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Steel Designers' Manual - 6th Edition (2003)
Os
D
elastic
neutral axis
stress p
Be/ae
(a) (b)
equivalent
steel area
example, in continuous construction, or in beams where the ductility of the shear
connection is not adequate.
The important properties of the section are the section modulus and the second
moment of area. First it is necessary to determine the centroid (elastic neutral axis)
of the transformed section by expressing the area of concrete in steel units by dividing
the concrete area within the effective breadth of the slab, Be, by an appropriate
modular ratio (ratio of the elastic modulus of steel to concrete).
In unpropped construction, account is taken of the stresses induced in the noncomposite
section as well as the stresses in the composite section. In elastic analysis,
therefore, the order of loading is important. For elastic conditions to hold,
extreme fibre stresses are kept below their design values, and slip at the interface
between the concrete and steel should be negligible.
The elastic section properties are evaluated from the transformed section as in
Fig. 21.6. The term ae is the modular ratio. The area of concrete within the profile
depth is ignored (this is conservative where the decking troughs lie parallel to the
beam). The concrete can usually be assumed to be uncracked under positive
moment.
The elastic neutral axis depth, xe, below the upper surface of the slab is determined
from the formula:
x
e
D D
r D s - p Ê ˆ
+ a e + Ds
2 Ë 2 ¯
=
( 1 + a r)
e
Analysis of composite section 607
Fig. 21.6 Elastic behaviour of composite beam. (a) Elastic stress distribution.
(b) Transformed section
(21.1)