D y n a m i c characteristics and wind induced response of a steel frame tower

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JOUR N.~_ OF ONNNND ELSEVIER Journal of Wind Engineering and Industrial Aerodynamics 54/55 (1995) 133-149 Dynamic characteristics and wind induced response of a steel frame tower M.J. Glanville*,K.C.S. K w o k The University of Sydney, School of Civil and Mining Engineering, Sydney, NSW 2006, Australia Abstract This paper presents the results of a field measurement program which was conducted on a steel frame tower. Dynamic characteristics of the tower were measured to determine its frequencies of vibration, mode shapes and damping values. A STRAND6 computer model was assembled and confirmed these findings. The dynamic response of the tower under wind loading was investigated before and after the attachment of ancillaries. 1. Introduction A microwave communications steel frame tower was constructed in 1992 amongst fiat category 2 terrain at Prospect in the western suburbs of Sydney. The 67 m high tower had to satisfy strict deflection limits for both static and dynamic loads to reduce signal transmission interference and loss. This was achieved using a 126 tonne frame system comprising four circular column sections rigidly joined to rolled section platforms. Tower geometry and mass distribution are shown in Fig. 1. Testing commenced in June 1992 before any microwave dishes were installed on the tower. The ancillaries shown in Fig. 1 were attached in July 1993 constituting around 5% of the tower projected area on any face. Their effect upon the dynamic response was then monitored. 2. Measurement program Two accelerometers were installed at the 57 m level and aligned orthogonally along the major axes of the tower. Accelerometer output was conditioned by a purpose built Corresponding author. Elsevier Science B.V. SSDI 0 1 6 7 -6 1 0 5 (9 4 )0 0 0 3 7 -E 134 8 M.J. Glanville, K,C.E Kwok/J. Wind Eng. Ind. Aerodyn, 54/55 (1995) 133-149 Y O" Y1 Ngo. b Xl 365kg 67m I Mast Anemometer JL -Q 59m 57m 4280k9 3800ks 3800k9 54m 3800k9 51m 3800ks 48m 3800ks 45m 42m 40,5m 51 00k9 5500k9 38m 5750kg 35m 5750kg 32m 5750kg 29m 27,5m 64~9k9 MEMBER SIZES o.,d457 x 9,5 C,H,S, b,d323 x 9,5 C,H,S, c,e'406 x 9,5 C,H,S, cL,219 x 4,8 C,H,S, e,.150 x 150 x 10 L £150 x 75 IS 9,360UB45 h,460UB67 I,.360UB57 j.,850uc73 k,d75 ROD L,75 x 75 x 5 L m,d139 x 5,4 C,H,S, 9750kg 24m 10270kg 20m I0270k9 16m 10870k9 12m 8m OL70k9 690k9 2,6m Om l]m I X t y Fig. 1. a) General arrangement of the Prospect tower. b) Mass distribution as modelled by STRAND6 including items not listed from a to m. These items include safety tails, ledders, cable trags, platform grating, bolts and some platform members. The ancillary mass is not included. M.J. Glanville, K.C.S. Kwok/J. WindEng. Ind. Aerodyn. 54/55 (1995) 133-149 135 amplifier and 10 Hz low pass filter. Wind speed and direction were measured at the same level using a cup anemometer and wind vane, respectively. The anemometer and vane sat 1.5 m from the western face of the tower in order to find free stream flow (see Fig. 1).Wind with yaw angle between 20 °and 100 °was not analysed to avoid interference from the tower. Analogue data was transmitted via coaxial cable to the base of the tower where it was logged by a 486 personal computer fitted with an analogue to digital converter. Dedicated software developed by Kwok and Macdonald [6] continually sampled the data in 14 min sections at 20 Hz. Investigation of the idealisation of wind speed spectrum over an extended frequency range reveals a spectral gap between 1 h and 10 min averaging periods. Hence an averaging period of 14 min duration was chosen to provide fairly stable mean values. Force vibration tests were performed on the tower in order to obtain damping decay curves for each mode of vibration. The tower was vibrationally excited by oscillating a body weight in time with a metronome at each natural frequency of the tower. Forcing ceased once the tower was resonating and at that instant the tower was allowed to vibrate freely until it came to rest. Force vibration tests were performed during still atmospheric conditions to eliminate any background excitation. Tower decay during force excitations was