AERODYANMIC AND RESPONSE CHARACTERISTICS OF SUPER- TALL BUILDINGS WITH VARIOUS CONFIGURATIONS

Transcription

1 The Eighth Asia-Pacific Conference on Wind Engineering, December 4, 23, Chennai, India AERODYANMIC AND RESPONSE CHARACTERISTICS OF SUPER- TALL BUILDINGS WITH VARIOUS CONFIGURATIONS Y. Tamura, Y.C. Kim 2, H. Tanaka 3, E.K. Bandi 4, A. Yoshida 5, K. Ohtake 6 Professor, Polytechnic University, Atsugi, Kanagawa, Japan, yukio@arch.t-kougei.ac.jp 2 Research professor, Korea University, Seoul, Korea, gentle95@gmail.com 3 Associate Chief Researcher, Takenaka Corporation, Inzai, Chiba, Japan, tanaka.hideyuki@takenaka.co.jp 4 Ph D Candidate, Tokyo Polytechnic University, Atsugi, Kanagawa, Japan, eswar@arch.t-kougei.ac.jp 5 Associate Professor, Tokyo Polytechnic University, Atsugi, Kanagawa, Japan, yoshida@arch.t-kougei.ac.jp 6 Associate Chief Researcher, Takenaka Corporation, Inzai, Chiba, Japan, ohtake.kazuo@takenaka.co.jp ABSTRACT Tall buildings have been traditionally designed to be symmetric rectangular, triangular or circular in plan, in order to avoid ecessive seismic-induced torsional vibrations due to eccentricity, especially in seismic-prone regions like Japan. However, recent tall building design has been released from the spell of compulsory symmetric shape design, and free-style design is increasing. This is mainly due to architects and structural designers challenging demands for novel and unconventional epressions. Another important aspect is that rather complicated sectional shapes are basically good with regard to aerodynamic properties for across-wind ecitations, which are a key issue in super-tall-building wind-resistant design. The authors group has conducted a series of wind tunnel eperiments for super-tall buildings with various configurations. The present paper summarizes the main findings including variations in peak pressures, aerodynamic and response characteristics, wind load combination effects, and flow field characteristics by CFD. The results of these eperiments have led to comprehensive understanding of the aerodynamic and response characteristics of super-tall buildings with various configurations and cross-sections. Keywords: Tall building, peak pressure, dynamic response, Wind load combination effect, CFD analysis Introduction Since the completion of Burj Kalifa in 2, several super-tall buildings over,m high have been planned. The current tallest building in the world is the 828m-high Burj Khalifa, and the tallest building in the net decade will be Kingdom Tower (over m), which will be completed in 28, making Burj Khalifa the third tallest. According to a report (Tamura et al., 2) that eamined world skyscrapers under construction as of January 2, 56% of those within the top highest buildings had been completed since 2, and many tall buildings higher than 6m are still under construction. This trend of manhattanization requires attention, particularly the preference for free-style building shapes, which are seen in Burj Kalifa and Shanghai Tower, presently under construction. Tall buildings have been traditionally designed to be symmetric rectangular, triangular or circular in plan, in order to avoid ecessive seismic-induced torsional vibrations due to eccentricity. However, freewheeling building shapes have advantages not only in architectural design reflecting architects challenging spirits for new forms but also in structural design reducing wind loads. Development of analytical techniques and of vibration control techniques has greatly contributed to this trend. In particular, across-wind response, which is a major factor in safety and habitability of tall buildings, is greatly suppressed. Copyright 23 APCWE-VIII. Published by Research Publishing Services. ISBN: :: doi:.385/ _key-2 K-29

2 K-22 Y. Tamura et al. The effectiveness of aerodynamic modification to reduce wind loads has been widely reported (Hayashida and Iwasa (99); Hayashida et al. (992); Shiraishi et al. (986); Kwok et al. (988); Miyashita et al. (993); Amano (995); Kawai (998); Cooper et al. (997); Kim and You (22); Kim et al. (28); Kim and Kanda (2;23); Kim et al. (2); Dutton and Isyumou (99); Bandi et al. (22)). However, most of the above papers have focused on the effect of one or two aerodynamic modifications that change systematically. None have comprehensively investigated aerodynamic characteristics of various types of tall buildings with different configurations. The authors group has conducted wind tunnel eperiments for the super-tall buildings with unconventional configurations to investigate the variations in peak pressures and aerodynamic and response characteristics. The present paper summarizes the main findings including variations in peak pressures, aerodynamic and response characteristics, wind load combination effects, and flow field characteristics by CFD. These findings can provide the structural designer with comprehensive wind tunnel test data that can be used in the preliminary design stage, and can be helpful in evaluating the most effective structural shape in wind-resistant design for tall buildings with various aerodynamic modifications. Configurations of super-tall buildings The super-tall building models used for the eperiments are shown in Table. The full-scale height and the total volume of each building model are commonly set at H = 4m (8 stories) and about,,m 3. The width B of the Square model shown in Table (a) is 5m and the aspect ratio H/B is 8. The geometric scale of the wind tunnel models is set at /. The tall building models eamined in this study are classified into 9 categories as follows. (a) Basic models The Square, Rectangular, Circular, and Elliptic plan models shown in Table (a) are classified as Basic models. The side ratio of the Rectangular and Elliptic models is :2. For the Circular and Elliptic models, the effect of Reynolds number Re should be discussed when considering the correspondence to the full-scale structure. Generally it is quite difficult to simulate a large Re that is similar to the full-scale value, so in the present work, Re is just mentioned as a reference for the smooth-surfaced models. The Re obtained from the diameter of the Circular model used in the wind tunnel eperiment is Re= (b) Corner modification models Although there are several methods for corner modification, i.e. corner chamfered, corner cut, corner rounding, fin, and so on, the eamination of corner modification focuses on a Corner Cut model and a Corner Chamfered model as shown in Table (b). Referring to past researches on aerodynamic characteristics of structures and buildings with corner chamfered and corner cut models (Shiraishi et al. (986); Amano (995); Kawai (998)), the modification length is set at.b, where B is the building width. (c) Tilted models For the Tilted model, the roof floor is displaced by 2B from the base floor, and for the Winding model, the floors at.25h and.75h are shifted by.5b to the left and right side, respectively, from the middle floor, and the walls have smoothly curved surfaces as shown in Table (c). (d) Tapered models The tapered models include the following five types: a 2-Tapered model with only two tapered surfaces, a 4-Tapered model with four tapered surfaces, an Inversely 4-Tapered model with the inverse building shape of the 4-Tapered model, and a Bulged model whose sectional area at mid-height is epanded as shown in Table (d). When the taper ratio is between 5%

