Civil Engineering Reference
In-Depth Information
Curling can be reduced or eliminated by using design
and construction techniques that minimize shrinkage dif-
ferentials and by using techniques described earlier to
reduce temperature and moisture-related volume changes.
Thickened edges, shorter joint spacings, permanent vapor-
impermeable sealers, and large amounts of reinforcing
steel placed 50 mm (2 in.) below the surface all help reduce
curling (
Ytterberg 1987
).
Inelastic
deformation
f
f
Modulus of elasticity = E =
ELASTIC AND INELASTIC DEFORMATION
Compression Strain
The series of curves in Fig. 15-22 illustrate the amount of
compressive stress and strain that results instantaneously
due to loading of unreinforced concrete. With water-cement
ratios of 0.50 or less and strains up to 1500 millionths, the
upper three curves show that strain is closely proportional
to stress; in other words, the concrete is almost elastic. The
upper portions of the curves and beyond show that the con-
crete is inelastic. The curves for high-strength concrete have
sharp peaks, whereas those for lower-strength concretes
have long and relatively flat peaks. Fig. 15-22 also shows
the sudden failure characteristics of higher strength, low
water to cement ratio, concrete cylinders.
When load is removed from concrete in the inelastic
zone, the recovery line usually is not parallel to the orig-
inal line for the first load application. Therefore, the
amount of permanent set may differ from the amount of
inelastic deformation (Fig. 15-23).
Strain,
Permanent set
Fig. 15-23. Generalized stress-strain curve for concrete.
The term “elastic” is not favored for general discus-
sion of concrete behavior because frequently the strain
may be in the inelastic range. For this reason, the term
“instantaneous strain” is often used.
Modulus of Elasticity
The ratio of stress to strain in the elastic range of a stress-
strain curve for concrete defines the modulus of elasticity
(
E
) of that concrete (Fig. 15-23). Normal-density concrete
has a modulus of elasticity of 14,000 to 41,000 MPa
60
Water-to-cement ratio:
8
0.33
50
0.40
P
6
40
0.50
30
4
150 mm
(6 in.)
20
0.67
2
10
1.00
0
1000
2000
3000
4000
5000
Strain-concentric compression tests, millionths
Fig. 15-22. Stress-strain curves for compression tests on 150
300-mm (6
12-in.) concrete cylinders at an age of 28 days
(
Hognestad, Hanson, and McHenry 1955
).
