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Experimental investigation of aerodynamic forces and wind pressures acting on tall buildings with various unconventional configurations
J. Wind Eng. Ind. Aerodyn. 107–108 (2012) 179–191
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Journal of Wind Engineering and Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia
Experimental investigation of aerodynamic forces and wind pressures acting on tall buildings with various unconventional configurations Hideyuki Tanaka a,n, Yukio Tamura b, Kazuo Ohtake a, Masayoshi Nakai c, Yong Chul Kim b a
Takenaka Corporation Research & Development Institute 1-5-1, Ohtsuka Inzai, Chiba 270-1395, Japan Department of Architecture, Tokyo Polytechnic University, 1583, Iiyama Atsugi, Kanagawa, Japan c Takenaka Corporation, 1-1-1, Shinsuna, Koto-ku, Tokyo, Japan b
a r t i c l e i n f o
abstract
Article history: Received 2 August 2011 Received in revised form 13 April 2012 Accepted 14 April 2012 Available online 16 May 2012
Tall buildings have been traditionally designed to be symmetric rectangular, triangular or circular in plan, in order to avoid excessive 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 expressions. Another important aspect is that rather complicated sectional shapes are basically good with regard to aerodynamic properties for crosswind excitations, which are a key issue in tall-building wind-resistant design. A series of wind tunnel experiments have been carried out to determine aerodynamic forces and wind pressures acting on square-plan tall building models with various configurations: corner cut, setbacks, helical and so on. The results of these experiments have led to comprehensive understanding of the aerodynamic characteristics of tall buildings with various configurations. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Tall building Corner modification Setback Tapered building Helical-shaped building Building with openings
1. Introduction The 828 m-high Burj Khalifa was completed in January 2010, and the world record for skyscraper height was then updated from the previous Taipei 101, which was 508 m high. According to a report (Tamura et al., 2011) that examined world skyscrapers under construction as of January 2010, 56% of those within the top 100 highest buildings had been completed since 2000, and currently tall buildings higher than 600 m are still under construction. Attention should be paid to this trend of tall building construction, i.e., Manhattanization, and increased construction of ingenious tall buildings acting as landmarks or city symbols should also be highlighted. Tall buildings have been traditionally designed to be symmetric rectangular, triangular or circular in plan, in order to avoid excessive seismic-induced torsional vibrations due to eccentricity. However, recent tall building design has been released from the spell of compulsory symmetric shape design, and free-style design is increasing, reflecting structural designers’ challenging demands for new and unconventional expressions. Development of analytical techniques and of vibration control techniques has greatly contributed to this trend. The fact that rather complicated sectional shapes can reduce wind
n
Corresponding author. Tel.: þ81 476 47 4597; fax: þ 81 476 47 7333. E-mail address: [email protected] (H. Tanaka).
0167-6105/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jweia.2012.04.014
loads, which are an important issue in tall-building wind-resistant design, has also contributed to the current trend. The effectiveness of aerodynamic modification to reduce wind loads has been widely reported, and aerodynamic modifications thought to be effective include those to sectional shape (horizontally) such as polygon or Y-type (Hayashida and Iwasa, 1990; Hayashida et al., 1992) and corners (Shiraishi et al., 1986; Kwok et al., 1988; Miyashita et al., 1993; Amano, 1995; Kawai, 1998), building shape (vertically) such as taper (Cooper et al., 1997; Kim and You, 2002; Kim et al., 2008; Kim and Kanda, 2010a; 2010b) and setback (Kim and Kanda, 2010a,b), as well as introduction of openings (Dutton and Isyumou, 1990, Miyashita et al., 1993). However, most of the above papers have focused on the effect of one aerodynamic modification that changes systematically. For example, for corner-modification buildings, various modification shapes and various modification lengths were highlighted, and for tapered buildings, the effects of different taper ratios were the main concern. Although there have been some reports on cross comparisons of different aerodynamic modifications using a limited number of aerodynamic modifications, none have comprehensively investigated aerodynamic characteristics of various types of tall buildings with different configurations. Therefore, a series of wind tunnel experiments were conducted to investigate the aerodynamic characteristics and to evaluate the most effective structural shape in wind-resistant design for tall buildings with various aerodynamic modifications.
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Fluctuating aerodynamic forces on tall building models with the same volume were firstly measured, and wind pressure measurements were conducted on building models, showing excellent aerodynamic characteristics. This paper presents comprehensive and detailed discussions on the aerodynamic characteristics of the shapes tested.
2. Outline of wind tunnel experimental models 2.1. Configuration of tall building models The tall building models used for the experiments are shown in Table 1(a)–(g). The full-scale height and the total volume of each building model are commonly set at H¼400 m (80 stories) and about 1,000,000 m3. The width B of the Square Model shown in Table 1(a) is 50 m and the aspect ratio H/B is 8. The geometric scale of the wind tunnel models is set at 1/1000. The tall building models examined in this study are classified in 7 categories as follows. (a) Basic models The Square, Circular, Rectangular, and Elliptic plan models shown in Table 1(a) are classified as Basic Models. The side ratio of the Rectangular and Elliptic Models is 1:2. 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 which is similar to full-scale, 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 experiment is Re ¼2.9 104. (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 examination of corner modification focuses on a Corner Cut Model and a Corner Chamfered Model as shown in Table 1(b). Referring to past researches on aerodynamic characteristics of structures and buildings with corner chamfered and corner cut models (Shiraishi et al. 1986; Amano, 1995; Kawai, 1998), the modification length is set at 0.1B, 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 0.25H and 0.75H are shifted by 0.5B to the left and right side, respectively, from the middle floor, and the walls have smoothly curved surfaces as shown in Table 1(c). (d) Tapered models The tapered models include the following five types: a 2-Tapered Model which has only two tapered surfaces, a 4-Tapered Model which has four tapered surfaces, an Inversely 4-Tapered Model which has the inverse building shape of the 4-Tapered Model, and a Bulged Model whose sectional area at mid-height is expanded as shown in Table 1(d). When
Table 1 Configuration of test models.
(e) Helical models
(a) Basic models Square
Rectangular L
H=400
α=0o α
y
B=50
z
Circular
180o Helical Square
270o Helical Square
360o Helical Square
180o Helical Rectangular
y D x
x
y
z
Corner Cut
y
x
(b) Corner modification models Corner Chamfered
90o Helical Square
Elliptic
z
x
y
z
x
y
z
x
z
y
(c) Tilted models Tilted
x
y
z
x
y
z
x
y
z
x
(f) Opening models (f-1) Cross Opening
Winding
h/H=2/24
h/H=5/24
(f-2) Oblique Opening h/H=11/24
h/H=2/24
h/H=5/24
H=400
h
y
z
x
y
z
100 50
x
y
z
x
y 25 50 25
z
x
y
(d) Tapered models 2-Tapered
y
z
4-Tapered
x
y
z
x
y
z
x
x
y
z
x
(f)
Inversely 4-Tapered
Setback
z
y
z
y
z
x y
x
y
z
x
y
z
x
(g) Comp os ite models 360o
h/H=11/24
x
z
4-Tapered Helical Setback & 360o Helical & Corner Cut & Corner Cut & Corner Cut
(f-2)
Bulged
y
z
x
y
z
x
y
z
x
y
z
x
Setback & 45o Rotate
y
z
x
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the taper ratio is between 5% and 10%, a model with a larger tapering ratio shows better aerodynamic behavior (Kim and Kanda, 2010a,b). Thus, for the 4-Tapered Model, the taper ratio was set at 10% and the area ratio of the roof floor to the base floor was set at 1/6. 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 1/6 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 1/3. (e) Helical models The sectional shapes of the helical models are square and rectangular, and the twist angle y between the roof floor and the base floor is set at 901, 1801, 2701 and 3601, as shown in Table 1(e). The sectional shapes together with the twist angle are used as a prefix of the model name. For example, the 1801 Helical Square Model means the helical model whose sectional shape is square with a twist angle of 1801. (f) Opening models In the category of opening models, three cross opening models and three oblique opening models, whose openings are provided at the top-center and top-corner of the walls, respectively, are classified as shown in Table 1(f). Three different opening heights h¼ 2H/24, 5H/24, and 11H/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 is almost the same, their widths are fixed. However, for the three Cross Opening Models, the opening volume is included in the building volume, because of the compatibility of aspect ratio with the other models. (g) Composite models The composite models have the combined configurations of the primary configurations shown in Table 1(a)–(f), and the aerodynamic characteristics of the following four composite models shown in Table 1(g) are investigated: 3601 Helical and Corner Cut Model; 4-Tapered and 3601 Helical and Corner Cut Model; Setback and Corner Cut Model; and 451 Rotating Setback Model, where the rotating angle of each setback layer is 451.
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Fig. 1. Flow conditions of wind tunnel experiment.
