Design of a one-way slab - Reinforced Concrete with FRP Bars: Mechanics and Design - page 240

Nigro et al. propose the following equation to estimate the ultimate
strength of the end anchorage in a zone with a temperature of at least 50
degrees Celsius.

l − l

d f_50C

f := ksi=456.8ksi ⋅

f_50C

0.1 ⋅φ

f_bar

Step E. Estimate the maximum bar stress.
The maximum usable FRP bar stress can be computed as the smaller of
the tensile strength at a temperature Tf f (computed in Step A) and the end
anchorage strength at 50 degrees Celsius.

f f_fire := min(ρfT fT ⋅ f fu ,f f_50C ) = 9⋅ksi

The reduced FRP tensile modulus of elasticity can be computed as fol-
lows using the reduction factor computed in Step B.

E f_fire := ρ ET ⋅ E f = 468⋅ksi

The ultimate FRP tensile strain can, therefore, be computed as follows.

f
E

f_fire

ε := = 0.02

f_fire

f_fire

Step F. Compute the reduced bending moment capacity at a fire exposure
time of 120 min.
The following stress - strain relationship is assumed for the concrete in
compression:

ε

c

3 ⋅

0.0025

f ′ ⋅ if ε≤ 0.0025

c c

3

ε

()

c

σε := 2 + c

c_fire

0.0025

0.02
0.02

−ε

c

f

′ ⋅

if 0.0025 ≤ε ∧ε ≤ 0.02

c c c

− 0.0025

The FRP design properties are substituted with the reduced FRP proper-
ties estimated in Step E. It is assumed that the failure is controlled by the
FRP failure.
The effective concrete compressive strain at failure as a function of the
neutral axis depth, x, is:

ε

f_fire

ε (x,y):= dx y ⋅

c2_fire

−

f2