Design of a one-way slab - Reinforced Concrete with FRP Bars: Mechanics and Design - page 206

Similarly, the effective tensile strain in the FRP reinforcement can be
computed as a function of the neutral axis depth, x:

ε if ρρ

ε

<

fu f1 fb1

ε (x):= if ρ≥ρ

)

f1

(

f1 fb1

cu

min ⋅ dx, −ε

f1 fu

x

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

ε (x,y)

c1

2" ⋅σ ⋅

c

ε

∫

x

c0

C x) := b ⋅ psidy

c1

2

0in

ε (x,y)

c1

1 +

ε

c0

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

T f1 (x) := A f1 ∙E f ∙ε f1 (x)

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

x 01 := 0.1d f1

Given:

f 1 (x) := C c1 (x) - T f1 (x)

c u1 := root (f 1 (x 01 ),x 01 )

The neutral axis depth is

c u1 = 0.86∙in.

The nominal bending moment capacity can be computed as follows:

⋅ ε

(c ,y)

c1 u1

2" ⋅σ

c

c u1

ε

∫

() ( )

c0

M =b ⋅ y ⋅ psidy+Tc ⋅ dc 17 ft kip − =⋅ ⋅

n1 f1 u1 f1 u1

( )

2

ε c y

0

c1 u1

1 +

ε

c0