not be investigated for concrete deck slabs in multi-girder applications.” “Fatigue of the reinforcement need not be checked for fully prestressed components designed to have extreme fiber tensile stress due to Service III Limit State within the tensile stress limit specified in Table 5.9.4.2.2-1.” 5.5.3.2 Reinforcing Bars “The stress range in straight reinforcement and welded wire reinforcement without a cross weld in the high-stress region resulting from the fatigue load combination, specified in Table 3.4.1-1, shall satisfy: f f ≤ 24 − 0.33 fmin” “The stress range in straight welded wire reinforcement with a cross weld in the high-stress region resulting from the fatigue load combination, specified in Table 3.4.1-1, shall satisfy: f f ≤ 16 - 0.33fmin” 5.5.3.3 Prestressing Tendons “The stress range in prestressing tendons shall not exceed: • 18.0 ksi for radii of curvature in excess of 30.0 ft., and • 10.0 ksi for radii of curvature not exceeding 12.0 ft.” A-21

AASHTO LRFD Article Basic Provision 5.5.3.4 Welded or Mechanical Splices of Reinforcement “For welded or mechanical connections that are subject to repetitive loads, the range of stress, f f, shall not exceed the nominal fatigue resistance given in Table 1.” 5.6.3.6 Crack Control Reinforcement “The ratio of reinforcement area to gross concrete area shall not be less than 0.003 in each direction.” 5.7.3.4 Control of Cracking by Distribution of Reinforcement “The spacing s of mild steel reinforcement in the layer closest to the tension face shall satisfy the following: 700 2e c s ss s d f γ β ≤ − ” “If the effective depth, de, of nonprestressed or partially prestressed concrete members exceeds 3.0 ft., longitudinal skin reinforcement shall be uniformly distributed along both side faces of the component for a distance de/2 nearest the flexural tension reinforcement. The area of skin reinforcement Ask in in.2/ft. of height on each side face shall satisfy: ( )0.012 30 4 s ps sk c A A A d + ≥ − ≤ ” 5.8.5 Principal Stresses in Webs of Segmental Concrete Bridges “The principal tensile stress resulting from the long-term residual axial stress and maximum shear and/or maximum shear combined with shear from torsion stress at the neutral axis of the critical web shall not exceed the tensile stress limit of Table 5.9.4.2.2-1 at the Service III Limit State of Article 3.4.1 at all stages during the life of the structure, excluding those during construction. When investigating principal stresses during construction, the tensile stress limits of Table 5.14.2.3.3-1 shall apply.” A-22

AASHTO LRFD Article Basic Provision 5.9.3 Stress Limitations for Prestressing Tendons “The tendon stress due to prestress or at the service limit state shall not exceed the values: • Specified in Table 1, or • Recommended by the manufacturer of the tendons or anchorages.” 5.9.4.1.1 Compression Stresses “The compressive stress limit for pretensioned and post- tensioned concrete components, including segmentally constructed bridges, shall be 0.60 f′ci (ksi).” 5.9.4.1.2 Tension Stresses “The limits in Table 1 shall apply for tensile stresses.” 5.9.4.2.1 Compression Stresses “Compression shall be investigated using the Service Limit State Load Combination I specified in Table 3.4.1-1. The limits in Table 1 shall apply.” 5.9.4.2.2 Tension Stresses “For service load combinations that involve traffic loading, tension stresses in members with bonded or unbonded prestressing tendons should be investigated using Load Combination Service III specified in Table 3.4.1-1. The limits in Table 1 shall apply.” 5.9.4.3 Partially Prestressed Components AASHTO is considering eliminating partial prestressing “Compression stresses shall be limited as specified in Articles 5.9.4.1.1 and 5.9.4.2.1 for fully prestressed components.” “Tensile stress in reinforcement at the service limit state shall be as specified in Article 5.7.3.4, in which case fs shall be interpreted as the change in stress after decompression.” A-23

AASHTO LRFD Article Basic Provision 5.10.8 Shrinkage and Temperature Reinforcement “For bars or welded wire fabric, the area of reinforcement per foot, on each face and in each direction, shall satisfy: ( ) 1.30 2s y bh A b h f ≥ + 0.11 0.60 s A≤ ≤ ” 5.10.10.1 Splitting Resistance “The splitting resistance of pretensioned anchorage zones provided by reinforcement in the ends of pretensioned beams shall be taken as: r s sP f A= with the stress in steel not to exceed 20 ksi 5.14.2.3.3 Construction Load Combinations at the Service Limit State “Flexural tension and principal tension stresses shall be determined at service limit states as specified in Table 1, for which the following notes apply: • Note 1: equipment not working, • Note 2: normal erection, and • Note 3: moving equipment. Stress limits shall conform to Article 5.9.4.” 5.14.2.6.2 Construction Load Combinations “Tensile stresses in segmental substructures during construction shall be computed for applicable load combinations of Table 5.14.2.3.3-1.” 5.14.1.4.9c Positive Moment Connection Using Prestressing Strand “The stress in the strands used for design, as a function of the total length of the strand, shall not exceed: ( 8) 0.228 dsh pslf − =  ( 8) 0.163 dsh pulf − =  “ Some of the limit states are deterministic or represent detailing requirements. The literature search did not yield information on the background of these limit states and they were A-24

deemed uncalibrateable or “deemed to satisfy”. The literature search yielded information on the following limit states and the information is summarized in the following sections:: • live load deflection of structures, • fatigue of rebar and prestressing strands, • cracking of reinforced concrete components, • tensile stresses of prestressed concrete components, • compressive stresses of prestressed concrete components, As stated in Chapter 1, these limit states and the associated load and resistance factors for SLS are based on apparent successful past practice and have not been subject to a reliability-based calibration. There are no consistent performance levels associated with these limit states although some are associated with differences in environmental or traffic exposure. A.3.1.1 Limitations on the Live Load Deflection of Bridge Structures The current requirements for deflection limits in the AASHTO LRFD have their roots in the corresponding provisions of the Standard Specifications for Highway Bridges, 17th Edition (2002). These provisions have been reviewed repeatedly. Summaries by Wright and Walker (1972), Roeder, et al. (2002), and Barker and Barth (2007) are often referenced. Historically, deflection limits were treated as an issue specific to steel bridges. The ASCE Committee on Deflection Limitations of Bridges of the Structural Division (1958) reported on their examination of the live load deflection limits and depth-to-span ratios in the 1953 American Association of State Highway Officials (AASHO) Standard Specifications for Highway Bridges. A comprehensive review of the deflection limits and depth-to-span ratios and their evolution was completed. The earliest deflection limits were adopted in 1871 by the Phoenix Bridge Company which limited deflection to 1/1200 of the span length for a train moving 30 miles per hour. The American Railway Engineering Association (AREA) adopted depth-to-span ratios in the early 1900’s though the limits were without basis. Depth-to-span ratios for highway bridges were initially set forth in 1913 and adopted by AASHO in 1924. Vibrations became an issue in the 1930’s and the Bureau of Public Roads attempted to provide a correlation between the bridges with vibration problems and bridge properties. The result was limiting deflections to L/800 for simple and continuous spans without pedestrians, L/1000 for simple and continuous spans with pedestrians, and L/300 for cantilevered spans. The ASCE Committee surveyed state highway departments to obtain data on the behavior of bridges and the views of experienced bridge designers. The conclusions of the survey include: maximum oscillations occur with passage of medium weight vehicles not heavy vehicles, reports of objectionable vibrations came from continuous span bridges more often than simple span bridges, and there is no defined level of vibration which constitutes being undesirable. The vibration of the bridge is affected by the following quantities: • Bridge flexibility and associated natural frequency • Flexibility of vehicle suspension and associated natural frequency • Relative weight of vehicles and bridge • Vehicle speed • Profile of approach roadway and bridge deck • Frequency of load application • Motion caused by loads in adjacent spans of continuous span structures A-25

• Damping characteristics of bridge and vehicle The use of depth-to-span ratios began in the early 1900’s with the American Railway Engineering and Maintenance of Way Association (AREMA) specification (at that time AREA) stating that pony trusses and plate girders should have a depth not less than 1/10 of the span length. These ratios have changed little over the years. The current depth-to-span limits are 1/10 for trusses and 1/12 for steel rolled shapes and plate girders. At the time, railroads did not use concrete bridges of any significant length. The early specifications for highway bridges adopted with some modification the depth- span ratios from AREMA for use in steel highway bridges. Deflection limits in the American Association of State Highway Officials (AASHO) Standard Specifications for Highway Bridges was limited to steel composite and noncomposite bridges. No limits or method of calculation of deflections of concrete structures specified. Starting in 1977, provisions related to deflections of concrete bridges were incorporated in the AASHTO Standard Specifications for Highway Bridges: • A method of calculating deflections of concrete structures was introduced in the 1977 Twelfth Edition of AASHTO Standard Specifications for Highway Bridges, however, no deflection limits were specified. • Superstructure depth limitations for continuous structures were introduced in the 1983 Thirteenth Edition of AASHTO Standard Specifications for Highway Bridges, with a requirement that simple spans should have about 10 percent greater depth. Still no deflection limits were specified for concrete structures. • The 1989 Fourteenth Edition of AASHTO Standard Specifications for Highway Bridges contained superstructure depth limitations for both simple and continuous spans as shown in Table A-2. In addition, deflection limits of 1/1000 and 1/800 span length were specified for bridges with and without pedestrian traffic, respectively. For cantilevered arms, deflection limits of 1/375 and 1/300 of cantilever length were specified for bridges with and without pedestrian traffic, respectively. These are the same limits historically specified for steel bridges in AASHTO. Table A-2 Recommended Minimum Depth of Concrete Structures in 1989 AASHTO Superstructure Type Minimum depth in feet Simple spans* Continuous spans* Bridge slabs with main reinforcement parallel to traffic 1.2(S+10)/30 (S+10)/30 T-Girders 0.070S 0.065S Box-Girders 0.060S 0.055S Pedestrian Structure girders 0.033S 0.033S *S = Span length The available research on deflection deals largely with the deflection of steel bridges and the deck cracking which is thought by some to be exacerbated by the flexibility of steel girders. Deflection of concrete bridges is usually investigated as part of the comparison to steel bridge deflections. The available literature indicates that transverse deck cracking can be affected by many different items. Additionally there is disagreement on whether limiting static live load deflection (girder flexibility) is a satisfactory method to prevent deck cracking. Researchers are A-26

