(2003) full scale measurements of the structural response of a 50m guyed mast under wind loading

Engineering Structures 25 (2003) 859867www.elsevier.com/locate/engstruct

Full scale measurements of the structural response of a 50 mguyed mast under wind loading

P. Harikrishna , A. Annadurai, S. Gomathinayagam, N. LakshmananStructural Engineering Research Centre, CSIR Campus, Chennai 600 113, India

Received 12 July 2002; received in revised form 13 December 2002; accepted 23 December 2002

Abstract

Guyed masts are used for wireless communication, meteorological measurements, and recently, even for power transmission.The behaviour of the mast is non-linear due to its slenderness and compliant guy-support system. The guys also exhibit non-linear behaviour especially at low values of pretension due to possible multimodal excitations and dynamic response to windturbulence. This paper presents the results of measured wind characteristics and associated dynamic response of a 50 m tall guyedmast located on the east coast of India in ambient wind conditions. The measured root mean square values of displacements havebeen compared with a patch load method suggested by Davenport and Spalding [4]. The adequacy of current design practice isreviewed, in the light of the full scale experimental observations. 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Field experiment; Guyed mast; Wind and terrain characteristics; Structural response; Turbulence length scale; Spectral peaks; Probabilitydensity; Damping ratio; Root mean square displacements

1. Introduction

Modern tall guyed masts constructed of high-strengthand light weight materials tend to be more flexible andlightly damped than those in the past. Therefore, the sen-sitivity of such guyed mast to dynamic excitation bywind, attains considerable importance. Dynamic exci-tation of the masts is mainly caused by the gustiness ofthe wind. The full scale measurement of wind and struc-tural response of tall guyed masts would lead to betterunderstanding of the dynamic responses involving manymodes under random wind conditions. Measured fielddata can lead to design guidelines and codification, tocheck wind tunnel results and to develop computationalfluid dynamics technology. Earlier, Peil and Nolle [1]compared the measured bending moment response of a344 m tall guyed mast with the theoretically evaluatedvalues using the measured wind and terrain character-

Corresponding author. Tel.: +91-44-254-1605; fax: +91-44-254-1508.

E-mail addresses: [email protected] (P. Harikrishna); [email protected] (A. Annadurai); [email protected] (S.Gomathinayagam); [email protected] (N. Lakshmanan).

0141-0296/03/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved.doi:10.1016/S0141-0296(03)00005-1

istics. The paper concluded that the static calculationunderestimates the bending stresses of the mast whileover-estimating the stress due to normal force. However,the resulting maximum stresses from static calculationwere reported to be safe.

Structural Engineering Research Centre (SERC),Chennai, India, had conducted full scale field experi-ments on self-supporting lattice towers [2,3] under nor-mal and cyclone wind conditions to obtain wind, terrainand structural characteristics. In the present investi-gation, full scale field measurements were carried out ona 50 m tall guyed lattice mast located on the east coastof India near Kalpakkam to study the wind, terrain andstructural characteristics. This paper reports variouswind and terrain characteristics such as mean wind speedprofiles, turbulence intensities, turbulence length scales,exponential decay coefficient, turbulence spectrum, andprobability density function of wind speed evaluatedfrom the measured wind speed data. This paper also dis-cusses the frequencies at which the guyed mast indicatesresonant type response and the damping ratios of theguyed mast obtained from the acceleration measure-ments on the mast. Fluctuating displacements of the mastare evaluated from the measured accelerations and the

860 P. Harikrishna et al. / Engineering Structures 25 (2003) 859867

root mean square (r.m.s.) values of displacement arecompared with the values obtained from the theoreticalanalysis of the guyed mast using the patch load patternssuggested by Davenport and Spalding [4].