2.2. Experimental conditions 2.2.1. Aerodynamic force measurements Wind tunnel experiments were performed in a closed-circuittype boundary-layer wind tunnel whose working section is 1.8 m high by 2.0 m wide. Fig. 1 shows the condition of the approaching turbulent boundary layer flow with a power-law index of 0.27, representing an urban area. The wind velocity and turbulence intensity at the top of the model are about UH ¼7.0 m s 1 and IUH ¼9.2%, respectively. The turbulence scale near the model top is about 0.360 m, and that of Architectural Institution of Japan (2004) is 365 m. Therefore, when considering the length scale of 1/1000, 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 a is changed from 01, which is normal to a wall surface, to 451 or 1801 every 51 depending upon the building configuration. The measured wind forces and aerodynamic moments are normalized by qHBH2 to get wind force coefficients and moment coefficients. Here, qH is the velocity pressure at the model height H, and B is commonly set at the width of the Square Model. Therefore, the force and moment coefficients of the models can be directly compared. Fig. 2 shows
Fig. 2. Coordinate system.
the definitions of wind forces, moments, and the coordinate system employed in this study. The Reynolds number Re based on the mean wind velocity at the roof height UH and the width of the Square Model B is Re ¼2.6 104.
2.2.2. Wind pressure measurements Wind pressure measurements were conducted on 8 models as shown in Fig. 3. 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 measurement were to examine the characteristics of local wind forces and aerodynamic phenomena in detail. The coordinate system and approaching flow for the wind pressure measurements are the same as for the aerodynamic force measurement (see Figs. 1 and 2), except that the wind velocity at model height was 11.8 m s 1. Also, the wind direction
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was changed from 01 to 3551 at 51 intervals as for the aerodynamic force measurements. The fluctuating wind pressures of each pressure tap were measured and recorded simultaneously using a vinyl tube 80 cm long through a multi-channel pressure transducer. The sampling frequency was 1 kHz with a low-pass filter of 500 Hz. 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 20 measurement points on one level on four surfaces, as shown in Fig. 3, and the measurement points were instrumented at 10 levels (12 levels only for Setback Model), giving about 200 measurement points. The wind pressure coefficients Cp were obtained by normalizing the fluctuating pressures p by the velocity pressure qH at model height. The local wind force coefficients, CfD for along-wind, CfL for across-wind and CmT for
Fig. 3. Test models for wind pressure measurement. (a) Square, (b) cross opening, (c) corner chamfered, (d) corner cut (h/H¼5/24), (e) 4-Tapered, (f) setback, (g) 901 helical and (h) 1801 helical.
torsional moment, were derived by integrating the wind pressure coefficients Cp using the building width of the Square Model B (B2 for torsional moment) regardless of building shape.
3. Results of wind force measurements 3.1. Mean overturning moment coefficients Fig. 4 shows the variation of the mean along-wind overturning moment (o.t.m.) coefficient C MD and the mean across-wind o.t.m. coefficient C ML with wind direction a for eight typical building models. Fig. 5 shows the maximum values of the mean alongwind and across-wind o.t.m. coefficients, 9C MD 9max and 9C ML 9max considering all wind directions. The mean along-wind o.t.m. coefficient C MD and across-wind o.t.m. coefficient C ML of the Square Model show maximum values of 0.60 and 0.20 at wind direction a ¼ 451 and 151, respectively. The maximum along-wind o.t.m. coefficient 9C MD 9max and acrosswind o.t.m. coefficient 9C ML 9max of the Circular Model is smallest among all experimental models, and those of the Rectangular Model and Elliptic Model are larger than those of the Square Model because of their larger widths. The maximum mean along-wind o.t.m. coefficients 9C MD 9max 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 maximum mean along-wind o.t.m. coefficient 9C MD 9max does not decrease as much as those of the 4-Tapered Model and Setback Model. This may be because of the reduced effectiveness of the openings as the wind direction approaches 451. The maximum mean across-wind o.t.m. coefficients 9C ML 9max of the Corner Cut Model and Corner Chamfered Model are small. The maximum mean across-wind o.t.m. coefficients of the Helical Square Model and the Cross Opening h/H¼11/24 Model, whose opening size is the largest, are also small. The small coefficients of those models are related to vortex formation and shedding. Inversely, the models whose along- and across-wind o.t.m. coefficients are larger than those of the Square Model are the 2-Tapered Model, the 1801 Helical Rectangular Model and the Tilted Model with larger projected area for a certain wind direction, and the Inversely 4-Tapered Model with larger projected area at its upper height. The maximum mean o.t.m. coefficients 9C MD 9max and 9C ML 9max of a Helical Square Model with a larger twist angle tends to show smaller values. And, as can be seen in Fig. 4, the variations of
Fig. 4. Variation of mean overturning moment coefficients on wind direction for some test models. (a) Along-wind direction and (b) across-wind direction.
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Fig. 5. Comparison of maximum mean overturning moment coefficients.
Fig. 6. Variation of fluctuating overturning moment coefficients on wind direction for some test models. (a) Along-wind direction and (b) across-wind direction.
mean o.t.m. coefficients C MD and C ML of the 901 Helical Square and 1801 Helical Square Models with wind direction are very small. In particular, the 1801 Helical Square Model shows values almost independent of wind direction. For the opening models, as the opening size h/H becomes larger, the maximum mean o.t.m. coefficient 9C ML 9max decreases. However, the decreasing tendency is not significant for the maximum mean along-wind coefficient 9C MD 9max for both the Cross Opening Models 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 3601 Helical and Corner cut are almost the same as those of the 3601 Helical Model, implying that the aerodynamic characteristics have not been further improved by corner modification. 3.2. Fluctuating overturning moment coefficients Fig. 6 shows the variation of the fluctuating o.t.m. coefficients 0 0 CMD and CML with wind direction a for the test models which show specific aerodynamic force characteristics, where the fluctuating 0 0 o.t.m. coefficients CMD and CML are defined as the standard deviation of the o.t.m. coefficients. Fig. 7 shows the maximum along-wind and across-wind fluctuating o.t.m. coefficients, 0 0 CMD max and CML max, considering all wind directions.
The maximum fluctuating o.t.m. coefficients of the basic 0 0 Square Model are CMD max ¼0.12 and CML max ¼ 0.14 for wind direction of a ¼ 01 as shown in Fig. 6. As shown in Fig. 7, the maximum fluctuating along-wind o.t.m. 0 coefficients CMD max of the Corner Chamfered, Corner Cut, 4-Tapered and Setback Models are smaller. Like the mean o.t.m. coefficients, the smaller projected area at upper height is related to the smaller fluctuating o.t.m. coefficients of the 4-Tapered Model and the Setback Model, and for the Corner Chamfered Model and the Corner Cut Model, the elongated separated shear layer causes smaller coefficients. (Tamura and Miyagi, 1999). The 0 maximum fluctuating across-wind o.t.m. coefficients CML max of the 4-Tapered, Setback, Helical Square, and Cross Opening 11/24 Models show relatively small values. Detailed aerodynamic phenomenon will be discussed later. These trends are the same as those of the maximum mean o.t.m. coefficients. And, the effect of twist angle y 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 maximum mean o.t.m. coefficients. 3.3. Relationship between overturning moment coefficients The relationship between maximum mean o.t.m. coefficients and maximum fluctuating o.t.m. coefficients for all building
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Fig. 7. Comparison of maximum fluctuating overturning moment coefficients.
Fig. 8. Relationship of o.t.m. coefficients. (a) Relationship between maximum mean and maximum fluctuating o.t.m. coefficients (b-1) maximum mean o.t.m. coefficients (b-2) maximum fluctuating o.t.m. coefficients and (b) Relationship between along-wind direction and across-wind direction.
models are shown in Fig. 8(a) for the along-wind direction and for the across-wind direction. Fig. 8(b) shows the relationship between the maximum mean o.t.m. coefficients in the along-wind direction and those in the across-wind direction (Fig. 8(b-1)), and the
relationship between the maximum fluctuating o.t.m. coefficients in both directions (Fig. 8(b-2)). As described in Section 3.2, the maximum mean and fluctuating o.t.m. coefficients show a similar tendency, and high correlations between them are observed as
H. Tanaka et al. / J. Wind Eng. Ind. Aerodyn. 107–108 (2012) 179–191
shown in Fig. 8(a). And, it is interesting to note that the high correlations between mean/fluctuating o.t.m. coefficients in the along-wind direction and in the across-wind direction are observed. 3.4. Power spectral densities of across-wind overturning moment coefficients As the across-wind power spectra generally exceed the alongwind power spectra, the power spectra of across-wind overturning moment coefficients fSCML whose peak is the largest among all wind directions are shown in Fig. 9, and are categorized by model types. The power spectrum of the Square Model shown in Fig. 9(a)–(g) has a sharp peak near the Strouhal component of 0.1. Although the peak of the Rectangular Model shown in Fig. 9(a) is not as sharp, the values of power spectrum in the frequency range higher than 0.01 are relatively large. The peaks of the Corner modification models (Fig. 9(b)), the 4-Tapered and Setback Models (Fig. 9(d)), the Helical Models (Fig. 9(e)), and the Cross Opening Model h/H¼ 11/24, which show smaller overturning moment coefficients, decrease significantly
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compared with that of the Square Model, showing that the periodic vortex shedding is effectively suppressed. On the other hand, the peaks of the Tilted and Inversed 4-Tapered Models are larger than that of the Square Model. For the power spectra of the Helical Square Models shown in Fig. 9(e), even though the twist angle y is large, relatively sharp peaks can be observed, but their values are small. And there are no significant differences in peaks and shapes of power spectra when the twist angle is more than 1801. The peaks of the Cross Opening and Oblique Opening models shown in Fig. 9(f-1) and (f-2) decrease with opening size h/H. For the Cross Opening h/H¼ 11/24 Model, the peak of the Strouhal component becomes flat, but another peak is observed at the reduced frequency fB/UH of 0.2. For the Composite Models (Fig. 9(g)), the peaks of the Strouhal component for the 4-Tapered and 3601 Helical and Corner Cut, Setback and Corner Cut, and 451 Rotating Setback Models are hardly noticeable. In the calculation of wind-induced responses, the spectral values are important, and those corresponding to a 500-year return period wind speed and a 1-year return period wind speed
Fig. 9. Power spectral densities of across-wind overturning moment coefficients. (a) Basic models, (b) corner modification models, (c) tilted models, (d) tapered models, (e) helical models, (f-1) cross opening models, (f-2) oblique opening models and (g) composite models.
