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38
2.0
1.8 JSCE, 2001
Carolin and
U-Wrapping Taljsten, 2005b
1.6
Khalifa et al., 1998
1.4 CSA S806, 2002
Chajes et al., 1995
Vf / (bw df) (ksi)
1.2
Hutchinson and
Rizkalla, 1999
1.0
ACI 440, 2008
0.8
Cao et al., 2005
Zhang Pellegrino and
0.6 and Hsu, Modena, 2002
2005 vfr
Chaallal et al.,
0.4 2002
fib-TG9.3, 2001
0.2 Monti and
Liotta, 2005
Triantafillou and
vfnr Antonopoulos, 2000 Chen & Teng, 2003a,b
0.0
0 25 50 75 100 125 150 175 200 225 250 275
f E f (ksi)
Figure 3.1. Influence of FRP axial rigidity on FRP shear stress resistance.
Comparison of this expression with the test data yields an (Chen and Teng, 2003a,b; Zhang and Hsu, 2005) provide
average strength ratio (bias) of 1.44, and a corresponding values similar to those obtained from the models that provide
COV of 0.25. the best estimates of FRP shear contribution (i.e., Triantafil-
These expressions are only applicable for RC and PC mem- lou and Antonopoulos, 2000; and fib-TG9.3, 2001).
bers in which dv /bv < 4.0, and the calculated R value should
not be taken greater than one (i.e., R 1.0).
Figure 3.1 shows the calculated shear stress capacity pro- 3.2 Design Guidelines
vided by the FRP reinforcement (Vf /bw df) as a function of the
Recommended design guidelines for concrete girders
axial rigidity of the FRP reinforcement (f Ef) for 15 models and
strengthened in shear with FRP were developed based on the
the two relationships identified in this study for a member
findings of this research. The guidelines, provided as Attach-
having a rectangular cross-section and the following properties:
ment B, were drafted in LRFD format to facilitate incorpo-
ration into the AASHTO LRFD Bridge Design Specifications
· Dimensions: 7.09 inches wide, 19.69 inches high, and a
(AASHTO, 2008).
shear span-to-depth ratio of 3.5
· FRP reinforcement: CFRP sheets externally bonded with
fibers oriented at 90° in a U-wrap configuration over a 3.3 Design Examples
height of 17.32 inches
· Concrete compressive strength: 8,557 psi Six design examples were prepared to illustrate the use of
· Modulus of elasticity of the CFRP sheets: 33,939 ksi the proposed design. Four of the design examples consider RC
· Ultimate tensile strength of the CFRP sheet: 653 ksi T-beams (i.e., two with transverse steel reinforcement and two
without transverse steel reinforcement) with a U-wrap FRP
The case of full anchorage for which FRP rupture failure is strengthening scheme with and without anchorage (i.e., two
expected is labeled by vfr, and the case of less than full anchor- with mechanical anchorage and two without any anchorage).
age for which debonding or other non-rupture failure modes The other two design examples consider PC I-girders with
are expected is labeled vfnr. Figure 3.1 shows that the strength transverse steel reinforcement and U-wrap FRP strengthening
when full anchorage is not provided is less than when full scheme with and without anchorage (i.e., one with mechanical
anchorage is provided. In addition, the two relationships anchorage and one without any anchorage).
