Shear Strengthening of Concrete Members - Strengthening Design of Reinforced Concrete with FRP - page 154

w f

d

d fv

h

w f S f

S f

FIGURE 6.2 Variables for FRP shear-strengthening design.

where V c is computed based on Equations (11.3) to (11.8) of ACI 318-05, V s is com-
puted based on Section 11.5.7.2 of ACI 318-05 as specified by ACI 440.2R-08. The
value of Ψ f is determined to be 0.85 for U-wraps and side bonding based on a reli-
ability study of existing experimental data. On the other hand, Ψ f is selected to be
0.95 for fully wrapped section based on the lower bond dependence. V f is computed
based on the following equations:

( )

Af sin os α+ α d

fv fe fv

V =

(6.3)

f

S

f

where

Antw
fv

2 (6.4)

f f

f =ε E

fe

(6.5)

fe f

where ε fe is the effective tensile strain developed in the FRP shear stirrups at nomi-
nal shear strength. This effective tensile strain is controlled by the failure of the
strengthened concrete member and by the failure of the FRP stirrups. The variables
d fv and S f are denoted in Figure 6.2.

6.4 DETERMINATION OF ε fe
The value of ε fe is determined as follows:

1. Fully wrapped section : The loss of aggregate interlock of the concrete is
observed to take place at a fiber strain much lower than the ultimate fiber
strain (Priestley, Seible, and Calvi 1996):

ε= ≤ε
fe

0.004 0.75 (6.6)

fu

2. U-wraps or plies bonded to two sides : U-wraps (three-sided wraps) and
bonded side plies (two-sided strips) have been observed to delaminate
from concrete prior to the loss of aggregate interlock. Accordingly, bond