Civil Engineering Reference
In-Depth Information
Figure 4.9
Bending moment diagrams with redistribution
For simplicity, only the middle span is considered, and only symmetrical
arrangements of variable load.
Bending moment distributions for the middle span, ABC, given by
'uncracked' elastic analysis are shown in Fig. 4.9 for permanent load plus
the following arrangements of variable load:
(1)
q
on all spans,
(2)
q
on the centre span only,
(3)
q
on the end spans only.
The moments are given as multiples of
gL
2
/8. Questions (a) to (c) are
now answered.
Without redistribution, the peak hogging moment, 2.4
gL
2
/8, curve
(1), governs the design, and since
M
Rd
(a)
=
2
M
′
Rd
,
M
Rd
≥
4.8
gL
2
/8
(b)
The peak hogging moment at each support is reduced by 40%
to 1.44
gL
2
/8, curve (4). The corresponding sagging moment is
(0.6
1.56
gL
2
/8. Elastic analysis for loadings (2) and
(3) gives curves (2) and (3), respectively. Redistribution of 10% is
used, so that their peak hogging moments are also 1.44
gL
2
/8.
This
value governs the design, so that
0.96)
gL
2
/8
+
=
M
Rd
≥
2.88
gL
2
/8
(c)
The method used is explained in Section 4.3.3. Redistribution is unlim-
ited, so that support moments for loading (1) are reduced by 58%, to
