Generalization of Wind-Induced Loading between Two Tall Buildings

*Wonsul Kim1)1), Yukio Tamura2)2), Akihito Yoshida3) and Jin-Hak Yi4)4)

1), 4) Costal Engineering Research Division, Korea Institute of Ocean Science and Technology, Ansan 15627, Korea

2) Beijing’s Key Laboratory of Structural Wind Engineering and Urban Wind Environment, School of Civil Engineering, Beijing Jiaotong University, Beijing 100044,

China3) Wind Engineering Research Center, Tokyo Polytechnic University, Atsugi, 243-0297,

Japan1) w.kim@kiost.ac.kr

2) yukio@arch.t-kougei.ac.jp3) yoshida@arch.t-kougei.ac.jp

4) yjh@kiost.ac.kr

ABSTRACT

Codification of wind loads with interference effects among the grouped tall buildings is an issue in wind engineering. However, it is difficult to codify a guideline or codification because of the complex nature of the problem and the large number of variables involved. Apart from this complexity and difficulty, generalized and simplified guidelines for structural design wind loads will be useful in estimating approximate structural wind loads on tall buildings in preliminary design. In this study, interference effects on mean wind loads and dynamic wind loads between two buildings were investigated though wind tunnel tests. To reach some critical conclusions that could be used to improve a design code, Design Interference Factor (DIF) on wind loads was suggested for the assessment of wind-induced interference effects between two tall buildings.

1. INTRODUCTION

The interference effects have been studied by many researchers over the past several decades. They produced not only experimental data for the database from a huge number of wind tunnel experiments, but also empirical formulas for evaluating wind loads or pressure distributions among tall buildings. However, most of previous studies have mainly focused on the shielding effect for mean wind loads, and the magnification effect for wind-induced dynamic responses and peak pressures on a tall building due to interference (Kim et al., 2015).

1)1) Post-Doctoral Research Scientist, Ph.D.2)2), 3) Professor, Ph.D.4)4) Principal Research Scientist, Ph.D.

In general, the interference effects on mean base moments in along-wind direction have been known that the shielding effects are dominated, i.e. it tends to decrease mean wind loads on a tall building in the presence of an adjacent building directly upstream. The Australian Standard (AS/NZS 1170.2:2002) refers explicitly to the wind-induced interference effects on the wind loading of buildings, but only deals with shielding effects as shielding multiplier(Ms) and it does not address cases for which wind loads may actually increase due to interference. Khanduri et al. (2000) studied on interference effect on a tall building with an adjacent building of small, medium and large sizes, for several wind directions and various upstream exposure conditions by extensive experiments. Then they suggested Interferecne Influence Grids (IIGs) for mean loads, but these results presented only beneficial shielding on the principal building. Xie and Gu (2004) studied on mean interference effects between two and among three tall buildings for several wind directions by huge wind tunnel tests. They reported that the upstream adjacent buildings cause not only shielding effect by decreasing the mean wind load on the principal building, but also channeling effect by increasing the mean wind load on the principal building significantly. However, most previous studies have considered several wind directions and overall wind loads and responses due to the huge amount of experimental workload and complexity of many variables. The interference effects on local wind forces for wind directions from 0 to 355 have rarely been studied. To reach some critical conclusion that could be used in design codes, this paper have been focused on design wind loads between two buildings with various height ratios and locations of an adjacent building. Design Interference Factor (DIF) is proposed for the assessment of wind-induced interference effects between two tall buildings.

2. WIND TUNNEL TESTS

2.1 Simulated natural wind

Wind tunnel experiments were performed in a Boundary Layer Wind Tunnel whose working section was 1.8 m high by 2.0 m wide at Tokyo Polytechnic University, Japan. Fig. 1 shows the condition of the approaching turbulent flow with a power law exponent of 0.27, representing an urban area. The wind velocity and the turbulence intensity at the top of the study model were UH = 8.2m/s and IU = 20%, respectively. The turbulence scale near the model top was 268 m in full scale.