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pffiffiffiffiffiffiffiffiffiffi were calculated and their square root values SCML are shown in Fig. 10(a) and (b). Here, the square root values for Vp,1, pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi frequency SCML ,max (Vp,1), are the values on the reduced p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi fB/UH ¼0.17, and the square root values for Vp,500, SCML ,max pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi SCML , peak because the (Vp,500) correspond to the peak values maximum values in power spectral density were selected in the ranges where the reduced frequency is larger than 0.07 (fB/ UH Z0.07). The 1st natural frequency is assumed to be f1 ¼ 0.1 Hz, and the design wind speeds for corresponding return periods are assumed to be Vp,500 ¼71 m s 1 and Vp,1 ¼30 m s 1 in Tokyo, respectively. And, Fig. 10(c) shows the bandwidth Bw of power
spectral densities shown in Fig. 9. The bandwidth Bw was obtained by approximating the power spectra fSCML to the Eq. (1) through the least-square method (Vickery and Clark, 1972). f SCML
s2
" 2 # 1f =f peak ¼ k pffiffiffiffi exp Bw pf peak Bw f
ð1Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi The values of SCML,peak for the Corner Cut, Tapered, Setback, Helical Square (y ¼1801 3601), and Cross Opening (h/H¼11/24) Models, which show small mean and fluctuating o.t.m. coefficients, are smaller than that of the Square Model, meaning that those
Fig. 10. Comparison of across-wind power spectral densities. (a) Maximum peak values of power spectral densities (Design wind speed corresponding to 500-year return period), (b) design wind speed corresponding to 1-year return period and (c) bandwidths.
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pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi models have the advantage in safe design. The values of SCML,peak for the 4-Tapered and 3601 Helical and Corner Cut and 451 Rotating Setback Models, which are Composite models, are much smaller than that of the Square Model, and it can be said that the Combination modelpisffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a very ffieffective building shape for safe design. The values of, SCML,max (Vp,1), for the Tilted Models, Tapered models and Oblique Opening Modelsp are generally large, and even ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi for the Tapered and Setback Models, SCML,max (Vp,1), is larger than that of the Square Model. However, the values of the Corner Cut, Helical Square, and Cross Opening h/H¼11/24 Models are smaller than that of the Square Model, showing that these building shapes are superior to the square shape for habitability design. Although some composite models contain Tapered and Setback, the values ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi of SCML,max (Vp,1) become smaller than that of the Square Model. The bandwidths Bw shown in Fig. 10(c) show an inverse trend to the spectral peaks shown in Fig. 10(a), and when the bandwidth is small, the spectral peak becomes very sharp as shown for the Square Model, implying that strong vortices are shed regularly. But when the bandwidth is large, as the spectral peak becomes flat and the spectral shape becomes wide, it can be assumed that the vortex shedding becomes random and irregular. This randomness contributes largely to the smaller wind forces discussed in Sections 3.1 and 3.2, and this is more profound for the composite models whose bandwidths are very large.
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3.5. Effect of twist Angle y for helical square models As shown above, because the aerodynamic characteristics of Helical Models are better than those of other models with single modification, detailed comparisons are summarized in Fig. 11. From Fig. 11(a)–(c), the o.t.m. coefficients and the spectral peak values show the tendency to decrease with increasing twist angle y, and the decrease in the fluctuating component of across-wind is significant, as shown in Fig. 11(b) and (c). But note that there are small differences in o.t.m. coefficients, spectral peaks and bandwidths when the twist angle is larger than 180o. From this, it can be assumed that the effects of twist angle y on regular vortex shedding appear mostly when the twist angle is less than 901, and the relative effects of twist angle y become smaller at larger twist angle i.e.
4. Results of wind pressure measurements The representative wind direction is assumed to be 01 for the models shown in Fig. 3(a)–(f), and those of the 901 Helical and 1801 Helical Models are 601 and 351, respectively, which are normal to one surface at z/H¼0.7. Basically, the wind pressure measurements refer to the representative wind direction unless stated otherwise.
Fig. 11. Effect of twist angle y for the Helical Square Models. (a) Maximum mean o.t.m. coefficients, (b) maximum fluctuating o.t.m. coefficients, (c) peak values of power spectral densities and (d) bandwidths of power spectral densities.
Fig. 12. Vertical profile of mean local wind force coefficients. (a) Along-wind, (b) across-wind and (c) torsion.
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4.1. Distribution of mean local wind force coefficients The distribution of mean local wind force coefficients is shown in Fig. 12. The mean local wind force coefficients of across-wind (Fig. 12(b)) and torsional moments (Fig. 12(c)) are shown for the wind directions at which the mean 9C FD 9 and 9C MT 9 become maximum. The mean local wind force coefficients for the along-wind direction C f D , across-wind direction C f L and torsional moment C mT of the Square Model are the largest throughout the height. The C f D , 9C f L 9 and C mT of the Corner Chamfered and Corner Cut
Models are smaller than that of the Square Model throughout the height. Especially, C mT values are less than the half of the Square Model (Fig. 12(c)). From this, the torsional moment coefficients are assumed to decrease as well as the overturning moment coefficients in the along-wind direction and the across-wind direction, as shown in Section 3.1. For the 4-Tapered and Setback Models whose projected areas become small with height, the torsional moment coefficients decrease as for the mean local wind force coefficients in the along-wind direction shown in Fig. 12(a). And there are large differences in C f D values for the Setback Model and the 4-Tapered Model near z/H¼0.75, 0.50 and 0.25. For
Fig. 13. Vertical profile of fluctuating local wind force coefficients. (a) Along-wind, (b) across-wind and (c) torsion.
Fig. 14. Power spectral densities of across-wind local wind force coefficients. (a) Square (a ¼01), (b) cross opening (a ¼01), (c) corner chamfered (a ¼ 01), (d) corner cut (a ¼ 01), (e) 4-Tapered (a ¼01), (f) setback (a ¼ 01), (g) 901 helical (a ¼601) and (h) 1801 helical (a ¼351).
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the 901 Helical and the 1801 Helical Models, C f L and C mT become positive or negative depending on z/H, reflecting the building shapes. This results in smaller aerodynamic characteristics as shown in Section 3.1. The C f D , C f L and C mT of the Cross Opening Model are smaller than that of the Square Model near the opening, which is affected by the opening, showing little difference at other heights to the Square Model. 4.2. Distribution of fluctuating local wind force coefficients The vertical distribution of the fluctuating local wind force coefficients is shown in Fig. 13. For the along-wind and acrosswind directions, the variation trends are similar to those of the mean local wind force coefficients shown in 4.1 (Fig. 13(a) and (b)). Similar observations can also be made for torsional moment, i.e., the CmT0 values of the Corner Chamfered and Corner Cut Models are smaller than that of the Square Model, the CmT0 values of the 4-Tapered and Setback Models at z/HZ0.5 are smaller than that of the Square Model, and the CmT0 values of the 901 Helical and 1801 Helical Models become positive and negative depending on z/H shown in Fig. 13(c). However, the CmT0 values near the opening of the Cross Opening Model is larger than that of the Square Model, meaning that the opening has an inverse impact on fluctuating local wind force. 4.3. 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/H¼0.5 are shown in Fig. 14. The Strouhal number St corresponding to the vortex shedding frequency, and the bandwidth Bw were obtained and the vertical profiles are shown in Figs. 15 and 16. The power spectra in Fig. 14 were plotted against the reduced frequency, which was obtained by using the width of the Square Model B (constant) regardless of building shape. The bandwidths Bw were obtained by approximating the power spectra fSCfL to Eq. (1). Sharp peaks near z/H¼0.5 were observed for the Square Model (Fig. 14(a)), but they become relatively flat near the model top because of the three-dimensional effect of flow. This again implies that regular vortex shedding exists near z/H¼0.5 and the
Fig. 16. Vertical profile of bandwidth of across-wind local wind force power spectra.
regularity collapses near the model top, and the bandwidth shown in Fig. 16 near the z/H¼0.5 is smaller than that of the model top. The power spectral densities of other models in Fig. 14(b)–(h) show similar results. The Strouhal numbers St of the Square Model shown in Fig. 15 vary little with height, showing almost constant values throughout the height. This means that all the vortex components are shed almost the same time throughout the height, greatly exciting the models in across-wind direction. Contrary to the Square Model, those of the 4-Tapered Model, Setback Model and 1801 Helical Model vary greatly with height. For those models, because the shedding frequencies of each height are different, the resulting across-wind force decreases correspondingly. Similar discussion can be made for the bandwidth shown in Fig. 16, i.e., regular and strong vortices with narrow-band are shed throughout the height for the Square Model, but for the other models, vortices with wide band are shed randomly, effectively suppressing the across-wind force. The bandwidth of 1801 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 for the 1801 Helical Model the weak vortices with wide-band are shed irregularly throughout the height, and this results in the better aerodynamic behaviors discussed above. 4.4. Distribution of mean wind pressure coefficient
Fig. 15. Vertical profile of Strouhal number.
