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

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A T T A C H M E N T A Recommended Guide Specification for the Design of Bonded FRP Systems for Repair and Strengthening of Concrete Bridge Elements This Guide Specification is the recommendation of the research team for NCHRP Project 10-73 that was conducted at Georgia Institute of Technology. The Guide Specification has not been approved by NCHRP or any AASHTO committee; nor has it been formally accepted for the AASHTO specifications.

C O N T E N T S SECTION 1- GENERAL REQUIREMENTS 1.1 SCOPE………………………………………………………………………………………... A- 1 1.2 DEFINITIONS………………………………………………………………………………... A-1 1.3 SYMBOLS AND NOTATION………………………………………………………………. A-2 1.4 DESIGN BASIS………………………………………………………………………………. A-5 1.5 LIMIT STATES……………………………………………………………………………… A-7 1.6 LOADS AND LOAD COMBINATIONS…………………………………………………... A-9 1.7 EVALUATION OF EXISTING BRIDGE ELEMENTS………………………………….. A-10 REFERENCES……………………………………………………………..……………………. A-11 SECTION 2- MATERIALS REQUIREMENTS 2.1 SCOPE………………………………………………………………………………………... A-13 2.2 MATERIAL REQUIREMENTS……………………………………………………………. A-13 REFERENCES…………………………………………………………………………………… A-17 SECTION 3- MEMBERS UNDER FLEXURE 3.1 GENERAL REQUIREMENTS…………………………………………………………….. A-18 3.2 DESIGN ASSUMPTIONS…………………………………………………………………... A-18 3.3 FATIGUE LIMIT STATES………………………………………………………………… A-19 3.4 STRENGTH LIMIT STATES……………………………………………………………… A-20 REFERENCES…………………………………………………………………………………... A-25 SECTION 4- MEMBERS UNDER SHEAR AND TORSION 4.1 GENERAL REQUIREMENTS…………………………………………………………….. A-28 4.2 STRENGTHENING SCHEMES…………………………………………………………… A-28 4.3 STRENGTH IN SHEAR…………………………………………………………………….. A-30 4.4 STRENGTH IN TORSIO N ….. ……………………………………………………………... A-35 4.5 STRENGTH IN INTERFACE SHEAR TRANSFER-SHEAR FRICTION…………….. A-37 REFERENCES…………………………………………………………………………………... A-42 SECTION 5- MEMBERS UNDER COMBINED AXIAL FORCE AND FLEXURE 5.1 GENERAL REQUIREMENTS…………………………………………………………….. A-44 5.2 METHODS FOR STRENGTHENING WITH FRP REINFORCEMENT……………… A-44 5.3 COLUMNS IN AXIAL COMPRESSION………………………………………………….. A-44 5.4 COMBINED AXIAL COMPRESSION AND BENDING………………………………… A-47 5.5 AXIAL TENSION…………………………………………………………………………… A-48 REFERENCES…………………………………………………………………………………… A-49

A-1 SECTION 1: GENERAL REQUIREMENTS 1.1 SCOPE C1.1 This Guide Specification is intended for the repair and strengthening of reinforced and prestressed highway bridge structures using externally-bonded fiber-reinforced polymeric (FRP) systems. This Guide Specification supplements the AASHTO LRFD Bridge Design Specifications, 4th Edition (AASHTO 2007). Except where specifically provided below, all provisions of the LRFD Bridge Design Specifications shall apply. This Guide Specification states only the minimum requirements necessary to provide for public safety and are not intended to supplant proper training or the exercise of judgment by the Engineer of Record. The Owner or the Engineer of Record may require the structural design or the quality of materials and construction to exceed the minimum requirements. This Guide Specification employs the Load and Resistance Factor Design (LRFD) methodology, in which the load and resistance factors have been developed from structural reliability theory based on current probabilistic/statistical models of loads and structural performance. Seismic design shall be in accordance with either the provisions in the appropriate sections of the LRFD Specifications or the provisions in the AASHTO Guide Specifications for LRFD Seismic Bridge Design. Except where specifically provided below, all provisions of the LRFD Bridge Construction Specification shall apply. Article 1.1 discusses the scope of the guide specifications, its applicability and limitations. This article is analogous to the opening articles, Articles X.1, of each of the sections of the AASHTO LRFD Bridge Design Specifications, 4th Edition. The commentary is not intended to provide a complete historical background concerning the development of these or previous Specifications, nor is it intended to provide a detailed summary of the studies and research data reviewed in formulating the provisions of the Specification. However, references to North American and international guidelines (ACI 440.2R-02, 2000; ISIS Canada Design Manuals, 2001; fib technical report bulletin 14 , fib 2001; CNR-DT 200, 2006; JSCE, 2001; AFGC, 2003 ; and Avis Technique 3/01-345, 2001) as well as relevant research data dealing with externally bonded FRP reinforcement for reinforced and prestressed concrete structures are provided for those who wish to study the background material in depth. NCHRP Report 609 presents recommended construction specifications concerning the use of externally bonded FRP reinforcement for strengthening concrete structures. The commentary directs attention to other documents that provide suggestions for carrying out the requirements and intent of these Guide Specifications. However, the commentary and references herein are not part of these Guide Specifications. 1.2 DEFINITIONS Definitions and terms related to the use of fiber- reinforced polymeric (FRP) materials in bridge engineering, rehabilitation and retrofit shall be as stipulated in ASTM D3878. Terms related to adhesives shall be as specified in ASTM D907.

A-2 Definitions and terms related to highway bridge design shall be as stipulated in the AASHTO LRFD Bridge Design Specifications, 4th Edition. 1.3 SYMBOLS AND NOTATION Variables used throughout the guide specifications as well as references to their usage are listed alphabetically below: frpA = effective area of FRP reinforcement for shear-friction (in 2) gA = gross area of column section (in 2) hA = area of one leg of the horizontal reinforcement (in2) sA = area of nonprestressed tension reinforcement (in2) ' sA = area of compression reinforcement (in 2) stA = total area of longitudinal steel reinforcement (in 2) vfA = area of steel reinforcement required to develop strength in shear friction (in 2) b = width of rectangular section (in) frpb = width of the FRP reinforcement (in.) vb = effective shear web width (in) wb = girder width (in) C = clamping force across the crack face (kips) c = depth of the concrete compression zone (in) gD = external diameter of circular column (in) frpd = effective FRP shear reinforcement depth (in) sd = distance from extreme compression surface to the centroid of nonprestressed tension reinforcement (in.) vd = effective shear depth (in)

A-3 aE = modulus of elasticity of adhesive (ksi) cE = modulus of elasticity of the concrete (ksi) frpE = modulus of the FRP reinforcement in the direction of structural action cf = stress in concrete at strain c (ksi) ' cf = 28 - day compression strength of the concrete (ksi) ' ccf = compressive strength of confined concrete (ksi) frpuf = characteristic value of the tensile strength of FRP reinforcement (ksi) lfrpf = ultimate confinement pressure due to FRP strengthening (ksi) peelf = peel stress at the FRP reinforcement concrete interface (ksi) sf = stress in the steel tension reinforcement at development of nominal flexural resistance (ksi) ' sf = stress in the steel compression reinforcement at development of nominal flexural resistance (ksi) yf = specified yield stress of steel reinforcement (ksi) yff = yield strength of steel reinforcement for shear-friction (ksi) aG = characteristic value of the shear modulus of adhesive (ksi) h = depth of section (in); overall thickness or depth of a member (in.) TI = moment of inertia of an equivalent FRP transformed section, neglecting any contribution of concrete in tension (in4) ak = a coefficient that defines the effectiveness of the specific anchorage system ek = strength reduction factor applied for unexpected eccentricities 2k = multiplier for locating resultant of the compression force in the concrete dL = development length (in)

A-4 ul = unsupported length of compression member (in) rM = factored resistance of a steel-reinforced concrete rectangular section strengthened with FRP reinforcement externally bonded to the beam tension surface (kip-in) uM = factored moment at the reinforcement end-termination (kip-in) bN = FRP reinforcement strength per unit width at a tensile strain of 0.005 (kips/in) e frpN = effective strength per unit width of the FRP reinforcement (kips/in) )( , rN wfrp = tensile strength of a closed (wrapped) jacket (kips/in) sN = FRP reinforcement strength per unit width at a tensile strain of 0.004 (kips/in) utN = the characteristic value of the tension strength per unit width of the FRP reinforcement (kips/in) rP = factored axial load resistance (kips) r = girder corner radius (in) vs = spacing of FRP reinforcement (in) frpT = tension force in the FRP reinforcement (kips) rT = the factored torsion strength of a concrete member strengthened with an externally bonded FRP system (kip-in) at thickness of the adhesive layer (in) frpt thickness of the FRP reinforcement (in) cV = the nominal shear strength provided by the concrete (kips) frpV = the nominal shear strength provided by the externally bonded FRP reinforcement (kips) niV = nominal shear-friction strength (kips) pV = component of the effective prestressing force in the direction of applied shear (kips) rV = factored shear strength of a concrete member strengthened with an externally bonded FRP system (kips)

A-5 sV = nominal shear strength provided by the transverse steel reinforcement (kips) uV = factored shear force at the reinforcement end-termination (kips) frpw = total width of FRP reinforcement (in) y = distance from the extreme compression surface to the neutral axis of a transformed section, neglecting any contribution of concrete in tension (in) = angle between FRP reinforcement principal direction and the longitudinal axis of the member; angle between the shear-friction reinforcement and the shear plane (°) 1 = ratio of average stress in rectangular compression block to the specified concrete compressive strength c = strain in concrete frp = strain in FRP reinforcement ut frp = characteristic value of the tensile failure strain of the FRP reinforcement o = the concrete strain corresponding to the maximum stress of the concrete stress-strain curve = coefficient of friction = strain limitation coefficient that is less than unity a = Poisson’s ratio of adhesive a = characteristic value of the limiting shear stress in the adhesive (ksi) int = interface shear transfer strength (ksi) frp = resistance factor for FRP component of resistance 1.4 DESIGN BASIS C1.4 1.4.1 Bridge elements strengthened with externally bonded reinforcement shall be designed to achieve the objectives of constructability, safety, and serviceability, with regard to issues of inspectability, The resistance criteria in this Guide Specification were developed using modern principles of structural reliability analysis, which are consistent with those on which the AASHTO LRFD Bridge

