Bridges for Service Life Beyond 100 Years: Service Limit State Design (2014)

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14 2.1 Approach As part of Phase 1, an assessment of the current state of the art related to service limit states (SLSs) was conducted as follows: • A review of technical literature was conducted and is sum- marized in Section 2.2. • A survey was made of the requirements for SLSs in several modern bridge design specifications, including the Amer- ican Association of State Highway and Transportation Officials’ (AASHTO) AASHTO LRFD Bridge Design Speci- fications. This survey included reconstructing the back- ground of the existing SLS requirements. Much of the detail on concrete requirements was developed under NCHRP Project 12-83 after initial identification was made in SHRP Project R19B. This approach is consistent with the relationship between these projects as introduced in Chapter 1. The requirements of the Eurocode and the Canadian Highway Bridge Design Code (CHBDC) (2006) were also reviewed, and significant clauses are summa- rized here. • A survey of owners and some industry groups was con- ducted by the R19B research team. Surveys were also conducted by the R19A and NCHRP 12-83 teams. The survey results obtained by the R19B team are discussed in detail in Section 2.4.1, and the results obtained during NCHRP 12-83 and those obtained during R19A that relate to R19B are summarized in Sections 2.4.2 and 2.4.3, respectively. 2.2 Summary of Literature Survey Results of the literature survey as they relate to the current requirements in various design specifications are summarized in Section 2.3. 2.2.1 Serviceability, SLS, Deterioration, and Maintenance in the Technical Literature A limited survey was made of sources readily available at Modjeski and Masters and on the Internet to investigate the range of issues and phenomena various organizations associate with the terms serviceability, SLS, deterioration, and maintenance. The results are listed in the following subsections. Serviceability • Merriam-Webster (2010)—Fit for use, of adequate quality (comes from definition for serviceable). • Wikipedia (2010)—Conditions under which a structure is still considered useful. • Manual for Bridge Evaluation (2008)—A term that denotes restrictions on stress, deformation, and crack opening under regular service conditions. • Steel Construction Manual (2011)—A state in which the function of a building, its appearance, maintainability, dura- bility, and comfort of its occupants are preserved under normal usage. • ASCE/SEI 7-10: Minimum Design Loads for Buildings and Other Structures (2010)—Structural systems, and members thereof, shall be designed to have adequate stiffness to limit deflections, lateral drift, vibration, or any other deforma- tions that adversely affect the intended use and performance of buildings and other structures. • 2006 Seattle Building Code (International Code Council 2007)—Structural systems and members thereof shall be designed to have adequate stiffness to limit deflections and lateral drift as set by code writing bodies such as the Ameri- can Concrete Institute (ACI), the American Institute of Steel Construction (AISC), and the International Building Code (IBC). C h A p t e r 2 Current State of the Art

15 • Eurocode (EN 1992-2 2005)—Perform adequately under all expected actions. • ISO 2394 (1998)—Ability of a structure or structural ele- ment to perform adequately for normal use under all expected actions. Service Limit State • Wikipedia (2010)—Fails to meet technical requirements for use while remaining strong enough to stand (service- ability limit). • Manual for Bridge Evaluation (2008)—Limit state relating to stress, deformation, and cracking. • AASHTO LRFD (2012) 44 Service I—Deflection control, crack-width control in R/C members, slope stability; 44 Service II—Control yielding of steel structures, slip of slip-critical connections; 44 Service III—Crack control in prestressed concrete members; 44 Service IV—Relating to tension in prestressed concrete columns with the objective of crack control; 44 Deformations—Article 2.5.2.6; 44 Concrete—Cracking, deformation, and concrete stresses specified by Articles 5.7.3.4, 5.7.3.6, and 5.9.4; 44 Steel—Permanent deformations due to localized yield- ing that would impair rideability under severe traffic loadings as specified by Articles 6.10.4.2 and 6.11.4; and 44 Decks—Deck deformation (9.5.2). • AISC Steel Design Guide 3 (2003)—Define the functional performance of the structure (should be met), involve response of people and objects to the behavior of the struc- ture under load. • AISC Steel Construction Manual (2011)—Limiting con- dition affecting the ability of a structure to preserve its appearance, maintainability, durability or the comfort of its occupants or function of machinery, under normal usage. • ASCE/SEI 7-10: Minimum Design Loads for Buildings and Other Structures (2010)—Conditions in which the functions of a building or other structure are impaired because of local minor damage or deterioration of building components or because of occupant discomfort or annoyance. • 2006 Seattle Building Code (International Code Council 2007)—A condition beyond which a structure or member becomes unfit for service and is judged to be no longer useful for its intended function. • Eurocode (EN 1992-2 2005)—Associated with conditions of normal use, concerned with the performance of structure or part of structure, comfort of people, and appearance of structure. • CHBDC (2006)—See Section 2.3.3. • ISO 2394 (1998)—A state that corresponds to conditions beyond which specified service requirements for a structure or structural element are no longer met. 44 Local damage (includes cracking) that may reduce the working life of the structure or affect the efficiency or appearance of structural or nonstructural elements; 44 Unacceptable deformations that affect the efficient use or appearance of structural or nonstructural elements or functioning of equipment; and 44 Excessive vibrations that cause discomfort to people or affect nonstructural elements or functioning of equipment. • International Federation for Structural Concrete (fib) Bulle- tin 34 (Fédération Internationale du Béton 2006)—States that correspond to conditions beyond which specified ser- vice requirements for a structure or structural member are no longer met. • Louisiana Department of Transportation and Development LRFD Bridge Design Manual (2006)—Stress, deformation, and crack width are limited under service conditions. 44 Pile foundations—settlement and horizontal movement. • West Virginia Department of Transportation (DOT), Divi- sion of Highways, Bridge Design Manual (2006)—Covers cracking, deformations, deflections and concrete stresses. Deterioration • Merriam-Webster (2010)—Action or process of deterio- rating (deteriorating defined as “to make inferior in quality or value”). • Wikipedia (2010)—To make worse. • CHBDC (2006)—Includes corrosion. • U.S. Army Corps of Engineers Coastal Engineering Manual (2002)—Gradual aging of the structure and or its compo- nents over time. • Bridge Inspector’s Reference Manual (2002)—Definition: decline in quality over a period of time due to chemical or physical degradation. • Bridge Inspector’s Reference Manual (2002)—Types of dete- rioration for different materials. 44 Timber. 4▪ Natural defects—checks, splits, shakes, fungi, and insects; 4▪ Chemical—acids, bases or alkalis; and 4▪ Other types—delamination, loose connections, sur- face depressions, fire, impact or collisions, abrasion or mechanical wear, overstress, weathering or warping, protective coating failure. 44 Concrete. 4▪ Reinforced concrete—cracking, scaling, delamina- tion, spalling, chloride contamination, efflorescence, ettringite formation, honeycombs, pop-outs, wear, collision damage, abrasion, overload damage;

16 4▪ Prestressed concrete—structural cracks, exposed pre- stressing tendons, corrosion of tendons in bond zone, loss of camber due to creep or prestress losses; 4▪ Reinforcement—corrosion; and 4▪ Causes—temperature fluctuation, chemical attack, moisture absorption, differential foundation move- ment, design and construction deficiencies, fire. 44 Steel—corrosion, fatigue cracking, overloads, collision, heat, paint failures; 44 Concrete decks—cracking, scaling, delamination, spall- ing, efflorescence, honeycombs, pop-outs, wear, collision damage, abrasion, overload damage, reinforcement corro- sion, prestressed concrete deterioration; and 44 Steel decks—bent, damaged, or missing members; corro- sion, fatigue cracks, other stress-related cracks. Maintenance • Merriam-Webster (2010)—The upkeep of property or equipment. • Wiktionary (2010)—Actions performed to keep a system or machine functioning or in service. • Eurocode (EN 1992-2 2005)—Under “Use and Maintenance”: Monitoring performance, inspection for deterioration or distress, investigation of problems, and certification of work. • Ontario Traffic Manual: Book 5: Regulatory Signs (2000)— The upkeep of highways, traffic control devices, other trans- portation facilities, property, and/or equipment. • CHBDC (2006)—Under “Inspection and Maintenance” of commentary: Without routine inspection, maintenance, repair or rehabilitation it is unlikely that any structure will achieve its design life. • U.S. Army Corps of Engineers’ Coastal Engineering Manual (2002)—Recognize potential problems and take appropri- ate action to assure project continues to function at accept- able level. • Bridge Inspector’s Reference Manual (2002)—Basic repairs performed on a facility to keep it at an adequate level of service. • ISO 2394 (1998)—Total set of activities performed during the design working life of a structure to enable it to fulfill the requirements for reliability. • fib Bulletin 34 (Fédération Internationale du Béton 2006)— Set of activities that [is] planned to take place during the service life of the structure in order to fulfill the require- ments of reliability. • Maryland Manual on Uniform Traffic Control Devices for Streets and Highways (2006)—Activities performed to retain the legibility and visibility of the device, and to retain proper functioning of the device. • Ohio DOT Bridge Design Manual (2007)—Keeping all por- tions in good condition with regard to strength, safety, and rideability. There is broad similarity in the use of the terms investi- gated, especially for maintenance and deterioration, with the Bridge Inspector’s Reference Manual providing much more detail, as would be expected. The term serviceability gener- ally relates to high-level statements on structural behavior. SLS ranges from generalities to very specific quantitative requirements, although most of the surveyed sources deal with vibrations, deflections including foundation settlement, user comfort, and cracking. There is little mention of appearance-related issues such as rusting of steel or cracking or discoloration of concrete in relation to serviceability. Generally, the SLSs currently specified in AASHTO LRFD consider most of the behaviors found in this part of the litera- ture survey. This does not preclude the improvement of func- tionality through calibration, nor the possibility that new limit states might be identified through other aspects of the litera- ture search reported in this section; more extensive evaluation of the state of the art summarized in Sections 2.2 and 2.3; the results of surveys reported in Section 2.4; or the experience of the research team. 2.2.2 Search for SLSs not yet Implemented Several reports were reviewed to determine whether any additional SLSs should be considered when designing bridges. The additional information was meant to supplement the literature review performed as part of SHRP 2 Project R19A. Reports were gathered from sources such as the National Cooperative Highway Research Program, the Federal Highway Administration, the ACI Structural Journal, American Con- crete Institute (ACI) committee documents, and conference proceedings of the Structures Congress and the American Society of Civil Engineers (ASCE). The investigated reports pertained to establishing foun- dation limit states, concrete cracking of beams and bridge decks, concrete shrinkage, fatigue of prestressed concrete members, and methods of controlling vibration. Each report was reviewed to determine the usefulness of the information. Any methods that could potentially be used in creating new SLSs were noted and investigated further. Many sources provided information that was too general to be useful, with many of the discussed methods for reduc- ing serviceability issues relating to nonstructural 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 ser- viceability issues such as crack width, crack spacing, and pre- stressed concrete fatigue. Bridge-related research problem statements are reviewed annually by Technical Committee 11 of the Highway Subcom- mittee on Bridges and Structures. It was thought that a review

