Environmental Effects on a Suspension Bridge’s Dynamic Response.Mr. R. J . Westgate, Dr. K. Y. Koo, Prof. J. M. W. Brownjohn

Department of Civil and Structural Engineering, The University of Sheffield, Sheffield, S1 3JD, Englandemail: r.westgate@sheffield.ac.uk

ABSTRACT: Past research has demonstrated that a bridge’s dynamic performance may be influenced by the environmental loadingto which it is subjected, such as thermal effects. This is certainly the case for the Tamar Suspension Bridge in south west England,which also exhibits this behavior, since the modal frequencies fluctuate in a daily cycle. One significant aim of Structural HealthMonitoring (SHM) research is to filter out these environmental effects to reveal effects of damage or other anomalous behavior.

More than three years of continuously monitored data for the Tamar Suspension Bridge are available, collected from a largearray of sensors. The dynamic response is monitored by accelerometers in the bridge’s deck and the stay cables, and a robotictotal station (RTS) monitors its static performance. In addition, there are numerous sensors monitoring the local environmentalconditions of the bridge. A detailed Finite Element (FE) model was also developed with the research to predict the behavior ofTamar Suspension Bridge under particular environmental conditions, such as thermal and traffic loading.

The natural frequencies of the bridge have been shown to drop quite significantly in the day; in particular the first lateralsymmetric mode varies by 10%. It has been noted, both from the monitored results and the FE model, that this may be a result ofeither the thermal expansion of the bridge elements, or the cumulative mass of the traffic on the bridge.

KEY WORDS: Tamar Suspension Bridge; modal response; static configuration; temperature; vehicles

1 INTRODUCTION

Structural Health Monitoring (SHM) is a term developed for therange of systems which monitor civil infrastructure, in order toassist and inform the operators whether the structure is in anacceptable condition, or has suffered gradual or instantaneousdamage [1]. Modal parameters have been used to detectchanges in the performance of the structure and have, undercontrolled conditions, been used to identify forms of damageand deterioration for two bridges subjected to induced damageand dynamic assessment [2] [3].

Several papers have identified the significance of environmen-tal conditions to dynamic parameters [4] [5] [6], since they mayaffect physical parameters in the structure, such as the materialproperties, boundary conditions, strains and stresses withinthe structure. In the majority of these tests, temperature wasdetermined as the dominant variable from monitored results.

The research of the Vibration Engineering Section has beenaddressing two issues in the environmental effects on long termmonitoring results. The first is to determine their influenceon a suspension bridge’s dynamic performance, so that theireffect can be filtered to reveal structural changes. The otherissue is to quantify the static and dynamic response due to achange in an environmental variable. This behaviour will besupported by predictions from mathematical models. This paperwill demonstrate some of the research achieved so far on theTamar Suspension Bridge.

2 BRIDGE DESCRIPTION

The Tamar Suspension Bridge, shown in Figure 1, crosses theRiver Tamar between Plymouth and Cornwall in UK, and wasbuilt in 1961 with a design by Mott Hay and Anderson. The

bridge has an overall span of 563m, with a main span of 335m.The towers are nearly 73m tall and the suspension cables have adiameter of 0.38m. The original concrete deck is supported bya 4.9m deep and 15.240m wide truss, with vertical 0.05m widehangers distributed every 9.2m.

Figure 1. Photograph of the Tamar Suspension Bridge.

In 2001 a program of strengthening and widening the bridgeto accommodate increased levels of traffic was completed. Thisinvolved replacing the previous concrete deck with a steelorthotropic deck, and cantilevering two additional 6m widelanes on either side of the truss. In addition, eight pairsof additional stay cables were used to support the additionalvertical loads. Most of the stay cables are 102mm in diameter;six pairs link between the towers and the truss, and two pairsspan from the top of the main towers to the base of side towers.

Proceedings of the 8th International Conference on Structural Dynamics, EURODYN 2011Leuven, Belgium, 4-6 July 2011G. De Roeck, G. Degrande, G. Lombaert, G. Muller (eds.)ISBN 978-90-760-1931-4

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3 INSTRUMENTATION

Once the strengthening and widening process was completed,Fugro Structural Monitoring installed a sensor system, whichconsists of several strain gauges and level pressure sensors tomeasure the vertical displacements and stay cable forces, and aset of thermometers and anemometers to monitor environmentalparameters. Fugro data are sampled at 0.1Hz, and compiledin hourly summaries. Additionally, vehicles are counted andcategorized hourly at the toll booths on the Plymouth side of thebridge, and a webcam on the Plymouth tower provides snapshotsof the traffic every 30 seconds.