3 Aerodyanmic and Response Characteristics of Supertall Buildings with Various Configurations K-22 and %, a model with a larger tapering ratio shows better aerodynamic behavior (Kim and Kanda (2)). Thus, for the 4-Tapered model, the taper ratio was set at % and the area ratio of the roof floor to the base floor was set at /6. The Setback model with a 4-layer setback is also classified in this category. The area ratio of the roof floor to the base floor is set at /6 for the 2-Tapered, Setback, and Inversely 4-Tapered models. For the Bulged model, the ratio of roof floor or base floor area to the largest middle floor area is /3. (e) Helical models The sectional shapes of the helical models are square and rectangular, and the helical angle between the roof floor and the base floor is set at 6, 9, 8, 27 and 36, as shown in Table (e). The sectional shapes together with the helical angle are used as a prefi of the model name. For eample, the 8Helical Square model means the helical model whose sectional shape is square with a helical angle of 8. (f) Opening models There are three cross-opening models and three oblique-opening models, with openings at the top-center and top-corner of the walls, respectively, as shown in Table (f). Three different opening heights h = 2H/24, 5H/24, and H/24 are considered to clarify the effects of opening size on the aerodynamic characteristics. For the three Oblique Opening models, the opening volume is not included in the building volume, and since the building volumes of those models are almost the same, their widths are fied. However, for the three Cross Opening models, the opening volume is included in the building volume to maintain compatibility of aspect ratio with the other models. (g) Composite models The composite models have the combined configurations of the primary configurations shown in Tables (a) ~ (f), and the aerodynamic characteristics of the following four composite models shown in Table (g) are investigated: 36 Helical + Corner Cut; 4-Tapered + 36 Helical + Corner Cut; Setback + Corner Cut; and 45 Rotating Setback models, where the rotating angle of each setback layer is 45. (h) Triangular models Equilateral triangle models with a side dimension of.76 m were used. Their crosssectional areas were the same as that of the Square model. Triangular models include Triangular, Corner Cut, Clover, 6 Helical, 8 Helical, and 36 Helical Triangular models. The triangular plan models are shown in detail in Bandi et al. (22). (g) Polygon models Equilateral cross-sections were used and the cross-sectional areas were the same as that of the Square model. Cross-sectional shapes were pentagon, heagon, octagon, and dodecagon. To eamine the effect of the helical configuration, models with 8 helical angle were also implemented. Table : Configurations of super-tall buildings (a) Basic models Square Rectangular Circular Elliptic (b) Corner modification models Corner Corner Cut Chamfered H=4 L = o y D B=5

4 hh=4 K-222 Y. Tamura et al. Tilted (c) Tilted models Winding (d) Tapered models 2-Tapered 4-Tapered Setback Inversely 4-Tapered Bulged o Helical Square 8 o Helical Square (e) Helical models 27 o Helical Square 36 o Helical Square 8 o Helical Rectangular (f) Opening models (f-) Cross Opening (f-2) ObliqueOpening h/h=2/24 h/h=5/24 h/h=/24 h/h=2/24 h/h=5/24 (f) (f-2) h/h=/24 36 o Helical & Corner Cut (g) Composite models 4-Tapered & 36 o Helical & Corner Cut Setback & Corner Cut Setback & 45 o Rotate

5 Aerodyanmic and Response Characteristics of Supertall Buildings with Various Configurations K-223 Eperimental conditions Wind tunnel eperiments were performed in a closed-circuit-type boundary-layer wind tunnel whose working section is.8m high by 2.m wide. Fig. shows the condition of the approaching turbulent boundary layer flow with a power-law inde of.27, representing an urban area. The wind velocity and turbulence intensity at the top of the model were about UH =7.m/s and IUH =9.2%, respectively. The turbulence scale near the model top was about.36m, and that of AIJ-RLB (AIJ (24)) is 365m. Therefore, when considering the length scale of /, the flow conditions of the present work are thought to be appropriately simulated. Dynamic wind forces were measured by a 6-component high-frequency force balance (HFFB) supporting light-weight and stiff models. Wind direction was changed from, which is normal to a wall surface, to 45 or 8 every 5 depending upon the building configuration. The measured wind forces and aerodynamic moments are normalized by qhbh and qhbh 2 to get wind force coefficients and moment coefficients, respectively. Here, qh is the velocity pressure at the model height H, and B is commonly set at the width of the Square Model. Thus, the force and moment coefficients of the models can be directly compared. Fig. 2 shows the definitions of wind forces, moments, and the coordinate system employed in this study. z/h Turbulence intensity I U (%) Mean wind velocity Turbulence intensity U H.5 U/U H (z/h).27.5 I U (z/h) ( ).5.5 Mean wind velocity U/U H Fig. Flow conditions of wind tunnel eperiment y L C MD z C MT C FL C ML D C FD Fig. 2 Coordinate system Wind pressure measurements were conducted on 28 models. They were determined from the results of aerodynamic force measurements and for relatively realistic building shapes in the current era. The aims of the pressure measurements were to eamine the characteristics of local wind forces and aerodynamic phenomena in detail. In addition, response analyses were conducted using the results of the pressure measurement. The coordinate system and approaching flow for the wind pressure measurements are the same as for the aerodynamic force measurement (see Fig. and Fig. 2), ecept that the wind velocity at model height was.8m/s. Also, the wind direction was changed from to 355 at 5 intervals as for the aerodynamic force measurements. The fluctuating wind pressures of each pressure tap were measured and recorded simultaneously using a vinyl tube 8cm long through a synchronous multi-pressure sensing system (SMPSS). The sampling frequency was khz with a low-pass filter of 5Hz. The total number of data was 32,768. The fluctuating wind pressures were revised considering the transfer function of the vinyl tube. There were about 2 measurement points on one level on four surfaces, and the measurement points were instrumented at levels (2 levels only for Setback model), giving more than

