Civil Engineering Reference
In-Depth Information
Figure 4.6
Factor C
4
for an end span of a continuous beam
where
v
a
is Poisson's ratio for steel. For an I-section with the web (only)
encased in concrete, as used in the design example here,
Et b
2
aw f
k
=
(4.21)
2
16
h
(
1
+
4
nt b
/ )
s
w
f
where
n
is the modular ratio for long-term effects, and
b
f
is the width of
the steel flange. Equation 4.21 was derived by elastic theory, treating the
concrete on one side of the web (Fig. 3.31) as a strut that restrains upwards
movement of the steel bottom flange below it.
The buckling moment
M
cr
is strongly influenced by the shape of the
bending-moment distribution for the span considered. This is allowed for
by the factor
C
4
, values for which were obtained by finite-element analyses.
They range from 6.2 for uniform hogging moment, to above 40 where the
region of hogging moment is less than one-tenth of the span, and are
given in Reference 17. Values relevant to the design example are given in
Fig. 4.6.
In Equation 4.15 the term
GI
at
gives the contribution from St Venant
torsion of the section. It is usually small compared with
k
s
L
2
/
2
and can
then be neglected with little loss of economy. The expression then becomes
π
)(
k
s
E
a
I
afz
)
1/2
M
cr
≈
(
k
c
C
4
/
π
(4.22)
which is independent of the span
L
. This enables the values of
C
4
to be
used for all span lengths.
Equation 4.15 for
M
cr
is valid only where rules for minimum spacing of
connectors, bending stiffness of the composite slab, and proportions of
the steel I-section, are satisfied. A more detailed explanation of this method
and simplified versions of some of its rules are available [17].
