Flexural members - Reinforced Concrete with FRP Bars: Mechanics and Design - page 90

the maximum reinforcement ratio, ρ max , for an FRP-RC member in flexure
would be:

f f

E

′ 0.003

0.003

=β ′

c c

ρ= β 0.85 91.1

max 1 1

0.004 E + 0.004

f f

It should be noted that this value of ρ max cannot be physically attained in
GFRP RC flexural members as it would be impossible to it the many bars
in a cross section.

COMMENTARY
Considering a worst case scenario of low compressive strength concrete,
compute ρ max and the corresponding number of bars for a slab and a beam
using the following data:

Slab Beam

Size: Size:

b = 12.0 in.
d = 6.0 in.

b = 12.0 in.
d = 24.0 in.

Concrete:
f ′ c = 3.0 ksi
β 1 = 0.85
Reinforcement:
E f = 6,000 ksi
ρ max = 0.387
#6 = 0.44 in. 2 #9 = 1.00 in. 2

Solution: Solution:

A f = 2.78 in. 2
Or 6#6 bars which would barely fit
in the given width (clear spacing of
1.25 in.)

A f = 11.15 in. 2
Or 11#9 bars which would not fit in the
given width

4.5.5 Examples—Flexural strength
The examples presented here (US customary only) are intended to show
an application of the algorithms discussed in the preceding sections. More
exhaustive design examples are given in Chapters 6, 7, and 10 that deal
with one-way slab, beam, and isolated footing, respectively.
Design equations aim at (a) calculating the flexural strength of an existing
beam or (b) calculating design parameters such as size and reinforcement