17 of these documents could show a need for additional SLSs that were not approved for funding but may still be worthwhile in the context of this project. However, there is apparently no archive of old research problem statements. 2.2.3 Joints and Bearings The design lives of bearings and expansion joints are impor- tant with regard to the serviceability of bridges. With the exception of deck deterioration, poor performance of these components probably results in most of the deterioration and maintenance activities on typical bridges. Even a cursory investigation into the design life of these components showed widely varying results. Several codes and design guides included expected lives of bearings: • fib Bulletin 34—10 to 25 years (Fédération Internationale du Béton 2006). • Queensland Government Main Roads Specification MRS81: Bridge Bearings (2012), Section 6.3—100 years for Expo- sure Classification B1, design life for bearings in Second Gateway Bridge (Outokumpu 2013). The steps involved to achieve a specified service life include 44 Definition of the characteristics of the environment; 44 Identification of the potential deterioration mechanisms in that environment; 44 Determination of the likely rate of deterioration; 44 Assessment of the material life; 44 Definition of the required material performance; 44 Consideration of a probabilistic approach to the vari- ability of the relevant parameters; and 44 Assessment and definition of the need for further protection. • Steel Bridge Bearing Selection and Design Guide (1996)— Shorter than that of other bridge elements. • Japan (Itoh and Kitagawa 2001)—25 to 35 years with an average replacement at 30 years (these values are estimated to determine life-cycle cost). • Indian Railways Institute of Civil Engineering (Bridge Bear- ings 2006)—Attempt to specify a bearing with an expected life similar to that of the bridge. Project R19A completed a survey of state DOTs with regard to their experiences with bearings. The results from their interim report are summarized below: • Elastomeric—15 to 50 years experienced, 50 to 75 expected. • Polytetrafluoroethylene—20 to 50 years experienced, 20 to 75 expected. • Cotton duck—35 to 50 years experienced, 75 expected. • High-load multirotational—For pots, 10+ years experi- enced; for other high-load multirotational, 15 to 40 years experienced, 30 to 75 expected. • Fabricated steel—15 to 100 years experienced, 50 to 75 expected. In addition to the suggested or expected design service life of bearings proposed by various design manuals or industry publications, bearing manufacturers also provided expected life for their products. The expected life of the bearing depends on the manufacturer and the quality of installation, but is typically within the range of 20 to 80 years. Maurer Söhne (2011) suggests that their MSM sliding bearings provide a service life of up to 80 years. Agom International, srl. (2013) and D. S. Brown (Kaczinski 2008) suggest a service life of more than 50 years for their pot bearings and steel-reinforced elas- tomeric bearings, respectively. Technoslide (2013) provides documentation on plain bearings manufactured by Bearing Technologies that suggests a service life of 20 to 40 years for elastomeric bearings; stainless steel, polytetrafluoroethylene, and CSB-10 bearings have a life that is assumed to match the life of the bridge. CSB-10 is a proprietary material manufac- tured by CSB Bearings Co. The service life for expansion joints has been examined by at least two agencies within the United States. Reports sum- marizing estimated service life along with a minimum and maximum estimate were developed. The results are shown in Table 2.1 (Indiana sent out two surveys; the results of both surveys are included in the table). Several other organizations and projects have also looked into the service life of expansion joints. The Bridge Joint Association (2010) suggests that the service life of the expan- sion joint should equal the service life of adjacent surfaces. The same life-cycle cost analysis completed in Japan (Itoh and Kitagawa 2001) for bearings also suggested the service life of expansion joints as 15 to 25 years, with the average being 20 years. NCHRP Synthesis 319 (Purvis 2003) noted that in Florida elastomers used in joint seals must provide a service life warranty for a minimum of 5 years. Research completed as part of Project R19A (AASHTO 2013) shows the following for estimates of service lives: • Field molded joints—1 to 3 years. • Strip seal joints—3 to 30 years. • Compression seal joints—3 to 30 years (also listed as 2 to 20 years). • Finger plate joints—10 to 50 years. • Modular expansion joints—10 to 50 years. As joints and bearings typically have service lives much less than the 100-year criterion for this project, these elements were not calibrated, but instead should be designed to be

18 replaceable. Expansion joint manufacturers also provided esti- mates of service life for their products. One modular expan- sion joint manufactured by Maurer provides an estimated service life of 40 years and 20 years for replaceable components. D. S. Brown (Kaczinski 2008) notes that soft joints (silicone– urethane and asphaltic plug joints) have a life expectancy of less than 5 years. Miska (2013) noted that their neoprene com- pression seal has over 30 years of proven durability. 2.3 Serviceability requirements in Several Modern Bridge Design Specifications 2.3.1 AASHTO LRFD The current AASHTO LRFD (2012) SLSs include limits on • Live load deflection of structures. • Fatigue of steel and concrete details. • Cracking of reinforced-concrete components. • Tensile stresses in prestressed concrete components. • Compressive stresses in prestressed concrete components. • Settlement of shallow and deep foundations. • Permanent deformations of compact steel components. • Slip of slip-critical friction bolted connections. Design provisions are specified either in the resistance sec- tions or Section 3 of AASHTO LRFD. The design load combi- nations in AASHTO LRFD are presented in Table 3.4.1-1. As stated in Chapter 1, these SLSs and the associated load and resistance factors 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. As decisions were made as to the retention or modification of the current AASHTO LRFD provisions, background infor- mation for the current SLSs is provided below. Settlement of Shallow and Deep Foundations Serviceability aspects of foundations and walls are related to the deformation characteristics of geomaterials and struc- tural elements. In the current AASHTO LRFD (2012), Sec- tion 10 (Foundations) and Section 11 (Abutments, Piers, and Walls) present a variety of formulations for estimating defor- mation of foundations and walls. These formulations are not consistent in the sense that they range from theoretical, semiempirical formulations to charts based on measured deformations. For example, the vertical settlement of spread footings is based on Hough’s (1959) method, which is largely a theoretical method, but the settlement of pile groups is based on a choice of one of four idealized cases that use Hough’s method. In contrast, the lateral deformations of retaining walls are based on semiempirical methods and charts. Such approaches are adopted for all types of foundations and walls in Sections 10 and 11 of AASHTO LRFD. Although this wide range of approaches is understandable given that foundation design is more an art based on observations than a science, it created a challenge in the context of SLS calibration using a consistent basis. The calibration processes proposed for geo- technical features in Chapter 6 could be considered to estab- lish a consistent framework for foundations and walls. An example of this approach is demonstrated for vertical settle- ment of spread footings. Tolerable VerTical DeformaTion criTeria From the viewpoint of serviceability of a bridge structure, the geotechnical limit states relate to foundation deforma- tions. Uneven displacements of bridge abutments and pier Table 2.1. Service Life of Expansion Joints Joint Type Arizona Indiana Mean Min Max Mean Min Max Pourable seals 11.5 4 30 5.2, 5.6 1, 0 15, 20 Compression seals 12.7 5 25 11.7, 10.3 0, 2 20, 20 Strip seals 18.0 8 30 11.9, 10.9 0, 1.5 20, 25 Finger or slide plate joints 28.1 10 75 — — — Modular joints 19.2 10 25 — — — Integral abutments 50.9 15 100 8.7, 7.3–9.8 0, 1.5 20, 15–20 Polymer-modified asphalt — — — 3.5, 5.7–5.8 1, 0–1.5 10, 10–20 Note: — = not available. Sources: For Arizona, Evaluation of Various Types of Bridge Deck Joints 2006; for Indiana, Chang and Lee 2001.

19 foundations can affect the ride quality, functioning of deck drainage, and the safety of the traveling public, as well as the structural integrity and aesthetics of the bridge. Such move- ments often lead to costly maintenance and repair measures. However, overly conservative criteria can be wasteful. Deter- mination of deformation criteria should be a collaboration between the geotechnical engineer and the structural engi- neer to find the optimum solution. Within the context of foundation deformation, the geotechnical limit states can be broadly categorized into vertical and horizontal deforma- tions for any foundation type (e.g., spread footings, driven piles, drilled shafts, or micropiles). Agencies often limit the deformation to values of 1 in. or less without any rational basis. The literature survey revealed that the only definitive rational guidance related to the effect of foundation deformations on bridge structures is based on a report by Moulton et al. (1985). From an evaluation of 314 bridges nationwide, the report offered the following conclusions: The results of this study have shown that, depending on type of spans, length and stiffness of spans, and the type of construc- tion material, many highway bridges can tolerate significant magnitudes of total and differential vertical settlement without becoming seriously overstressed, sustaining serious structural damage, or suffering impaired riding quality. In particular, it was found that a longitudinal angular distortion (differential settlement/span length) of 0.004 would most likely be tolerable for continuous bridges of both steel and concrete, while a value of angular distortion of 0.005 would be a more suitable limit for simply supported bridges (Moulton et al. 1985). Another study states the following: In summary, it is very clear that the tolerable settlement criteria currently used by most transportation agencies are extremely conservative and are needlessly restricting the use of spread foot- ings for bridge foundations on many soils. Angular distortions of 1/250 of the span length and differential vertical movements of 2 to 4 in. (50 to 100 mm), depending on span length, appear to be acceptable, assuming that approach slabs or other provi- sions are made to minimize the effects of any differential move- ments between abutments and approach embankments. Finally, horizontal movements in excess of 2 in. (50 mm) appear likely to cause structural distress. The potential for horizontal move- ments of abutments and piers should be considered more care- fully than is done in current practice. (Wahls 1983) AASHTO LRFD used data from Moulton et al. (1985) and Wahls (1983) to produce the guidance summarized in Table 2.2 for the evaluation of tolerable vertical movements in terms of angular distortions. The criteria in Table 2.2 suggest that for a 100-ft span, a differential settlement of 4.8 in. is acceptable for a continu- ous span, and 6 in. is acceptable for a simple span. These relatively large values of differential settlement create con- cern for structural designers, who often arbitrarily limit tol- erable movements to one-half to one-quarter of the values listed in Table 2.2 or develop guidance such as that shown in Table 2.3. Another example of the use of more stringent criteria is from Chapter 10 of the Arizona Department of Transportation (ADOT) Bridge Design Guidelines (2009), which states the following: The bridge designer should limit the total settlement of a foundation per 100 ft span to 0.5 in. Linear interpolation should be used for other span lengths. Higher total settlement Table 2.2. Tolerable Movement Criteria for Highway Bridges (AASHTO LRFD 2012) Limiting Angular Distortion, d/L (radians) Type of Bridge 0.004 Multiple-span (continuous-span) bridges 0.008 Simple-span bridges Table 2.3. Tolerable Movement Criteria for Highway Bridges (Geotechnical Design Manual 2012) Total Settlement at Pier or Abutment Differential Settlement over 100 ft Within Pier or Abutments and Differential Settlement Between Piers (Implied Limiting Angular Distortion, radians) Action d ≤ 1 in. d100 ft ≤ 0.75 in. (0.000625) Design and construct 1 in. < d ≤ 4 in. 0.75 in. < d100 ft ≤ 3 in. (0.000625–0.0025) Ensure structure can tolerate settlement d > 4 in. d100 ft > 3 in. (>0.0025) Need departmental approval

20 limits may be used when the superstructure is adequately designed for such settlements. The designer shall also check other factors such as rideability and aesthetics. Any total set- tlement that is higher than 2.5 in, per 100 ft span, must be approved by the ADOT Bridge Group. Although from the viewpoint of structural integrity there are no technical reasons for structural designers to set arbi- trary additional limits to the criteria listed in Table 2.2, there are often practical reasons based on the tolerable limits of deformation of other structures associated with a bridge, such as approach slabs, wingwalls, pavement structures, drainage grades, utilities on the bridge, and deformations that adversely affect ride quality. Thus, the relatively large differential settle- ments based on Table 2.2 should be considered in conjunc- tion with functional or performance criteria not only for the bridge structure but also for all associated facilities. Samtani and Nowatzki (2006) suggest the following steps in this regard: 1. Identify all possible facilities associated with the bridge structure and the tolerance of those facilities to movement. An example of a facility on a bridge is a utility (e.g., gas, power, or water). The owners of the facility can identify the tolerance of their facility to movements. Alternatively, the facility owners should design their facilities for the movements anticipated for the bridge structure. 2. Due to the inherent uncertainty associated with estimated values of settlement, determine the differential settlement by using conservative assumptions for geomaterial properties and prediction methods. It is important that the estimation of angular distortion be based on a realistic evaluation of the construction sequence and the magnitude of loads at each stage of the construction sequence. 3. Compare the angular distortion from Step 2 with the various tolerances identified in Step 1 and in Table 2.2. Using this comparison, identify the critical component of the facility. Review this critical component to check if it can be relo- cated or if it can be redesigned to more relaxed tolerances. Repeat this process as necessary for other facilities. In some cases, a simple resequencing of the construction of the facility based on the construction sequence of the bridge structure may help mitigate the issues associated with intolerable movements. This three-step approach can be used to develop project- specific limiting angular distortion criteria that may differ from the general guidelines listed in Table 2.2. For example, if a compressed-gas line is fixed to a simple-span bridge deck and the gas line can tolerate an angular distortion of only 0.002, then the utility will limit the angular distortion value for the bridge structure, not the criterion listed in Table 2.2. However, this problem is typically avoided by providing flexible joints along the utility such that it does not control the bridge design. Tolerable HorizonTal DeformaTion criTeria Horizontal deformations cause more severe and widespread problems for highway bridge structures than do equal magni- tudes of vertical movement. Tolerance of the superstructure to horizontal (lateral) movement will depend on bridge seat or joint widths, bearing type(s), structure type, and load distri- bution effects. Moulton et al. (1985) found that horizontal movements less than 1 in. were almost always reported as being tolerable, while horizontal movements greater than 2 in. were typically considered to be intolerable. On the basis of this observation, Moulton et al. (1985) recommended that hor- izontal movements be limited to 1.5 in. The data presented by Moulton et al. (1985) show that horizontal movements resulted in more damage when accompanied by settlement than when occurring alone. Limitations on the Live Load Deflection of Structures The current requirements for live load deflection limits in the AASHTO LRFD have their roots in the corresponding provi- sions of the Standard Specifications for Highway Bridges, 17th ed. (2002). These provisions have been reviewed repeatedly. Sum- maries by Wright and Walker (1972), Roeder et al. (2002), and Barker and Barth (2007) are often referenced. The ASCE Committee on Deflection Limitations of Bridges of the Structural Division (1958) reported on their examina- tion 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. The earliest deflection limits were adopted in 1871 by the Phoenix Bridge Company, which limited deflection to 1/1,200 of the span length for a train moving 30 mph. The American Rail- way Engineering Association (AREA) adopted depth-to-span ratios in the early 1900s, although 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 1930s, and the Bureau of Public Roads attempted to provide a correlation between the bridges with vibration problems and bridge properties. The result was limit- ing deflections to L/800 for simple and continuous spans with- out pedestrians, L/1,000 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 included the follow- ing: maximum oscillations occur with passage of medium- weight vehicles, not heavy vehicles; reports of objectionable vibrations came from continuous-span bridges more often

