Recommended Guide Specification for the Design of Externally Bonded FRP Systems for Repair and Strengthening of Concrete Bridge Elements (2010)

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4The major research product of this project is a set of rec- ommended guide specifications. The technical basis for these recommendations is described in this chapter. 2.1 Review of Current Practice This task consisted of a review of relevant available FRP en- gineering practice, specifications, design guides, data, and re- search findings from both national and international sources. A brief review concerning the development of externally bonded plates for strengthening reinforced concrete bridge structures is provided below. FRP composite materials provide effective and potentially economical solutions for rehabilitating and upgrading existing reinforced and prestressed concrete bridge structures that have suffered deterioration. Whether a bridge has been damaged due to overload or material deterioration or requires strength- ening to resist increased future live loads due to traffic, wind or seismic forces, FRPs provide an efficient, cost-effective, and easy-to-construct means to reinforce concrete members. FRP composites may be designed to act as flexural, shear or con- finement reinforcement. They may be placed in situ with less disruption of bridge utilization and other functions than is usual when rehabilitation involves the addition of steel rein- forcement. (Meir and Betti 1997; Seible et al. 1997; Deaver et al. 2003; Hamelin et al. 2005; Triantafillou 2007) The concept of using externally bonded FRP reinforce- ment to strengthen concrete structures was developed as an improvement to the use of externally bonded steel plates. Strengthening with externally bonded steel plates commenced in 1964 in Durban, South Africa, to address the problem of the accidental omission of steel reinforcing bars of a base- ment beam in an apartment complex (Dussek 1980). This in- novative idea was developed further on a variety of construc- tion projects involving bridges, parking garage decks, and office buildings in South Africa and Europe (Fleming and King 1967; Parkinson 1978). A review of research and devel- opment related to strengthening with externally bonded steel plate can be found in Eberline et al. (1988). Realizing some difficulties associated with the handling and construction of the relatively heavy weight steel plates used for strengthening purposes, the Swiss Federal Laboratories for Materials Testing and Research Institute (EMPA) initi- ated an extensive research investigation in the early 1970s, the result of which suggested that lightweight carbon fiber rein- forced composite plates could be used in lieu of heavy steel plates for externally strengthening reinforced concrete struc- tures (Meier 1987; Kaiser 1989; Meier 1992; Meier et al.1993). The EMPA efforts led to the first field implementation of FRP rehabilitation for both bridge and building applications. The Ibach Bridge near Lucerne, Switzerland, and the City Hall of Gossau St. Gall in northeastern Switzerland both were strengthened in 1991 by bonding pultruded carbon fiber poly- mer plates to the exterior surfaces of the concrete structures. Details on some of these and other early applications are de- scribed by Meier et al. (1993). The EMPA success in using carbon-fiber reinforced poly- mer composites for externally bonded repair and strengthen- ing of reinforced concrete structures motivated researchers in North America, Europe, Asia, and Australia to further inves- tigate the use of externally bonded FRP materials in structural rehabilitation. The results from these investigations led to a number of recommended design guides and specifications, including the following: • ACI 440.2R-02 “Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures” (ACI 2002). • ISIS Canada Design Manuals, 2001, “Strengthening Rein- forced Concrete Structures with Externally-Bonded Fiber- Reinforced Polymers,” Winnipeg, Manitoba (ISIS 2001). • fib technical report bulletin 14, “Externally bonded FRP re- inforcement for RC structures,” published in Europe (fib 2001). C H A P T E R 2 Findings

