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Notations
a Shear span length
a/d Shear span-to-depth ratio
Ac Concrete area
Acf Effective flange concrete area
Acw Web concrete area = bwh
Af Cross-sectional area of FRP
Ap Cross-sectional area of strengthening material [Sim et al., 2005]
Asw, Av Area of transverse steel reinforcement
b, bv, bw Minimum width of cross-section over effective depth
bf Width of FRP strip [Carolin and Taljsten, 2005]
C Constant strain rate = 110×10-6 mm-1
d, dv Effective depth of cross-section
df Effective depth of FRP reinforcement
Dfrp Stress distribution factor for FRP intersected by the shear crack [Chen
and Teng, 2003 a and b]
dFRP FRP sheet height along side of beam web [Deniaud and Cheng, 2001,
2004]
Df Modified FRP strain distribution factor = Dfrp/ [Cao et al., 2005]
dS Stirrup height
e spacing of stirrups [Sim et al., 2005]
Ef, Efrp Elastic modulus of FRP
(Ef f)lim Limiting value of FRP rigidity separating debonding and FRP rupture
failure modes
Es Elastic modulus of steel reinforcement
fc, f c Concrete compressive strength
fck Concrete characteristic cubic strength
fcm Mean cylindrical compressive strength of concrete
fctm Concrete mean tensile strength
ffd Design ultimate strength of FRP
ffdd Debonding FRP strength

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ffe Effective tensile stress in FRP sheet/strip in the direction of the prin-
cipal fibers
ffed Design effective strength of the FRP shear strengthening
ffrp Tensile strength of FRP in the main fiber direction [Chen and Teng,
2003 a and b]
ffrp, ed Average/effective design stress of FRP intersected by shear crack at beam
failure
ffu FRP ultimate tensile strength
fpy Yield strength of strengthening material [Sim et al., 2005]
fy, fvy, Fy, fsy Yield strength of steel reinforcement
h Height of RC/PC member
hfrp, hfrp,e Effective FRP height
hj Depth of U-jacket strengthening [Al-Sulaimani et al., 1994]
hs Depth of each FRP strip [Al-Sulaimani et al., 1994]
hv Effective depth of the concrete beam [Malek and Saadatmanesh,
1998]
hw Height of web [Monti and Liotta, 2005]
hw Height of shear wing strengthening [Al-Sulaimani et al., 1994]
k Experimentally determined factor [Deniaud and Cheng, 2001, 2004]
ka Coefficient describing anchorage considerations [Deniaud and Cheng,
2001, 2004]
kb Covering/scale coefficient
ke Integer describing number of debonding ends
L Girder span length
lb Available bond length of FRP
Le, Leff, Lfe, le Effective bond length
leq Bonded length projected vertically that would be necessary if the
fabric strain was uniform
Lmax Maximum bond length
n Number of FRP plies
n Ratio of elastic modulus of FRP to elastic modulus of transverse steel
(Ef /Es) [Chaallal et al., 2002]
n Number of spaces between stirrups [Deniaud and Cheng, 2001, 2004]
ns Total number of stirrups crossing concrete shear plane
pf FRP spacing measured orthogonal to the FRP orientation [Monti and
Liotta, 2005]
_ _
_ _ _ _ _ _
Q12, Q13, Q22, Q23 Stiffness elements of FRP
R Ratio of effective stress/strain in the FRP sheet to its ultimate strength/
strain
R* Additional reduction factor for debonding failures of beams with
steel web reinforcement [Pellegrino and Modena, 2002]
rc Corner rounding radius of concrete section for which FRP is wrapped
Rck Concrete characteristic cubic strength
RL Remaining bonded width over initial width ratio [Deniaud and Cheng,
2001, 2004]

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S Girder spacing
s Spacing of stirrups
sf, sfrp Spacing of FRP strips
sf FRP slip at debonding [Monti and Liotta, 2005]
sf,max Maximum spacing limitation for FRP strips
sxe Crack spacing parameter
t, tf, tfrp FRP thickness
t Spacing of strengthening material [Sim et al., 2005]
TFRP Tension force in FRP
tp Nominal thickness of FRP sheet or bonded plate
ts Width of each FRP strip
Tv Tension force in stirrups
V Shear force
Vc Shear contribution of concrete
Vcy Concrete contribution to shear resistance corresponding with yield-
ing of the stirrups along the primary shear crack
Vcu Concrete contribution to shear resistance corresponding with the
ultimate (maximum) load carried by the girder
Vexp Experimentally measured ultimate shear strength
Vf, Vfd, Vf,max, Vf,max, Vfrp Shear contribution of FRP
VFE Analytically (Finite Element) predicted ultimate shear strength
Vf,model FRP contribution to shear resistance predicted by analytical models
vfnr Relationship developed for the case of less than full anchorage such
that debonding or other non-rupture failures are expected
vfr Relationship developed for the case of full anchorage such that FRP
rupture failure is expected
Vfrp,d Contribution of external FRP reinforcement (design value)
[Triantafillou, 1998]
Vf,test Experimentally measured shear strength of a test beam with FRP re-
inforcement minus the experimentally measured shear strength of the
corresponding control beam without FRP reinforcement
Vfy FRP contribution to shear resistance corresponding with yielding of
the stirrups along the primary shear crack
Vfu FRP contribution to shear resistance corresponding with the ultimate
(maximum) load carried by the girder
Vn Total shear capacity
Vn,norm Normalized shear strength
Vn,test Experimentally measured shear strength of a beam
VP Fiber glass plate component of shear capacity [Al-Sulaimani et al.,
1994]
Vr Total shear resistance [Deniaud and Cheng, 2001, 2004]
VRd,f Shear carried by FRP [Monti and Liotta, 2005]
Vs, Vse Shear contribution of stirrups
Vsy Transverse steel (stirrup) contribution to shear resistance correspon-
ding with yielding of the stirrups along the primary shear crack