6 K-224 Y. Tamura et al. 2 measurement points. The wind pressure coefficients Cp were obtained by normalizing the fluctuating pressures by the velocity pressure qh at model height. The local wind force coefficients, CfD for along-wind, CfL for across-wind and CmT for torsional moment, were derived by integrating the wind pressure coefficients Cp using the building width B of the Square Model (B 2 for torsional moment) regardless of building shape. Overturning moment coefficients Fig. 3 shows the variation of the mean along-wind overturning moment (o.t.m.) coefficient C and the mean across-wind o.t.m. coefficient MD C ML with wind direction for the test models, which show specific aerodynamic force characteristics. The C MD and C of ML the Square model show their maimum values of.6 and.2 at wind directions 45 o and 5 o. The C MD ma of the 4-Tapered and the Setback models whose sectional areas decreased with height were relatively small. The C ML ma of the Corner cut and the Helical Square models were small: that of the Corner cut model was /5 that of the Square model. The C MD ma and C ML ma of the Helical Square model with larger twist angle tended to become smaller. And as can be seen in Fig. 3, the variation of C MD and C of the Helical Square models on wind ML directions was small, and the variation of the 8 o Helical Square model was more noticeable, implying the independence of mean overturning moment coefficients on wind direction. Square Corner cut Setback 8 Helical Square Corner chamfered 4-Tapered 9 Helical Square Cross Opening h/h=/ C MD C ML (deg.) (deg.) (a) Along-wind direction (b) Across-wind direction Fig. 3 Variation of mean overturning moment coefficients on wind direction for some test models (Tanaka et al. (22)) Fig. 4 shows the variation of the fluctuating overturning moment coefficients CMD, CML with wind direction. The coefficients CMD and CML are the standard deviation of the o.t.m. For the Square and Corner cut models, the across-wind component, CML, is larger than the along wind component, CMD, but for the other models, the coefficients show the inverse trend. A maimum CM ma=.42 is shown for the Square model for wind direction o (9 o ). A small CM ma=.82 is shown for the Setback model, being 6% of that of the Square model. The fluctuating overturning moment coefficients of the 9 o Helical Square and the 8 o Helical Square models vary little with wind direction. In particular, the 8 o Helical Square model shows almost constant values regardless of wind direction, which is also seen in the mean o.t.m coefficients.

7 Aerodyanmic and Response Characteristics of Supertall Buildings with Various Configurations K-225 C MD ' Square Corner cut Setback 8 Helical Square (deg.) C ML ' Corner chamfered 4-Tapered 9 Helical Square Cross Opening h/h=/ (deg.) (a) Along-wind direction (b) Across-wind direction Fig. 4 Variation of fluctuating overturning moment coefficients on wind direction for some test models (Tanaka et al. (22)) Fig. 5 shows the maimum values of the mean along-wind and across-wind o.t.m. ma and C ML ma considering all wind directions. The maimum along-wind ma and across-wind o.t.m. coefficient C ML ma of the Circular model is coefficients, C MD o.t.m. coefficient C MD smallest among all eperimental models, and those of the Rectangular model, the Triangular and Elliptic models are larger than those of the Square model because of their larger widths. The maimum mean along-wind o.t.m. coefficients C MD ma of the 4-Tapered model and the Setback model, whose sectional area decreases with height, are relatively small. However, for the three Cross Opening models, whose projected areas also decrease at their upper parts, the maimum mean along-wind o.t.m. coefficient C MD ma does not decrease as much as those of the 4-Tapered and the Setback models. This may be because of the reduced effectiveness of the openings as the wind direction approaches 45. The maimum mean across-wind o.t.m. coefficients C ML ma of the Corner Cut and Corner Chamfered models are small. The maimum mean across-wind o.t.m. coefficients of the Helical Square and the Cross Opening h/h=/24 models whose opening size is the largest are also small. The small coefficients of those models are related to vorte formation and shedding. Conversely, the models whose along- and across-wind o.t.m. coefficients are larger than those of the Square model are the 2- Tapered, the 8 o Helical Rectangular and the Tilted models with larger projected area for a certain wind direction, and the Inversely 4-Tapered model with larger projected area at its upper height. The maimum mean o.t.m. coefficients C ma of a Helical C MD ma and ML Square/Triangular model with a larger helical angle tends to show smaller values. And, as can be seen in Fig. 3, the variations of mean o.t.m. coefficients C MD and C of the 9Helical ML Square and 8Helical Square models with wind direction are very small. In particular, the 8Helical Square model shows values almost independent of wind direction. For the opening models, as the opening size h/h becomes larger, the maimum mean o.t.m. coefficient C ML ma decreases. However, the decreasing tendency is not significant for the maimum mean across-wind coefficient C MD ma for both the Cross Opening and the Oblique Opening models. The aerodynamic characteristics of the composite models with multiple modifications are mostly superior to those of the models with single modification. However, note that the mean o.t.m coefficients of the 36 Helical + Corner-cut model are almost the same as those of the 36 Helical model, implying that the aerodynamic characteristics have not been further improved by corner modification.