A-6 economy and aesthetics, as stipulated in Article 2.5 of the LRFD Bridge Specifications, 4th Edition. 1.4.2 The provisions of this Guide Specification are limited to concretes with specified compressive strength 'cf not exceeding 8 ksi. 1.4.3 The characteristic value of the strength or failure strain in tension of FRP reinforcement used in bridge strengthening shall not exceed the 10th percentile value of the strength or failure strain, defined by a two-parameter Weibull distribution. The characteristic value shall be determined using a minimum of 10 samples. If the coefficient of variation in determined from this initial sample exceeds 15%, an additional 10 samples shall be tested, and the sample mean and sample coefficient of variation used to determine the parameter of interest shall be based on 20 samples. The test method shall be specified by the Engineer of Record. 1.4.4 The provisions of this Guide Specification shall apply to bridge elements for which the factored resistance satisfies the following requirement: )( IMLLDWDCR ir rR = factored resistance computed in accordance with Section 5 of the LRFD Bridge Specifications, 4th Edition. i = load modifier specified in Article 1.3.2 of the LRFD Bridge Specifications, 4th Edition. DC = force effects due to component and attachments DW = force effects due to wearing surfaces and utilities LL = force effects due to live loads IM = force effects due to dynamic load allowance Design Specifications are based. Structural reliability analysis takes the uncertainties in concrete, steel and FRP material strengths and stiffnesses into account using rational statistical 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, , equal to 3.5 under inventory loading, which was the target value assumed in the development of the AASHTO LRFD Bridge Design Specifications. The factored resistance and factored loads used in these checks are consistent with those found in customary engineering practice to facilitate their use in practice and to minimize the likelihood of misinterpretation. The strength of FRP reinforcement depends on the engineering characteristics of the fibers and matrix and adhesive systems and on the workmanship in fabrication and installation. The resistance criteria in these Guide Specifications are based on the assumption that the nominal ultimate tensile strength of the FRP is the 10th percentile value of the two- parameter Weibull distribution that defines the uncertainty in the strength. Accordingly, to ensure the level of performance envisioned in these Guide Specification, the nominal strength stipulated in the construction documents should be the 10th percentile value of strength. The two-parameter Weibull distribution is defined by u x exF 1)( , 0x in which u and are parameters of the distribution, which can be determined from the sample mean, x , and sample coefficient of variation, COV. As an approximation, xCOVu )8/3(1

A-7 COV 2 . 1 The 10 th percentile of the Weibull distribution then is estim ated by, / 1 10 . 0 1054 . 0 u x This Guide Specification are intended to apply only to bridge structural me mbers and components that have a mi nim um strength prior to strengthening by externally bonded FRP reinforcem ent. If such a minim um cannot be shown by analysis or test to exist, the behavior of the strengthened me mber will depend al mo st entirely on the perform ance of the FRP reinforcement and if the field application of the FRP is deficient or if the bridge is accidentally overloaded, da ma ge or failure ma y occur without warning. The lim itation on strength prior to strengthening is intended to minim ize the likelihood of occurrence of such da ma ge or failure. 1.5 LIMIT STATES Structural me mbers shall satisfy Eq. 1.3.2.1-1 of the LRFD Bridge Specifications, 4 th Edition , for each lim it state, unless otherwise specified The load factors, ’s, in Eq. 1.3.2.1-1 of the LRFD Specifications shall be as defined in LRFD Tables 3.4.1-1, 3.4.1-2 and 3.4.1-3. The resistance factors, ’s, are defined in Chapters 3, 4 and 5 of this Guide Specification. C1.5 This Guide Specification applies to strength limit states I and II, serviceability lim it states I, III and IV, Extrem e Event lim it states I and II, and the Fatigue lim it state, as defined in Article 3.4 of the LRFD Bridge Design Specifications . 1.5.1 Service Limit States C1.5.1 Structural me mbers shall satisfy LRFD Eq. 1.3.2.1-1 for the applicable com binations of factored force effects as specified at each of the following service lim it states: Service I - Load co mb ination relating to the norm al operational use of the bridge with a 55 m ph wind Service lim it states custom arily are defined by restrictions on stress, deformation, and crack width under regular service conditions. Co mp ression in prestressed concrete com ponents and tension in prestressed bent caps are investigated using the Service I load com bination. The Service III lim it- state load combination is used to investigate tensile and all loads taken at their nominal values. stresses in prestressed concrete components.

A-8 Service III - Load combination for longitudinal analysis relating to tension in prestressed concrete superstructures with the objective of crack control and to principal tension in the webs of segmental concrete girders Service IV - Load combination relating only to tension in prestressed concrete columns with the objective of crack control. The LRFD Service II limit state load combination is not applicable to concrete bridge structures reinforced with FRP systems as it is only applied to steel structures. The live load specified in the LRFD Specifications reflects current exclusion weight limits mandated by various jurisdictions. Vehicles permitted under these limits were in service for many years prior to 1993. For longitudinal loading, there is no nationwide evidence that these vehicles have caused cracking in existing prestressed concrete components. The 0.80 factor on live load in the Service III combination reflects the fact that the event is expected to occur about once a year for bridges with two traffic lanes, less often for bridges with more than two traffic lanes, and about once a day for bridges with a single traffic lane. The Service I limit-state load combination should be used for checking tension related to transverse analysis of concrete segmental girders. 1.5.2 Strength Limit States Structural members of a bridge shall satisfy LRFD Eq. 1.3.2.1-1 for the applicable combinations of factored extreme force effects, specified as follows: Strength I - Basic load combination relating to the normal random vehicular use of the bridge without wind. Strength II - Load combination relating to the use of the bridge by Owner-specified special design vehicles, evaluation permit vehicles, or both without wind. Strength III - Load combination relating to the bridge exposed to wind velocity exceeding 55 mph. Strength IV - Load combination relating to very high C1.5.2 Design for strength limit states ensures that local and global strength and stability are provided to resist the specified load combinations that a bridge is expected to experience in its design life. The background for the load combination requirements in the LRFD Specifications is presented in Nowak (1993). dead load to live load force effect ratios. Strength V - Load combination relating to normal random vehicular use of the bridge with wind of 55 mph velocity.

A-9 1.5.3 Extreme-event Limit States Structural me mbers of a bridge shall satisfy LRFD Eq. 1.3.2.1-1 for the applicable com binations of factored extreme force effects as specified at each of the following: Extrem e-event I - Load combination including earthquake. Extrem e-event II - Load combination relating to ice load, collision by vessels and vehicles, and certain hydraulic events with a reduced live load other than that which is part of the vehicular collision load. C.1.5.3 Consideration of extrem e-event lim it states is aim ed at ensuring that the bridge structure survives a ma jor earthquake or flood, collision from a vessel or heavy vehicle, or ice flow, or possible foundation scour. 1.5.4 Fatigue Limit State C1.5.4 Structural me mbers, connections and components of a bridge shall satisfy LRFD Eq. 1.3.2.1-1 for the Fatigue I lim it-state load combination, the load combination related to infinite load-induced fatigue life The fatigue limit states place restrictions on stress range resulting from a single design truck occurring at the num ber of expected stress range cycles. Concrete bridge structures are designed to provide a theoretically infinite fatigue design life. The load factor for the Fatigue I load combination applied to a single design truck having the axle spacing specified in LRFD Article 3.6.1.4.1 reflects load levels found to be representative of the maxim um stress range of the truck population. The Fatigue II li mi t-state load combination is not applicable to concrete bridge structures reinforced with FRP system s as it is not generally applicable to concrete components and connections. 1.6 LOADS AND LOAD COMBINATIONS 1.6.1 Loads C1.6.1 The loads defined in LRFD Article 3.3.2 and characterized in LRFD Article 3.6 through 3.15 shall be applied for designing reinforced concrete and The loads required for the design and evaluation of concrete bridge structures reinforced with FRP syste ms are classified in the LRFD Specifications as prestressed highway bridge me mb ers strengthened with externally bonded FRP reinforcem ent perm anent and transient loads. 1.6.2 Load Combinations The load combination requirem ents shall be determ ined in accordance with Article 3.4 of the AASHTO LRFD Bridge Design Specifications.

A-10 1.7 EVALUATION OF EXISTING BRIDGE ELEMENTS C1.7 Bridge evaluations shall be performed using the evaluation criteria stipulated in the AASHTO Manual for Bridge Evaluation, First Edition (MBE, 2008). Eq. 6A.4.2.1-1 of the MBE shall be used in determining the load rating of each component and connection subjected to a single force effect (i.e., axial force, flexure, or shear). The load rating shall be carried out at each applicable limit state with the lowest value determining the controlling rating factor. Limit states and load factors for load rating shall be selected from MBE Table 6A.4.2.2-1.Interaction of load effects (i.e., axial-bending interaction or shear- bending interaction), shall be considered, as provided in the MBE under the sections on resistance of structures, in developing the rating. . Bridge load ratings are performed for specific purposes, such as: NBI and BMS reporting, local planning and programming, determining load posting or bridge strengthening needs, and overload permit review. Live load models, evaluation criteria, and evaluation procedures are selected based upon the intended use of the load rating results. Live-load models used in evaluation are comprised of the design live load, legal loads, and permit loads. Strength is the primary limit state for load rating; service and fatigue limit states are selectively applied in accordance with the provisions of the MBE. Live-load models for load rating include: Design Load: HL-93 Design Load per LRFD Specifications Legal Loads: AASHTO Legal loads, as specified in MBE Article 6A.4.4.2.1.1, and (2) The Notional Rating Load as specified in MBE Article 6A.4.4.2.1.2 or State legal loads. Permit Load: Actual Permit Truck Bridges that do not satisfy the HL-93 design load check should be evaluated for legal loads in accordance with the provisions of MBE Article 6A.4.4 to determine the need for load posting or strengthening. Legal loads for rating given in MBE Article 6A.4.4.2.1.1 that model routine commercial traffic are the same family of three AASHTO trucks (Type 3, Type 3S2, and Type 3-3) used in current and previous AASHTO evaluation Manuals. The single-unit legal load models given in MBE Article

