Civil Engineering Reference
In-Depth Information
Table 5.5
Mean values (
μ
) and
standard deviations (
σ
),
n ¼
0,
0.1,0.2, 0.3
Variable
Unit
μ
σ
m
kg
50
nμ
m
kg
75
nμ
m
kg
85
nμ
This hardly represents the possible combinations on a footbridge, and therefore a more detailed study is made to bring
light onto how sensitive the acceleration property
a
is to different assumptions for the pedestrian weight. This involves
considering a total of 12 combinations of mean values and standard deviations for pedestrian weight ranging from models in
which the pedestrian weight is treated as a random variable, to models where it is treated as a deterministic property.
The considerations (variation possibilities) may quickly expand, and therefore focus is only on bridge C, being the bridge
for which resonant excitation is most likely to occur.
5.5.1 Weight of Pedestrian
As for the pedestrian weight, three different mean values were considered; a low, a medium, and a high value (50, 75 and
85 kg) as shown in Table
5.5
.
Table
5.5
also defines the standard deviations that are assumed associated with the mean values, and for each mean value
four different standard deviations are considered. With
n
¼
0, the standard deviation is set to zero hereby handling
pedestrian weight as a deterministic parameter. However, three other options for non-zero standard deviation is also
considered (
n
0.1, 0.2, and 0.3) all modelling pedestrian weight as a random variable are considered. As
n
increases,
so does the standard deviation (from low over medium to high). The standard deviation introduced in Sect.
5.3
is fairly close
to assuming
n
¼
¼
0.2 hereby giving some idea of the standard deviation ranges considered for the present studies.
5.5.2 Other Study Assumptions
The step frequency and stride length was modelled as in Sect.
5.3
. In Sect.
5.3
three different models for the dynamic load
factor were introduced, but for the present studies model 1 was employed.
5.5.3 Computations
Basically, the computations followed the same scheme as that already outlined in Sect.
5.4.3
. On various study assumptions
the acceleration property in focus in this paper was identified, hereby allowing assessments to be made as to how sensitive the
acceleration property is to variations in pedestrian weight modelling.
5.5.4 Results
The results are presented by employing the ratio
k
defined in (
5.11
):
km
ð
;
n
Þ¼
am
ð
;
n
Þ=
a
75
ð
;
0
Þ
(5.11)
Basically, the ratio normalises the acceleration property,
a
, calculated for any studied combination of (
m
,
n
) by the
acceleration property,
a
, calculated for (
m
,
n
)
(75 kg, 0). The normalisation constant represents the acceleration property
calculated assuming the pedestrian weigh to be 75 kg and a deterministic model for the pedestrian weight (as
n
¼
0). The
normalisation is believed to enhance the interpretation of results. As
n
grows above zero, the pedestrian weight is handled as
a random variable, and as
n
increases, the standard deviation of pedestrian weight increases.
The results in terms the ratios
k
, are given in Table
5.6
. For ease of overview, only approximate ratios are provided.
¼