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Vsu Transverse steel (stirrup) contribution to shear resistance correspon-
ding with the ultimate (maximum) load carried by the girder
wf, wfrp Width of FRP strip
wfe Effective width of FRP strip
Z Limit state function
z Length of a vertical tension tie
zb Co-ordinate of lower edge of effective FRP bonded to the sides of a
beam
zrid,eq Vertically projected length of the FRP strip, minus the effective bond
length where bond is building up, plus a bonded length that would be
necessary if the FRP stress was uniform under the debonding slip
zt Co-ordinate of upper edge of effective FRP bonded to the sides of a
beam
Angle of inclination of transverse steel reinforcement to longitudi-
nal axis of beam
Reduction factor [Triantafillou and Antonopoulos, 2000]
Crack inclination angle [Carolin and Taljsten, 2005]
Angle between principal direction of FRP sheets and the longitudinal
axis of the beam [Deniaud and Cheng, 2001, 2004]
Strength efficiency factor [Sim et al., 2005]
f Angle between principal direction of FRP sheets and the longitudinal
axis of the beam [Hutchinson and Rizkalla, 1999]
MF Random variable for uncertainties in material and fabrication tolerances
Angle of inclination of FRP fibers to longitudinal axis of member
Factor relating effect of longitudinal strain on the shear capacity of
concrete, as indicated by the ability of diagonally cracked concrete to
transmit tension [AASHTO LRFD, 2008]
L Bond length coefficient
r Reliability index
r,target Reliability index targeted by most AASHTO calibration studies
w FRP strip width coefficient
1, 2 Strains in the principal 12 directions
bond Maximum allowable strain without achieving anchor failure [Car-
olin and Taljsten, 2005]
c max Maximum allowable strain to achieve concrete contribution
cr Critical FRP strain
f,ave Average strain in FRP at failure [Hutchinson and Rizkalla, 1999]
fe, f,e, frp,e, eff Effective tensile strain of FRP
fk,e Characteristic effective FRP strain in principal fiber direction
[Triantafillou and Antonopoulos, 2000]
f,e,A Effective FRP strain in principal fiber direction--ACI code format
[Triantafillou and Antonopoulos, 2000]
f max, f, max Maximum strain in FRP sheet
fu Ultimate tensile strain of FRP
f (y) Strain in FRP fibers at height y [Carolin and Taljsten, 2005]

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max Maximum or limiting value of FRP strain
max Maximum FRP strain over remaining bonded width [Deniaud and
Cheng, 2001, 2004]
max,A Limiting value of effective FRP strain--ACI code format [Triantafillou
and Antonopoulos, 2000]
s Tensile strain in cracked concrete in direction of tension tie
se Effective stirrup strain at failure [Hutchinson and Rizkalla, 1999]
sy, y Yield strain of steel stirrups
ultFRP Ultimate FRP strain [Deniaud and Cheng, 2001, 2004]
vcu Ultimate vertical tensile strain of the concrete taken as 0.005 [Chajes
et al., 1995]
_
z Normalized strain in FRP [Chen and Teng, 2003b]
_
z,max Maximum normalized strain in FRP [Chen and Teng, 2003 b]
f Shear strength reduction factor for FRP
R Coefficient accounting for the effects of sheets wrapped around a
corner
f, frp, Rd Partial safety factor for FRP
fs The ratio of the vertical component of average strain in the FRP sheets
to the average strain in the steel stirrups
f,d Partial safety factor depending on the FRP application accuracy
Fk Specific fracture energy of the FRP-concrete bond interface
Average fiber utilization (effectiveness) factor
GDF Random variable for girder distribution factor
Shear span-to-effective depth ratio
Normalized maximum bond length of FRP = Lmax /Le [Chen and Teng,
2003a]
frp Normalized FRP bond length = Lmax /Le [Cao et al., 2005]
Constant that represents the contribution of compressive strength of
concrete
, c Shear crack angle or angle of diagonal compression
Angle between the principal tensile stress and the fiber direction
[Carolin and Taljsten, 2005]
f Shear plane angle in flange
w Shear plane angle in web
P Random variable for analysis model accuracy
Af 2n f t f w f
f, frp FRP reinforcement ratio = = (wf = sf = 1.0 for continu-
bv s f bv s f
ous wraps)
f FRP reinforcement ratio = (Af per unit length/bd) = 2tf /bd [Chaallal
et al., 2002]
s Shear steel reinforcement ratio = (Av per unit length/bd) = Av /sbd
[Chaallal et al., 2002]
s,f Stiffness ratio between the transverse steel shear reinforcement and
FRP shear reinforcement [Pellegrino and Modena, 2002]

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tot Total shear reinforcement ratio [Chaallal et al., 2002]
Av
v Transverse steel reinforcement ratio =
bv s
cu Concrete compressive strength
frp,max Maximum stress in FRP intersected by shear crack [Chen and Teng,
2003b]
frp,max,d Maximum stress in FRP intersected by shear crack for design [Chen
and Teng, 2003a]
frp,z Stress in the FRP at the ultimate limit state at the location where the
intersecting critical shear crack is at a coordinate z [Chen and Teng,
2003a]
Shear stress
ave Average shear stress
max Ultimate direct bond shear strength between FRP and concrete
ult Interface shear strength between concrete and fiberglass plates
[Al-Sulaimani et al., 1994]
Coordinate ratio of the upper edge to the lower edge of the effective
FRP = zt /zb
DC Random variable for component dead load
LL+IM Random variable for highway live load including impact loads
WS Random variable for wearing surface dead load