Design of a T-beam - Reinforced Concrete with FRP Bars: Mechanics and Design - page 257

This reinforcement ratio corresponds to an area of

A f _ des1 := ρ f _ des1 ∙b w ∙d f1 = 3.109∙in. 2

The required number of bars is

A
A

f_des1

N: = =3.958

f_des1

f_bar

As discussed in Chapter 4, the failure mode depends on the amount of
FRP reinforcement. If ρ f is larger than the balanced reinforcement ratio, ρ fb ,
then concrete crushing is the failure mode. If ρ f is smaller than the balanced
reinforcement ratio, ρ fb , then FRP rupture is the failure mode.
Equation (8-3) of ACI 440.1R-06:

f'
f

E ⋅ε

c f cu

ρ :0.85 = β ⋅ ⋅ =0.0126

1

fb1

E ⋅ε ⋅ +f

fu f cu fu

The selected reinforcement ratio is smaller than the ratio corresponding
to the balanced conditions, as shown:

ρ
ρ

fb1

=1.476

f_des1

The following number of FRP bars is selected:

N bar1 := 4

A f1 := N bar1 ∙A f _ bar = 3.142∙in 2

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

A
bd =0.00863

f1

ρ : =

f1

⋅

w f1

FRP bar spacing: The clear bar spacing is

bN − c in

N1

⋅ φ−−
−

eff bar1f_bar c

s : = = 19.167 in. ⋅

f10_clear

bar1

The clear bar spacing is taken equal to

s f1 _ clear := 3 in.

The minimum required bar spacing is

s f _ min1 := max(1∙in, ϕ f _ bar ) = 1∙in.