Civil Engineering Reference
In-Depth Information
σ
a3
=
M
(
h
t
−
x
)/
I
(3.91)
σ
a4
=
M
(
h
a
+
h
t
−
x
)/
I
(3.92)
Deflections
Deflections are calculated by the well-known formulae from elastic theory,
using Young's modulus for structural steel. For example, the deflection of
a simply-supported composite beam of span
L
due to distributed load
q
per unit length is
δ
c
=
5
qL
4
/(384
E
a
I
)
(3.93)
from Equation
3.63), the increase in deflection due to longitudinal slip depends on the
method of construction. The total deflection
Where the shear connection is partial (i.e.,
η
<
1, with
η
δ
is given approximately in
BS 5950 [19] as
δ
=
δ
c
[1
+
k
(1
−
η
)(
δ
a
/
δ
c
−
1)]
(3.94)
with
k =
0.5 for propped construction and
k =
0.3 for unpropped construc-
tion, where
δ
a
is the deflection for the steel beam acting alone.
This expression is obviously correct for full shear connection (
η
=
1),
and gives too low a result when
0
.
EN 1994-1-1, unlike BS 5950, allows this increase in deflection to be
ignored in unpropped construction where:
η
=
•
either
0.5 or the forces on the connectors found by elastic analysis
do not exceed 0.8
P
Rk
, where
P
Rk
is their characteristic resistance, and
η
≥
•
for slabs with ribs transverse to the beam, the height of the ribs does
not exceed 80 mm.
The arbitrary nature of these rules arises from the difficulty of predict-
ing deflections accurately.
3.7.2
The use of limiting span-to-depth ratios
Calculations using formulae like those derived above are not only long;
they are also inaccurate. It is almost as much an art as a science to predict
during design the long-term deflection of a beam in a building. It is
possible to allow in calculations for some of the factors that influence
deflection, such as creep and shrinkage of concrete; but there are others that
cannot be quantified. In developing the limiting span/depth ratios for the