2. Test structure, instrumentation and datacollection

The 50 m high test mast is square in plan of size60 cm 60 cm for the full height from ground level andis built-up using four steel angles of size L 65 65 6 mm3 as verticals. The leg members are interconnectedby welding steel rods of 20 mm diameter at 30 cm spac-ing on a pair of parallel faces which were also used asladders. Steel angles of size L 35 35 5 mm3 wereused in inclined lacing at 60 cm spacing on the remain-ing two faces. The mast is supported by guys (12 mmdiameter) at four levels, viz. at 12, 24, 36, and 48 mlevels from ground with four guys at each level. Fourreaction blocks were built at distances of 25 m from thecentre of the mast and along the diagonals. The guyslocated at four different levels and aligned in a singlevertical plane were anchored to one reaction block. Themast is supported on a pedestal with a hinge arrange-ment.

The 50 m tall guyed mast is instrumented with three-cup anemometers and direction vanes at four levels, viz.at 10, 17, 29 and 50 m above ground level, to measurethe wind speed and direction. The guyed mast is alsoinstrumented with triaxial accelerometers at two levels,viz. at 29 and 50 m levels to measure accelerationresponse in two orthogonal directions (X and Y) at eachlevel. A schematic view of the instrumented guyed mastis shown in Fig. 1. All the sensors are connected to acomputer based data acquisition system for collection ofdata at a sampling rate of 20 Hz and for a duration of20 min.

Fig. 1. Schematic view of the instrumented guyed mast.

A large number of data have been collected over aperiod of 6 months. The collected data have been quali-fied by performing stationarity check for the measuredwind speed. These stationary data are grouped based onthe mean values of the measured wind direction, in dif-ferent wind azimuths, viz. south, south-west, west, north-west, and north. The wind and terrain characteristicsobserved for the south direction have already been dis-cussed elsewhere [5]. In the present study, the data col-lected in the south-west direction have been consideredfor detailed analysis. These data were collected understable approach wind reaching the site through peninsu-lar India.

3. Analysis of data

3.1. Wind and terrain characteristics

Statistical analysis of the wind speed has been carriedout to obtain the values of the mean and standard devi-ation. The variation of mean wind speed averaged overa time duration of 15 min along the height has beenstudied using the power law and the log law [6]. Thepower law coefficient, a, and terrain roughness length,zo, are obtained using the following equations:

U (z)U (zref) zzdzrefzd

a

, (1)

U (z) 2.5u ln[(zzd) /zo], (2)where U is mean wind speed, z the height above groundlevel, zref the reference height (10 m), u the shear fric-tion velocity, and zd is the zero planedisplacement/height.

In the present study, a value of 0 has been assignedfor zd, since the site is surrounded by a fairly open terrainwith very few habitats in the south-west direction. The

861P. Harikrishna et al. / Engineering Structures 25 (2003) 859867

mean wind speed profile along the height for a typicaldata is shown in Fig. 2.

The turbulence intensity, Iv(z), values are evaluatedas follows:

Iv(z) s(z)U (z), (3)

where s is standard deviation of wind speed.The variation of the turbulence intensity values along

the height for a typical data is shown in Fig. 3.The evaluated mean wind speed, power law coef-

ficient, terrain roughness height and turbulence intensityvalues for 20 data sets are given in Table 1. The variationof power law coefficient and terrain roughness lengthwith mean wind speed at 10 m level is shown in Fig. 4.

Fig. 5 shows the reduced power spectra of wind turbu-lence at different levels evaluated for a typical data.

The horizontal turbulence length scales, xLu, at differ-ent levels are evaluated from auto-correlation analysisusing Taylors hypothesis [7] and also from turbulencespectrum as per spectral peak method [7]. The averagevalues of turbulence length scales, xLu, are comparedwith the values obtained using the empirical expressionsuggested by ESDU (cf. [6]) as shown in Fig. 6.

The coherence function obtained from the auto-spec-tra and cross-spectra of wind speeds at any two levelsz1 and z2 is given by

Cohz1z2(n) Sz1z2(n)2

Sz1(n)Sz2(n). (4)

The square root of coherence is usually fitted by an

Fig. 2. Variation of measured mean wind speed with height for atypical data.