In addition, the University of Sheffield installed a set ofaccelerometers in 2006. Three of which were installed atthe centre of the main span, and four pairs were clampedonto stay cables P4N, P4S, P1N and S2S. The data from theaccelerometers are sampled at 64Hz and summarized every halfhour.

In 2009 the University of Sheffield also installed a RoboticTotal Station (RTS) to monitor the location of several reflectorspositioned on the deck and towers of the bridge. Thisprovides information about the change of the bridge’s staticconfiguration.

4 FINITE ELEMENT MODEL

A theoretical prediction of the bridge’s behaviour can be derivedby applying possible conditions, such as temperature and trafficloads, upon a finite element model of the bridge. Thusto accompany the research a detailed 3D model of TamarSuspension Bridge was created in ANSYS, shown in Figure 2.The model uses nearly 5200 nodes, and most of the elementswere modelled as SHELL63 or BEAM4, whilst cable elementswere modelled as LINK10. Table 1 shows how closely themodal results from the FE model relates to results from aprevious ambient vibration test [7]. Further information aboutthe FE model can be found in a paper by Westgate [8].

Figure 2. Finite element model of Tamar Suspension Bridge.

Table 1. Modal properties determined from FE model

Mode Frequency Monitored(Hz) Frequency (Hz)

1 (VS1) 0.393 0.3932 (LS1a) 0.452 0.4573 (VA1) 0.543 0.5954 (LS1b) 0.625 -5 (TS1) 0.766 0.726

where VS1 is the first vertical symmetric mode, VA1 is thefirst vertical anti-symmetric mode, LS1a and LS1b are twosimilar lateral symmetric modes, and TS1 is the first symmetrictorsional mode.

5 INITIAL RESULTS

5.1 Modal response

Following the post-processing of the data, it was apparent thatthe natural frequencies appeared to fall throughout the morningthen rise during the evening, as demonstrated by Figure 3. Mostnotably, the first lateral frequency (LS1a) fluctuates by nearly10% of its mean result, which would otherwise hinder damagedetection in SHM systems.

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Figure 3. Fluctuation of modal frequency results over a dailyperiod.

5.2 Possible influences

Further post-processing proved that other data show dailyvariation; some of the more notable sets are shown in Figure 4.Static displacements of the bridge deck were investigated sincethey rise and fall like the frequencies: the bridge is expandingand sagging during the day, and vice versa at night. A possibleexplanation is that the static configuration of a particularsuspension bridge is linked to its dynamic characteristics, sinceboth are significantly affected by the tension in the mainsuspension cables.

It was reasoned that the environmental paramters were havinga significant influence on the static and dynamic behavior ofthe bridge, based on the similarities in the daily variation. Forthe purposes of this study, only temperature and traffic masseswere investigated, since there is little research little researchliterature presently available on their influence on suspensionbridges, whilst there are many papers that consider wind effectson suspension bridges.

6 ENVIRONMENTAL RESPONSE

6.1 Temperature

Temperature was first considered, since there was lessuncertainties compared to the vehicle data, and the bridge’sresponse could be reasonably well predicted from the FE model.

Temperature data collected from the FUGRO system showedthat, for most of the year, the temperature of the suspensioncable, orthotropic deck and truss were close, as a result ofovercast weather and since the elements are mostly affected bythe temperature of the air. For this reason it was acceptableto apply the same temperature on all nodes of the FE model.However, during the summer solar radiation plays a greater role,and this results in the deck being warmer than the cable due to its

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Figure 4. Other notable responses which fluctuate with time.Top: Longitudinal expansion at quarter span. Middle:Temperature of cable. Bottom: Total approximated massof vehicles on bridge.

large surface area and thin depth, compared to the truss, which isshaded by the cantilever and hence is much cooler. Thus in theFE model the applied temperatures on the deck and truss changeto a linear function of the cable temperature when it is warmerthan 15◦C.

The static displacements closely relates to the cabletemperature, as shown in Figure 5; the longitudinal expansionhas a correlation coefficient of 0.96 with temperature, andvertical elevation has a correlation coefficient of -0.92. Theresults from the FE model are also similar to those demonstratedby the monitored results, so the results can be reasonablypredicted.

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Figure 5. Monitored and modelled displacement of the bridge,regarding temperature.

