Civil Engineering Reference
In-Depth Information
Steel reinforcing
bars
400 mm
F
IGURE
7.18
Reinforced concrete
column of Ex. 7.5
400 mm
The total cross-sectional area,
A
S
, of the steel reinforcement is
π
4
×
20
2
1257mm
2
A
S
=
4
×
=
The cross-sectional area,
A
C
, of the concrete is reduced due to the presence of the
steel and is given by
400
2
158 743mm
2
A
C
=
−
1257
=
Equations (7.38) then give
10
3
200 000
×
1000
×
76
.
0N
/
mm
2
σ
S
=
200 000
=
158 743
×
15 000
+
1257
×
10
3
15 000
×
1000
×
5
.
7N
/
mm
2
σ
C
=
200 000
=
158 743
×
15 000
+
1257
×
The deflection,
δ
, of the column is obtained using either side of Eq. (7.40). Thus
10
3
σ
C
L
E
C
=
5
.
7
×
5
×
δ =
=
1
.
9mm
15 000
THERMAL EFFECTS
It is possible for stresses to be induced by temperature changes in composite members
which are additional to those produced by applied loads. These stresses arise when
the components of a composite member have different rates of thermal expansion and
contraction.
First, let us consider a member subjected to a uniform temperature rise,
T
, along its
length. The member expands from its original length,
L
0
, to a length,
L
T
, given by
L
T
=
L
0
(1
+
α
T
)
where
α
is the coefficient of linear expansion of the material of the member. In the
condition shown in Fig. 7.19 the member has been allowed to expand freely so that no
stresses are induced. The increase in the length of the member is then
L
T
−
L
0
=
L
0
α
T
