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59 ATTACHMENT B Recommended Design Guidelines for Concrete Girders Strengthened in Shear with FRP These proposed guidelines are the recommendations of the NCHRP Project 12-75 Research Team at the Missouri University of Science and Technology. These guidelines have not been approved by NCHRP or any AASHTO committee nor formally accepted for the AASHTO specifications.

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60 SPECIFICATIONS COMMENTARY B1 GENERAL This attachment presents recommended design guidelines for concrete girders strengthened in shear using externally bonded fiber reinforced polymers (FRPs). Design examples developed using these guidelines are presented in the appendix. B1.1 Design Philosophy The proposed design guidelines were based on the traditional reinforced concrete (RC) design principles adopted by the current AASHTO LRFD Bridge Design Specifications and the knowledge on the mechanical behavior of FRP obtained from work performed under the NCHRP Project 12-75. As such, the factored shear resistance, Vn, of a concrete member should meet or exceed the factored shear force applied to the member, Vu. The applied factored shear force and the factored shear resistance should be computed based on the load and resistance factors specified in the AASHTO LRFD Bridge Design Specifications. The factored shear resistance shall be determined as: Vn Vu (B1-1) where: Vn : Nominal shear resistance Vu : Required shear strength : Strength reduction factor (0.9) Careful consideration for all possible failure modes and subsequent strains and stresses should be considered in determining the nominal shear strength of a member. B1.2 Scope These design guidelines focus on presenting design procedures including design equations. Specific limits of applying the proposed design guidelines are also presented in the relevant sections throughout this document. B2 EVALUATION AND REPAIR OF EXISTING RC CB2 BEAMS FRP strengthening is usually performed on structurally Information, such as evaluation and repair of existing RC deficient or damaged RC beams. Before a strengthening beams as well as proper application of FRP, is available; an procedure is implemented, the extent of deficiency and attempt was made to provide references to other publications suitability of FRP strengthening should be evaluated. The where additional details can be found. necessary evaluation criteria for repair of existing concrete structures and post repair evaluation criteria are well established in the following documents.

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61 SPECIFICATIONS ACI 201.1R: Guide for Making a Condition Survey of Concrete in Service ACI 224.1R: Causes, Evaluation, and Repair of Cracks in Concrete ACI 364.1R-94: Guide for Evaluation of Concrete Structures Prior to Rehabilitation ACI 440.2R-08: Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures ACI 503R: Use of Epoxy Compounds with Concrete ACI 546R: Concrete Repair Guide International Concrete Repair Institute (ICRI) ICRI 03730: Guide for Surface Preparation for the Repair of Deteriorated Concrete Resulting from Reinforcing Steel Corrosion International Concrete Repair Institute (ICRI) ICRI 03733: Guide for Selecting and Specifying Materials for Repairs of Concrete Surfaces NCHRP Report 609: Recommended Construction Specifications Process Control Manual for Repair and Retrofit of Concrete Structures Using Bonded FRP Composites Relevant specifications and guidelines provided by FRP manufacturers should also be carefully reviewed prior to the design of any strengthening syste m. B3 STRENGTHENING SCHEMES CB3 FRP shear reinforcement is commonly attached to a Complete wrapping of the cross section is the most effective beam, as shown in Figure B3.1 with (a) side bonding, in scheme and is commonly used in strengthening columns which the FRP is only bonded to the sides, (b) U-wrap, in where there is sufficient access for such application. Beams which FRP U-jackets are bonded to both the sides and soffit, are typically limited to U-wrap and side bonding applications and (c) complete wrapping, in which the FRP is wrapped since the integral slab makes it impractical to completely around the entire cross section. wrap such members. U-wrapping has been experimentally shown to be more effective in improving the shear resistance of a member than side bonding. (a) (b) (c) Figure B3.1 Strengthening Scheme: Cross-Sectional View (a) Side bonding, (b) U-wrap, and (c) Complete wrap For all wrapping schemes, the FRP can be applied continuously along the portion of the member length to be strengthened or as discrete strips. The fibers of the FRP may also be oriented at various angles to meet a range of strengthening requirements as shown in Figure B3.2

