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a lower threshold, it is proposed to limit shear reinforcement contribu-
tion,
V
f
,
to 3
V
c
.
By imposing a new ceiling on the combination of the two
components of the shear resistance, the set of elements with
V
f
≥
3
V
c
is
excluded from the sample population as expressed by Equations (4.102)
and (4.103).
Equation (4.103) covers those cases in which the design is governed by
nonstrength considerations, such as achieving higher ductility through a tight
arrangement of the stirrups.
Leaving out the cases with
V
f
≥
3
V
c
from the sample population, the
statistical parameters are calculated for the remainder population
(Table 4.6, fifth row) with a considerable improvement in consistency of
behavior (
δ
R
decreases from 0.353 to 0.226). Using these new parame-
ters, the strength-reduction factors are recalculated (Table 4.7, last row)
and show a strength-reduction factor of 0.77 for the target reliability of
β
T
= 3.5.
Combining these two limits, the shear strength equations of ACI 440.1R-06
may be reintroduced as
(4.110)
V
5
f bc
=
′
c
c
w
V
n
=
V
c
+
V
f
≤ 4
V
c
(4 .111)
Table 4.6
Strength-reduction and statistical parameters of FRP reinforced beams
subject to shear
FRP RC
Bias (
λ
)
CoV(
δ
)
ϕ
a
β
T
V
f
= 0 (no stirrups)
0.75
3.5
1.93
0.238
No limit on
V
f
0.75
3.5
1.64
0.353
V
f
= 0 (
k
< 0.16)
0.75
3.5
1.67
0.227
V
f
> 3
V
c
0.75
3.5
1.22
0.614
V
f
≤ 3
V
c
0.75
3.5
1.80
0.226
Steel RC
Bias (
λ
)
c
CoV(
δ
)
c
ϕ
b
β
T
c
Shear
0.75
3.5
1.23
0.109
ACI 440.1R-06. ACI Committee 440. Guide for the design and construction of structural concrete
reinforced with FRP bars.
a
ACI 318-11. ACI Committee 318. Building code requirements for reinforced concrete, ACI 318-11.
American Concrete Institute, Farmington Hills, MI (2011).ACI 318-11.
b
A. S. Nowak and M. M. Szerszen.
ACI Structural Journal
100 (3): 383-391 (2003).
c
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