5• CNR-DT 200, “Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Exist- ing Structures,” Italian Advisory Committee on Technical Recommendations for Construction, Rome, Italy (CNR- DT 200 2006). • Japan Society of Civil Engineers (JSCE), “Recommenda- tions for Upgrading of Concrete Structures with Use of Continuous Fiber Sheets,” (JSCE 2001). • The French Association of Civil Engineers, Title : Répara- tion et renforcement des structures en béton au moyen des matériaux composites (AFGC 2003). • Avis Technique 3/01-345, “Élement de structure renforcés par un procédé collage de fibres de carbone,” Entriprise FREYSSINET, France (Freyssinet 2001). • German Provisional Regulations, Allgemeine Bauauf- sichtliche Zulassung, Nr. Z-36.12-65 vom 29, Deutsches In- stitut Für Bautechnik, Berlin (German Provisional 2003). • Polish Standardization Proposal for Design Procedures of FR Strengthening (Gorski and Krzywon 2007) • Caltrans Bridge Memo to Designers-MTD 20-4 (Caltrans 2007) • GDOT Specification: Proposed Specifications-Polymeric Composite Materials for Rehabilitating Concrete Structures (Zureick 2002). • NCHRP Report 514: Bonded Repair and Retrofit of Concrete Structures Using FRP Composites—Recommended Construc- tion Specifications and Process Control Manual (Mirmiran et al. 2004). • NCHRP Report 609: Recommended Construction Specifica- tions and Process Control Manual for Repair and Retrofit of Concrete Structures Using Bonded FRP Composites (Mirmiran et al., 2008). 2.2 Development of Proposed Guide Specifications The information gathered from national and interna- tional design guides as well as published and unpublished research reports and archival journal papers germane to the repair and strengthening of concrete structures was assem- bled. The essential elements of all available design guides were identified, selected, and categorized in a manner con- sistent with the AASHTO LRFD Bridge Design Specification, 4th Edition (AASHTO 2007), yielding the following five sections: • Section 1: General Provisions, • Section 2: Material Requirements, • Section 3: Members under Flexure, • Section 4: Members under Shear, and • Section 5: Members under Combined Axial Force and Flexure. Each section is further divided into subsections. The Guide Specification (Attachment A) was also organized into these five sections to facilitate its use by the professional bridge en- gineering community. The recommendations contained in the Guide Specifica- tions utilize the load combination requirements found in the AASHTO LRFD Bridge Design Specifications. The resistance criteria were developed using the same principles of struc- tural reliability analysis on which the AASHTO LRFD Bridge Design Specification are based. Structural reliability analysis takes the uncertainties in concrete, steel, and FRP material strengths and stiffnesses into account using rational statisti- cal models of these key engineering parameters. The criteria for checking safety and serviceability of structural members and components that have been strengthened with externally bonded FRP reinforcement are based on a target reliability index, β, of 3.5 (the target value assumed in the development of the AASHTO LRFD Bridge Design Specification). The fac- tored resistance and factored loads used in these checks are consistent with those found in customary engineering prac- tice to facilitate their use and to minimize the likelihood of misinterpretation. 2.3 Development of Reliability- Based Guide Specifications 2.3.1 Probability-Based Load and Resistance Factor Design Design criteria for safety-related limit states in modern probability-based codes based on the notions of load and re- sistance factor design (LRFD) are represented by the follow- ing relationship: in which the required strength is determined from struc- tural analysis using factored loads, and the design strength (or factored resistance) is determined using nominal material strengths and dimensions and partial resistance factors. The load and resistance factors account for uncertainties associ- ated with the inherent randomness of the load and resistance variables, uncertainties arising from the use of approximate models to represent the mechanics of structural behavior, and consequences of failure, i.e., local vs. general or ductile vs. brittle. In the AASHTO LRFD Bridge Design Specification, these load and resistance factors are set in such a way that structural members, components, and systems are designed to achieve a target performance goal, which is expressed in terms of a reliability index, β = 3.5 (at the inventory load level). The design equation has the following form: η γ φi i i n rQ R R≤ =∑ ( . )2 2 Required Strength Q Design Strength Rd d( ) ≤ ( ) ( . )2 1