21 than simple-span bridges; and there is no defined level of vibration that 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. • Damping characteristics of bridge and vehicle. The use of depth-to-span ratios began in the early 1900s with the American Railway Engineering and Maintenance of Way Association (AREMA) (at that time AREA) specification 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 rolled shapes and plate girders. The early specifications for highway bridges adopted with some modification the depth-to-span ratios from AREMA. The changes in depth-to-span ratios for highway bridges are shown in Table 2.4 for selected time periods. Both AREMA and AASHTO specifications included state- ments that required flanges to be strengthened if section depths smaller than those required by the limiting depth-to-span ratio were used. The use of depth-to-span ratios was primarily to limit deflections, but it was also driven by economics. The limiting values of depth-to-span ratios have decreased with time, while allowable stresses have increased. This would result in shallower sections being used, which would result in larger deflections. This result confused the ASCE Committee on Deflection Limitations of Bridges of the Structural Division, which was tasked with investigating the origins of the deflec- tion and depth-to-span limits. The committee quoted the 1905 AREA Committee’s explanation of their depth-to-span ratios: “We established the rule because we could not agree on any. Some of us in designing a girder that is very shallow in proportion to its length decrease the unit stress or increase the section according to some rule which we guess at. We put that in there so that a man would have a warrant for using whatever he pleased.” The report concluded that the reasons for the two criteria, deflection limit and depth-to-span ratio, are of different ori- gin. The deflection limit is to limit undesired vibration, but the depth-to-span ratio is a result of economics. In addition, the report writers could not provide recommendations as to what constitutes undesirable deflection or vibration or how best to limit deflections or vibrations. The ASCE Committee had minor modifications, but due to the empirical nature of the current limits, they believed that they could not suggest the revisions. They also believed that the then-current limits were sufficient until further test data became available, but that girders with composite action should be limited to smaller deflections. In U.S. practice, the deflection of bridges supporting vehic- ular traffic is generally limited to the span length divided by 800 for simple spans and continuous spans and divided by 300 for cantilever arms. The specifications have placed fur- ther limits on bridges also intended to carry pedestrian and bicycle traffic. There is little technical support for the efficacy of the current deflection provisions. They are simple to use, but they do not directly relate to the actual issue of concern, namely, the vibration response under live load. Although the quasistatic deflection and dynamic response both involve the stiffness of the bridge, the dynamic response also involves the mass, damping, and the characteristics of the forcing function, which is in turn related to the surface roughness, suspension characteristics of the vehicle, and other parameters. Wright and Walker (1972) developed a summary of the experience with the deflection limitation provisions in the era during which the bulk of the steel structures were of non- composite construction. Roeder et al. (2002) revisited the subject decades later and suggested that • the current AASHTO limits are insufficient for control of vibrations and should ultimately be removed; • the current limit of L/800 for bridges without pedestrians is not always sufficient to control vibrations, but should not be removed as there is insufficient documentation to warrant removing it from the design specifications; and • the applied loading and use of load factors and distribu- tion factors should be clarified. Roeder et al. (2002) also suggested immediately removing the L/1,000 deflection limit for bridges with pedestrian access. As alternatives to the deflection limits (L/800 and L/1,000) and until a method for controlling vibration frequency and amplitude is approved by AASHTO, they suggest using the Table 2.4. Historic Depth-to-Span Ratios for Highway Bridges Year Trusses Plate Girders Rolled Shapes 1913, 1924 1/10 1/12 1/20 1931 1/10 1/15 1/20 1935, 1941, 1949, 1953 1/10 1/25 1/25 2012 1/10 1/25 1/25

22 equations developed by Wright and Walker (1972) or the cri- teria provided in the CHBDC (2006) for simple-span bridges. Barker and Barth (2007) have compared the procedure in AASHTO LRFD, which was intended to provide some unifor- mity in application, to the specific procedures used in several states. They found wide variations in load, load distribution, and deflection limits. In some states, the individual interpreta- tion is severe enough to frequently control the design, particu- larly of steel bridges, by a significant margin. A sample of the reported variation follows: • Bridges without pedestrian access 44 L/1,600 (one state); 44 L/1,100 (one state); 44 L/1,000 (five states); and 44 L/800 (40 states). • Bridges with pedestrian access 44 L/1,600 (one state); 44 L/1,200 (two states); 44 L/1,100 (one state); 44 L/1,000 (39 states); and 44 L/800 (three states). • Loads used based on AASHTO load factor design (LFD) requirements 44 HS20 truck only (one state); 44 HS20 truck plus impact (16 states); 44 HS20 lane load plus impact (one state); 44 HS20 truck plus lane load without impact (one state); 44 Larger of HS20 truck plus impact or HS20 lane load plus impact (seven states); 44 HS20 truck plus lane plus impact (17 states); 44 Military or permit vehicles (four states); and 44 HS25 truck (eight states). Live load deflection is sometimes postulated to be a con- tributor to the cracking of concrete decks. A sample of the conflicting literature on this issue follows: • Fountain and Thunman (1987) conducted a study in which they examined the live load deflection criteria for steel girder bridges with concrete decks and how the deflection criteria are associated with cracking of the concrete deck. Cracking can be caused by numerous factors, including plastic shrinkage, deck restraint, drying shrinkage, long- term flexure due to service loads, and repetitive vibrations. The results indicated that the live load deflection criteria did not meet the desired goals, which were strength, dura- bility, and safety of steel bridges. Fountain and Thunman questioned the applicability of the live load deflection cri- teria as a majority of steel girder bridges are built with composite decks, and composite decks lead to small tensile stresses in the deck. In addition, as bridge stiffness increases, the stresses in the deck may also increase due to interac- tion between the deck and girder. The increased stresses may lead to additional cracking or deterioration of the bridge deck. Dynamic response of the bridge is affected minimally by increases in flexibility; the increased flexibil- ity leads to more lateral distribution of the load to adja- cent girders. • Krauss and Rogalla (1996) examined available literature; surveyed 52 transportation agencies in the United States and Canada; and performed research using analytical methods, as well as field and laboratory measurements. The survey was used to develop an understanding of how often transverse cracks are noted in new bridge decks, as well as how they are believed to form. More than 18,000 bridges were analyzed to examine the stresses in the concrete deck. Laboratory testing indicated that concrete mix, environ- mental conditions during concrete placement, and con- struction practices significantly affected the formation of transverse cracks. It was also determined that bridge charac- teristics such as deck geometry and girder type, spacing, and size significantly affect the formation of transverse cracks. It was determined that continuous multigirder steel spans are more susceptible to transverse cracks due to restraint of the deck. Krauss and Rogalla also noted that longer spans are more susceptible to cracking than shorter spans. • Goodpasture and Goodwin (1971) evaluated whether any relationship existed between deck deterioration and live load deflection. They examined 27 bridges to determine which bridge type had the most cracking. Bridge types included plate girders, rolled shapes, concrete girders, pre- stressed girders, and trusses. Ten continuous steel girder bridges were evaluated to determine if the stiffness of the bridge influenced transverse cracking. The results indi- cated no correlation between girder flexibility and amount of transverse cracking. • Walker and Wright’s (1971) analysis indicated that spalling, scaling, and longitudinal cracking are not associated with girder flexibility. Transverse deck moments result in tension along the top surface of the deck, possibly resulting in deck cracking. Increased girder flexibility results in larger posi- tive transverse moments and smaller negative moments resulting in reduced likelihood of deck cracking. • Nevels and Hixon (1973) examined 195 girder bridges consisting of simple- and continuous-span steel plate and rolled girders and prestressed concrete girders. Span lengths ranged from 40 to 115 ft. They concluded that there was no relationship between flexibility and deck deterioration. Similarly, the Portland Cement Association (1970) pre- sented results of a study in which substantial evidence was collected that indicated flexible bridges, typically steel girder bridges, do not have a greater tendency to exhibit deck cracking damage than other bridge types.

23 • Barker et al. (2008) examined deflection limits and deflec- tion loadings from various states for a suite of 10 bridges for both LFD and load and resistance factor design methods. The results indicate that states using larger loads and more restrictive deflection limits end up with designs controlled by deflection. To meet the more restrictive deflection limits, a significantly stiffer bridge would be needed. Furthermore, it was noted that the 10 bridges were performing well and had not demonstrated any detrimental effects, either user comfort or structural damage, due to excessive deflections. The suite of 10 bridges would not satisfy the deflection cri- teria in several states and would require additional steel be added; the additional steel would not be required for strength but rather to meet the deflection criteria. The literature reviewed above indicates that transverse deck cracking can be affected by many factors. In addition, there is disagreement on whether limiting static live load deflections (girder flexibility) is a satisfactory method to pre- vent deck cracking. Of the articles reviewed, the conclusions are 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 presented above, concrete material fac- tors may be more important to reduce the formation of early age deck cracks. Some modern specifications, such as the Ontario High- way Bridge Design Code (1979) and its successor the CHBDC, use a combination of frequency, perception levels, and deflec- tion limits to distinguish between acceptable and unacceptable response. Figure 2.1, taken from CHBDC (2006), illustrates this approach, which has the benefit of directly addressing the design issue of vibration control. This is similar to the procedure for building design developed by Murray et al. (2003). In the Eurocode, live loads include a vibration factor to account for stresses caused by vibration; no checks for fre- quency 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 been removed. Several proposed dynamics-based approaches in the litera- ture are summarized below: • Wright and Walker (1972) recommended limits based on vertical acceleration to control vibration; this includes composite action. 44 ds = static deflection caused by live load with a wheel line distribution factor of 0.7 on one stringer acting with its share of deck Source: Canadian Standards Association. 0 1 2 3 4 5 6 7 98 10 without sidewalks with sidewalks, 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 Figure 2.1. Deflection provisions in CHBDC (2006).