The mean wind pressure coefficients (Fig. 17) based on the local wind force characteristics will be discussed in the following sections for the Square, Corner Cut, Setback and 1801 Helical Models. Although the building surface of the 1801 Helical Model changes arbitrarily among windward surface, side surface, and leeward surface depending on the height, the mean wind pressure coefficients show their maximums at z/H¼7/8, and decrease near the peripheral parts, showing similar distributions to the other test models. For the Corner Cut Model, large negative wind pressures occur at the leading edge of the side surface, and their distribution varies greatly from the leading edge and trailing edge, showing a different distribution from the Square Model. The absolute values of mean wind pressures at the leeward surface are smaller than those of the Square Model, resulting smaller local
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(2)
(3)
(4)
(5)
(6)
Fig. 17. Distribution of mean wind pressure coefficients. (a) Square, (b) corner cut, (c) setback and (d) 1801 helical.
wind forces than the Square Model as shown in Fig. 12(a). The distributions of side surface and leeward surface of the Setback Model are similar to those of the Square Model. The distribution of the side surface of the 1801 Helical Model is very complex, and the absolute values for the leeward surface are smaller than those for the other models. The absolute values for the leeward surface of the 1801 Helical Model are smaller than those for the other models, and the distribution for the side surface is very complex, resulting in different characteristic from the other models, as shown in Fig. 12(b) and (c).
5. Conclusion
(7)
(8)
better aerodynamic behaviors in the along-wind direction, and Corner modification models, Helical models, and Cross Opening models whose opening sizes are h/H ¼11/24 show better aerodynamic behaviors in the across-wind direction. For the maximum fluctuating overturning moment coefficients, Corner modification models, 4-Tapered and Setback Models show better aerodynamic behaviors in both alongwind and across-wind directions. Cross Opening Model with h/H ¼11/24 and the Helical models also show better aerodynamic behaviors in the across-wind direction. For all building models, the correlations between maximum mean coefficients and maximum fluctuating coefficients are high for both along-wind and across-wind directions. And, the high correlations between maximum mean (and fluctuating) overturning moment. coefficients in along-wind direction and those in the across-wind direction are again observed. The power spectral densities of the models mentioned (2) decrease significantly compared with the Square Model, showing good performance in safety design for the design wind speed corresponding to a 500-year return period. However, 4-Tapered and Setback Models have disadvantages in the evaluation of habitability for the design wind speed corresponding to a 1-year wind speed. Conversely, Corner Chamfer, Corner Cut, Helical, and Cross Opening (h/H¼11/24) Models show superior aerodynamic behaviors in both safety and habitability design to the Square Model. 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 overturning moment coefficients of 3601 Helical and Corner cut are almost the same as those of the 3601 Helical Model, implying that the aerodynamic characteristics have not been improved by corner modification and the advantages of corner modification seem to be eliminated somewhat by the helical shape. The building configurations mentioned in (1) and (2) show better aerodynamic behavior in both along-wind and acrosswind directions, and the local wind force coefficients of torsional moment are also small. However, the opening of the Cross Opening Model has an adverse influence on the fluctuating local wind forces. For the Square Model, all the vortex components are shed at almost the same time throughout the height, greatly exciting the models in across-wind direction. Contrary to the Square Model, those of the 4-Tapered Model, the Setback Model and the 1801 Helical Model vary greatly with height. For those models, because the shedding frequencies of each height are different, the resulting across-wind force decreases correspondingly. For 1801 Helical Model, weak vortices with wide-band are shed irregularly throughout the height, and this results in the better aerodynamic behaviors as discussed above.
Acknowledgment N. Koshika of Kajima Corp., K. Yamawaki of NIKKEN SEKKEI Ltd., Y. Hitomi of NIHON SEKKEI Ltd., Y. Hayano of MAD Tokyo and S. Igarashi of Takenaka Corp. provided us with helpful advice for setting experimental cases. This study comprised part of a project funded by the Ministry of Land, Infrastructure, Transport and Tourism, Japan.
Aerodynamic force measurements and wind pressure measurements were conducted for tall building models with various building shapes and the same height and volume. Comparison and discussion of the aerodynamic characteristics of tall buildings led to the following conclusions.
Reference
(1) For the maximum mean overturning moment coefficients, tapered models such as 4-Tapered and Setback Models show
Architectural Institution of Japan, 2004. Recommendations for Loads on Buildings, 2004. Architectural Institution of Japan, Tokyo.
H. Tanaka et al. / J. Wind Eng. Ind. Aerodyn. 107–108 (2012) 179–191
Amano, T., 1995. The Effect of corner-cutting of three dimensional square cylinders on vortex-induced oscillation and galloping in uniform flow. Journal of Structural and Construction Engineering, AIJ 478, 63–69. in Japanese. Cooper, K.R., Nakayama, M., Sasaki, Y., Fediw, A.A., Resende-Ide, S., Zan, S.J., 1997. Unsteady aerodynamic force measurements on a super-tall building with a tapered cross section. Journal of Wind Engineering and Industrial Aerodynamics 72, 199–212. Dutton, R., Isyumou, N., 1990. Reduction of tall building motion by aerodynamic treatments. Journal of Wind Engineering and Industrial Aerodynamics 36, 739–747. Hayashida, H., Iwasa, Y., 1990. Aerodynamic shape effects on tall building for vortex induced vibration. Journal of Wind Engineering and Industrial Aerodynamics 33 (1-2), 237–242. Hayashida, H., Mataki, Y., Iwasa, Y., 1992. Aerodynamic damping effects of tall building for a vortex induced vibration. Journal of Wind Engineering and Industrial Aerodynamics 43 (3), 1973–1983. Kawai, H., 1998. Effect of corner modifications on aeroelastic instabilities of tall buildings. Journal of Wind Engineering and Industrial Aerodynamics 74-76, 719–729. Kim, Y.C., Kanda, J., 2010a. Characteristics of aerodynamic forces and pressures on square plan buildings with height variations. Journal of Wind Engineering and Industrial Aerodynamics 98, 449–465. Kim, Y.C., Kanda, J., 2010b. Effects of taper and set-back on wind force and wind-induced response of tall buildings. Wind and Structures 13 (6), 499–517.
191
Kim, Y.M., You, K.P., 2002. Dynamic responses of a tapered tall building to wind load. Journal of Wind Engineering and Industrial Aerodynamics 90, 1771–1782. Kim, Y.M., You, K.P., Ko, N.H., 2008. Across-wind response of an aeroelastic tapered tall building. Journal of Wind Engineering and Industrial Aerodynamics 96, 1307–1319. Kwok, K.C.S., Wilhelm, P.A., Wilkie, B.G., 1988. Effect of edge configuration on wind-induced response of tall buildings. Engineering Structures 10, 135–140. Miyashita, K., Katagiri, J., Nakamura, O., Ohkuma, T., Tamura, Y., Itoh, M., Mimachi, T., 1993. Wind-induced response of high-rise buildings. Journal of Wind Engineering and Industrial Aerodynamics 50, 319–328. Shiraishi, N., Matsumoto, M., Shirato, H., Ishizaki, H., Osada, M., Matsui, T., 1986, On aerodynamic stability effects for bluff rectangular cylinders by their corners cut. Proceedings of the 19th National Symposium on Wind Engineering, Japan, pp. 193–198 (in Japanese). Tamura, T., Miyagi, T., 1999. The effect of turbulence on aerodynamic forces on a square cylinder with various corner shapes. Journal of Wind Engineering and Industrial Aerodynamics 83, 35–145. Tamura, Y., Nakai, M., Ohtake, K., Koshika, N., Yamawaki, K., Hitomi, Y., 2011. Study on wind resistant design method of super high-rise buildings with various unconventional configurations. The Ministry of Land, Infrastructure, Transport and Tourism, Japan. (accessed 2011/01/17) (in Japanese). Vickery, B.J., Clark, A.W., 1972, Lift or across-wind response of tapered stacks. Proceedings of the American Society of Civil Engineers, 98, ST1, pp. 1–20.
