15thh Australasian W Wind Engineeriing Society Wo orkshop Syd dney, Australia 23--24 February 20012
Evalu ation of HFBB H Analysis un nder the Effects E off Surroun nding Buildings K.T. Tse e1 and K.K.C C. Wong2 1
Departtment of Civi l and Environ nmental Eng gineering The Hong Kong g University of Science and a Technolo ogy, Hong Koong 2
AECOM, 13 3/F Grand Central C Plaza, T Tower 2, 138 Shatin Rura al Committee e Road, Shatin, Hong Konng Ab bstract
veersatility and reliability r of thhe LMS metho od as well as the ap pplication of mo ode shape correection factors. The details off the wiind tunnel testss, results and pperformance of the methods unnder different wind lo oading environm ments due to th he surroundingss are utlined and discussed in this paaper. ou
As an alternative tto the more connventional appllication of geneeral mode shape correcction factors in the high frequeency base balannce FBB) analysis, a methodologyy referred to ass the linear-modde(HF shaape (LMS) methhod has been reecently develop ped to allow bettter estiimates of the ggeneralized forcces by establish hing a new sett of cen ntres at which tthe translationaal mode shapess are linear. T The LM MS method was applied to a talll building project in Hong Koong in the current stuudy, which is located in a heavily h developped bussiness district and surroundeed by tall buildings and mixxed terrrain. The HFB BB results validated the versaatility of the LM MS metthod for the structural desiign of an acttual tall buildiing sub bjected to the varied wind characteristicss caused by the surrroundings. Inn comparison, the application n of mode shaape corrrection factors in the HFBB analysis a did nott directly take innto acccount the influeence of the site specific charracteristics on the actu ual wind loads,, hence their esttimates of the building b responnses hav ve a higher variability.
De etails of the Subject S Build ding and its Surroundings S s Th he subject building considerred in this pap per is a 36-stoorey residential towerr on top of a 44-level commercial podium. The tower structure consists of loadd bearing walls and a simple beam an nd slab construction. Laterall wind loads acting on the toower are resisted by th he core walls annd load bearing walls of the tow wer. Th he tower structu ure is supportedd on a transfer beam b sitting onn the co olumns and walls of the podium m. A typical floor f plan, show wing the reference axees, and an elevaation of the building are presennted he studied buildding has a heigh ht of approximaately in Figure 1. Th 15 51 m above grround level ove ver a small sitee coverage areaa of ap pproximately 25 2 m by 13 m m, resulting in an aspect ratio r (H H:W:D) of 12:6:1.
Introduction Thee high-frequenccy base balancee (HFBB) techn nique has becoome onee of the most common windd tunnel testin ng techniques for predicting wind-innduced forces for tall buildin ng design sincee it wass developed in the early 1980ss (Davenport an nd Tschanz, 19881; Tscchanz and Daveenport, 1983). Recent trends towards irreguular building shapes an and increased building b heightss have resultedd in buildings having ssignificantly noonlinear and/or three-dimension onal (3D D) mode shapes that have typpically been treeated through the app plication of moode shape corrrection factors (e.g. Boggs aand Petterka, 1989; Chhen and Kareem m, 2004; Holm mes, 1987; Holm mes et al., a 2003; Lam aand Li, 2009; Xu X and Kwok, 1993). 1 Howevver, the correction facttors inherently introduce otherr uncertainties aand o the generalissed the effects of surrroundings on the accuracy of win nd force predicttions have not been b investigatted in detail in the liteerature. An alternative analyysis methodolog gy, referred to as the linear-mode--shape (LMS) method, has been recenntly veloped to m minimise the potential unceertainties in the dev estiimation of geneeralised wind forces f by “linearizing” the sw way com mponents of thee 3D mode shaapes without th he need to assum ume or surmise s the likeely form of the wind load distrributions.
Fig gure 1. Elevation n and typical plann of the subject bu uilding.