24 44 Natural frequency for simple or equal spans: 2 2 f L E I g wb b b = pi 44 Speed parameter: 2 v f Lb α = 44 Impact factor: DI = a + 0.15 44 Dynamic component of acceleration = a = 2 2 DI fs b)(× δ pi must be less than 100 in./s2 • Barth and Wu (2007) provide equations to estimate the natural frequency of continuous-span steel I-girder bridges 44 2f fsb= λ for continuous spans 44 2 2 f L E I g wsb b b = pi for simple spans 44 2 max a I L c bλ = where L = span length; EbIb = flexural rigidity of composite steel girder; g = acceleration due to gravity; w = weight per unit length of composite steel girder; Lbmax = maximum span length; and Ic = average moment of inertia of composite girder section. 44 For two-span bridges 4▪ a = 0.95 (1.44 for metric units) 4▪ b = 0.046 4▪ c = 0.032 44 For three- or more span bridges 4▪ a = 0.88 (1.49 for metric units) 4▪ b = -0.033 4▪ c = 0.033 Presently, specifications based on determining the fre- quency 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 devel- oped for continuous structures of regular geometry. His- torically, frequencies could be calculated using the Rayleigh method typically implemented through Newmark’s numer- ical integration. Roeder et al. (2002) summarized empirical equations that are based not only on theoretical structural 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 any imped- iment to adopting an approach similar to that specified in the CHBDC. Fatigue-and-Fracture Limit States 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 for concrete and steel bridges in Sections 5 and 6 of the AASHTO LRFD, respectively, were modified accordingly. loaDs 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 on extensive research of structural steel highway bridges. 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 ft. The live load load factors for the fatigue limit state load combinations are summarized in Table 2.5. 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 on a 1-in-10,000 rate of exceedance (Dexter and Fisher 2000). The infinite-life fatigue or constant amplitude fatigue threshold stress range is the stress range below which the inherent flaws in steel do not propagate significantly during the design life of the bridge. If all 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 stress range is revisited in Section 6.6 through simulation using weigh-in-motion data. Finite-Life Fatigue NCHRP Report 267 (Fisher et al. 1983) established that the root mean cube of the stress ranges experienced by a steel- bridge detail characterizes accumulated fatigue damage well when portions of the stress range distribution exceed the constant amplitude fatigue threshold more often than the 1-in-10,000 rate cited above, no matter how small these por- tions exceeding the threshold are. Thus, the effective stress Table 2.5. Fatigue Live Load Load Factors Fatigue Limit State Load Combination Live Load Load Factor Fatigue I 1.50 Fatigue II 0.75

25 range for estimating accumulated fatigue damage may be taken as shown by Equation 2.1: (2.1)effective 3 3 i i ∑( )( )∆σ = ∆σ The Fatigue II load factor produces a force effect that rep- licates the fatigue damage due to the entire spectrum of stress ranges experienced by the bridge detail. In other words, the fatigue damage due to passage of the effective truck over the bridge for a total number of cycles, equal to the average daily truck traffic averaged over the 75-year life span, is assumed equal to the fatigue damage due to the actual truck traffic crossing the bridge in 75 years. Recommendations The stress ranges represented by both load factors (the root mean cube and the exceedance of 1 in 10,000) are based on observations of steel highway bridges and structural steel laboratory specimens. Extending these stress ranges to steel reinforcement, both nonprestressed and prestressed, is quite appropriate as the stress ranges represent fatigue damage accu- mulation 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. A validation of these principles for concrete highway bridges is far beyond the scope and funding of this study. faTiGue resisTance of concreTe sTrucTures The fatigue resistance values of concrete, nonprestressed re inforcement and prestressing tendons in the AASHTO LRFD are based on ACI 215R-74(92), Considerations for Design of Concrete Structures Subjected to Fatigue Loading (ACI Committee 215 1974). This reference includes an exten- sive 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 in Article 5.5.3.1 of AASHTO LRFD 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 com- pressive stress limit represents an infinite-life check, as the Fatigue I limit state load combination corresponds with infi- nite 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 (indicated by a horizontal S-N curve) up to that point. Further, it suggests that the compression stress limit of 0.40fc′ is based on 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 average daily truck traffic of 2,000 trucks per day would experience over 50 million cycles during its 75-year design life. For this study, the research by Ople and Hulsbos (1966) used to define these S-N curves was reevaluated to estimate the fatigue resistance to about 108 (100 million) cycles, a prac- tical upper bound for highway bridges. The uncertainty of the fatigue resistance is quantified in terms of bias, mean, and coefficient of variation. Nonprestressed Reinforcement As used here, nonprestressed 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 by Equation 2.2: 24 0.33 (2.2)TH minF f( )∆ = − where fmin is the minimum stress; TH is threshold. For welded-wire reinforcement with a cross weld in the high-stress region, the fatigue resistance is specified by Equation 2.3: 16 0.33 (2.3)TH minF f( )∆ = − Equations 2.2 and 2.3 implicitly assume a ratio of radius to height (i.e., 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 nonprestressed 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 fatigue threshold has been drawn beneath all 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 reanalyzed to estimate constant ampli- tude fatigue thresholds for each case (analogous to the vari- ous detail categories defined for steel details) that could be

26 identified in the research 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 following fatigue of nonprestressed reinforcement. Such nonprestressed rein- forcement fracture results in distress such as excessive deflec- tion and wide cracks, which facilitate detection and subsequent repair. This consequence suggests that a target reliability index (bT) less than that for ultimate limit states (ULSs) is acceptable (in other words, bT < 3.5). Prestressing Tendons Fully prestressed components satisfying the tensile stress lim- its specified in AASHTO LRFD Table 5.9.4.2.2-1 at the Ser- vice III limit state load combination are exempt from fatigue considerations. (The Service III limit state load combination and its calibration are discussed in Chapter 6.) This exemption acknowledges that tendons in uncracked prestressed beams do not experience stress ranges resulting in fatigue cracking. Most prestressed concrete bridge members are covered by this exemption. For segmentally constructed bridges, AASHTO LRFD Arti- cle 5.5.3.3 specifies the fatigue resistance of prestressing ten- dons as given in Table 2.6. Reductions in constant amplitude fatigue threshold limits for fretting fatigue are not included in the tabulated values. In-service fatigue cracking of prestressing tendons has not been observed, thus justifying the exemption. The majority of research on fatigue cracking of prestressing strands is based on 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 doc- umented. In addition, the determination of stress ranges in cracked prestressed concrete members is complicated and beyond the normal prestressed concrete member design pro- cedure (Abeles et al. 1969, 1974; Abeles and Brown 1971). The uncertainty of this determination is also not well defined. In response to these various uncertainties, 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% 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 contained in NCHRP Research Results Digest 197 (1994). 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 in struc- tural 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% level of confidence that 95% 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 life- time 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). sTeel sTrucTures Finite-Life Fatigue The statistical bias and coefficient of variation of finite-life steel fatigue resistances are relatively well defined. NCHRP Report 286 (Keating and Fisher 1986) summarizes the mean finite-life fatigue resistance curves for the AASHTO detail categories A through E′ and their standard deviations. The AASHTO nominal finite-life fatigue resistance curves, defined in log-log space, are illustrated in Figure 2.2 (Fig- ure C6.6.1.2.5-1 of AASHTO LRFD). The finite-life fatigue resistances are represented by the sloping portions of the curves. The nominal fatigue resistance curves are determined by subtracting two standard deviations from the mean curves. The finite-life fatigue resistance (i.e., the allowable stress range to reach a certain number of cycles) is defined by Equa- tion 2.4: (2.4) 1 3A N( )∆σ = Table 2.6. Prestressing Tendon Fatigue Resistance Radius of Curvature (ft) Constant Amplitude Fatigue Threshold (ksi) >30 18 ≤30 and >12 Linear interpolation between 18 and 10 ≤12 10

27 where A is a constant defined for each detail category, and N is the number of cycles to failure. The current constant, A, is tabulated for each detail category in Table 2.7 for the mean finite-life fatigue resistance. The current estimates of uncertainty for finite-life fatigue resistances are tabulated in Table 2.8. Infinite-Life Fatigue The uncertainty of statistical parameters for infinite-life fatigue resistances is not well defined. The infinite-life fatigue resistance is defined by a constant amplitude fatigue thresh- old for each detail category. These thresholds, used for design, are tabulated in Table 2.9 (Table 6.6.1.2.5-3 of the AASHTO LRFD). These threshold values were not determined as rigorously as the finite-life curves discussed above because experimental Source: American Association of State Highway and Transportation Officials. Figure 2.2. Nominal fatigue resistances in AASHTO LRFD. Table 2.7. Constant A for Mean Fatigue Resistance Detail Category A (108) A 700 B 240 B′ 146 C 57 C′ 57 D 35 E 18 E′ 10 Table 2.8. Statistical Parameters for Finite-Life Fatigue Resistance Detail Category Bias Coefficient of Variation A 2.8 0.59 B 2.0 0.71 B′ 2.4 0.67 C 1.3 0.83 C′ 1.3 0.83 D 1.6 0.77 E 1.6 0.77 E′ 2.5 0.63 Table 2.9. Nominal Constant Amplitude Fatigue Thresholds Detail Category Nominal Constant Amplitude Fatigue Threshold (ksi) A 24 B 16 B′ 12 C 10 C′ 12 D 7 E 4.5 E′ 2.6

28 testing near the threshold is time consuming and costly. Con- servative thresholds were estimated graphically by using limited experimental test observations. Thus, the uncertainty of these threshold values is not defined. A Delphi process was employed to investigate the un - certainty of the infinite-life fatigue resistances represented by the constant fatigue thresholds. At the winter 2010 meeting of the Bridge Task Force, in conjunction with the winter 2010 meeting of AASHTO Technical Committee T-14, the topic of the uncertainty of the thresholds was discussed. As the same characteristics that influence the uncertainty of the finite-life fatigue resistance of welded details influence the uncertainty of the infinite-life fatigue resistance, the Bridge Task Force concluded that the statistical parameters associated with the well-defined finite-life fatigue resistance (i.e., the bias and coefficient of variation) would be assumed appropriate for the infinite-life fatigue resistance, as well. With this assumption, the mean values of infinite-life fatigue resistance are tabulated in Table 2.10 below. The statistical parameters for infinite-life fatigue resis- tance are those tabulated in Table 2.8 for finite-life fatigue resistance. Cracking in Concrete Structures Cracking in concrete structures is controversial but must be controlled for aesthetic purposes, durability, and corro- sion 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 spacing, the most significant parameters to con- trol cracking are widely agreed on. 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 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 dis- cussed below. crack conTrol reinforcemenT This section reviews previous research studies on control of cracking and predicting crack width in concrete members. A significant amount of research has been conducted to investi- gate 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 concrete members with cover less than 2.5 in. and are not applicable for beams with larger con- crete cover. Different equations have been adopted by differ- ent codes. 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) the area of the beam section, and (4) the distance from the bottom reinforcement to the beam bottom surface. 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. On the basis of these results, Equation 2.5 was developed to predict the average crack width of the concrete beams. The maximum crack width was estimated by multi- plying the average crack width by 1.64 (Clark 1956). 1 (2.5)ave 1 2w C D p f C p ns= − +         where wave = average width of cracks (in.); C1, C2 = coefficients that depend on distribution of bond stress, bond strength, and tensile strength of con- crete; for Clark’s study, C1 = 2.27 × 10-8 (h - d)/d, C2 = 56.6; D = diameter of reinforcing bar (in.); p = As/Ae = cross-sectional area of reinforcement/ cross-sectional area of concrete; Ae = bd (in.2); b = width of component (in.); fs = computed stress in reinforcement (psi); Table 2.10. Mean Infinite-Life Fatigue Resistance Detail Category Constant Amplitude Fatigue Threshold (ksi) A 67 B 32 B′ 29 C 13 C′ 16 D 11 E 7 E′ 6

29 n = ratio of modulus of elasticity of steel to concrete (assumed to be 8 in Clark’s study); h = overall depth of beam/slab (in.); and d = distance from compressive face of beam/slab to centroid of longitudinal tensile reinforcement. Kaar and Mattock (1963) also developed a well-known crack-width equation for bottom face cracking, as given by Equation 2.6: 0.115 (2.6)4w f Ab s= β where wb = maximum crack width (taken as 0.001 in.); b = ratio of distances to neutral axis from extreme tension fiber and from centroid of reinforcement; fs = steel stress calculated by elastic cracked-section the- ory (ksi); and A = average effective concrete area around reinforcing bar, having same centroid as reinforcement (in.2). Broms (1965) conducted tests on 37 tension and 10 flexural members to analyze crack width and crack spacing. Broms observed that 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 reinforce- ment. 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 shown in Equation 2.7: 0.076 (2.7)3w f Adb s c= β where wb = maximum crack width (taken as 0.001 in.); b = ratio of distances to neutral axis from extreme tension fiber and from centroid of reinforcement; fs = steel stress calculated by elastic cracked-section the- ory (ksi); dc = bottom cover measured from center of lowest bar (in.); and A = average effective concrete area around reinforcing bar, having same centroid as reinforcement (in.2). 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 by Frosch (1999), crack widths were determined from an equation developed from 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 bars. Crack control can be achieved by limiting the spac- ing of these reinforcing bars. On the basis of these research findings, Frosch (1999) suggested that limiting the maximum bar spacing would prevent large cracks in concrete beams. The equation to calculate the maximum crack width for uncoated reinforcement was developed on the basis of the physical model as shown by Equation 2.8 (Frosch 1999): 2 2 (2.8)2 2 w f E d s c s s c ( )= β +  where s = maximum permissible bar spacing (in.); wc = limiting crack width (in.) [0.016 in., based on ACI 318-95 (ACI Committee 318 1995)]; Es = elastic modulus of steel reinforcement (can be taken as 29,000 ksi); b = 1.0 + 0.08dc; dc = bottom cover measured from center of lowest bar (in.); and fs = stress in steel reinforcement. Frosch (1999) suggested that for epoxy-coated reinforce- ment, Equation 2.8 (for uncoated reinforcement) should be multiplied by a factor of 2. Equation 2.8 has been rearranged to solve for the allowable uncoated bar spacing, as shown in Equation 2.9: 2 2 (2.9) 2 2s w E f dc s s c= β     −     The following design recommendation, which was based on the physical model and addresses the use of both uncoated and coated reinforcement, was presented. The equation to calculate the maximum spacing of reinforcement was given as shown by Equation 2.10 (Frosch 1999): 12 2 3 12 (2.10)s d s c s s= α − α     ≤ α where 36 fs s cα = γ

