Civil Engineering Reference
In-Depth Information
1200 mm
0.4
s
cu
n
C
618 mm
T
F
IGURE
12.14
Reinforced concrete
T-beam of Ex. 12.10
0.87
s
Y
A
s
the solution of which gives
n
=
59mm
Now taking moments about the centroid of the compression concrete we have
A
s
618
59
2
10
6
500
×
=
0
.
87
×
410
×
−
which gives
2381
.
9mm
2
A
s
=
12.3 S
TEEL AND
C
ONCRETE
B
EAMS
In many instances concrete slabs are supported on steel beams, the two being joined
together by shear connectors to form a composite structure. We therefore have a
similar situation to that of the reinforced concrete T-beam in which the flange of the
beam is concrete but the leg is a standard steel section.
Ultimate load theory is used to analyse steel and concrete beams with stress limits
identical to those applying in the ultimate load analysis of reinforced concrete beams;
plane sections are also assumed to remain plane.
Consider the steel and concrete beamshown in Fig. 12.15(a) and let us suppose that the
neutral axis lies within the concrete flange. We ignore the contribution of the concrete
in the tension zone of the beam to its bending strength, so that the assumed stress
distribution takes the form shown in Fig. 12.15(b). A convenient method of designing
the cross section to resist a bending moment,
M
, is to assume the lever arm to be
(
h
c
+
h
s
)
/
2 and then to determine the area of steel from the moment equation
(
h
c
+
h
s
)
M
=
0
.
87
σ
Y
A
s
(12.27)
2
The available compressive force in the concrete slab, 0
.
4
σ
cu
bh
c
, is then checked to
ensure that it exceeds the tensile force, 0
.
87
σ
Y
A
s
, in the steel. If it does not, the
neutral axis of the section lies within the steel and
A
s
given by Eq. (12.27) will be too
