Design of a T-beam - Reinforced Concrete with FRP Bars: Mechanics and Design - page 276

The tensile stress in the FRP can also be expressed as a function of the
reinforcement ratio, ρ f _ creep :

M

( )

3_creep0

f ρ : =

( )

f3_creep0f_creep

k ρ

f_creep3f_creep

ρ⋅ bd 1 ⋅

2

⋅ −

w

f_creep f3

3

Solving for ρ f _ creep :

ρ f _ creep0 = 0.002

Given:

fρ 3 (ρ f _ creep ) := f f3 _ creep0 (ρ f _ creep ) - (f f _ creep )

ρ f _ creep3 := root(fρ 3 (ρ f _ creep0 ), ρ f _ creep0 )

The reinforcement ratio required for creep rupture is

ρ f _ creep3 := 0.021

FRP longitudinal reinforcement design: The design reinforcement ratio
can be selected as the maximum between ρ f _ bend and ρ f _ creep :

ρ f _ des3 := max(ρ f _ bend3 , ρ f _ creep3 ) = 0.021

This reinforcement ratio corresponds to an area of

A f _ des3 := ρ f _ des3 ·b w ·d f3 = 7.646·in. 2

The required number is

A
A

f_des3

N: = = 9.735

f_des3

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 is

β ⋅ ′

f
f

E ⋅ε

⋅ε

c f cu

ρ :0.85 = ⋅ = 0.0126

1

fb3

E + f

fu f cu fu

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

ρ
ρ

fb3
f_des3

= 0.6