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62 SPECIFICATIONS COMMENTARY Center-to-Center Spacing of FRP Strip (sf) Width of FRP Strips (wf) (a) Center-to-Center Spacing of FRP Strip (sf ) Width of FRP Strips (wf ) (b) Figure B3.2 Strengthening Scheme: Side View -- (a) Fibers at 90 Direction, and (b) Fibers at Inclined Direction B4 APPLICATION OF FRP B4.1 General CB4.1 In general, procedures for the installation of FRP It is recommended that FRP applications be performed systems are developed by the manufacturer and can vary by a contractor trained in accordance with the installation between different systems. Procedures may also vary procedures specified by the manufacturer. Comprehensive depending on the type and condition of the structure to be guidelines in this regard are provided in NCHRP Report 609, strengthened. The application of FRP systems will not stop Recommended Construction Specifications and Process the ongoing corrosion of existing steel reinforcements. The Control Manual for Repair and Retrofit of Concrete cause of corrosion to internal steel reinforcements should be Structures Using Bonded FRP Composites addressed and corrosion-related deterioration should be repaired prior to application of any FRP system. B4.2 Surface Preparation CB4.2 The concrete surface should be prepared to a minimum Bond behavior of the FRP system is highly dependent on concrete surface profile (CSP) 3 as defined by the ICRI- a sound concrete substrate and can significantly influence the surface-profile chips (ICRI 03732, NCHRP Report 609). integrity of the FRP strengthening system. Proper Localized out-of-plane variations, including form lines, preparation and profiling of the concrete substrate is should not exceed 1/32 inch or the tolerances recommended necessary to achieve optimum bond strength. Improper by the FRP system manufacturer, whichever is smaller. Bug surface preparation can lead to premature debonding or holes and voids should be filled with epoxy putty. It is delamination. recommended that surface preparation be accomplished using abrasive or water-blasting techniques. All laitance, dust, dirt, oil, curing compound, existing coatings, and any other matter that could interfere with the bond between the FRP system and concrete substrate should be removed. When fibers are wrapped around corners, the corners should be rounded to a minimum 1/2 inch radius to prevent stress concentrations in the FRP system and voids between the FRP system and the concrete. Rough edges should also be smoothed by grinding or with putty prior to FRP application.