A-11 6A.4.4.2.1.2 represent the increasing presence of Form ula B mu lti-axle specialized hauling vehicles in the traffic stream in ma ny States. REFERENCES ACI (2005). Building code requirements for structural concrete (ACI Standard 318-05). Am erican Concrete Institute, Farm ington Hills, MI. ACI 440.2-R02 (2002) Guide for the design and construction for externally bonded FRP syste ms for strengthening concrete structures,” Evaluation of Concrete Structures Prior to Rehabilitation," Am erican Concrete Institute, Farm ington Hills, Michigan. AFGC (2003). Réparation et renforcement des structures en béton au mo ye n des ma tériaux com posites, Association Française de Génie Civil, Déce mb re, 92225 Bagneaux Cedex, France. CNR-DT 200 (2006), “Guide for the Design and Construction of Externally Bonded FRP System s for Strengthening Existing Structures,” Italian Advisory Committee on Technical Recommendations for construction. Rom e, Italy. fib (2001) technical report bulletin 14, “Externally bonded FRP reinforcem ent for RC structures”, published in Europe (fib, CEB-FIP, 2001). JSCE (2001). , “Recommendations for Upgrading of Concrete Structures with Use of Continuous Fiber Sheets,” Japan Society of Civil Engineers. ISIS (2001). ISIS Canada Design Manuals, “Strengthening Reinforced Concrete Structures with Externally-Bonded Fiber-Reinforced Polymers,” Winnipeg, Manitoba. MBE (2008). The Manual for Bridge Evaluation, AASHTO, Washington, D.C. NCHRP Report 609 (2008). Recommended

A-12 construction specifications and process control manual for repair and retrofit of concrete structures using bonded FRP composites, Transportation Research Board, Washington, D.C. Nowak, A. S. (1993). “Live load model for highway bridges,” Journal of Structural Safety, Volume 13, No. 1 and 2, December, pp.53-66.

A-13 SECTION 2: MATERIALS REQUIREMENTS 2.1 SCOPE This section defines the requirements for polymeric composite material systems intended for use for repair and strengthening of concrete bridge elements. 2.2 MATERIAL REQUIREMENTS 2.2.1 The contractor shall submit for approval evidence of acceptable quality control procedures followed in the manufacture of the composite reinforcement system. The quality control procedure shall include, but not be limited to, specifications for raw material procurement, the quality standards for the final product, in-process inspection and control procedures, test methods, sampling plans, criteria for acceptance or rejection, and record keeping standards. 2.2.2 The contractor shall furnish information describing the fiber, matrix, and adhesive systems intended for use as reinforcing materials that is sufficient to define their engineering properties. Descriptions of the fiber system shall include the fiber type, percent of fiber orientation in each direction, and fiber surface treatments. Where required by the Engineer of Record, the matrix and the adhesive shall be identified by their commercial names and the commercial names of each of their components, along with their weight fractions with respect to the resin system. 2.2.3 The contractor shall submit for approval test results that demonstrate that constituent materials and the composite system are in conformance with the physical and mechanical property values stipulated by the Engineer of Record. These tests shall be conducted by a testing laboratory approved by the Engineer of Record. For each property value, the batches from which test specimens were drawn shall be identified and the number of tested specimens from each batch, the mean value, the minimum value, the maximum value, and the coefficient of variation shall be reported. The minimum number of tested samples shall be 10. 2.2.4 When cured under conditions identical to those of the intended use, the composite material system as well as the adhesive system, if used, shall conform to the following requirements:

2.2.4.1 The characteristic value of the glass transition temperature of the composite system, determined in accordance with ASTM D4065, shall be at least 40oF higher than the maximum design temperature, MaxDesignT , defined in Section 3.12.2.2 of the AASHTO LRFD Bridge Design Specifications. C 2.2.4.1 The glass transition temperature, Tg, is the approximate temperature value or temperature range at which the matrix changes from a glassy to a rubbery state. Above Tg , the composite softens and loses its mechanical properties, as illustrated in Figure C2.1 . In addition, it is to be noted that Tg decreases as the moisture content in the composite increases. Figure C2.1 Effect of temperature on the properties of polymer composite materials (Zureick and Kahn, 2001) 2.2.4.2 The characteristic value of the tensile failure strain in the direction corresponding to the highest percentage of fibers shall not be less than 1%, when the tension test is conducted according to ASTM 3039. A-14

A-15 2.2.4.3 The average value and coefficient of variation of the moisture equilibrium content determined in accordance with ASTM D 5229/D 5229M shall not be greater than 2% and 10%, respectively. A minimum sample size of 10 shall be used in the calculation of these maximum values. C2.2.4.3 The diffusion of moisture into organic polymers results in pronounced changes in mechanical, chemical, and thermophysical properties of practically all composite reinforcing systems. All organic matrix systems and organic reinforcing fibers absorb moisture to a certain degree. While both glass and carbon fibers are considered to be impervious to moisture absorption, aramid fibers absorb more moisture than many matrix systems. In all cases when moisture migrates through the matrix system and ultimately reaches the fiber-matrix interface, adhesion of the matrix system to the fibers become weak and the structural integrity of the composite system degrades. 2.2.4.4 After conditioning in the following environments, the characteristic value of the glass transition temperature determined in accordance with ASTM D4065 and the characteristic value of the tensile strain, determined in accordance with ASTM D3039, of the composite in the direction of interest shall retain 85% of the values established in Art. 2.2.4.1 and 2.2.4.2, respectively. A. Water: Samples shall be immersed in distilled water having a temperature of 100 ± 3°F (38 ± 2°C) and tested after 1,000, hours of exposure. B. Alternating ultraviolet light and condensation humidity: Samples shall be conditioned in an apparatus under Cycle 1 -UV exposure condition according to ASTM G154 Standard Practice. Samples shall be tested within two hours after removal from the apparatus. C. Alkali: The sample shall be immersed in a saturated solution of calcium hydroxide (pH ~11) at ambient temperature of 73 3oF (23 2oC) for 1000 hours prior to testing. The pH level shall be monitored and the solution shall be maintained as needed. C2.2.4.4. The physical and mechanical properties of FRP materials and of the concrete structure reinforced with an externally bonded reinforced system are sensitive to various environmental conditions that can affect one or more of the followings: Chemical and/or physical changes in the polymeric matrix. Loss of bond at the fiber/matrix interface and at the FRP-concrete interface. Strength and stiffness degradation of the reinforcing fibers. The durability requirements in Article 2.2.4.4 are based on those developed for CALTRANS (Steckel et al., 1999a, 199b;; Hawkins et al., 1999) and for GDOT (Zureick, 2002). Cycle No 1 UV exposure condition uses UVA-340 lamps that simulate direct solar radiation and have negligible UV output below 300nm, considered to be the “cut-on” wavelength for terrestrial sunlight. D. Freeze-thaw: Composite samples shall be exposed to 100 repeated cycles of freezing and thawing in an apparatus meeting the requirements of ASTM C666.

2.2.5 Where impact tolerance is stipulated by the Engineer, the stipulated im pact tolerance shall be determ ined by ASTM D7136. 2.2.6 Adhesive: when adhesive ma terial is used to bond the FRP reinforcem ent to the concrete surface, the following requirem ents shall be me t: 2.2.6.1 After conditioning in the environments stipulated in Article 2.2.4.4 A-D, the characteristic value of the glass transition te mp erature of the adhesive ma terial determ ined in accordance with ASTM D 4065, shall be at least 40 o F higher than the maxim um design tem perature , MaxDesign T , defined in Section 3.12.2.2 of AASHTO LRFD Bridge Design Specifications. 2.2.6.2 After conditioning in the environments stipulated in Article 2.2.4.4 A-D, the bond strength (ksi), determ ined by tests specified by the Engineer of Record, shall be at least ' 064 . 0 c f , where ' c f (ksi) is the specified co mp ression strength of the concrete. C.2.2.6.2 The bond strength lim it of ' 064 . 0 c f is based on tests conducted by Naam an (1999) on reinforced concrete beams strengthened with externally bonded FRP reinforcement A-16

A-17 REFERENCES Naaman, A. E. (1999). “Repair and strengthening of reinforced concrete beams using CFRP laminates, Volumes. 1- 7, Michigan Department of Transportation, Report No. RC-1372. Hawkins, G. F. Johnson, and Nokes, (1999). “Qualifications for Seismic Retrofitting of Bridge Columns Using Composites”, Volume 3: Composite Properties Characterization, Prepared for the California Department of Transportation, Contract No. SA0A011, The Aerospace Corporation, El Segundo California. Steckel, G.L., Bauer, J.L., Hawkins, G.F. and Vanik, (1999). “Qualifications for Seismic Retrofitting of Bridge Columns Using Composites”, Volume 2: Composite Properties Characterization, Prepared for the California Department of Transportation, Contract No. SA0A011, The Aerospace Corporation, El Segundo California Steckel, G. L., Hawkins, G. F. and Bauer, J. L. (1999). “Qualifications for Seismic Retrofitting of Bridge Columns Using Composites”, Volume 1: Composite Properties Characterization, Prepared for the California Department of Transportation, Contract No. SA0A011, The Aerospace Corporation, El Segundo California. Zureick, A. and Kahn, L. (2001). “Rehabilitation of Reinforced Concrete Structures Using Fiber- Reinforced Polymer Composites, ASM Handbook, Volume 21, Composites, pp. 906-913. Zureick, A. (2002). “Proposed Specifications- Polymeric Composite Materials for Rehabilitating Concrete Structures,” Report Prepared for the Georgia Department of Transportation, Atlanta, Georgia.