30 dc = thickness of concrete cover measured from extreme tension fiber to center of bar or wire located closest thereto, in.; s = maximum spacing of reinforcement (in.); as = reinforcement factor; gc = reinforcement coating factor: 1.0 for uncoated reinforce- ment, 0.5 for epoxy-coated reinforcement, unless test data can justify a higher value; and fs = calculated stress in reinforcement at service load (ksi). The calculated stress in reinforcement at service load ( fs) should be computed as the moment divided by the product of steel area and internal moment arm; fs should not exceed 60% of the specified yield strength fy. Frosch (2001) summarized the physical model for cracking and illustrated the development and limitations of the pro- posed design method. He recommended formulas for calculat- ing the maximum crack width for uncoated and epoxy-coated reinforcement, as well as the design recommendation for their use, similar to those in Frosch (1999). In general, the largest crack widths are expected at the extreme tensile face of the beam. However, Beeby (1979) con- ducted studies that showed the largest crack widths in the web along the beam side face occurred at about midheight. Frosch (2002) conducted research on the modeling and con- trol of cracking on the side face of concrete beams. The study showed that to provide adequate crack control, the maximum skin reinforcement spacing is a function of the side cover. It was also shown that a maximum bar spacing of 12 in. pro- vides reasonable crack control for 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 informa- tion regarding optimum locations for placing skin reinforce- ment 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. As the maximum crack width was observed halfway between the reinforcement and neutral axis, Equation 2.11 can be used to solve for crack width wc at x = (d - c)/2: 1 2 (2.11)2 2 w d d cc s s )( )(= ε + − where es = strain in steel reinforcement = fs/Es; ds = concrete cover for skin reinforcement (in.); d = effective depth (in.); and c = depth of neutral axis from compression face (in.). The study of the physical model showed that sections with an 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. Maximum effective depth decreases for covers thicker than 3 in. for Grade 60 reinforcement, resulting in the maximum depth (d = 36 in.). 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 (ws) was calcu- lated halfway between the primary reinforcement and the first skin reinforcement bar at a distance x = s/2, yielding Equation 2.12: 2 2 (2.12)2 2 w f E d s s s s s )(= + For sections with skin reinforcement, it is necessary to determine the location in the section at which the reinforce- ment can be discontinued. As crack widths are controlled by skin reinforcement below its end point, it is necessary to calcu- late the maximum distance where the skin reinforcement can be eliminated. The maximum crack width will occur approxi- mately halfway between the neutral axis and the location of the first layer of skin reinforcement at a distance x = sna/2 from the neutral axis (Frosch 2002). The maximum crack width can be calculated with Equation 2.13 based on the physical model developed by Frosch (2002): 2 (2.13)2 2 w s d c d s s na s s na) )( (= ε − + where sna is the maximum distance where the skin reinforce- ment 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 ten- sion faces. Frosch (2002) recommended the maximum spacing of flexural tension reinforcement as given by Equa- tion 2.14: 12 2 3 12 (2.14)s d s c s s= α − α     ≤ α where 36 ; fs s α =

31 dc = thickness of concrete cover (in.) (for bottom face reinforcement, measured from extreme tension fiber to center of bar, and for skin reinforcement, mea- sured from side face to center of bar); s = maximum spacing of reinforcement (in.); as = reinforcement factor; and fs = calculated stress in reinforcement at service load (ksi). The fs value should be computed as the moment divided by the product of steel area and internal moment arm; fs should not be more than 60% of the specified yield strength fy. Skin reinforcement is 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 calcu- lated by Equation 2.15: 42 2 36 (2.15)d ds c s= α − ≤ α 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 with uncoated reinforcement (Blackman and Frosch 2005). Blackman and Frosch investigated crack widths in concrete beams by using epoxy-coated reinforcement. The primary variables used in the study included epoxy coating thickness and reinforcing bar spacing. Blackman and Frosch designed 10 slab specimens to examine the effect of epoxy coating on cracks and con- cluded that the epoxy coating thickness did not significantly affect the concrete cracking behavior. Frosch (1999, 2001, 2002) and Blackman and Frosch (2005) presented an equa- tion, given here as Equation 2.16, to compare the average measured crack spacing for the uncoated and epoxy-coated bars with the calculated values: (2.16)S dc s= ψ p where Sc = crack spacing (in.); d* = controlling cover distance (in.); and ψs = crack spacing factor (1.0 for minimum crack spacing, 1.5 for average crack spacing, and 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 harsh environmental exposure. Recently, increased concrete cover coupled with high-performance concrete has become increasingly popular because of its durability. However, this practice results in unrealistically small bar spacing and prevents the use of con- temporary crack control practices that are based on statistical studies. Thus, 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 crack widths in transversely posttensioned concrete deck slabs in box girder bridges. They tested four full-scale concrete box girder segments and derived the maximum-crack-width equation from the testing data, as given by Equations 2.17 and 2.18: 3 10 (2.17)max 6 0 ,eff 0.75 w f f A A A h x d xs s t st pt ( )= × − φ + ξ     − − − 1 (2.18) n n ap as s p ( )ξ = τ τ pi + − pi φ φ where Ast = total area of reinforcing bars (mm2); Apt = total area of prestressing tendons (mm2); At,eff = effective tensile concrete area (mm2); d = effective depth (mm); fs = increment of reinforcing bar stress after decompres- sion (MPa); f0 = steel stress at initial occurrence of crack (MPa); h = height of cross section (mm); n = number of strands in a flat duct; x = depth of neutral axis (mm); wmax = predicted maximum crack width (mm); fs = diameter of reinforcing bar (mm); fp = diameter of prestressing tendons (mm); and ap as τ τ = 0.465 for grouted posttensioned tendons. conTrol of cracks in currenT coDe ProVisions The current 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 particu- larly 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 a yield strength of 60,000 psi is used. ACI 318-08 Article 10.6 (ACI Commit- tee 318 2008) does not distinguish between interior and exterior exposure because 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) does not exceed that given by Equation 2.19 15 40,000 2.5 (2.19)s f c s c=     −

32 but not greater than 12 40,000 , fs     where cc is the least dis- tance from the 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 in Equation 2.19 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 318-99/318R-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/ 318R-02 (ACI Committee 318 2002). The maximum bar spacing to directly control cracking is specified. Similar rec- ommendations have been stated for deep beams with the requirement of skin reinforcement. AASHTO LRFD (2012) also provides provisions of rein- forcement spacing to control flexural cracking. Like ACI, AASHTO emphasizes the importance of reinforcement detail- ing 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 the distribution of reinforcement to control cracking. The equation in AASHTO LRFD (2008) is based on the phy- sical crack model of Frosch (2001) rather than the statisti- cally based model used in previous editions. The equation (given here as Equation 2.20) limits bar spacing rather than crack width: 700 2 (2.20)s f de s ss c≤ γ β − where bs = 1 0.7 d h d c c( )+ − (the geometric relationship between crack width at tension face versus crack width at reinforcement level); ge = exposure factor (1.00 for Class 1 exposure, 0.75 for Class 2 exposure); dc = thickness of concrete cover measured from extreme tension fiber to center of the flexural reinforcement located closest thereto, in.; fss = tensile stress in steel reinforcement at the SLS (ksi); and h = overall thickness of depth of the component (in.). Unlike ACI, AASHTO specifies exposure conditions to meet the needs of the authority having jurisdiction. The 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 or corrosion. This exposure class can be thought of as an upper bound in regard to crack width for appearance and corrosion. The Class 2 exposure con- dition generally applies to decks and substructures exposed to water and any other components exposed to corrosive envi- ronments. AASHTO LRFD (2008) also specifies requirements for skin reinforcement based on ACI 318-11 (ACI Committee 318 2011). AASHTO Equation 5.7.3.4-1 (given here as Equa- tion 2.20) applies to both reinforced and prestressed concrete, with specifications on the steel stresses used. In general, if the AASHTO Class 2 exposure condition is used, AASHTO spac- ings are less than those derived by the ACI equation. How- ever, if the Class 1 exposure condition is used, ACI spacing becomes more conservative. PrinciPal sTresses in Webs of seGmenTal concreTe briDGes Okeil (2006) studied the allowable tensile stress for webs of prestressed segmental concrete bridges by using a reliability- based approach. In this study, six prestressed segmental con- crete bridge designs were analyzed. Okeil stated that by complying with the allowable tensile stresses, flexural crack- ing 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. To control shear cracking, the principal stress must be limited to an allowable tensile stress ( ft,all). This issue was addressed by the Florida DOT (Structures Manual 2013) and resulted in a recommendation for the allowable tensile stresses to be used in checking web tensile principal stress (s1). However, the recommendation ignored the accompanying compressive principal stress (s2), which has a significant effect on the ten- sile strength of concrete. The objective of Okeil’s study was to develop an allowable stress limit under which cracking in webs of prestressed segmental 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 2.21 to 2.23, respectively: 6.7 (2.21)tu 0.5 f fc( )= ′ 1.59 (2.22)tu 0.67 f fc( )= ′ 1.38 (2.23)tu 0.69 f fc( )= ′ where ftu is uniaxial tensile strength of concrete (psi), and f ′c is concrete compressive strength (psi).

33 Okeil (2006) concluded that Equation 2.23 provides a better estimate of the tensile strength over a wider range of concrete compressive strengths. Using a biaxial state of stress and regres- sion analysis, Okeil developed a relationship between the tensile strength and the corresponding compressive strength, as shown in Equation 2.24: 1 0.85 (2.24)tu tu cu f fc σ = + σ ′ where scu and stu are the ultimate strengths of concrete under a compression–tension biaxial state of stress (psi). By combining Equations 2.23 and 2.24, Equation 2.25 is obtained: 1.38 1 0.85 (2.25)tu 0.69 cuf fc c ( )σ = ′ + σ ′     After a detailed parametric study and reliability analysis, Okeil (2006) recommended an expression, given in Equa- tion 2.26, for estimating the allowable tensile stress in the webs of posttensioned segmental bridges under biaxial stresses: 0.60 1 0.85 (2.26)ct 0.7 2f f fc c ( )= ′ + σ ′     where s2 is the principal stress in the centroidal stress block in the web of a posttensioned segmental bridge. The findings of this study are limited to the range of con- crete compressive strengths between 5 and 8 ksi. sTress limiTaTions for PresTressinG TenDons AASHTO LRFD (2012) provides stress limits for prestressing tendons at various service conditions. These stress limits are listed in Table 2.11. ACI 318-08 provides similar limits on the tensile stress in prestressing tendons and rebars (ACI Committee 318 2008). Major revisions to the limits were 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 for prestressing steel are listed as fol- lows (ACI Committee 318 2008): Due to prestressing steel jacking force: 0.94fpy but not greater than the lesser of 0.80fpu and the maximum value recom- mended by the manufacturer of prestressing steel or anchor- age devices. Immediately after prestress transfer: 0.82fpy but not greater than 0.74fpu. Post-tensioning tendons, at anchorage devices and couplers, immediately after force transfer: 0.70fpu. EN 1992-2 (Eurocode 2): Design of Concrete Structures (EN 1992-2 2005) restricts inelastic deformation of the steel in concrete structures at the SLS to prevent large, perma- nently open cracks. In EN1992-2, at the SLSs, the stress limit for prestressing steel is 0.75fpk after allowance for losses, where fpk is the characteristic tensile strength of prestressing steel. The exact meaning of characteristic tensile strength is not defined in EN1992-2 and is interpreted here as the specified strength. This limit of 0.75fpk is listed in EN1992-2 Section 7. concreTe Tension sTresses The early discussion of cracking control is diverse. At the First United States Conference on Prestressed Concrete in 1951, Table 2.11. 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 before transfer (fpbt) 0.70fpu 0.75fpu — At SLS after all losses (fpe) 0.80fpy 0.80fpy 0.80fpy Posttensioning Before seating, short-term fpbt may be allowed 0.90fpy 0.90fpy 0.90fpy At anchorages and couplers immediately after anchor set 0.70fpu 0.70fpu 0.70fpu Elsewhere along length of member away from anchorages and couplers immediately after anchor set 0.70fpu 0.74fpu 0.70fpu At SLS after losses (fpe) 0.80fpy 0.80fpy 0.80fpy Note: — = not applicable.

