Design of a two-way slab - Reinforced Concrete with FRP Bars: Mechanics and Design - page 314

σ⋅ ε

(x,y)

c

2"

c

x

ε

∫

c0

C(x): = psidy

c

2

ε (x,y)

0in

c

1+

ε

c0

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

T f (x) := A f ·E f ·ε f (x)

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

x 0 := 0.1 min(d f1 ,d f2 )

Given:

f 0 (x) := C c (x) - T f (x)

C u := root(f 0 (x 0 ),x 0 )

The neutral axis depth is

cu = 0.953·in.

The nominal bending moment capacity per unit width can be computed
as follows:

( )

⋅ ε

c,y

cu

2" ⋅σ

c

ε

c

ft kip
ft

⋅

u

( )

∫

c0

()

( )

m:=y ⋅ psidy+Tc ⋅ mind ,d − c =19 ⋅

n f u f1 f2 u

2

( )

0

ε c,y

cu

1+

ε

c0

The strain distribution over the cross section is shown next.