Civil Engineering Reference
In-Depth Information
1.0
gL
2
/8. The corresponding sagging moment is (0.6
1.4)
gL
2
/8,
(curve (5)). Smaller redistributions are required for the other loadings.
The available resistances at the supports and at mid-span are fully
used, when
+
M
Rd
=
2.0
gL
2
/8
The preceding three results for
M
Rd
show that the resistance required is
significantly reduced when the degree of redistribution is increased.
For some composite beams, use of rigid-plastic analysis can imply even
larger redistribution than the 58% found here. However, design is then
usually governed by serviceability criteria.
4.3.2.3
Corrections for cracking and yielding
Cracking of concrete and yielding of steel have less influence on deflections
in service than they do on analyses for ultimate limit states, because the
design loads are lower. In short cantilevers and at some internal supports
there may be very little cracking, so deflections may be over-estimated by
an analysis where redistribution is used as explained above. Where a low
degree of shear connection is used, deflections may be increased by longi-
tudinal slip between the slab and the steel beam.
For these reasons, design codes give modified methods of elastic analysis
for the prediction of bending moments at internal supports of continuous
beams. First, a method from BS 5950 for uniform beams is given that
allows only for the effects of support moments. Let these hogging moments
be
M
1
and
M
2
, for a loading that would give a maximum sagging moment
M
0
and a maximum deflection
δ
0
, if the span were simply-supported. It
can be shown by elastic analysis of a uniform member with uniformly-
distributed load, that the moments
M
1
and
M
2
reduce the mid-span deflec-
tion from
δ
0
to
δ
c
, where
δ
c
=
δ
0
[1
−
0.6(
M
1
+
M
2
)/
M
0
]
(4.35)
This equation is quite accurate for other realistic loadings. It shows the
significance of end moments. For example, if
M
1
=
M
2
=
0.42
M
0
, the
deflection
δ
0
is halved. It is not strictly correct to assume that the max-
imum deflection always occurs at mid-span but the error is negligible.
For cracking and yielding, the methods of EN 1994-1-1 are now
described, followed by those of BS 5950. Shear lag has little effect on
deflections, but section properties based on the effective flange width are
often used, as they are needed for other calculations.
The general method given for allowing for the effects of cracking at inter-
nal supports is for beams with all ratios of span lengths, and is applicable