Th he mode shapes correspondiing to the firsst three modess of vib bration, associiated with thee storey mass centres over the bu uilding height, are displayed iin Figure 2. It should be nooted that the torsionaal components were multipliied by the oveerall radius of gyration (i.e. ~8.3 m) of the buiilding to mainntain dimensional conssistency amongg the three (x, y,, z) componentss for he first mode of o vibration haas a the sake of pressentation. The ominant translaational compoonent along th he x axis annd a do sig gnificant torsio onal componentt. The second d mode is basiccally a translational mode of vibrration (i.e. haaving a negliggible nent) with a ddominant comp ponent along thhe y torsional compon ax xis. The third d mode is a ppredominantly torsional modee of vib bration with modest m translattional componeents. The nattural freequencies of the first three moodes were 0.238 8 Hz, 0.258 Hz and 0.4 429 Hz respectively.
Thee LMS methodd has been evaluated and co ompared with the metthods using moode shape corrrection factors for a rectanguular building, which w was wind tunneel tested in isolation in an oppen terrrain (Tse et all., 2009). Thee results demo onstrated that the LM MS method haas the potentiial to providee more accurrate predictions of the wind-induced loads l and respo onses for buildinngs witth translationall-torsional couupled mode sh hapes. For the currrent study, a rreal tall buildinng and its surrroundings, whhich included tall builldings and miixed terrain, were w modelled to exaamine the effe fects of the surroundings s on o the accuraacy,
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bu uilding. A map m showing thhe coverage of o the surroundding bu uildings is preseented in Figuree 4, in which th he buildings havving heeights significan ntly taller than the subject bu uilding are hatched. Th he remaining areas are maainly slopes, open spaces and strructures with heights h less thann 100 m. Forr ease of refereence, the distribution of o approaching w wind condition ns is also illustrrated in Figure 4.
Figu ure 2. Mode shappes of the subject building.
Thee building site is close to the harbourfront in n Hong Kong aand surrrounded by toppography compprising mixturees of open watter, urb ban and built-uup terrain on both b sides of the harbour, aand mountainous areass on Hong Konng Island to thee south and in the w Territories tto the north. A 1:2000 scale topographiical New stud dy was undertaaken to quantifyy the effects off local topograpphy on mean and gust wind speeds appproaching the site of the subjject building. Resultss of the topoggraphical study showed that the building has relatiively open expoosures towards the northeast aand norrthwest directioons, whereas it is i sheltered from m southerly winnds by nearby mountaains with peakks in excess of 400 m – 500 m. Forr the majority oof wind directioons, wind conditions approachiing the building site were similar to t wind flow over a large ccity cen ntre and were ddesignated as condition c A. For F the remainiing win nd directions tested, wind condditions were sim milar to wind fllow oveer urban terrainn and designateed as condition n B. Mean wiind speeed and turbulence intensity profiles for the two approaach con nditions are prresented in Figure 3 along with power llaw fun nctions that provvided the best overall o fit to thee measured dataa.
Fig gure 4. Coverage of the 1:400 scalle model.
It is evident that the t subject buillding was exposed to a wide raange off wind loading environments, resulting from m the combinattions off the two different approaching ng wind conditions and the efffects off the nearby su urrounding builldings. For ex xample, at a wind w direction of 20o, the subject buiilding is located downstream of a talll building com mplex; at a wiind direction of o 100o, the uppper lev vels of the sub bject building w were exposed to t the approachhing wiind whereas the t up-stream buildings provided significant sh hielding to the lower l levels; at wind directio ons of 140o – 150o, the subject build ding was againn situated dow wnstream of a tall bu uilding complex x and it was suubjected to the less l turbulent wind w co ondition A. It was evident thhat the wind loaads experiencedd by the subject build ding were connsiderably altered by the vaaried su urroundings an nd unlikely too follow the approaching wind w prrofiles.
height at prototype scale
350 Condition A: mean speed Condition A: turbulence in ntensity Condition A: power law (e exponent = 0.24) Condition B: mean speed Condition B: turbulence in ntensity Condition B: power law (e exponent = 0.35)
300 250 200 150 100 50 0 0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4 4
wind characteristics
Co omparison off HFBB Analyysis Methods s Figu ure 3. 1:400 scalle wind characterristics: approachiing wind conditi ons A and B.
