Design of a T-beam - Reinforced Concrete with FRP Bars: Mechanics and Design - page 267

The ratio of depth of neutral axis to reinforcement depth, kf, f , can be writ-
ten as a function of the reinforcement ratio, ρ f_creep :

( ) ( )

2

k ρ : = 2 ⋅ρ ⋅ n +ρ⋅ n −ρ ⋅ n

f_creep2f_creep f_creep f f_creep f f_creep f

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

M

( )

2_creep0

f ρ : =

( )

f2_creep0f_creep

k ρ

f_creep2f_creep

ρ⋅ Ad 1 ⋅ ⋅ −

c2

f_creep f2

3

Solving for ρ f_creep :
First guess:

ρ f_creep20 := 0.002

Given:

f ρ2 (ρ f_creep ) := f (ff_creep) (ρ f_creep ) - (f f_creep )

ρ f_creep2 := root(f ρ2 (ρ f_creep20 ), ρ f_creep20 )

The reinforcement ratio required for creep-rupture is

ρ f_creep2 := 0.0071

FRP longitudinal reinforcement design: The design reinforcement ratio
can be selected as the maximum between ρ f_bend and ρ f_creep :

ρ f_creep2 := max(ρ f_bend2, ρ f_creep2 ) = 0.0071

This reinforcement ratio corresponds to an area of

A f_des1 := ρ f_des2 ·A c2 = 5.411·in. 2

The required number of bars is

A
A

f_des2

N: = = 6.889

f_des2

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.