Flexural members - Reinforced Concrete with FRP Bars: Mechanics and Design - page 132

transverse FRP reinforcement (stirrups) were investigated independently as
follows: (a) Test results compiled by Miano [38] in combination with results
from Matta et al. [35] provided a statistical database for beams without stir-
rups, and (b) a similar database for beams with shear reinforcement (stirrups)
was collected by Vitiello [39].
Based on the databases, statistical parameters of FRP RC beams with-
out stirrups under shear failure are calculated as λ R = 1.93 and δ R = 0.238
(Table 4.6, first row). Similarly, statistical parameters of FRP reinforced
beams under shear failure are calculated as λ R = 1. 64 and δ R = 0.353
(Table 4.6, second row). For each of these two cases, the comparative
reliability equation may be used to calculate the shear strength-reduc-
tion factor. Substituting the probabilistic parameters of shear failure of
a steel RC beam from Table 4.6 (last row) ( ϕ 1 = 0.75, λ 1 = 1.23, and δ 1
= 0.109) and an FRP RC beam from Table 4.6 ( λ 2 and δ 2 from either of
the first two rows), the strength-reduction factor for the latter can be
calculated for the presumed value of target reliability of β T = 3.5 (the first
two rows of Table 4.7). Evidently, the current shear strength-reduction
factor of 0.75 for FRC RC is relatively conservative for beams with no
stirrups, while in presence of such reinforcement, a drastic modification
(from existing ϕ = 0.75 to no less than ϕ = 0.50) appears to be neces-
sary. However, two simple modiications to the limitations of the shear
design equation (i.e., one for a minimum value of V c and one for maximum
amount of shear reinforcement) can reduce the likelihood of unnecessary
overdesign or undesired underdesign, while the anticipated level of safety
is maintained.
FRP RC beams without stirrups: With reference to ACI 318-11, the
shear strength proposed by ACI 440.1R-06 may be rewritten as

5
2

=

(4.106)

V k V cFRP , cSteel ,

In case of lightly FRP reinforced flexural members such as slabs and
footings, for which the longitudinal reinforcement is normally next to the
minimum allowable, the current formulation of shear resistance from ACI
440.1R-06 leads to results that might appear unrealistic. Here, an attempt is
made to investigate whether a minimum can be imposed on the contribution
of concrete.
From the database of beams with no stirrups, those specimens were
extracted whose tensile stiffness ( ρ f E f ) is less than a steel reinforced slab