building, and these researh results indiated that it is the double orner reession modifiation that redues RMS of aross-wind aerodynami fore by 40%, al

Transcription

1 The Seventh International Colloquium on Bluff Body Aerodynamis and Appliations (BBAA7) Shanghai, China; September 2-6, 2012 Effets of orner reession modifiation on aerodynami oeffiients of square tall buildings Zhang Zhengwei a,b, Quan Yong a, Gu Ming a, Tu Nankun a, Xiong Yong a Sate Key Laboratory for Disaster Redution in Civil Engineering, Tongji University, Shanghai, China b Shool of Arhiteture Engineering, Nantong University, Nantong, China Sihuan Road & Bridge Co., Ltd, Chengdu, China, bluer.xiong@gmail.om ABSTRACT: With high frequeny fore balane (HFFB) tehnique, 14 square tall buildings models with reessed orners were tested in two different simulated wind fields to obtain aerodynami fores. The effets of turbulene intensities and orner reession ratios on mean and RMS oeffiients of the aerodynami base moment and torque in typial wind diretions were analyzed. The test results indiate that two types of orner reession have dramati effets on the aerodynami oeffiients of base moment and torque, and the model with a orner reession ratio of 7.5% is the best one to ut down the aerodynami fores oeffiients. Empirial formulae are fitted for aerodynami fore oeffiients of square tall buildings with different orner reession ratios, whih provide tehnial support for the revisions and supplements of load odes. KEYWORDS: aerodynami fore oeffiients, orner reession, empirial formula, HFFB tehnique, tall building, wind tunnel test. 1 INTRODUCTION With enormous utilization of light-weight and high-strength materials, super-tall buildings are beoming ever-inreasingly high, flexible, and low in damping. These flexible strutures are totally sensitive to dynami wind load, whih plays a signifiant role in the struture design and should be put more emphasis. Aross-wind response of super-tall buildings gradually exeeds along-wind response as their heights inrease, whih is the rux of strutural wind-resistant design [1]. Besides, omfort problem is beoming more and more serious espeially under strong winds. Reently, primary wind-indued vibration ontrol measures of super-tall building onsist of struture measures, mehanial treatments and aerodynami wind-resistant measures [2], whih play an essential role in initial projet design of the super tall building to vitally redue wind load and wind-indued response [3]. Corner reession modifiation serves as one type of typial aerodynami measures for high-rise buildings. Melbourne and Cheung [4], Miyashita et [5], Gu and Quan [6] have disussed the effets of orner reession modifiation on aerodynami harateristis for high-rise buildings through high frequeny balane test and aeroelasti model test, and point out that orner reession modifiation basially redues the peak value of power spetra densities for aross-wind base moment, and that the model with orner reession ratio of 10% greatly redues the peak value of spetrum for aerodynami fore. Besides, Kawai [7] has disussed the effets of orner reession modifiation on aerodynami instability of square and retangular models, and states that orner reession ratio of 5% would effetively prevent aerodynami aeroelasti divergene, espeially for the square model; however, as for high sidelength ratio of retangular setion orner modifiation measure is not effetive in preventing divergene. Irwin [8], Suresh et [9] have disussed harateristis of wind load of Taipei