equally divided between those that concluded that girder flexibility affects deck cracking and those that concluded that girder flexibility does not affect deck cracking. As indicated by some of the studies, concrete material factors may be more important to reduce the formation of early- age deck cracks. Some modern specifications such as the Ontario Highway Bridge Design Code (OHBDC) and its successor the CHBDC utilize a combination of frequency, perception levels and deflection limits to distinguish between acceptable and unacceptable response. Figure A-1, taken from the 2006 Edition of the CHBDC, illustrated this approach which has the benefit of directly addressing the design issue, vibration control. This is similar to the procedure for building design developed by Murphy. Figure A-1 Deflection provisions in 2006 edition of CHBDC. In the Eurocode live loads include a “vibration factor” to account for stresses caused by vibration, no checks for frequency or displacement are required (EN 1990, 2002). In New Zealand vertical velocity is limited to 0.055 m/s (2.2 in/s) under two 120 kN (27 kip axles) of one HN unit if a bridge carries significant pedestrian traffic or where cars are likely to be stationary. Previous versions included span-to-depth ratios and deflection limits, but these have now been removed. To date, specifications based on determining the frequency have not received wide acceptance in U.S. practice. There has been a perceived difficulty in determining the first fundamental frequency of the bridge. Equations for simple span structures have been available for decades, e.g. Biggs (1964). Similarly, formulas for frequency have been developed for continuous structures of regular geometry. Historically, frequencies could be calculated using the Rayleigh method typically implemented through Newmark’s numerical integration. Roeder, et al. (2002) summarized empirical equations that are based not only on theoretical structural 0 1 2 3 4 5 6 7 98 10 without sidewalks with sidewalk, occasional pedestrian use with sidewalks, frequent pedestrian use first flexural frequency, Hz 1000 500 200 100 50 20.0 10.0 5.0 2.0 1.0 st at ic d ef le ct io n, m m ACCEPTABLE UNACCEPTABLE A-27

dynamics but also have adjustments for apparent behavior in the field. Modern refined computational methods make the determination of frequencies and mode shapes relatively straightforward. Thus there does not seem to be impediments to adoption of an approach similar to that specified by the CHBDC. A.3.1.2 Fatigue-and-fracture Limit States A.3.1.2.1 General The fatigue-and-fracture limit state is divided into two load combinations: Fatigue I for infinite-life fatigue resistance and Fatigue II for finite-life fatigue resistance. These relatively new provisions appeared in the 2009 interim changes to load provisions in Section 3 of the AASHTO LRFD published in early 2009. The fatigue resistance provisions of both concrete and steel bridges in Sections 5 and 6 of the AASHTO LRFD, respectively, were modified accordingly. A.3.1.2.2 Loads General The fatigue load of AASHTO LRFD Article 3.6.1.4 and the fatigue live-load load factors of AASHTO LRFD Table 3.4.1-1 are based upon extensive research on structural-steel highway bridges. The use of this load was extended to fatigue of concrete, reinforcement and prestressing strand. As the origin of fatigue load is in the design of steel bridges, frequent references are made to steel bridges in the discussion below. The fatigue load is the AASHTO LRFD design truck (HS20-44 truck of the Standard Specifications for Highway Bridges) but with a fixed rear-axle spacing of 30 feet. The live-load load factors for the fatigue limit-state load combinations are summarized in Table A-3. Table A-3 Fatigue Live-Load Load Factors Fatigue Limit-State Load Combination LL Load Factor Fatigue I 1.50 Fatigue II 0.75 Infinite-life Fatigue The Fatigue I load factor of 1.50, used to design highway bridges with higher traffic volumes for infinite fatigue life, is based upon a 1-in-10,000 rate of exceedance (Dexter and Fisher 2000). This stress range is the stress range below which the inherent flaws in steel do not propagate to significant crack sizes during the design life of the bridge. If all of the stress ranges experienced by a detail are below this value, the detail is assumed to have infinite life. Thus, this stress range represents a maximum limit to achieve infinite life. This value was revisited in this study through simulation using weigh-in-motion (WIM) data. A-28

Finite-life Fatigue This limit state is not used for concrete structures and, therefore, is not discussed in this report. Limited information related to revisions to the finite-life fatigue (Fatigue II limit state) provisions in AASHTO LRFD are provided for information only as they are parallel to the revisions to Fatigue I provisions that are applicable to concrete components. The development of the information on Fatigue II limit state can be found in Kulicki et. al. (2013). Recommendations The stress ranges represented by both of these load factors (the RMC and the exceedance of 1 in 10,000) are based upon observations on steel highway bridges and structural-steel laboratory specimens. Extending these stress ranges to steel reinforcement, both non-prestressed and prestressed, is quite appropriate as the stress ranges represent fatigue-damage accumulation in steel. It is assumed that these fatigue-damage accumulation models apply to concrete in compression as well as steel reinforcement. This approach is proposed for this study as well. A validation of these principles for concrete highway bridges is far beyond the scope and funding of this study. A.3.1.2.3 Fatigue Resistance of Concrete Structures The fatigue resistance of concrete, non-prestressed reinforcement and prestressing tendons in the AASHTO LRFD is based upon ACI Committee Report ACI 215R-74(92), Considerations for Design of Concrete Structures Subjected to Fatigue Loading (1997). This reference includes an extensive bibliography on fatigue resistance of concrete and its reinforcement. Concrete The compressive stress limit of 0.40fc′ for fully prestressed components in other than segmentally constructed bridges of AASHTO LRFD Article 5.5.3.1 applies to a combination of the Fatigue I limit-state load combination (which includes only live load) plus one-half the sum of the effective prestress and permanent loads after losses (a load combination derived from a modified Goodman diagram). This suggests that it represents an infinite-life check as the Fatigue I limit-state load combination corresponds with infinite fatigue life. ACI 215R-74(92) indicates that the fatigue resistance of concrete in the form of an S-N curve (stress range versus number of cycles) is approximately linear between 100 and 10 million cycles. It does not exhibit a constant-amplitude fatigue threshold up to that point (would be indicated by a horizontal S-N curve). Further, it suggests that the compression stress limit of 0.4fc′ is based upon a target fatigue life of 10 million cycles. For highway bridges, a target fatigue life of 10 million cycles is significantly less than the design life. A highway bridge with an ADTT of 2,000 trucks per day would experience over 50 million cycles during its 75-year design life. For this study, the research used to define these S-N curves, Ople and Hulsbos (1966), was re-evaluated to estimate the fatigue resistance to about 108 cycles (100 million), a practical upper bound for highway bridges. The uncertainty of the fatigue resistance will be quantified in terms of bias, mean, and coefficient of variation (COV). A-29

For this study, the research used to define these S-N curves, Ople and Hulsbos (1966), was re-evaluated to estimate the fatigue resistance to about 108 cycles (100 million), a practical upper bound for highway bridges. The uncertainty of the fatigue resistance will be quantified in terms of bias, mean and coefficient of variation (COV). Non-prestressed Reinforcement As used herein, non-prestressed reinforcement includes straight reinforcing bars and welded-wire reinforcement. AASHTO LRFD Article 5.5.3.2 specifies the fatigue resistance of these types of reinforcement. The fatigue resistance of straight reinforcing bars and welded-wire reinforcement without a cross weld in the high-stress region (defined as one-third of the span on each side of the section of maximum moment) is specified as: ( ) min24 0.33THF f∆ = − (A-1) where fmin is the minimum stress. For welded-wire reinforcement with a cross weld in the high-stress region, the fatigue resistance is specified as: ( ) min16 0.33THF f∆ = − (A-2) Equations (A-1) and (A-2) implicitly assume a ratio of radius to height (in other words, r/h) of the rolled-in transverse bar deformations of 0.3. These fatigue resistances are defined as constant-amplitude fatigue thresholds in AASHTO LRFD. ACI Committee Report ACI 215R-74(92) and the supporting literature indicate that non-prestressed reinforcement exhibits a constant-amplitude fatigue threshold yet it is unclear that these equations are in fact the threshold values. ACI 215R-74(92) suggests that the resistances are “a conservative lower bound of all available test results.” In other words, a horizontal constant-amplitude threshold has been drawn beneath all of the curves. The studies used to define the fatigue resistance of non-prestressed reinforcement (Fisher and Viest, 1961; Pfister and Hognestad, 1964; Burton and Hognestad, 1967; Hanson, et al., 1968; Helgason, et al., 1976; Lash, 1969; MacGregor, et al., 1971; Amorn, et al., 2007) were re-analyzed to estimate constant-amplitude fatigue thresholds for steel reinforcement in tension and concrete in compression and to determine their uncertainty, in terms of bias, mean and coefficient of variation. The various thresholds were grouped together to make design practical and more rational than the single threshold currently defined. The AASHO Road Test (1962) demonstrated that a bridge does not necessarily collapse due to fracture subsequent to fatigue of non-prestressed reinforcement. Such non-prestressed- reinforcement fracture yields distress such as excessive deflection and wide cracks which facilitates detection and subsequent repair. This consequence suggests that a target reliability index less than that for strength limit states would be acceptable (in other words, βT < 3.5). A-30

