Engineering Structures 30 (2008) 2771–2781

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Engineering Structures

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The Stuttgart TV Tower — displacement of the top caused by the effects of sunand windPeter Breuer a, Tadeusz Chmielewski b,∗, Piotr Górski b, Eduard Konopka a,b, Lesław Tarczyński ba University of Applied Sciences, Schellingstrasse 24, 70174 Stuttgart, Germanyb Opole University of Technology, ul. Katowicka 48, 45-061 Opole, Poland

a r t i c l e i n f o

Article history:Received 10 January 2008Received in revised form11 March 2008Accepted 17 March 2008Available online 2 May 2008

Keywords:GPSFull-scale measurementsMonitoring of displacements and vibrationcharacteristics

a b s t r a c t

Themonitoring of static, quasi-static and dynamic deformations of long-period structures is nowpossibleusing Global Positioning System (GPS) technology. This paper describes theway inwhich the Stuttgart TVTowerwasmonitored using static and kinematic GPSmodes. The displacements of the towerwere causedby two factors. Quasi-static displacements were caused by the combined influence of solar radiation anddaily air temperature variation during different weather seasons and conditions. Dynamic displacementswere caused by wind. The results clearly demonstrate that the procedure using GPS measurementsallows us to collect displacement data which could be used to determine the displacement thresholdsof the tower and/or to examine the changes of vibration characteristics. This data was valuable for theassessment of the integrity and reliability of the tower.

© 2008 Elsevier Ltd. All rights reserved.

1. Introduction

In the last ten years Global Positioning System (GPS) with10–20 Hz sampling rates has become a useful tool for measuringand monitoring static, quasi-static and dynamic responses inlong-period civil engineering structures exposed to gust-winds,earthquakes or temperature variation. GPS has been appliedmainly in conventional geodetic surveys, but also in seismologicaland geological studies, to detect, measure, and monitor subtlechanges in the shape or relative position of the Earth’s surface(e.g. Helz [1]). The first ever, permanent and pioneering installationof GPS units on the rooves of two buildings, one in Los Angelesand one in San Francisco, has now been completed. Records ofmotions caused by earthquakes and strong wind will be used tocompute drift ratios and changes in the dynamic characteristicsof these buildings — Çelebi [2], Çelebi et al. [3]. Among others,Ashkenazi and Roberts [4], Roberts et al. [5], Brown et al. [6],Nakamura [7], applied temporarily installed GPS units to measurethe displacement responses of long-span cable-supported bridgesunder gust-wind. Lovse et al. [8], Breuer et al. [9], Tamura et al. [10]applied GPS technology to study the displacement responses oftall slender structures such as TV Towers, industrial chimneysor steel towers. Kijewski and Kareem [11], Chen et al. [12],Çelebi and Sanli [3], Bashor et al. [18] applied GPS to measure

∗ Corresponding author. Tel.: +48 77 4539877; fax: +48 77 4565084.E-mail address: t.chmielewski@po.opole.pl (T. Chmielewski).

0141-0296/$ – see front matter© 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.engstruct.2008.03.008

the displacement response of tall buildings under wind andearthquake.

Recently, some calibration tests have been conducted to assessGPS accuracy. Nickitopoulou et al. [13] made a large number oftests, in which harmonic motions were generated by a rotatingGPS rover antenna, and the coordinates thus measured werecompared with the real ones. Chan et al. [14] developed a motionsimulation table which simulated various types of 2D motions,for either tall buildings in a horizontal plane or long-span bridgesin a vertical direction. Calibration tests have been conducted byTamura et al. [10], Breuer et al. [9] and some others. The firstwork to document the accuracy of GPS to record higher vibrationfrequencies (up to 4 Hz), and to identify more than one dominantfrequency, has been done by Psimoulis et al. [20].

In everyday engineering life, there is a great need formeasuringwind-induced dynamic displacement responses or sun-inducedquasi-static displacement responses of tall industrial chimneysor TV Towers, mainly in the horizontal plane. In order tocontribute to a solution to these problems, the GPS units havebeen temporarily installed on top of the Stuttgart TV Tower. Thispaper describes field tests conducted on this tower to measurethe displacements at the tower top caused by wind and by thecombined influence of solar radiation and daily air temperaturevariation during different weather seasons and conditions. Thesetests provided data indicating that there has been no excessivedisplacement and no change in first natural frequency sinceit was estimated experimentally in 1959. So, the Stuttgart TVTower after 50 years in service life appears to be structurallyundamaged.

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Fig. 1. The Stuttgart TV Tower with a tower head and a viewing platform. Smallbalconies with danger-lights and lighthouse installations are above the platform.

