Civil Engineering Reference
In-Depth Information
a
b
c
1st modal frequency vs. temperature
3rd modal frequency vs. temperature
4th modal frequency vs. temperature
0.264
0.354
0.198
0.262
0.352
0.196
0.26
0.35
0.194
0.258
0.348
0.192
0.256
0.346
0.19
0.254
0.344
15
20
25
30
35
40
15
20
25
30
35
40
15
20
25
30
35
40
Temperature (C)
Temperature (C)
Temperature (C)
d
e
5th modal frequency vs. temperature
7th modal frequency vs. temperature
0.42
0.49
0.415
0.485
0.41
0.48
0.405
0.4
0.475
15
20
25
30
35
40
15
20
25
30
35
40
Temperature (C)
Temperature (C)
Fig. 8.5
Relationship of modal frequency and temperature: (
a
) 1st mode, (
b
) 3rd mode, (
c
) 4th mode, (
d
) 5th mode, and (
e
) 7th mode
To evaluate the performance of the bridge with the change of temperature, studies on the modal frequencies and
temperature are performed. As a large scale structure, the New Carquinez Suspension Bridge has very low natural
frequencies as shown in Fig.
8.3
with the first mode near 0.19 Hz. Due to the design of the structure, the second modal
frequency is very close to the first mode, roughly 0.01 Hz a part. As a result, the second mode is not always autonomously
detected by the automated modal analysis tools. In addition, the sixth mode is a torsional mode which has less energy and
thus more difficult to detect. Therefore, the first, third, fourth, fifth and seventh modal frequencies are used for most of the
analyses presented herein. Figure
8.5
shows the distribution of modal frequencies as a function of temperature. Modal
frequency data presented in Fig.
8.5
are obtained using the SSI method and least square linear fitting is employed to present
the trend of the data. It is shown that the 4th and 7th modes have stronger trending behavior of decreasing modal frequency
as temperature increases as compared to the other three modes. However, decreasing modal frequencies as a function of
temperature are generally observed for all of the modes. The modal frequency floating range is within 2 % of the mean value.
As the observed data is not evenly distributed over the temperature range, it is hard to make a direct conclusion of the
variance of the data for different temperature ranges.
Figure
8.6
shows the distribution of modal frequencies as a function of the time of the day. The sensor networks are
configured to acquire data 6 times a day separated by 4 h apart. Data from roughly 60 consecutive days are included in this plot
and spline of the mean values at each sensing point is fitted to show the data trend. From Fig.
8.6b, c
, d, e, the data shows the
trend that the modal frequencies decrease during the early half of the day and increase in the late half of the day. Besides
the temperature variation (Fig.
8.6f
), change of the traffic load is another important event that happens during the day which
would also temporarily change the performance of the bridge because traffic imposes dynamic loads and increases the weight
of the structure. It is difficult to acquire accurate traffic load data, but a good estimation could be made based on the
relationship of traffic and time of the day. Traffic loads are higher during the day time compared to the night time and the peaks
occur at rush hour (8 a.m. and 5 p.m.). In Fig.
8.6d, e
, the frequencies seem to dip lower at rush hour as compared to
frequencies from other non-rush hour periods. In Fig.
8.7
the mean of the normalized frequency data of each mode and the
mean of normalized temperature data at each sampling time are presented on the same figure. The amplitudes of the modal
frequency data curves are amplified by 20 times to exaggerate the trend. Modal frequency data are fitted by splines. Only the
first mode data behaves differently than the other modes in the trending over time of the day. The rest of the modes
(third, fourth, fifth and seventh) have similar general trending with frequency declining while the temperature is rising and
vice versa. Therefore, the influence of temperature and traffic loads on the NewCarquinez Bridge is certain and not negligible.
For a certain mode, the bridge tends to operate in a frequency lower than the natural frequency as the temperature and/or the
traffic loads increase and tends to operate in a frequency higher than the natural frequency as the temperature and/or the traffic
loads decrease.