Prestressing Tendons Fully prestressed components satisfying the tensile stress limits specified in AASHTO LRFD Table 5.9.4.2.2-1 at the Service III limit-state load combination are exempt from fatigue considerations. (The Service III limit-state load combination and its calibration is discussed in other sections of this report) This exemption acknowledges that tendons in uncracked prestressed concrete components designed to the requirements of Article 5.9.4 of AASHTO LRFD do not experience stress ranges which result in fatigue cracking. Most prestressed concrete bridge members are covered by this exemption. For segmentally constructed bridges, AASHTO LRFD Article 5.5.3.3 specifies the fatigue resistance of prestressing tendons as given in Table A-4. Reductions in stress range limits for fretting fatigue are not included in the tabulated values. Table A-4 Prestressing-Tendon Fatigue Resistance Radius of Curvature (Feet) Constant-Amplitude Fatigue Threshold (Ksi) > 30 18 ≤ 30 and > 12 Linear Interpolation Between 18 and 10 ≤ 12 10 No in-service fatigue cracking of prestressing tendons has been observed, thus justifying the exemption. The majority of the research on fatigue cracking of prestressing strands is based upon testing of tendons in air. Application of the resultant fatigue resistance to concrete members with prestressing tendons is questionable (Hanson, et al., 1970; Tachau, 1971; Warner and Hulsbos, 1966). Thus, the uncertainty of the fatigue resistance of prestressing tendons in concrete members is not well documented. Further, the determination of stress ranges in cracked prestressed concrete members is complicated and beyond the normal prestressed concrete member design procedure (Abeles, et al., 1969; Abeles and Brown, 1971; Abeles, et al., 1974). The uncertainty of this determination is also not well defined. As such, it is proposed that this fatigue limit state not be calibrated. Welded and Mechanical Splices of Reinforcement In AASHTO LRFD Article 5.5.3.4, constant-amplitude fatigue thresholds are given in Table 5.5.3.4-1. These values are used in the general fatigue limit state equation (AASHTO LRFD Equation 5.5.3.1-1) for the design of welded or mechanical splices of reinforcement for infinite fatigue life. Review of the available test data in NCHRP Research Results Digest 197 (1994) suggests that any splice capable of developing 125 percent of the yield strength of the bar will sustain 1 million cycles of a 4 ksi constant-amplitude stress range. This fatigue limit is a close lower bound for the splice fatigue data obtained in NCHRP Research Results Digest 197 (1994). A-31

NCHRP Research Results Digest 197 (1994) found that there is substantial uncertainty in the fatigue performance of different types of welds and connectors much as structural-steel details. However, all types of splices appeared to exhibit a constant-amplitude fatigue limit for repetitive loading exceeding about 1 million cycles. The stress ranges for over 1 million cycles of loading given in AASHTO LRFD Table 5.5.3.4-1 are based on statistical tolerance limits to constant-amplitude staircase test data, such that there is a 95 percent level of confidence that 95 percent of the data would exceed the given values for 5 million cycles of loading. These values may, therefore, be regarded as a fatigue limit below which fatigue damage is unlikely to occur during the design lifetime of the structure. This is the same basis used to establish the fatigue design provisions for unspliced reinforcing bars in AASHTO LRFD Article 5.5.3.2, which is based on fatigue tests reported in NCHRP Report 164 (Helgason, et al., 1976). Table A-5 Constant-Amplitude Fatigue Threshold of Splices from AASHTO LRFD Table 5.5.3.4-1 Type of Splice (ΔF)TH for greater than 1,000,000 cycles Grout-filled sleeve, with or without epoxy-coated bar 18 ksi Cold-swaged coupling sleeves without threaded ends and with or without epoxy-coated bar; Integrally-forged coupler with upset NC threads; Steel sleeve with a wedge; One-piece taper-threaded coupler; and Single V-groove direct butt weld 12 ksi All other types of splices 4 ksi . A.3.1.3 Cracking of Reinforced Concrete Structures Cracking in reinforced concrete structures is controversial but must be controlled for aesthetic purposes, durability, and corrosion resistance. Cracking is primarily caused by flexural and tensile stresses, but also from temperature, shrinkage, shear, and torsion. Although researchers do not agree on any single crack width equation, the most significant parameters to control cracking are widely agreed upon. The most sensitive factor is the reinforcing steel stress, followed by concrete cover, bar spacing, and the area of concrete surrounding each bar. It has been agreed upon that the bar diameter is not a major variable. For engineering practice, equations in the ACI 318-08 Code (ACI Committee 318, 2008) and AASHTO LRFD (2012) are used to control cracking. The corresponding provisions are discussed below. A.3.1.3.1 Crack Control Reinforcement This section reviews previous research studies on control of cracking as well as predicting crack width in concrete members. A significant amount of research has been conducted to investigate crack control in concrete members. The research resulted in the development of numerous equations to predict the crack width on the tension surface and the side faces at the level of reinforcement. Equations available to predict crack width were developed for the concrete members with cover less than 2.5 in. and are not applicable for beams with larger concrete cover. Different equations have been adopted by different codes. A-32

However, for calibration purposes, these equations were evaluated with regard to accuracy and applicability. The results from various equations were compared and validated using data collected from available literature. One of the early studies by Clark (1956) included testing 58 specimens and collecting over 105 crack width readings. Clark concluded that the average crack width is closely related to the following parameters: 1) the diameter of the reinforcing bar, 2) the total reinforcement ratio, 3) area of the beam section, and 4) the distance from the bottom reinforcement to the beam bottom surface. Moreover, Clark stated that the average width was also proportional to the stresses in the reinforcing bars beyond the cracking stress. He suggested that the width of the cracks can be reduced by using a large number of small diameter bars and by increasing the amount of the steel reinforcement. Based on these results, Equation (A-3) was developed to predict the average crack width of the concrete beams. The maximum crack width was estimated by multiplying the average crack width by 1.64 (Clark 1956). 1 2 1 ave s Dw C f C n p p    = − +      (A-3) where eA = bd, in² b = width of component, in. 1C , 2C = coefficients that depend on distribution of bond stress, bond strength, and tensile strength of concrete, for Clark’s study; ( )81 2.27 10 /C h d d−= × − , 2 56.6C = d = distance from compressive face of beam/slab to centroid of longitudinal tensile reinforcement, in. D = diameter of reinforcing bar, in. sf = computed stress in reinforcement, psi h = overall depth of beam/slab, in. n = ratio of modulus of elasticity of steel to concrete (assumed to be 8 in Clark’s study) p = /s eA A = cross-sectional area of reinforcement/cross-sectional area of concrete avew = average width of cracks, in. Kaar and Mattock (1963) also developed a well-known crack width equation for bottom face cracking as follows: 40.115b sw f Aβ= (A-4) where A-33

A = average effective concrete area around reinforcing bar, having same centroid as reinforcement, in² sf = steel stress calculated by elastic crack section theory, ksi bw = maximum crack width, 0.001 in. β = ratio of distances to neutral axis from extreme tension fiber and from centroid of reinforcement Broms (1965) conducted tests on 37 tension and 10 flexural members to analyze crack width and crack spacing. Broms observed that the crack spacing decreased rapidly with increasing load and a number of primary tensile cracks formed on the surface of flexural and tension members. Secondary tensile cracks were confined to the surrounding area of reinforcement. The study concluded that the absolute minimum visible crack spacing is the same as the distance from the surface to the center of the reinforcing bar located nearest to the surface of the member. Thus, the theoretical minimum crack spacing is equal to the thickness of the concrete cover (Broms, 1965). Gergely and Lutz (1968) developed an equation to predict the crack width based on a detailed statistical assessment of experimental data available in the literature at the time. Gergely and Lutz identified various parameters, such as reinforcing bar locations, stresses in the reinforcement, concrete cover depth, and spacing of the reinforcement, as the controlling factors affecting the crack width. The Gergely and Lutz equation is presented as follows: 30.076b s cw f Adβ= (A-5) where A = average effective concrete area around reinforcing bar, having same centroid as reinforcement, in² cd = bottom cover measured from center of lowest bar, in. sf = steel stress calculated by elastic crack section theory, ksi bw = maximum crack width, 0.001 in. β = ratio of distances to neutral axis from extreme tension fiber and from centroid of reinforcement The maximum concrete cover tested in this study was 3.31 in. However, only three test specimens over 2.5-in. cover were tested in the study. In the study by Frosch (1999), the crack widths were determined from an equation developed based on a physical model. Results were compared with the test data used in Kaar and Mattock (1963) and Gergely and Lutz (1968). The crack width model developed in this study showed that the crack spacing and width are functions of the distance between the reinforcing steel. Crack control can be achieved by limiting the spacing of these reinforcing bars. Based on the research findings, Frosch (1999) suggested that limiting the maximum bar spacing would prevent large cracks in the concrete beams. A-34

Based on the physical model, the equation to calculate the maximum crack width for uncoated reinforcement was developed as shown below (Frosch, 1999): 2 22 2 s c c s f sw d E β   = +      (A-6) where sE = elastic modulus of steel reinforcement (can be taken as 29000 ksi) cd = bottom cover measured from center of lowest bar, in. sf = stress in steel reinforcement, ksi s = maximum permissible bar spacing, in. cw = limiting crack width, in. (0.016 in, based on ACI 318-95 (ACI Committee 318, 1995)) β = 1.0 + 0.08 cd Frosch (1999) suggested that for epoxy-coated reinforcement, the above equation for uncoated reinforcement should be multiplied by a factor of 2. Equation (A-6) is rearranged to solve for the allowable bar spacing as follows: 2 22 2 c s c s w Es d f β     = −     (A-7) Based on the physical model, the following design recommendation that addresses the use of the both uncoated and coated reinforcement was presented. The equation to calculate the maximum spacing of reinforcement was given as follows (Frosch, 1999): 12 2 12 3 c s s s ds α α α   = − ≤    (A-8) where 36 s c sf α γ= cd = thickness of concrete cover measured from extreme tension fiber to center of bar or wire located closest thereto, in. sf = calculated stress in reinforcement at service load, ksi. It shall be computed as the moment divided by the product of steel area and internal moment arm. sf shall not exceed 60 percent of the specified yield strength yf . A-35

s = maximum spacing of reinforcement, in. sα = reinforcement factor cγ = reinforcement coating factor: 1.0 for uncoated reinforcement; 0.5 for epoxy-coated reinforcement, unless test data can justify a higher value Frosch (2001) summarized the physical model for cracking, and illustrated the development and limitations of the proposed design method. He recommended formulas for calculating the maximum crack width for uncoated and epoxy-coated reinforcement as well as the design recommendation for their use similar to those in Frosch’s paper published in 1999. In general, largest crack widths are expected at the extreme tensile face of the beam. However, Beeby (1979) conducted studies that showed the largest crack widths occurring in the web along the beam side face occurred at about mid-height. Frosch (2002) conducted research on the modeling and control of cracking in side face of the concrete beams. The study showed that to provide adequate crack control the maximum skin reinforcement spacing is a function of the side concrete cover. It was also shown that a maximum bar spacing of 12 in. provides reasonable crack control up to 3 in. of concrete cover. The crack model developed by Frosch (2002) allows for the calculation of the crack width at any location along the cross section. A profile of the crack width through the depth of the section is more easily created and allows for information regarding optimum locations for placing skin reinforcement for the purpose of controlling side face cracks. Frosch (2002) showed that the crack spacing and crack width along the side face are functions of the distance from the reinforcement, so the crack can be controlled by adding skin reinforcement and limiting the reinforcement spacing. Since the maximum crack width was observed at halfway between the reinforcement and neutral axis, the following equation can be used to solve for the crack width at ( ) / 2x d c= − : ( ) 2 2 1 2c s s w d d cε  = + −    (A-9) where c = depth of neutral axis from compression face, in. sd = concrete cover for skin reinforcement, in. d = effective depth, in. sε = reinforcing strain = /s sf E The study of the physical model showed that sections with effective depth of 36 in. and covers up to 3 in. can be designed without skin reinforcement. For thicker covers, the maximum effective depth not requiring skin reinforcement should be decreased. Additionally, maximum effective depth decreases for covers thicker than 3 in. for Grade 60 reinforcement resulting in the maximum depth, d = 36 in. A-36