Contents lists available at SciVerse ScienceDirect
Journal of Wind Engineering and Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia
Experimental investigation of aerodynamic forces and wind pressures acting on tall buildings with various unconventional configurations Hideyuki Tanaka a,n, Yukio Tamura b, Kazuo Ohtake a, Masayoshi Nakai c, Yong Chul Kim b a
Takenaka Corporation Research & Development Institute 1-5-1, Ohtsuka Inzai, Chiba 270-1395, Japan Department of Architecture, Tokyo Polytechnic University, 1583, Iiyama Atsugi, Kanagawa, Japan c Takenaka Corporation, 1-1-1, Shinsuna, Koto-ku, Tokyo, Japan b
a r t i c l e i n f o
abstract
Article history: Received 2 August 2011 Received in revised form 13 April 2012 Accepted 14 April 2012 Available online 16 May 2012
Tall buildings have been traditionally designed to be symmetric rectangular, triangular or circular in plan, in order to avoid excessive 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 expressions. Another important aspect is that rather complicated sectional shapes are basically good with regard to aerodynamic properties for crosswind excitations, which are a key issue in tall-building wind-resistant design. A series of wind tunnel experiments have been carried out to determine aerodynamic forces and wind pressures acting on square-plan tall building models with various configurations: corner cut, setbacks, helical and so on. The results of these experiments have led to comprehensive understanding of the aerodynamic characteristics of tall buildings with various configurations. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Tall building Corner modification Setback Tapered building Helical-shaped building Building with openings
1. Introduction The 828 m-high Burj Khalifa was completed in January 2010, and the world record for skyscraper height was then updated from the previous Taipei 101, which was 508 m high. According to a report (Tamura et al., 2011) that examined world skyscrapers under construction as of January 2010, 56% of those within the top 100 highest buildings had been completed since 2000, and currently tall buildings higher than 600 m are still under construction. Attention should be paid to this trend of tall building construction, i.e., Manhattanization, and increased construction of ingenious tall buildings acting as landmarks or city symbols should also be highlighted. Tall buildings have been traditionally designed to be symmetric rectangular, triangular or circular in plan, in order to avoid excessive seismic-induced torsional vibrations due to eccentricity. However, recent tall building design has been released from the spell of compulsory symmetric shape design, and free-style design is increasing, reflecting structural designers’ challenging demands for new and unconventional expressions. Development of analytical techniques and of vibration control techniques has greatly contributed to this trend. The fact that rather complicated sectional shapes can reduce wind
n
Corresponding author. Tel.: þ81 476 47 4597; fax: þ 81 476 47 7333. E-mail address: [email protected] (H. Tanaka).
0167-6105/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jweia.2012.04.014
loads, which are an important issue in tall-building wind-resistant design, has also contributed to the current trend. The effectiveness of aerodynamic modification to reduce wind loads has been widely reported, and aerodynamic modifications thought to be effective include those to sectional shape (horizontally) such as polygon or Y-type (Hayashida and Iwasa, 1990; Hayashida et al., 1992) and corners (Shiraishi et al., 1986; Kwok et al., 1988; Miyashita et al., 1993; Amano, 1995; Kawai, 1998), building shape (vertically) such as taper (Cooper et al., 1997; Kim and You, 2002; Kim et al., 2008; Kim and Kanda, 2010a; 2010b) and setback (Kim and Kanda, 2010a,b), as well as introduction of openings (Dutton and Isyumou, 1990, Miyashita et al., 1993). However, most of the above papers have focused on the effect of one aerodynamic modification that changes systematically. For example, for corner-modification buildings, various modification shapes and various modification lengths were highlighted, and for tapered buildings, the effects of different taper ratios were the main concern. Although there have been some reports on cross comparisons of different aerodynamic modifications using a limited number of aerodynamic modifications, none have comprehensively investigated aerodynamic characteristics of various types of tall buildings with different configurations. Therefore, a series of wind tunnel experiments were conducted to investigate the aerodynamic characteristics and to evaluate the most effective structural shape in wind-resistant design for tall buildings with various aerodynamic modifications.
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Fluctuating aerodynamic forces on tall building models with the same volume were firstly measured, and wind pressure measurements were conducted on building models, showing excellent aerodynamic characteristics. This paper presents comprehensive and detailed discussions on the aerodynamic characteristics of the shapes tested.
2. Outline of wind tunnel experimental models 2.1. Configuration of tall building models The tall building models used for the experiments are shown in Table 1(a)–(g). The full-scale height and the total volume of each building model are commonly set at H¼400 m (80 stories) and about 1,000,000 m3. The width B of the Square Model shown in Table 1(a) is 50 m and the aspect ratio H/B is 8. The geometric scale of the wind tunnel models is set at 1/1000. The tall building models examined in this study are classified in 7 categories as follows. (a) Basic models The Square, Circular, Rectangular, and Elliptic plan models shown in Table 1(a) are classified as Basic Models. The side ratio of the Rectangular and Elliptic Models is 1:2. 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 which is similar to full-scale, 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 experiment is Re ¼2.9 104. (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 examination of corner modification focuses on a Corner Cut Model and a Corner Chamfered Model as shown in Table 1(b). Referring to past researches on aerodynamic characteristics of structures and buildings with corner chamfered and corner cut models (Shiraishi et al. 1986; Amano, 1995; Kawai, 1998), the modification length is set at 0.1B, 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 0.25H and 0.75H are shifted by 0.5B to the left and right side, respectively, from the middle floor, and the walls have smoothly curved surfaces as shown in Table 1(c). (d) Tapered models The tapered models include the following five types: a 2-Tapered Model which has only two tapered surfaces, a 4-Tapered Model which has four tapered surfaces, an Inversely 4-Tapered Model which has the inverse building shape of the 4-Tapered Model, and a Bulged Model whose sectional area at mid-height is expanded as shown in Table 1(d). When
Table 1 Configuration of test models.
(e) Helical models
(a) Basic models Square
Rectangular L
H=400
α=0o α
y
B=50
z
Circular
180o Helical Square
270o Helical Square
360o Helical Square
180o Helical Rectangular
y D x
x
y
z
Corner Cut
y
x
(b) Corner modification models Corner Chamfered
90o Helical Square
Elliptic
z
x
y
z
x
y
z
x
z
y
(c) Tilted models Tilted
x
y
z
x
y
z
x
y
z
x
(f) Opening models (f-1) Cross Opening
Winding
h/H=2/24
h/H=5/24
(f-2) Oblique Opening h/H=11/24
h/H=2/24
h/H=5/24
H=400
h
y
z
x
y
z
100 50
x
y
z
x
y 25 50 25
z
x
y
(d) Tapered models 2-Tapered
y
z
4-Tapered
x
y
z
x
y
z
x
x
y
z
x
(f)
Inversely 4-Tapered
Setback
z
y
z
y
z
x y
x
y
z
x
y
z
x
(g) Comp os ite models 360o
h/H=11/24
x
z
4-Tapered Helical Setback & 360o Helical & Corner Cut & Corner Cut & Corner Cut
(f-2)
Bulged
y
z
x
y
z
x
y
z
x
y
z
x
Setback & 45o Rotate
y
z
x
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the taper ratio is between 5% and 10%, a model with a larger tapering ratio shows better aerodynamic behavior (Kim and Kanda, 2010a,b). Thus, for the 4-Tapered Model, the taper ratio was set at 10% and the area ratio of the roof floor to the base floor was set at 1/6. 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 1/6 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 1/3. (e) Helical models The sectional shapes of the helical models are square and rectangular, and the twist angle y between the roof floor and the base floor is set at 901, 1801, 2701 and 3601, as shown in Table 1(e). The sectional shapes together with the twist angle are used as a prefix of the model name. For example, the 1801 Helical Square Model means the helical model whose sectional shape is square with a twist angle of 1801. (f) Opening models In the category of opening models, three cross opening models and three oblique opening models, whose openings are provided at the top-center and top-corner of the walls, respectively, are classified as shown in Table 1(f). Three different opening heights h¼ 2H/24, 5H/24, and 11H/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 is almost the same, their widths are fixed. However, for the three Cross Opening Models, the opening volume is included in the building volume, because of the compatibility of aspect ratio with the other models. (g) Composite models The composite models have the combined configurations of the primary configurations shown in Table 1(a)–(f), and the aerodynamic characteristics of the following four composite models shown in Table 1(g) are investigated: 3601 Helical and Corner Cut Model; 4-Tapered and 3601 Helical and Corner Cut Model; Setback and Corner Cut Model; and 451 Rotating Setback Model, where the rotating angle of each setback layer is 451.
181
Fig. 1. Flow conditions of wind tunnel experiment.