measured using the installed accelerometers and a laser beam. A H e -N e laser was placed at the base of the tower and magnified through a zenith plummet. The beam was projected onto a grid placed at the top of the tower. The relative movement of the grid to the stationary beam was then filmed for later analysis. Mode shape of the tower was measured using an additional set of accelerometers. After calibration at the 57 m level of the tower, one pair of accelerometers was moved step by step to lower levels. Mode shape was determined from the ratio of simultaneously recorded acceleration signals. The presence of any torsional modes was similarly detected using an additional pair of accelerometers eccentrically placed at the 57 m level. 3. Computer model Natural frequencies and mode shapes for the tower were calculated using STRAND6. STRAND6 is a commercially available suite of full three-dimensional finite element programs including a natural frequency solver. The natural frequency solver calculates the natural frequencies (eigenvalues 2) and vibration modes (eigenvectors {x})based on a lumped mass assumption and solving the equation [K]{x} 2[M]{x}.K] and I-M] represent the banded stiffness matrix and the lumped (diagonal) mass matrix, respectively. 136 M.J. Glanville, K.CS. Kwok/J. Wind Eng. Ind. Aerodyn. 54/55 (1995) 133-149 Y-Y Ax (s 2 r oo C o 1 0 z_ 1 O0 ii z-2 I UF I' 0 8_ 'l l p i ,L ,3~ 1' 2 3 pequen cy l l 4 Hz) 5 Fig. 2. Power spectra of acceleration. 4. Results 4.1. Dynamic characteristics 4.1.1. Natural frequency Power spectral density was computed for the acceleration response of the tower under wind loading (Fig. 2).Spectral peaks indicate that mode one dominates the response of the tower at 1.08 Hz. The two smaller peaks represent the second and third modes of tower vibration. The differences in natural frequencies along perpendicular axes are less than 2% producing strong coupling between the X -X and Y -Y axis. Natural frequency values obtained through full scale measurement are compared to those calculated by STRAND6 in Table 1. The computed results agree well with those measured, particularly modes one and two. 4.1.2. Mode shape The mode shapes measured in full scale are compared to those calculated by STRAND6 in Fig. 3. Fig. 4 is a STRAND6 three-dimensional representation of mode one vibrating along the Y Y axis. 137 M.J. Glanville, K.C.S. Kwok/J. Wind Eng. Ind. Aerodyn. 54/55 (1995) 133-149 Table 1 Tower natural frequencies Natural frequency Full scale STRAND6 STRAND6-MAST X -X axis (Hz) Y Y axis (Hz) Mode 1 Mode 2 Mode 3 Mode 1 Mode 2 Mode 3 1.08 1.10 1.14 1.41 1.40 3.53 3.22 3.52 6.06 1.07 1.10 1.14 1.39 1.40 3.54 3.28 3.54 6.07 Measured Mode Shape Computed Mode Shape J I 1 11, 1 I i" i t i I X-X Y-Y Xl-Xl I Y1-Y1 MODE 1 MODE2 MODE 3 Fig. 3. Computed and measured mode shapes. Mode one displays typical quarter sine wave bending with the top mast dominating the displacement of the tower. The ratio of mast displacement to tower displacement is about 2.5:1. The ratio of mast to tower displacement in mode two is about 24:1 suggesting that this mode of vibration is due to the vibration of the top mast alone. Mode three displays the full sine wave shape with a small amount of torsion towards the top of the tower. Some torsion was measured in full scale at mode three only. Two eccentrically placed channel sections running up one side of the top third of the tower are probably responsible for this behaviour. It should be noted that a purely torsional mode was calculated by S T R A N D 6 at 2.7 Hz, however, no evidence of this mode was found during full scale measurement. STRAND6 was used to simulate removal of the top mast from the tower. Table 1 summarises the new frequencies found after the mast was removed. The natural frequency and mode shape of mode two without the mast is almost identical to that of mode three before the mast was removed. The natural frequency of the mast alone removed 138 M.J. Glanville, K.C.S. Kwok/J. Wind Eng. lnd. Aerodyn. 54/55 (1995) 133-149 Fig. 4. Mode 1 Y-Y axis. from the tower was also calculated by STRAND6 at 1.4 Hz. This confirms that the second mode of the tower is simply the natural frequency of the top mast. Removing the mast would remove this mode of vibration. 