In order to prevent excessive cracks throughout the depth of the section, maximum spacing of the reinforcement should be determined. According to Frosch (2002), the placement of the first bar is the most critical for the spacing of the skin reinforcement. The maximum crack width was calculated halfway between the primary reinforcement and the first skin reinforcement bar at a distance / 2x s= , yielding the following equation: 2 22 2 s s s s f sw d E  = +     (A-10) For sections where skin reinforcement exists, it is necessary to determine the location in the section where the reinforcement can be discontinued. Since crack widths are controlled by skin reinforcement below its end point, it is required to calculate the maximum distance sna where the skin reinforcement can be eliminated. The maximum crack width will occur approximately halfway between the neutral axis and the location of the first layer of skin reinforcement at a distance / 2nax s= from the neutral axis (Frosch, 2002). The maximum crack width, ws, can be calculated with the following equation based on the physical model developed by Frosch (2002): 2 2 2 s na s na s sw s d d c ε   = +   −    (A-11) where nas = maximum distance where the skin reinforcement can be eliminated. Frosch (2002) recommended that the design formula should be based on a physical model to address the control of cracking in reinforced concrete structures and to unify the design criteria for controlling cracking in side and bottom faces. Frosch (2002) recommended the maximum spacing of flexural tension reinforcement as follows: 12 2 12 3 c s s s ds α α α   = − ≤    (A-12) where 36 s sf α = cd = thickness of concrete cover, in., for bottom-face reinforcement, measured from extreme tension fiber to center of bar, and for skin reinforcement, measured from side face to center of bar sf = calculated stress in reinforcement at service load, ksi. It shall be computed as the moment divided by the product of steel area and internal moment arm. It shall be A-37

permitted to take sf as not more than 60 percent of the specified yield strength yf . s = maximum spacing of reinforcement, in. sα = reinforcement factor Skin reinforcement shall be required along both side faces of a member for a distance d/2 from the nearest flexural tension reinforcement if the effective depth exceeds the depth calculated by Equation (A-12) shown below: 42 2 36s c sd dα α= − ≤ (A-13) Epoxy-coated reinforcement is widely used to increase the durability of structures. The epoxy coating has been shown to decrease bond strength which can decrease crack spacing and increase crack widths when compared to uncoated reinforcement (Blackman and Frosch, 2005). Blackman and Frosch investigated crack width of the concrete beams with epoxy-coated reinforcement. The primary variables used in the study include epoxy coating thickness and reinforcing bar spacing. Blackman and Frosch designed ten slab specimens in order to examine the effect of epoxy coating on cracks. It was concluded that the epoxy coating thickness does not affect the concrete crack significantly. Frosch (1999), Frosch (2001), Frosch (2002), and Blackman and Frosch (2005) presented an equation to compare the average measured crack spacing for the uncoated and epoxy-coated bars with the calculated values: * c sS dψ= (A-14) where cS = crack spacing, in. *d = controlling cover distance, in. sΨ = crack spacing factor: 1.0 for minimum crack spacing; 1.5 for average crack spacing; 2.0 for maximum crack spacing Cracking of structures is rather common and is not always damaging to the structure. However, when considering a bridge deck, moderately sized cracks can be detrimental to the longevity of the structure due to the exposure to harsh environments. Recently, increased concrete cover, coupled with the use of high-performance concrete, are becoming increasingly popular because of their durability. This results in unrealistically small bar spacing and prevents the use of contemporary crack control practices that are based on statistical studies. Therefore, it is desirable to develop methods to predict average and maximum crack widths of reinforced concrete members with thicker concrete covers at various locations. Choi and Oh (2009) studied the crack width for transversely post-tensioned concrete deck slabs in box girder bridges. They tested four full-scale concrete box girder segments, and then derived the maximum crack width equation from the testing data as follows: A-38

( ) 0.75 ,6 max 03 10 t eff s s st pt A h xw f f A A d x −   − = × −   + −  φ ξ (A-15) ( )1 = ap s as p n n τ π φ ξ τ π φ + − (A-16) where stA = total area of reinforcing bars, mm2 ptA = total area of prestressing tendons, mm 2 ,t effA = effective tensile concrete area, mm 2 d = effective depth, mm sf = increment of reinforcing bar stress after decompression, MPa 0f = steel stress at the initial occurrence of crack, MPa h = height of cross section, mm = number of strands in a flat duct. x = depth of neutral axis, mm maxw = predicted maximum crack width, mm sφ = diameter of reinforcing bar, mm pφ = diameter of prestressing tendons, mm ap as τ τ = 0.465 for grouted post-tensioned tendons A.3.1.3.2 Control of Cracks in Current Specifications Provisions The code provisions specifying the distribution of reinforcement are reviewed in this section. ACI requirements for flexural crack control in beams and thick one-way slabs are based on the statistical analysis of maximum crack width data from several sources (Gergely and Lutz, 1968). ACI maintains that crack control is particularly important when reinforcement with yield strength over 40,000 psi is used. Good detailing practices such as concrete cover and spacing of reinforcement should lead to adequate crack control even when reinforcement with yield strength 60,000 psi is used. ACI 318-08 (ACI Committee 318, 2008) Article 10.6 does not distinguish between interior and exterior exposure since corrosion is not clearly correlated with surface crack widths in the range normally found at service load levels. ACI 318-08 only requires that the spacing of reinforcement closest to the tension face, s, shall not exceed that given by: 40,000 15 2.5 c s s c f   = −    (A-17) A-39

but not greater than 40,000 12 sf       , where cc is the least distance from surface of reinforcement or prestressing steel to the tension face. If there is only one bar or wire nearest to the extreme tension face, s used in Equation (A-17) is the width of the extreme tension face. These provisions are not sufficient for structures subject to very aggressive exposure or designed to be watertight. Special investigation is required for structures subject to very aggressive exposure or designed to be watertight. ACI 318-99 (ACI Committee 318, 1999) limited the maximum spacing to 12 in., but this limitation was removed in ACI 318-08 (ACI Committee 318, 2008). ACI 318-08 also recommends the use of several bars at moderate spacing rather than fewer bars at larger spacing to control cracking. These provisions were updated recently to reflect the higher service stresses that occur in flexural reinforcement with the use of the load combinations introduced in ACI 318-02 (ACI Committee 318, 2002). The maximum bar spacing is specified to directly control cracking. Similar recommendations have been stated for deep beams with the requirement of skin reinforcement. AASHTO LRFD (2012) also provides provisions of reinforcement spacing to control flexural cracking. Similar to the equation adopted in ACI, AASHTO emphasizes the importance of reinforcement detailing and that smaller bars at moderate spacing tend to be more effective than an equivalent area of larger bars. AASHTO LRFD also agrees with ACI 318-08 on the most important parameters affecting crack width and specifies a formula for distribution of reinforcement to control cracking. The equation in AASHTO LRFD (2008) is based on the physical crack model of Frosch (2001) rather than on the statistically-based model used in previous editions. The equation limits bar spacing rather than crack width as follows: 700 2e c s ss s d f γ β ≤ − (A-18) where cd = thickness of concrete cover measured from extreme tension fiber to center of the flexural reinforcement located closest thereto (in.) ssf = tensile stress in steel reinforcement at the SLS (ksi) h = overall thickness of depth of the component (in.) 1 0.7( ) c s c d h d β = + − (geometric relationship between crack width at tension face versus crack width at reinforcement level) eγ = exposure factor = 1.00 for Class 1 exposure, 0.75 for Class 2 exposure As shown above, unlike ACI, AASHTO specifies exposure conditions to meet the needs of the authority having jurisdiction. Class 1 exposure condition is based on a maximum crack width of 0.017 in. and applies when cracks can be tolerated due to reduced concerns of appearance and/or corrosion. This exposure class can be thought of as an upper bound in regards to crack width for appearance and corrosion. Class 2 exposure condition generally applies to decks and substructures exposed to water and any other components exposed to A-40

corrosive environments. AASHTO LRFD (2008) also specifies requirements for skin reinforcement based on ACI 318-11 (ACI Committee 318, 2011). AASHTO LRFD Equation 5.7.3.4-1, or Equation (A-18) above, also applies to both reinforced and prestressed concrete, with specifications on the steel stresses used. In general, if AASHTO Class 2 exposure condition is used, all AASHTO spacings were less than those derived by the ACI equation. However, if Class 1 exposure condition is used, ACI spacing becomes more conservative. A.3.1.4 Principal Stresses in Webs of Segmental Concrete Bridges Recently, Okeil (2006) studied the allowable tensile stress for webs of prestressed segmental (PS) concrete bridges using a reliability-based approach. In this study, six PS concrete bridge designs were analyzed. Okeil states that by complying with the allowable tensile stresses, flexural cracking at the top and bottom fibers is controlled. However, for the webs, cracks might develop due to a biaxial stress state resulting from a combination of shear and normal stresses. Controlling shear cracking requires that the principal stress be limited to an allowable tensile stress, ft ,all . This issue has been addressed by the Florida Department of Transportation (Structures Manual, 2013) and produced a recommendation for the allowable tensile stresses to be used in checking web tensile principal stress, σ1. However, the recommendation ignored the accompanying compressive principal stress, σ 2 , which has a significant effect on the tensile strength of concrete. The objective of Okeil’s study was to develop an allowable stress limit under which cracking in webs of PS bridges under service load conditions can be controlled. Three equations were considered: ACI (ACI Committee 318, 2005), Kupfer and Gerstle (1973), and Oluokun (1991), as shown in Equations (A-19) through (A-21), respectively: ftu = 6.7( fc ' )0.5, in psi (A-19) ftu =1.59( fc ' )0.67 , in psi (A-20) ftu =1.38( fc ' )0.69 , in psi (A-21) where cf ′ = concrete compressive strength, psi ftu = uniaxial tensile strength of concrete, psi Okeil concluded that Equation (A-21) provides better estimate of the tensile strength over a wider range of concrete compressive strength. Using a biaxial state of stress and regression analysis, Okeil (2006) developed a relationship between the tensile strength and the corresponding compressive strength as follows: 1 0.85tu cu tu cf f σ σ = + ′ (A-22) where A-41

