Civil Engineering Reference
In-Depth Information
In 1968 the following equation was developed for the purpose of estimating the max-
imum widths of cracks that will occur in the tension faces of flexural members.
9
It is
merely a simplification of the many variables affecting crack sizes.
3
w
0.076
h
f
s
d
c
A
where
w
the estimated cracking width in thousandths of inches
h
ratio of the distance to the neutral axis from the extreme tension concrete
fiber to the distance from the neutral axis to the centroid of the tensile steel
(values to be determined by the working-stress method)
f
s
steel stress, in kips per square inch at service loads (designer is permitted to
use 0.6
f
y
for normal structures)
d
c
the cover of the outermost bar measured from the extreme tension fiber to
the center of the closest bar or wire. (For bundled bars
d
c
is measured to
the c.g. of the bundles.)
A
the effective tension area of concrete around the main reinforcing (having
the same centroid as the reinforcing) divided by the number of bars
This expression is referred to as the Gergely-Lutz equation after its developers. In ap-
plying it to beams, reasonable results are usually obtained if
h
is set equal to 1.20. For
thin one-way slabs, however, more realistic values are obtained if
h
is set equal to 1.35.
The number of reinforcing bars present in a particular member decidedly affects the
value of
A
to be used in the equation and thus the calculated crack width. If more and
smaller bars are used to provide the necessary area, the value of
A
will be smaller, as will
the estimated crack widths.
Should all the bars in a particular group not be the same size, their number (for use in
the equation) should be considered to equal the total reinforcing steel area actually pro-
vided in the group divided by the area of the largest bar size used.
Example 6.3 illustrates the determination of the estimated crack widths occurring in a
tensilely reinforced rectangular beam.
EXAMPLE 6.3
Assuming
h
1.20 and
f
y
60 ksi, calculate the estimated width of flexural cracks that will occur
in the beam of Figure 6.13. If the beam is to be exposed to moist air, is this width satisfactory as
compared to the values given in Table 6.3 of this chapter? Should the cracks be too wide, revise the
design of the reinforcing and recompute the crack width.
SOLUTION
Substituting into the Gergely-Lutz equation
6
16
3
3
w
(0.076)(1.20)(0.6
60)
(3)
15.03
1000
0.015 in.
0.012 in.
N.G.
9
Gergely, P., and Lutz, L. A., 1968, “Maximum Crack Width in Reinforced Flexural Members,”
Causes,
Mechanisms and Control of Cracking in Concrete
, SP-20 (Detroit: American Concrete Institute), pp. 87-117.