4.1.3. Damping High amplitude free vibration decay curves obtained from filtered acceleration records for mode one are shown in Fig. 5. Percentage critical damping along the Y -Y axis is greater than that along the X -X axis. This may be attributed to the higher number of bolted connections which offer additional damping along the Y -Y axis. Alignment of the ladders and cable trays running up the centre of the tower also contribute to the higher value of damping. Damping for modes two and three was similarly determined at 0.25% critical damping and 1.5% critical damping, respectively. A low value of damping at mode two is expected since this mode represents vibration of the mast alone. The decay curves shown in Fig. 5 are peculiar since they exhibit lower damping at higher amplitudes. This may be explained by the large dependence of mode one upon the vibration of the lightly damped mast which acts as an excitation mechanism during tower decay. Fig. 6 is a plot of the peak tower displacements as mapped from the laser trace during the free vibration decay along the X -X axis of the tower. Both methods of decay analysis produce the same damping values as expected. An autocorrelation analysis was employed to measure tower damping at relatively low amplitudes under wind loading alone (less than 5 mg).One of the requirements for an autocorrelation analysis to be stable statistically is stationarity of the data on M.J. Glanville, K.C.S. Kwok/J. Wind Eng. Ind. Aerodyn. 54/55 (1995) 133-149 a) 139 AxLs Y-Y c~ 68. E cO o~ 50 40 Tower ¢I~ 0.75~ decay u 38 2@ i 2".1® AAA ~AAA AAAAAAAAA 0_ %1~8 b) nth 2~3 X-X Cycle 3~3 48 Ax:s 0) I 168 @1, Tower decoy o 12® 0.75% c_ e 88 3 3 @i 4@ 28 nth 48 Cycle 68 Fig. 5. Free vibration decay curves obtained from acceleration records. which the analysis is based. Jeary [5] describes the run test for stationarity based on the variation of acceleration response. Fig. 7 presents the results of such a run test performed on a sample of data obtained from the tower. From 40 samples nineteen 140 M.J. Glanville, K.C.S. Kwok/J. Wind Eng. Ind. Aerodyn. 54/55 (1995) 133-149 X-X 4@ E E 3@ Axis T o w e r .decoy 0.75~ E28 ©1@ x x 2b 4b 6e n f.,h C y c l e Fig. 6. Free vibration decay mapped, from laser trace. 33 E c O 4~ L_ @6) O O ©q-0 d co 28 Sampl e 48 number" Fig. 7. Run test for stationarity using 40 samples. runs were found, satisfying the ct =0.05 level of significance set down by Bendat and Piersol [1].This 468 s sample was the only data found which exhibited such stationarity in wind excited structural response over a significant time frame. Having effectively removed the forcing (wind) non-stationarity from the data, what remains is the non-linear response of the tower itself. M.J. Glanville, K.C.S. Kwok/J. Wind Eng. Ind. Aerodyn. 54/55 (1995) 133-149 141 0 1 ©8~'k~"X -X Ax :s sL -L, y-y oe 4O 2e ®c@ 0 ©0 8 D nLh 2b Cycle 38 Fig. 8. Autocorrelationfunction of first mode acceleration. The stationary set of data was then bandpass filtered at the first mode and an autocorrelation analysis performed. The resulting autocorrelation curves shown in Fig. 8 indicate that damping along both tower axes is of similar magnitude at low amplitudes. Both levels of damping are typical for a steel structure under serviceability stress levels 1,7].4.2. Wind induced response A time history of tower acceleration and wind velocity over a 40 s period is shown in Fig. 9. Mode one is seen to dominate while modes two and three contribute towards the background response of the tower. Between 20 and 40 s an increase in along-wind (Y -Y )response can be seen due to wind energy fluctuating near the natural frequency of the tower. A locus of dynamic response over another 50 s period is shown in Fig. 10. Along-wind and cross-wind components are of similar magnitude due to the strongcoupling which exists between the two axes. The dynamic response of the tower in the along-wind direction is plotted against the fluctuation in wind speed au in Fig. 11. There is a general increase in tower response with increased buffeting by wind gust. Fig. 12 illustrates the increase in cross-wind response due to lateral turbulence v' wind direction changes).The relationship between the standard deviation of tower acceleration response and mean wind speed is shown in Figs. 13 and 14. The relationship is presented before and after the installation of ancillaries. The addition of ancillaries is seen to have little effect upon dynamic response. In both cases dynamic response increases in proportion to mean wind speed with an exponent of approximately 2.5. This is in agreement with full scale measurements completed by Glass et al. I-2] and Hiramatsu and Akagi I-3] 142 M.J. Glanville, K.C.S. Kwok/J. WindEng. lnd. Aerodyn. 