Mode Shape Co orrection Facttors Fo or each of the 36 wind direcctions tested, the measured wind w loads were comb bined with the ddynamic propeerties of the subbject bu uilding to evalu uate analyticallyy the dynamic loads and buildding responses corresp ponding to a reeturn period of 50 years (Buildding KSAR 2004). Structural dam mping ratios forr the Deepartment, HK su ubject building were w assumed tto be 1.5% of critical c dampingg for modes 1 and 2 an nd 2% of criticaal damping for mode m 3.
Wind Tunnel HF FBB Test Settup l 1:400 scale moddel of the subjject building w was A lightweight, mounted on a rigiid base balancee such that the overall mass aand stifffness of the enttire system prodduced sway and d torsional natuural freq quencies that w were well abovve the range of o interest for tthe HFBB tests. The force balancce was calibrated by applyingg a nge of known sttatic loads to thhe model prior to t the wind tunn nnel ran testting to providde direct measurements of the wind loaads. Meeasurements weere taken for 366 wind direction ns at 10o intervaals, o for the full 360 aazimuth, wheree a wind directtion of 0o or 3660o corrresponds to ann incident windd approaching directly from the norrth, and winds ffrom 30o are appproximately peerpendicular to the wid de face of the suubject building..
In n the convention nal HFBB anallysis, the generralised wind foorces weere computed using three different setss of mode shhape co orrection factorrs, as listed in Table 1, whicch are intrinsiccally related to the pow wer law exponeents of the build ding’s mode shaapes an nd the mean wind speed profille for the corresponding approoach co ondition. The mode shape poower law expon nents were obtaiined by y performing a least-squaress fit to the mode m shape vallues. Siimilarly, the power law expoonents of the mean wind sppeed prrofiles were fou und to be 0.244 and 0.35 for wind conditionns A an nd B, respectiv vely. It worthh noting that th he measured mean m wiind speed profiles and the buillding’s mode sh hapes, in particcular
Alll known existing and plannned surroundin ng buildings aand topographical feattures within a raadius of 500 m were modelledd to the same linear sscale and were included in th he HFBB testss to sim mulate their effeects on wind fllows around th he site and subjject 130
peak overturning moment response coefficients for this wind direction are 1.38 and 1.11, obtained from the application of low and high correlation mode shape correction factors.
the torsional component of mode 1 and the x-translational component of mode 3, were not satisfactorily fitted with a power law function. Hence uncertainties were inherently introduced in the calculations of mode shape correction factors and the subsequent generalised wind force predictions. Low Correlation (Xu & Kwok, 1993)
High Correlation (Boggs, 1989)
Simplified (Holmes, 1987)
Translation (Xjx, Xjy)
3 + 2α 1 + 2α + 2 β
2 +α 1+α + β
4 1 + 3β
Twist (Xjθ)
1 + 2α 1 + 2α + 2 β
1+ α 1+α + β
1 1 + 2β
In terms of the accuracy of the different methods considered in this study, the results presented in Figure 5 demonstrated a similar trend to the results of the benchmark building tested in isolation (Tse et al., 2009). Comparable results were found for the simplified correction factor and the LMS method, providing values in between the upper and lower limits obtained from the application of low and high correlation mode shape correction factors, respectively. Furthermore, the results of the high correlation mode shape correction factors may underestimate the base moment responses for some wind directions.
α is the power law exponent of the mean wind speed profile; and β is the mode shape power law exponent
base moment response coefficient, CMx
1.5
Table 1. Correction factors for the estimation of generalised wind forces.
The three sets of mode shape correction factors, corresponding to low and high correlations of wind load and the simplified form, were subsequently computed. The low and high correlation mode shape correction factors had the largest and smallest values respectively, whilst the simplified factors were essentially between the two limits. Comparing the two approach wind conditions, the simplified mode shape correction factors are the same for both wind conditions since the calculations were independent of the power law exponent of the mean wind velocity profile. For the low and high correlation factors, the mode shape correction factors for wind condition A were always smaller than those for wind condition B because of the smaller power law exponent of the mean wind velocity profile for wind condition A.
LMS method Low correlation High correlation Simplified
1.2
0.9
0.6
0.3
0.0 0
90
180
270
360
wind direction
Figure 5. Maximum base overturning moment response about x-axis.
