Civil Engineering Reference
In-Depth Information
Figure 4.12
Cracked section of composite slab, for hogging bending
If it can be shown that the UB steel section used here qualifies for the
relaxation given by Equation 4.28, then no check on lateral buckling is
needed. It can be shown to qualify, by a new method given elsewhere
[17]; but its resistance to lateral buckling is now determined, to illustrate
the method of Equations 4.22 to 4.24.
In Equation 4.22,
)(
k
s
E
a
I
afz
)
1/ 2
M
cr
≈
(
k
c
C
4
/
π
(4.22)
the term
k
s
represents the stiffness of the U-frame:
k
s
=
k
1
k
2
/(
k
1
+
k
2
)
(4.18)
Equation 4.21 gives
k
2
for a concrete-encased web. It is assumed that
the normal-density encasement has a modular ratio of 20.2 for long-term
effects, so that
Et b
2
210 000
.
××
7 8
178
2
aw f
× 10
6
Ν
k
2
=
/ )
=
=
1.82
16
h
(
1
+
4
nt b
16
×
393 1
( . . /
+
80 8
×
7 8 178
)
s
w
f
From Equation 4.19,
k
1
4
E
a
I
2
/
a
, where
E
a
I
2
is the 'cracked' stiffness of
the composite slab in hogging bending. To calculate
I
2
the trapezoidal rib
shown in Fig. 3.9 is replaced by a rectangular rib of breadth 162
=
−
13
=
149 mm. Using a modular ratio
n
=
20.2, the transformed width of rib
is 149/(0.3
24.6 mm per metre width of slab, since the ribs are
at 0.3 m spacing. The transformed section is thus as shown in Fig. 4.12.
Reinforcement within the rib (Fig. 3.12) is neglected.
The position of the neutral axis is given by
×
20.2)
=
24.6
x
2
1
2
×
=
336(126
−
x
)
whence
x
=
47 mm
then
10
−6
I
2
0.079
2
0.47
3
/3
2.95 mm
4
/m
=
336
×
+
24.6
×
=