2.2. Experimental conditions 2.2.1. Aerodynamic force measurements Wind tunnel experiments were performed in a closed-circuittype boundary-layer wind tunnel whose working section is 1.8 m high by 2.0 m wide. Fig. 1 shows the condition of the approaching turbulent boundary layer flow with a power-law index of 0.27, representing an urban area. The wind velocity and turbulence intensity at the top of the model are about UH ¼7.0 m s 1 and IUH ¼9.2%, respectively. The turbulence scale near the model top is about 0.360 m, and that of Architectural Institution of Japan (2004) is 365 m. Therefore, when considering the length scale of 1/1000, 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 a is changed from 01, which is normal to a wall surface, to 451 or 1801 every 51 depending upon the building configuration. The measured wind forces and aerodynamic moments are normalized by qHBH2 to get wind force coefficients and moment coefficients. Here, qH is the velocity pressure at the model height H, and B is commonly set at the width of the Square Model. Therefore, the force and moment coefficients of the models can be directly compared. Fig. 2 shows
Fig. 2. Coordinate system.
the definitions of wind forces, moments, and the coordinate system employed in this study. The Reynolds number Re based on the mean wind velocity at the roof height UH and the width of the Square Model B is Re ¼2.6 104.
2.2.2. Wind pressure measurements Wind pressure measurements were conducted on 8 models as shown in Fig. 3. 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 measurement were to examine the characteristics of local wind forces and aerodynamic phenomena in detail. The coordinate system and approaching flow for the wind pressure measurements are the same as for the aerodynamic force measurement (see Figs. 1 and 2), except that the wind velocity at model height was 11.8 m s 1. Also, the wind direction
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was changed from 01 to 3551 at 51 intervals as for the aerodynamic force measurements. The fluctuating wind pressures of each pressure tap were measured and recorded simultaneously using a vinyl tube 80 cm long through a multi-channel pressure transducer. The sampling frequency was 1 kHz with a low-pass filter of 500 Hz. 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 20 measurement points on one level on four surfaces, as shown in Fig. 3, and the measurement points were instrumented at 10 levels (12 levels only for Setback Model), giving about 200 measurement points. The wind pressure coefficients Cp were obtained by normalizing the fluctuating pressures p by the velocity pressure qH at model height. The local wind force coefficients, CfD for along-wind, CfL for across-wind and CmT for
Fig. 3. Test models for wind pressure measurement. (a) Square, (b) cross opening, (c) corner chamfered, (d) corner cut (h/H¼5/24), (e) 4-Tapered, (f) setback, (g) 901 helical and (h) 1801 helical.
torsional moment, were derived by integrating the wind pressure coefficients Cp using the building width of the Square Model B (B2 for torsional moment) regardless of building shape.
3. Results of wind force measurements 3.1. Mean overturning moment coefficients Fig. 4 shows the variation of the mean along-wind overturning moment (o.t.m.) coefficient C MD and the mean across-wind o.t.m. coefficient C ML with wind direction a for eight typical building models. Fig. 5 shows the maximum values of the mean alongwind and across-wind o.t.m. coefficients, 9C MD 9max and 9C ML 9max considering all wind directions. The mean along-wind o.t.m. coefficient C MD and across-wind o.t.m. coefficient C ML of the Square Model show maximum values of 0.60 and 0.20 at wind direction a ¼ 451 and 151, respectively. The maximum along-wind o.t.m. coefficient 9C MD 9max and acrosswind o.t.m. coefficient 9C ML 9max of the Circular Model is smallest among all experimental models, and those of the Rectangular Model and Elliptic Model are larger than those of the Square Model because of their larger widths. The maximum mean along-wind o.t.m. coefficients 9C MD 9max 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 maximum mean along-wind o.t.m. coefficient 9C MD 9max does not decrease as much as those of the 4-Tapered Model and Setback Model. This may be because of the reduced effectiveness of the openings as the wind direction approaches 451. The maximum mean across-wind o.t.m. coefficients 9C ML 9max of the Corner Cut Model and Corner Chamfered Model are small. The maximum mean across-wind o.t.m. coefficients of the Helical Square Model and the Cross Opening h/H¼11/24 Model, whose opening size is the largest, are also small. The small coefficients of those models are related to vortex formation and shedding. Inversely, the models whose along- and across-wind o.t.m. coefficients are larger than those of the Square Model are the 2-Tapered Model, the 1801 Helical Rectangular Model and the Tilted Model with larger projected area for a certain wind direction, and the Inversely 4-Tapered Model with larger projected area at its upper height. The maximum mean o.t.m. coefficients 9C MD 9max and 9C ML 9max of a Helical Square Model with a larger twist angle tends to show smaller values. And, as can be seen in Fig. 4, the variations of
Fig. 4. Variation of mean overturning moment coefficients on wind direction for some test models. (a) Along-wind direction and (b) across-wind direction.
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Fig. 5. Comparison of maximum mean overturning moment coefficients.
Fig. 6. Variation of fluctuating overturning moment coefficients on wind direction for some test models. (a) Along-wind direction and (b) across-wind direction.
mean o.t.m. coefficients C MD and C ML of the 901 Helical Square and 1801 Helical Square Models with wind direction are very small. In particular, the 1801 Helical Square Model shows values almost independent of wind direction. For the opening models, as the opening size h/H becomes larger, the maximum mean o.t.m. coefficient 9C ML 9max decreases. However, the decreasing tendency is not significant for the maximum mean along-wind coefficient 9C MD 9max for both the Cross Opening Models 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 3601 Helical and Corner cut are almost the same as those of the 3601 Helical Model, implying that the aerodynamic characteristics have not been further improved by corner modification. 3.2. Fluctuating overturning moment coefficients Fig. 6 shows the variation of the fluctuating o.t.m. coefficients 0 0 CMD and CML with wind direction a for the test models which show specific aerodynamic force characteristics, where the fluctuating 0 0 o.t.m. coefficients CMD and CML are defined as the standard deviation of the o.t.m. coefficients. Fig. 7 shows the maximum along-wind and across-wind fluctuating o.t.m. coefficients, 0 0 CMD max and CML max, considering all wind directions.
The maximum fluctuating o.t.m. coefficients of the basic 0 0 Square Model are CMD max ¼0.12 and CML max ¼ 0.14 for wind direction of a ¼ 01 as shown in Fig. 6. As shown in Fig. 7, the maximum fluctuating along-wind o.t.m. 0 coefficients CMD max of the Corner Chamfered, Corner Cut, 4-Tapered and Setback Models are smaller. Like the mean o.t.m. coefficients, the smaller projected area at upper height is related to the smaller fluctuating o.t.m. coefficients of the 4-Tapered Model and the Setback Model, and for the Corner Chamfered Model and the Corner Cut Model, the elongated separated shear layer causes smaller coefficients. (Tamura and Miyagi, 1999). The 0 maximum fluctuating across-wind o.t.m. coefficients CML max of the 4-Tapered, Setback, Helical Square, and Cross Opening 11/24 Models show relatively small values. Detailed aerodynamic phenomenon will be discussed later. These trends are the same as those of the maximum mean o.t.m. coefficients. And, the effect of twist angle y 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 maximum mean o.t.m. coefficients. 3.3. Relationship between overturning moment coefficients The relationship between maximum mean o.t.m. coefficients and maximum fluctuating o.t.m. coefficients for all building
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Fig. 7. Comparison of maximum fluctuating overturning moment coefficients.
Fig. 8. Relationship of o.t.m. coefficients. (a) Relationship between maximum mean and maximum fluctuating o.t.m. coefficients (b-1) maximum mean o.t.m. coefficients (b-2) maximum fluctuating o.t.m. coefficients and (b) Relationship between along-wind direction and across-wind direction.
models are shown in Fig. 8(a) for the along-wind direction and for the across-wind direction. Fig. 8(b) shows the relationship between the maximum mean o.t.m. coefficients in the along-wind direction and those in the across-wind direction (Fig. 8(b-1)), and the
relationship between the maximum fluctuating o.t.m. coefficients in both directions (Fig. 8(b-2)). As described in Section 3.2, the maximum mean and fluctuating o.t.m. coefficients show a similar tendency, and high correlations between them are observed as
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shown in Fig. 8(a). And, it is interesting to note that the high correlations between mean/fluctuating o.t.m. coefficients in the along-wind direction and in the across-wind direction are observed. 3.4. Power spectral densities of across-wind overturning moment coefficients As the across-wind power spectra generally exceed the alongwind power spectra, the power spectra of across-wind overturning moment coefficients fSCML whose peak is the largest among all wind directions are shown in Fig. 9, and are categorized by model types. The power spectrum of the Square Model shown in Fig. 9(a)–(g) has a sharp peak near the Strouhal component of 0.1. Although the peak of the Rectangular Model shown in Fig. 9(a) is not as sharp, the values of power spectrum in the frequency range higher than 0.01 are relatively large. The peaks of the Corner modification models (Fig. 9(b)), the 4-Tapered and Setback Models (Fig. 9(d)), the Helical Models (Fig. 9(e)), and the Cross Opening Model h/H¼ 11/24, which show smaller overturning moment coefficients, decrease significantly
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compared with that of the Square Model, showing that the periodic vortex shedding is effectively suppressed. On the other hand, the peaks of the Tilted and Inversed 4-Tapered Models are larger than that of the Square Model. For the power spectra of the Helical Square Models shown in Fig. 9(e), even though the twist angle y is large, relatively sharp peaks can be observed, but their values are small. And there are no significant differences in peaks and shapes of power spectra when the twist angle is more than 1801. The peaks of the Cross Opening and Oblique Opening models shown in Fig. 9(f-1) and (f-2) decrease with opening size h/H. For the Cross Opening h/H¼ 11/24 Model, the peak of the Strouhal component becomes flat, but another peak is observed at the reduced frequency fB/UH of 0.2. For the Composite Models (Fig. 9(g)), the peaks of the Strouhal component for the 4-Tapered and 3601 Helical and Corner Cut, Setback and Corner Cut, and 451 Rotating Setback Models are hardly noticeable. In the calculation of wind-induced responses, the spectral values are important, and those corresponding to a 500-year return period wind speed and a 1-year return period wind speed
Fig. 9. Power spectral densities of across-wind overturning moment coefficients. (a) Basic models, (b) corner modification models, (c) tilted models, (d) tapered models, (e) helical models, (f-1) cross opening models, (f-2) oblique opening models and (g) composite models.
