Research
Projects: Past Projects
Simulation of Damage on the Dowling Hall Footbridge
Research Team: Babak Moaveni (PI), Alyssa Kody (undergrad student)
Funding: Tufts Summer Scholars, NSFBRIGE (1125624)
Duration: 4/2011 – 12/2011
Relevant publications to date:
The objective of this project was to simulate damage on the Dowling Hall
Footbridge without compromising the safety of this structure. This is done by
increasing the mass of the bridge. Damage to a bridge is often caused by a loss
of stiffness, which can be detected through changes in natural frequencies. By
increasing the mass of the bridge, the frequency of the bridge will decrease,
simulating damage (a loss of stiffness) to the bridge without actually harming
the structure. To determine the best location and distribution of the added
mass, a finite element (FE) model of the Dowling Hall Footbridge was developed
to analyze the changes in natural frequencies due to the addition of mass at
different locations and with different distributions. The FE model was developed
in SAP2000, a structural analysis software, as shown in Figure 1. Using this
model, the effect of additional mass on the natural frequencies of the
footbridge was studied.
Figure 1. A finite element model of the Dowling Hall Footbridge in SAP2000
The FE model of the Dowling Hall Footbridge was used to determine the location
of the mass where the natural frequencies would have the greatest percent
change. During analysis, added masses were applied as point masses to the joints
of shell elements representing the deck and in a manner that is equivalent to a
distributed load. The total mass was divided so that each side of the bridge
would hold half the total mass. For example, for a 5kips total mass, each side
of the bridge would hold 2.5kips. Analyses with various total masses (2kips,
5kips, 6kips), and distribution lengths (8ft, 16ft, 24ft) were performed.
Figure 2 shows the percent change in natural frequencies versus the location of
a 5kip applied mass along a 16ft length on each side of the bridge. Station
0ft is the upper campus side support, 72ft is the support at middle pier, and
144ft is the support at the Dowling Hall side. Through these analyses, the
smallest changes in the natural frequencies resulted from placing the mass on or
next to the supports. The highest changes in natural frequency are observed when
the mass is placed in the middle of a span. Because 6 of the 8 accelerometers on
the Dowling Hall Footbridge are located between the campusside abutment and
middle pier, more accurate identification results can be obtained by placing the
mass on this span rather than on the span closer to Dowling Hall.
Figure 2. Changes in natural frequencies versus location of distributed 5kip
mass
The FE model of the Dowling Hall Footbridge was also used to determine the
smallest mass required to observe changes in the measured natural frequencies.
If the chosen total mass is too small, its effects would be overshadowed by
measurement noise or identification errors. If the chosen total mass is too
large, it may pose a threat to pedestrians, cause structural damage, or be too
difficult to move onto the bridge.
For the FE model analysis, masses ranging from 1kip to 9kips were considered,
and the percent change in natural frequencies were compared among them (Figure
3). Reviewing the percent change in natural frequency, a 5kip mass would
produce the necessary changes in frequencies so that three of the first six
vertical modes would be outside the ambient variability ranges outlined by Moser
and Moaveni (2011) (Mode 2 = 6.03 Hz ±3%, Mode 3 = 7.25 Hz ±4%, Mode 4 = 8.99 Hz
±3%). Hence, adding a 5kip distributed mass over the proposed area was expected
to result in observable changes in the natural frequencies in the presence of
noise and estimation error. A 5kip mass is also a reasonable amount to add to
the bridge, as it could be moved on and off the bridge relatively easily, and
would not take up too much walking area on the deck of the bridge.
Figure 3. Percent change in natural frequencies for various total masses
Table 1 shows the predicted natural frequencies and percent change in natural
frequency due to the addition of 5000lbs distributed along the sides of the
bridge. Each side of the bridge holds 2500lbs distributed over a 16ft length.
These predictions were made assuming the mass is placed between 24ft and 40ft
from the campusside abutment. Figure 4 shows the loading plan for the Dowling
Hall Footbridge using concrete blocks.
Table 1. Predicted natural frequencies and percent change in natural frequency
due to mass
Figure 4. Sketches of the loading plan
Table 2 reports the identification success rate, a percentage representating how
many times a mode was correctly identified during the test loading (72 hours).
Mode 1 was identified the least (71%), while mode 4 was identified the most
(100%). All other modes were identified between 98% and 99%. This result is
consistent with longterm indentificaiton success rates. Moser and Moaveni
(2011) identified mode 4 as the most reliably identified mode (99%), and mode 1
as having one of the lowest identification success rates (86%).
Table 2. Identification success rate during the load test
Figure 5 shows the natural frequencies of the six modes using hourly measured
data from July 28, 2011 to August 3, 2011. Natural frequencies from data
collected without the mass are shown in blue and those from data collected with
the mass on the deck are shown in red. Due to the addition of the mass, there is
a clear decrease in the identified natural frequencies of modes 14, but modes
56 do not show a clear trend due to addition of the mass. To determine the
percent change in the identified natural frequencies, the mean natural frequency
for each mode was calculated using data points from July 29 at 14:00 to August 1
at 11:00 (the time period when the entire mass was on the deck). These values
were then compared to the mean frequencies from the day before the test, July
28, from 0:00 to 23:00. Data from the test loading was compared to the July 28
data because factors that affect the natural frequency, such as environmental
factors, would most closely match the conditions of the test loading. Table 3
lists the mean natural frequencies for each mode on July 28, the mean
frequencies from the test loading, and the percent difference between the two.
Mean natural frequencies of the first four modes are significantly reduced due
to the addition of mass with maximum decrease in the second mode (7.4%).
Figure 5. Identified natural frequencies versus time
Table 3. Mean identified natural
frequencies with and without the added mass
Table 4 and Figure 6 compare the reduction in natural frequencies of the six
vibration modes estimated from the FE model versus those identified from
experimentally measured data (mean value reduction). The FE model predicted that
mode 4 would have the highest percent change in natural frequency with 4.72%.
The model also predicted that modes 5 and 6 would have the lowest percent change
in natual frequencies with less than 1% change. The model predicted that the
percent change in natural frequency for modes 1, 2, and 3 would fall in the
range of 2 to 4 percent. The actual reduction in the identified natural
frequencies of modes 1, 3, and 5 are very close to their FE model predicted
counterparts. The measured reduction in modes 4 and 6 is slightly different from
model predictions but is within an acceptable range. The largest discrepancy
between FE predicted and experimentally identified natural frequency reduction
due to the addition of mass is observed for mode 2 (3.07% versus 7.41%). This
could be due to some modeling error as well as larger identification
uncertainty/variability of this mode (see variation of this natural frequency in
Figure 5).
Table 4. Comparison between FE predicted and experimentally identified reduction
in natural frequencies due to addition of mass
Figure 6. Percent reduction in natural frequencies of the six modes:
FE model versus mean identified
This experiment provides a unique dataset that can be used by researchers at
Tufts and other universities to verify different vibrationbased damage
identification and structural health monitoring methodologies. In addition, this
data set can be used in SHM courses to demonstrate damage identification of a
realworld structure.