8 K-226 Y. Tamura et al. CMDaaaa C ma.8 CML C ML ma C MD ma C ML ma.6.4 Effect of twist angle Effect of opening size h/h.2 Fig. 5 Comparison of maimum mean overturning moment coefficients (Tanaka et al. (22)) Fig. 6 shows the maimum along-wind and across-wind fluctuating o.t.m. coefficients, CMD ma and CML ma, considering all wind directions. As shown in Fig. 6, the maimum fluctuating along-wind o.t.m. coefficients CMD ma of the Corner Chamfered, Corner Cut, 4- Tapered and Setback models are smaller. The maimum fluctuating across-wind o.t.m. coefficients CML ma of the 4-Tapered, Setback, Helical Square, and Cross Opening /24 models show relatively small values. Detailed aerodynamic phenomena will be discussed later. These trends are the same as those of the maimum mean o.t.m. coefficients. And, the effect of helical angle for the Helical Square models, the effects of opening size for the two types of Opening models, and the composite effect also show the same tendency as those of the maimum mean o.t.m. coefficients..2 CMD'aaaa C ' ma CML' C ' ma C MD ' ma C ML ' ma.5..5 Effect of twist angle Effect of opening size h/h Fig. 6 Comparison of maimum fluctuating overturning moment coefficients (Tanaka et al. (22))

9 Aerodyanmic and Response Characteristics of Supertall Buildings with Various Configurations K-227 The relationships between maimum o.t.m. coefficients are shown in Fig. 7.The maimum mean and fluctuating o.t.m. coefficients show a similar tendency, and high correlations between them are observed as shown in Fig. 7(a). And, it is interesting to note that the high correlations between mean and fluctuating o.t.m. coefficients in the along-wind direction and in the across-wind direction are observed as shown in Fig. 7(b) and (c). (a) Maimum mean and maimum fluctuating o.t.m. coefficients (b) Maimum mean o.t.m. coefficients (c) Maimum fluctuating o.t.m. coefficients Fig. 7 Relationship between maimum overturning moment coefficients (Tanaka et al. (23)) Power spectral densities of across-wind overturning moment coefficients Fig. 8 shows the crosswind power spectra for the specified wind directions at which the peak is the largest, and spectral values corresponding to 5-year and -year return periods. From Fig. 8(a), the sharp peaks observed for the Square and Straight Triangle models are reduced dramatically compared to those of the other models, implying the reduced effects of regular vorte shedding. The peak value corresponding to a 5-year return period wind speed (fb/uh=.7) for the 8 o Helical is almost /5 that for the Square model, showing the advantages of a safer design. Response analyses conducted by the spectral modal method show that the maimum displacement,, of the Square is =.5H, and that of the 8 o Helical is =.3H. For the 8 o Helical Square, the displacement of the Setback is also small (=.4H). On the other hand, for values corresponding to a -year return period wind speed (fb/uh=.7), although the maimum acceleration for the Setback is larger than that for the Square, the maimum acceleration for the 8 o Helical Square is almost half that for the Square, showing that the 8 o Helical Square is an effective structural shape on the basis of safety and habitability criteria.

10 K-228 Y. Tamura et al. Fig. 8(b) and 8(c) show a detailed comparison of the square root of the power spectra for the design wind speed corresponding to 5- and -year return periods. The design wind speeds in Tokyo for the corresponding return periods are assumed to be Vp,5=7m/s and Vp,=3m/s, respectively. The values for the Corner Cut, Tapered, Setback, Helical Square (T=8 o ~36 o ), and Cross Opening (h/h=/24) models are almost one third or one fourth that of the Square model, showing advantages for safety design. And the values for the Corner cut + 4-Tapered + 36 o Helical Square and Setback + 45 o Rotate models are almost one tenth that of the Square model, so it can be said that the Combination models are very effective building shapes for safety design (Fig. 8(b)). The spectral values corresponding to a -year return period for the Tilted, Tapered and Oblique Opening models (Fig. 8(c)) are generally large, and even for the 4-Tapered and Setback model, the values are larger than that for the Square model. But the values for the Corner cut, Helical Square (T=8 o ~36 o ), and Cross Opening (h/h=/24) are smaller than that for the Square model, meaning that these building shapes are superior to the Square model from the viewpoint of habitability design. For all the composite models, the values become smaller than that for the Square model. (a) Power spectral density (b) Spectral values for Vp,5