2. The stuttgart TV Tower and its dynamic characteristics, aspreviously measured

The TV Tower in Stuttgart was designed and built by ProfessorFritz Leonhardt in 1953–1955. It was the first television tower inthe world which was constructed as a concrete tube. The concreteshaft is 161mhigh. Its diameter is 10.8m at the bottom and 5.04mat the end. The wall thickness decreases from 60 cm to 19 cm. Atthe upper end of the shaft is mounted a steel antennamast (Fig. 1),which is 51 m high. The total height of the TV Tower in 1955 was212 m. Its absolute height above sea level is 700 m.

The idea for the tower, its structural system, some details ofthe construction, costs, all assumptions for the static calculationsand the first measurements of the settlement of the foundationand quasi-static displacements of the shaft of the tower due tosolar radiation and daily air temperature variation are all givenin Leonhardt’s paper [15]. The idea, project and structural systemwere made in 1953–1954 by Leonhardt, but the static calculationsof the tower were made in the Pieckert design office. They alsomade the calculations for the fundamental natural vibration periodof this tower with the following results: T1 = 4.71 s – working onthe assumption that the base of the tower is fixed; and T1 = 6.0 s– if the flexibility of the soil under the tower’s foundation is takeninto account.

The quasi-static displacement of one point of the tower shaft,125 m above the ground, approximately 11 m below the towerhead, were measured by a conventional geodetic method, duringone day in August 1956 (exact day is not given). The path ofthe movement of this point described an ellipse with longer axisequal to 8 cm in the East–West direction. The weather conditionsfor that day are not given. In Leonhardt’s paper [15] there arealso instructions that the wind response of the tower should bemeasured — when it would be possible. This was achieved 3 yearslater by Lenk [16] and again 50 years later by the authors of thispaper.

The first preliminary wind-induced vibration response mea-surements were made by Sauer [17]. These have not been pub-lished. The measurements were taken in the period from 3rd Mayto 28th May 1956. In the lift room, at a height of 155 m, heinstalled the instrument known in German as a Lemag-Seismo-Schwingschreiber [16] which was able to measure and record ona strip of paper the wind response of the tower but only in theEast–West direction. From his measurements of wind-induced vi-bration, based on a wind velocity of approximately 8 m/s (asmeasured at 10 m above the ground), he determined the first twonatural periods of vibration as follows: T1 = 4.6 s and T2 = 0.77 s.

Fig. 2. The Stuttgart TV Tower with GPS-Antenna (Rover Station) mounted on thehandrail of the balcony, 5 m above viewing platform.

Three years later the measurements of free vibration responseand wind response of the tower were made by Lenk [16]. Themeasurements of the wind response were taken continuouslyfrom 23rd June to 22nd December 1959. He installed two Lemag-Seismo-Schwingschreibers, at a height of 155 m, which were ableto measure the tower response in two directions, i.e. East–Westand South–North. In the free vibration test the towerwas disturbedfrom its static equilibrium position using a rope with a diameter of24 mm, which was fixed to the top of the tower and then pulledby a winch (auto crane) on the ground. The rope was cut and thefree vibration of the tower as it returned to its upright positionwas recorded. The free vibration tests were repeated four times.From the free vibration records Lenk [16] determined the first twonatural periods of vibration with the following results: T1 = 5.18 s(f1 = 0.193 Hz) and T2 = 0.79 s (f2 = 1.27 Hz) and logarithmicdecrements δ1 = 0.039 and δ2 = 0.021. These values are the meanvalues from four tests.

Lenk’s main measurements dealt with the wind velocity andthe wind response of the tower. In his paper [16] he states thatthe second half of the year 1959 was warm with relatively weakwinds. For such conditions he was able to draw a diagram for thecross-wind response as a function of wind velocity and a diagramfor the wind pressure distributions measured at three heights:61.0, 104.8 and 140.4 m. On these levels he installed 6 pressuresensors (equally distributed around the tower). Based on thesemeasurements he compiled a wind velocity profile and a windpressure distribution profile.

The Stuttgart TV Tower has been temporarily monitored by theauthors of this paper since 1998. The Rover Antenna was tightlyfixed on the handrail of the southern light balcony, as shown inFig. 2. The stiffness of the frame is very high because of its case-formed diameter. Only during strong winds could a vibration ofthe handrail itself be assumed, but in fact awind-induced vibrationof that frame was never observed. Of course, a manually excitedvibration of the handrail is possible up to a lateral displacementof some millimetres. That is a very small displacement against theexpected displacement of the tower top of several centimetres.Furthermore the free vibration of the handrail was measured on4th March 2008 and found to have a first natural frequency ofabout 11 Hz. That frequency is of a different order from the firstnatural frequency of the tower which is approximately equal to0.2 Hz. Therefore a possible vibration of the handrail should haveno influence on our interpretation of wind response.

