Civil Engineering Reference
In-Depth Information
80
70
28-day strength
Moist cured cylinders
10000
60
8000
50
6000
40
30
4000
20
2000
10
0
0
0.25
0.35
0.45
0.55
0.65
0.75
0.85
Water-cement ratio
Fig. 1-18. Testing a 150 x 300-mm (6 x 12-in.) concrete
cylinder in compression. The load on the test cylinder is
registered on the display. (68959)
Fig. 1-17. Range of typical strength to water-cement ratio
relationships of portland cement concrete based on over
100 different concrete mixtures cast between 1985 and 1999.
The torsional strength for concrete is related to the
modulus of rupture and the dimensions of the concrete
element.
Hsu (1968)
presents torsional strength correlations.
Shear strength-compressive strength relationships are
discussed in the ACI 318 building code. The correlation
between compressive strength and flexural, tensile,
torsional, and shear strength varies with concrete ingredi-
ents and environment.
Modulus of elasticity, denoted by the symbol
E
, may
be defined as the ratio of normal stress to corresponding
strain for tensile or compressive stresses below the propor-
tional limit of a material. For normal-weight concrete,
E
ranges from 14,000 to 41,000 MPa (2 to 6 million psi) and
can be approximated as 5,000 times the square root of the
compressive strength in megapascals (57,000 times the
square root of the compressive strength in pounds per
square inch). Like other strength relationships, the modu-
lus of elasticity to compressive strength relationship is mix-
ingredient specific and should be verified in a laboratory
(
Wood 1992
).
To determine compressive strength, tests are made on
specimens of mortar or concrete; in the United States,
unless otherwise specified, compression tests of mortar are
made on 50-mm (2-in.) cubes, while compression tests of
concrete are made on cylinders 150 mm (6 in.) in diameter
and 300 mm (12 in.) high (see Fig. 1-18). Smaller cylinders,
100 x 200 mm (4 x 8 in.) are also used for concrete.
Compressive strength of concrete is a primary physical
property and frequently used in design calculations for
bridges, buildings, and other structures. Most general-use
concrete has a compressive strength between 20 and 40
MPa (3000 and 6000 psi). Compressive strengths of 70 to
140 MPa (10,000 to 20,000 psi) have been used in special
bridge and high-rise building applications.
The flexural strength or modulus of rupture of
concrete is used to design pavements and other slabs on
ground. Compressive strength, which is easier to measure
than flexural strength, can be used as an index of flexural
strength, once the empirical relationship between them has
been established for the materials and the size of the
element involved. The flexural strength of normal-weight
concrete is often approximated as 0.7 to 0.8 times the square
root of the compressive strength in megapascals (7.5 to 10
times the square root of the compressive strength in
pounds per square inch).
Wood (1992)
illustrates the rela-
tionship between flexural strength and compressive
strength for concretes exposed to moist curing, air curing,
and outdoor exposure.
The direct tensile strength of concrete is about 8% to
12% of the compressive strength and is often estimated as
0.4 to 0.7 times the square root of the compressive strength
in megapascals (5 to 7.5 times the square root of the
compressive strength in pounds per square inch). Splitting
tensile strength is 8% to 14% of the compressive strength
(Hanson 1968)
. Splitting tensile strength versus time is
presented by
Lange (1994)
.
Density
Conventional concrete, normally used in pavements, build-
ings, and other structures, has a density (unit weight) in the
range of 2200 to 2400 kg/m
3
(137 to 150 lb/ft
3
). The density
of concrete varies, depending on the amount and density of
the aggregate, the amount of air that is entrapped or pur-
posely entrained, and the water and cement contents,
which in turn are influenced by the maximum size of the
aggregate. Reducing the cement paste content (increasing
aggregate volume) increases density. Values of the density
of fresh concrete are given in Table 1-1. In the design of re-
inforced concrete structures, the combination of conven-
tional concrete and reinforcing steel is commonly assumed
to weigh 2400 kg/m
3
(150 lb/ft
3
).
