Structural Concrete - Hassoun

6.6 Cracks in Flexural Members 245
the concrete surface, corroding the steel reinforcement [11]. The oxide compounds formed by
deterioration of steel bars occupy a larger volume than the steel and exert mechanical pressure
that perpetuates extensive cracking [12, 13]. This type of cracking may be severe enough to result
in eventual failure of the structure. The failure of a roof in Muskegan, Michigan, in 1955 due to
the corrosion of steel bars was reported by Shermer [13]. The extensive cracking and spalling
of concrete in the San Mateo–Hayward Bridge in California within 7 years was reported by
Stratful [12]. Corrosion cracking may be forestalled by using proper construction methods and
high-quality concrete. More details are discussed by Evans [14] and Mozer and others [15].
6.6.2 Main Cracks
Main cracks develop at a later stage than secondary cracks. They are caused by the difference in
strains in steel and concrete at the section considered. The behavior of main cracks changes at two
different stages. At low tensile stresses in steel bars, the number of cracks increases, whereas the
widths of cracks remain small; as tensile stresses are increased, an equilibrium stage is reached.
When stresses are further increased, the second stage of cracking develops, and crack widths
increase without any significant increase in the number of cracks. Usually one or two cracks start
to widen more than the others, forming critical cracks (Fig. 6.7).
Main cracks in beams and axially tensioned members have been studied by many investigators;
prediction of the width of cracks and crack control were among the problems studied. These
are discussed here, along with the requirements of the ACI Code.
Crack Width. Crack width and crack spacing, according to existing crack theories, depend on
many factors, which include steel percentage, its distribution in the concrete section, steel flexural
stress at service load, concrete cover, and properties of the concrete constituents. Different
equations for predicting the width and spacing of cracks in reinforced concrete members were presented
at the Symposium on Bond and Crack Formation in Reinforced Concrete in Stockholm,
Sweden, in 1957. Chi and Kirstein [16] presented equations for the crack width and spacing as a
function of an effective area of concrete around the steel bar: A concrete circular area of diameter
equal to four times the diameter of the bar was used to calculate crack width. Other equations were
presented over the next decade [17–23].
Gergely and Lutz [23] presented the following formula for the limiting crack width:
√
3
W = 0.076βf s Adc × 10 −6 (in.) (6.15)
where β, A, andf s are as defined previously and d c is the thickness of concrete cover measured
from the extreme tension fiber to the center of the closest bar. The value of β canbetakentobe
approximately equal to 1.2 for beams and 1.35 for slabs. Note that f s is in psi and W is in inches.
The mean ratio of maximum crack width to average crack width was found to vary between
1.5 and 2.0, as reported by many investigators. An average value of 1.75 may be used.
In SI units (mm and MPa), Eq. 6.15 is
√
3
W = 11.0βf s Adc × 10 −6 (6.16)
Tolerable Crack Width. The formation of cracks in reinforced concrete members is unavoidable.
Hairline cracks occur even in carefully designed and constructed structures. Cracks are usually measured
at the face of the concrete, but actually they are related to crack width at the steel level, where
corrosion is expected. The permissible crack width is also influenced by aesthetic and appearance
requirements. The naked eye can detect a crack about 0.006 in. (0.15 mm) wide, depending on the
surface texture of concrete. Different values for permissible crack width at the steel level have been