Civil Engineering Reference
In-Depth Information
simultaneously. Such a section is known as a
critical
or
economic
section. The position
of the neutral axis is obtained directly from Eq. (12.13) in which
σ
s
,
σ
c
,
m
and
d
1
are
known. The required area of steel is then determined from Eq. (12.16).
E
XAMPLE
12.3
A rectangular section reinforced concrete beam has a breadth of
200mm and is 350mm deep to the centroid of the steel reinforcement which consists
of two steel bars each having a diameter of 20mm. If the beam is subjected to a bending
moment of 30 kNm, calculate the stress in the concrete and in the steel. The modular
ratio
m
is 15.
The area
A
s
of the steel reinforcement is given by
π
4
×
20
2
628
.
3mm
2
A
s
=
2
×
=
The position of the neutral axis is obtained from Eq. (12.10) and is
&
(
×
×
×
15
628
.
3
200
2
200
350
'
)
=
n
=
1
+
−
1
140
.
5mm
×
15
628
.
3
Now using Eq. (12.11)
140
.
5
3
3
200
×
140
.
5)
2
10
6
mm
4
I
c
=
+
15
×
628
.
3(350
−
=
598
.
5
×
The maximum stress in the concrete follows from Eq. (12.12), i.e.
10
6
30
×
×
140
.
5
7
.
0N
/
mm
2
(compression)
σ
c
=−
=−
10
6
598
.
5
×
and from Eq. (12.14)
10
6
15
×
30
×
157
.
5N
/
mm
2
(tension)
σ
s
=
(350
−
140
.
5)
=
×
10
6
598
.
5
E
XAMPLE
12.4
A reinforced concrete beam has a rectangular section of breadth
250mm and a depth of 400mm to the steel reinforcement, which consists of three
20mm diameter bars. If the maximum allowable stresses in the concrete and steel are
7
.
0N
/
mm
2
and 140N/mm
2
, respectively, determine the moment of resistance of the
beam. The modular ratio
m
=
15
.
The area,
A
s
, of steel reinforcement is
π
4
×
20
2
942
.
5mm
2
A
s
=
3
×
=
From Eq. (12.10)
&
(
15
×
942
.
5
250
2
×
250
×
400
'
)
=
n
=
1
+
−
1
163
.
5mm
15
×
942
.
5
