Flexural members - Reinforced Concrete with FRP Bars: Mechanics and Design - page 102

0.80
φ

Jawaheri Zadeh and Nanni (2013)

0.75

0.70

ACI 440.1R-06

0.65

0.60

0.55

ε fd

0.50

0.006 0.007 0.008 0.009 0.010

Figure 4.10 Comparison of the strength-reduction factors ( ε fu = 0.01).

4.6.3 Examples—Flexural strength-reduction factor
Example 4.12

Calculate the strength reduction factors and the ultimate strength of
the cross sections in Examples 4.1-4.4.

Solution:

Equation (4.52) can be rewritten in terms of f, the stress level in FRP
reinforcement, as 0.65 ≤ ϕ = 1.15- f /2 ≤ 0.75.

Example Stress level ϕ - factor Design strength

1: f = 0.862 ϕ = 0.719 ϕ M n = 308.3 ft-kip

2: f = 0.946 ϕ = 0.678 ϕ M n = 323.3 ft-kip

3: f = 1 ϕ = 0.65 ϕ M nb = 252.3 ft-kip

4: f = 1 ϕ = 0.65 ϕ M n = 170.7 ft-kip

COMMENTARY

Validation of strength-reduction factors can be attained by the reliability
analysis that links the probability of failure to the load and safety factors,
providing a basis for their calibration to achieve desired levels of safety.
Conventionally, the reliability index is defined as an indicator of the prob-
ability of failure of a member with a resistance of R against the loads it may
experience during its lifetime, Q, with both Q and R being random variables.