The preliminary results of our measurements are published ina paper [9]. New results and the comparisons with the dynamiccharacteristics previously measured are given in Sections 6–8 ofthis paper.

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Fig. 3. 24 h Skyplot of the available satellites with their tracks at the Stuttgart TVTower. There are no tracks in the Northern sector of the sky. The Rover Antenna isplaced in the South of the gallery, in order that the tower itself blocks the Northernsector only, where no satellites appear.

3. Applied GPS methodology

Monitoring the displacements of the top of the tower usingoptical surveying methods, can only be carried out duringdaylight with sufficient visibility. Vibration cannot be monitoredby traditional surveying techniques because the frequency of theoscillation is too high.

Using a Global Positioning System (GPS) data can be takenregardless of the visibility or the weather. Using sophisticated GPSequipment with two Dual Frequency Receivers (Reference andRover Station) the satellite signals can be tracked with a data ratedown to 0.05 s, which is straightforward and is adequate for thepurpose of recording vibrations with great precision. Automaticregistration permits the collection of GPS data over several days.

GPS positioning needs the availability and reception of satellitesignals. For static GPS application at least 4 satellites are needed;for kinematic GPS application at least 5 satellites are required. Thebest conditions for receiving the satellite signals are when there isa clear sight of the sky. This condition is true both for the ReferenceAntenna and for the Rover Antenna.

In addition, local obstacles like buildings or trees may impedereception by shadowing and blocking the broadcasted signals.Therefore GPS positioning in narrow streets or close to buildingsor close to other obstacles may be difficult or impossible. Thisproblem occurs when the Rover Antenna is not able to bemountedabove a tower deck, but only on the gallery of that tower, wherea large sector of the horizon is blocked by the structure itself. Tominimize the number of blocked signals, the Rover Antenna shouldbe mounted in the very South of the structure and as far away aspossible from the tower wall.

The distribution of satellites in the sky is not homogeneous. Inthe Northern hemisphere there is a distinct lack of satellites in theNorthern sector of the sky. If it is possible to mount the antenna inthe described favourable manner to optimize signal reception, thenumber and duration of blocked signals can be reduced (Fig. 3).During the day the number of available satellites varies (from 4 toas many as 10) and their position in the sky is not constant, butusually the chance for a successfully positioning will arise.

From our own experiences on the top decks of chimneys, partialblocked satellite signal reception causes a loss of 5%–10% of thebaseline solutions during the period of one day. The number of lostsolutions depends on the local conditions and on the quality of theapplied GPS units.

Furthermore, there is another GPS problem caused by theproximity of buildings or other reflecting surfaces. The so-calledmultipath effect, which occurs in terrestrial electronic distancemeasurements, sometimes also appears in GPS applications. This

occurs when the sensor receives not only the direct signal but alsoa reflected signal from some reflecting surfaces in the vicinity. Thisevent produces systematic deviations in positioning for a certaintime, i.e. a deviation up to some centimetres for a period of someminutes. Geodesy and surveying attempts to minimize the effectof this by extending the time period of GPS monitoring. Anotherway to detect and to avoid the influence of multipath, is to repeatthe observation at another time, because the satellite coveragechanges during the day. Another way to receive independentresults is to use a second Reference Station.

To detect and to minimize the mentioned systematic errors,long monitoring sessions (up to 100 h) and a large number ofrepetitions (up to 200), have been applied in GPS monitoring ofstructures, as described in the following sections. Therefore posi-tioning resultswhichwere systematically falsified bymultipath ef-fects could be recognized and eliminated (approximately 3%).

Also, the problem of reflection is much reduced because thetower has a curved surface rather than planes. When monitoringa wind-induced vibration, a systematic falsified absolute positionis not significant, if the period of the vibration is much smallerthan the period of the systematical falsification induced bymultipathing or other systematical influences. The wind responseof the structure is monitored as a relative displacement for aperiod of some seconds only. Therefore, if the focus is not directedto the static component of the wind response, the amplitudeand frequency of the vibration can be analysed precisely andindependently of the absolute Rover position and its accuracy.

The positions of the Rover Antenna can be processed in theso-called Static Mode or in the Kinematic Mode. The StaticMode is applied if no movement of the Rover Antenna duringmeasurements is assumed and is the common method applied insurveying. Since GPS monitoring of the tower was restricted totime intervals over 10 min, the position of the construction wasassumed to be stable during that period in spite of amoderate shiftdue to temperature change (maximum 4 cm/h). The KinematicMode is applied to monitor dynamic effects, e.g. if the tower startsto be shaken by thewind. In the KinematicMode corrections to thesatellite signals of the Rover Antenna are calculated from another,simultaneously-operating Reference Antenna which is fixed in anearby position.