SECTION 3: MEMBERS UNDER FLEXURE 3.1 GENERAL REQUIREMENTS The factored resistance of structural members subjected to flexure shall equal or exceed the required strength calculated for the factored loads and forces in combinations stipulated by this Guide Specification. Except where specifically provided below, all provisions of the AASHTO LRFD Bridge Design Specification (2007 edition), Article 5.7.3, shall apply. 3.2 DESIGN ASSUMPTIONS C3.2 The calculation of the strength of reinforced concrete members externally reinforced with FRP materials shall be based on the following assumptions: The distribution of strains over the depth of the member is linear and conditions of force equilibrium and strain compatibility are satisfied. Perfect bond exists between the reinforcing steel, FRP reinforcement and the concrete. The contribution of tension stresses in the concrete to flexural strength is neglected. The stress-strain behavior for FRP reinforcement is linear-elastic to the point of failure. The stress-strain behavior of steel reinforcement is bilinear, with elastic behavior up to yielding and perfectly plastic behavior thereafter. The maximum usable compression strain in the concrete is equal to 0.003. The maximum usable strain at the FRP/concrete interface is 0.005. The strength in flexure of a reinforced concrete member that has been additionally reinforced by an externally bonded FRP plate is derived from the classic Bernoulli-Navier hypothesis that plane sections remain plane and perpendicular to the neutral axis during flexure. The stresses on the section can be determined from the constitutive relations for the concrete, reinforcing steel and FRP reinforcement, and the flexural strength at any section is determined from requirements for axial force and moment equilibrium at that section. A-18

A-19 When concrete compressive strain is 0.003 under conditions of force equilibrium, it is permitted to model the distribution of concrete stress in compression as having a uniform stress of cf85.0 over a depth ca 1 , in which c = depth to the neutral axis from the compression face of the beam and 1 = stress block factor specified in Article 5.7.2.2 of the AASHTO LRFD Bridge Design Specifications. When concrete compressive strain is less than 0.003 under conditions of force equilibrium, the concrete compression stress distribution shall be modeled as parabolic according to the following equation: 21 9.02 oc occ c ff (3.2-1) where c c o E f71.1 (3.2-2) and cf = stress in concrete at strain c (ksi) c = strain in concrete cf = the 28 - day compression strength of the concrete (ksi) o = the concrete strain corresponding to the maximum stress of the concrete stress-strain curve cE = the modulus of elasticity of the concrete specified in Section 5.4.2.4 of the AASHTO LRFD Bridge Design Specifications (ksi) When the compression strain in the extreme fiber of the concrete is less than 0.003 at force equilibrium, the Whitney compression stress block may no longer describe the compression resultant in the concrete accurately, and a more exact representation of the distribution of concrete stress in the compression zone is required. Eq (3.2-1), which provides this representation, was presented by Desayi and Krishnan, S. (1964) and by Todeschini et al. (1964). 3.3 FATIGUE LIMIT STATES C3.3 3.3.1 Subjected to the fatigue load combination specified in Article 3.4.1 of the AASHTO LRFD By limiting the maximum strain in the concrete to that specified in Eq. 3.3-1, the stress range in the

Bridge Design Specifications, the maximum compression strain in the concrete, c , the strain in the steel reinforcement, s , and the strain in the FRP reinforcement, frp , shall meet the following requirements ' 0.36 cc c f E (3.3-1) ys 8.0 (3.3-2) u frpfrp (3.3-3) where u frp = characteristic value of the tensile failure strain of the FRP reinforcement when tested in accordance with ASTM D3039 = strain limitation coefficient that is less than unity. The Engineer of Record shall stipulate the value of based on experimental data for the materials specified, and this value shall be provided in the contract documents. In the absence of such data, a value of = 0.8, 0.5, and 0.3 shall be used for carbon, aramid, and glass fiber reinforcement, respectively. concrete will be kept within '40.0 cf . Limiting the strain of the steel reinforcement under service load to 80% of the yield strain of the steel is equivalent to the recommendation of ACI Committee 440, where the stress in the reinforcing steel under service load is limited to 80% of the yield stress of the steel; this recommendation is based on the analytical work of El-Tawil et al. (2001). Strain limits on the FRP reinforcement are placed to avoid creep-rupture of the reinforcement. Polymer composites reinforced with carbon fibers are less susceptible to creep rupture than those reinforced with glass or aramid fibers. The recommended strain reduction factors of 0.8, 0.5, and 0.3 are based on studies reported by Yamaguchi et al. (1997) and Malvar (1998) and are recommended for the design of externally bonded FRP reinforcement for reinforced concrete structures by fib Task Group 9.3 (fib, 2001), and by ACI 440 Committee (ACI 440.2R-02). As the design is often governed by service limit state, FRP strains at Service I load combination are sufficiently low that creep rupture of the FRP is typically not of concern. 3.4 STRENGTH LIMIT STATES 3.4.1 Factored Flexural Resistance 3.4.1.1 Rectangular Sections The factored resistance, rM , of a steel-reinforced concrete rectangular section strengthened with FRP reinforcement externally bonded to the beam tension surface shall be taken as ckhT dckfAckdfAM frpfrp ssssssr 2 ' 2 '' 29.0 C3.4.1 The factored resistance is in line with the design strength determination in accordance with Article 5.7.3.2 of AASHTO LRFD Bridge Design Specifications, and is written so that the design strength for a reinforced concrete flexural member is simply augmented by the contribution of the externally bonded FRP reinforcement. This format ensures that when the FRP reinforcement is slight, the design strength approaches that of a flexural member without FRP reinforcement. (3.4.1.1-1) A-20

A-21 where bfrpfrp NbT (3.4.1.1-2) 2 2 2 arctan2 1 o c o c o c k (3.4.1.1-3) 2 2 1 c o c o Ln (3.4.1.1-4) sA = area of nonprestressed tension reinforcement ' sA = area of compression reinforcement (in2) sf = stress in the steel tension reinforcement at development of nominal flexural resistance (ksi) ' sf = stress in the steel compression reinforcement at development of nominal flexural resistance (ksi) c = depth of the concrete compression zone (in) sd = distance from extreme compression surface to the centroid of nonprestressed tension reinforcement (in) h = depth of section (in) frpT = tension force in the FRP reinforcement (kips)

frp = resistance factor equal to 0.85 2k = multiplier for locating resultant of the compression force in the concrete frpb = width of the FRP reinforcement (in) bN = FRP reinforcement strength per unit width, corresponding to 0.5% strain in the FRP reinforcement when subjected to tension in accordance with ASTM D3039. 3.4.1.2 Flanged Sections For flanged sections subjected to flexure about one axis where the neutral axis, based upon the stress distribution specified in Article 3.2, lies within the flange, the factored resistance, r M , shall be computed in accordance with Article 3.4.1.1. When the neutral axis falls outside the flange , the factored flexural resistance shall be determined by an analysis based on the assumptions specified in Article 3.2. C3.4.1.2 For most practical cases involving flanged sections strengthened externally with bonded FRP reinforcement to the tension surface, the depth of the neutral axis falls within the flange. When the neutral axis falls below the flange, the compression force exerted in the concrete is the sum of two components, one of which corresponds to the flange and one corresponds to the portion of the web under compression. Due to the nature of the assumed nonlinear stress-strain relationship of Eq. 3.2-1, the determination of the compressive force requires integration of the stress-strain function expressed in Eq. 3.2-1 over the area of the cross-section. 3.4.1.3 Other Cross-Sections For cross-sections other than rectangular or flanged sections, the factored flexural resistance, r M , shall be determined by an analysis based on the assumptions specified in Article 3.2. 3.4.1.4 Prestressed Sections For rectangular and nonrectangular prestressed concrete sections subjected to flexure about one axis, the factored flexural resistance shall be determined by an analysis based on the assumptions specified in Article 3.2 3.4.2 Ductility requirements The strain developed in the FRP reinforcement at the C3.4.2 This provision ensures that the tension steel reinforcement yields before the point of incipient A-22

A-23 ultimate limit state defined by eq (3.4.1.1-1) shall be equal to or greater than 2.5 times the strain in the FRP reinforcement at the point where the steel tension reinforcement yields. debonding of the externally bonded FRP reinforcement, thereby enabling the development of a ductile mode of flexural failure. 3.4.3 Detailing requirements C3.4.3 Flexural members shall be detailed to permit the development of the factored resistance defined by Eq (3.4-1). The externally bonded FRP reinforcement must be installed and detailed in such a manner that the assumptions in Section 3.2 are valid and the flexural capacity defined in eq (3.4-1) can be fully developed. 3.4.3.1 Development length C3.4.3.1 The tension development length ,Ld, shall be taken as frp frp d b T L int (3.4.3.1-1) where FRPT = tensile force (kips) in the FRP reinforcement corresponding to an FRP strain of 0.005 and int 0.065 cf is the interface shear transfer strength, (ksi). The minimum development length is required to allow the full tension strength of the FRP reinforcement to be developed in the region of maximum moment. The interface shear transfer strength limit of int 0.065 cf is based on the recommendation of Naaman and Lopez (1999) and Naaman et al. (1999) from tests conducted on uncracked and precracked reinforced concrete beams externally bonded with FRP reinforcement and subjected to bending with 300 freeze-thaw cycles. The limit also represents a lower bound for experimental data conducted on short-term direct tension tests of FRP reinforcement bonded to concrete surfaces (Haynes, 1997; Binzindavyi and Neale, 1999). 3.4.3.2. Reinforcement End Peeling C3.4.3.2 The peel stress at the end of externally bonded reinforcement shall meet the following requirement: '065.0 cpeel ff (3.4.3.2-1) in which: The end of an externally bonded reinforcement system, when subjected to combined shear and flexure, may separate in the form of debonding in three different modes: critical diagonal crack debonding with (Yao and Teng 2007) or without (Oehlers and Seracino, 2004) concrete cover separation; concrete cover separation (Teng et al., 2002); and plate end interfacial debonding (Teng et al., 2002). Critical diagonal crack debonding may occur where the FRP end is located in a zone of high shear force and the amount of steel shear reinforcement is