54/55 (1995) 133-149 10 x x ce,erat,on IL A O3 E o -10 i,AA,t, Y-~Accelerati0n 10 5 A a j l O3 E o tIv!tt"71v!Jvvlvl!glt!)ttIitlltl 17 ,W i n d speed 15,~I I A 09 E 11 rllr 9 Wind direction ,r,r- O J, lO ll .I I 20 30 t q 40 Time (seconds) Fig. 9. Time history of tower acceleration, wind speed and direction. on lattice towers of varying height and more conventional design built from lighter angular steel sections. The 14 min samples have been split up into short 60 s samples to help extrapolate the data shown in Figs 13 and 14. The long 14 min samples display less scatter than the short records due to smaller statistical errors. Variation in turbulence also contributes to the scatter. A standard deviation of acceleration of 8 mg under a mean wind speed of 20 m/s corresponds to a peak resonant deflection of about 7 mm assuming sinusoidal response at mode one. This resonant component must be added to the static deflection M.J. Glanville, K.CS. Kwok/J. Wind Eng. Ind. Aerodyn. 54/55 (1995) 133-149 4 E 3 I::0 2 17 °0 0 X 0 2! 5 }1 6 |8 i J -6 4 2 0 2 X -X Axis Acceleration (rag) Fig. 10. Locus of tower acceleration. 33 E 18 AI o n g -tnd dO .J CO 8ol 1 O-u (m /s }Fig. 11. Standard deviation of acceleration response versus wind speed fluctuation. 143 144 M.3 Glanville, K.C.S. Kwok/J. Wind Eng. Ind. Aerodyn. 54/55 (1995) 133-149 Cposs-~E 1@ tnd C o 7 J 1 ~1 _ 1"I ~T qk'#lJP~'z.S, b5 ~q Z'%EII~oJ 8 e ee _.-o I. I .01 h'l!a uS, 1 .CO 8 o l I v "m/s) Fig. 12. Standard deviation of acceleration response versus lateral turbulence. caused by mean wind forces in the along wind direction and to the background deflection in order to produce the peak deflection. The ratio of along-wind to cross-wind acceleration response of each 14 rain sample is plotted versus mean wind speed in Fig. 15. The results are split into 2 m/s intervals with the standard deviation of the data within each interval indicated by error bars on the plot. The ratio remains close to unity for increasing mean wind speed with a slight tendency towards a larger cross-wind response. This is contrary to Australian wind codes 1-7] which suggest that the cross-wind response of porous lattice towers may be neglected unless there are substantial enclosed parts of the tower near the top. Fig. 16 shows the relationship between turbulence intensity (au/U) and mean wind speed U. au/U levels offto about 0.151 at wind speeds greater than 10 m/s. This is the value assumed by ASl170.2 for terrain category 2 at 50 m height. Deviation from 0.151 at lower mean wind speeds is partly due to the inertial and overspinning characteristics of the anemometer cups. Design considerations are often based upon the maximum acceleration experienced by a structure during a period of time T. The ratio of peak acceleration to rms acceleration is defined as the peak factor 9. Davenport has derived an "average" peak factor 9R for resonant response based on a narrow band Gaussian process according to the equation 9. 21n(nl T) Y/x/21n(n, T).Y is the Euler constant equal to 0.5772 whilst nl is the first natural frequency of the tower. The measured peak factor of each 14 min sample along either axis is plotted M.9~ Glanville, K.C.S. Kwok/J. Wind Eng. Ind. Aerodyn. 54/55 (1995) 133-149 145 a) AI ong-N E tnd o@@45U 8 o long ×x x shop L pecopds pecopds 2" L 6 o 4 3 2 x x x 3 2 CO 5 b) E ~2@ Cposs-N o~18 18 15 U( m /s )25 knd @o@Q45U2.E 8 o~ c 6 1) o 4 ~R x x X 2 x x x 2 x x x 09 5 18 15 U( m /s )2(3 25 Fig. 13. Standard deviation of acceleration response versus mean wind speed. Before ancillaries were installed.)146 M.J. Glanville, K. C.S. Kwok /J. Wind Eng. lnd. Aerodyn. 