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63 SPECIFICATIONS COMMENTARY B4.3 Inspection, Evaluation, and Acceptance CB4.3 Application of FRP systems should be inspected by a When concrete and atmospheric temperatures exceed licensed engineer or qualified inspector knowledgeable in 90F, difficulties may be experienced in application of the FRP systems and installation procedures. The following epoxy compound owing to acceleration of the reaction and should be recorded at the time of installation: hardening rates. If ambient temperatures above 90F are Date and time of installation anticipated, work should be scheduled when the temperature Ambient temperature, relative humidity, and general is lower, such as in the early morning hours. If it is weather observations and surface temperature of necessary to apply epoxy compounds at temperatures concrete exceeding 90 F, the work should be supervised by a person Surface dryness, surface preparation methods and experienced in applying epoxy at high temperatures. Epoxy resulting profile using the ICRC-surface-profile- systems formulated for elevated temperature are available chips (ACI 530R-93). Qualitative description of surface cleanliness At temperatures below 40F, difficulties may occur due Type of auxiliary heat source, if applicable to deceleration of the reaction rates. The presence of frost or Widths of cracks not injected with epoxy ice crystals may also be detrimental to the bond between the Fiber or pre-cured laminate batch number(s) and FRP and the concrete. approximate locations in structure Evaluate moisture content or outgassing of the concrete Batch numbers, mixture ratios, mixing times, and by determining if moisture will collect at bond lines between qualitative descriptions of the appearance of all old concrete and epoxy adhesive before epoxy has cured. mixed resins, including primers, putties, saturants, This may be accomplished by taping a 4 x 4 ft (1 x 1 m) adhesives, and coatings mixed for the day polyethylene sheet to concrete surface. If moisture collects Observations of progress of cure of resins on underside of polyethylene sheet before epoxy would cure, Conformance with installation procedures then allow concrete to dry sufficiently to prevent the Location and size of any delaminations or air voids possibility of a moisture barrier between old concrete and General progress of work new epoxy (ACI 530R-93). Level of curing of resin in accordance with ASTM During installation, sample cups of mixed resin should be D3418. prepared according to a predetermined sampling plan and Adhesion strength retained for testing to determine level of curing in accordance with ASTM D3418. The relative cure of the resin can also be evaluated on the project site by physical observation of resin tackiness and hardness of work surfaces or hardness of retained resin samples. For bond-critical applications, tension adhesion testing of cored samples should be conducted using the methods in ACI 530R or ASTM D 4541 or the method described by ISIS (1998). The sampling frequency should be specified. Tension adhesion strengths should exceed 200 psi and exhibit failure of the concrete substrate before failure of the adhesive (ACI 440.2R-08). B5 MATERIAL PROPERTIES OF FRP The following mechanical properties should be obtained from manufacturers or coupon tests in accordance with ASTM D3039. E f : the modulus of elasticity of FRP fu : the ultimate strain of FRP. Then, the nominal resistance, f fu , can be determined assuming linear behavior of FRP stress-strain relationship up to failure as: f fu Ef fu (B5-1)

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64 SPECIFICATIONS COMMENTARY B6 NOMINAL SHEAR RESISTANCE An interaction is known to exist between the shear contributions of concrete, transverse steel reinforcement, and FRP. However, this interaction mechanism is not yet fully understood and thus is not reflected in the design procedures. Therefore, following the current reinforced concrete design principals, the nominal shear resistance ( Vn ) is determined by adding the contribution of the FRP reinforcement to the contributions from concrete and internal transverse steel reinforcement: Vn Vc Vs V f (B6-1) where, Vc is the contributions of concrete, Vs is the contribution of transverse steel reinforcement (stirrups), and V f is the contribution of FRP. The contributions from the concrete ( Vc ) and transverse steel reinforcement ( Vs ) can be computed based on the current AASHTO LRFD Bridge Design Specifications. Calculation of the FRP contribution ( V f ) is presented in the following sections. B7 SHEAR CONTRIBUTION OF FRP B7.1 Calculation of Contribution of FRP CB7.1 The contribution of FRP ( V f ) can be computed using the 45 truss model as: Af f fe d f ( sin f + cos f ) V f sf A f Ef fe d f ( sin f + cos f ) (B7-1) sf f Ef fe bv d f ( sin f + cos f ) where, Af is the area of FRP covering two sides of the beam and can be determined by 2n f t f w f ( n f is number of FRP plies, t f is the FRP reinforcement thickness, w f is the width of the strip), f fe is the effective stress of FRP, d f is the effective depth of FRP measured from the top of FRP reinforcement to the centroid of the longitudinal reinforcement, s f is the center-to-center spacing of FRP, f is the angle of inclination of FRP with respect to the longitudinal axis of the member as shown in Figure B3.2, E f is the modulus of elasticity of FRP, fe is the effective strain of FRP, f is the reinforcement ratio of FRP, and bv is the effective web width taken as the minimum web width within the effective depth ( d f )

