The Eighth Asia-Pacific Conference on Wind Engineering,
December 10–14, 2013, Chennai, India
AERODYNAMIC AND RESPONSE CHARACTERISTICS OF TALL
BUILDINGS WITH VARIOUS POLYGON CROSS-SECTIONS
Yong Chul, Kim1, Eswara Kumar, Bandi2, Yukio, Tamura3, Akihito, Yoshida4
1
Research professor, Korea University, Seoul, Korea, [email protected]
GCOE Associate Professor, Tokyo Polytechnic University, Atsugi, Kanagawa, Japan
2
Ph D Candidate, Tokyo Polytechnic University, Atsugi, Kanagawa, Japan, [email protected]
3
Professor, Polytechnic University, Atsugi, Kanagawa, Japan, [email protected]
4
Associate Professor, Tokyo Polytechnic University, Atsugi, Kanagawa, Japan, [email protected]
ABSTRACT
A series of wind tunnel tests were conducted on 13 straight and helical tall buildings with various polygon crosssections, including triangle, square, pentagon, hexagon, octagon, dodecagon, and circular. The primary purpose
of the present study is to investigate the effect of increasing number of side on aerodynamic characteristics for
the straight and helical tall buildings. The results show that the overturning moment coefficients and the spectral
values decrease with increasing number of side, showing the largest mean and fluctuating overturning moments
for the straight triangle model, and the largest spectral values for the straight square model. And the effects of
helical shape on the aerodynamic characteristics decrease with increasing the number of side, but large
differences were found in the spectral values for the safety level design wind speed, hence the largest maximum
displacement.
Keywords: Tall buildings, Wind-induced responses, Polygon cross-section, Helical shape
Introduction
The current tallest building in the world is the 828m-high Burj Khalifa, and the tallest
building in the next decade will be Kingdom Tower (over 1000m), which will be completed
in 2018. The current trend of tall building construction, i.e., manhattanization with various
building shapes, requires attention. Their free-wheeling building shapes are expressed by
taper, set-back, helical, or changing cross-sections, reflecting architects’ and engineers’
challenging spirits for new forms. These atypical and unconventional building shapes are a
resurrection of an old characteristic, but they have the advantage of suppressing across-wind
responses, which is a major factor in safety and habitability design of tall buildings.
Besides changing building shapes, many current tall buildings have various polygon
cross-sections, not being limited to the simple square cross-section. So far, there have been
some studies that have investigated the aerodynamic characteristics of tall buildings with
various polygon cross-sections. Chien et al. (2010) examined mean drag forces, in terms of
shape factors, for 8 kinds of polygon high mast structures using 2-dimensional CFD analyses.
In their study, the mean drag force becomes constant for the polygon structures with more
than 10-side.Tang et al. (2013) investigated the mean drag forces and wake flows on straight
and twisted polygon tall buildings using numerical simulations. They examined the effect of
increasing number of sides, rounded corners of square cross-section, and twisting angle of the
square cross-section tall building. They used 10 straight tall buildings for various polygon
cross-sections, 11 rounded square cross-sections with various fillet radiuses, and 9 twisted tall
buildings with twisting angle up to 180º by the interval of 22.5º. From 2-dimensional
numerical simulations, they found that the mean drag force decreases with increasing the side
numbers, and the decrease becomes very slow when the number of sides is larger than 14. The
mean drag force of 14-side polygon tall building is only 40% of that of a square tall building.
And also from the 2-dimensional numerical simulations for various fillet radius r, the mean
Proc. of the 8th Asia-Pacific Conference on Wind Engineering – Nagesh R. Iyer, Prem Krishna, S. Selvi Rajan and P. Harikrishna (eds)
c 2013 APCWE-VIII. All rights reserved. Published by Research Publishing, Singapore. ISBN: 978-981-07-8011-1
Copyright doi:10.3850/978-981-07-8012-8 079
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Proc. of the 8th Asia-Pacific Conference on Wind Engineering (APCWE-VIII)
drag force drops quickly until the radius-to-width ratio r/b reaches 0.15, and further increase
of fillet radius has little influence on the mean drag force. To support above two finding, they
showed the width of wake flow, which is almost constant after the case of 14-side polygon
tall buildings and after the radius-to-width r/b of 0.15. The effect of twisting angle from 0º
(Straight) to 180º was examined using the 3-dimensional numerical simulations for tall
buildings with aspect ratio of 5. The mean drag forces increase or decrease depending on
twisting angles, and Tang et al. (2013) concluded that the efficiency of aerodynamic
modifications is best for the rounded corners, and next is increasing edge numbers, and the
next is twisting the building shape. Chien et al. (2010) and Tang et al. (2013) only focused the
mean drag force, and only uniform flow was used in their study.