54/55 (1995) 133-149 a> c~1 @AI on 9-~E C tn d 18, Q Q 4 5 U 2"E 8 x xx O xX'~X x xx 6 x x e,×XXx~ X O) x x x x x fJ(X ~x x C3 I r" x r 18 1B U( m /s )Cr'oss b) 28 N tn d 2 E 2B 5 3° 8 8 4 ~U x w x O x x C_ x× X x ~9 o 4 i xX xx x c~ co 2 5I~B I 18 15 U( m /s )28 25 Fig. 14. Standard deviation of acceleration response versus mean wind speed. After ancillaries were installed.)M.J. Glanville, K.C.S. Kwok/J. Wind Eng. Ind. Aerodyn, 54/55 (1995) 133-149 147 1 6 4 u b \1 <1 2 8 b8 8 8 6 8 4s 6 lb U( m /s )Fig. 15. The ratio of along-wind to cross-wind standard deviation of acceleration versus mean wind speed. 8.4 ~8.3 \AS11 7 8 .2 D b@.2 8.1 e°e 5 1@ U( m /s 1~ Fig. 16. Turbulence intensity versus mean wind speed. versus the mean wind speed of the sample in Fig. 17. There is a close agreement between the measured peak factor g and the Davenport estimate gs up to 10 m/s. At higher wind speeds g becomes larger than gR. Many of the strong winds encountered were short duration gusts lying inside the micrometeorological peak region (periods ranging from 10 min to less than 3 s).A strong 5 min burst in wind speed contained within a 14 min sample will increase the acceleration maxima to a greater degree than it will the standard deviation of acceleration. Such a non-stationary set of data will then display a higher peak factor than would be expected from a statistically stationary 14 min sample typically found at lower wind speeds. 148 M.J. Glanville, K.C.S. Kwok/J. Wind Eng. Ind. Aerodyn. 54/55 (1995) 133-149 8 7 6 Q3 3 5 18 U( m /9 )15 Fig. 17. Peak factor versus mean wind speed. Acceleration due to tower tilting was not separated from the acceleration signals since its contribution was found to be negligible. Tilt acceleration was estimated based on the assumption that the tower deflected under the first mode shape alone during resonant response. A peak dynamic response of 32 mg corresponding to 7 m m lateral displacement will produce 0.2 mg of acceleration in the vertical component. 5. Conclusions Natural frequencies and mode shapes of the Prospect tower were measured in full scale and were found to agree well with a S T R A N D 6 computer prediction. Mode one dominated the response of the tower at 1.08 Hz whilst mode two represented vibration of the top mast on the tower alone. Damping was determined by large amplitude (5-170 mg) free vibration decay and low amplitude (5 mg) autocorrelation analysis. D a m p i n g for the tower under wind loading was around 1% critical damping for mode one which is typical for a steel tower under serviceability conditions. Both the along-wind and cross-wind response of the tower was found to increase in proportion to wind speed as a power of approximately 2.5. This is similar to the response expected from more conventional steel lattice towers built from steel angle sections. An increase in tower response was found with increasing wind speed fluctuation and lateral turbulence. The attachment of ancillaries constituting 5 %of the tower face projected area had negligible impact upon the dynamic response of the tower. References [1] J. Bendat and A. Piersol, Measurement and analysis of random data (Wiley, New York, 1966).I2] T. Glass, B.W. Cook, R.W. Banks, B.L. Schafer and J.D. Holmes, The dynamic characteristics and response to wind of tall free-standing lattice towers, in: Proc. IEA Structural Engineering Conf.,Adelaide, 1990, p. 19. M.J. Glanville, K.CS. Kwok/J. Wind Eng. Ind. Aerodyn. 54/55 (1995) 133-149 149 I-3] K. Hiramatsu and H. Akagi, The response of latticed steel towers due to the action of wind, J. Wind Eng. Ind. Aerodyn. 30 (1988) 7-16. 4] J.D. Holmes, Lattice towers-wind loads and dynamic response, Wind Engineering course notes, Department of Mechanical Engineering, Monash University (1992) Ch. 8. 5] A.P. Jeary, Establishing non-linear damping characteristics of structures from non-stationary response time histories, The Structural Engineer, Vol. 70, Paper No. 4 (1992) p. 61. 1-6] K.C.S. Kwok and P.A. Macdonald, Full scale measurement of wind induced acceleration response of Sydney Tower, Eng. Struct. 12 (1990) 153. 7] SAA loading code, Part 2. Wind Loads, ASl170.2-1989 (Standards Australia, North Sydney, 1989).
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D y n a m i c characteristics and wind induce..