4/1 3 a frp frp a avpeel t t E Ef (3.4.3.2-2) T frp u afrpfrp a uav I yht M ttE GV 2/1 (3.4.3.2-3) and where: h = overall thickness or depth of a member (in.) y = distance from the extreme compression surface to the neutral axis of a transformed section, neglecting any contribution of concrete in tension (in). TI = moment of inertia of an equivalent FRP transformed section, neglecting any contribution of concrete in tension (in4) at = thickness of the adhesive layer (in) frpt = thickness of the FRP reinforcement (in) 2 1a a aE G Young’s modulus of adhesive (ksi) aG = characteristic value of the shear modulus of adhesive when tested in accordance with ASTM D5656 (ksi). a = Poisson’s ratio of adhesive, taken as equal to 0.35 a = characteristic value of the limiting shear stress in the adhesive (ksi), determined according to ASTM D 5656. In the absence of experimental data, a value of 5a ksi can be used. uV = factored shear force at the reinforcement end limited. In such a case a major diagonal shear crack forms and intersects the FRP, and then propagates towards the end. This failure mode is suppressed if the shear strength of the strengthened member remains higher than the flexural strength. In beams with heavy steel shear reinforcement, multiple diagonal cracks of smaller widths instead of a single major shear crack dominate the behavior, so concrete cover separation may take over as the controlling debonding failure mode. Failure of the concrete cover is initiated by a crack near the FRP end due to the stress concentration at that point. The crack then propagates to and then along the level of steel tension reinforcement. This mode of failure has been demonstrated experimentally for beams with externally bonded steel plates (Jones et al., 1988; Oehlers and Moran, 1990) and FRP reinforcement (Malek et al., 1998; Lopez and Naaman, 2003; Yao and Teng 2007). Plate-end interfacial debonding is also initiated by high interfacial shear and normal stresses near the end of the FRP that exceed the strength of the weakest element, generally the concrete. Debonding in this case propagates from the end of the FRP towards the middle, near the FRP-concrete interface. Note that this failure mode is only likely to occur when the FRP is significantly narrower than the beam section. In summary, provided that shear failure is suppressed (through shear strengthening, if needed), stress concentrations near the FRP reinforcement end may result in debonding through the concrete layer near the level of the longitudinal steel (or, rarely, near the FRP-concrete interface). Although a wide range of predictive models that include numerical, fracture mechanics, data-fitting, and strength of material-based methods have been developed to address this complex mode of failure (Yao, 2004), the equations presented in 3.4.3.2 are based on the approximate analysis of Roberts (1989), due to its simplicity for design purposes. At present, there is no standard test method for A-24

A-25 (kips) u M = factored mo ment at the reinforcement end (kip-in) determ ining the peel strength between an FRP reinforcem ent syste m and a concrete surface. Until such a test me thod is developed, the ASTM Standard Test Method D 3167 is recomm ended for determ ining the peel strength within the adhesive layer. ASTM D3167 is used for determ ining the peel resistance of adhesive bonds between one rigid adherend and one flexible adherend. For cases in which the peeling occurs within the concrete layer, it is recomm ended that the peeling strength be lim ited to '065.0 cf . REFERENCES ACI 440.2R-02 (2002). “Guide for the Design and Construction of Externally Bonded FRP System s for Strengthening Concrete Structures,” Am erican Concrete Institute, Farm ington Hills, Michigan. Bizindavyi, L.and Neale K. W. (1999). “Transfer Length and Bond Strengths for Com posite Bonded to Concrete, ASCE Journal of Com posites for Construction, Vol. 3, No. 4, Novem ber, pp. 153-160. Desayi, P. and Krishnan, S. (1964). “Equation for the stress-strain curve of concrete.” Journal the American Concrete Institute 61(3): 345-350. El-Tawil, S., Ogunc, C., Okeil, A. M., and Shahawy, M. (2001) “Static and Fatigue Analyses of RC Beam s Strengthened with CFRP Lam inates,” Journal of Composites for Construction, ASCE, Vol. 5, No. 4, pp. 258-267. fib (2001) technical report bulletin 14, “Externally bonded FRP reinforcem ent for RC structures”, published in Europe (fib, CEB-FIP, 2001). Jones, R., Swam y, R. N., and Charif, A. (1988). “Plate separation and anchorage of reinforced concrete beams strengthened with epoxy-bonded steel plates,” The Structural Engineer, Volum e 66, No. 5, pp. 85-94.

A-26 Haynes, L. (1997). “An investigation of bond between concrete and externally bonded carbon fiber reinforced plastic plates,” M.S. special report submitted to the faculty of the School of Civil Engineering in partial fulfillment of the requirements of the degree of Master of Science in Civil Engineering, Georgia Institute of Technology, Atlanta, Georgia. Lopez, M. M., Naaman A.E. (2003). Concrete Cover Failure or Tooth type failure on RC beams strengthened with FRP laminates, Proceedings of the Sixth International Symposium on Fiber Reinforced Polymer (FRP) for Reinforced Concrete Structures (FRPRCS-6). pp. 317-326. Malek, A.; Saadatmanesh, H.; and Ehsani, M. (1998). “Prediction of Failure Load of R/C Beams Strengthened with FRP Plate Due to Stress Concentrations at the Plate End,” ACI Structural Journal, Volume 95, No. 1, pp. 142-152. Malvar, L. (1998). “Durability of Composites in Reinforced Concrete,” Proceedings of the First International Conference on Durability of Composites for Construction, Aug., Sherbrooke, Canada, pp. 361-372. Naaman, A. E. and Lopez, M. (1999). “Repair and strengthening of reinforced concrete beams using CFRP Laminates, Behavior of beams subjected to freeze-thaw cycles,” Michigan Department of Transportation, Report No. RC-1372., April Naaman, A. E. , Lopez, M., and Pinkerton, L. (1999).” Repair and strengthening of reinforced concrete beams using CFRP Laminates , Behavior of beams under Cyclic loading at low temperature,” Michigan Department of Transportation, Report No. RC-1372., April. Oehlers, D. J. and Moran, J. P. (1990). "Premature failure of externally plated reinforced concrete beams." Journal of the Structural Division of the American Society of Civil Engineers, Vol. 116, No. 4, pp. 978-995.

A-27 Oehlers D. J. and Seracino R. (2004). Design of FRP and Steel Plated RC Structures, Elsevier Science Publishers, Etc., Oxford, UK. Roberts, T. M. (1989). “Approximate analysis of shear and normal stress concentrations in the adhesive layer of plated RC beams, The Structural Engineer, Volume 67, No.12/20 June, pp. 229-233. Teng, T. G., Chen, J. F., Smith, S. T., and Lam, L. (2002). FRP Strengthened RC Structures, John Wiley & Sons, Ltd, Chichester, UK. Todeschini, C.E., Bianchini, A.C. and Kesler, C.E. (1964). “Behavior of concrete columns reinforced with high strength steels.” ACI Journal 61(6):701- 716. Yamaguchi, T.; Kato, Y.; Nishimura, T.; and Uomoto, T. (1997). “Creep Rupture of FRP Rods Made of Aramid, Carbon and Glass Fibers,” Third International Symposium on Non-Metallic (FRP) Reinforcement for Concrete Structures (FRPRCS-3), V. 2, Japan Concrete Institute, Tokyo, Japan, pp. 179-186. Yao, J. (2004). “Debonding failures in RC beams and slabs strengthened with FRP plates,” Ph.D. Thesis, The Hong Kong Polytechnic University. Yao J. and Teng, J. G. (2007). “Plate end debonding in FRP-plated RC beams-I-Experiments,” Engineering Structures, 29, pp. 2457-2471.

SECTION 4: MEMBERS UNDER SHEAR AND TORSION 4.1 GENERAL REQUIREMENTS C4.1 The factored shear and torsion resistance of structural members at all sections shall equal or exceed the required strength in shear or in torsion calculated for the factored loads and forces in combinations stipulated in Article 3.4 of the AASHTO LRFD Bridge Design Specification, 4th Edition (2007). Except where specifically provided below, all provisions of the AASHTO LRFD Bridge Design Specification, 4th Edition (2007), Article 5.8, shall apply. The provisions for strengthening reinforced concrete structural members and components for shear and torsion using externally bonded FRP reinforcement have been developed with the assumption that all design requirements for shear and torsion in Article 5.8 of the AASHTO LRFD Bridge Design Specification, 4th Edition (2007) shall apply, except as specifically provided for in Section 4. Any duplication of provisions in these two documents is intended solely to facilitate the use and interpretation of provisions in Section 4. 4.2 STRENGTHENING SCHEMES Reinforced concrete bridge elements shall be strengthened with externally bonded FRP reinforcement using one of the following methods: Side bonding U-jacketing U-jacketing combined with anchorage Complete wrapping Transverse reinforcement shall be provided symmetrically on both sides of the element with spacing not to exceed the smaller value of 0.4 dv or 12 inches, where dv is the effective shear depth defined in Article 5.8.2.9 of AASHTO LRFD Bridge Design Specifications C4.2 Typical FRP strengthening schemes for beams and columns are summarized as follows: Side bonding (Fig. C4.2-1) is the least effective FRP shear reinforcement scheme due to premature debonding under shear loading and should be avoided if possible. Side bonding does not allow for the development of the shear-resisting mechanism based on a parallel chord truss model that was first proposed by Ritter (1899), due to the lack of tensile diagonals. Shear Reinforcement sfwf Shear reinforcement Figure C4.2-1 Side bonding A-28

A-29 U-jacketing (Fig. C4.2-2) is the most common externally bonded shear strengthening method for reinforced concrete beams and girders. The key drawback of this system is the possibility of premature debonding of the FRP, which may reduce its effectiveness. Despite this drawback, the system is quite popular in practice, due to its simplicity. Figure C 4.2-2 Jacketing combined with anchorage (Fig. C4.2-3) aims to increase the effectiveness of FRP by anchoring the fibers, preferably, in the compression zone. Properly designed anchors may result in the fibers reaching their tensile capacity, permitting the jacket to behave as if it were completely wrapped. Figure C 4.2-3 Jacketing with anchorages tf Spike anchor