2 building, and these researh results indiated that it is the double orner reession modifiation that redues RMS of aross-wind aerodynami fore by 40%, along-wind mean wind load by 20% and total base moment by 25%. Moreover, Tse et [10] investigate the impat of aerodynami modifiations on the building eonomis of tall strutures and indiate that orner reession models at more effetively than orner utting model in dereasing base moment. Those researhes primarily aim at wind-indued effet of models with speifi orner reession ratio, espeially the aerodynami power spetra of aross-wind response and wind-indued response, and the author gave some qualitative onlusions, however, there existed no omprehensive empirial formula portraying the effet of aerodynami modifiation measures on square building whih an be diretly applied as standard. In this paper, 14 square tall buildings models were tested to determine the effets of two types of orner reession modifiation on harateristis of aerodynami fore. In order to provide tehnial support for the revisions and supplements of load odes, empirial formulae for effet of orner reession modifiation on base aerodynami oeffiients are provided by using the nonlinear least-squares method. However, due to spae onstraints, only the preliminary results are given in this paper to illustrate the influenes of orner reession modifiation on oeffiients of base moment and torque. The effets on power spetra of base moment and torque will be disussed in other future papers. 2 WIND TUNNEL TESTS AND RESULTS Turbulene Intensity sale ratio 1:300 results from wind tunnel GB-2006 turbulene intensity Mean speed Mean speed =0.16 = Height(m) ns u (n)/ 2 ns u (n)/ U/U g nz/u (a) (b) () (a) Mean wind speeds and turbulene intensity profiles (b) PSD of turbulene at height of 60 m in terrain B () PSD of Turbulene at height of 60 m in terrain D Fig.1. Simulated wind parameters of the terrain ategories B and D This test is arried out in TJ-1 Boundary Layer Wind Tunnel, whose working setion is 1.8m in width and 1.8m in height, and the wind speed ranges ontinuously from 3 to 32m/s. With passive simulation method, i.e., different arrangement of three devies (turbulene generating spires, barrier and roughness element) in wind tunnel [11], the wind harateristis are ahieved to simulate two kinds of wind onditions, orresponding to terrain ategories B and D in the wind tunnel at a length sale of 1/300 in aordane with Chinese ode [12]. Fig 1 shows simulated wind parameters of the terrain ategories B and D where z is height; U stands for wind speed; U g 2 represents height for gradient wind; Su ( n) is power spetra of wind speed, and represents mean square value of wind speed; n is frequeny. The turbulene intensity 60 m above model is 12.6% and 16.5% for the two ategories of terrain, respetively, and turbulent integral sale at the same height is aording 34 m and 36 m (in wind tunnel), orresponding to atual turbulent integral sale 100 m and 110 m, respetively. Despite mean wind profiles at one-third height nz/u 960

3 The Seventh International Colloquium on Bluff Body Aerodynamis and Appliations (BBAA7) Shanghai, China; September 2-6, 2012 for terrain ategories D was larger than normative standard values, this error an be ignored sine the ontribution to base moment made by aerodynami fore below one-third height of this building is less than 5%. The two types of ross-setion modified by orner reession shown in Fig. 2 onsist of type I and type II (double onave orner) developing from the fundamental type I. The orner reession ratio is defined as b/ B (1) where B denotes setion width, and b is utting length of orner reession. (a) type I (orner reession) (b) type II (double orner reession) Fig. 2.Cross setions of the building models Table 1 Testing ases Types of orner reession Test wind Corner reession ratio b/ B Wind angle speed(m/s) Terrain type I 0%,5%,7.5%,10%,12.5%,15%,20%,30% 0~45 6, 8 B, D type II 0%,7.5%,10%,12.5%,15%,20%,30% 0~45 6, 8 B, D The aluminum tube, whose ross-setion area is 50mm 50mm, height is 600mm and thikness is 1mm, serves as mandrel to provide rigidity, and external foam was employed to satisfy different shape parameters for building simulation, ensuring little mass but large stiffness for models and enough high natural frequeny for balane-model system. Additionally, in order to ensure the validity of the test data and preision of the measured signal, final test result is average of the two sets of test data under wind speed 6 m/s and 8 m/s, and all of the test data is used to fit the empirial formulae. Besides, the alulation program is employed to serve as automati reognition of the modal parameters (free vibration frequeny and damping ratio) for balane system aording to output time-history data of high frequeny fore balane, and aerodynami base moment deoupled from output of high frequeny fore balane signals is then revised, and the details of modified proess is shown in paper [13]. The work ases is shown in table 1, and there exists totally 14 different models (13 model with orner reession modifiation and basi model with no orner reession modifiation whose dimension is 600mm 120mm 120mm) having been tested in terrain ategories B and D. Owing to symmetry of square setion 5 serves as a wind angle interval and wind range is from 0 to 45. Moreover, the measuring range of base (torque) moments is 30 Nm, and the measuring preision is Nm, and sampling frequeny is 600 Hz, and sampling time is 60 s. Non-dimensional oeffiients of base aerodynami fore are defined as: CM M /, /, /, / D D qhbh CM D M q D HBH CM L M q L HBH CM T M q T HB H (2) 2 where qh U H is the dynamis pressure at the top of buildings, and B represents building width normal to the approahing flow, and H stands for the height of the building, and UH is the wind veloity at the top of buildings. In addition, M is the mean base moment in along-wind; D 961