cuσ , tuσ = ultimate strengths of concrete under compression-tension biaxial state of stress Equation (A-23) is obtained by combining Equation (A-21) and Equation (A-22): σ tu =1.38( fc ' )0.69(1+ 0.85 σ cu fc ' ) , in psi (A-23) After a detailed parametric study and reliability analysis, Okeil (2006) recommended an expression for estimating the allowable tensile stress in webs of post-tensioned segmental bridges under biaxial stresses as follows: 0.7 20.60( ) (1 0.85 )ct c c f f f σ′= + ′ (A-24) where 2σ = principal stresses in centroidal stress block in web of PS bridge, ksi It should be noted that the findings of this study are limited to the range of concrete compressive strength between 5 to 8 ksi. A.3.1.5 Stress Limitations for Prestressing Tendons AASHTO LRFD (2012) provides stress limits for prestressing tendons at various service conditions. The stress limit values are listed in Table A-6. ACI 318-08 provides similar limits on the tensile stress in prestressing tendons and rebar (ACI Committee 318, 2008). Major revision of the limits was made in the 1983 version of ACI 318 to incorporate the higher yield strength of low-relaxation wire and strand (ACI Committee 318, 1983). The ACI 318-08 stress limits in prestressing steel are listed as follows (ACI Committee 318, 2008): Due to prestressing steel jacking force: pyf94.0 but not greater than the lesser of puf80.0 and the maximum value recommended by the manufacturer of prestressing steel or anchorage devices. Immediately after prestress transfer: pyf82.0 but not greater than puf74.0 . Post-tensioning tendons, at anchorage devices and couplers, immediately after force transfer: puf70.0 . EN1992-2 (Eurocode 2): Design of Concrete Structures (EN1992-2, 2003) restricts inelastic deformation of the steel in concrete structures at the SLS to prevent large, permanently open cracks. In EN1992-2, at the SLSs, the stress limit for prestressing steel is pkf75.0 after A-42

allowance for losses, where pkf is characteristic tensile strength of prestressing steel. The exact meaning of “characteristic” tensile strength is not defined in EN1992-2 and is interpreted herein as the specified strength. This limit of pkf75.0 is listed in EN1992-2, Section 7. Table A-6 Stress Limits for Prestressing Tendons (AASHTO LRFD, 2012) Condition Tendon Type Stress-Relieved Strand and Plain High-Strength Bars Low Relaxation Strand Deformed High- Strength Bars Pretensioning Immediately prior to transfer ( pbtf ) pu f70.0 puf75.0 _ At SLS after all losses ( pef ) py f80.0 pyf80.0 pyf80.0 Post-Tensioning Prior to seating - short-term pbtf may be allowed pyf90.0 pyf90.0 pyf90.0 At anchorages and couplers immediately after anchor set puf70.0 puf70.0 puf70.0 Elsewhere along length of member away from anchorages and couplers immediately after anchor set puf70.0 puf74.0 puf70.0 At SLS after losses ( pef ) py f80.0 pyf80.0 pyf80.0 A.3.1.6 Concrete Tension Stresses The early discussion of cracking control is diverse. At the First United States Conference on Prestressed Concrete in 1951, some experts opined that a completely crackless concrete member is only better for a specific purpose, but others thought that cracking of prestressed concrete beams is as important as yielding. In 1958, the “Tentative Recommendations for Prestressed Concrete” proposed by ACI-ASCE Joint Committee 323 suggested that prestressed concrete before losses due to creep and shrinkage should meet the following limits (note unit in the following provisions is psi for the allowable tensile stress): 3 cif ′ for members without non-prestressed reinforcement; A-43

6 cif ′ for members with non-prestressed reinforcement provided to resist the tensile force in concrete; computed on the basis of an uncracked section. The 1963 Building Code Requirements for Reinforced Concrete (ACI Committee 318, 1963) included the recommendation for the tensile stress limits, in psi, as proposed by ACI- ASCE Joint Committee 323 (1958), with some modifications, as follows: 3 cif ′ for members without auxiliary reinforcement in the tension zone; When the calculated tension stress exceeds 3 cif ′ , reinforcement shall be provided to resist the total tension force in the concrete computed on the assumption of uncracked section. The 1977 Building Code Requirements for Reinforced Concrete modified the allowable tensile stress limit, in psi, as follows (ACI Committee 318, 1977): 6 cif ′ for the extreme fiber stress in tension at ends of simply supported members; 3 cif ′ for the extreme fiber stress in tension at other locations. In the current ACI 318-11, Section 18.4.1 specifies the allowable tensile stress in concrete immediately after prestress transfer (before time-dependent prestress losses) as follows (ACI Committee 318, 2011): Where computed concrete tensile strength, tf , exceeds 6 cif ′ at ends of simply supported members, or 3 cif ′ at other locations, additional bonded reinforcement shall be provided in the tensile zone to resist the total tensile force in concrete computed with the assumption of an uncracked section. The AASHTO Standard Specifications for Highway Bridges (1992) specified the allowable tensile stresses, before losses due to creep and shrinkage, as follows: 200 psi or 3 cif ′ for members in tension areas with no bonded reinforcement; Where the calculated tensile stress exceeds this value, reinforcement shall be provided to resist the total tension force in the concrete computed on the assumption of uncracked section. The maximum tensile stress shall not exceed 7.5 cif ′ . Table A-7 shows the tensile stress limits and provisions by the AASHTO LRFD (2012). A-44

Table A-7 Tensile Stress Limits in Prestressed Concrete at SLS after Losses, Fully Prestressed Components (AASHTO LRFD, 2012, Table 5.9.4.2.2-1) Bridge Type Location Stress Limit Other Than Segmentally Constructed Bridges Tension in the precompressed Tensile Zone Bridges, Assuming Uncracked Sections For components with bonded prestressing tendons or reinforcement that are subjected to not worse than moderate corrosion condition. For components with bonded prestressing tendons or reinforcement that are subjected to severe corrosive conditions For components with unbonded prestressing tendons 0.19 ( )cf ksi′ 0.0948 ( )cf ksi′ No tension Segmentally Constructed Bridges Longitudinal Stresses Through Joints in the Precompressed Tensile Zone Joints with minimum bonded auxiliary reinforcement through the joints sufficient to carry the calculated longitudinal tensile force at a stress of 0.5 fy; internal tendons or external tendons Joints without the minimum bonded auxiliary reinforcement through joints 0.0948 ( )cf ksi′ No tension Transverse Stress Through Joints Tension in the transverse direction in precompressed tensile zone 0.0948 ( )cf ksi′ Principal Tensile Stress at Neutral Axis in Web All types of segmental concrete bridges with internal and/or external tendons, unless the Owner imposes other criteria for critical structures. 0.110 ( )cf ksi′ A.3.1.7 Existing Limit States that are Deterministic or Represent Detailing Requirements The following limit states exist in AASHTO LRFD. Reviewing the background of these limit states revealed that they are either deterministic or represent detailing requirements that cannot be calibrated. No calibration is anticipated for these limit states. Fatigue in Concrete Deck Slabs and Culvert Top Slabs (AASHTO LRFD Article 5.5.3.1) Stresses measured in concrete deck slabs of bridges and top slabs of box culverts in service are far below infinite fatigue life, most probably due to internal arching action. AASHO Standard Specifications for Highway Bridges (1974 and 1975 Interims) include the background that led to waiving fatigue requirements for these components A-45

Fatigue of Reinforcement of Fully Prestressed Components (AASHTO LRFD, Article 5.5.3.1) For fully prestressed components designed to have extreme fiber tensile stress due to Service III Limit State within the tensile stress limit specified in the AASHTO LRFD Table 5.9.4.2.2-1, the fatigue limit-state load factors, the girder distribution factors, and dynamic load allowance cause fatigue limit-state stress to be considerably less than the corresponding value determined from SLS III. For fully prestressed components, the net concrete stress is usually significantly less than the concrete tensile stress limit specified in AASHTO LRFD Table 5.9.4.2.2-1. Therefore, the calculated flexural stresses are significantly reduced. For this situation, the calculated steel stress range, which is equal to the modular ratio times the concrete stress range, is almost always less than the steel fatigue stress range limit specified in Article 5.5.3.3. Fatigue of Prestressing Tendons (AASHTO LRFD, Article 5.5.3.3) With fatigue in fully prestressed components waived, see above, these provisions are only applicable to segmental bridges. Little data is available on the uncertainty of load and resistance of segmental bridges. There is no evidence of fatigue damage on these structures so no changes are recommended and calibration was not necessary. Crack Control Reinforcement for Components Designed using Strut and Tie Model (AASHTO LRFD, Article 5.6.3.6) Birrcher, et. al., (2009) proposed the new provisions regarding the crack control reinforcement as follows: “The spacing of the bars in these grids shall not exceed the smaller of d/4 and 12.0 in” “The reinforcement in the vertical and horizontal direction shall satisfy the following: 0.003v w v A b s ≥ , 0.003h w h A b s ≥ (A-25) where vA , hA = total area of vertical and horizontal crack control reinforcement within spacing vs and hs , respectively, in2 wb = width of member web, in. vs , hs = spacing of vertical and horizontal crack control reinforcement, respectively, in. “Crack control reinforcement shall be distributed evenly near the side faces of the strut. Where necessary, interior layers of crack control reinforcement may be used.” A-46

