Civil Engineering Reference
In-Depth Information
B
0.4
s
cu
h
f
d
1
Neutral
axis
F
IGURE
12.13
Ultimate
load analysis of a
reinforced concrete
T-beam
0.87
s
Y
A
s
(a)
(b)
from which
3793
.
8mm
2
A
st
=
The ultimate load analysis of reinforced concrete T-beams is simplified in a similar
manner to the elastic analysis by assuming that the neutral axis does not lie below the
lower surface of the flange. The ultimate moment of a T-beam therefore corresponds
to a neutral axis position coincident with the lower surface of the flange as shown in
Fig. 12.13(a).
M
u
is then the lesser of the two values given by
0
.
4
σ
cu
Bh
f
d
1
−
h
f
2
M
u
=
(12.25)
or
0
.
87
σ
Y
A
s
d
1
−
h
f
2
M
u
=
(12.26)
For T-beams subjected to bending moments less than
M
u
, the neutral axis lies within
the flange and must be found before, say, the amount of tension reinforcement can
be determined. Compression reinforcement is rarely required in T-beams due to the
comparatively large areas of concrete in compression.
E
XAMPLE
12.10
A reinforced concrete T-beam has a flange width of 1200mm and
an effective depth of 618mm; the thickness of the flange is 150mm. Determine the
required area of reinforcement if the beam is required to resist a bending moment of
500 kNm. Take
σ
cu
=
30N
/
mm
2
and
σ
Y
=
410N
/
mm
2
.
M
u
for this beam section may be determined using Eq. (12.25), i.e.
150
618
150
2
10
−
6
M
u
=
0
.
4
×
30
×
1200
×
−
×
=
1173 kNm
Since this is greater than the applied moment, we deduce that the neutral axis lies
within the flange. Then from Fig. 12.14
1200
n
618
n
2
10
6
500
×
=
0
.
4
×
30
×
−
