Civil Engineering Reference
In-Depth Information
Figure 4.5
Inverted-U frame
and minor axes of a steel section, respectively. British practice has been
to use x and y.) The dimensions
h
s
and
z
c
are shown in Fig. 4.5.
The term
k
s
is the stiffness of the U frame, per unit length along the
span, that opposes lateral displacement of the bottom flange. It relates a
disturbing force
F
per unit length of beam (Fig. 4.3(c)) to the lateral
displacement of a flange,
, caused by force
F
, as follows. The rotation at
B that would cause displacement
δ
/
h
s
; and the bending moment at B
is
Fh
s
. The stiffness
k
s
is moment/rotation, so
δ
is
δ
Fh
2
/
k
s
k
s
=
Fh
s
/(
δ
/
h
s
)
hence,
δ =
The flexibility 1/
k
s
is the sum of the flexibilities of the slab, denoted 1/
k
1
,
and of the steel web, denoted 1/
k
2
, so that
k
s
=
k
1
k
2
/(
k
1
+
k
2
)
(4.18)
The stiffness of the slab is represented by
k
1
. Where the slab is in fact
continuous over the beams, even when it is designed as simply-supported,
the stiffness may be taken as
k
1
=
4
E
a
I
2
/
a
(4.19)
where
a
is the spacing of the beams and
E
a
I
2
is the 'cracked' flexural
stiffness of the slab above the beams.
The stiffness of the web is represented by
k
2
. For an uncased web,
Et
3
aw
k
2
=
(4.20)
41
( )
− ν
h
2
a
s
