Design of a T-beam - Reinforced Concrete with FRP Bars: Mechanics and Design - page 255

FRP ultimate design properties: The ultimate design properties are
calculated per Section 7.2 of ACI 440.1R-06:

f fu := C E ∙f fuu = 64∙ksi Design tensile strength

ε fu = C E ∙ε fuu = 0.0112 Design rupture strain

FRP creep-rupture limit stress: The FRP creep-rupture limit stress is
calculated per Section 8.4 of ACI 440.1R-06:

f f _ creep := k creep _ R ∙f fu = 12.8∙ksi

7.6.1 Case 1—Exterior support
Reinforcement required to resist bending moments: As discussed in Chapter 4,
the following design condition shall be satisfied: ϕM n > M u . When the failure
is due to concrete crushing: φ=φ

− β

1

MAfd c.

Considering the lower

n ffuf u

2

bound condition (ϕM n = M u ) and solving for A f , the following can be written:

− β

1

A = M φ Af d c = › u u

f—req—bend ffuf

2

− β

1

=ρ › = A bd = MAfd φ cbd u u

f—req—bend f—req—bend f ffuf f

2

Assuming a ϕ-factor of 0.65 and a neutral axis depth equal to 15% of the
effective reinforcement depth, the longitudinal reinforcement ratio required
for bending, ρ f _ req _ bend , can be estimated. The effective reinforcement depth is

−− φ

f_bar

d:hc = in.f1 ⋅

c

f1

2

The longitudinal reinforcement ratio required for bending is

M 1

bd =0.00472

u1

ρ : = ⋅

f_req_bend1

− β

⋅

1 w f1

0.65 f ⋅ ⋅ d 2 ⋅ 0.15d

fu f1 f1

The minimum reinforcement requirement has to be verified. Equation
(8-8) of ACI 440.1R-06 is used. If the failure is not governed by FRP rup-
ture, this requirement is automatically achieved:

4.9fpsi
f

⋅ ′ ⋅

bd, 300psi
f

( )

c

2

A: = f_min1 ⋅ bd ⋅ =1.706 in ⋅

w w

f_min1 f1 f1

fu fu

A
bd =0.004687

f_min1

ρ : =

f_min1

⋅

w f1