Flexural members - Reinforced Concrete with FRP Bars: Mechanics and Design - page 72

4.2.3 Cross-sectional properties
The analysis of a reinforced concrete frame should reflect the potential for
cracking and inelastic action for each member. However, this approach would
require selecting different stiffnesses for all members. For this reason, when
analyzing concrete frames, the gross sectional properties are generally used.
Transformed section. The elastic-beam theory of de Saint-Venant can
be applied to FRP reinforced concrete mechanics only if the FRP concrete
section is transformed to an all-concrete section (this is generally preferred
to an all-FRP section) [1]. In fact, an area of FRP bars equal to A f can
be considered equivalent to an area of concrete equal to n f A f , where the
modular ratio, n f , is equal to

E
E

f

n = (4.7)

f

c

When computing the neutral axis depth below the top fiber of the cross-
section, c g , of uncracked reinforced concrete, the contribution of the FRP
reinforcement can, generally, be neglected. In this case, the neutral axis
intersects the geometrical centroid of the gross section.
In a cracked section, the neutral axis intersects the mechanical centroid
of the section. For a rectangular cross section, the cracked neutral axis
depth, c cr , can be computed as follows:

( )

( )

2

c d ==ρ+ρ 2 n n − ρ⋅ n d (4.8)

cr f f f f f f f f

where ρ f is the FRP reinforcement ratio and d f is the effective depth of the
FRP reinforcement.
T-sections. A T-beam section is generally considered when a beam is
built integrally with the slab. ACI 318-11 defines the effective width of the
slab, b eff , acting as a T-beam flange as the minimum of: (a) one-quarter of
the beam span length, (b) eight times the slab thickness, or (c) one-half the
clear distance to the next beam.
For a spandrel beam (or reverse L-beam), ACI 318-11 mandates the effec-
tive flange width, b eff , not to exceed: (a) 1/12 of the beam span length, (b) six
times the slab thickness, or (c) half the clear distance to the next beam.

COMMENTARY

Equation (4.8) can be used for T-sections when the cracked neutral axis is
included within the slab thickness, t slab , which occurs when the following con-
dition applies:

t

2

slab

b nAdt ( )

≥ −

(4.9)

eff f f f slab

2