Design of square footing for a single column - Reinforced Concrete with FRP Bars: Mechanics and Design - page 377

Based on cross-section compatibility, the effective concrete compressive
strain at failure can be computed as a function of the neutral axis depth, x:

ε if ρ ≥ρ

cu f fb

ε (x): =

c

ε

u

⋅ x f ρ <ρ

f fb

d-x

f

Based on cross-section compatibility, the effective tensile strain in the
FRP reinforcement can be computed as a function of the neutral axis
depth, x:

ε if ρ<ρ

fu f fb

ε (x): =

ε

f

( )

cu

min ⋅ d-x, ε if ρ≥ρ

f fu f fb

x

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

ε (x)

c

2" ⋅σ ⋅

c

x

ε

∫

c0

C(x):b =. psidx ompressive forceinthe concrete

c

2

ε (x)

0in

c

1+

ε

c0

The tensile force in the 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 01 := 0.1d f

Given:

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

c u := root(f o (x 01 ),x 01 )

The neutral axis depth is

c u = 3.314·in.