Civil Engineering Reference
In-Depth Information
5.1
Introduction
The walking-induced vibrations in the London Millennium Bridge [
1
] serve as an example of a scenario where walking loads
have caused serviceability problems. However, it is by far the only footbridge, which has shown to be problematic in the
serviceability-limit-state, but probably it is the most well-known bridge, that has had problems in this area.
When addressing the serviceability-limit-state, many codes of practise employ a deterministic approach in which the
walking parameters influencing the walking load is handled as deterministic properties (such as in [
2
,
3
]). The weight of a
pedestrian is set to 75 kg, the dynamic load factor for a pedestrian is set to 0.4, etc. In [
4
] a new way of thinking (modelling)
was introduced in which at least some of the walking parameters were modelled as random variables rather than determin-
istic properties. This is more reasonable as walking parameters are stochastic by nature as documented in [
4
-
6
]. At the same
time the load modelling procedure is more complex, as there are many decisions to be made prior to launching calculations
predicting the footbridge response. These decisions encompass settling on mean values, standard deviations, distribution
type etc. for the various walking parameters.
In the paper focus is on setting up such assumptions for two main characteristics describing the load action, namely the
pedestrian weight and the dynamic load factor. Furthermore, and quite important, it is examined how sensitive the footbridge
response actually is to the decisions made along the way.
Overall the idea is to get an understanding of how the various decisions impact the predictions of footbridge response, or
in other words how sensitive footbridge response predictions are to the various decisions to be made. One study of this paper
is devoted to decisions about the dynamic load factor. Another is devoted to decisions about the pedestrian weight.
To facilitate the investigations, footbridge models are needed, and to this end pin-supported footbridges (idealised as a
single-degree-of-freedom systems, SDOF-systems) are employed. Actually five different pin-supported bridges are consid-
ered, such that the results of sensitivity studies do not only reflect results obtained for a single randomly selected bridge.
The bridge response characteristic in focus is defined in the paper.
Dynamic characteristics of the bridges considered in this paper are outlined in Sect.
5.2
, and the way in which walking
loads are modelled is outlined in Sect.
5.2
. Section
5.3
and
5.4
presents the sensitivity studies and Sect.
5.5
summarizes the
results.
5.2 Bridge Dynamic Characteristics
Five different pin-supported footbridges are considered for the studies of this paper. The dynamic characteristics of the
bridges are shown in Table
5.1
. The parameter
f
0
represents the undamped bridge frequency (first vertical bending mode),
M
the associated modal mass, and
represents the damping ratio of the bridge.
Basically, bridge length,
L
, is not a dynamic characteristic as such. However, as it is a parameter having impact on bridge
response to the action of walking, it is a parameter, which need to be defined for a study like this.
Bridge C would have the highest risk of resonating as a result of walking loads, as for this paper the mean value of step
frequency is assumed to be 1.87 Hz, but the other bridges might also be brought into resonance as a result of walking loads
although it is less likely. Bridge A and E have frequencies in the lower and upper frequency range of natural walking,
respectively, which would suggest that resonance action will not occur that often, but that it is a possibility.
All together, the range of bridges outlined above is believed to be suitable for the parametric studies of this paper.
A variability of pin-supported bridges is considered and it is also believed that there is a fair relationship between bridge
frequency, modal mass and bridge length.
ζ
Table 5.1
Bridge dynamic
characteristics
Bridge
f
0
(Hz)
M
(kg)
ζ
(%)
L
(m)
10
3
A
1.60
61.5
0.5
54
10
3
B
1.75
51.5
0.5
49
10
3
C
1.90
44.0
0.5
45
10
3
D
2.05
37.5
0.5
42
32.5
10
3
E
2.20
0.5
39