4.3 STRENGTH IN SHEAR C4.3 The factored shear strength, V r , of a concrete me mb er strengthened with an externally bonded FRP syste m shall equal or exceed the required shear strength, V u , determined from the effect of the factored loads. Shear strengthening of reinforced concrete me mb ers using FRP reinforcem ent may be provided by bonding the external reinforcem ent (typically in the form of sheets) with the principal fiber direction as parallel as practically possible to that of ma xim um principal tensile stresses, so that the effectiveness of FRP is maxi mi zed. For the mo st common case of structural me mb ers subjected to lateral loads, in which loads are perpendicular to the me mb er axis (e.g. beams under gravity loads or colum ns under seism ic forces), the maxi mu m principal stress trajectories in the shear- critical zones form an angle with the me mber axis which may be taken roughly equal to 45 o . However, it is norm ally more practical to attach the external FRP reinforcem ent with the principal fiber direction perpendicular to the me mb er axis. Experim ental and analytical investigations of the behavior of reinforced concrete me mb ers strengthened in shear have revealed the following failure m odes: 1 - Steel yielding followed by FRP debonding 2 - Steel yielding followed by FRP fracture 3 - FRP debonding before steel yielding 4 - Diagonal concrete crushing Depending on the amount of usable steel shear reinforcement in the structural element, FRP debonding can occur either before or after steel yielding. The third failure mode is, in fact, highly unlikely to occur if proper detailing is provided. Diagonal concrete crushing in the direction perpendicular to the tension field can be suppressed by lim iting the total am ount of steel and FRP reinforcem ent. Note that fracture of the FRP reinforcem ent is highly unlikely to occur because the strain when FRP debonds is substantially lower than that corresponding to the FRP fracture strength. A-30

A-31 4.3.1 Factored Strength The factored shear strength, rV shall be defined as r c s p frp frpV V V V V (4.3.1-1) in which: cV = the nominal shear strength provided by the concrete in accordance with Articles 5.8.3.3 of the AASHTO LRFD Bridge Design Specifications. sV = 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; pV = 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; frpV = the nominal shear strength provided by the externally bonded FRP system in accordance with Article 4.3; = 0.9 frp is a resistance factor, defined as follows: 0.40 for side bonding shear reinforcement; 0.55 for U-jacketing; 0.60 for U-jacketing combined with anchorages; 0.65 for complete wrapping. C4.3.1 The shear provisions in Article 4.3 draw upon the traditional ACI approach embodied by Chapter 11 of the ACI Standard 318-05, supplemented by the report of ACI Committee 440.2R-02 (ACI, 2002). The contribution of the externally bonded FRP reinforcement to shear strength is based on fiber orientation and an assumed crack pattern following the formulation of Khalifa, et al (1998). Its contribution to member shear strength may be treated analogously to the treatment of internal steel, assuming that the FRP plate carries only normal stresses in the principal FRP material direction and that at the ultimate limit state in shear (concrete diagonal tension), the FRP develops an effective strain in the principal material direction of approximately 0.004. This limiting strain is conservative with respect to what tests have indicated (Sato et al., 1996; Araki et al., 1997; Triantafillou, 1998, Carolin, and Taljsten,2005; Chajes et al., 1995; Deniaud and Cheng, 2001;). Such a limiting strain value was also proposed by Priestley et al. (1996) to control circular bridge column dilation and was adopted by ACI Committee 440 (2002). Statistical data to support the reliability-based determination of resistance factors were available only for U-jacketing. The resistance factor for that case was found to be 0.55; resistance factors for other methods of reinforcement were set by judgment. .

Exception: When structural members without shear stirrups are being evaluated for possible upgrading, Vs in eq (4.1) shall be zero and shall be 0.60. Exception: For load combinations involving earthquake effects, and frp in eq (4.1) shall be reduced by 20%. 4.3.2 Limitation on strength provided by concrete and steel The sum of Vc + Vs shall not exceed 0.25 c v vf b d , in which bv and dv are effective web width and shear depth, defined in Article 5.8.2.9, in which cf is expressed in ksi units. 4.3.3 Regions requiring externally bonded shear reinforcement C4.3.3 Except for slabs, footings and culverts, shear reinforcement shall be provided where the required strength exceeds 0.5 c pV V in which cV , pV , and are defined in Article 4.3.1, or where consideration of torsion is required by Eqs 5.8.2.1-3 or 5.8.6.3-1 of the AASHTO LRFD Bridge Design Specification. It is permitted to waive this minimum requirement if it can be demonstrated by test that the required shear strength can be developed when shear reinforcement is omitted. Such tests shall simulate the in-service effects of creep, shrinkage, temperature change and differential settlement. Shear reinforcement shall be provided in all reinforced concrete flexural members where there is a significant probability that diagonal cracking will occur. A-32

A-33 The contribution of the externally bonded FRP plate to the no mi nal shear strength shall be determined as follows: a) For interm ittent FRP reinforcem ent si n c os e f rp fr p f rp frp v N w d V s (4.3.4.1-1) b) For continuous FRP reinforcement sin co s e f rp frp fr p V N d (4.3.4.1-2) Where f rp w = width of FRP reinforcem ent; v s = spacing of FRP reinforcement (m easured parallel to the me mb er axis); f rp d = Effective FRP shear reinforcem ent depth; and e f rp N = effective strength per unit width of the FRP reinforcem ent, determ ined in accordance with Article 4.3.4.2. = angle between FRP reinforcem ent principal direction and the longitudinal axis of the me mb er. The contribution of the FRP to the shear strength of a member is based on an assumed crack pattern of 45o and the fiber orientation (angle between the principal fiber orientation and longitudinal axis of member in Fig. C4.3.4.1-1a. Eq (4.3.4.1-1) is analogous to the equation for shear appearing in Chapter 11 of ACI Standard 318-05. The effective strength per unit width in Eq (4.3.4.1-1) or Eq (4.3.4.1-2) may be taken equal to the mean FRP stress along the shear crack. The value of this stress at each location along the shear crack depends mainly on the strengthening scheme (complete wrapping, U-jacketing, anchored U- jacketing, and side bonding) and on the bond stress – slip relation at the FRP-concrete interface (Triantafillou 1998). d fr p d a ? ? s v s v w fr p t f R b w Figure C4.3.4.1 4.3.4 Strength provided by externally bonded FRP reinforcement 4.3.4.1 Nominal Strength C4.3.4.1

4.3.4.2 Effective strength of FRP reinforcement C4.3.4.2 The effective strength of FRP reinforcement for each of the strengthening methods specified in Article 4.2 shall be determined as follows: Equations defining the effective strength of FRP shear reinforcement are based on the work of Priestley et al. (1996) and the work of Monti et al. (2004a, 2004b) simplified for design purposes. In such formulations the stress multiplied by thickness terms were replaced by the strength per unit width for consistency throughout these Guide Specifications. 4.3.4.2.1 For side bonding and U-jacketing without anchorage: e frp sN N (4.3.4.2.1-1) where sN = FRP tensile strength per 1-inch width corresponding to a tensile strain of 0.004 4.3.4.2.2 For U-jacketing combined with anchorage swfrpas e frp NNkNN ,2 1 (4.3.4.2.2-1) in which ka is a coefficient that depends on the effectiveness of the specific anchorage system. If the anchorage system is engineered in accordance with Articles D.3 and D.4 of Appendix D in ACI Standard 318-05 ka = 1. Otherwise, ka shall be taken as equal to zero. wfrpN , is the tensile strength of a closed (wrapped) jacket applied to a member of radius at the corners of the cross section not less than ½ in., defined as: sutwfrp NNN 5.0, (4.3.4.2.2-2) utN = nominal tensile strength of the FRP reinforcement; sN = Strength of FRP reinforcement corresponding to a strain of 0.004 The term ka in eq 4.3.4.2.2-1 is a coefficient that defines the effectiveness of the specific anchorage system. In view of the limited available test data, on FRP reinforcement with mechanical anchorage systems, it is recommended that if the anchorage is engineered, the strength can be fully developed and ka = 1; otherwise, its strength contribution is unknown. A-34

A-35 4.3.4.2.3 Complete wrapping (closed jackets) swfrps e frp NNNN ,2 1 (4.3.4.2.3-1) 4.3.5 Maximum nominal shear strength provided by reinforcement C4.3.5 The nominal shear strength provided by all shear reinforcement (steel stirrups plus externally bonded FRP plate) shall not exceed: '8s frp c wV V f b d (4.3.5-1) The limitation on the total shear reinforcement that can be provided is based on the criterion given for steel alone in ACI Standard 318-05. The purpose of this limitation is to minimize the likelihood of sudden failure caused by yielding of the transverse steel or debonding of the FRP reinforcement. 4.4 STRENGTH IN TORSION C4.4 The factored torsion strength, Tr, of a concrete member strengthened with an externally bonded FRP system shall equal or exceed the required torsion strength, Tu, determined from the effect of the factored loads. Strengthening for increased torsional capacity may be required in conventional beams and columns, as well as in box girders and other structural members with hollow sections. The principles applied to strengthening in shear are also valid, for the most part, for the case of torsion. The user of these Guide Specifications is cautioned that, in contrast to the provisions in Articles 4.2 and 4.3, supporting experimental data on the enhancement of the capacity of a member to withstand torsion by externally bonded FRP reinforcement does not exist. Accordingly, in situations where this limit state is considered, the Engineer of Record should consider the option of confirmatory testing.

