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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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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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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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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 90°F, 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 90°F 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 40°F, 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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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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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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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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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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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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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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Figure 4. Final design of FRP strengthening.

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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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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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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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(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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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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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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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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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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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"

OCR for page 59

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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.