6where ηi = load modifier, a factor relating to ductility, redun- dancy, and operational importance; γi = load factor; Qi = force effects; Rn = nominal resistance; Rr = factored resistance; and φ = Resistance factor defined in the AASHTO LRFD Bridge Design Specifications. 2.3.2 Statistical Models for Structural Loads Structural loads acting on bridges may be classified as perma- nent and transient in nature. Permanent loads remain on the bridge for an extended period of time and consist of the weight of the structure and permanently attached non-structural components. Transient loads include vehicular traffic, pedes- trian loads, and environmental loads such as those caused by wind, ice floes, earthquakes, etc. The relative importance of the different loads in bridge performance depend on nu- merous factors, including type of construction, length of span, and the nature of the environmental exposure at the bridge site. For short- and medium-span girder bridges, the most important load combination is live load and dead load. Environmental effects are significant for long-span bridges. This project is focused on short- and medium-span bridges with spans ranging from 30 ft to 200 ft. Only dead load, live load (LL), and dynamic load (IL) were considered in the reliability analysis on which the recommendations are based. Dead Load. Dead load is the weight of structural compo- nents and nonstructural attachments permanently connected to the bridge. The following are four components of dead load: • DL1 — weight of factory made elements, • DL2 — weight of cast in place concrete, • DL3 — weight of traffic wearing surface, and • DL4 — weight of miscellaneous nonstructural components. Statistical parameters for each component of dead load have been developed in previous research (Nowak 1999) and are summarized in Table 2.1 The bias factors, λ, define the ratio of the mean to nominal dead load, enabling the statis- tics of dead load in situ to be determined for a variety of sit- uations once the nominal value is identified from the design documentation. The coefficient of variation (COV), V, is de- fined as the ratio of standard deviation to mean value and is the fundamental measure of uncertainty in structural relia- bility analysis. Live Load. The live load is represented by the forces pro- duced by vehicles moving on the bridge. The statistical mod- els and parameters of live load effects (maximum moments or shears) have been developed previously (Nowak 1999; Eom and Nowak 2001). In these models, the static (truck weight) and dynamic (impact) components of the live load, LL and IL, are considered separately. The statistical parameters of the load effect were estimated based on data obtained from a truck survey (Agarwal and Wolkowicz 1976). The ratio of the mean maximum 75-year shear to AASHTO LRFD HL-93 design shear, λLL, varies from 1.28 to 1.22 depending on the span length, while coefficient of variation, V, is 0.12 for all spans. In the case of two-lane bridges, it was found that the maximum 75-year live load effect was caused by two trucks side by side (Nowak 1999). Based on numerous field tests (Kim and Nowak 1997; Eom and Nowak 2001), the mean dynamic load factor has been assumed to equal 0.1 with a coefficient of variation of 0.8. Combination of Dead and Live Loads. This load combi- nation consists of the three components of dead load, static live load, and dynamic load: The mean, μQ, and variance, σ 2Q, of Q are: where μDL1 and σDL1 = mean and standard deviation of the dead load due to factory made (precast) elements, μDL2 and σDL2 = mean and standard deviation of the dead load due to cast in place concrete, μDL3 and σDL3 = mean and standard deviation of the dead load due to miscellaneous nonstructural components, and μLL+IL and σLL+IL = mean and standard deviation of the live load with impact. σ σ σ σ σQ DL DL DL LL IL 2 1 2 2 2 3 2 2 2 5= + + + + ( . ) μ μ μ μ μQ DL DL DL LL IL= + + + +1 2 3 2 4( . ) Q DL DL DL LL IL= + + + +1 2 3 2 3( . ) *A 35-in. thick wearing surface is assumed. Dead Load Component Bias Factor Coefficient of Variation, V DL 1 1.03 0.08 DL 2 1.05 0.1 DL 3 1.00* 0.25 DL 4 1.05 0.10 Table 2.1. Statistical parameters of dead load components.