During data collection, the GPS data was recorded for staticpost-processing providing one coordinate triple for every session.Converting the assembled data to the so-called RINEX format,a parameter for kinematic post-processing (KOF = KinematicOn-the-Fly) can be introduced. Kinematic processing providesabout 1000 positions during every session. The average of these1000 positions corresponds with the unique result from the staticsolution. As a first step, it was attempted to evaluate each 10 msession applying the Static Mode. Only for those sessions whenwind was present, was a Kinematic Mode solution attemptedafterwards.

4. Precision of GPS application in laboratory tests

For all our studies in the last 10 years, Leica Geoystem GPSreceivers (Type 300, 500, 1200) were exclusively used. Since 2006only GPS1200 was applied to monitor the Stuttgart TV Tower. Thereceiver GPS1200 in combination with the proper LGO softwareprovides better positioning, even during unfavourable satellitewindows. The number of unresolved base lines (no Ambiguityresolution) during the day is clearly reduced compared with theolder equipment by approximately 50%.

Before using the GPS application for the Stuttgart TV Tower in1998 and 1999, a test was made to estimate the accuracy to beexpected [19]. The idea was to track a well-known trace of theRover Antenna using a pattern or template and to compare the

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Fig. 4. Foreground: Rover Antenna mounted on a tripod provided with a rotatingarm. Background: Reference Antenna on a concrete pillar block.

Fig. 5. Result of the Rover Antenna’s kinematic GPS tracing applied on twodifferentradii (diameter 25 & 49 cm).

processed GPS positions with the given route. A straight rule, orthe edges of a right-angled triangle, can be used as a convenienttemplate for a test, along the edges of which the Rover Antenna ismoved in a straight line manually. The disadvantage of a manuallyguided antenna is the inaccuracy in following the edge and the lossof antenna verticality caused by the friction along the template andthe roughness of the surface. A high precision of the test procedureis given, if the Rover Antenna is fixed on a rotating arm turningaround a fixed centre.

Fig. 4. shows the prototype of such a construction, which hasbeen used since 1998/99 to test the precision of GPS positioningbased on different baseline length from 100m to 10 km [19]. Fig. 5.displays the resultsmonitoring the track of the Rover Antennawithtwo different circle diameters (25 and 49 cm). The mean squaredeviation from the given course is about 3–4mm, if themonitoringperiod does not exceed 5 min; otherwise the above discussedpossible systematic influences produce a systematic shift. For thegraphic analysis in the ground map it is recommended to restrictthe number of orbits to the minimum, otherwise the design canbe confusing. Fig. 5 presents 7 orbits of the Rover Antenna duringa time period of 2.5 min, containing 300 antenna positions. Longsecants at the circle periphery indicate an intended faster rotation.A regular rotating velocity during the test is not necessary becausein reality the displacement of structures, mainly vibration, donot appear with a linear velocity but with positive and negativeacceleration. The circular course is a very appropriate way to checkthe precision of tracing in every direction.

Nickitopoulou et al. [13] prefer to trace harmonic motionsproduced by an electric motor enabling different constant angularvelocities. They aim to check whether the accuracy of kinematicGPS positioning depends on the velocity of the motion. The

Fig. 6. Equipment for a simple field test using a tripod plate giving a template for acontrolled circle-shaped motion of the GPS Rover Antenna. The results of trackingare shown in Fig. 7.

Fig. 7. Positions of the Rover Antenna evaluated by kinematic post-processing overthree Antenna orbits (77 s) with a data rate of 1 s-intervals (Otmuchów, 2004-07-02, 6 satellites, GDOP 3.4).

laboratory tests were carried out for an velocity of 0.1–1.0 m/s.They conclude that under their test conditions (sample orcompacted data) a faster motion leads to a reduced accuracy inpositioning.

In the following sections of this paper a maximum oscillationvelocity of 8 cm/s (as shown in Fig. 12) will be assumed. Forthis velocity, Nickitopoulou’s diagrams showa coordinate standarderror of less than 5 mm. This value is very close to the rms-value for the radius in Fig. 7. Nickitopoulou’s test of GPS heightaccuracy (z-coordinate) confirms the commonknown relationship:the accuracy in the component z decreases against the componentsx/y by a factor of 2–3. Therefore in our studies theGPS heightswereused only to check the trend of the variation in height. For moreprecise analysis in z-deviation, levelling of the top of the structurewas used, as described in Section 6.

