Flexural members - Reinforced Concrete with FRP Bars: Mechanics and Design - page 101

ACI 318-11). For fiber-reinforced concrete (FRC) RC flexural members, the
relationship between reinforcing ratio and its tensile strain is

′

f
f

ε
ε+ε

c
f

cu

ρ= 0.85 1 β (4.49)

f

cu f

Therefore,

ρ
ρ

f
f

ε+ε
ε+ε

ε
ε

ε+ε
ε+ε

f fu cu fu fu cu fu

= = (4.50)

fb f cu f f cu f

And the strength-reduction factor can be reformulated as

ε
ε

ε+ε
ε+ε

fu cu fu

0.55 ≤φ= 0.30 + 0.25 ≤ 0.65 (4.51)

f cu f

The strength-reduction factor expressed by Equation (4.51) is calibrated
by targeting a level of reliability of at least 3.5. This target reliability,
however, is not always obtainable even by ordinary steel RC flexural
members [13].

4.6.2 New approach
An attempt by Jawaheri Zadeh and Nanni [14] to equalize the reliability
indices of the two member types (steel RC vs. FRP RC) leads to ϕ with a
lower limit of 0.70 (instead of 0.55) and an upper limit of 0.75 (instead of
0.65). Based on a conservative interpretation of these values, a new ϕ may
be formulated as

ε
ε

f

(4.52)

0.65 ≤φ= 1.15 − ≤ 0.75

2

fu

It should be noted that ACI 318-11 also imposes a strength-reduction fac-
tor of ϕ = 0.65 on compression-controlled sections, which is lower than the
value (0.75) proposed by Equation (4.52). Nevertheless, a reliability-based
calibration of the strength-reduction factors of steel RC members [13] con-
firms the adequacy of ϕ = 0.75. Figure 4.10 compares the two ϕ-factors
(Equation 4.51 vs. Equation 4.52) for different levels of maximum tensile
strain if ε fu = 0.01.
In the design examples presented in Chapters 6-8 and 10, the values
of ϕ M n computed according to both methods (i.e., ACI 440.1R-06 and
Jawaheri Zadeh and Nanni [14]) are shown.