The factored torsion strength, Tr, shall be defined as: r n frp frpT T T (4.4.1-1) in which: nT = nominal strength in torsion specified in Article 5.8.3.6 of the AASHTO LRFD Bridge Design Specifications; frpT = nominal shear strength provided by the externally bonded FRP system in accordance with Article 4.4.2; = 0.90 frp = 0.65 4.4.2 Nominal strength in torsion Externally bonded FRP reinforcement used to strengthen members in torsion shall be completely wrapped, as defined in Article 4.2.The nominal strength in torsion shall be calculated as follows: For intermittent FRP reinforcement, 1 1 e frp frp t frp N d x y T s (4.4.2-1) For continuous FRP reinforcement 1 1 e frp frp frp tT N d x y (4.4.2-2) in which 1 10.66 0.33 1.5t y x 1x = lesser dimension of the member 1y = larger dimension of the member 4.4.1 Factored strength in torsion A-36

A-37 4.5 STRENGTH IN INTERFACE SHEAR TRANSFER – SHEAR FRICTION The factored strength in shear-friction of a concrete member strengthened with an externally bonded FRP system shall equal or exceed the required shear strength, Vu, determined from the effect of the factored loads C4.5 The provisions for interface shear transfer in Article 4.5 are presented for consistency with Section 5.8.4 of the AASHTO LRFD Bridge Design Specifications. The user of these Guide Specifications is cautioned that, in contrast to the provisions in Articles 4.2 and 4.3, supporting experimental data on the enhancement of the capacity of a member to withstand shear friction by externally bonded FRP reinforcement does not exist. Accordingly, in situations where this limit state is considered, the Engineer of Record should consider the option of confirmatory testing. 4.5.1 Applicability It is permitted to determine the factored strength by shear-friction when shear transfer occurs across a given plane, such as an existing or potential crack, an interface between dissimilar materials, an interface between two concretes cast at different times, or the interface between different elements of the cross section. A crack shall be assumed to occur along the shear plane considered, and the required area of shear- friction reinforcement, Avf, across the shear plane shall be calculated using 4.5.3. All reinforcement provided to resist interface shear transfer shall be appropriately placed along the shear plane and shall be anchored to fully develop the required strength on both sides of the interface. C4.5.1 In shear-friction analysis, it is presumed that a crack will form in an unfavorable location and that reinforcement must be provided across the crack to resist relative displacement along the crack. When shear acts along a crack, one crack face slips relative to the other. In reinforced concrete construction, the crack faces are irregular and this slip is accompanied by separation of the crack faces. The slip movement and irregularities on the crack face introduce tension in the reinforcement that crosses the crack, and causes a clamping force to be developed normal to the crack. The applied shear then is resisted by friction between the crack faces (including shearing of aggregate protruding on the crack faces) and, usually to a lesser extent, by “dowel” action of the reinforcement that crosses the crack. The effectiveness of the shear- friction mechanism in withstanding applied shear depends on assuming the correct location of the crack.

4.5.2 Factored Strength for Shear-Friction The factored strength for shear friction shall be ri niV V (4.5.2-1) in which Vni = nominal shear-friction strength calculated in accordance with 4.5.3; =0.90 C4.5.2 The format for factored strength for shear-friction in Eq (4.5.2-1) is different from the format for factored strength for shear strength in Eq (4.3.1-1) because the load-resisting mechanism of interface shear transfer is different from that represented by Article 4.3. The contribution of the FRP reinforcement is included in the clamping force that appears in the expression for Vni, rather than additive to the factored shear strength. Similarly, the resistance factor for contribution of the FRP reinforcement is embedded in the clamping force. A-38

A-39 4.5.3.1 - Where shear-friction reinforcement is perpendicular to the shear plane defined in Article 4.5.1, Vni shall be computed by: niV C (4.5.3.1-1) in which C = clamping force across the crack face, defined in Article 4.5.3.3; = coefficient of friction defined in 4.5.3.4 The calculation of nominal strength for interface shear transfer in Article 4.5.3 is based on Section 11.7 of ACI Standard 318-05 rather than Article 5.8.4.1 of the AASHTO LRFD Bridge Design Specification. The ACI approach is based on the assumption that the resistance to interface shear transfer is directly proportional to the net clamping force. This resistance is determined simply as Cµ, in which C is the clamping force normal to the shear plane and µ is the coefficient of friction. The assumption that all shear resistance is due to friction between the crack faces neglects the contribution of dowel action of the steel reinforcement crossing the crack and necessitates the use of artificially high values of µ so that the calculated strength will be consistent with test results. The ACI approach is simpler than the AASHTO approach in ascribing the resistance to interface shear transfer entirely to the clamping force. Furthermore, Article 5.8.4.1 of the AASHTO Specification contains several experimental constants (c, K1 and K2) that would have to be revised to account for the presence of FRP shear reinforcement. The clamping forces in Articles 4.5.3.2 and 4.5.3.3 have been modified to account for the presence of FRP reinforcement crossing the crack. To preserve the familiar format of the factored resistance, the resistance factor, frp , is included in the expression for the clamping force 4.5.3.2 – Where shear-friction reinforcement is inclined to the shear plane, such that the shear force produces tension in shear-friction reinforcement, Vni shall be computed by: sin cosniV C (4.5.3.2-1) in which = angle between the shear-friction reinforcement and the shear plane. 4.5.3 Nominal strength for shear-friction C 4.5.3

4.5.3.3 – The clamping force, C , shall be determined as follows: vf yf frp frp frp frpC A f A E (4.5.3.3-1) In which vfA = area of steel reinforcement for shear-friction; yff = yield strength of steel reinforcement for shear-friction; frpA = effective area of FRP reinforcement for shear-friction; frpE = effective modulus of FRP reinforcement for shear-friction; frp = strain in FRP reinforcement for shear- friction, and frp = 0.65 The strain in the FRP reinforcement for shear- friction shall be taken as 0.004 unless test data are provided to support an alternative value. 4.5.3.4 – The coefficient of friction, µ, shall be determined as follows: 1.4 for concrete placed monolithically; 1.0 for concrete placed against hardened concrete intentionally roughened 0.7 for concrete anchored to structural steel by studs or other mechanical devices 0.6 for concrete placed by other methods than those above in which 1.0 for normal weight concrete 0.75 for light weight concrete A-40

A-41 4.5.3.5 The nominal shear strength Vn shall not exceed the smaller of 0.2 c cf A or 800 cA , where cA is the area of the concrete section resisting shear transfer. 4.5.3.6 Net tension across the shear plane shall be resisted by additional reinforcement. The value of fy used for design of shear-friction reinforcement shall not exceed 60 ksi. It is permitted to take permanent net compression across the shear plane as additive to the force in the shear-friction reinforcement, Avf fy, when calculating the required Avf

A-42 REFERENCES ACI (2005). Building code requirements for structural concrete (ACI Standard 318-05). American Concrete Institute, Farmington Hills, MI. ACI Committee 440 (2002). Guide to the design and construction of externally bonded FRP systems for strengthening concrete structures (ACI 440.2R). American Concrete Institute, Farmington Hills, MI Araki, N., Matsuzaki, Y., Nakano, K., Kataoka, T., and Fukuyama, H. (1997). “Shear capacity of retrofitted rc members with continuous fiber sheets.” Non-Metallic (FRP) Reinforcement for Concrete Structures, Japan Concrete Institute, 1, 515-522. Brosens, K. and Van Gemert, D. (1999), “Anchorage design for externally bonded carbon fiber reinforced polymer laminates”, Proceedings of Fourth International Symposium on FRP Reinforcement for Concrete Structures, Baltimore, USA, 635-645. Carolin, A. and Taljsten, B. (2005). “Experimental study of strengthening for increased shear bearing capacity”, ASCE J. Comp. Constr., 9(6), 488-496. Chajes, M. J., Januska, T. F., Mertz, D. R., Thomson, T. A., and Finch, W. W. (1995). “Shear strengthening of reinforced concrete beams using externally applied composite fabrics.” ACI Struct. J., 92(3), May-June, 295-303 Deniaud, C. and Cheng, R. (2001). “Shear behaviour of reinforced concrete T-beams with externally bonded fiber-reinforced polymer sheets”, ACI Struct. J., 98(3), May-June, 386-394 Holzenkämpfer,P. (1994), Ingenieurmodelle des verbundes geklebter bewehrung für betonbauteile. Dissertation, TU Braunschweig (In German). Khalifa, Ahmed, Gold, William J., Nanni, A., and Abdel Aziz, M.I. (1998). “Contribution of Externally Bonded FRP to Shear Capacity of FRP Members,” ASCE Journal of Composites for Construction, Vol 2, No. 4, pp. 195-202.

A-43 Monti, G., Santinelli, F. and Liotta, M. A. (2004a), “Shear strengthening of beams with composite materials”, Proceedings of the International Conference on FRP Composites in Civil Engineering – CICE 2004, Ed. R. Seracino, Adelaide, Australia, 569- 577. Monti, G., Santinelli, F., and Liotta, M.A. (2004b). Mechanics of shear FRP-strengthening of RC beams. ECCM 11, Rhodes, Greece. Priestly, M. J.N., Seible, F., and Calvi, M. (1996). “Seismic design and retrofit of bridges,” John Wiley and Sons, Inc, New York. Ritter, W. (1899). “Die Bauweise Hennebique,” Schweizerische, Bauzeitung, Vol. 33, No. 7 pp. 59–61. Sato, Y., Ueda, T., Kakuta, Y., and Tanaka, T. (1996). “Shear reinforcing effect of carbon fiber sheet attached to side of reinforced concrete beams.” Advanced Composite Materials in Bridges and Structures, M. M. El-Badry, ed., 621-627. Triantafillou, T. C. (1998), “Shear strengthening of reinforced concrete beams using epoxy-bonded FRP composites”, ACI Structural Journal, 95(2), 107-115.

