Flexural members - Reinforced Concrete with FRP Bars: Mechanics and Design - page 88

Conversely, the bending moment capacity for failure controlled by bond
can be computed based on the following equation:

− β

c

1 b

MAfd = (4.42)

n f e f

2

COMMENTARY

Equation (4.39) is based on the work by Wambeke and Shield [11]. They
reviewed a database of 269 beam bond tests, including beam-end tests, notch-
beam tests, and splice tests. The majority of the bars included in the study
were GFRP. A linear regression of the normalized average bond stress, u,
versus the normalized cover and embedment length was performed and
resulted in the following relationship:

u
f

C
d

d
l

b
e

4.00.3 100 (4.43)

=+ +

′ c b

By considering the free-body diagram of an FRP bar of diameter d b and area
A f,bar , embedded in concrete for a length equal to l e , the equilibrium of forces
was written as follows:

l e π d b u = A f,bar f f (4.44)

Wambeke and Shield [11], then, solved Equations (4.43) and (4.44) for the
achievable bar stress given the existing embedment length and cover obtain-
ing Equation (4.3).

ACI 440.1R-06 recommends avoiding embedment lengths shorter than
20 d b , and limiting the ratio C / d b to 3.5 to prevent pullout failure. The factor
α is generally taken equal to 1.5 for bars with more than 12 in. (305 mm)
of concrete cast below them (“top bars”), or 1.0 when the bars are in the
bottom 12 in. (305 mm) of the formwork when the concrete is cast. When
there is insufficient embedment length to develop full anchorage of a bar, a
bent bar may be used.

4.5.3 Minimum FRP reinforcement
ACI 440.1R-06 prescribes that at every section of a flexural member where
tensile reinforcement is required by analysis, A f provided should not be less
than the area given by

f ′

c

A = 4.9 bd (4.45)

w

f

f

fu