4 MD ML and MT are the RMS values of the base moment for along-wind, aross-wind and torsion diretion, respetively; C MD is the mean oeffiients of along-wind base moment, C MD C ML and C MT are the RMS oeffiients of the base moment for the along-wind, arosswind and torsion diretion, respetively. To illustrate the effet of different orner reession ratio on oeffiients of base moment, the orretion fator is defined as: MD ( ) CMD ( )/ CMD0 (3) Ml ( ) C Ml ( )/ C Ml0, l D, L, T (4) where MD ( ) stands for orretion fator for mean oeffiients of along-wind base moment; CMD0 and CMD ( ) represent mean oeffiients of along-wind base moment with orner reession and with no reession, respetively. Additionally, Ml ( ) represents orretion fator for RMS oeffiients of base moment (torque). C Ml 0 and C Ml ( ) are RMS oeffiients of base moment (torque) with orner reession and with no reession, respetively. Besides, subsript 0 represents basi square model with no orner reession and subsripts D, L, and T denote alongwind, aross-wind, and torsional diretions, respetively. In order to failitate the engineering appliation, empirial formulae for effet of orner reession modifiation on oeffiients of base moment and torque are provided by using the nonlinear least-squares method. Moreover, error rate failitating quantitative analysis is defined as follows: Error ratio=(fitted result-)/ 100% (5) 3 EXPERIMENT RESULT 3.1 Mean oeffiients of base moment 0 5 Terrain B Terrain D Type I Type II Fig. 3. Effet of orner reession ratio on the mean oeffiient of along-wind base moment Fig. 3 illustrates the effet of orner reession ratio on C MD of square model, where orner reession ratio 0 represents basi model with no orner reession. Seen from Fig.3, mean oeffiients of base moment of models with no orner reession in terrain ategories B and D are 5 and 2, respetively. With orner reession ratio inreasing from 0% to 7.5%, CMD derease gradually and it reahes the minimum when is 7.5%. C MD, however, would onversely inreases if ontinues to grow over 7.5%, and proessing to C MD0 when reahes 30%. In 962

5 The Seventh International Colloquium on Bluff Body Aerodynamis and Appliations (BBAA7) Shanghai, China; September 2-6, 2012 sum, C MD an be diminished when ranges from 0% to 30%, and reahes its minimum at the point 7.5%, roughly equivalent to 60% of C MD0. Despite C MD tested from terrain ategories D is lower than the one from terrain ategories B, effet of terrain ategories B and D on C MD is not obvious in error allow range. That regularity of the vortex shedding has been transformed and leeward negative pressure has been then redued may explain for the phenomenon that the influene of two types of orner reession on C MD is basially the same. Besides, type I orner reession is more effetive than type II at reduing mean oeffiients of base moment. Modifiation fator MD Result of formula (6) orner reession ratio C (a) Corner reession type I Modifiation fator MD Result of formula (7) orner reession ratio C (b) Corner reession type II Fig. 4. Comparison of Modifiation fator MD between the testing results and orresponding fitted ones Empirial formulae are derived by nonlinear least-squares method tehnique, expressed as: % MD, Type I (6) % 4.8 C0 C 7.5% MD,Type (7) C C 7.5% C Fig. 4 portrays the distintion between test and alulation results obtained from formulae (6) and (7). The average of the error rate of alulation results obtained from formula (6) is 6% and RMS is 3.08%, and as for formula (7) the average and RMS of the error rate are 0.08% and 4.36%, respetively. 963

