Design of a one-way slab - Reinforced Concrete with FRP Bars: Mechanics and Design - page 213

The FRP reinforcement ratio (Equation 8-2 of ACI 440.1R-06) is

A
bd

f2

ρ= ⋅ : = 0.00467

f2

f2

Design flexural strength (Equation 8-3 of ACI 440.1R-06):

β ⋅ ′

f
f

E ⋅ε

f cu
f cu fu
The effective concrete compressive strain at failure as a function of the
neutral axis depth, x, is

c

ρ= :0.85 ⋅ = 0.00748

fb2 1

E ⋅ε + f

fu

ε

cu

⋅ yif ρ≥ρ

f2 fb2

x

( )

ε x, y: =

c2

ε

fu

dx yif

⋅ ρ<ρ

f2 fb2

−

f2

The effective tensile strain in the first layer of FRP reinforcement as a
function of the neutral axis depth, x, is

ερ<ρ if

fu f2 fb2

()

ε x: =

ε

f2

( )

cu

min ⋅ dx, −ε if ρ≥ρ

f2 fu f2 fb2

x

The compressive force in the concrete as a function of the neutral axis
depth, x, is

( )

ε x, y

c2

2" ⋅σ ⋅

c

ε

x

∫

c0

() =⋅

Cx:b psidy

c2

2

( )

ε x, y

0in

c2

1 +

ε

c0

The tensile force in the first layer of FRP reinforcement as a function of
the neutral axis depth, x, is

T f2 (x) := A f2 ∙ E f ∙ ε f2 (x)

The neutral axis depth, cu, can be computed by solving the equation of
equilibrium C c - T f = 0:

Given: f 2 (x) := C c2 (x) - T f2 (x)