Fig. 3. Variation of measured turbulence intensity with height for atypical data.

exponential function proposed by Davenport [8] as fol-lows:

Coh(n) expCznz1z2U ave , (5)where n is frequency in Hz, U ave = (U (z1) + U (z2)) / 2,and Cz is the exponential decay coefficient. Fig. 7 showsthe evaluated coherence function for a typical data witha fitted curve using a value of Cz = 6.5.

The probability distributions of wind speed measuredat four levels are evaluated and are compared with nor-mal probability function as shown in Fig. 8. The vari-ation of Kurtosis values evaluated for all the wind speeddata with the increase in mean wind speed at 10 m levelis shown in Fig. 9.

3.2. Structural response characteristics

From the auto-spectral analysis of the two componentsof accelerations (X and Y) measured on the guyed mastat 29 and 50 m levels, the predominant spectral peaksare identified and the corresponding frequencies arenoted. The auto-spectra of the measured accelerations ofthe guyed mast for a typical data are shown in Fig. 10.

The critical damping ratio of the guyed mast at ident-ified spectral peaks/natural frequencies is evaluatedusing the half power method [9] as follows:

z (f2f1)

(f2 f1), (6)

where f1 and f2 are lower and upper frequency boundlimits, respectively, of spectra of acceleration having


Table 1Statistical parameters of wind characteristics for south-west direction

S. no. Mean wind speed (m/s) at levels above GL Power law Terrain roughness Turbulence intensity, Iv, at levels above GL(m) coefficient, a length, zo (m) (m)

10 17 29 50 10 17 29 50

1 6.409 6.754 7.5 8.295 0.164 0.052 0.206 0.179 0.152 0.1372 6.94 7.412 8.2 8.996 0.164 0.0511 0.216 0.192 0.169 0.1673 7.465 7.67 8.412 9.244 0.137 0.0163 0.166 0.151 0.135 0.134 6.548 6.843 7.657 8.314 0.155 0.0357 0.167 0.157 0.148 0.145 6.006 6.208 7.051 7.965 0.182 0.098 0.15 0.147 0.132 0.136 7.98 8.465 9.286 10.35 0.163 0.0501 0.197 0.169 0.153 0.1357 5.742 5.752 6.35 7.115 0.139 0.0188 0.184 0.18 0.169 0.1648 7.384 7.669 8.466 9.518 0.161 0.0478 0.196 0.19 0.184 0.1669 8.92 9.427 10.26 11.12 0.139 0.0173 0.216 0.199 0.195 0.18810 8.183 8.473 9.308 10.28 0.145 0.0245 0.187 0.186 0.184 0.16511 6.638 6.962 7.668 8.715 0.171 0.0684 0.205 0.179 0.17 0.15612 7.254 7.511 8.287 8.888 0.132 0.0118 0.217 0.214 0.192 0.17113 6.241 6.43 7.134 7.807 0.145 0.0237 0.177 0.168 0.152 0.15214 9.329 10 10.95 12.21 0.167 0.0587 0.214 0.185 0.166 0.15515 8.318 8.677 9.501 10.31 0.137 0.0157 0.193 0.167 0.151 0.15116 9.06 9.489 10.32 11.34 0.141 0.0196 0.177 0.165 0.157 0.13917 5.492 5.641 6.296 7.24 0.175 0.0827 0.182 0.162 0.162 0.14918 6.162 6.459 7.136 7.992 0.164 0.0538 0.192 0.176 0.171 0.15119 6.788 7.182 7.93 8.952 0.173 0.0741 0.161 0.14 0.138 0.1220 7.06 7.56 8.341 9.272 0.171 0.066 0.175 0.14 0.129 0.118Average 0.15625 0.044305 0.1889 0.1723 0.16045 0.1492

Fig. 4. Variation of power law coefficient and terrain roughnesslength with mean wind speed.

