Civil Engineering Reference
In-Depth Information
6
ƒ
c
′= 6
ƒ
c
′= 5
5
ƒ
c
′= 4
4
ƒ
c
′= 3
3
ƒ
c
′= 2
2
ƒ
c
′= 1
1
0
0.001
0.002
0.003
0.004
strain
Figure 1.1
Typical concrete stress-strain curve, with short-term loading.
(d)
Concrete does not have a definite yield strength; rather, the curves run smoothly on
to the point of rupture at strains of from 0.003 to 0.004. It will be assumed for the
purpose of future calculations in this text that concrete fails at 0.003.
The reader
should note that this value, which is conservative for normal-strength concretes, may
not be conservative for higher-strength concretes in the 8000-psi-and-above range.
(e)
Many tests have clearly shown that stress-strain curves of concrete cylinders are
almost identical to those for the compression sides of beams.
(f)
It should be further noticed that the weaker grades of concrete are less brittle than
the stronger ones—that is, they will take larger strains before breaking.
Static Modulus of Elasticity
Concrete has no clear-cut modulus of elasticity. Its value varies with different concrete
strengths, concrete age, type of loading, and the characteristics and proportions of the ce-
ment and aggregates. Furthermore, there are several different definitions of the modulus:
(a)
The
initial modulus
is the slope of the stress-strain diagram at the origin of the
curve.
(b)
The
tangent modulus
is the slope of a tangent to the curve at some point along
the curve—for instance, at 50% of the ultimate strength of the concrete.
(c)
The slope of a line drawn from the origin to a point on the curve somewhere be-
tween 25 and 50% of its ultimate compressive strength is referred to as a
secant
modulus
.
(d)
Another modulus, called the
apparent modulus
or the
long-term modulus
, is de-
termined by using the stresses and strains obtained after the load has been ap-
plied for a certain length of time.