A.3.2 Eurocode The Eurocode contains the following sections to which reference is made in some other sections of this report. EN 1990 (Eurocode 0): Basis of Structural Design EN 1991 (Eurocode 1): Actions on Structures EN 1992 (Eurocode 2): Design of Concrete Structures EN 1993 (Eurocode 3): Design of Steel Structures EN 1994 (Eurocode 4): Design of Composite Steel and Concrete Structures EN 1995 (Eurocode 5): Design of Timber Structures EN 1996 (Eurocode 6): Design of Masonry Structures EN 1997 (Eurocode 7): Geotechnical Design EN 1998 (Eurocode 8): Design of Structures for Earthquake Resistance EN 1999 (Eurocode 9): Design of Aluminum Structures These sections allow the user countries to incorporate country-specific requirements through the incorporation of a National Annex. The Eurocode replaced most previous country specifications, such as the German Institute for Standardization (DIN) and the British BS5400 and is expected to eventually replace all other European Union member country specifications. It is assumed that the requirements of the Eurocode encompass those of the previous specifications and, thus, no other European specifications were reviewed. A.3.2.1 Definition of SLS The Eurocode defines the SLSs as those concerning (EN 1990, 2002): • The functioning of the structure or structural members under normal use; • The comfort of users; • The appearance of the construction works. The Eurocode (EN 1990, 2002) includes requirements calling for: • The serviceability requirements to be agreed upon for each individual project. • A distinction to be made between reversible and irreversible serviceability limit states. • The verification of SLS based on criteria concerning the following aspects: a) Deformations that affect – The appearance, – The comfort of users, or – The functioning of the structure (including the functioning of machines or services), or that cause damage to finishes or non-structural members. b) Vibrations – That cause discomfort to people, or – That limit the functional effectiveness of the structure. c) Damage that is likely to adversely affect – The appearance, A-47

– The durability, or – The functioning of the structure. In the context of serviceability, the Eurocode considers the term “appearance” to be concerned with such criteria as high deflection and extensive cracking, rather than aesthetics (EN 1990, 2002). A.3.2.2 Background on the Eurocode’s Reliability Basis The Eurocode specifies that structures be designed for a particular design working life, Tu (EN 1990, 2002). The design working life is defined as the period for which a structure is assumed to be usable for its intended purpose with anticipated maintenance but without major repair being necessary. Examples of the selection of the design working life are given in Table A-8. Table A-8 Design Working Lives (EN 1990, 2002, adapted from Table (2.1)) Design Working Life Category Design Working Life (Years) Examples 1 10 Temporary structures 2 10 to 25 Replaceable structural parts, e.g. gantry girders, bearings 3 15 to 30 Agricultural and similar structures 4 50 Building structures and other common structures 5 100 Monumental building structures, bridges and other civil engineering structures The levels of reliability relating to the ULS and SLS (In the Eurocode, the ULS and SLS are termed the ultimate and serviceability limit states, respectively.) can be achieved by suitable combinations of protective measures (e.g. protection against fire, protection against corrosion, etc.), measures relating to design calculations (e.g. choice of partial factors), measures relating to quality management, measures aimed to reduce errors in design (e.g., project supervision) and execution (construction) of the structure (e.g., inspection during execution) and other kinds of measures. The Eurocode defines three different levels of consequences classes (CC), CC1, CC2 and CC3, as defined in Table A-9. Three reliability classes (RC); RC1, RC2, RC3; may be associated with the three consequence classes; CC1, CC2 and CC3. A-48

Table A-9 Eurocode Consequence Classes (EN 1990, 2002, adapted from Table (B1)) Consequence Class Description Related To Consequences Reliability Class CC1 Low consequence for loss of human life; economic, social or environmental consequences small or negligible RC1 CC2 Moderate consequence for loss of human life; economic, social or environmental consequences considerable RC2 CC3 Serious consequences for loss of human life, or for economic, social or environmental concerns RC3 The vast majority of bridges are designed to CC2 with CC3 a possibility only for those bridges with very high consequences of failure, such as a signature bridge. The provisions of the Eurocode, specifically EN 1990 (2002) with the partial factors given in Annex A1 and EN 1991 to EN 1999, yield designs consistent with reliability class RC2. The Eurocode uses the multiplication factors, KF1, given in Table A-10 applied to load factors to differentiate the three reliability classes. Other measures (differing levels of quality control, for example) in lieu of modifying the load factors are sometimes preferred. Table A-10 Multiplication Factor, KF1, for Reliability Differentiation Reliability Class KF1 RC1 0.9 RC2 1.0 RC3 1.1 Table A-11 below summarizes the probabilities of failure, pF, inherent to the Eurocode and the AASHTO LRFD for strength, along with the corresponding reliability indices, β, below them in italics. The defining probabilities of failure in the case of the Eurocode and the defining reliability indices for the AASHTO LRFD are shown in boldface. A-49

Table A-11 Target Probabilities of Failure (pF) and Reliability Indices (βT) Code Reference Period (years) 1 50 75 100 120 Eurocode CC2 (KF1 = 1.0) 1.00E-06 5.00E-05 7.50E-05 1.00E-04 1.20E-04 4.75 3.89 3.79 3.72 3.67 CC3 (KF1 = 1.1) 1.00E-07 5.00E-06 7.50E-06 1.00E-05 1.20E-05 5.20 4.42 4.33 4.26 4.22 AASHTO LRFD typical bridges (ηI = 1.0) 2.67E-06 1.33E-04 2.00E-04 2.67E-04 3.20E-04 4.55 3.65 3.50 3.46 3.41 important bridges (ηI = 1.05) 9.60E-07 4.80E-05 7.20E-05 9.60E-05 1.15E-04 4.76 3.90 3.80 3.73 3.68 SLS Reliability The SLSs of the Eurocode are categorized as reversible and irreversible. Reversible SLSs are those for which no consequences remain once the load exceeding the specified SLS load is removed. Irreversible SLSs are those for which consequences remain. For example, a crack-width limit state with limited width is a reversible limit state, whereas one defined by a large width (such as 0.5 mm) is irreversible because, if the crack width is high enough, once the live load is removed the crack does not close completely. The irreversible SLSs, which do not concern the safety of the traveling public, are calibrated to a lower probability of failure and corresponding reliability index than the strength limit states, as shown in Table A-12. Table A-12 Irreversible SLS Target Probabilities of Failure and Corresponding Reliability Indices (EN 1990, 2002, adapted from Table (C2)) Reliability Class Reference Period (Years) 1 50 RC2 1.00E-03 1.00E-01 2.9 1.5 SLS Load Combinations EN 1990 (2002) includes three different types of load combinations for the SLSs: characteristic combination, frequent combination and quasi-permanent combination. Table A-13 summarizes the Eurocode’s service limit-state load combinations. A-50

Table A-13 SLS Combinations SLS Load Combinations Type Description Type Acceptance of Infringement Example Reversible those limit states that will not be exceeded when the actions which caused the infringement are removed frequent specified duration and frequency of infringements are accepted the crack-width limit state of a prestressed concrete beam with bonded tendons characterized by a 0.2 mm crack width quasi-permanent specified long- term infringement is accepted the crack-width limit state for a reinforced concrete or prestressed concrete beam with unbonded tendons characterized by a 0.3 mm crack width Irreversible those limit states that remain permanently exceeded even when the actions which caused the infringement are removed characteristic (5% probability of exceedance) no infringement accepted the crack-width limit state characterized by a 0.5 mm crack width, because such a wide crack cannot completely close once the loads that caused it are removed A.3.2.3 Serviceability Design Basic Approach A.3.2.3.1 Basic Equation The basic equation in the Eurocode (EN 1990, 2002) for verifying that a SLS is satisfied is: Ed ≤ Cd where A-51

Cd = the limiting design value of the relevant serviceability criterion. Ed = the design value of the effects of actions specified in the serviceability criterion, determined on the basis of the relevant combination. A.3.2.3.2 Serviceability Criteria Specific serviceability criteria such as crack width, stress or strain limitation and slip resistance exist in separate sections (EN 1991 to EN 1999). In addition to these requirements, project specific deformations to be considered in relation to serviceability requirements are required to be as detailed in relevant code annexes in accordance to the type of construction works, or agreed with the client or the National authority. A.3.2.3.3 Combination of Actions (Load Combinations) The combinations of actions (load combination) for serviceability limit states in the Eurocode are defined symbolically by the following expressions: a) Characteristic (rare) Combination: , ,1 0, , 1 1 d k j k k i k i j i E E G P Q Qψ ≥ >   = + + + ⋅     ∑ ∑ (A-26) The characteristic combination is normally used for irreversible limit states. b) Infrequent Combination: , 1,1 ,1 1, , 1 1 d k j k k i k i j i E E G P Q Qψ ψ ≥ >   ′= + + ⋅ + ⋅     ∑ ∑ (A-27) c) Frequent Combination: , 1,1 ,1 2, , 1 1 d k j k k i k i j i E E G P Q Qψ ψ ≥ >   = + + ⋅ + ⋅     ∑ ∑ (A-28) The frequent combination is normally used for reversible limit states. d) Quasi-permanent Combination: , 2, , 1 1 d k j k i k i j i E E G P Qψ ≥ >   = + + ⋅     ∑ ∑ (A-29) where: A-52