Fig. 5. Spectra of measured wind speeds of a typical data.

Fig. 6. Comparison of average turbulence length scales.


Fig. 7. Coherence function of a typical wind speed data.

Fig. 8. Comparison of probability density functions of a typical windspeed data at (a) 10, (b) 17, (c) 29, and (d) 50 m.

Fig. 9. Kurtosis values of measured wind speed data.

half the value of amplitude at the spectral peak. Fig. 11shows the variation of damping ratios with the increasein mean wind speed at 10 m level.

The probability distributions of acceleration responsemeasured at two levels are evaluated and are comparedwith normal probability function as shown in Fig. 12.The variation of Kurtosis values evaluated for all theacceleration data with the increase in mean wind speedat 10 m level is shown in Fig. 13.

In the present investigation, the displacement time his-tories of the guyed mast are deduced from the measuredacceleration time histories using numerical integrationbased on higher order polynomials. Simpsons rulewhich is derived by replacing the actual time history byparabolic arcs (second order: [h(y1 + 4y2 + y3) /3]) isfound to be adequate [10]. From these evaluated dis-placement time histories, the r.m.s. values of displace-ments are calculated. For a typical data, the spectra ofthe evaluated displacement time histories are shown inFig. 14. The variation of the calculated r.m.s. values ofdisplacements with increase in square of the mean windspeed at 10 m level is shown in Fig. 15.

4. Discussion

4.1. Wind and terrain characteristics

From Table 1, the average power law coefficient (a)and terrain roughness length (zo) are observed to be0.156 and 0.0443, respectively. The power law coef-ficient and terrain roughness length values for open ter-rain are reported in literature as 0.16 and a range of0.030.1, respectively [11]. Hence the terrain in thesouth-west direction is considered as open terrain fromthe wind speed measurements and also as per visualobservation at site. It can be seen in Fig. 4 that the powerlaw coefficient (a) and terrain roughness length (zo)decrease with increase in mean wind speed at 10 m level.Similar observation is made during earlier experiment ina different terrain [2]. This observation indicates that theeffect of roughness of terrain on the wind speed profilealong the height reduces with increase in wind speed.The average values of turbulence intensities at 10, 17,29, and 50 m levels are obtained as 0.19, 0.17, 0.16, and0.15, respectively.

Fig. 5 shows the comparison of the auto-spectra of themeasured wind speeds at 10, 17, 29 and 50 m levelswith the turbulence spectra evaluated from theexpression suggested by von Karman (cf. [11]). Thepresence of same order of spectral energy contents in allthe measured levels indicates the existence of isotropicturbulence in the atmospheric boundary layer. It can beseen from the figure that the measured spectra comparewell with the von Karman spectrum up to a reduced fre-quency value of two and beyond which the measured


Fig. 10. Spectra of measured accelerations of a typical data.

Fig. 11. Variation of damping ratios with mean wind speed.

spectra are observed to be decaying faster than the vonKarman spectrum. This may be due to the limitation infrequency response of the three-cup anemometers athigh frequency.

The horizontal turbulence length scales, xLu which areevaluated using the Taylors hypothesis and spectralpeak method are observed to be increasing with increasein height above ground level. It can be seen from Fig.6 that average values of the evaluated turbulence lengthscales using spectral peak method compare well withthose obtained by the empirical expression suggested byESDU (cf. [6]), while the values evaluated using Tay-lors hypothesis are more at all levels.

The values of the exponential decay coefficient, Cz,obtained by fitting the coherence function are observedto be in the range 5.57.0 with an average value of 6.4.

Fig. 12. Comparison of probability density functions of acceleration(a) X at 29 m (b) Y at 29 m (c) X at 50 m (d) Y at 50 m.

However it can be seen from Fig. 7 that in low frequencyregion with reduced frequency values of less than 0.05,the coherence function is observed to be having a fewvalues close to 1.0. It indicates thatsegments/components of structures in terrains of thistype will be exposed to highly correlated wind loadswhich may lead to the failure of those components andconsequently the collapse of the structure itself.