7The mean value, μLL_ P+IL, of the combination of live load, LL, and dynamic load, IL, per girder is calculated as: where LL = the nominal HL-93 live load, 1.1 = the mean dynamic impact, λGDF = the bias factor for the girder distribution factor, and λLL_P = the live load analysis factor, which is assumed to equal 1. The coefficient of variation, VLL_ P , and standard deviation, σLL_ P, of the static part of the live load are: where VLL is the coefficient of variation of the live load, and VP is the coefficient of variation of the live load analysis fac- tor equal to 0.12, and μLL_P is the mean value of the static part of the live load. The standard deviation, σLL_P+IL, and the coefficient of vari- ation, VLL_P+IL, for the mean maximum load combination of live load and dynamic load are: 2.3.3 Resistance Model The resistance, R, is modeled as the product of four components: where M = the variation of the material parameters, F = variable reflecting the uncertainties in fabrication, R R MFPn= ( . )2 11 VLL P IL LL P IL LL P L _ _ _ ( . )+ + + = σ μ 1 2 10 σ σ σLL P IL LL P IL_ _ ( . )+ = + 2 2 2 9 σ μLL P LL P LL PV_ _ _ ( . )= i 2 8 V V VLL P LL P_ ( . )= + 2 2 2 7 μ λ λ λLL P IL LL GDF LL PLL_ _. ( . )+ = 1 1 2 6i i i i P = the analysis factor (theoretical model error), and Rn = nominal resistance. The mean value of resistance, μR, is: where μM, μF, and μP are the mean values for M, F, and P, respectively. As with the load models, it is convenient to express the re- sistance, R, in terms of the nominal resistance, Rn, and a bias factor, λR. The bias factor, λR, and the coefficient of variation, VR, of the resistance, R, are: Where λM, λF, and λP are the bias factors, and VM, VF, and VP are the coefficients of variation of M, F, and P, respectively. 2.3.3.1 Material Strengths Statistical parameters reflecting the variability due to ma- terial and fabrication uncertainties are those of concrete, re- inforcing steel rebars, and FRP reinforcement. These statis- tical data should be representative of values that would be expected in a structure, and should reflect uncertainties due to inherent variability, modeling and prediction, and meas- urement. There are extensive databases that describe the prob- abilistic models obtained from previous probability-based code studies (e.g., Galambos, et al. 1982; MacGregor, et al. 1983; Bartlett and MacGregor 1996). These data are summa- rized in Table 2.2 for concrete and grade 60 reinforcement. The mean compressive strength of concrete reflects the dif- ference between standard-cured and in situ conditions, and includes an allowance for aging. For FRP reinforcement, the strength depends on the engi- neering characteristics of the fibers, matrix and adhesive sys- tems and on the workmanship in fabrication and installation. In general, FRP composites used for strengthening reinforced concrete structures are made of aramid, carbon or glass fibers V V V VR m F P= ( ) + ( ) + ( )2 2 2 2 14( . ) λ λ λ λR M F P= ( . )2 13 μ μ μ μR n M F PR= ( . )2 12 Material Property Mean/Nominal COV CDF Rebar yield strength tension 1.12 0.10 Lognormal Concrete compressive strength fc = 4000 psi 1.00 0.18 Normal fc = 6000 psi 1.20 0.15 Normal Table 2.2. Statistical parameters of concrete and reinforcing steel properties.

8with a thermoset resin matrix to bind them together. Zureick and Kahn (2001) classified these systems in two groups: • Shop-manufactured composites. Pre-manufactured com- posites in the form of plates, shells, or other shapes that are bonded in the field to the surface of the concrete member using structural adhesives. These composites are manufac- tured by a variety of techniques such as the pultrusion, filament winding, and resin transfer molding. • Field-manufactured composites. Fibers in the form of tows or fabrics are impregnated in the field and placed on the surface of the structure requiring strengthening. Methods of impregnation have been done manually (hand lay-up), by a portable impregnator machine, or infusion under vac- uum. The composite is bonded to the concrete and then left to cure under ambient or elevated temperature. An advantage of the shop-manufactured composites over the field-manufactured composites is the ability to control the quality and uniformity in the composite reinforcing systems. Conversely, field-manufactured composites are better able to conform to non-uniform concrete surfaces. Figures 2.1 and 2.2 illustrate the scatter in material data for field-manufactured and shop-manufactured composites, respectively. In this project, four single-layered and multilayered uni- directional carbon fiber-reinforcement systems evaluated for the strengthening of bridge pier caps in Georgia (Deaver et al. 2003) were examined. Figure 2.1. Load-strain relation for shop-manufactured composite system. Figure 2.2. Load-strain relation for a field-manufactured composite system (not to failure).