Effect of Action (E) Effect of actions (or action effect) on structural members, (e.g. internal force, moment, stress, strain) or on the whole structure (e.g. deflection, rotation) Permanent Action (G) Action that is likely to act throughout a given reference period and for which the variation in magnitude with time is negligible, or for which the variation is always in the same direction (monotonic) until the action attains a certain limit value Variable Action (Q) Action for which the variation in magnitude with time is neither negligible nor monotonic Combination Value of a Variable Action (Ψ0 Qk) Value chosen - in so far as it can be fixed on statistical bases - so that the probability that the effects caused by the combination will be exceeded is approximately the same as by the characteristic value of an individual action. It may be expressed as a determined part of the characteristic value by using a factor (Ψ0 ≤1.0) Frequent Value of a Variable Action (Ψ1 Qk) Value determined - in so far as it can be fixed on statistical bases - so that either the total time, within the reference period, during which it is exceeded is only a small given part of the reference period, or the frequency of it being exceeded is limited to a given value. It may be expressed as a determined part of the characteristic value by using a factor (Ψ1 ≤1.0) Quasi-permanent Value of a Variable Action (Ψ2 Qk) Value determined so that the total period of time for which it will be exceeded is a large fraction of the reference period. It may be expressed as a determined part of the characteristic value by using a factor (Ψ2 ≤1.0) Gk,j = characteristic (extreme) value of permanent action j Gkj,sup/Gkj,inf = upper/lower value of permanent action j P = relevant prestressing value of prestressing action Qk,l = characteristic value of the leading (dominant) variable action l Qk,I = characteristic value of the accompanying variable action i Ψ0 = factor for combination value of a variable action Ψ1 = factor for frequent value of a variable action Ψ2 = factor for quasi-permanent value of a variable action The Eurocode allows some of the above expressions to be modified and gives detailed rules in relevant sections of the code (Parts of EN 1991 to EN 1999). As each of the Eurocode countries has its own National Annex where the country-specific requirements are placed, the Eurocode allows that the serviceability criteria desired by each country to be specified in the National Annex. Recommended values of the Ψ factors for different types of structures (e.g. buildings, highway bridges or railway bridges) are tabulated in the Eurocode. Table A-14 shows the recommended values for highway bridges. A-53

Table A-14 Recommended Values of Ψ Factors for Highway Bridges in the Eurocode (EN 1990, 2002, adapted from Table A2.1) Action Symbol Ψ0 Ψ1 Ψ2 Traffic Loads (EN 1991-2, 2003 , Table 4.4) gr1a (LM1+pedestrian or cycle-track loads)1) TS 0,75 0,75 0 UDL 0,40 0,40 0 Pedestrian+cycle-track loads2) 0,40 0,40 0 gr1b (Single Axle) 0 0,75 0 gr2 (Horizontal Forces) 0 0 0 gr3 (Pedestrian Loads) 0 0 0 gr4 (LM4 – Crowd Loading) 0 0,75 0 gr5 (LM3 – Special Vehicles) 0 0 0 Wind Forces Fwk - Persistent Design Situations - Execution 0,6 0,8 0,2 - 0 0 F*W 1,0 - - Thermal Actions Tk 0,63) 0,6 0,5 Snow Loads Qsnk (During Execution) 0,8 - - Construction Loads Qc 1,0 - 1,0 1) The recommended values of Ψ0, Ψ1, Ψ2, for gr1a and gr1b are given for roads with traffic corresponding to adjusting αQi, αqi, αqr, and βQ equal to 1. Those relating to UDL correspond to the most common traffic scenarios, in which an accumulation of lorries can occur, but not frequently. Other values may be envisaged for other classes of routes, or of expected traffic, related to the choice of the corresponding α factors. For example, a value of Ψ2 other than zero may be envisaged for the UDL system of LM1 only, for bridges supporting a severe continuous traffic. See also EN 1998-2 (2005). 2) The combination value of the pedestrian and cycle-track load, mentioned in Table 4.4a of EN 1991-2 (2003), is a “reduced” value. Ψ0 and Ψ1 factors are applicable to this value. 3) The recommended Ψ0 value for thermal actions may in most cases be reduced to 0 for ultimate limit states EQU, STR and GEO. See also the design Eurocodes. NOTE 1: The Ψ values may be set by the National Annex. Recommended values of Ψ factors for the groups of traffic loads and other more common actions are given in: • Table A2.1 for road bridges • Table A2.2 for foot bridges • Table A2.3 for railway bridges NOTE 2: When the National Annex refers to the infrequent combination of actions for some serviceability limit states of concrete bridges, the National Annex may define the values of Ψ1infq. The recommended values of Ψ1infq are: A-54

• 0,80 for gr1a (LM1), gr1b (LM2), gr3 (pedestrian loads), gr4 (LM4, crowd loading) and T (thermal actions) • 0,60 for FW in persistent design situations • 1,00 in other cases (i.e. the characteristic value is substituted for the infrequent value) NOTE 3: The characteristic values of wind actions and snow loads during execution are defined in EN 1991-1-6 (2005). Where relevant, representative values of water forces (Fwa) may be defined for the individual project. A.3.2.4 Existing Limit State A summary of the SLS requirements in the Eurocode is attached as Appendix B. A.3.3 Canadian Highway Bridge Design Code (CHBDC) A.3.3.1 Background The CHBDC (2006) and earlier OHBDC (1991) cover Strength Limit States (ULS) and SLS. The serviceability limit states in the CHBDC include fatigue, deflection, cracking and compressive stress in concrete. The SLS acceptability criteria were determined by reference to past practice. As an example of this process, special consideration was given to the tensile stress limit state in prestressed concrete girders. The acceptability criterion was formulated in terms of the minimum return time period between exceeding the decompression moment. It was assumed that the girders will crack anyway due to shrinkage prior to installation, or under exceptionally heavy trucks, and then the crack will reopen each time the decompression moment is exceeded. An open crack, even for a fraction of a second, is assumed to allow water with salt or other pollutants to penetrate, and eventually reach the rebar and prestressing steel, resulting in corrosion, delamination, spalling of concrete, and, eventually, girder failure. The minimum acceptable return time period for decompression moment was then determined by a group of experts invited by the Code Control Committee using a process of expert elicitation (Delphi process). The group was asked to provide their expert opinion. They deliberated and came to a conclusion that a return period of three weeks is acceptable. However, the group did not feel strongly about it, so they agreed that the target probability of exceeding this limit state is 50%, which corresponds to the target reliability index βT = 0. A.3.3.2 Existing Limit States In general, the SLSs in the CHBDC are very parallel to the SLSs currently specified in AASHTO LRFD. There are some differences in application, but the general phenomena being treated are basically the same. Based on the 2006 CHBDC, no new limit states that do not exist in AASHTO LRFD were found in the CHBDC. Clause 3.5.1 and Table 3.1 in particular, contain the requirements for load factors and load combinations. Table 3.6.1(a) lists only two load combinations for serviceability limit states. Service load combinations use a load factor of 0.9 for the live load based on the CL-W-625 truck (140.5 kips, 59 ft long) or lane loading. This unfactored live load is considerably larger than the A-55

HL93 truck, alone, i.e., without the Unified Distribution Load (UDL). Load Combination 2 applies to superstructure vibration only. The CHBDC also specifies a lane load which consists of 80% of the axles of the CL-W truck superimposed on a UDL of 9 kN/m which is similar to the UDL used with the HL93 loading. Clause 8.5.1 states that cracking, deformation, stress and vibrations SLS should be considered. Clause 8.5.2 specifies serviceability limit states for concrete structures and it indicates that these are cracking, deformations, stress, and vibration. Clause 8.5.2.2 deals with a cross-reference to Clause 8.12 with some limits on earth cover. Clause 8.5.2.3 deals with deformation provisions and indicates that short-term and long- term deformations may affect the function of the structure. Clause 8.5.2.4 deals with stresses in the component not exceeding certain values of Clauses 8.7.1, 8.8.4.6, and 8.23.7. Clause 8.5.2.5 deals with vibrations and refers back to clauses in Section 3 on loads. The commentary for Clause 8.5.2.1 speaks to the fact that, in general, nonprestressed and partially prestressed components are expected to crack under the service loads and indicates that it is generally a good practice to provide sufficient prestress so that under the permanent loads any cracks previously caused due to the application of live load will be closed under the permanent loads. This is to enhance durability. Clause 8.12 deals with control of cracking by specifying distribution requirements and a tensile strain limitation. Clause 8.12.3.1 specifies limits on crack width for non-prestressed and prestressed components for several types of exposure. Clause 8.12.3.2 provides guidance on calculating the crack width and spacing based on parameters which include the average strain in the reinforcing. A distinction is made for epoxy- coated reinforcement for which the calculated crack width is increased 20%. A.4 Search for SLSs Not Yet Implemented Several reports were reviewed in an effort to determine whether any additional concrete SLSs should be considered when designing bridges. The additional information was meant to supplement the literature review and the bridge owners’ survey. Reports were gathered from sources such as the NCHRP, the FHWA, ACI Structural Journal, ACI Committee documents, and conference proceedings of the Structures Congress and the American Society of Civil Engineers (ASCE). The investigated reports pertained to establishing concrete cracking of beams and bridge decks, concrete shrinkage, fatigue of prestressed concrete members. Each report was A-56

reviewed to determine the usefulness of the information. Any methods that could potentially be used in creating new SLSs were noted and investigated further. Much of the information was found to be too general to be useful. Many of the methods discussed for reducing serviceability issues related to non-structural aspects of the design process, which would not be useful in calibrating limit states. Some of the sources, however, provided useful methods of anticipating and determining the effects of serviceability issues such as crack width, crack spacing, and prestressed concrete fatigue. Bridge related research problem statements are reviewed annually by Technical Committee 11 of the HSCOBS. It was thought that a review of these documents could show a need for additional SLSs that were not approved for funding but which might still be worthwhile in the context of this project. However, there is apparently no archive of old research problem statements. A.5 References AASHO Road Test: Report 4 - Bridge Research. 1962. Special Report 61D. AASHO, Highway Research Board, Washington, DC. AASHTO LRFD Bridge Design Specifications, 4th ed. 2008. Including 2008 Interim. AASHTO, Washington, DC. AASHTO LRFD Bridge Design Specifications, 6th ed. 2012. AASHTO, Washington, DC. Abeles, P., and E. Brown, II. 1971. Expected Fatigue Life of Prestressed Concrete Highway Bridges as Related to the Expected Load Spectrum. In Second International Symposium on Concrete Bridge Design. SP-26. American Concrete Institute, Detroit, MI, pp. 962–1010. Abeles, P., E. Brown, II, and C. Hu. 1974. Fatigue Resistance of Under-Reinforced Prestressed Beams Subjected to Different Stress Ranges; Miner's Hypothesis. In Abeles Symposium: Fatigue of Concrete. SP-41. American Concrete Institute, Detroit, MI, pp. 279–300. Abeles, P., F. Barton, and E. Brown, II. 1969. Fatigue Behavior of Prestressed Concrete Bridge Beams. In First International Symposium on Concrete Bridge Design. SP-23. American Concrete Institute, Detroit, MI, pp. 579–599. ACI Committee 215. 1974. Considerations for Design of Concrete Structures Subjected to Fatigue Loading. ACI 215R-74. American Concrete Institute, Detroit, MI. ACI Committee 318. 1963. Building Code Requirements for Reinforced Concrete. ACI 318-63. American Concrete Institute, Detroit, MI. ACI Committee 318. 1977. Building Code Requirements for Reinforced Concrete. ACI 318-77. American Concrete Institute, Detroit, MI. ACI Committee 318. 1983. Building Code Requirements for Reinforced Concrete. ACI 318-83. American Concrete Institute, Detroit, MI. A-57