To test GPS accuracy in the field, a much simpler test withmoreprimitive equipment can be used, for example the circular hole inthe tripod plate, which can serve as a circle template. Figs. 6 and7 describe such an experiment as a part of some other tests. TheRover Antenna was guided alongside the inner border of the holefor about 3 orbits over an interval of 77 s. The restriction to 3 orbitsaims to preserve the clarity of the course in the ground sketch. TheAntenna’s positions were recorded at 1 s-intervals. Fig. 7 presentsthe processed positions within a 2× 2 cm grid. Almost all antennapositions are properlywithin a small circular ring. Themean squareerror of the positions is close to 3mm. This value corresponds withthe results of our earlier studies [19]. The conclusion is, clearly, thatevery relative displacement of the Rover Antenna which exceeds

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Fig. 8. The Stuttgart TV Tower, daily drift of the top due to solar radiation and daily temperature variation with hourly positions and time marks (4th–8th July 2006). InNorth-East of the ground plan two outliers are shown, caused by a thunderstorm with wind from South-West at a velocity of about 17 m/s.

6–9 mm can be recognized with a high reliability (95%–99%) as atrue change of position.

The accuracy of results in the described studies depends onthe number of available satellites and their geometrical positionin the sky (DOP = Dilution of Precision). During such a testin the laboratory it is to be assumed that any obstacles whichmight block the signal reception are to be avoided. In the fieldand on the tower gallery the conditions for the signal receptionare – as discussed above – quite different and not consistentlyexcellent. The estimation of the accuracy of these results cannotbe based only on the described laboratory tests. For a full scale testto monitor structures a more sophisticated valuation is needed,i.e. a set of repetitions under different GPS conditions, as will bepresented in the following sections.

5. Daily drift of the tower top due to solar radiation and dailyair temperature variation

It has been recognized that the temperature distribution onthe external surface of a TV shaft varies with environmentalconditions. Fig. 10 shows the time-dependent records of the airtemperature and the intensity of sun radiation during 4 days ofmeasurements (4th–8th July 2006). During the sunny day, theenlightened surface of the tower shaft is subjected to thermalexpansion due to nonsymmetrical warming.

Due to changes in temperature gradient within the crosssection of the shaft of the tower additional stresses and horizontaldeformations of the tower are induced. During a sunny day thepath of the top of the tower describes an ellipse related to theposition of the sun.

The side exposed to the sun will be extended and the towerand its top will incline away from the sun. Since during the daythe sun moves from the East, via the South, to the West, the top of

the tower describes an elliptical pathWest–North-East. The size ofthe displacement depends on the temperature difference betweenthe exposed side and the shaded side, i.e. the intensity of direct sunirradiation. During the night the temperature differences betweenthe two sides are balanced and the tower returns to a certain zeroarea.

During a sunny day, for example, a tower with a height of h =

160 m at temperature gradient between sunny and shady side of1t = 100, with an expansion coefficient of reinforced concreteα = 11.5 × 10−6 K−1, the sunny side might be 18.4 mm longerthan the shady side, resulting in an inclination of the tower witha nonlinear bending line. The higher and the more flexible thestructure is, the more the end of its bending line will be dislocatedout of the vertical reference line.

This paper deals with a study in summer 2006 (4th–8th July),when the Stuttgart TV Tower was monitored by GPS for about100 h. Every 30 min a data series was registered covering 10 minwith a data rate of 0.5 s. Since the equipment Leica GPS 500 has astart-up delay of 90 s before it can track satellites, each data serieswas restricted to 1020 data sets. To get the positions of the dailydrift the post-processing was carried out applying the so-calledStaticMode. For every hour amoving averagewas calculated basedon 3 values of half-hour positions. Figs. 8 and 9 present the resultsin a 2 × 2 cm grid.

The daily temperature drift occurs in Fig. 8 as several ellipticalloops with long axis in the West–East direction (17 cm) and ashorter axis in the South–North direction (9 cm). The path isdivided into 1 h-intervals. Points mark the date and the time ofthe position, e.g. 5–16:00 means the 5th of July at 4.00 p.m. Thistrajectory is not the same day after day, since sunshine durationand temperature vary from day to day. This can be observed inFig. 10, which depicts the corresponding meteorological data. Themaximum displacement of the top towards West appears only

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Fig. 9. The Stuttgart TV Tower, static and dynamic components of the wind response during a thunderstorm producing an outline of the daily temperature drift (see Fig. 8).The wind from South-West with a velocity of about 17 m/s causes a North-East displacement (static component) of about 6 cm. The main direction of vibration is at a rightangle to the wind direction with a displacement of 9–14 cm (5th July 2006).