11 Aerodyanmic and Response Characteristics of Supertall Buildings with Various Configurations K-229 (c) Spectral values for Vp, Fig. 8 Power spectral density of crosswind direction and spectral values (Kim et al. (23)) Power spectral density of across-wind local wind force coefficients The power spectra of the across-wind local wind force coefficient fscfl higher than z/h=.5 are shown in Fig. 9. The Strouhal number St corresponding to the vorte shedding frequency, and the bandwidth Bw were obtained and the vertical profiles are shown in Fig.. The power spectra in Fig. 9 are plotted against the reduced frequency, which was obtained by using the width B (constant) of the Square model regardless of building shape. The bandwidths Bw were obtained by approimating the power spectra fscfl to Eq. () through the least-square method (Vickery and Clark (972)). fs CfL 2 = k f f peak B w - ep- f / f B w peak 2 () Sharp peaks near z/h=.5 are observed for the Square model (Fig. 9(a)), but they become relatively flat near the model top because of the three-dimensional effect of flow. This again implies that regular vorte shedding eists near z/h=.5 and the regularity collapses near the model top, and the bandwidth shown in Fig. 9 near the z/h=.5 is smaller than that of the model top. The power spectral densities of other models in Fig. 9(b) ~ (h) show similar results. The Strouhal numbers St of the Square model shown in Fig. vary little with height. This means that all the vorte components are shed at almost the same time throughout the height, greatly eciting the models in the across-wind direction. Contrary to the Square model, those of the 4-Tapered, Setback and 8 o Helical models vary greatly with height. For those models, because the shedding frequencies of each height are different, the resulting acrosswind force decreases correspondingly. Similar discussion can be made for the bandwidth shown in Fig., i.e., regular and strong vortices with narrow bands are shed throughout the height for the Square model, but for the other models, vortices with wide bands are shed randomly, effectively suppressing the across-wind force. The bandwidth of the 8 o Helical model is very large, and when considered in conjunction with the large variation of Strouhal number and small spectral peak with height, it can be assumed that weak vortices with wide bands are shed irregularly throughout the height, and this results in the better aerodynamic behaviors discussed above.

12 K-23 Y. Tamura et al. fs CfL. z/h=.975 z/h=.925 z/h=.85 z/h=.775 z/h=.7 z/h=.6 z/h=.5 fs CfL. Section z/h=.975 z/h=.925 z/h=.85 z/h=.775 z/h=.7 z/h=.6 z/h=.5 fs CfL. Section z/h=.975 z/h=.925 z/h=.85 z/h=.775 z/h=.7 z/h=.6 z/h=.5 fs CfL. Section z/h=.975 z/h=.925 z/h=.85 z/h=.775 z/h=.7 z/h=.6 z/h= fb/u H.. fb/u H.. fb/u H.. fb/u H (a) Square (b) Cross Opening (c) Corner Chamfered (d) Corner Cut fs CfL. z/h=.975 z/h=.925 z/h=.85 z/h=.775 z/h=.7 z/h=.6 z/h=.5 fs CfL. z/h=.975 z/h=.925 z/h=.85 z/h=.775 z/h=.725 z/h=.625 z/h=.525 fs CfL. z/h=.975 z/h=.925 z/h=.85 z/h=.775 z/h=.7 z/h=.6 z/h=.5 fs CfL. z/h=.975 z/h=.925 z/h=.85 z/h=.775 z/h=.7 z/h=.6 z/h= fb/u H.. fb/u H.. fb/u H.. fb/u H (e) 4-Tapered (f) Setback (g) 9 o Helical (h) 8 o Helical Fig. 9 Power spectral densities of across-wind local wind force coefficients (Tanaka et al. (22)) z/h Square Cross Opening Corner chamfered Corner cut 4-Tapered Setback 9Helical 8Helical z/h Square Corner chamfered 4-Tapered 9Helical Cross Opening Corner cut Setback 8Helical Bandwidth B w S t (=f peak B/U H ) Fig. Vertical profile of Strouhal number (left) and bandwidth of across-wind local wind force power spectra (right) (Tanaka et al. (22)) Variations of peak pressures The maimum of the largest negative peak pressure coefficients C is defined as p, ma the maimum value of the largest negative peak pressure coefficientc among those for all p the wind directions selected for each model, as shown in Fig.. Due to the modification of

13 Aerodyanmic and Response Characteristics of Supertall Buildings with Various Configurations K-23 the corner regions, C reduces and the values are equal for the Triangular Corner Cut and p, ma Clover models. The C values of the Square Corner Cut model and the Setback model p, ma increase to around 6% and 2% greater than that of the Square model, as can be seen in Fig. (a) and (b). For the Straight Polygonal models, the overall trend of C decreases from p, ma Triangular model to Circular model, but the locations of the pressure taps may cause slight variation in the trend for the Pentagon and Dodecagon models. As the helical angle of the helical model increases, C also increases for the Triangular and Square models, as can be p, ma seen in Fig. (c) and (d). The polygonal helical models also show the same trend as the Straight Polygonal models, as can be seen in Fig. (e). The combined effects of helical and corner cut (8 Helical + Corner Cut) increase C to 3% greater than that of the Square p, ma model. The combined effects of taper and helical (Tapered + 8 Helical), and helical and corner cut (Tapered + 36 Helical + Corner Cut) increase C to around 2% and 7% p, ma greater than that of the Tapered model. The Setback model with 45 Rotation increases C p, ma to 5% greater than that of the Setback model. (a) Corner modification models of Triangular (left) and Sqaure cross-section (right) (b) Tapered models (c) Helical models of Triangular cross-section

14 K-232 Y. Tamura et al. (d) Helical models of Square cross-section (e) Straight and 8 Helical models (f) All models Fig. Comparison of maimum largest negative peak pressures (Bandi et al. (23)) Response analysis Fig. 2 shows the vertical profiles of the accelerations, story shear forces, displacements, and torsional moments of 8 test models. The values in Fig. 2 are the largest values for all wind directions within the design wind speed ranges. The accelerations of the Corner-modification models and Helical models are greatly reduced compared with that of the Square model, having higher mode effects. The story shear forces of the Corner-modification, Setback, and Helical models are also reduced compared to that of the Square model, but do not show higher mode effects. For displacements, there are no higher model effects, and the displacements of all models show smaller values than that of the Square model. For the torsional moments, the effect of helical angle is clearly seen, i.e. the larger torsional moment at upper height becomes smaller when changing the helical angle from 9 to 8.