ACI Committee 318. 1995. Building Code Requirements for Structural Concrete and Commentary. ACI 318-95/318R-95. American Concrete Institute, Farmington Hills, MI. ACI Committee 318. 1999. Building Code Requirements for Structural Concrete and Commentary. ACI 318-99/318R-99. American Concrete Institute, Farmington Hills, MI. ACI Committee 318. 2002. Building Code Requirements for Structural Concrete and Commentary. ACI 318-02/318R-02. American Concrete Institute, Farmington Hills, MI. ACI Committee 318. 2005. Building Code Requirements for Structural Concrete and Commentary. ACI 318-05. American Concrete Institute, Farmington Hills, MI. ACI Committee 318. 2008. Building Code Requirements for Structural Concrete and Commentary. ACI 318-08. American Concrete Institute, Farmington Hills, MI. ACI Committee 318. 2011. Building Code Requirements for Structural Concrete and Commentary. ACI 318-11. American Concrete Institute, Farmington Hills, MI. ACI-ASCE Joint Committee 323. 1958. Tentative Recommendations for Prestressed Concrete. Journal, American Concrete Institute, Vol. 54, No. 1, pp. 545–578. Amorn, W., J. Bowers, A. Girgis, and M. Tadros. 2007. Fatigue of Deformed Welded-Wire Reinforcement. Journal, Precast/Prestressed Concrete Institute, Vol. 52, No. 1, pp. 106–120. Barker, M., and K. Barth. 2007. Live Load Deflection Serviceability of HPS Composite Steel Girder Bridges. 2007 World Steel Bridge Symposium Papers, New Orleans, LA. Beeby, A. 1979. The Prediction of Crack Widths in Hardened Concrete. The Structural Engineer, Vol. 57A, No. 1, pp. 9. Biggs, J. 1964. Introduction to Structural Dynamics. McGraw-Hill, New York, NY. Birrcher, D., R. Tuchscherer, M. Huizinga, O. Bayrak, S. Wood, and J. Jirsa. 2009. Strength and Serviceability Design of Reinforced Concrete Deep Beams. FHWA/TX-09/0-5253-1. Center for Transportation Research at the University of Texas at Austin, Texas Department of Transportation, FHWA, Austin, TX. Blackman, D., and R. Frosch. 2005. Epoxy Coated Reinforcement and Crack Control. In Serviceability of Concrete: A Symposium Honoring Dr. Edward G. Nawy. SP-225. American Concrete Institute, Farmington Hills, MI, pp. 163–178. Broms, B. 1965. Crack Width and Crack Spacing In Reinforced Concrete Members. Journal, American Concrete Institute, Vol. 62, No. 10, pp. 1237. Burton, K., and E. Hognestad. 1967. Fatigue Test of Reinforcing Bars-Tack Welding of Stirrups. Journal, American Concrete Institute, Vol. 64, No. 5, pp. 244–252. Canadian Highway Bridge Design Code. 2006. Includes Supplement 1, Supplement 2, and Supplement 3. Canadian Standards Association International, Toronto, ON, Canada. A-58

Choi, Y., and B. Oh. 2009. Crack Width Formula for Transversely Post-Tensioned Concrete Deck Slabs on Box Girder Bridges. Structural Journal, American Concrete Institute, Vol. 106, No. 6, pp. 753–761. Clark, A. 1956. Cracking in Reinforced Concrete Flexural Members. Journal Proceedings, American Concrete Institute, Vol. 52, No. 4, pp. 851. Committee on Deflection Limitations of Bridges of the Structural Division. 1958. Deflection Limitations. ASCE Journal of the Structural Division, Vol. 84, No. 3, pp. 1633.1–1633.20. Dexter, R., and J. Fisher. 2000. Fatigue and Fracture. In Bridge Engineering Handbook. Chen and Duan (Eds). CRC Press, New York, NY, pp. 53.1–53.23. EN 1990 (Eurocode 0): Basis of Structural Design. 2002. European Committee for Standardization, Brussels, Belgium. EN 1991-1-6 (Eurocode 1): Actions on Structures - Part 1-6: General Actions - Actions during Execution. 2005. European Committee for Standardization, Brussels, Belgium. EN 1991-2 (Eurocode 1): Actions on Structures - Part 2: Traffic Loads on Bridges. 2003. European Committee for Standardization, Brussels, Belgium. EN 1992-2 (Eurocode 2): Design of Concrete Structures - Part 2: Concrete Bridges - Design and Detailing Rules. 2005. European Committee for Standardization, Brussels, Belgium. EN 1998-2 (Eurocode 8): Design of Structures for Earthquake Resistance - Part 2: Bridges. 2005. European Committee for Standardization, Brussels, Belgium. Fisher, J., and I. Viest. 1961. Fatigue Tests of Bridge Materials of the AASHO Road Test. Special Report 66. American Association of State Highway Officials, Highway Research Board, Washington, DC. Frosch, R. 1999. Another Look at Cracking and Crack Control in Reinforced Concrete. Structural Journal, American Concrete Institute, Vol. 96, No. 3, pp. 437–442. Frosch, R. 2001. Flexural Crack Control in Reinforced Concrete. In Design and Construction Practices to Mitigate Cracking. SP-204. American Concrete Institute, Farmington Hills, MI, pp. 135–154. Frosch, R. 2002. Modeling and Control of Side Face Beam Cracking. Structural Journal, American Concrete Institute, Vol. 99, No. 3, pp. 376–385. Gergely, P., and L. Lutz. 1968. Maximum Crack Width in Reinforced Concrete Members. In Causes, Mechanisms and Control of Cracking in Concrete. SP-20. American Concrete Institute, Detroit, MI, pp. 87–117. Hanson, J., K. Burton, and E. Hognestad. 1968. Fatigue Tests of Reinforcing Bars-Effect of Deformation Pattern. Journal of the Portland Cement Association Research and Development Laboratories, Vol. 10, No. 3, pp. 2–13. A-59

Helgason, T., J. Hanson, N. Somes, W. Corley, and E. Hognestad. 1976. NCHRP Report 164: Fatigue Strength of High Yield Reinforcing Bars. TRB, National Research Council, Washington, DC. Kaar, P., and A. Mattock. 1963. High Strength Bars as Concrete Reinforcement, Part 4 - Control of Cracking. Portland Cement Association Development Department Bulletin D59, pp. 15–38. Kupfer, H., and K. Gerstle. 1973. Behavior of Concrete under Biaxial Stress. ASCE Journal of the Engineering Mechanics Division, Vol. 99, No. 4, pp. 853–866. Lash, S. 1969. Can High-Strength Reinforcement be used in Highway Bridges. In First International Symposium on Concrete Bridge Design. SP-23. American Concrete Institute, Detroit, MI, pp. 283–300. MacGregor, J., I. Jhamb, and N. Nuttall. 1971. Fatigue Strength of Hot Rolled Deformed Reinforcing Bars. Journal Proceedings, American Concrete Institute, Vol. 68, No. 3, pp. 169– 179. Manning, D. G. 1994. NCHRP Research Results Digest 197: Fatigue Behavior of Welded and Mechanical Splices in Reinforcing Steel. TRB, National Research Council, Washington, DC. Okeil, A. 2006. Allowable Tensile Stress for Webs of Prestressed Segmental Concrete Bridges. Structural Journal, American Concrete Institute, Vol. 103, No. 4, pp. 488–495. Oluokun, F. 1991. Prediction of Concrete Tensile Strength from its Compressive Strength: Evaluation of Existing Relations for Normal Weight Concrete. Materials Journal, American Concrete Institute, Vol. 88, No. 3, pp. 302–309. Ontario Highway Bridge Design Code. 1979. Ontario Ministry of Transportation, Toronto, ON, Canada. Ople, F., and C. Hulsbos. 1966. Probable Fatigue Life of Plain Concrete with Stress Gradient. Journal Proceedings, American Concrete Institute, Vol. 63, No. 1, pp. 59–82. Pfister, J., and E. Hognestad. 1964. High Strength Bars as Concrete Reinforcement, Part 6 - Fatigue Tests. Journal of the Portland Cement Association Research and Development Laboratories, Vol. 6, No. 1, pp. 65–84. Roeder, C., K. Barth, and A. Bergman. 2002. NCHRP Web Document 46: Improved Live Load Deflection Criteria for Steel Bridges. TRB, National Research Council, Washington, DC. Standard Specifications for Highway Bridges, 11th ed. 1975. Including 1974 and 1975 Interims. AASHO, Washington, DC. Standard Specifications for Highway Bridges, 12th ed. 1977. AASHTO, Washington, DC. Standard Specifications for Highway Bridges, 13th ed. 1983. AASHTO, Washington, DC. Standard Specifications for Highway Bridges, 14th ed. 1989. AASHTO, Washington, DC. A-60

Standard Specifications for Highway Bridges, 15th ed. 1992. AASHTO, Washington, DC. Standard Specifications for Highway Bridges, 17th ed. 2002. AASHTO, Washington, DC. Standard Specifications for Highway Bridges, 6th ed. 1953. AASHO, Washington, DC. Structures Manual. 2013. Florida Department of Transportation, Tallahassee, FL. Tachau, H., C. Hulsbos, and D. VanHorn. 1971. Discussion of Fatigue Tests on Prestressed Concrete I-Beams. ASCE Journal of the Structural Division, Vol. 97, No. 9, pp. 2429–2431. Warner, R., and C. Hulsbos. 1966. Probable Fatigue Life of Prestressed Concrete Beams. Journal, Precast/Prestressed Concrete Institute, Vol. 11, No. 2, pp. 16–39. Wright, R., and W. Walker. 1972. Vibration and Deflection of Steel Bridges. Engineering Journal, American Institute of Steel Construction, Vol. 9, No. 1, pp. 20–31. A-61