So far, some studies on the effect of increasing number of side on aerodynamic
characteristics have been conducted, but in the studies only mean drag force has been focused
on by the numerical simulations under a uniform flow, no discussions were found on the
characteristics of other wind force components and responses using a boundary layer flow. In
the present study, the effects of various polygon cross-sections (triangle, square, pentagon,
hexagon, octagon, dodecagon, and circular) on aerodynamic characteristics were investigated
systematically using pressure measurement results. And for the helical angle of 180º, the
aerodynamic characteristics of the helical tall buildings with various number of sides were
also investigated.
Wind Tunnel Test
Table 1 shows the 13 tall building models which were used for wind tunnel tests.
Table 1: Tall building models with various polygon cross-sections
Straight
models
TR
SQ
PE
HE
OC
DO
TR-180H
SQ-180H
PE-180H
HE-180H
OC-180H
DO-180H
CI
Helical
models
Considering the results of Tanaka et al. (2012) on the effect of helical angles of square section
tall buildings, a helical angle of 180º was used in the present study. Equilateral cross-sections
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were used and the cross-sectional area of all building models was set the same. The model
height was H=400m in common, giving the same total volume for all building models. The
profiles of mean wind speed and turbulence intensity are plotted in Fig. 1. The experiments
were conducted under urban area flow (power-law index, Į = 0.27) for various wind
directions. The wind speed at the model height was about UH = 12 m/s, and the turbulence
intensity was about IuH = 11%. Fig. 2 shows the coordinate system used in the study;
structural axes, MX and MY, not wind axes, MD and ML, were used. Wind direction of 0º is
defined when wind is normal to one side of cross-section, and the considered wind directions
are different depending on building models.
A length scale of 1/1000 and a time scale of 1/167 were assumed. There were more
than 200 pressure taps and all the pressures were measured simultaneously with a sampling
frequency of 781 Hz, and a low pass-filter with a cut-off frequency of 300 Hz was cascaded in
each data acquisition channel to eliminate aliasing effects. The measuring time was adjusted
such that 33 samples were obtained, which one sample corresponds to 10-minute sample in
full time scale. The Reynolds number which is defined by the width of square model and
wind speed at model height was about Re = 4.2×104, and as the number of side increases, the
Reynolds number effect becomes significant, but in the present study the only a Reynolds
number in subcritical range was considered.
X
Iu,h ; z-0.32
0.27
MX
Uh ; z
MY
Y
(a) mean wind speed
(b) turbulenc intensity
Fig. 1 Profiles of incident flow
ș
Wind
Fig. 2 Coordinate system
Results and Discussion
Considering the tributary area of each pressure tap, the time series of overturning
moments (o.t.m.) were obtained, and using Eqs. (1) ~ (3), o.t.m. coefficients were calculated.
CMX = MX/(qHBHH)
(1);
CMY = MY/(qHBHH)
(2);
CMZ = MZ/(qHBHB)
where,
MX, MY, and MZ: overturning moment about X-, Y-, and Z-direction;
qH: velocity pressure defined at model height;
B: width of the square model(representative width);
H: model height
Mean and fluctuating overturning moment coefficients
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(3)
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MX
MY
MZ
(a) Straight models
MX
MY
MZ
(b) Helical models
Fig. 3 Variation of mean overturning moment coefficients in X-direction.
Fig. 3 shows the variations of mean o.t.m. coefficients for X-direction CMX . Fig. 3(a) is
for the straight models, and Fig. 3(b) is for the helical models. The dotted line indicates the
mean o.t.m. coefficient of circular model (CI). For all models, mean coefficients decrease
with wind directions, showing their largest absolute values near the wind direction of ș = 90º
~ 100º. And it seems that the mean coefficients of the models with larger number of sides are
smaller. One characteristic point is that the variations of mean coefficients near the wind
directions of ș = 0º. Only for the straight triangle (TR) and square (SQ) models in Fig. 3(a)
show clear positive slope ( dCMX dθ > 0 ) near the small wind directions, meaning a possibility
of occurrence of instability vibrations. For the straight octagon (OC) model, a positive slope is
observed, but the slope is very small and can be ignored.