15 Aerodyanmic and Response Characteristics of Supertall Buildings with Various Configurations K Story Square Story Cross Opening Corner Chamfered Corner Cut 4-Tapered Setback Helical 2.5 8Helical Accelerationm/s Story shear force 5 kn Displacementm Torsion moment 5 knm Fig. 2 Vertical profile of wind-induced responses with single modification for 5-year return period design wind speed (Tanaka et al. (23)) The maimum acceleration, maimum story shear coefficient, maimum displacement, maimum story deformation angle, maimum story shear force, maimum overturning moment, and maimum torsional moment of all models are shown in Fig. 3. All maimum values in Fig. 3 are shown as their ratio to that of the Square model. The single modification models that show smaller responses for all items are Corner Cut, Corner Chamfered, 9 Helical and 8 Helical. For the 4-Tapered, Setback, Cross Opening, the maimum acceleration and the maimum story shear coefficient are larger than that of the Square model. All composite models show smaller values for all items. When comparing the 4-Tapered + 8 Helical model with the 4-Tapered model with the same structural characteristics, the suppression of response is significant. For the 8 Helical + Corner Cut model and the 4- Tapered + Helical + Corner Cut model, only the maimum torsional moment is suppressed. For two composite models with different helical angles of 4-Tapered + 8 Helical + Corner Cut model and 4-Tapered + 36 Helical + Corner Cut model, there is little difference for all items, implying that the helical angle of 8 is enough. Although the analysis models for habitability are the same, the dynamic characteristics were changed slightly to consider the effects of secondary members; the natural frequencies were assumed to be 2% higher, and the damping ratios were assumed to be.7%. The design wind speed for habitability is 3m/s. As the sensitivity of the human body to vibration depends on the natural frequencies and corresponding accelerations, the acceleration responses of the st ~ 4 th modes were not superimposed. Fig. 4 compares the maimum accelerations of from the st to 4 th modes for all wind directions. All maimum accelerations in Fig. 4 are shown as their ratios to that of the Square model. Of the single modification models, the 9 Helical and 8 Helical models show smaller maimum accelerations, showing better habitability. The first mode accelerations of the Corner Cut and Corner Chamfered models are smaller than that of the Square model, but those of the third and fourth modes are larger. The habitabilities of the 4-Tapered, Setback, and Cross Opening models are worse than that of the Square model. In particular, the second mode acceleration of the Cross Opening model is significantly larger, and this is because the second mode shape is similar to the vertical distribution of shear. For composite models, the 8Helical + Corner Cut and the 4-Tapered + 8Helical models show smaller maimum accelerations than the 4-Tapered model, but when corner cut is combined (Tapered + 8Helical + Corner Cut), the third and fourth maimum accelerations becomes larger.

16 K-234 Y. Tamura et al..5 Ma. Acceleration Ma. Story shear coefficient Ma. Displacement Ma. Story deformation angle Ma. Story shear force Ma. Overturning moment Ma. Torsion moment Ratio to Square Model.5 Composite Models Fig. 3 Comparison of wind-induced responses for 5-year return period design wind speed (Tanaka et al. (23)) 2 3. Ratio to Square Model.5.5 st mode 2nd mode 3rd mode 4th mode Composite Models Fig. 4 Comparison of accelerations for -year return period design wind speed (Tanaka et al. (23)) Wind-load combination effect Fig. 5 shows the trajectory and cross-correlation coefficients of various overturning moments for the Square and 8 o Helical Square models. The trajectory of CMD-CML for the Square model shows a rounded wedge or semi-circular shape, implying no correlation

17 Aerodyanmic and Response Characteristics of Supertall Buildings with Various Configurations K-235 between them. But the wedge shape also means that when CMD is a maimum, the maimum CML may occur. This is also shown in Fig. 5(a) by a red dotted line, which is the crosscorrelation of absolute values of coefficients, CMD - CML. Moderate correlation was observed for CMD and CML, meaning that the correlations of absolute wind force components should be taken into account carefully. For CML and CMT, high correlations were observed for both original and absolute wind force components. No correlation for CMD and CML and moderate correlation for CMD and CMT were observed for the 8 o Helical Square model, showing the opposite trend to the Square model. (a) Square () (b) 8Helical (35) Fig. 5 Trajectory and cross-correlation coefficients of overturning moment coefficients (Kim et al. (23))

18 K-236 Y. Tamura et al. 5 FY M Z FX Col. 4 Col. 2 Col. 3 Col. Peak tensile stress (kn/cm 2 ) Wind direction (Degree) (a) Frame model (b) Peak tensile stress Fig. 6 Frame model and effect of wind directions on peak stress for ALL loadings (=%) (Kim et al. (23)) Local wind forces at each level were calculated using wind pressures, and input to the frame model to eamine the effects of wind directions, loading conditions, and damping ratio on peak normal stresses in columns. A schematic view of the frame model is shown in Fig. 6(a). Building dimensions (B D H) are 5m 5m 4m, and for simplicity, all the beams are assumed to be rigid, and the columns are assumed to be square tubes of the same size for all heights. The column size was determined such that the first natural period becomes H/5 (Tamura, 22), and all connections were assumed to be rigid. The local wind forces at each level were applied at the center of the floor, as shown in Fig. 6(a). The analyses were made in two ways: quasi-static analyses and dynamic response analyses considering the resonant effect for various damping ratios. To eamine the various loading conditions, 7 different loading conditions were considered. In the study, no dead load and no live load were applied. The effects of wind direction on the peak normal stress of a square model are shown in Fig. 6(b) for ALL loading conditions. ALL loading condition means that FX, FY, and MZ were applied to the frame mode simultaneously. Peak tensile stresses generally decrease with increasing wind directions, and those of Col. and Col. 3, which are located at the leading edges, show larger values than those of Col. 2 and Col. 4. The largest value is shown for wind direction =º for Col. and Col. 3, showing nearly kn/cm 2. When wind direction becomes 45º, the peak normal stresses of Col. 2 and Col. 3 show similar values. The peak compressive stresses show similar trends with wind direction, but the largest value is found for Col 2 and Col. 4 for wind direction =º. The effects of seven different loading conditions on peak tensile stresses are shown in Tables 2 and 3 for quasi-static analysis and dynamic analysis, respectively, with damping ratio =% for wind direction =º for the square model. As epected, the results from dynamic response analysis are larger than those of quasi-static analysis, and the contribution of FX is the largest, and that of MZ is the smallest. It seems that the effect of MZ can be ignored, because the peak tensile stresses from ALL loading condition and from FX+FY are almost the