Fig. 8 shows that the probability density functions ofmeasured wind speeds at 10, 17, 29 and 50 m levelscompare well with the normal probability density func-tion. The Kurtosis values of the measured wind speedsare observed to be scattered between 2.0 and 3.5 withlittle variation with increase in mean wind speed (Fig.9). The average value of the Kurtosis is observed to be


Fig. 13. Kurtosis values of measured acceleration data.

Fig. 14. Spectra of evaluated displacements for a typical data.

Fig. 15. Variation of r.m.s. displacements with (mean wind speed)2.

2.6 which is very close to the value of 3.0 for normallydistributed data.

4.2. Structural response characteristics

Fig. 10 shows the auto-spectra of the measured accel-eration responses of the guyed mast at 29 and 50 m lev-els in two orthogonal directions (X and Y). The spectraof acceleration in X-direction at both 29 and 50 m levelsshow excitation modes (spectral peaks) at 1.914, 2.44,and 3.67 Hz. However, the predominant peaks areobserved to be at 2.44 and 1.914 Hz at 29 and 50 mlevels, respectively. The spectra of acceleration in Y-direction at both 29 and 50 m levels show excitationmodes (spectral peaks) at 1.25, 2.03, and 3.05 Hz. How-ever, the predominant peaks are observed to be at 3.05and 2.03 Hz at 29 and 50 m levels, respectively. Theresponse spectra clearly indicate the closely spacedmodes of guyed mast and multimodal excitations.

The evaluated damping ratios at the observed spectralpeaks for the X and Y components of the measured accel-eration responses of the guyed mast at 29 and 50 m lev-els are observed to be scattered between 1 and 3% withlittle variation with increase in mean wind speed at 10m level (Fig. 11). The average damping ratio is obtainedas 1.6% which compares well with the value of 2% forbolted steel structures.

Fig. 12 shows that the probability density functionsof measured acceleration responses of the guyed mastare symmetrical but more peaked about the mean thana normally distributed process. This can be seen fromFig. 13, with all the Kurtosis values of the measuredacceleration responses being above 3.5. The average ofthese Kurtosis values is obtained as 4.35. Hence, theresponse of the guyed mast subjected to wind speedswith normal distribution is observed to be non-normal.


Fig. 14 shows the spectra of the displacement timehistories evaluated from the double integration of accel-eration time histories. The background componentaccounts for about 8095% of the total variance. Ther.m.s. values of displacements are observed to increasenon-linearly with increase in square of mean wind speedat 10 m level as shown in Fig. 15 with power form offit with index more than one. This indicates the contri-butions of resonant and non-linear dynamic responses inaddition to background response. However, the increasein r.m.s. values of displacements at 50 m level (the tipof the guyed mast with no guyed support) is observedto be steeper than the increase in r.m.s. values of dis-placements at 29 m level (middle of the mast span sup-ported by guys at 24 and 30 m levels).

In the present investigation, the r.m.s. values of dis-placements of the guyed mast have been evaluated theor-etically using the patch load patterns suggested by Dav-enport and Spalding [4]. In this patch load method, aseries of static load patterns are used to recreate theeffects of gusty wind. The specified load patterns consistof lateral loads applied in turn to each span of the mastand then from midpoint to midpoint of adjacent spansof the mast. The patch loads should be applied to guyedmast in its static equilibrium position, i.e. after updatingthe mast geometry using the displacements obtainedafter applying the mean wind pressures on the guyedmast. For each load pattern, an equivalent static pressure,PPL, is defined by the expression as follows:

PPLi 2IoQoK2(zi), (7)where Io is turbulence intensity at reference height (i.e.10 m), Qo the mean wind pressure at reference height(i.e. 10 m), and K2(zi) is ratio of mean wind speed at zito mean wind speed at reference height (i.e. 10 m).