Fig. 10. Weather records for the air temperature and the intensity of sun radiation during GPS campaign (Stuttgart-Echterdingen, 4th–8th July 2006).

during the first three days (4th–6th July). During the final twodays (7th–8th July) the positions of the top stabilized around thezero-spot area, indicating a reduced motion rate. Zero-spot areais defined as the location of the structure during the night orcloudy day where movement is minimal and insignificant within,say, a 2 cm radius. Thus the change of movement is based on thechange of meteorological conditions. Fig. 10 shows the recordedtemperature and the intensity of sun radiation during the GPSsession. The data was collected at the German MeteorologicalStation in Echterdingen (located 7 km from the Tower). Duringthe first two days the temperature rose to 30 ◦C–32 ◦C at noon,accompanied by an evident high radiation rate. On the 6th ofJuly the rise in temperature and levels of sunshine stoppedsuddenly at 12:30. At the same time in Fig. 8 the path leaves thewestbound direction and turns back towards the zero spot. Duringthe following two days the temperature did not exceed 21 ◦C andthe appearance of sunshine was minimal. Therefore the moving

rate of the top of the tower is strongly reduced and the trackedGPS positions rest within the zero-spot area.

6. Response to wind

In the evening of 5th of July a thunderstorm occurred from22:00 to 23:00 h. That event can be noticed from the temperaturecurve in Fig. 10,where at 21:30 the temperature dropped suddenly.The wind velocity is shown in Fig. 11, where during this time(22.00–23:00) a maximum wind velocity of 11 m/s was observed.The speed of the wind was recorded at the meteorological stationof the Airport Stuttgart–Echterdingen, at a distance of 7 kmsouthwest of the Stuttgart TV Tower. Since the anemometers ofall meteorological stations are mounted 10 m above ground, anextrapolation of data must be applied to the altitude of the top ofthe tower (161 m), namely the end of the concrete shaft. Using thepower law, an average velocity of 17–18m/s at the top of the towercan be calculated.

P. Breuer et al. / Engineering Structures 30 (2008) 2771–2781 2777

Fig. 11. The wind velocity and its direction recorded during GPS session (Stuttgart, 4th–8th July 2006).

Theupper right-hand corner of Fig. 8,which is separately shownas Fig. 9, illustrates the response to the wind between 22:00and 22:30 h, and visualizes the trace of vibration for 3 separatedtime intervals over 1 min within the two 10 min sessions. Everyvibration trace inclines to an elliptical form, whose axis azimuthchanges slightly. The graphic design shows two components:

• The static component = the displacement to the North-East ofabout 6 cm from the daily temperature path, and about 10 cmfrom the zero-spot area.

• The dynamic component = the vibration in cross-winddirection with the amplitude ±7 cm.

The time marks 5–22:00 and 5–22:30 indicate the averageposition of the tower within the point cloud of 1020 GPS positions.The centre of both point clouds is situated about 10 cm northeastof the zero-spot area. The distance of the actual temperature path,i.e. between the time marks 5–21:00 and 5–22:00, is 6 cm. It canbe concluded that the North-East displacement of 6 cm from theactual temperature course is caused by the static component ofwind response.

Both point clouds contain about 1000 GPS positions at 0.5 sintervals. The positions were processed using the KinematicMode, the so-called Kinematic On-the-Fly method (KOF). To showmovement it is necessary to connect all consecutive positions by aline (vector). Since the movement is not regular, the drawing of aline connecting all 2000 points would be very obscure. Thereforethe plotted lines were limited to 3 intervals lasting 60 s. In Fig. 9the three time intervals are explained by a legend. The behaviourof all 3 courses is similar, i.e. the main axis of vibration is at a rightangle to the direction of the wind, with the amplitude of the mainaxis being 4.5 to 7 cm. In addition to the change in the amplitudes, asignificant change in the azimuth of the main dislocation direction(cross wind) occurs according to the change of wind direction.

In wind direction (along wind) the amplitude of oscillationchanges from 0 up to 7 cm. If the transversal movement (crosswind) occurs close to the point cloud, the longitudinal amplitudeis reduced; otherwise the amplitude is increased.

Besides the path in the ground plan, the vibrations are designedover the time axis as shown in Fig. 12. The zero axis of displacementis fixed by the centre of the point cloud. The presentation hasbeen restricted to the extreme oscillation at 22:30. For the totalobservation interval 22:32:20 to 22:40:00 a ribbon of oscillationwas drawn, i.e. for the along-wind component of the vibrationshown in Fig. 12a, and for the cross-wind component of thevibration shown in Fig. 12b. Fig. 12c and d show all data points (at0.5s intervals) for the same 60 s interval taken from a section ofthe time series shown in Fig. 12a and b. For the civil engineer, thedensity of themeasured positions (interpolation points) shows theconsecutive analysis is valid and that the number of interpolationpoints is sufficient, within the vibration period for reliable analysis.