19 Aerodyanmic and Response Characteristics of Supertall Buildings with Various Configurations K-237 same. As the aspect ratio of the frame model is large, the increasing ratios for FY and MZ are much larger than that for FX when the resonant component is considered. For only the FX condition, larger differences in Col. and Col. 2 (or Col. 3 and Col. 4) are caused by the larger aial force. This means that the contribution of aial force is large in the frame model used in the present study. The ratios of ALL / Only FX are.2 for quasi-static analysis and.5 for dynamic analysis, showing small discrepancies. However, the ratios ALL / Only FY are 3.8 for quasi-static analysis and.7 for dynamic analysis. Table 2: Effect of various loading conditions on peak tensile stress for quasi-static (wind direction of =º, kn/cm 2 ) (Kim et al. (23)) Peak tensile ALL ALL / ALL / Only F stress loading X Only F Y Only M Z F X+F Y F X+M Z F Y+M Z Only F X Only F Y Col Col Col Col Table 3: Effect of various loading conditions on peak tensile stress for =% (wind direction of =º, kn/cm 2 ) (Kim et al. (23)) Peak tensile ALL ALL / ALL / Only F Stress loading X Only F Y Only M Z F X+F Y F X+M Z F Y+M Z Only F X Only F Y Col Col Col Col MX (knm, 5 ) - Column MY (knm, 5 ) MX (knm, 5 ) - Column MY (knm, 5 ) MX (knm, 5 ) - Column MY (knm, 5 ) (a) =.3% (b) =% (c) Quasi-static Fig. 7 Effect of damping ratios on phase plane epression for ALL loading (=º) (Kim et al. (23)) Fig. 7 shows the effect of damping ratios on phase plane epression of bending moments MX and MY for the ALL loading condition for wind direction =º. As damping ratio

20 K-238 Y. Tamura et al. increases, the decrease in MX is significant, implying that the effect of FY increases with decreasing damping ratio as shown before. Numerical simulations For the numerical simulation, large eddy simulation (LES) was used, and for the SGS models, the standard Smagorinsky model with Cs=.2 was used. The approaching flow was simulated in the driver domain in the same way as in the wind tunnel, and the numerical calculations were conducted in the simulation domain using the approaching flow as the inflow boundary condition. Four building models, Square, Corner Cut, Setback, and 8 Helical Square, were used in the simulation. Fig. 8 Driver and simulation domain (Tanaka et al. (23)) The approaching flow in the driver domain was simulated by modeling the spires and roughness blocks as shown in Fig. 8, and Fig. 9 shows the vertical profiles of the mean component U/UH and the turbulence intensity I of the simulated approaching flow used as inflow boundary condition. The power spectrum of the fluctuating component UH at building height is shown in Fig. 9. In the numerical simulations, the intervals of the normalized time difference were tuh/b=2. -3, and the results of -minute full scale data corresponding to the normalized time differencing tuh/b=85 are shown. The Reynolds number of the numerical simulation was Re= Fig. 9 Inflow boundary condition (Tanaka et al. (23)) To visualize the conditions of vorte shedding around buildings, the instantaneous isosurfaces of pressure coefficients are shown in Figs. 2 and 2. Fig. 2 shows the isosurface

21 Aerodyanmic and Response Characteristics of Supertall Buildings with Various Configurations K-239 of pressure coefficients of -.7, which demonstrates the 3-dimensional vorte structure. Fig. 2 shows horizontal distributions of instantaneous pressure coefficients at two heights. (a) Square (b) Corner Cut (c) Setback (d) 8 Helical Square Fig. 2 Visualization of instantaneous vorte structures around buildings (Isosurface of pressure coefficient of Cp=.7) (Tanaka et al. (23)) For the Square model, large negative-pressure regions resulting from periodic Karman vorte shedding were formed in the wake, as shown in Fig. 2(a). These regions were observed throughout most of the building height, as shown in Fig. 2(a). Because of this periodic and well-correlated Karman vorte shedding, a large across-wind force was applied to the Square model. For the Corner Cut model, although uniform vorte structures were found in the spanwise direction as for the Square model (Fig. 2(b)), large negative-pressure regions were only found near the leading edges. This is because the circulation flows near the corner cut regions at the leading edges approimate the separated shear layers to the building side surfaces, disturbing the periodic vorte shedding, as shown in Fig. 2(b). For the Setback and 8 o Helical Square models whose building shapes are modified in the spanwise direction, the vorte structures are significantly different from that of the Square model (Fig. 2(c) and (d)). The vortices shed in the wake are quite small, and vorte components at each height are shed at different time intervals (Fig. 2(c) and (d)), resulting in smaller across-wind forces. When considering dimensions of Bw, vertical variations of St and peak power spectral values of local wind forces all together, the randomness or irregularity of vorte shedding is more profound in the 8 o Helical Square model than in the Setback model. For the Corner Cut, Setback and 8 o Helical Square models, as the vorte is formed in a position further from the building s leeward surface, the leeward pressures increase (absolute values decrease), resulting in a decrease in along-wind force. Thus, the mitigations of vorte shedding are effective for suppression of not only across-wind force but also along-wind force, showing high correlation between them (Tanaka et al. (22)). (a) Square