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pffiffiffiffiffiffiffiffiffiffi were calculated and their square root values SCML are shown in Fig. 10(a) and (b). Here, the square root values for Vp,1, pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi frequency SCML ,max (Vp,1), are the values on the reduced p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi fB/UH ¼0.17, and the square root values for Vp,500, SCML ,max pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi SCML , peak because the (Vp,500) correspond to the peak values maximum values in power spectral density were selected in the ranges where the reduced frequency is larger than 0.07 (fB/ UH Z0.07). The 1st natural frequency is assumed to be f1 ¼ 0.1 Hz, and the design wind speeds for corresponding return periods are assumed to be Vp,500 ¼71 m s 1 and Vp,1 ¼30 m s 1 in Tokyo, respectively. And, Fig. 10(c) shows the bandwidth Bw of power
spectral densities shown in Fig. 9. The bandwidth Bw was obtained by approximating the power spectra fSCML to the Eq. (1) through the least-square method (Vickery and Clark, 1972). f SCML
s2
" 2 # 1f =f peak ¼ k pffiffiffiffi exp Bw pf peak Bw f
ð1Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi The values of SCML,peak for the Corner Cut, Tapered, Setback, Helical Square (y ¼1801 3601), and Cross Opening (h/H¼11/24) Models, which show small mean and fluctuating o.t.m. coefficients, are smaller than that of the Square Model, meaning that those
Fig. 10. Comparison of across-wind power spectral densities. (a) Maximum peak values of power spectral densities (Design wind speed corresponding to 500-year return period), (b) design wind speed corresponding to 1-year return period and (c) bandwidths.
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pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi models have the advantage in safe design. The values of SCML,peak for the 4-Tapered and 3601 Helical and Corner Cut and 451 Rotating Setback Models, which are Composite models, are much smaller than that of the Square Model, and it can be said that the Combination modelpisffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a very ffieffective building shape for safe design. The values of, SCML,max (Vp,1), for the Tilted Models, Tapered models and Oblique Opening Modelsp are generally large, and even ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi for the Tapered and Setback Models, SCML,max (Vp,1), is larger than that of the Square Model. However, the values of the Corner Cut, Helical Square, and Cross Opening h/H¼11/24 Models are smaller than that of the Square Model, showing that these building shapes are superior to the square shape for habitability design. Although some composite models contain Tapered and Setback, the values ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi of SCML,max (Vp,1) become smaller than that of the Square Model. The bandwidths Bw shown in Fig. 10(c) show an inverse trend to the spectral peaks shown in Fig. 10(a), and when the bandwidth is small, the spectral peak becomes very sharp as shown for the Square Model, implying that strong vortices are shed regularly. But when the bandwidth is large, as the spectral peak becomes flat and the spectral shape becomes wide, it can be assumed that the vortex shedding becomes random and irregular. This randomness contributes largely to the smaller wind forces discussed in Sections 3.1 and 3.2, and this is more profound for the composite models whose bandwidths are very large.
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3.5. Effect of twist Angle y for helical square models As shown above, because the aerodynamic characteristics of Helical Models are better than those of other models with single modification, detailed comparisons are summarized in Fig. 11. From Fig. 11(a)–(c), the o.t.m. coefficients and the spectral peak values show the tendency to decrease with increasing twist angle y, and the decrease in the fluctuating component of across-wind is significant, as shown in Fig. 11(b) and (c). But note that there are small differences in o.t.m. coefficients, spectral peaks and bandwidths when the twist angle is larger than 180o. From this, it can be assumed that the effects of twist angle y on regular vortex shedding appear mostly when the twist angle is less than 901, and the relative effects of twist angle y become smaller at larger twist angle i.e.
4. Results of wind pressure measurements The representative wind direction is assumed to be 01 for the models shown in Fig. 3(a)–(f), and those of the 901 Helical and 1801 Helical Models are 601 and 351, respectively, which are normal to one surface at z/H¼0.7. Basically, the wind pressure measurements refer to the representative wind direction unless stated otherwise.
Fig. 11. Effect of twist angle y for the Helical Square Models. (a) Maximum mean o.t.m. coefficients, (b) maximum fluctuating o.t.m. coefficients, (c) peak values of power spectral densities and (d) bandwidths of power spectral densities.
Fig. 12. Vertical profile of mean local wind force coefficients. (a) Along-wind, (b) across-wind and (c) torsion.
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4.1. Distribution of mean local wind force coefficients The distribution of mean local wind force coefficients is shown in Fig. 12. The mean local wind force coefficients of across-wind (Fig. 12(b)) and torsional moments (Fig. 12(c)) are shown for the wind directions at which the mean 9C FD 9 and 9C MT 9 become maximum. The mean local wind force coefficients for the along-wind direction C f D , across-wind direction C f L and torsional moment C mT of the Square Model are the largest throughout the height. The C f D , 9C f L 9 and C mT of the Corner Chamfered and Corner Cut
Models are smaller than that of the Square Model throughout the height. Especially, C mT values are less than the half of the Square Model (Fig. 12(c)). From this, the torsional moment coefficients are assumed to decrease as well as the overturning moment coefficients in the along-wind direction and the across-wind direction, as shown in Section 3.1. For the 4-Tapered and Setback Models whose projected areas become small with height, the torsional moment coefficients decrease as for the mean local wind force coefficients in the along-wind direction shown in Fig. 12(a). And there are large differences in C f D values for the Setback Model and the 4-Tapered Model near z/H¼0.75, 0.50 and 0.25. For
Fig. 13. Vertical profile of fluctuating local wind force coefficients. (a) Along-wind, (b) across-wind and (c) torsion.
Fig. 14. Power spectral densities of across-wind local wind force coefficients. (a) Square (a ¼01), (b) cross opening (a ¼01), (c) corner chamfered (a ¼ 01), (d) corner cut (a ¼ 01), (e) 4-Tapered (a ¼01), (f) setback (a ¼ 01), (g) 901 helical (a ¼601) and (h) 1801 helical (a ¼351).
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the 901 Helical and the 1801 Helical Models, C f L and C mT become positive or negative depending on z/H, reflecting the building shapes. This results in smaller aerodynamic characteristics as shown in Section 3.1. The C f D , C f L and C mT of the Cross Opening Model are smaller than that of the Square Model near the opening, which is affected by the opening, showing little difference at other heights to the Square Model. 4.2. Distribution of fluctuating local wind force coefficients The vertical distribution of the fluctuating local wind force coefficients is shown in Fig. 13. For the along-wind and acrosswind directions, the variation trends are similar to those of the mean local wind force coefficients shown in 4.1 (Fig. 13(a) and (b)). Similar observations can also be made for torsional moment, i.e., the CmT0 values of the Corner Chamfered and Corner Cut Models are smaller than that of the Square Model, the CmT0 values of the 4-Tapered and Setback Models at z/HZ0.5 are smaller than that of the Square Model, and the CmT0 values of the 901 Helical and 1801 Helical Models become positive and negative depending on z/H shown in Fig. 13(c). However, the CmT0 values near the opening of the Cross Opening Model is larger than that of the Square Model, meaning that the opening has an inverse impact on fluctuating local wind force. 4.3. 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/H¼0.5 are shown in Fig. 14. The Strouhal number St corresponding to the vortex shedding frequency, and the bandwidth Bw were obtained and the vertical profiles are shown in Figs. 15 and 16. The power spectra in Fig. 14 were plotted against the reduced frequency, which was obtained by using the width of the Square Model B (constant) regardless of building shape. The bandwidths Bw were obtained by approximating the power spectra fSCfL to Eq. (1). Sharp peaks near z/H¼0.5 were observed for the Square Model (Fig. 14(a)), but they become relatively flat near the model top because of the three-dimensional effect of flow. This again implies that regular vortex shedding exists near z/H¼0.5 and the
Fig. 16. Vertical profile of bandwidth of across-wind local wind force power spectra.
regularity collapses near the model top, and the bandwidth shown in Fig. 16 near the z/H¼0.5 is smaller than that of the model top. The power spectral densities of other models in Fig. 14(b)–(h) show similar results. The Strouhal numbers St of the Square Model shown in Fig. 15 vary little with height, showing almost constant values throughout the height. This means that all the vortex components are shed almost the same time throughout the height, greatly exciting the models in across-wind direction. Contrary to the Square Model, those of the 4-Tapered Model, Setback Model and 1801 Helical Model vary greatly with height. For those models, because the shedding frequencies of each height are different, the resulting across-wind force decreases correspondingly. Similar discussion can be made for the bandwidth shown in Fig. 16, i.e., regular and strong vortices with narrow-band are shed throughout the height for the Square Model, but for the other models, vortices with wide band are shed randomly, effectively suppressing the across-wind force. The bandwidth of 1801 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 for the 1801 Helical Model the weak vortices with wide-band are shed irregularly throughout the height, and this results in the better aerodynamic behaviors discussed above. 4.4. Distribution of mean wind pressure coefficient
Fig. 15. Vertical profile of Strouhal number.