6 3.2 RMS oeffiients of along-wind base moment Fig. 5 illustrates the effet of orner reession ratio on C MD of square model. With orner reession ratio inreasing, C MD firstly dereases, then inreases, and finally dereases. C MD appears to be roughly equivalent to 80% of C MD0 when =30%, and reahes its minimum when 7.5%, and probably equals 55% of C MD0 when 7.5%. In brief, orner reession ratio ranging from 0 to 30% an redue C MD and further inreasing orner reession ratio over 7.5% is really ineffetive at reduing C MD. Finally, effet of two types of orner reession on C MD is basially the same whether in terrain ategories B or D Terrain B Terrain D Type I Type II 0.10 C' MD Fig. 5. Effet of orner reession ratio on the RMS oeffiient of along-wind base moment Modifiation fator 'MD Result of formula (8) orner reession ratio C (a) Corner reession type I Modifiation fator 'MD Result of formula (9) orner reession ratio C (b) Corner reession type II Fig. 6. Comparison of Modifiation fator MD between the testing results and orresponding fitted ones 964

7 The Seventh International Colloquium on Bluff Body Aerodynamis and Appliations (BBAA7) Shanghai, China; September 2-6, 2012 Pieewise funtion is adopted in fitting proess beause regular pattern of C MD in 0-7.5% is not onsistent with that in 7.5%-30%. Empirial formulae refleting the effet of two types of orner reession modifiation on C MD are shown as: % MD 3, Typ e (8) / % % MD, Type (9) Fig. 6 presents the omparison between testing results and the orresponding fitted ones obtained from formula (8) and (9). The average of the error rate of orresponding fitted results obtained from formula (8) is -0.18%and RMS value is 3.71%; the average and RMS of the error rate obtained from formula (9) are 0.21% and 4.86%, respetively. 3.3 RMS oeffiients of base aross-wind moment 0.20 Terrain B Terrain D Type I Type II 0.15 C' MD Fig. 7. Effet of orner reession ratio on the RMS oeffiient of aross-wind base moment Fig. 7 illustrates the effet of orner reession ratio on C ML of square model. With orner reession ratio inreasing, C ML firstly dereases, and then inreases, and finally onversely dereases. C ML dramatially and sharply drops when =7.5%, and gradually inreases with varying from 7.5% to 12.5%, and then dereases when grows over 12.5% whose derease amplitude is relatively small. The essential hange in vortex shedding would explain for this variation rule of C ML after grows over 7.5%. In brief, C ML an be diminished with varying from 0 to 30%, and appears to be roughly equivalent to 65% of C ML0 when =7.5%. However, further inreasing is really ineffetive at reduing C ML. Besides, the effet of two types of orner reession on C ML are basially the same whether in terrain ategories B or D, but dereasing amplitude of C ML indued by type I is larger than that of type II, whose usable area is larger than type I as for the same. Despite the absene of test data on 5% for C ML of type II, linear funtion is adopted in fitting proess for type II in 0~7.5% beause the regularity in both types are similar. Empirial formulae for the effet of orner reession modifiation on C ML are provided as: % ML 7, Type (10) 11 e

8 % ML,Type (11) 1/ ( / ) 7.5 Fig. 8 presents the distintion between test and alulated results obtained from formula (10) and (11). The mean error rate of fitted results obtained from formula (10) is 0.16% and RMS is 7.1%, and as for formula (11) mean and RMS of error rate are -6% and 6.39%, respetively, demonstrating high preision of formula Modifiation fator 'ML Result of formula (10) orner reession ratio C (a) Corner reession type I Modifiation fator 'MT Result of formula (11) orner reession ratio C (b) Corner reession type II Fig. 8. Comparison of Modifiation fator ML between the testing results and orresponding fitted ones 3.4 RMS oeffiients of base torque Terrain B Terrain D Type I Type II 0.03 C' MT Fig. 9. Effet of orner reession ratio on the RMS oeffiient of base torque 966

