Flexural members - Reinforced Concrete with FRP Bars: Mechanics and Design - page 118

For the case of a beam continuous only at one end, the following expres-
sion can be used:

I e, ave = 0.85 I e. midspan + 0.15 I e, sup1 (4.76)

Effective moment of inertia for FRP RC. For FRP reinforced members,
Branson's equation is adapted by including the reduction coefficient β d as
the multiplier of the first term in Equation (4.74). β d is expressed by

ρ
ρ

1
5

f

≤

β= 1.0 (4.77)

d

fb

β d is a reduction coefficient related to the reduced tension stiffening of FRP
when compared to steel reinforcement. This reduced tension stiffening can
be attributed to the lower modulus of elasticity and different bond stresses
for the FRP reinforcement as compared with those of steel.
The expression of the effective average moment of inertia for the flex-
ural member, I e,av , computed for traditional steel RC is also applicable to
FRP RC.

COMMENTARY

With reference to the continuous T-beam in Figure 4.12, the gross moment
of inertia can be computed as follows (Figure 4.14a):

3 2

( )

3

bt t b ht −

2

eff lab slab w slab

( ) ( )

I bt d bht d ht

= + − + + − −−

g eff lab g w slab g slab

12 2 12

(4.78)

When the cracked section in the negative moment region is considered,
such as Section A-A of the T-beam in Figure 4.12, the neutral axis depth
intersects the web of the beam and its depth from the bottom of the
section can be computed using Equation (4.8). The cracked moment of
inertia (see Figure 4.14b) can then be computed as

3

( )

b d w f 2

( )

I

= +

nAd 1

−

k (4.79) cr f f f

3

When the cracked section at midspan is analyzed, such as Section B-B of
the T-beam in Figure 4.12, the section can be studied as rectangular if the
cracked neutral axis depth falls within the depth of the flange. This occurs