The mean wind pressure coefficients (Fig. 17) based on the local wind force characteristics will be discussed in the following sections for the Square, Corner Cut, Setback and 1801 Helical Models. Although the building surface of the 1801 Helical Model changes arbitrarily among windward surface, side surface, and leeward surface depending on the height, the mean wind pressure coefficients show their maximums at z/H¼7/8, and decrease near the peripheral parts, showing similar distributions to the other test models. For the Corner Cut Model, large negative wind pressures occur at the leading edge of the side surface, and their distribution varies greatly from the leading edge and trailing edge, showing a different distribution from the Square Model. The absolute values of mean wind pressures at the leeward surface are smaller than those of the Square Model, resulting smaller local
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(2)
(3)
(4)
(5)
(6)
Fig. 17. Distribution of mean wind pressure coefficients. (a) Square, (b) corner cut, (c) setback and (d) 1801 helical.
wind forces than the Square Model as shown in Fig. 12(a). The distributions of side surface and leeward surface of the Setback Model are similar to those of the Square Model. The distribution of the side surface of the 1801 Helical Model is very complex, and the absolute values for the leeward surface are smaller than those for the other models. The absolute values for the leeward surface of the 1801 Helical Model are smaller than those for the other models, and the distribution for the side surface is very complex, resulting in different characteristic from the other models, as shown in Fig. 12(b) and (c).
5. Conclusion
(7)
(8)
better aerodynamic behaviors in the along-wind direction, and Corner modification models, Helical models, and Cross Opening models whose opening sizes are h/H ¼11/24 show better aerodynamic behaviors in the across-wind direction. For the maximum fluctuating overturning moment coefficients, Corner modification models, 4-Tapered and Setback Models show better aerodynamic behaviors in both alongwind and across-wind directions. Cross Opening Model with h/H ¼11/24 and the Helical models also show better aerodynamic behaviors in the across-wind direction. For all building models, the correlations between maximum mean coefficients and maximum fluctuating coefficients are high for both along-wind and across-wind directions. And, the high correlations between maximum mean (and fluctuating) overturning moment. coefficients in along-wind direction and those in the across-wind direction are again observed. The power spectral densities of the models mentioned (2) decrease significantly compared with the Square Model, showing good performance in safety design for the design wind speed corresponding to a 500-year return period. However, 4-Tapered and Setback Models have disadvantages in the evaluation of habitability for the design wind speed corresponding to a 1-year wind speed. Conversely, Corner Chamfer, Corner Cut, Helical, and Cross Opening (h/H¼11/24) Models show superior aerodynamic behaviors in both safety and habitability design to the Square Model. 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 overturning moment coefficients of 3601 Helical and Corner cut are almost the same as those of the 3601 Helical Model, implying that the aerodynamic characteristics have not been improved by corner modification and the advantages of corner modification seem to be eliminated somewhat by the helical shape. The building configurations mentioned in (1) and (2) show better aerodynamic behavior in both along-wind and acrosswind directions, and the local wind force coefficients of torsional moment are also small. However, the opening of the Cross Opening Model has an adverse influence on the fluctuating local wind forces. For the Square Model, all the vortex components are shed at almost the same time throughout the height, greatly exciting the models in across-wind direction. Contrary to the Square Model, those of the 4-Tapered Model, the Setback Model and the 1801 Helical Model vary greatly with height. For those models, because the shedding frequencies of each height are different, the resulting across-wind force decreases correspondingly. For 1801 Helical Model, weak vortices with wide-band are shed irregularly throughout the height, and this results in the better aerodynamic behaviors as discussed above.
Acknowledgment N. Koshika of Kajima Corp., K. Yamawaki of NIKKEN SEKKEI Ltd., Y. Hitomi of NIHON SEKKEI Ltd., Y. Hayano of MAD Tokyo and S. Igarashi of Takenaka Corp. provided us with helpful advice for setting experimental cases. This study comprised part of a project funded by the Ministry of Land, Infrastructure, Transport and Tourism, Japan.
Aerodynamic force measurements and wind pressure measurements were conducted for tall building models with various building shapes and the same height and volume. Comparison and discussion of the aerodynamic characteristics of tall buildings led to the following conclusions.
Reference
(1) For the maximum mean overturning moment coefficients, tapered models such as 4-Tapered and Setback Models show
Architectural Institution of Japan, 2004. Recommendations for Loads on Buildings, 2004. Architectural Institution of Japan, Tokyo.
H. Tanaka et al. / J. Wind Eng. Ind. Aerodyn. 107–108 (2012) 179–191
Amano, T., 1995. The Effect of corner-cutting of three dimensional square cylinders on vortex-induced oscillation and galloping in uniform flow. Journal of Structural and Construction Engineering, AIJ 478, 63–69. in Japanese. Cooper, K.R., Nakayama, M., Sasaki, Y., Fediw, A.A., Resende-Ide, S., Zan, S.J., 1997. Unsteady aerodynamic force measurements on a super-tall building with a tapered cross section. Journal of Wind Engineering and Industrial Aerodynamics 72, 199–212. Dutton, R., Isyumou, N., 1990. Reduction of tall building motion by aerodynamic treatments. Journal of Wind Engineering and Industrial Aerodynamics 36, 739–747. Hayashida, H., Iwasa, Y., 1990. Aerodynamic shape effects on tall building for vortex induced vibration. Journal of Wind Engineering and Industrial Aerodynamics 33 (1-2), 237–242. Hayashida, H., Mataki, Y., Iwasa, Y., 1992. Aerodynamic damping effects of tall building for a vortex induced vibration. Journal of Wind Engineering and Industrial Aerodynamics 43 (3), 1973–1983. Kawai, H., 1998. Effect of corner modifications on aeroelastic instabilities of tall buildings. Journal of Wind Engineering and Industrial Aerodynamics 74-76, 719–729. Kim, Y.C., Kanda, J., 2010a. Characteristics of aerodynamic forces and pressures on square plan buildings with height variations. Journal of Wind Engineering and Industrial Aerodynamics 98, 449–465. Kim, Y.C., Kanda, J., 2010b. Effects of taper and set-back on wind force and wind-induced response of tall buildings. Wind and Structures 13 (6), 499–517.
191
Kim, Y.M., You, K.P., 2002. Dynamic responses of a tapered tall building to wind load. Journal of Wind Engineering and Industrial Aerodynamics 90, 1771–1782. Kim, Y.M., You, K.P., Ko, N.H., 2008. Across-wind response of an aeroelastic tapered tall building. Journal of Wind Engineering and Industrial Aerodynamics 96, 1307–1319. Kwok, K.C.S., Wilhelm, P.A., Wilkie, B.G., 1988. Effect of edge configuration on wind-induced response of tall buildings. Engineering Structures 10, 135–140. Miyashita, K., Katagiri, J., Nakamura, O., Ohkuma, T., Tamura, Y., Itoh, M., Mimachi, T., 1993. Wind-induced response of high-rise buildings. Journal of Wind Engineering and Industrial Aerodynamics 50, 319–328. Shiraishi, N., Matsumoto, M., Shirato, H., Ishizaki, H., Osada, M., Matsui, T., 1986, On aerodynamic stability effects for bluff rectangular cylinders by their corners cut. Proceedings of the 19th National Symposium on Wind Engineering, Japan, pp. 193–198 (in Japanese). Tamura, T., Miyagi, T., 1999. The effect of turbulence on aerodynamic forces on a square cylinder with various corner shapes. Journal of Wind Engineering and Industrial Aerodynamics 83, 35–145. Tamura, Y., Nakai, M., Ohtake, K., Koshika, N., Yamawaki, K., Hitomi, Y., 2011. Study on wind resistant design method of super high-rise buildings with various unconventional configurations. The Ministry of Land, Infrastructure, Transport and Tourism, Japan. (accessed 2011/01/17) (in Japanese). Vickery, B.J., Clark, A.W., 1972, Lift or across-wind response of tapered stacks. Proceedings of the American Society of Civil Engineers, 98, ST1, pp. 1–20.