9The strength of FRP in tension is described by a two- parameter Weibull distribution, defined by: where u and α are parameters of the distribution that can be related to the sample mean and sample coefficient of varia- tion, as described subsequently. The parameters u and α can be estimated from the sample mean, x–, and sample coefficient of variation, V (Zureick, Bennett, and Ellingwood 2006). As an approximation: Statistical data for four systems of FRP reinforcement are summarized in Table 2.3. 2.3.3.2 Modeling (or Analysis) Error In addition to the uncertainties in resistance that arise from the uncertainties in material strength and fabrication, the sta- tistics of resistance must include the effect of modeling un- certainties. The equations defining the limit states of interest invariably are based on idealizations of structural behavior. For example, in the Bernoulli-Navier hypothesis regarding beam behavior, strain hardening is neglected in steel rein- forcement, structural materials are assumed to be homoge- neous, etc. These factors are reflected in the mean and coeffi- cient of variation in the parameter, P, in Equation 2.11. These statistical parameters describe the bias and variability that are not explained by the analytical model used to predict resist- ance. The mean and COV of P are determined by calculating the mean and coefficient of variation in the ratio of test-to- calculated strengths where the calculated strengths are deter- mined from material strengths determined from companion specimen tests and known specimen geometry. When the structural mechanics of a limit state is well-understood and the design equation captures this understanding (beams in flexure usually fall into this category), μP normally is close to 1.0 and VP is approximately 0.05. Conversely, when the me- α = 1 2 2 17 . ( . ) V u V x= + ( )[ ]1 3 8 2 16( . ) F x e x x u( ) = − ≥−⎛⎝⎜ ⎞⎠⎟1 0 2 15 α , ( . ) chanics is not well understood and the design equation is based on approximations of behavior (as with reinforced con- crete beams in shear), μP typically is greater than 1.0 (because the approximate equations normally are selected to be con- servative for design purposes) and VP may range from 0.15 to 0.20 or more, representing a substantial contribution to VR in Equation 2.14. 2.3.3.3 Resistance A summary of the resistance statistics for typical reinforced concrete bridge girders without externally bonded FRP rein- forcement is presented in Table 2.4, where the components of the statistics of the parameters in Equation 2.11 are also pre- sented. These statistics were determined from previously pub- lished assessments of statistics in resistance of reinforced con- crete structures (MacGregor et al. 1983; Bartlett and MacGregor 1996; Nowak 1999). 2.4 Reliability Basis for Proposed Resistance Criteria 2.4.1 Selection of Representative Structural Members Representative bridge members were analyzed for purposes of developing reliability-based resistance factors. These are 1. Members under flexure: • Non-prestressed rectangular sections having overall di- mensions of 12 in. × 24 in. with a wide range of rein- forcement ratios. • AASHTO Type III prestressed girder. Shop- Manufactured Field-Manufactured System 1 System 2 System 3 System 4 Sample Size 30 16 25 15 COV 4.3% 24.2 18.2 12.2 Bias 1.06 1.48 1.32 1.19 Table 2.3. Statistical data for various FRP reinforcing systems in tension. Type of Structure FM P R FM VFM P VP R VR Reinforced Concrete Moment 1.12 0.12 1.02 0.06 1.14 0.13 Shear with steel 1.13 0.12 1.08 0.10 1.20 0.16 Shear without steel 1.17 0.14 1.20 0.10 1.40 0.17 Prestressed Concrete Moment 1.04 0.05 1.01 0.06 1.05 0.08 Shear with steel 1.07 0.10 1.08 0.10 1.15 0.14 Table 2.4. Statistical parameters of resistance.