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65 SPECIFICATIONS COMMENTARY The FRP shear reinforcement ratio, is determined f , as: For discrete strips 2n f t f w f f (B7-2) bv s f For continuous sheets 2n f t f f (B7-3) bv The effective strain ( fe ) represents the average strain The effective strain, fe , is largely dependent on the experienced by the FRP at shear failure of the strengthened failure modes as discussed in Appendix A - Sections A3 and member and can be expressed as: A4. Therefore, the experimental database collected in this project was grouped by the failure mode of the test specimens, i.e., either as debonding or rupture of the FRP and For Full Anchorage (Rupture Failures Expected): then regression analyses were performed to obtain Eqn. B7-4 Complete Wrap or U-Wrap with Anchors and B7-5. fe Rf fu (B7-4) .67 The upper bound for the quantity fEf in Eqs. B7-4 and B7-5 where R f 0.088 4( f Ef ) 1.0 is 300 ksi. Substituting this value in these two equations results in the lower bound value of Rf shown in the two For Other Anchorage (Non-Rupture Failures more equations. likely): Side bonding or U-Wrap fe Rf fu 0.012 (B7-5) .67 where R f 0.066 3( f Ef ) 1.0

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66 SPECIFICATIONS COMMENTARY B7.2 Limitations B7.2.1 Shear span-to-depth ratio The reduction factors (Rf) were developed from tests in which the loading was at a distance from the support sufficient to assume plane sections before deformation remain plane after deformation, i.e. shallow beam behavior. Thus, these provisions are only applicable to beams with a shear span-to-depth ratio greater than 2.5. B7.2.2 Maximum Amount of FRP Shear Reinforcement CB7.2.2 The amount of FRP should be determined so that the This provision is required to avoid web crushing failure nominal shear strength calculated by Eq. B 6-1 should not of FRP strengthened beams due to excessive transverse shear exceed the nominal shear strength calculated by reinforcement (both FRP and steel stirrups). Vn 0.25 f c bv dv Vp (AASHTO 5.8.3.3-2) B.7.2.3 Maximum Spacing of FRP Shear Reinforcement The clear spacing between externally bonded FRP shear reinforcement shall not exceed the maximum permitted spacing ( smax ) in accordance with the current AASHTO LRFD Bridge Design Specifications, expressed as: If vu 0.125 fc' then smax 0.8dv 24in. (AASHTO 5.8.2.7-1) ' If vu 0.125 f then smax c 0.4d v 12in. (AASHTO 5.8.2.7-2) where vu = the shear stress calculated in accordance with AASHTO LRFD Article 5.8.2.9 (ksi) and d v =effective shear depth as defined in AASHTO LRFD -- Article 5.8.2.9 (in.) B7.3 Use of Anchorage Systems Different types of anchorage systems are available for shear strengthening with FRP. Examples of mechanical anchorage systems consisting of FRP composite plates and concrete anchor bolts are available in the literature [NCHRP Report 12-75]. However, it should be noted that additional horizontal FRP strips cannot ensure FRP rupture failure. Thus, it is recommended that Equation B7-5 be used to calculate the FRP contribution, realizing that such approach will result in conservative estimates.

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67 APPENDIX Design Examples The following six design examples are presented to illustrate use of the recommended guidelines: Example 1-1: RC T-beam without internal transverse steel reinforcement strengthened with FRP in U-wrap configuration without anchorage systems Example 1-2: RC T-beam without internal transverse steel reinforcement strengthened with FRP in U-wrap configuration with an anchorage system Example 2-1: RC T-beam with internal transverse steel reinforcement strengthened with FRP in U-wrap configuration without anchorage systems Example 2-2: RC T-Beam with internal transverse steel reinforcement strengthened with FRP in U-wrap configuration with an anchorage system Example 3-1: PC I-Beam with internal transverse steel reinforcement strengthened with FRP in U-wrap configuration without anchorage systems Example 3-2: PC I-Beam with internal transverse steel reinforcement strengthened with FRP in U-wrap configuration with an anchorage system