SECTION 5: MEMBERS UNDER COMBINED AXIAL FORCE AND FLEXURE 5.1 GENERAL REQUIREMENTS The factored resistance of structural members subjected to axial forces and combined axial forces and flexure shall equal or exceed the required strength at all sections calculated for the factored loads and forces in combinations stipulated by these Guide Specifications. Except where specifically provided below, all provisions of Article 6.9 of the AASHTO LRFD Bridge Design Specifications, 4th Edition (2007), shall apply. . 5.2 METHODS FOR STRENGTHENING WITH FRP REINFORCEMENT 5.2.1 Columns shall be strengthened with FRP reinforcement using the complete wrapping method specified in Article 4.2. 5.3 COLUMNS IN AXIAL COMPRESSION 5.3.1 General Requirements The factored axial load resistance, rP , for a confined column shall be taken as follows: For members with spiral reinforcement stystgccr AfAAfP '85.085.0 (5.3.1-1) For members with tie reinforcement stystgccr AfAAfP '85.080.0 (5.3.1-2) C5.3.1 The design procedure for columns strengthened with FRP is the same as for reinforcement concrete columns without strengthening. However, the concrete compressive strength 'cf is substituted by the increased confined concrete compressive strength 'ccf as calculated according to Article 5.3.2.2. The multipliers of 0.85 and 0.80 in Equations 5.3.1-1 and 5.3.1-2 reflect the effect of minimum accidental eccentricities of axial force (0.05h and 0.10h, respectively, for columns with spiral or tied reinforcement) which impart small end moments to columns. Columns with eccentricities greater than these values must be designed using the provisions of Section 5.5.to take these extra moments into account. A-44

A-45 where = resistance factor specified in Article 5.5.4.2 of the AASHTO Bridge Design Specifications, 4 th Editio n g A = gross area of section (in 2 ) g A = total area of longitudinal reinforcem ent, (in 2 ). y f = specified yield strength of reinforcem ent (ksi) cc f ' = com pressive strength of the confined concrete determined according to Article 5.3.2.2. Confined circular colum ns sustain ultim ate axial strains that are far greater than those of non- confined columns. Any gain in strength due to strain hardening of the steel reinforcem ent is not accounted for in the above equation, thus providing additional safety. This gain is a function of the ultim ate axial strains, unless buckling of the steel reinforcem ent initiates failure of the colu mn . 5.3.2 Short Columns in Compression Colum ns in compression shall be fully wrapped over the entire length. C5.3.2 The provisions in Article 5.3.2 apply to short columns in which second-order effects are negligible and the limit state of instability can be ignored. 5.3.2.1 Limitations Provisions in this section shall apply to circular columns in which the slenderness parameter lu Ddoes not exceed 8 and to rectangular columns in which the aspect ratio, h b does not exceed 1.1, the minimum radius of corners is one inch, and the slenderness parameter, lu b, does not exceed 9, where: D = external diameter of the circular me mb er b = sm aller dimension of the rectangular me mb er h = larger di me nsion of the rectangular me mber C5.3.2.1 The limitations are similar to those in the Canadian guidelines for column strengthening (ISIS 2001). The limitation on column slenderness in this section ensures that the development of column strength not prevented by colum n instability. 5.3.2.2 Confinement in Columns C5.3.2.2

The compressive strength of the confined concrete, ccf ' , shall be determined from: ' 21'' c l ccc f fff (5.3.2.2-1) The confinement pressure due to FRP strengthening, lf [ksi] for circular columns shall be determined as: 11 2 2 ' e cfrp frpl k f D Nf (5.3.2.2-2) where ek is a strength reduction factor applied for unexpected eccentricities. It shall be taken as follows: ek =0.80 for tied columns, and ek = 0.85 for spiral columns. frpN = Strength per width of FRP reinforcement corresponding to a strain of 0.004. frp = 0.65, The confinement pressure shall be greater or equal to 600 psi. For rectangular columns, the diameter D in Eq (5.3.2.2-2) shall be replaced with the smaller dimension of the width and depth. The bonding of FRP sheets, where the fiber orientation is perpendicular to the column axis to limit the circumferential strains in the column, constitutes confinement. Various confinement models have been developed over the years and comparisons among the most common models have been presented by Rocca et al. (2008). The expression for the compressive strength of confined concrete adopted in these guides is similar to that of ISIS Canada due to its simplicity. The stress-strain curve for concrete confined by FRP reinforcement can be considered to be bilinear, but differs from the situation where the confinement is provided by spiral reinforcement or steel jacketing. The secondary stiffness depends on the hoop stiffness of the confining reinforcement. The maximum value of the confinement pressure specified in Eq 5.3.2.2-2 was established to limit the axial compression strains in overstrengthened columns. The minimum confinement pressure of 600 psi reflects the fact that the effectiveness of the confinement pressure depends upon a certain level of ductility. Relevant background related the maximum and minium values of confinement pressure in FRP reinforcement jackets in axially loaded columns is given by Thériault and Neale (2000). When Equation 5.3.2.2-2 is applied to rectangular columns after replacing D with the smaller dimension of the rectangular section, the factored axial strength estimated from eqs. 5.3.1- 1 or 5.3.1-2 errs on the conservative side. At present, this is justified owing to the limited properly documented available test data. The gain in strength provided by the confinement of rectangular sections is very little compared to that attainable for circular sections. As a result, neither minimum nor maximum limits are specified for rectangular sections since the attainable confinement pressure, which relies on ductility development, is very limited for rectangular columns. A-46

A-47 5.3.3 Slender columns C5.3.3 Columns not meeting the limitations on slenderness in 5.3.2.1 shall be designated as slender and their design shall be based on forces and moments determined from rational analysis. Such an analysis shall take into account the influence of forces, deflections and foundation rotations, and duration of loads on member stiffness and on the development of moments, shears and axial forces. The provisions for short columns in Article 5.3.2 are adequate for the majority of rehabilitation projects because second-order structural actions leading to instability seldom would occur. There is only limited test data to support the development of column strength provisions in situations where this is not the case. In such situations, the required columnstrength should be determined by rational analysis, supplemented by confirmatory testing, where feasible. 5.4 COMBINED AXIAL COMPRESSION AND BENDING 5.4.1 General requirements C5.4.1 Mem bers subjected to mo ment in combination with axial load shall be designed for the maxi mu m mo ment that can accompany the axial load. The factored axial force at given eccentricity shall not exceed r P given in Section 5.3.1. The ma xim um required mo me nt, M u , shall be magnified, as appropriate, for slenderness effects. The design procedure for the members strengthen with FRP is the sameas for reinforcement concrete members without strengthening. However, the concrete compressive strength f ' is substituted by the increased confined concrete compressive strength f ' as calculated according to articles cc c 5.3.2.2. 5.4.2 Design Basis Design of colu mn s subject to co mb inations of axial force and flexure shall be based on stress and strain compatibility. The ma xi mu m usable strain in the extrem e concrete co mp ression fiber shall be assumed to equal 0.003. Externally bonded FRP reinforcem ent of colum ns strengthened to withstand end mo ments due to lateral load shall be reinforced over a distance from the colum n ends equal to the maxim um colu mn dim ension or the distance over which the mo me nt exceeds 75% of the maxim um required mo ment, whichever distance is larger.

The tensile strength of the FRP reinforcement in the longitudinal direction of the colum n shall be determ ined by rational analysis. However, the strength in the longitudinal direction shall not be less than 50% of the strength in the perim eter direction. 5.4.3. Limitations The contribution of the FRP reinforcem ent to colum n capacity shall not be considered at eccentricity ratios greater than those corresponding to balanced strain conditions, at which tension reinforcem ent reaches the strain corresponding the steel yield strength and concrete in compression reaches an ultim ate strain of 0.003 at any cross section. C5.4.3 Provisions in Article 5.4 are limited to members subjected to combined axial loading and bending where failures occur by concrete crushing in compression rather than reinforcement yielding in tension. If the eccentricity of axial force present in the member is greater than 0.10h for the spirally reinforced columns or 0.05h for tied columns, strengthening requires externally bonded FRP reinforcement to withstand force in the longitudinal direction of the columnin addition to its perimeter. 5.5 AXIAL TENSION 5.5.1 Limitation Mem bers that are axially loaded in tension shall be reinforced symm etrically with respect to the colum n cross section principal axes. 5.5.2 General requirements C5.5.2 The factored axial load resistance, P r , for an axially loaded me mb er with externally bonded FRP reinforcement shall be frp frp frp y s r w N f A P 9 . 0 In which frp = 0.5 frp N = tensile strength per unit width in the load direction at a strain value of 0.005. frp w = total length of FRP reinforcem ent along the cross section. FRP systems can be used to provide additional tensile strength to concrete members. The tension strength provided by the FRP is limited by the design tensile strength of the FRP and the ability to transfer stresses into the substrate through bond. The effective strain in the FRP can be determined based on the criteria given for shear strengthening. For members completely wrapped by the FRP systems, loss of the aggregate interlock of concrete occurs at fiber strain less than the ultimate fiber strain. To preclude this mode of failure, the maximumdesign strain should be limited to 0.4%: A-48

A-49 fu fe 75 . 0 004 . 0 where fe is the effective strain level in FRP reinforcement attained at failure fu is the design rupture strain of FRP reinforcement References ISIS (2001). ISIS Canada Design Manuals, “Strengthening Reinforced Concrete Structures with Externally-Bonded Fiber-Reinforced Polym ers,” Winnipeg, Manitoba. Mirm iran, A., Shahawy, M. (1997). “Behavior of concrete columns confined by fiber com posites.” J. Struct. Engrg. ASCE 123(5):583-590. Mirm iran, A., Shahawy, M., Sam aan, M., El Echary, H., Mastrapa, J.C. and Pico, O. (1998) “Effect of col um n param eters on FRP-confined concrete.” J. Composites for Construction, ASCE 2(4):175-185. Saam an, M., Mirm iran, A. and Shahawy, M. (1998). “Model of concrete confined by fiber com posites.” J. Struct. Engrg. ASCE 124(9):1025-1031. Rocca, S., Galati, N. and Nanni, N. (2008) ASCE Journal of Co m posites for Construction, Vol. 12, No. 1,February, pp.80-92. Thériault, M. and Neale, K.W. (2000). “ Design equations for axially loaded reinforced concrete columns strengthened with fibre reinforced polym er wraps, Canadian Journal of Civil Engineering , 27 (5): 1011.1020. Val, D. (2003). “Reliability of fiber-reinforced polym er-confined reinforced concrete colum ns.” J. Struct. Engrg. ASCE 129(8):1122-1130.