34 some experts opined that a completely crackless concrete member is only better for the specific purpose, but others thought that cracking of prestressed concrete beams is as important as yielding. In 1958, the Tentative Recommenda- tions 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 units in the following provisions are in pounds per square inch for the allowable tensile stress): 3 fci′ for members without nonprestressed reinforcement; 6 fci′ for members with nonprestressed reinforcement pro- vided to resist the tensile force in concrete; computed on the basis of an uncracked section. The 1963 Building Code Requirements for Reinforced Con- crete (ACI Committee 318 1963) included the recommenda- tion for the tensile stress limits proposed by ACI-ASCE Joint Committee 323 (1958), with some modifications: 3 fci′ for members without auxiliary reinforcement in the tension zone; [w]hen the calculated tension stress exceeds 3 fci′ , rein- forcement 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 Con- crete modified the allowable tensile stress limit as follows (ACI Committee 318 1977): 6 fci′ for the extreme fiber stress in tension at ends of simply supported members; 3 fci′ 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 stresses, ft, exceeds 6 fci′ at ends of simply supported members, or 3 fci′ at other locations, additional bonded reinforcement shall be pro- vided 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 fci′ for members in tension areas with no bonded reinforcement; [w]here the calculated tensile stress exceeds this value, re inforcement 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 fci′ . Table 2.12 shows the tensile stress limits and provisions of AASHTO LRFD (2008). 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. Table 2.12. Tensile Stress Limits in Prestressed Concrete at SLS After Losses, Fully Prestressed Components (AASHTO LRFD Table 5.9.4.2.2-1 [2008]) 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 f c ′ (ksi) 0.0948 f c ′ (ksi) No tension Segmentally Con- structed Bridges Longitudinal Stresses Through Joints in the Precompressed Tensile Zone Joints with minimum bonded auxiliary reinforcement through the joints sufficient to carry the calcu- lated 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 f c ′ (ksi) No tension Transverse Stress Through Joints Tension in the transverse direction in precompressed tensile zone 0.0948 f c ′ (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 f c ′ (ksi)

35 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 (1975) includes the background that led to waiving fatigue require- ments for these components. 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 a Service III limit state within the ten- sile stress limit specified in AASHTO LRFD Table 5.9.4.2.2-1, the fatigue limit state load factors, the girder distribution fac- tors, and dynamic load allowance cause fatigue limit state stress to be considerably less than the corresponding value deter- mined from Service 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. As a result, 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 AASHTO LRFD 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 are available on the randomness of load and resistance of segmental bridges. There is no evidence of fatigue damage on these structures, so no changes are recom- mended, and calibration will not be made. Crack Control Reinforcement for Components Designed Using Strut and Tie Model (AASHTO LRFD Article 5.6.3.6) Birrcher et al. (2009) proposed new provisions regarding 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.” Moreover, they continued, “The reinforcement in the ver- tical and horizontal direction shall satisfy the following [shown here as Equation 2.27]”: 0.003, 0.003 (2.27) A b s A b s v w v h w h ≥ ≥ where Av, Ah = total area of vertical and horizontal crack control reinforcement within spacing sv and sh, respectively; bw = width of member web (in.); and sv, sh = spacing of vertical and horizontal crack control reinforcement, respectively. Birrcher et al. (2009) concluded that “[c]rack control rein- forcement shall be distributed evenly near the side faces of the strut. Where necessary, interior layers of crack control reinforcement may be used.” Control of Permanent Deformation Steel structures are subject to requirements intended to pre- vent changes in riding quality and appearance resulting from permanent deflections in service. Starting with specifications for LFD in the early 1970s, steel structures have been subject to two limitations to guard against these undesirable behav- iors. There is a requirement that the service-load stress under an overload be less than 95% of yield in a composite girder or 80% of yield in a noncomposite girder and that slip-critical connections be designed for the same overload requirement. In LFD, the overload requirement was dead load plus 5/3 of the HS20 loading. Due to the increased demand of the HL-93 live load, the corresponding provisions in the AASHTO LRFD are investigated at the Service II limit state, which involves a load factor on live load of 1.30. The response of girder structures to excessive overloads was one of several issues explored during the AASHO Road Test of the late 1950s and early 1960s and documented in a series of reports issued by the Highway Research Board (AASHO Road Test 1962), the predecessor of the Transpor- tation Research Board. The structures of the AASHO Road Test were designed to undergo many repetitions to relatively high stresses. Table 2.13 shows a summary of the initial stresses in steel bridges of composite and noncomposite construction. The nominal yield stress for the material in these bridges was 33 ksi, so it can be seen that in many cases these bridges were subjected to loads beyond the yield stress. Table 2.13 also indicates the number of live load passages to which these structures were subjected. After the repetitions of actual truck loading, some of the structures were subjected to further cycles of load to investigate fatigue through the use of eccentric mass dampers. In American Iron and Steel Institute Bulletin 15, Vincent (1969) summarizes the basis for LFD of steel structures. Bulletin 15 contains the following statement: “There is, how- ever, a definite need for a control on the possibility of perma- nent deformations under infrequent overloads which may impair the riding quality of the bridges.” The establishment of the 80% and 95% criteria is demonstrated in Figure 2.3, taken from Bulletin 15, which shows the permanent set at midspan of several of the bridges from the AASHO Road Test and the corresponding ratio between test stress and the actual measured yield point of the steel in the bridges. The two criteria for composite and noncomposite struc- tures are seen to produce an accumulated displacement of

36 approximately 1 in. at the midspan of bridges of an approxi- mately 50-ft span. Deflection measurements at various times during the road test indicate that most structures accumu- lated most of the eventual permanent set in the very early repetitions of loading. The provisions for control of permanent deformations in steel structures were incorporated into AASHTO LRFD with an adjustment for the increased live load with the intent of providing generally the same, or even higher, level of over- load performance as was provided by LFD in most cases. Consider Figure 2.4, which shows the ratio of the HL-93 loading to the HS20 loading in the Standard Specifications. The load factor in the Standard Specifications for this case was 1.67; the current load factor for the AASHTO LRFD Ser- vice II load combination is 1.3. That means that whenever the moment ratio in Figure 2.4 is greater than 1.28, then the Table 2.13. Data from AASHO Road Test (1962) Summary of Initial Stresses in Steel Bridges No. of Vehicle PassagesDesign Stress (ksi) Actual Stress (ksi) Bridge Center Beam Exterior Beam Interior Beam Center Beam Exterior Beam To First Cracking Total Noncomposite Bridges 1A 27.0 — 25.3 27.7 30.1 536,000 557,400 1B 34.8 — 32.5 35.4 40.5 — 235 2A 35.0 — 35.0 39.4 41.1 — 26 3A 27.3 — 28.6 30.9 35.4 — 392,400 4A 34.7 — 35.9 38.9 41.1 — 106 4B 34.7 — 39.1 42.1 42.3 — 106 9A — 27.0 22.9 24.7 25.5 477,900 477,900 9B — 27.0 24.0 24.6 26.0 477,900 477,900 Composite Bridges 2B 35.0 — 30.2 33.8 35.8 531,500 558,400 3B 26.9 — 26.0 28.8 31.0 535,500 557,800 Note: — = not available. Source: Vincent (1969). Reproduced with permission from the American Iron & Steel Institute. Figure 2.3. Development of service stress limits.

37 current demand is higher than that required by the Standard Specifications. Several issues arose regarding retention of, or revisions to, the provisions related to control of permanent deformations; these are discussed in Section 6.4. 2.3.2 Eurocode The Eurocode contains the following sections, to which refer- ence is made in subsequent 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 Structure • 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 Structure • 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 Eurocode sections allow the user countries to incorpo- rate country-specific requirements through the incorporation of a national annex. The Eurocode replaced most previous country specifica- tions, such as the German Institute for Standardization and the British BS5400, and it 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 Euro- pean specifications were reviewed. Definition of SLS The Eurocode (EN 1990 2002) defines SLSs as those concerning • The functioning of the structure or structural members under normal use; • The comfort of users; and • The appearance of the construction works. The Eurocode (EN 1990 2002) includes requirements call- ing for • The serviceability requirements to be agreed on for each individual project; • A distinction to be made between reversible and irrevers- ible serviceability limit states; and • The verification of SLS based on criteria concerning the following aspects: a. Deformations that affect – The appearance, – The comfort of users, – The functioning of the structure (including the functioning of machines or services), or – That cause damage to finishes of nonstructural 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, – 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). Background on the Eurocode’s Reliability Basis The Eurocode specifies that structures be designed for a par- ticular design working life (EN 1990 2002). The design work- ing life is defined as the period for which a structure is assumed to be usable for its intended purpose with anticipated mainte- nance but without major repair being necessary. Examples of design working life are given in Table 2.14. The levels of reliability relating to ULS and SLS can be achieved by suitable combinations of protective measures (e.g., protection against fire or corrosion), measures relating to design calculations (e.g., choice of partial factors), mea- sures relating to quality management, measures aimed to reduce errors in design (e.g., project supervision), and Source: American Association of State Highway and Transportation Officials. Figure 2.4. Ratio of HL-93 moment to HS20 moment.

38 execution (construction) of the structure (e.g., inspection during execution) and other kinds of measures. The Eurocode defines three levels of consequences classes (CC1, CC2, and CC3), as defined in Table 2.15. Three reli- ability classes (RC1, RC2, and RC3) may be associated with the three consequence classes. The vast majority of bridges are designed to CC2, with CC3 a possibility only for those bridges with very high con- sequences of failure, such as a signature bridge. The provisions of the Eurocode, specifically EN 1990 (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 2.16 applied to load factors to differentiate the three reliability classes. Other measures (e.g., differing levels of quality control) in lieu of modifying the load factors are some- times preferred. Table 2.17 summarizes the probabilities of failure (Pf) inher- ent to the Eurocode and the AASHTO LRFD for ULSs, along with the corresponding reliability indices (b) 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. sls reliabiliTy The SLSs of the Eurocode are categorized as reversible and irre- versible. Reversible SLSs are those for which no consequences remain once a load is removed from a structure. For example, a crack-width limit state with a sufficiently small size is a revers- ible limit state, but one defined by a high width (e.g., 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 higher probability of failure and corresponding reliability index than the strength limit states, as shown in Table 2.18. sls loaD combinaTions EN 1990 (2002) includes three types of load combinations for the SLSs: characteristic combination, frequent combination, and quasipermanent combination. Table 2.19 summarizes the Eurocode SLS load combinations. Serviceability Design Basic Approach basic equaTion The basic equation in the Eurocode (EN 1990 2002) for verify- ing that an SLS is satisfied is E Cd d≤ where Cd = is the limiting design value of the relevant service- ability criterion and Ed = is the design value of the effects of actions specified in the serviceability criterion, determined on the basis of the relevant combination. Table 2.14. Design Working Lives Design Working Life Category Design Working Life (years) Examples 1 10 Temporary structures 2 10–25 Replaceable structural parts (e.g., gantry girders, bearings) 3 15–30 Agricultural and similar structures 4 50 Building structures and other common structures 5 100 Monumental building struc- tures, bridges, and other civil engineering structures Source: Adapted from Table 2.1 of EN 1990 (EN 1990 2002). Table 2.15. Eurocode Consequence Classes 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 Source: Adapted from Table B1 of EN 1990 (EN 1990 2002). Table 2.16. Multiplication Factor (KF1) for Reliability Differentiation Reliability Class KF1 RC1 0.9 RC2 1.0 RC3 1.1