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68 DESIGN EXAMPLE 1-1: RC T-Beam without Internal Transverse Steel Reinforcement Strengthened with FRP in U-wrap Configuration without Anchorage Systems 1. INTRODUCTION This example demonstrates the design procedures for externally bonded FRP shear reinforcement of an older reinforced concrete (RC) bridge using a U-wrap configuration without anchorage. The bridge consists of simply supported T-beams spanning 42 feet and spaced at 4.5 feet on center. The T-beams contain no transverse steel reinforcement. Additional details of the T-beam are provided in Figures 1 and 2. 114 ft 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 42 ft 4.5 ft Figure 1. Bridge plan and transverse section. 2. MATERIAL PROPERTIES The following material properties have been chosen to represent those anticipated in an older bridge for which shear deficiencies might be expected. 2.1. Concrete Compressive strength f'c := 3.0 ksi 1.5 Modulus of elasticity Ec := 33 ( 1.5 ) f'c 1000 ksi Ec = 3321 ksi

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69 1 := 0.85 if f'c 4 0.65 if f'c 8 ( 0.85 - 0.05 f'c - 4 ) otherwise 1 = 0.85 2.2. Longitudinal Reinforcement Yield strength fy := 60 ksi Modulus of elasticity Es := 29000 ksi 2.3. FRP Reinforcement Carbon Fiber Sheets are used in this example. Thickness tf := 0.0065 in. Failure strength ffu := 550 ksi Modulus of elasticity Ef := 33000 ksi ffu Failure strain fu := Ef fu = 0.017 in/in 3. GEOMETRICAL PROPERTIES Total Height hT := 37 in. Flange Thickness hf := 7 in. Width of the web bv := 18 in. Effective Width of the Flange beff := 54 in. Tensile reinforcement = 12#11 As := 18.72 in2 Internal shear reinforcement = Not provided Av := 0.0 in2 Distance from the extreme compression fiber to the center of the steel at the section d := 32.7 in.

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110 Figure 4. Final design of FRP strengthening.

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111 DESIGN EXAMPLE 3-2: PC I-Beam with Internal Transverse Steel Reinforcement Strengthened with FRP in U-wrap Configuration with an Anchorage System 1. INTRODUCTION This example demonstrates the design procedures for externally bonded FRP shear reinforcement of a prestressed I-beam bridge using a U-wrap configuration with anchorage. The bridge consists of five simply supported prestensioned I-beams spanning 42 feet and spaced at 7.5 feet on center. The I-beams are lightly reinforced with transverse steel reinforcement. Additional details of the bulb-tees are provided in Figures 1 and 2. (a) Prestressed I-Beam Bridge Deck Cross-Section 6 Strands 8 Strands phi 23.0 in. 17.2 ft 4.3 ft Center Line Beam Length = 43 ft (b) Beam Tendon Geometry Figure 1. AASHTO bulb-tee bridge deck bridge (Ref. PCI Bridge Design Manual).

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112 2. MATERIAL PROPERTIES 2.1. Concrete 2.1.1 Deck Compressive strength f'cd := 4.0 ksi Modulus of elasticity Ecd := 33 (1.5)1.5 f'cd 1000 ksi Ecd = 3834 ksi 1d := 0.85 if f'cd 4 0.65 if f'cd 8 ( 0.85 - 0.05 f'cd - 4 ) otherwise 1d = 0.85 2.1.1 I-Beam Compressive strength f'cb := 7.0 ksi Modulus of elasticity Ecb := 33 (1.5)1.5 f'cb 1000 ksi Ecb = 5072 ksi 1b := 0.85 if f'cb 4 0.65 if f'cb 8 ( 0.85 - 0.05 f'cb - 4 ) otherwise 1b = 0.7 2.2. Prestressing Strands Specified tensile strength fpu := 270 ksi Yield strength fpy := 243 ksi Modulus of elasticity Eps := 28500 ksi Diameter = 0.5 in. Total Area of the 14 strands Aps := 2.142 in2 k := 0.28 for low-relaxation steel