Fig. 4 shows the variations of fluctuating o.t.m. coefficients on wind directions for X′ . The largest value is found for the straight square (SQ) model near the wind
direction CMX
direction of ș = 0º, and decrease with increasing wind directions. The difference among
models is not clear, but the smaller value seems to be found for the models with larger
number of sides, showing slightly larger values than that of the circular (CI) model.
The largest absolute mean and fluctuating o.t.m. coefficients were obtained for the
considered wind directions and the variations on number of side are shown in Fig. 5. For the
coefficients for X- and Y-directions, CMX becomes CMY and CMY becomes CMX depending on
the wind directions, thus larger absolute mean and fluctuating coefficients were selected
regardless of wind directions. Open symbols indicate the straight models, and solid symbols
indicate the helical models. And circle indicates the coefficients for X- and Y-directions, and
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triangle indicates the coefficients for Z-direction. The coefficients decrease with increasing
number of sides, and approaches to the value of the circular (CI) model. For the absolute
mean coefficients in Fig. 5(a), a decreasing slope changes largely from the square model, and
the difference between the straight and helical models also becomes small from the square
model. For the fluctuating coefficients in Fig. 5(b), the coefficients changes largely from the
pentagon or hexagon models, and the difference between the straight and helical models also
becomes small from the pentagon or hexagon models.
MX
MY
MZ
(a) Straight models
MX
MY
MZ
(b) Helical models
Fig. 4 Variation of fluctuating overturning moment coefficients in X-direction.
X- and
Y-dir.
X- and
Y-dir.
Z-dir.
Value of CI
Z-dir.
Value of CI
(a) Absolute mean coefficients
(b) Fluctuating coefficients
Fig. 5 Variation of largest coefficients for all wind directions.
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Power spectral densities of overturning moment coefficients
The power spectral densities of the straight triangle model are shown in Fig. 6 for the
considered wind directions. Abscissa indicates the reduced frequency which is normalized by
the representative width (width of the square model) and the wind speed at model height. For
the power spectra of Y-direction nSCMY shown in Fig. 6(a), the shape and power remains to be
the same for the wind directions of ș = 0º ~ 40º, and the power in low frequency range
decreases with increasing wind directions, still showing similar shape. But the shape of the
power spectra of X-direction nSCMX shown in Fig. 6(b) changes largely depending on wind
directions. For the wind direction which is normal to the surface (ș = 0º), clear peak is
observed near the reduced frequency of 0.5, and the peak is observed until the wind direction
of ș = 30º. For this ranges of ș = 0º ~ 30º, the peak frequencies slightly increase with
increasing wind directions. When wind direction becomes larger than ș = 40º, the shape of
power spectral densities changes similar to that of Y-direction nSCMY as shown in Fig. 6(a).
UD,500
UD,500 UD,1
UD,1
UD,500
UD,1
(a) Y-direction
(b) X-direction ș = 0º ~ 30º (left) and ș = 40º ~ 60º (right)
Fig. 6 Power spectral densities of the straight triangle (TR) model.
The largest spectral values of 500- and 1-year return period design wind speed for all
the considered wind directions were obtained and the variations on the number of side are
shown in Fig. 7. In Fig. 7(a), the largest spectral values of the straight model in X- and Ydirections increase or decrease depending on the number of side, and the straight square
model shows the largest value among them. The pentagon model shows very small values,
and the smallest value is found for the dodecagon model. For the helical models, the largest
spectral values decrease largely when compared with those of the straight models, especially
for the square cross-section model. For Z-directions, they decrease with increasing number of
sides, and the difference between the straight and helical shape becomes small when the
number of side is larger than 5. For the largest spectral values of 1-year return period design
wind speed in X- and Y-directions shown in Fig. 7(b), the straight square model also shows
the largest value among the models, and the largest spectral values of the pentagon, hexagon,
octagon, and dodecagon models are almost the same. In Fig. 7(b), the difference in the
straight and helical shape becomes small when the number of side is larger than 5. The largest
spectral values of the straight triangle model for Z-direction are largest among models, while
those of the straight square model are largest for X- and Y-directions as mention before
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Proc. of the 8th Asia-Pacific Conference on Wind Engineering (APCWE-VIII)
X- and
Y-dir.