7. Health monitoring of the Stuttgart TV Tower from possiblechanges in its natural frequencies

The Stuttgart TV Tower in its more than 50 year service lifehas undergone deterioration and damage due to various factors

Table 1The comparison of the first natural frequency estimated experimentally

Structure Lenk’s test f1 (Hz) Breuer’s et al. test f1 (Hz)

The Stuttgart TV Tower 0.193 0.191

such as operating load (i.e. wind load, live load), sun radiation anddaily air temperature variation, environmental erosion, fatigue,etc. Its structural failure could be catastrophic not only in termsof financial loss, but also in terms of social impact. That is whystructural damage detection is becoming an important researchsubject in engineering, for towers such as this and for many othercivil engineering structures.

In the case of this tower, it is possible to examine the changesto its vibration characteristics (such as natural frequencies, modeshapes and damping) in order to detect structural damage usingthe so-called vibration-based method. Local damage may cause adecrease in structural stiffness which will generate changes in thevibration characteristics of the tower. If the changes of these char-acteristics are confirmed, the locations andmagnitudes of damagescan then be identified. The key advantage of this method is that itis not necessary to know beforehand where the damage is located.

In our approach to detecting damage to the Stuttgart TV Tower,we assumed that the changes in the first natural frequency asa global property of the tower may be used as a measure ofpotential damage. The first two natural frequencies of the StuttgartTV Tower were derived in 1959 by Lenk [16]. Only now can thefirst natural frequency be measured conveniently and accuratelyby GPS (although only at one given point of the tower).

Fig. 13. shows the power spectral densities of the top of thetower as calculated by the FFT method for along- and cross-windresponses for the time series shown in Fig. 12. For both powerspectral densities there is one peak at 0.191 Hz (T = 5.24 s), asshown in Fig. 13, corresponding to the lowest natural frequency ofthe tower.

The comparison of the first natural frequency estimatedexperimentally by Lenk [16] in 1959 and by the authors of thispaper in 2006 is presented in Table 1.

There is no change between the first natural frequency asestimated experimentally in 1959 and that in 2006. Therefore, theStuttgart TV Tower, after 50 years of service life appears to bestructurally undamaged. Its structural stiffness has apparently notdecreased.

In the original study wind-induced responses were measuredfor 10 min intervals only. This interval was insufficient for us toestimate the damping ratio using Random Decrement technique.To do this it would be necessary to measure the wind responsecontinuously for approximately 2 h.

8. Seasonal drift due to solar radiation and daily air tempera-ture variation

Fig. 8 depicts the daily drift of the Stuttgart TV Tower during4 days in June 2006 2006. Figs. 14 and 15 show measurementsfor the same test conducted in November 2005 and again in

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Fig. 12. Stuttgart TV Tower — oscillation of the top of the tower during South-Westerly wind of 17–18 m/s (6 satellites available, GDOP = 3.0): (a) along-wind componentof the vibration over 7 min and 40 s, (b) cross-wind component of the vibration over 7 min and 40 s, (c) one minute detail, along-wind component, showing all 120 datapoints, (d) one minute detail, cross-wind component, showing all 120 data points.

Table 2Synopsis of 3 GPS observation campaigns during different seasons with different temperature profiles

# Observation period Hours Temperature interval (◦C) Maximum radiation (J/cm2) East–West (cm) North–South (cm)

1 8th–12th November 2005 99 3 to 13 147 6 122 15th–19th December 2005 97 −3 to +3 106 7 83 4th–8th June 2006 98 20 to 34 323 17 9

The table shows the maximummagnitudes of the main axis in the ground plan during the daily elliptical drift and the relevant meteorological data.

December 2005. Fig. 16 conflates the three sets of data into onefigure and a legend identifies the three campaigns. A synopsis ofkey parameters is given in Table 2.

In Stuttgart during summer time the sun is visible for up to 16 habove the horizon, whereas in winter time it is visible above thehorizon for 6 h at themost. Therefore themotion loop in summer is

much longer than in winter and extends in an extreme West–Eastdirection (as shown in Fig. 8). During summer mornings the topof the tower is displaced to the West, at noon to the North andin the late afternoon towards the East. In the ground plan themotion describes an elliptical loop whose main axis is orientatedin a West–East direction.

P. Breuer et al. / Engineering Structures 30 (2008) 2771–2781 2779

Fig. 13. The Stuttgart TV Tower, power spectral densities of tower responses: (a) for the along-wind component, (b) for the cross-wind component (5th July 2006), calculatedby FFT from the time series as shown in Fig. 12a and b.