22 K-24 Y. Tamura et al. (b) Corner Cut (c) Setback (d) 8 Helical Square Fig. 2 Horizontal distributions of instantaneous pressure coefficient (Tanaka et al. (23)) Figs. 22 and 23 show the mean vertical flow conditions W/UH near the building surface and around the building surface, respectively. As shown in Fig. 22(a), the mean vertical flows at the side surface are almost zero ecept at the building top for the Square model. For the 8 Helical model, however, the mean vertical flows near z/h=.,.5,. are large, and there are flows along the building surfaces in the direction of the arrow as shown in Fig. 22(b). These flows along the building surfaces for the 8 Helical Square model occurred possibly because the positive and negative pressures are mied on the same surface. The flow conditions around the buildings shown in Fig. 23 are also affected by these vertical flows, and the complicated flow conditions near and around the buildings including vertical flows make vorte shedding random or irregular, also resulting in a further position of vorte formation from the building s leeward surface.

23 Aerodyanmic and Response Characteristics of Supertall Buildings with Various Configurations K-24 (a) Square (b) 8 Helcial Square Fig. 22 Distribution of mean vertical velocity near building surface (Tanaka et al. (23)) (a) Square (b) 8 Helcial Square Fig. 23 Distribution of mean vertical velocity around building (Tanaka et al. (23)) Concluding remarks For the super-tall building models with various building shapes and the same height and volume, the aerodynamic force measurements, wind pressure measurements and LES (Large-Eddy Simulation) were conducted. Comparison and discussion of the aerodynamic and response characteristics of super-tall buildings led to the following conclusions.. For the maimum mean overturning moment coefficients, 4-Tapered and Setback models show better aerodynamic behaviors in the along-wind direction, and Corner modification models, Helical models, and Cross Opening models with h/h=/24 show better aerodynamic behaviors in the across-wind direction. 2. For the maimum fluctuating overturning coefficients, the Corner Modification, 4-Tapered and Setback models show better aerodynamic behaviors in both along-wind and across-

24 K-242 Y. Tamura et al. wind directions. The Cross Opening model with h/h=/24 and the Helical models also show better aerodynamic behaviors in the across-wind direction. 3. The aerodynamic characteristics of the composite models with multiple modifications are mostly superior to those of the models with single modification. 4. The effect of various building configurations and helical angle on peak pressures were eamined, showing that peak pressures greatly depend on building cross-section and helical angle. 5. Evaluations of aerodynamic and response characteristics depending on building shapes are indispensable in super-tall building projects, prior to planning the vibration control systems for super-tall buildings. 6. For the Square model, peak normal stresses in columns show the largest values when wind direction =º, and decrease with increasing wind directions. The difference between the ratios of ALL / Only FX for quasi-static analysis and dynamic analysis is small. And it was found that as the damping ratio decreases, the effect of FY increase significantly. 7. From the numerical simulations, for the Square model, all the vorte components are shed at almost the same time throughout the height, greatly eciting the models in the acrosswind direction. Unlike the Square model, those of the Setback and the 8 o Helical Square models vary greatly with height, resulting in corresponding across-wind force decreases. 8. The vertical flows on the 8 o Helical Square model are more significant than those on the Square model, encouraging more 3-dimensionalities. The vertical flows are assumed to make the vorte shedding random, forming a vorte further from the building surface in the wake. References Architectural Institution of Japan (24), Recommendations for loads on buildings 24. Amano, T. (995), The effect of corner-cutting of three dimensional square cylinders on vorte-induced oscillation and galloping in uniform flow, Journal of Structural and Construction Engineering, AIJ, No.478, pp (in Japanese). Bandi, E.K., Tamura, Y., Yoshida, A., Kim, Y.C., Yang, Q. (22), Local and total wind force characteristics of triangular-section tall buildings, Proceedings of the 22nd National Symposium on Wind Engineering, pp Bandi, E.K., Tanaka, H., Kim, Y.C., Ohtake, K., Yoshida, A., Tamura, Y. (23), Peak pressures acting on tall buildings with various configurations, International Journal of High-Rise Buildings (Accepted manuscript). Cooper, K.R., Nakayama, M., Sasaki, Y., Fediw, A.A., Resende-Ide, S., Zan, S.J. (997), Unsteady aerodynamic force measurements on a super-tall building with a tapered cross section, Journal of Wind Engineering and Industrial Aerodynamics, vol.72, pp Dutton, R., Isyumou, N. (99), Reduction of tall building motion by aerodynamic treatments, Journal of Wind Engineering and Industrial Aerodynamics, vol.36, pp Hayashida, H., Iwasa, Y. (99), Aerodynamic shape effects on tall building for vorte induced vibration, Journal of Wind Engineering and Industrial Aerodynamics, vol.33(-2), pp Hayashida, H., Mataki, Y., Iwasa, Y. (992), Aerodynamic damping effects of tall building for a vorte induced vibration, Journal of Wind Engineering and Industrial Aerodynamics, vol.43(3), pp Kawai, H. (998), Effect of corner modifications on aeroelastic instabilities of tall buildings, Journal of Wind Engineering and Industrial Aerodynamics, vol , pp Kim, Y.C., Kanda, J. (2), Characteristics of aerodynamic forces and pressures on square plan buildings with height variations, Journal of Wind Engineering and Industrial Aerodynamics, vol.98, pp