Civil Engineering Reference
In-Depth Information
steel in compression is
A
sc
, we have, equating compressive and tensile forces
0
.
4
σ
cu
bh
c
+
2
×
(0
.
87
σ
Y
)
A
sc
=
0
.
87
σ
Y
A
s
(12.30)
which gives
A
sc
and hence
h
sc
. Now taking moments
0
.
87
σ
Y
A
s
d
(0
.
87
σ
Y
)
A
sc
h
sc
−
h
c
2
h
c
2
M
u
=
−
−
2
×
(12.31)
E
XAMPLE
12.11
A concrete slab 150mm thick is 1.8mwide and is to be supported
by a steel beam. The total depth of the steel/concrete composite beam is limited to
562mm. Find a suitable beam section if the composite beam is required to resist a
bending moment of 709 kNm. Take
σ
cu
=
30N
/
mm
2
and
σ
Y
=
350N
/
mm
2
.
Using Eq. (12.27)
10
6
2
×
709
×
8286mm
2
A
s
=
562
=
0
.
87
×
350
×
The tensile force in the steel is then
10
−
3
0
.
87
×
350
×
8286
×
=
2523 kN
and the compressive force in the concrete is
10
3
10
−
3
0
.
4
×
1
.
8
×
×
150
×
30
×
=
3240 kN
The neutral axis therefore lies within the concrete slab so that the area of steel in
tension is, in fact, equal to
A
s
. From Steel Tables we see that a Universal Beam of
nominal size 406mm
×
×
67 kg/m has an actual overall depth of 412mm and
a cross-sectional area of 8530mm
2
. The position of the neutral axis of the composite
beam incorporating this beam section is obtained from Eq. (12.28); hence
152mm
0
.
4
×
30
×
1800
n
1
=
0
.
87
×
350
×
8530
which gives
n
1
=
120mm
Substituting for
n
1
in Eq. (12.29) we obtain the moment of resistance of the composite
beam
10
−
6
M
u
=
0
.
87
×
350
×
8530(356
−
60)
×
=
769 kNm
Since this is greater than the applied moment we deduce that the beam section is
satisfactory.
