Civil Engineering Reference
In-Depth Information
required. As for
σ
ct
, variable load should be assumed to act on both spans.
Using data from Section 4.6.1 and Fig. 4.14(b),
⎛
⎜
Mx
I
⎞
⎟
=
134 203
215
×
(
56
+
268
)
×
229
∑
4
σ
4,
a
=
+
278
2
=
126
+
267
=
393 N/mm
2
where
x
4
is the distance of the relevant neutral axis above the bottom
fibre. The result shows that yielding occurs (393
>
355), but not until after
the slab has hardened (126
<
355), so from Section 4.3.2.3,
f
2
=
0.7. The
hogging moments
M
1
for use in Equation 4.35 are
M
1
=
f
1
f
2
M
B
and are given in Table 4.6. The other end moment,
M
2
, is zero.
Deflections
δ
0
for each loading acting on a simply-supported span are
now required. These are, in general:
5
384
wL
EI
593 0
384
.
×
×
⎛
⎜
w
I
⎞
⎟
=×
4
4
9
δ
0
=
=
464
10
6
(/)
wI
mm
1
×
210
1
with
w
in kN/m and
I
1
in mm
4
. Using values from Table 4.6 in Equation
4.35 gives the total deflection:
δ
c
=
464
×
10
6
Σ
[(
w
/
I
1
)(1
−
0.6
M
1
/
M
0
)]
=
464[(12.4/215)
×
0.4
+
(5.2/636)(1
−
0.6
×
24/56)]
+
464[(24.8/636)(1
−
0.6
×
56/268)]
=
10.7
+
2.8
+
15.9
=
29.4 mm
This result is probably too high, because the factor
f
1
may be conservative,
and no account has been taken of the stiffness of the web encasement.
This total deflection is span/316, less than the guideline of
L
/300 given in
the UK's national annex to EN 1990 [12], for floors with plastered ceil-
ings and/or non-brittle partitions.
The total deflection of the simply-supported span of 8.6 m, for the same
loading, was found to be 35.5 mm. This would be 35.5
=
48.5 mm for the present span. The use of continuity at one end has reduced
this value by 19.1 mm, or 39%.
Even so, these deflections are fairly large for a continuous beam with a
ratio of span to overall depth of only 9300/556
×
(9.3/8.6)
4
16.7. This results from the
use of unpropped construction, high-yield steel and lightweight concrete.
=