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113 2.3. Internal Steel Shear Reinforcement Yield strength fyt := 60 ksi 2.4. FRP Reinforcement Carbon-Fiber Sheets are used in this example. Thickness tf := 0.0065 in. Failure strength ffu := 550 ksi Modulus of elasticity Ef := 33000 ksi ffu Failure strain fu := Ef fu = 0.017 in./in. 3. GEOMETRICAL PROPERTIES Total height including deck slab hT := 38 in. Flange thickness hf := 6 in. Width of the web bv := 7 in. Effective width of the flange beff := 79.0 in. Internal shear reinforcement = #3 at 12 in. spacing Av := 0.22 in2 sv := 12 in. := 90 deg (a) I-Beam Prestressing Pattern

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114 (b) Cross-Section of an Intermediate Beam Figure 2. Cross-section of an intermediate beam. 4. CALCULATION OF THE FACTORED SHEAR FORCE AND NOMINAL SHEAR RESISTANCE 4.1 Factored Shear Force at the Critical Section Vu_crit := 100 kips 4.2. Calculation of Nominal Shear Resistance For this example, the simplified approach is followed. := 45deg := 2 The nominal shear resistance provided by the concrete, Vc, is calculated in accordance with LRFD Eqn.5.8.3.3-3 as: The distance from the extreme compression fiber to the center of gravity of the strands at the midspan: dp := 34.6 in.

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115 Assuming rectangular section behavior with no compression steel, the distance from the extreme compression fiber to the neutral axis, cc, may be calculated as: Apsfpu cc := fpu 0.85f'cdbeff1d + kAps dp ( c ) = 2.482 in. c ac := 1dcc (a ) = 2.11 in. c check_ac := "Assumption is correct" ( if a c h f ) "Not behave as rectangular" otherwise ( check_a ) = "Assumption is correct" c The effective shear depth dv is taken as the distance, measured perpendicular to the neutral axis, between the resultants of the tensile and compressive forces due to flexure; it need not be taken to be less than the greater of 0.9de or 0.72h (LRFD Article5.8.2.9). Since some of the strands are harped, the effective depth varies point-to-point. However, the effective depth must be calculated at the critical section in shear, which is not yet determined; therefore, an iterative procedure is required. For this example, only the final cycle of the iteration is shown. Assume dv dv_trial := 27.36 in. Calculate the distance from the extreme compression face to the center of gravity of the strand, de at the location, dv away from the centerline of the support. ( 206.4 - d ) + 2 2 + (206.4 - d ) + 4 2 + (206.4 - d ) + 6 2 23 23 23 24 + 44 + v_trial v_trial v_trial 206.4 206.4 206.4 etr := 6+6+2 de := hT - etr de = 26.021 in.

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116 ac Determine dv dv1 := de - 2 dv2 := 0.9de (d v3 := 0.72hT ) (d := max (d , d , d )) v_max v1 v2 v3 (d := max (d , 0.5d cot())) v v_max v_max Final dv (d ) = 27.36 in. v dv_trial Check_dv1 := "OK" if 0.995 1.005 dv "Try Again" otherwise Check_dv1 = "OK" dv Check_dv2 := "OK" if 4 bv "NOT GOOD" otherwise Check_dv2 = "OK" The nominal shear resistance provided by the concrete is: Vc := 0.0316 f'cbbvdv (LRFD Eqn. 5.8.3.3-3) (V ) = 32 kips c The nominal shear resistance provided by the internal steel reinforcement is: Avfytdv(cot() + cot()) sin() Vs := (LRFD Eqn. 5.8.3.3-4) sv Vs = 30.1 kips Harped tendon force = 6 x 0.153 x 149.0 = 136.8 kips (assuming fpe = 149 ksi) slope of the tendons := 0.111 Vp := 136.8 Vp = 15.2 kips