The measured mean wind speed and turbulence inten-sity at 10 m level along with the terrain roughness length(zo) are used to evaluate the above parameters. The dis-placements obtained from the aforementioned load pat-terns are added as the root sum of squares to obtain thevalue of r.m.s. values of displacement as follows:

rPL n

i 1

rPLi2. (8)

Fig. 16 shows the comparison of the r.m.s. values ofdisplacements obtained using Davenports approach ofpatch loading with those obtained from the measuredacceleration response of the guyed mast. The r.m.s.values of displacements obtained using Davenportsapproach are observed to be well compared with thoseobtained from the measured accelerations in the meas-ured mean wind speed range of 510 m/s at 10 m level.However, comparison of the r.m.s. values of displace-ments at higher mean wind speeds requires moremeasurements.

Fig. 16. Comparison of experimental and theoretical r.m.s. displace-ments.

5. Conclusions

The dynamic response of a 50 m tall guyed mastwhich is located on the east coast of India near Kalpak-kam, under normal wind is experimentally and analyti-cally investigated. The estimated power law coefficientand terrain roughness length comply with that of an openterrain as observed in the field. The turbulence intensitiesin the measured wind direction (south-west) remainedsteady at each level with marginal fluctuations duringthe measured wind speed range.

The measured wind speeds were observed to be ofnormal distribution with Kurtosis values just less thanthree. However, the probability distributions of measuredacceleration response of the guyed mast were found tobe non-normal with Kurtosis values more than 3.5. Themeasured acceleration spectra indicated closely spacedmultimodal excitations. The background component indisplacement spectra varied between 80 and 95% oftotal variance.

The r.m.s. displacement values were observed toincrease non-linearly with increase in square of meanwind speed substantiating the contributions of resonantand non-linear dynamic responses. Resonant responsecould play significant role in the dynamic response ofthe mast at high wind speeds. Measurements at highwind speeds are essential to confirm this.

The r.m.s. values of displacements evaluated for themeasured wind speeds using the patch load patterns sug-gested by Davenport and Spalding [4], which avoid com-plex non-linear transient dynamic analysis of guyedmasts for evaluation of peak fluctuating responses, wereobserved to be comparable to the measured values at lowwind speeds observed during the measurement pro-gramme. The patch load pattern method is observed tobe acceptable for the evaluation of wind inducedresponse for this class (heights) of latticed guyed mastsup to the wind speeds investigated. The authors hopethat adequate information would be available from their


ongoing field testing programme to validate Davenportsmethod at high wind speeds also in the near future.

Acknowledgements

This paper is being published with the kind permissionof The Director, Structural Engineering Research Centre,Chennai. The authors wish to pay homage to their col-league (Late) Shri. J. Shanmugasundaram, DeputyDirector, who led the Field Experiments Laboratory withthe spirit of harmony. The authors also wish to acknowl-edge Mr V. Muthalagan, Mr K. Shankaranarayanan andMr N. Baskaran for their assistance in conducting theexperiment. The financial support for the project fromAERB and the cooperation rendered by the SafetyResearch Institute, IGCAR, Kalpakkam, are gratefullyacknowledged by the authors.

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[10] Shanmugasundaram J, Gomathinayagam S, Harikrishna P, Laksh-manan N. Full-scale measurements of dynamic response of a lat-tice tower. In: Proceedings of the International Seminar on Struc-tural AssessmentThe Role of Large and Full-scale Testing,Institute of Structural Engineers and City University, E&FNSPON, UK. 1997. p. 36372.

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Full scale measurements of the structural response of a 50 m guyed mast under wind loadingIntroductionTest structure, instrumentation and data collectionAnalysis of dataWind and terrain characteristicsStructural response characteristics

DiscussionWind and terrain characteristicsStructural response characteristics

ConclusionsAcknowledgementsReferences

(2003) full scale measurements of the structural response of a 50m guyed mast under wind loading

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