The predicted change in the suspension cable tension aredemonstrated by Figure 6. Blue markers indicate the tensionsat −5◦C, and the modelled temperature is increased until 30◦C,represented by the red markers. The parabolic profile of theresults show the axial tensions of the cable increase as the cablecurves upward due to the changing slope of the cable.

Figure 6 shows that as the cable temperature increases, thetension of the cable decreases uniformly, depending on whatspan it supports. This is a result of the cable expanding, andcauses the bridge deck to sag at high temperatures. The tensionin the Plymouth side span cable has to accommodate for thelongitudinal expansion of the bridge deck towards the Saltash

expansion gap, which may explain the low variation of cabletension.

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Figure 6. Modelled variation of suspension cable axial force,regarding temperature.

Figure 7 shows the FE model’s predicted variation offrequencies with temperature, as a result of expanding elements,and changes in material properties, stresses and strains of thestructure. Although the frequencies of vertical and lateralmodes drop with an increase in temperature, they do not varyas substantially as the monitored results (shown in Figure 3),which may indicate that temperature is a relatively insignificantparameter in relation to the variation of modal properties.Considering that ANSYS has to perform a static analysis priorto a modal analysis to incorporate thermal effects, then it seemsfeasible to rule out the effect of static configuration as well:the static displacements from thermal effects are not significantenough to cause the dramatic changes in the modal results. Thevariance of material properties, such as the Young’s modulusand density, causes only a very slight change to the structure’snatural frequencies.

However, the FE results show the frequency of the torsionalmodes can change significantly across just a few degrees.Investigations on other models of cable supported bridges, aswell as the Tamar FE model, have shown this may be due tothe transverse deck expansion of the bridge, coupled with theconnection to the cable. This behaviour, which is not observedon the prototype structure, will be the subject of future research.

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Figure 7. Modelled frequency change of the bridge, regardingtemperature.

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6.2 Traffic

The effect of traffic on modal properties was investigated next.The time series of the monitored frequencies show some troughsat rush hour periods, which may indicate traffic effects.

An approximation of the traffic mass was required, whichcould be used with the FE model to predict the bridge’sresponse. The number and classes of vehicle was establishedfrom toll records collected on Wednesdays, and the traffic masswas interpolated from web-cam images. Figure 8 shows theapproximated traffic mass for the monitored period, as well asa polynomial fitted curve to define a relationship between timeand mass.

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Figure 8. Approximated traffic mass upon bridge.

The FE model was loaded incrementally with equally-spacedvehicle masses, and had its dynamic properties observed.Figure 9 shows the change in frequency of the bridge as itundergoes increasing levels of traffic. The frequencies ofthe vertical modes behaved as expected, and decreased as themass increased. However, the first lateral mode rose withincreased levels of traffic, since the tensions in the suspensioncable increase with the additional imposed load, and creates anadditional stiffening effect.

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Figure 9. Predicted % change to the frequency due to increasedtraffic mass, according to the FE model.

Figure 10 provides an example of the monitored frequenciesfound on the first vertical mode, which illustrates the troughsformed at rush hour periods mentioned previously. Overlayingthese results are those predicted by the FE model. The amplitudeof the FE model prediction is about half of observed variation,

which may be due to an under-approximation of the totalvehicle mass, or the modal results may be more significantlyeffected by larger traffic masses, representing heavily-ladenlorries. However, the shape of the monitored and modal resultsfor the first vertical mode bear a strong correlation.

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Figure 10. Daily fluctuation of frequencies, comparisonbetween monitored and FE model results.

6.3 Influence of environmental parameters

Following the results above, the next step was to attemptto quantify the dynamic responses caused by each of theenvironmental effects, to see if the the performance of thebridge could be reasonably predicted, provided the operatingconditions were known. Additionally it is intended to supportthe previous suspicions that certain environmental effects mayhave a greater influence on particular modes than others.

Figures 11 and 12 show the change in suspension bridge’sfrequency caused by temperature and vehicles respectively.Both of the graphs were created with filtered data, wherethe other considered environmental parameters were minimal.For most of the modes a linear trend can be observed, asidentified by the FE model. It is noticeable that the first verticalmode, VS1, appears to be less affected by the environmentalconditions, but seems to be most influenced by the traffic mass.The first lateral symmetric mode, LS1, still has some uncertaintysince the data remains noisy.

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Figure 11. Effect of temperature against frequency; vehicle andwind effects filtered out.