X- and
Y-dir.
Value of CI
Z-dir.
Z-dir.
(a) For UD,500
(b) For UD,1
Fig. 7 Largest spectral values for all wind directions.
Wind-induced responses
The spectral modal analyses were conducted to investigate the characteristics of the
wind-induced responses. Conditions for the response analysis are shown in Table 2. The
response analyses are conducted for the structural axes because of easy determination of the
generalized stiffness. The 1st mode natural frequencies of translation directions for safety level
were assumed to be nX1=nY1=0.11Hz considering high-quality field measurement damping
data for steel buildings (nX1=nY1=42/H), and that of Z-direction nZ1 was set to 1.34 times
higher than the translation natural frequencies. And the natural frequencies for habitability
level were set to 20% higher than those of the safety level (Tamura, 2012). Different damping
ratios are used for the displacement and acceleration responses, i.e. 1% and 0.7% respectively.
The design wind speed at model height covers from 30m/s to 70m/s. The lowest design wind
speed corresponds to 1-year return period design wind speed for habitability level, and the
fastest one corresponds to 500-year return period design wind speed for safety level at Tokyo.
Table 2: Conditions for response analysis
Safety level
Habitability level
nX1
0.11
0.13
nY1
0.11
0.13
nZ1
0.15 (=1.34nX1)
0.17 (=1.34nX1)
Damping ratio (%)
1
0.7
Design wind speed at model height (m/s)
70
30
Natural frequency (Hz)
Building density (kg/m3)
Mode shape
250
st
The 1 linear mode
250
st
The 1 linear mode
The largest maximum displacements and peak accelerations were obtained for the
considered wind directions, and the results are shown in Fig. 8. The trends are very similar to
those of spectral values shown in Fig. 7, showing that the largest wind-induced responses
were found for the straight square (SQ) model for both safety and habitability levels. The
largest maximum displacements of the helical models are smaller than those of their
counterpart models, and the largest peak accelerations of the pentagon (PE), hexagon (HE),
octagon (OC), and dodecagon (DO) models show less difference regardless of their building
shapes.
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Value of CI
Value of CI
(a) Largest maximum displacement (m)
(b) Largest peak acceleration (m/s2)
Fig. 8. Largest wind-induced responses for all wind directions.
Concluding Remarks
Systematic wind pressure measurements were conducted to investigate the effect of
increasing number of sides and helical building shape on the aerodynamic characteristics for
the tall buildings with same volume. Comparison and discussion of the aerodynamic
characteristics led to the following remarks.
The overturning moment coefficients decrease with increasing number of sides,
approaching to that of the circular model. The overturning moment coefficients in X-direction
CMX show different variation trend near the wind direction of ș = 0º between the straight
triangle and square model, and others.
Such as the overturning moment coefficients, the spectral values decrease with
increasing number of sides, and the largest spectral values and thus largest wind-induced
responses were found for the straight square model for both safety and habitability level. For
the maximum displacements, although the largest mean displacement was found for the
straight triangle model, the largest fluctuating displacement was found for the straight square
model, giving larger maximum displacement.
The effects of helical shape on the aerodynamic characteristics of tall building
decrease with increasing the number of sides, but large differences were found in the spectral
values for the 500-year return period design wind speed, hence the largest maximum
displacement.
References
Chien, C.W., Jang, J.J., Li, Y.C. (2010), “Wind-resistant design of high mast structures”, Journal of the Chinese
Institute of Engineers 33 (4), 597-615.
Tamura, Y. (2012), “Amplitude dependency of damping in buildings and critical tip drift ratio”, International
Journal of High-Rise Buildings 1 (1), 1-13.
Tanaka, H., Tamura, Y., Ohtake, K., Nakai, M., Kim, Y.C. (2012), “Experimental investigation of aerodynamic
forces and wind pressures acting on tall buildings with various unconventional configurations”, Journal of
Wind Engineering and Industrial Aerodynamics 107-108, 179-191.
Tang, J.W., Xie, Y.M., Felicetti, P., Tu, J.Y., Li, J.D. (2013), “Numerical simulations of wind drags on straight
and twisted polygonal buildings”, The Structural Design of Tall and Special Buildings 22, 62-73.
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