Civil Engineering Reference
In-Depth Information
ultimate limit states, and then stresses and/or deflections in service are
less likely to influence design.
As shown below, elastic analysis of a composite section is more com-
plex than plastic analysis, because account has to be taken of the method
of construction and of the effects of creep. In principle, the following
three types of loading then have to be considered separately:
•
load carried by the steel beam,
•
short-term load carried by the composite beam, without creep, and
•
long-term load carried by the composite beam, with creep.
However, as an approximation, the composite beam may be analysed for
its whole loading using a reduced value for the creep coefficient.
3.7.1
Elastic analysis of composite sections in sagging bending
It is assumed first that full shear connection is provided, so that the effect
of slip can be neglected. All other assumptions are as for the elastic
analysis of reinforced concrete sections by the method of transformed
sections. The algebra is different because the flexural rigidity of the steel
section alone is much greater than that of reinforcing bars.
For generality, the steel section is assumed to be asymmetrical (Fig. 3.25)
with cross-sectional area
A
a
, second moment of area
I
a
, and centre of area
distance
z
g
below the top surface of the concrete slab, which is of uniform
overall thickness
h
t
and effective width
b
eff
.
The modular ratio for short-term loading is
n
0
=
E
a
/
E
cm
where the subscript 'a' refers to structural steel and
E
cm
is the mean value
of the elastic modulus for concrete, given in EN 1992-1-1. For long-term
loading, a value 3
n
0
is a good approximation. For simplicity, a single
value 2
n
0
is permitted for use with both types of loading. From here
onwards, the symbol
n
is used for whatever modular ratio is appropriate,
so it is defined by
n
=
E
s
/
E
c
′
(3.84)
where
E
c
′
is the relevant effective modulus for the concrete. (Note: the
symbol
n
is also used for number of shear connectors.)
It is usual to neglect reinforcement in compression, concrete in tension,
and also concrete between the ribs of profiled sheeting, even when the
sheeting spans longitudinally. The condition for the neutral-axis depth
x
to be less than
h
c
is
