Civil Engineering Reference
In-Depth Information
The use of 25-mm camber reduces the subsequent deflection to about
15 mm, or span/573, which should be satisfactory in most circumstances.
In practice, deflections would be slightly reduced by the stiffness of the
concrete in the bottom 55 mm of the slab, and by the stiffness of the
beam-to-column connections.
The use of camber was included here to illustrate the method. In prac-
tice, a better solution could be to use semi-rigid beam-to-column joints.
Maximum bending stress in the steel section
It is clear from the preceding results that yielding of the steel member
under service loading is unlikely, so no allowance is needed for the effect
of yielding on deflection. The maximum bending stress in the steel occurs
in the bottom fibre at mid-span. It is now calculated, to illustrate the
method.
Separate calculations are needed for the loadings given in Equations
3.118. For distributed load
w
per unit length, the stress is
σ
=
My
/
I
=
wL
2
y
/(8
I
)
=
9.25
wy
/
I
where
y
is the distance of the bottom fibre below the neutral axis. From
values given above, the stresses are:
for
g
1
:
σ
=
9.25
×
12.4
×
203/215
=
108 N/mm
2
for
g
2
and
q
:
σ
=
9.25
×
30 (556
−
178)/636
=
165 N/mm
2
The total stress is 273 N/mm
2
, well below the yield stress of 355 N/mm
2
.
Other bending stresses can be calculated in the same way.
3.11.3.2
Vibration
The method given in Section 3.9 is used. It is assumed that the source of
vibration is intermittent pedestrian traffic. The target value for the re-
sponse factor
R
is 4, if the traffic is continuous, increasing to 8, if there is
about one disturbance per minute.
Fundamental natural frequency
From Equations 3.118, the permanent load per beam is 17.6 kN/m. The
total imposed (variable) load is 24.8 kN/m, and only one-tenth of this will
be included, because vibration is likely to be worse where there are few
partitions and little imposed load. The design load is thus 20.1 kN/m for
beams at 4 m centres, giving a vibrating mass:
m
=
20 100/(4
×
9.81)
=
512 kg/m
2