9 The Seventh International Colloquium on Bluff Body Aerodynamis and Appliations (BBAA7) Shanghai, China; September 2-6, 2012 Fig. 9 illustrates the effet of two types of orner reession on RMS oeffiients of base torque C MT of square model. Seen from Fig.9, if orner reession ratio varies between 0 and 5%, orner reession modifiation basially has no influene on C MT. However, C MT dramatially derease with orner reession ratio inreasing over 5%, and both of two types of orner reession have suh effetiveness that C MT is less than 25% of C MT 0 when is 30%. Besides, effet of two types of orner reession on C MT are basially the same whether in terrain ategories B or D. Empirial formulae for the effet of orner reession modifiation on C MT are provided as: 5.6 MT e, 0 30% (12) 3 MT ,, 0 (13) Fig. 10 presents omparison between test values and fitted ones obtained from formula (12) and (13), and alulation results evenly distributed in two side of test level, demonstrating these formulae both is onise and meet the requirements for engineering appliation. Modifiation fator 'MT orner reession ratio C (a) Corner reession type I Modifiation fator 'MT 0.2 Result of formula (12) Result of formula (13) orner reession ratio C (b) Corner reession type II Fig. 10. Comparison of modifiation fator MT between the testing results and orresponding fitted ones 4 CONCLUSIONS This paper presents the test results of 14 rigid models with orner onession of square tall buildings with high frequeny fore balane (HFFB) tehnique in two simulated wind field onditions, and analyzes the effets of orner onession modifiation on the oeffiients of base moment and torque. The main findings of the present study are summarized as follows: 967

10 (1) Both type I and type II orner reession measures an redue the oeffiients of base moment and torque of square high-rise building, and the orner reession rate of 7.5% is the most effetive and optimal. (2) Eah of regularity in the oeffiients of base moment and torque for along-wind, rosswind and torsion diretion is different. For any kind of aerodynami oeffiients two types of orner onession measures have the same regularity, insensitive to turbulene intensity of wind field ondition. (3) The preision and appliability of the empirial formulae for the oeffiients of aerodynami fore were verified, whih provides tehnial support for the revisions and supplements of load odes. 5 ACKNOWLEDGMENTS This researh was supported by the National Natural Siene Foundation of China (Grant Nos and ). 6 REFERENCES 1 M. Gu. The researh proess and basi sientifi issues about ivil strutures. Siene Press, Beijing, Kareem, T. Kijewski, Y. Tamura. Mitigation of motions of tall buildings with speifi examples of reent appliations, Wind and Strutures, 3(1999) M. GU, Z.W. Zhang, Y. Quan, Y. Xiong. Aerodynami Measures for Mitigation of Aross-wind Responses of Super Tall Buildings: State of the Art, Journal of Tongji University: Natural Siene, (submitted) (in Chinese). 4 N.H. Melbourne, J.C.K. Cheung. Designing for servieable aelerations in tall buildings, Proeedings of the 4th International Conferene on Tall Buildings, Hong Kong and Shanghai, 1988, pp K. Miyashita, J. Katagiri, O.Nakamura, et al. Wind indued response of high rise building: effets of orner uts or opening in square building, Journal of Wind Engineering and Industrial Aerodynamis, 50(1993) M. Gu, Y. Quan. Aross-wind loads of typial tall buildings, Journal of Wind Engineering and Industrial Aerodynamis, 92(2004) H. Kawai. Effets of orner modifiations on aeroelasti instabilities of tall buildings, Journal of Wind Engineering and Industrial Aerodynamis, 74-76(1998) P.A. Irwin. Bluff body aerodynamis in wind engineering, Journal of Wind Engineering and Industrial Aerodynamis, 96(2008) K.K. Suresh, P.A. Irwin, A. Davies. Design of tall building for wind: wind tunnel vs. odes/standards, Proeedings of the 3 rd National Conferene on Wind Engineering, Calutta, India, 2006,pp K.T. Tse, P.A. Hithok, K.C.S. Kwok, et al. Eonomi perspetives of aerodynami treatments of square tall buildings, Journal of Wind Engineering and Industrial Aerodynamis, 43(2009) Chinese Code for Loading on Buildings and other Strutures, GB , 2006(in Chinese). 12 P. Huang, Y. Quan, M. Gu. Researh of passive simulation method of atmospheri boundary layer in TJ-2 wind tunnel, Journal of Tongji University :Natural Siene,1999,27(2) : (in Chinese). 13 M. GU, Z.W. Zhang, Y. Quan, Y. Xiong. RMS values of base torsional moment oeffiients of tall buildings with square and retangular ross-setions, Journal of Vibration and Shok, 30 (2011) 1-5 (in Chinese). 968