Fig. 14. The Stuttgart TV Tower, daily drift of the top due to solar radiation anddailytemperature variation with hourly positions and time marks (8th–12th November,2005). Motion is mainly oriented to the North.

Due to sunshine the motion in November 2005 is mainlyorientated to the North because the sun appears only in the Southand directs the top of the tower towards the North only (Fig. 14).In the December 2005 campaign the extension of the motion isreduced because the duration of the sun’s presence is the shortest.Furthermore, from Table 2 we can also see that the Novembercampaign was conducted during much sunnier, warmer days thanthe December campaign.

The clockwise rotation ceases during the night and the towerposition returns to a certain zero-spot area (defined in Section 6)whose position is not the same for each of the three campaigns,as can be seen in Fig. 16. For each campaign the zero-spot areais marked as a circle with a diameter of 4 cm. The position of thezero-spot area seems to depend on the season. To assume a uniquezero-spot area covering the tower’s night position for all 3

Fig. 15. The Stuttgart TV Tower, daily drift of the top due to solar radiation anddailytemperature variation, with hourly positions and timemarks (15th–19th December2005). The coldest days, with the shortest duration of sunlight. Accordingly, motionoutside the zero-spot area is the smallest of all the campaigns.

campaigns, the diameter of the circle would have to be doubledto 8 cm.

9. Looking to the future: monitoring tall slender structures

Until now, we have directed our efforts to the temporaryinstallation of GPS units on the Stuttgart TV Tower (in Germany)and on three tall multiflue industrial chimneys in Poland; one inthe power station in Opole (250 m tall), two in the power stationin Bełchatów (both 300 m tall). The results of the work have beenpublished in our papers [9,19,21]. The purpose of this study isto use the quasi-static response due to the combined influenceof solar radiation and daily air temperature variation or dynamicwind response measurements with GPS as a health monitoring

2780 P. Breuer et al. / Engineering Structures 30 (2008) 2771–2781

Fig. 16. The Stuttgart TV Tower. Synopsis of the daily drift of the top caused by solar radiation and daily air temperature variation during 3 GPS campaigns in differentseasons. The daily elliptical path of the shift extends mainly in a West–East direction during summertime, and in a Northern direction during winter.

tool. Currently, the GPS units are being temporarily installed forsome days on the structuresmentioned above at least twice a year.Measurements will provide data to show excessive displacementsor significant changes in the dynamic characteristics of thesetall structures. When a predetermined displacement threshold isreached, this information will become available to managers. Themanagers can then assess the quasi-static or dynamic responseof a structure (TV Tower or chimney) according to: (a) differentdisplacement thresholds (e.g. A and B as shown in Fig. 17); or (b)changing dynamic characteristics. In the case of a serious situation,the respective managements can make decisions for additionalinspection of the structure in order to secure its safety.

10. Conclusions

From our measurements we can draw the following conclu-sions:

(1) The results show clearly that it is possible to measure quasi-static response (due to temperature) and dynamic response(due to wind) in tall structures like the Stuttgart TV Towerusing GPS units. These measurements allow us to examineboth displacement levels and also changes of vibration

Fig. 17. Assumed hypothetical thresholds of displacements shown to demonstratehow GPS data can provide warning at different displacement values (e.g. ThresholdA may refer to the serviceability limit state, and Threshold B to the ultimate limitstate for a structure).

characteristics such as natural frequencies and damping, allof which provide information about potential damage to thestructure.

(2) For wind response and for a sample rate equal to 2 samples persecond (2 sps), GPS was able to measure only the first naturalfrequency (0.191 Hz) of the Stuttgart TV Tower.

(3) There is no apparent change (within the accuracy of thetests) between the first natural frequency as estimated

P. Breuer et al. / Engineering Structures 30 (2008) 2771–2781 2781

experimentally by Lenk in 1959 and as measured by Breueret al. in 2006. So, the Stuttgart TV Tower after 50 years ofservice life appears to be structurally undamaged. Its structuralstiffness is not decreased.

(4) GPS canmeasure the total dynamic wind response, not only itsdynamic fluctuating component but also the static component,i.e. a mean value which is measured directly. This has anadvantage over vibration measurements using accelerometersfor which measurement of a static component is verydifficult.

(5) The horizontal displacements of the top of the tower causedby the combined influence of solar radiation and daily airtemperature variation during a sunny summer day resemblean ellipse in relation to the position of the sun. This trajectoryis not identical day after day since sunshine duration andexternal temperature vary significantly over different days andseasons (see Figs. 8 and 14–16 and Table 2).

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