Table 2 was created using the filtered monitored results toprovide a metamodel approximation of the frequencies whenprovided with the environmental data. Table 3 compares

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Figure 12. Effect of traffic mass against frequency; temperatureand wind effects filtered out.

these coefficients with recorded maximum and minimumtemperatures, wind speeds and traffic masses to provide anindication of which variable may have a stronger influence onthe data. It gives a clear indication that mode 2 and mode 3 arethe most heavily influenced by the environmental parameters,from the temperature and vehicle mass in particular.

Table 2. Linear environmental coefficients for monitored modalfrequencies

ModeBase Environmental coefficients

Frequency Temperature Wind Traffic(Hz) (Hz/◦C) (Hz/mph) (Hz/ton)

1 0.394 -0.48E-4 -1.07E-4 -5.17E-52 0.489 -6.92E-4 -4.33E-4 -17.18E-53 0.605 -3.24E-4 -1.63E-4 -8.35E-54 0.692 -2.36E-4 -0.76E-4 0.47E-55 0.733 -1.98E-4 -2.42E-4 -6.34E-5

Table 3. Approximated change in frequency, from minimummonitored result to maximum

Mode Mode shapeApproximated change in frequency

Temperature Wind Traffic(Hz) (Hz) (Hz)

1 VS1 -1.17E-3 -4.13E-3 -7.48E-32 LS1a -16.78E-3 -16.74E-3 -24.85E-33 VA1 -7.84E-3 -6.33E-3 -12.08E-34 LS1b -5.73E-3 -2.92E-3 0.68E-35 TS1 -4.81E-3 -9.36E-3 -9.16E-3

In Table 3, it appears that the traffic mass and temperaturehave a greater influence on the frequencies than the wind speed.However, each mode has a unique response to environmentaleffects: either the response caused by temperature or traffic massdominates the mode, or their influence is equal. Whilst thistable does back-up the significant effect of traffic mass predictedby the FE model, it suggests the FE model may still not bepicking up the response caused by temperature, and thus willbe investigated further.

7 CONCLUSIONS

It is acknowledged that environmental conditions may have asignificant influence on the natural frequencies of suspensionbridges, which may be observed from long-term monitoredresults. The mode which appears to vary the most on the TamarSuspension Bridge is the first lateral symmetric mode.

Whilst the results show a very close relationship betweenthe temperature and the static configuration of the TamarSuspension Bridge, the FE model shows little evidence that thisaffects the modal properties significantly, although this is notnecessarily true for all modes.

However, the monitored and predicted results agree that, forthe Tamar Suspension Bridge, the total mass of traffic is the mostinfluential parameter on the bridge’s dynamic performance,followed by the temperature. This suggests that the additionalmass from the traffic in comparison to the mass of the deck is asignificant environmental parameter.

ACKNOWLEDGMENTS

The authors of this paper would like to thank David List,Richard Cole and the rest of the staff at the Tamar Bridge Officefor their cooperation, EU Framework 7 project IRIS for financialsupport, and our colleagues at the Vibration Engineering Section(VES) at the University of Sheffield.

REFERENCES[1] J.M.W. Brownjohn, Structural Health Monitoring of civil infrastructure,

Philosophical Transactions of the Royal Society A, 365:589-622, 2007.[2] J. Maeck and G. de Roeck, Damage assessment using vibration analysis

on the Z24-Bridge, Mechanical Systems and Signal Processing, 17(1):133-142, 2003.

[3] B. Jaishi and J.M.W. Brownjohn, Modal parameter estimation from ambientresponse data of S101 flyover, IRIS Working Document, 268:1-21, 2010.

[4] P. Cornwell, C.R. Farrar, D.W. Doebling and H. Sohn,, Environmentalvariability of modal properties Experimental Techniques, 23(6)45-48, 1999.

[5] B. Peeters and G. De Roeck, One year monitoring of the Z24-Bridge:Environmental effects versus damage events, Earthquake Engineering andStructural Dynamics, 30:149-171, 2001.

[6] Y.Q. Ni, X.G. Hua, K.Q. Fan and J.M. Ko, Correlating modal propertieswith temperature using long-term monitoring data and support vectormachine technique, Engineering Structures, 27:1762-1773, 2005.

[7] J.M.W. Brownjohn, A. Pavic, P. Carden and C. Middleton, Modal Testingof Tamar Suspension Bridge, IMAC XXV, Orlando, USA, 19-22 Februray2007.

[8] R.J. Westgate and J. M. W. Brownjohn, Development of a Tamar Bridgefinite element model IMAC XXVIII, Jacksonville, USA, February 2010.

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