39 of construction works or agreed with the client or the national authority. combinaTion of acTions (loaD combinaTions) The combinations of actions (load combinations) for service- ability limit states in the Eurocode are defined symbolically by Equation 2.28, which is the characteristic (rare) combination; Equation 2.29, which is the infrequent combination; Equa- tion 2.30, which is the frequent combination; and Equation 2.31, which is the quasipermanent combination. The characteristic combination (Equation 2.28) is normally used for irreversible limit states; the frequent combination (Equation 2.30) is nor- mally used for reversible limit states. (2.28), ,1 1 0, , 1 E E G P Q Qd k j k k j i k i i i∑ ∑= + + + ≥ > c (2.29), 1,1 ,1 1 1, , 1 E E G P Q Qd k j k k j i k i i i i∑ ∑= + + ′ + ≥ > c c Table 2.17. Target Probabilities of Failure (Pf) and Target Reliability Indices (bT) 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 (hI = 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 (hI = 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 Table 2.18. Irreversible SLS Target Probabilities of Failure and Corresponding Reliability Indices Reliability Class Reference Period (years) 1 50 RC2 1.00E-03 1.00E-01 2.9 1.5 Source: Adapted from Table C2 of EN 1990 (Eurocode 0) (EN 1990 2002). Table 2.19. SLS Combinations SLS Load Combination Type Description Type Acceptance of Infringement Example Reversible Limit states that will not be exceeded when the actions that caused the infringement are removed Frequent Specified duration and frequency of infringe- ments are accepted Crack-width limit state of a prestressed con- crete beam with bonded tendons charac- terized by a 0.2-mm crack width Quasipermanent Specified long-term infringement is accepted Crack-width limit state for a reinforced- concrete or prestressed-concrete beam with unbonded tendons characterized by a 0.3-mm crack width Irreversible Limit states that remain per- manently exceeded after the actions that caused the infringement are removed Characteristic (5% probability of exceedance) No infringement accepted 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 serViceabiliTy criTeria Specific serviceability criteria such as crack width, stress or strain limitation, and slip resistance exist in separate sections of the Eurocode (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 with the type

40 (2.30), 1,1 ,1 1 1, , 1 E E G P Q Qd k j k k j i k i i i i∑ ∑= + + + ≥ > c c (2.31), 1 2, , 1 E E G P Qd k j k j i k i i i∑ ∑= + + ≥ > c where 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,1 = characteristic value of the leading (domi- nant) Variable Action 1; Qk,i = characteristic value of the accompanying Variable Action 1; 0 = factor for characteristic value of a variable action; 1 = factor for frequent value of a variable action; and 2 = factor for quasipermanent value of a variable action. The terms in Equations 2.28 through 2.31 are further defined as follows: • 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 through- out a given reference period and for which the variation in magnitude with time is negligible, or for which the varia- tion is always in the same direction (monotonic) until the action attains a certain limiting value. • variable action (Q): Action for which the variation in magnitude with time is neither negligible nor monotonic. • characteristic value of a variable action (0 Qk): Value chosen (insofar as it can be fixed on statistical bases) so that the probability that the effects caused by the combi- nation 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 (0 ≤ 1.0). • frequent value of a variable action (1 Qk): Value deter- mined (insofar 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 refer- ence period, or the frequency of its being exceeded is lim- ited to a given value. It may be expressed as a determined part of the characteristic value by using a factor (1 ≤ 1.0). • quasipermanent value of a variable action (2 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 (2 ≤ 1.0). 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). Each Eurocode country has its own national annex in which country-specific require- ments are placed; thus, the Eurocode allows each country to specify its own serviceability criteria in its national annex. Recommended values of the  factors for different types of structures (e.g., buildings, highway bridges, or railway bridges) are tabulated in the Eurocode. Table 2.20 shows the recom- mended values for highway bridges. Note 1: The  values may be set by the National Annex. Rec- ommended values of  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; and • 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 1infq. The recommended values of 1infq are • 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; and • 1,00 in other cases (i.e., the characteristic value is substi- tuted 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). When relevant, representative values of water forces (Fwa) may be defined for the individual project. Existing Limit State A summary of the SLS requirements in the Eurocode is in Appendix A. 2.3.3 Canadian Highway Bridge Design Code Background The CHBDC (2006) and earlier Ontario Highway Bridge Design Code (1991) cover ULS and SLS. The serviceability limit states in the CHBDC include fatigue, deflection, cracking, and com- pressive stress in concrete. The SLS acceptability criterion was

41 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 accept- ability criterion was formulated in terms of the minimum return period for exceeding the decompression moment. It was assumed that the girders will crack due to shrinkage before installation or under exceptionally heavy trucks and that 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 con- crete, and girder failure. The minimum acceptable return period for exceeding the decompression moment was then determined by a group of experts invited by the Code Con- trol Committee using a process of expert elicitation (Delphi process). The group was asked to provide their expert opin- ion. They deliberated and came to a conclusion that a return period of 3 weeks is acceptable. However, the group did not feel strongly about it, so they agreed that the target probabil- ity of exceeding this limit state is 50%, which corresponds to the target reliability index (bT = 0). Existing Limit States In general, the SLSs in the CHBDC are very similar to the SLSs currently specified in AASHTO LRFD. There are some differences in application, but the general phenomena being treated are basically the same. No new limit states that do not exist in AASHTO LRFD were found in the 2006 CHBDC. 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 service- ability limit states. Service-load combinations use a load fac- tor of 0.9 for the live load that is based on the CL-W-625 truck (140.5 kips, 59 ft long) or lane loading. The CL-W-625 truck Table 2.20. Eurocode Recommended Values of  Factors for Highway Bridges Action Symbol 0 1 2 Traffic loads (EN 1991-2 Table 4.4 [EN 1991-2 2003]) gr1a (LM1 + pedes- trian or cycle-track loads)a TS 0,75 0,75 0 UDL 0,40 0,40 0 Pedestrian + cycle-track loadsb 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 0,6c 0,6 0,5 Snow loads Qsnk (during execution) 0,8 — — Construction loads Qc 1,0 — 1,0 a The recommended values of 0, 1, and 2 for gr1a and gr1b are given for roads with traffic corresponding to adjusting aQi, aqi, aqr, and bQ equal to 1. Those relating to unified distribution load (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 a factors. For example, a value of 2 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). b The combination value of the pedestrian and cycle-track load, which is mentioned in Table 4.4a of EN 1991-2 (2003), is a “reduced” value. 0 and 1 factors are applicable to this value. c The recommended 0 value for thermal actions may in most cases be reduced to zero for ULSs EQU, STR, and GEO. See also the design Eurocodes. Source: Adapted from Table A2.1 of EN 1990 (EN 1990 2002).

42 is considerably larger than the HL-93 truck alone (i.e., without the uniform distributed load). Load Combination 2 applies to superstructure vibration only. The CHBDC also specifies a lane load that 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 HL-93 loading. CHBDC Clause 6.4.1.3 deals with serviceability limit states and foundations. Three criteria are noted: • Foundation deformations that cause SLS limits to be exceeded; • Deformations that cause the riding surface or transitions between the approaches and the bridge to become un- acceptable; and • Deformations that cause unacceptable structural mis- alignment, distortion, or tilting. Clause 7.6.5.2 deals with construction requirements for pipe arches and limits to downward deflection. The commen- tary reinforces that this is a construction requirement rather than a design control. Clause 7.7.5.2 speaks to upward or downward crown deflec- tion during construction of metal box structures and pro- vides a 1% requirement. Little additional information is provided in the commentary, which notes that AASHTO Article 12.8.5.3 has limits for live load deflection. Clause 8.5.1 states that cracking, deformation, stress, and vibration SLSs should be considered. Clause 8.5.2 specifies serviceability limit states for concrete structures and indicates that these are cracking, deforma- tions, 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 indi- cates 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. The commentary indicates that it is generally a good practice to provide sufficient prestress so that under permanent loads, any cracks previously caused due to the application of live load are closed under per- manent loads to enhance durability. Clause 8.12 deals with control of cracking by specifying distribution requirements and a tensile strain limit. 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 that include the aver- age strain in the reinforcing. A distinction is made for epoxy- coated reinforcement, for which the calculated crack width is increased 20%. Clause 10.5.3.1 specifies serviceability limit states for steel structures; these include deflection, yielding, slipping of bolted joints, and vibrations. Clause 10.5.3.2 for deflections is a cross reference for Clause 10.16.4, which applies to orthotropic decks only. Clause 10.5.3.3 deals with the prevention of general yield- ing at the SLSs, which appears to pertain to Clause 10.11.4 (permanent deflections for composite sections). The latter is similar to the AASHTO overload requirements, except that the CHBDC load factor for live load is 0.9 as opposed to the AASHTO load factor of 1.3. As discussed in Chapter 6, the net result is probably similar because of the heavier CHBDC live load. This is not a new limit state, although the numerical values might differ somewhat from AASHTO. Clause 10.11.3 is an SLS for differential shrinkage between restrained and free shrinkage of concrete and steel composite members. 2.3.4 Japanese Geotechnical Society Foundation Design Guideline The Japanese Geotechnical Society (JGS) prepared a draft foun- dation design guideline in 2002. This document attempts to phrase the structural and geotechnical design principles follow- ing the general requirements of ISO 2394. Three limit states are defined on the basis of the following functional statements: • With respect to the various magnitudes and frequencies of loading during the expected service life, the structures shall satisfy structural performance as characterized by structural strength, stability, deformability, and durability, including serviceability, repairability, and safety with appropriate levels of reliability. • The structures shall be designed to be sufficiently safe so as to prevent serious injury to occupants and surrounding personnel during all possible design situations through the design working life. This functional statement is related to the topic of safety. • The structures may be designed, by judgment of the owner based on the importance of the structure, such that normal functions are preserved (serviceability) or damage is lim- ited within a certain tolerable level (repairability) against specified loading conditions during the design working life with appropriate reliability. • It is not prohibited for owners of the structures to specify additional functional statements other than those stated above based on their own judgment.

43 The above functional statements are in the context of design working life. The JGS document indicates that the design work- ing life may be determined by considering various factors including life-cycle cost, durability, deterioration, and the func- tional life of the structure. The document notes that care should be taken to ensure that the safety margin (i.e., reli- ability) introduced to each limit state is strongly related to the design working life of the structure. The structural perfor- mance requirements of the structure are specified by several limit states according to the load levels classified according to their frequencies, as follows: • High-frequency variable actions are those expected to occur once or a few times with significantly high probabil- ity during the design working life of the structure. • Low-frequency variable actions are those that may or may not occur during the design working life of the structure (i.e., a low-frequency variable action is an event with a very low occurrence probability). Using the preceding concepts, the JGS presents three major limit states in the following qualitative manner: • ULS—The structures may sustain considerable damages but not to the extent of collapse that would result in serious injury or loss of life. This limit state corresponds to the functional statement of safety as noted above. • Repairable limit state—Damage to the structure, although it may influence durability, is limited to a level that can be repaired at a reasonable cost and in a relatively short period of time. This limit state, therefore, can be interpreted as a state in which the majority of the value of the structure is preserved. Furthermore, this limit state sometimes implies a state in which marginal use of the structure is possible for rescue operations right after an extraordinary event such as a large earthquake. This limit state corresponds to the repairability defined in the functional statement above. • SLS—Damage to the structure is limited to a level at which all common functions of the structure are preserved and do not influence structural durability. This limit state corre- sponds to the serviceability defined in the functional state- ment above. The JGS document indicates that additional performance requirements and limit states other than those defined above may be defined as deemed necessary. With respect to the three limit states identified above, the JGS document provides a conceptual view of a performance matrix for describing the performance requirements of a structure. In the performance matrix, design situations and limit states are taken as the axes of the coordinate system, and performance requirements are coordinated according to the importance of the structure. The example performance matrix presented in Figure 2.5 consists of three levels of design situations and limit states. It reflects a seismic design situation, which for most structures in Japan is the critical design situation. The performance requirements defined above are required to be verified by two approaches: Approach A and Approach B. Damage to a Structure M agnitude of A ctions SLS Repairable Limit State ULS High frequency, low impact Important, ordinary and easily repairable structures — — Medium frequency, medium impact Important and ordinary structures Easily repairable structures — Low frequency, high impact — Important structures Ordinary and easily repairable structures Figure 2.5. Conceptual view of a performance matrix. Note: —  performance requirement not specified by Japanese Geotechnical Society.