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117 The nominal shear resistance of the member is: Vn := Vc + Vs + Vp (LRFD Eqn. 5.8.3.3-1) Vn = 77.3 kips 5. DESIGN OF FRP SHEAR REINFORCEMENT 5.1 Check if FRP Reinforcement is Necessary Strength reduction factor for shear ( := 0.9) Check_FRP_Needed := "NOT need shear reinforcement" if Vn Vu_crit "NEED shear reinforcement" otherwise Check_FRP_Needed = "NEED shear reinforcement" 5.2 Computation of Required Vf Vu_crit Vf_req := - Vn Vf_req = 33.8 kips 5.3 Selection of FRP Strengthening Scheme U-wrap configuration is used with anchorage systems at the end of the sheets. The FRP sheets will be applied at 90 degrees with respect to the longitudinal axis of the girder as shown in the Figure 3 below. First, the spacing of FRP strips is chosen to meet the maximum spacing requirement. Then, the width of the FRP strips is selected to adjust the amount of FRP strips. Figure 3. FRP strengthening scheme. Use number of plies of FRP sheets nf := 1 Use the width of FRP sheets wf := 4 in. Use the center-to-center spacing of FRP sheets sf := 12 in.

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118 Orientation of FRP sheets f := 90 deg Effective depth of FRP sheets df := dp hf df = 28.6 in. Check if the selected spacing is acceptable or not Shear stress on concrete is: Vu_crit - Vp vu := (LRFD Eqn. 5.8.2.9-1) bvdv (v ) = 0.501 ksi u The maximum spacing of the transverse reinforcement is: ( ) smax := min 0.8dv, 24 if vu < 0.125f'cb (LRFD Eqn. 5.8.2.7-1) min(0.4d , 12) otherwise v (LRFD Eqn. 5.8.2.7-2) smax = 21.9 Check_Spacing := "Acceptable" if sf smax "NOT_Acceptable_Change_the_Spacing" otherwise Check_Spacing = "Acceptable" 5.4 Calculation of Shear Resistance of FRP, Vf The FRP reinforcement ratio is: 2nfwftf f := (Attachment A Eqn. 5.8.3.3-10) bvsf ( ) = 6.19 10 f -4 The FRP strain reduction factor is: Rf := min 4 f Ef ( ) - 0.67, 1.0 (Attachment A Eqn. 5.8.3.3-8) Rf = 0.53 The effective strain of FRP is: fe := Rffu (Attachment A Eqn. 5.8.3.3-7) fe = 8.832 10 - 3 in./in.

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119 The effective stress of FRP is: ffe := feEf (Attachment A Eqn. 5.8.3.3-6) ( f ) = 291.4 ksi fe The shear contribution of the FRP can be then calculated. (V := E b d (sin( ) + cos( ))) f f f fe v f f f (Attachment A Eqn. 5.8.3.3-5) (V ) = 36.1 kips f Vf_check1 := "Change FRP Strengthening Scheme" ( if Vf < Vf_req ) "Provided FRP Strength Large Enough" otherwise Vf_check1 = "Provided FRP Strength Large Enough" Vf_check2 := "Provided FRP amount is adequate" ( if Vf_req Vf < 1.1Vf_req ) "Change the FRP amount slightly" otherwise Vf_check2 = "Provided FRP amount is adequate" 5.5 Calculation of Design Shear Resistance of the Member The design strength of the member is: ( Vn_total := Vc + Vp + Vs + Vf ) (Attachment A Eqn. 5.8.3.3-1) (V n_total ) = 102.1 kips Vn_check := "Not Good" if Vu_crit > Vn_total "OK" otherwise (V n_check ) = "OK" Web_crushing_limit := 0.25f'cbbvdvVp (LRFD Eqn. 5.8.3.3-2) Web_crushing_limit = 350.3 kips Check_web_crushing_limit := "OK" ( ) if Vc + Vs + Vf + Vp Web_crushing_limit "No Good" otherwise Check_web_crushing_limit = "OK"

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120 6. SUMMARY Externally bonded FRP sheets were designed in this example. The FRP sheets are applied at 90 degrees with respect to the longitudinal axis of the member with the U-wrap configuration and without anchorage systems as shown in Figure 4. The final design is summarized as: Use number of plies of FRP sheets nf = 1 Use the width of FRP sheets wf = 4 in. Use the center-to-center spacing of FRP sheets sf = 12 in. Figure 4. Final design of FRP strengthening.