Civil Engineering Reference
In-Depth Information
equal to 0.2 for uncracked concrete and 0.0 for cracked concrete. Unless
more accurate information is available, the linear coefficient of thermal
expansion may be taken equal to 10
10
6
per K.
2.3.3 Creep and Shrinkage
Creep and shrinkage of the concrete depend on the ambient humidity, the
dimensions of the element, and the composition of the concrete. Creep is
also influenced by the maturity of the concrete when the load is first applied
and depends on the duration and magnitude of the loading. According to
(
t
,
t
0
), is related to
E
c
, the tangent
modulus, which may be taken as 1.05
E
cm
. The code provides charts for
determining the creep coefficient, provided that the concrete is not sub-
jected to a compressive stress greater than 0.45
f
ck
(
t
0
) at an age
t
0
, the age
of concrete at the time of loading. The creep deformation of concrete
e
cc
(
1
,
t
0
) at a time
t¼1
for a constant compressive stress
s
c
applied at the
concrete age
t
0
is given by
'
e
cc
1
,
t
0
ð
Þ¼' 1
,
t
0
ð
Þ s
c
=
ð
E
c
Þ
ð
2
:
13
Þ
When the compressive stress of concrete at an age to exceed the value
sidered. The high stress can occur as a result of pretensioning, for example, in
precast concrete members at tendon level. In such cases, the nonlinear
notional creep coefficient should be obtained as follows:
'
nl
1
,
t
0
ð
Þ¼' 1
,
t
0
ð
Þ
exp 1
½
:
5
k
s
0
ð
:
45
Þ
ð
2
:
14
Þ
where
'
nl
(
1
,
t
0
) is the nonlinear notional creep coefficient, which replaces
'
(
1
,
t
0
);
k
s
is the stress-strength ratio
s
c
/
f
ck
(
t
0
), where
s
c
is the compressive
stress; and
f
ck
(
t
0
) is the characteristic concrete compressive strength at the
time of 1oading. The values of the final creep coefficient
(
1
,
t
0
) are given
in EC2 and are valid for ambient temperatures between
40
C and +40
C
and a mean relative humidity between RH
¼
40% and RH
¼
100%. In
determining
'
(
1
,
t
0
),
t
0
is the age of the concrete at time of loading in days
and
h
0
is the notional size
¼
2
A
c
/
u
, where
A
is the concrete cross-sectional
area and
u
is the perimeter of that part that is exposed to drying.
The total shrinkage strain, according to EC2, is composed of two com-
ponents, the drying shrinkage strain and the autogenous shrinkage strain.
The drying shrinkage strain develops slowly, since it is a function of the
migration of the water through the hardened concrete. The autogenous
'
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