Flexural members - Reinforced Concrete with FRP Bars: Mechanics and Design - page 113

4.9.1 Control of crack width
Crack width in FRP reinforced concrete is generally limited for aesthetic
reasons and to prevent water leakage. Differently from the case of steel
reinforced concrete, crack width limitations related to the potential corro-
sion of the reinforcement are not required for FRP reinforced concrete. ACI
440.1R-06 recommends the following limiting values: 0.020 in. (0.5 mm) for
exterior exposure and 0.028 in. (0.7 mm) for interior exposure. More strin-
gent crack width limits might be considered for the design of liquid-retaining
structures.
The maximum crack width at the tension face of a flexural member, w c , may
be computed by Equation (4.66), which is based on the work of Frosch [23]:

2

f
E

s

+

f

2

w = 2 β kd (4.66)

c b c

2

f

where f f is the reinforcement stress, d c is the thickness of cover from tension
face to center of closest bar, s is the bar spacing, β is the ratio between the dis-
tance from the neutral axis to the tension face of the member and the distance
from the neutral axis to the centroid of the tensile reinforcement, and k b is a
bond coefficient that accounts for the bond characteristics of the reinforce-
ment. Frosch's equation [23] is written in a more general fashion than Equation
(4.66), so that it can be applied regardless of whether the reinforcement is steel
or FRP. For the case of FRP reinforced concrete, Frosch's original equation
is modified by including the bond coefficient k b . k b varies between 0.60 and
1.70 and depends on the FRP bar manufacturer, the fiber type, the resin for-
mulations, and the surface treatments. Sand-coated bar surface treatments
generally trend toward the lower bound of this range. ACI 440.1R-06 con-
servatively recommends the value of 1.4 when k b is not based on experiments.

COMMENTARY

Reviewing the work of Broms [24], Frosch [23] had noted that the crack spac-
ing, S c , depends on the concrete cover and can be written as follows:

S c = Ψ s d * (4.67)

2

s
2

+

2

where d * =

is the controlling cover distance and ψ s is the crack
spacing factor, which was assumed equal to 1.0 for minimum crack spacing,
1.5 for average crack spacing, and 2.0 for maximum crack spacing.

d c