10 2. Members under shear: • Reinforced concrete rectangular sections, having the dimensions of 12 in. × 24 in. and 14 in. × 36 in. that are representative of a wide range of bridge girders. 3. Members under axial and under combined bending and axial loading: • A reinforced concrete circular section having a diameter of 36 in. • A reinforced concrete square section having the dimen- sions of 24 in. × 24 in. 2.4.2 Reliability Analysis Procedure The starting point for developing probability-based design criteria is a description of the limit states of concern by a math- ematical model, based on principles of structural mechanics and supported by experimental data. This model, denoted the limit state function, is given by: where X = (X1, X2, . . . Xm) = vector of resistance and load vari- ables that, in general, are random. The “failure” event is de- fined, by convention, such that the limit state is reached when G(X)<0. Thus, the limit state probability becomes: where fX(x) = joint probability density function of X, and the domain of integration, Ω, is that region of x where G(X)< 0. An alternative measure of safety is the reliability index, β, de- fined by the relationship Pf = Φ(−β), in which Φ(−β) = stan- dard normal probability distribution evaluated at −β (Elling- wood 1994; Melchers 1999). The AASHTO LRFD Bridge Design Specifications (2007) were developed using a target re- liability index equal to 3.5. Recent advances in computational reliability analysis have made it possible to determine Pf (or β) by Monte Carlo simulation, which facilitates analysis in situations in which the limit state function g(X) = 0 cannot be expressed conveniently in closed form. The reliability assess- ments in subsequent sections of this paper are performed by simulation. 2.4.3 Selection of the Target Reliability Indices The target reliability benchmarks for bridge structural mem- bers and components strengthened with externally bonded FRP reinforcement were selected through a comprehensive evaluation of selected representative bridge elements that were judged to be candidates for repair and/or strengthening. The starting point for this evaluation was the target reliability in- dices and LRFD criteria in the AASHTO LRFD Bridge Design P f x x x dx dx dxf X m m= ( )∫ 1 2 1 2 2 19, , . . . . . . ( . ) Ω G G X X XmX( ) = ( ) =1 2 0 2 18, , . . . ( . ) Specifications (2007), as documented in NCHRP Report 368 (Nowak 1999). For the design of new reinforced concrete or prestressed concrete girder bridges, the target reliability index is 3.5. For load rating existing reinforced concrete and pre- stressed concrete bridge girders using the LRFD method, the target reliability index, as specified in the AASHTO Manual for Bridge Evaluation, 1st Edition (2008), is 2.5. From this starting point, the special characteristics of FRP materials as strengthening agents required careful consideration. The fail- ure modes in FRP composite materials are brittle in nature; furthermore, as a relatively new rehabilitation technology, there is uncertainty in their performance in aggressive environ- ments over an extended period of time. Thus the overriding considerations for the determination of the target reliability indices were the consequences of failure of a strengthened member and the cost of strengthening (specifically, how much does it cost to increase the reliability index?). This comprehensive evaluation led to the conclusion that β should be 3.5 (or greater) for inventory loading and 2.5 (or greater) for operating/legal loads. The resistance criteria for strengthening concrete members with FRP reinforcement were developed for those reliability targets. 2.4.4 Development of Resistance Factors Resistance criteria for structural members that have been strengthened with FRP reinforcement were developed in a form that is consistent with the load factors and bridge per- formance objectives found in the LRFD Bridge Design Speci- fications, 4th Edition (2007). These requirements have a reli- ability basis. The similarities of the criteria in the Guide Specifications for FRP composite systems with criteria cur- rently used in steel or reinforced concrete bridge design and construction will facilitate use and minimize the likelihood of misinterpretation. Equations defining the key limit states of flexure, shear, and combined axial force and bending and suitable resistance factors to provide the target reliabilities identified in 2.4.3 were developed. The equations for factored resistance for flexure, shear, and axial compression are: For flexure: where As = area of nonprestressed tension reinforcement, As′ = area of compression reinforcement (in.2), fs = stress in the steel tension reinforcement at develop- ment of nominal flexural resistance (ksi), M A f d k c A f k c dr s s s s s s frp = −( ) + ′ ′ − ′( )⎢⎣ ⎥⎦ + 0 9 2 2. φ T h k cfrp −( )2 2 20( . )