It can also be seen from Figure 5 that the variations of base moment response coefficients obtained using the different methods were higher at some directions, such as for 300o – 360o. In order to more comprehensively investigate the performance of the various analyses under different wind conditions due to the surroundings, the “coefficient of variation” of the base overturning moment coefficients, defined as the standard deviation normalised by the mean value (i.e. σ M M ) and expressed as a percentage, are presented in Figure 6. The distribution of wind conditions and the locations of tall building complexes are also included in Figure 6 for better illustration. It is evident that the applicability and suitability of mode shape correction factors in the HFBB analysis were significantly influenced by the wind conditions and the characteristics of the surrounding terrain. For the wind directions of 50o – 130o and 180o – 260o, the subject building was relatively exposed as the surrounding buildings were shorter and the coefficients of variation were relatively small, with values as low as 1% or less. However, the coefficients of variation were considerably higher when the subject building was located downstream of a tall building complex, e.g. 20o – 40o, 140o – 160o, 270o, and 310o – 350o, and particularly under the influence of the higher turbulent wind condition B.
Linear-Mode-Shape (LMS) Method As an alternative to the conventional application of mode shape correction factors, Tse et al. (2009) developed an analysis methodology, referred to as the linear-mode-shape (LMS) method, to minimise the potential uncertainties in the estimation of generalised wind forces by “linearizing” the sway components of the 3D mode shapes without the need to assume or surmise the likely form of the wind load distributions. The LMS method allows the exact computation of the sway components of the generalised wind force to be determined by establishing a new set of centres, referred to as the LMS centres, at which the translational mode shapes are “linearized” by axis transformations. The torsional component of the generalised wind force is still reliant on an appropriate selection of a torsional mode shape correction factor, as the twist mode shapes are independent of the axis transformation. It should be pointed out that the LMS method is based on the linearization of the translational mode shapes via axis transformation, which relies entirely on the existence of the twist component of the mode shape to alter the shape of the sway components. Hence the LMS method is applicable to buildings with translationaltorsional coupled mode shapes. Detailed derivations and explanations of the LMS method were presented in Tse et al. (2009).
Conclusions HFBB test results for a real tall building project in Hong Kong were analysed by using mode shape correction factors and the LMS method to examine the reliability, versatility and accuracy of the two methods under varied wind loading environments. The results demonstrated that the accuracy and reliability of HFBB analysis methods depend significantly on the terrain characteristics of the nearby surroundings. When the subject building was relatively exposed to the approaching wind, consistent results among various methods were obtained. However, high coefficients of variation were found among the application of low and high correlation mode shape correction factors for the wind directions at which the tested building was downstream of a tall building complex, especially under highly turbulent winds. This is because the application of mode shape correction factors in the HFBB analysis did not directly take into
Base Overturning Moment Responses The peak base overturning moment response coefficients about the x-axis, CMx, were determined for each set of applied mode shape correction factors and the LMS method, as presented in Figure 5. The largest wind-induced base moment response coefficients were measured for a wind direction of 310o, i.e. for wind approaching the site approximately from the northwest. The measured results for 310o exhibited enhanced turbulent energy, probably due to the presence of the upstream structures northwest of the subject building. The maximum and minimum 131
account the influence of the site specific characteristics on the actual wind loads. Therefore, mode shape correction factors should be applied with caution in HFBB analyses when tall building complexes exist in the surrounding proximity. In comparison, the LMS method, which does not require knowledge of the wind load distributions, provided more reliable predictions and hence demonstrated its adaptability in typical tall building environments where wind loading conditions are significantly influenced by the surroundings.
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Figure 6. Coefficients of variation (%) for Mx over the different HFBB analysis methods.
Acknowledgments
Tse, K.T., Hitchcock, P.A. and Kwok, K.C.S. (2009) Mode Shape Linearization for HFBB Analysis of Wind-Excited Complex Tall Buildings, Engineering Structures, 31:675-685
This research project is funded by a Research Grants Council of Hong Kong Central Allocation Grant (Project CA04/05.EG01) and General Research Fund (Project 9041338). Thanks also go
Xu, Y.L. and Kwok, K.C.S. (1993) Mode shape corrections for wind tunnel tests of tall buildings, Engineering Structures, 15:387-392
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