44 Approach A does not require any specified method for perfor- mance verification of the structure. It requires, however, that the designer prove the structure satisfies the specified performance requirements with an appropriate level of reliability. A designer who uses Approach A is required to submit the necessary design report and documentation for examination to the administra- tive organization or local government responsible for control- ling the safety of the structure. In contrast, in Approach B the verification of performance requirements is based on specific design codes specified by the owner. The JGS document recom- mends use of the partial-factors format for design. 2.3.5 Overarching Characteristics of Other Specifications to Be Considered Reversible Versus Irreversible Limit States SLSs may be categorized as reversible and irreversible. Revers- ible SLSs are those for which no consequences remain once a load is removed from a structure. Irreversible SLSs are those for which consequences remain. Due to their reduced safety implications, irreversible SLSs, which do not concern the safety of the traveling public, are cali- brated to a higher probability of failure and a corresponding lower reliability index than the strength limit states. Reversible SLSs are calibrated to an even lower reliability index. Load-Driven Versus Non-Load-Driven Limit States The difference between load-driven and non-load-driven limit states is basically in the degree of involvement of externally applied load components in the formulation of the limit state function. In the load-driven limit states, the damage occurs due to accumulated applications of external loads, usually live load (trucks). Examples of load-driven limit states include decom- pression and cracking of prestressed concrete and vibrations or deflection. The damage caused by exceeding SLSs may be reversible or irreversible and, therefore, the cost of repair may vary significantly. However, in non-load-driven SLSs, the dam- age occurs due to deterioration or degradation as a function of time and aggressive environment or as inherent behavior due to certain material properties. Examples of non-load-driven SLSs include penetration of chlorides leading to corrosion of rein- forcement, leaking joints leading to corrosion under the joints, and shrinkage cracking of concrete components. In these exam- ples, the external load occurrence plays a secondary role. 2.3.6 Lessons Learned from Review of Existing Design Specifications Review of existing design specifications revealed that the SLSs covered by different specifications are somewhat similar. It was concluded that other specifications do not include “new” SLSs that need to be added to AASHTO LRFD. However, the review resulted in some concepts that were of interest. These concepts include • The target reliability index for SLSs may have different val- ues for different limit states. Furthermore, the target reli- ability for a certain limit state may vary depending on the consequences of exceeding that limit state. • To differentiate between different limit states according to the consequences of exceeding the limit state, the following factors were considered: 44 Whether the limit state is reversible or irreversible: Irre- versible limit states may have higher target reliability than reversible limit states. 44 Relative cost of repairs: Limit states that have the poten- tial to cause damage that is costly to repair may have higher target reliability than limit states that have the potential of causing only minor damage. 2.4 Surveys of Current practice 2.4.1 Summary of R19B Survey A focused survey was sent to 31 bridge owners, four industry representatives, and one university. A copy of the survey questionnaire and a summary of responses are included in Appendix B. The state bridge engineers who received the sur- vey specifically included the chairs of the AASHTO Technical Committees for joints and bearings, culverts, steel design, concrete design, loads, and foundations. Sixteen responses were received. The survey consisted of two parts: one was superstructure oriented, and the other was substructure and foundation movement oriented. Although there were only 16 responses, some consistency was apparent in the most significant items in structural main- tenance budgets, as seen in Figure 2.6. The most-cited responses confirmed that serviceability issues relating to expansion joints and deck cracking are widespread. Responses highlighted the following: deteriora- tion and section loss of beam ends, painting of steel mem- bers, problems with bearings, corrosion of reinforcement, and deck overlays. Although there were many serviceability issues, many responses indicated that the SLSs are adequate in their current form or would be adequate with some addi- tional limit states, such as • Foundation settlement; • Guidance on stress checks based on corrosion-reduced section properties; • Better crack control reinforcement provisions and stress limits for concrete flexural members; and

45 • Additional limit states for connections, expansion joints, and bearings. Despite suggestions for additional limit states, there was a common theme that additional limit states would not have affected or prevented the observed reduced serviceability. Approximately half the responses indicated that the respon- dents did not use deterioration models other than Pontis, while the other half used engineering judgment, had developed their own models, or were collecting data to develop their own model. In addition, approximately one-half of the responses indicated that no additional assessments were completed beyond those that are a part of Pontis, and one-quarter indi- cated that they complete additional qualitative assessments but no additional quantitative assessments. The other one-quarter of the responses indicated that they complete additional quali- tative and quantitative assessments, including condition sur- veys, chloride penetration depth measurements, ultrasonic testing, and condition scales for each component combined with figures and notes that show the overall condition and defi- ciencies. The qualitative assessments have indicated a correla- tion between deterioration and reduced serviceability, but the reduction in serviceability was not quantified. There were few responses to the second questionnaire about bridge movement and observed distress. The responses that were received focused on structures typically built within the last two decades. All the structures mentioned in the responses were continuous spans with integral or stub abut- ments. In addition, the approach fill was either a mechani- cally stabilized earth wall or fill with side slope. The responses regarding tolerable movements were split almost evenly between acceptable and not acceptable. The responses appeared to be specific to the structures described in the section about bridge movement and observed distress rather than a general- ized response indicative of a population of bridges. The final questions dealt with the allowable movement of new struc- tures, with a majority of agencies noting that they are not following the guidance on tolerable movements found in AASHTO LRFD Article C10.5.5.2. Agencies differed in what their criteria for allowable movements were, with some deter- mining criteria on a case-by-case basis, and others using general-purpose quantitative requirements. 2.4.2 Summary of NCHRP Project 12-83 Survey Related to Concrete Design A survey of current practices related to the SLSs of concrete structures was developed in NCHRP Project 12-83. The sur- vey was sent to major bridge owners across North America, including all 50 state DOTs, the Ministry of Transport in all 0 2 4 6 8 10 12 14 Ex pa n si o n Jo in ts St ee l P ai nt s Co n cr et e D ec ks D ec k O v er la ys B ea rin gs Co n cr et e St ee l R ep ai r/R ep la ce m en t R ep ai r/R ep la ce m en t A bu tm en ts Ti m be r Co m po ne n ts M o v ab le B rid ge s A pp ro ac h Sl ab s R ai lin gs an d Cu rb s R ei nf o rc em en t Fa tig ue B u ilt - u p St ee l C o rr o si on Sc o u r W el d Cr ac ki n g Sl o pe M ai nt en an ce A n ch or Ca bl es D ec k D ra in s Co n cr et e Co at in g D u ra bi lit y H ea de r Jo in t # o f R es po ns es Responses to SHRP 2 R19B Survey Question 1 Figure 2.6. Survey responses indicating the most significant structural maintenance budget items.

46 Canadian provinces, the District of Columbia, and many turnpike authorities, bridge authorities, and commissions. The survey included 20 questions covering the following topics: • Modifications to the specification loading (HL-93 loading) for SLSs; • Checking SLSs under the effects of legal loads as part of the normal design procedure; • Revisions to the SLS stress limits for prestressed concrete components; • Revisions to existing SLSs for concrete structures; • Method used for designing for control of cracking by dis- tribution of reinforcement; • Checking concrete superstructure and substructures for any additional service-load combinations beyond those in AASHTO LRFD; • Checking concrete structures for SLSs under overloads; • Cracking of pretensioned concrete beams immediately after prestressing force release; • Observations of cracking of prestressed concrete beams in service; • Damage to ends of prestressed beams under expansion joints; • Use of the deck empirical design method and the perfor- mance of these decks in service; • Observations of deck cracking; • Type of reinforcement bars used in newer decks (e.g., black bars, epoxy-coated, galvanized, stainless steel); • Average life span of concrete decks and the main reasons decks are replaced; • Types of concrete superstructures in use; • Problems with bearings in concrete structures; • Cracking of abutments and piers; • Average service life span of the concrete substructures; • Fatigue problems in concrete superstructures; and • Use of coatings in concrete substructures. Responses from 27 state DOTs and the Ontario Ministry of Transportation were received. The responses to the ques- tionnaire indicated that most bridge owners apply the SLSs included in AASHTO LRFD with few or no revisions. The additional limit states used by bridge owners appear to be related either to owner-specified vehicles or to address a spe- cific issue that does not seem to be shared by other bridge owners, 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 did not respond 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 ser- vice conditions and the desire expressed by some bridge designers to have guidance on applying permit vehicles to service conditions suggest a need exists for a service-load combination akin to the Strength II limit state that applies to permit (overload) vehicles. The load factors for live load for such a load combination can be determined using the same principles used for calibrating other SLSs. However, the sta- tistical parameters to be used for permit vehicles differ from those for random traffic. One important modification to the existing limit state is the load factor for live load in the Service III limit state in AASHTO LRFD. One state, Louisiana, uses a load factor of 1.0 for live load to check tension in prestressed concrete under the Service III limit state instead of the 0.8 specified in AASHTO LRFD. The higher load factor addresses an issue that has gained importance with AASHTO’s adoption of newer prestress loss equations in 2005. Some engineers are of the opinion that the lower load factor compensated for the conservatism in the older prestressing loss equations and, thus, guarded against excessive conservatism in the design. The use of the new equations, which are believed to provide a more accurate estimate of the prestressing losses, may have eliminated the need for the 0.8 load factor. 2.4.3 Summary of the R19As Survey as it Relates to R19B One of the main objectives in Phase 1 of Project R19A was the identification and ranking of the problematic areas preventing bridges from providing long service life. The research team considered two alternatives for ranking of the performance: • Ranking based on quantitative performance data that are obtained from experimental investigations or field obser- vations of bridges that are currently in service; and • Ranking based on qualitative opinion data (an expert elici- tation or Delphi process). The R19A research team concluded that despite the avail- ability of some experimental data, it is very difficult to quan- tify the performance of actual in-service components. The majority of the reported tests were performed using acceler- ated testing methods, which are not easily correlated with field conditions. They often focused only on the effect of one degradation process, while experience shows that reality is more complex, and often several degradation processes inter- act with the environmental loads. The combined effects and complexity of deterioration processes and the uncertain nature of environmental loads complicate the prediction of the ser- vice life for both new and existing structures. The other source of quantitative data is from long-term monitoring of bridges in service, but such data are not avail- able at this time. In summary, the research team concluded that there are no available data for quantitative evaluation

47 and ranking of existing or promising strategies to quantify the reduction in service life due to deterioration. As there are no quantitative data for ranking and selection of the problematic areas, the R19A research team prioritized the research topics based on the qualitative opinion of experts. Obtained information was organized and presented in tech- nology, strategy, and research tables that provide the informa- tion on the potential service life issues and available solutions. The tables also provide information on the advantages and disadvantages of different design concepts, along with other relevant data necessary to evaluate different strategies address- ing durability. Four major problem research areas were identi- fied: decks, joints, bearings, and durability. The major product from the R19A research effort is Design Guide for Bridges for Service Life (Azizinamini et al. 2013), which is intended to complement AASHTO LRFD specifica- tions and incorporate the design for durability and enhanced service life. The document provides a basis for the selection, design, fabrication, construction, inspection, management, and maintenance of bridge systems. Table 2.21. SLSs Identified for Development LRFD Article Reversible No. of Lanes MPF 2.5.2.6.2 Criteria for Deflection Yes Single — 3.4.1 Load Factors and Load Combinations for Fatigue No Single — 5.5.3.1 General—Compressive Stress Limit for Concrete— A Fatigue Criterion No Single No 5.5.3.2 Fatigue of Reinforcing Bars No Single — 5.5.3.4 Fatigue of Welded or Mechanical Splices of Reinforcement No Single — 5.6.3.6 Crack Control Reinforcement—To be revised but not calibrated—Deemed to satisfy No — — 5.7.3.4 Control of Cracking by Distribution of Reinforcement— Not calibratable—Deemed to satisfy No na — 5.9.3 Stress Limitations for Prestressing Tendons No Multiple Yes 5.9.4.2.2 Tension Stresses Yes Single No 6.10.4.2 Permanent Deformations of Steel Structures No Single No 6.13.2.8 Slip Resistance of Bolts No Single No 10.6.2.4 Settlement Analysis of Shallow Foundations No for footing, possible for superstructure Multiple for sands, none for clays — 10.8.2.2 Settlement (related to drilled shaft groups) No Multiple Yes 10.8.2.4 Horizontal Movement of Shaft and Shaft Groups No — — Note: MPF = multiple presence factor; — = current criteria do not specify whether or not the MPF is applicable; na = not applicable. In summary, the R19A research team stated that due to the lack of quantitative data with respect to almost all bridge ele- ments, it was difficult to propose or develop new design methodologies that are based on deterioration models. 2.5 SLSs to Be Considered in this report Potential limit states and possible calibration approaches for general requirements, concrete structures, steel structures, geo- technical issues, joints, and bearings have been reviewed. Some of the potential limit states have since been determined to be uncalibratable. For example, some are deterministic or are based on judgment and experience. The SLSs believed to be calibrat- able are listed in Table 2.21 along with whether the phenomena being addressed are reversible or irreversible and whether the live load involves single-lane or multiple-lane loading. Note that SLS references to partial prestressing have been removed. AASHTO no longer accepts partial prestressing as a design strategy.