11 fs′ = stress in the steel compression reinforcement at de- velopment of nominal flexural resistance (ksi), c = depth of the concrete compression zone (in.), ds = distance from extreme compression surface to the centroid of nonprestressed tension reinforcement (in.), ds′ = distance from extreme compression fiber to the centroid of compression reinforcement. h = depth of section (in.), Tfrp = tension force in the FRP reinforcement (kips), φfrp = resistance factor determined from reliability analysis, and k2 = multiplier for locating resultant of the compression force in the concrete. For shear: Where Vc = the nominal shear strength provided by the concrete in accordance with Article 5.8.3.3 of the AASHTO LRFD Bridge Design Specifications, Vs = the nominal shear strength provided by the transverse steel reinforcement in accordance with Article 5.8.3.3 of the AASHTO LRFD Bridge Design Specifications, Vp = component of the effective prestressing force in the direction of applied shear as specified in Article 5.8.3.3 of the AASHTO LRFD Bridge Design Specifications, Vfrp = the nominal shear strength provided by the exter- nally bonded FRP reinforcement, φ = 0.9, and φfrp = resistance factor determined from reliability analysis. For axial compression: where α = 0.85 for spiral reinforcement and 0.80 for tie rein- forcement; φ = resistance factor specified in Article 5.5.4.2 of the AASHTO Bridge Design Specifications, 4th Edition; Ag = gross area of section (in.2); Ast = total area of longitudinal reinforcement (in.2); fy = specified yield strength of reinforcement (ksi); and f ′cc = compressive strength of the confined concrete deter- mined according to Article 5.3.2.2. The starting point for the factored resistance (or design strength) in all cases was the equations that are found in Sec- tion 5 of the AASHTO Bridge Design Specifications or ACI Standard 318-05 (ACI 2005). The contribution of the FRP re- inforcement to factored resistance is added to the existing P f A A f Ar cc g st y st= ′ −( ) +[ ]αφ 0 85 2 22. ( . ) V V V V Vr c s p frp frp= + +( ) +φ φ ( . )2 21 term(s) for factored resistance. This format accomplishes two objectives: (1) In situations where only light FRP reinforce- ment is required, the design equation yields a factored resist- ance that is essentially the same as the factored resistance of the original structural member without FRP reinforcement and (2) Assigning a separate partial factor (φfrp) to the FRP contribution facilitates achieving the reliability objectives summarized in Section 2.4.3 throughout a range of material strengths, beam geometries, and spans. The reliability achieved in LRFD depends on both the nominal resistance and the resistance factor. As a manufac- tured product, the variability in strength of FRP reinforce- ment (Equation 2.15 and Table 2.3) must be reflected in the factored resistance. It has been customary in many structural engineering applications to identify the nominal strength with the 0.10-fractile (10 percent exclusion limit) of the strength distribution in the end use condition. Accordingly, the resistance criteria in these Guide Specifications are based on the assumption that the nominal ultimate tensile strength of the FRP is defined by the 10th percentile value of the two- parameter Weibull distribution as follows: in which the parameters are estimated from Equations 2.16 and 2.17. To ensure the level of structural performance envi- sioned in the reliability analysis, the nominal strength stipu- lated in the construction documents should be the 10th per- centile value of strength. The φfrp factors found in Sections 3, 4 and 5 of the Guide Specifications were determined by iteration. A series of typical structural members (as identified in Section 2.4.1 above) were designed using the dead and live load requirements in the AASHTO LRFD Bridge Design Specifications and a range of tentative φfrp factors (rounded to the nearest 0.05), and the reliability indices for these structural members were deter- mined using the procedure in Section 2.4.2. Following the completion of this reliability assessment, the resistance fac- tors proposed for the Guide Specifications were those that pro- vided the closest fit to the target reliability index β = 3.5. This approach was also used in developing the AASHTO LRFD Code (Nowak 1999). The applicability of the proposed Guide Specification is lim- ited to structural members, components, and systems that can be shown to have a minimum strength prior to the appli- cation of externally bonded FRP reinforcement. This limit has been imposed to avoid a situation where the behavior of the strengthened member depends unduly on the perfor- mance of the FRP reinforcement. If the field application of the reinforcement is deficient or if the strengthened bridge is loaded accidentally beyond the level of the enhanced factored resistance, a sudden and potentially catastrophic failure of the strengthened component is likely to occur. x u0 10 1 0 1054 2 23. . ( . )= ( ) α