0

20

40

60

80

100

0 4 8 12 16

Hei

ght (

mm

)

Mean wind velocity (m/s)

Mean wind velocity

Buildingheight

27.0

GG Z

zU

0

20

40

60

80

100

0 0.1 0.2 0.3 0.4

Hei

ght (

mm

)

Turbulence intensity

Turbulence intensity

Buildingheight

)05.027.0(

1.0

GZz

Hu UnL /

2/)

(u

un

nS

Measured velocity spectrum

Karman sepctrum

6/52

8.701

/4

H

u

u

u

u

UnL

UnLnS

(a) Mean wind speed (b) Turbulence Intensity (c) velocity power spectral density

Fig. 1. Simulated natural wind in wind tunnel

2.2 Experimental arrangements

The considered experimental model comprises two buildings: the pressure model, referred to as a principal building, and dummy model, referred to as an interfering building. The geometrical model scale of 1:400 was employed in this study. 252 pressure taps were installed on the wall of the principal building. They were non-uniformly distributed in the vertical direction (Kim et al., 2015). Table 1 shows cases of the experimental models used in this study. As shown in Table 1, adjacent buildings of various sizes are classified as height ratios (Hr = Hi / Hp) with the same cross sections as the principal building, but different heights, and breadth ratios (Br = Bi / Bp) with the same height as the principal building but different cross sections. Here Bi and Bp are the breadths and of an adjacent building and a principal building, and Hi and Hp are the heights of an adjacent building and a principal building.

Table 1 Experimental models

Experimental models

Dimensions (mm)(BpDpHp)a

(BiDiHi)b

Height ratios(Hr = Hi / Hp)

Breadth ratios(Br = Bi / Bp)

Locations

Principalbuilding 70×70×280 - - 1

Adjacent building

70×70×14070×70×28070×70×42049×49×280

105×105×280

0.51

1.511

111

0.71.5

3737373025

a BpDpHp : dimension of principal buildingb BiDiHi : dimension of interfering building

1.5B 5B X6B2B 3B 4B

2B

1B

3B

4B

5B

6B

Y

Wind

0o

2.5B

Location of interfering bldg.

Principal bldg.

Fig. 2. Coordinate system indicating different locations of interfering buildings

Fig. 2 shows the coordinate system and the grid used to define the relative locations of the building and wind directions. All adjacent buildings were orientated with their on-face normal to the principal building. They were placed in various locations while the principal building is fixed at (X, Y) = (0, 0). A total of 72 wind directions were considered, from 0o to 355o in 5o steps. The fluctuating wind pressure data were obtained by sampling at 781Hz and 800Hz in full scale for a period for an adjacent building with height ratios and breadth ratios, respectively. The overall number of test cases is 11952.

2.3 Definition of Design Interference factor (DIF)

Wind loads on structures under the buffeting action of wind gusts have traditionally been treated by the gust loading factor (GLF) method in most major codes and standards around the world originally proposed in Davenport (1967). It should be noted that the GLF method to the base bending moment (BBM) have been employed in wind loading codes and standards in almost all major countries (Kareem and Zhou, 2003), a BBM-based gust loading factor (MGLF) is defined as:

GM=M̂ / M̄ (1)

where GM is the MGLF, M̄ is the mean BBM, and M̂ is the expected extreme BBM response. The MGLF can be computed by

GM=1+gM σ~M /M̄(2)

in which gM is the peak factor, and σ ~M is the RMS BBM response. According to above equations, the expected extreme BBM response can be expressed by

M̂=M̄+gM σ~M (3)

The RMS of BBM response can be calculated by the following mode generalized equations of structural motion.

m1¿ ξ̈1 (t )+c1

¿ ξ̇1 ( t )+k1¿ ξ ( t )=~F1

¿ (t )(4)

where m1¿

, c1¿

, k1¿

, ~F1

¿ and ξ1 are the generalized mass, damping, stiffness, external

load and displacement in the first mode, respectively. Accordingly, the generalized

equivalent-static wind loads, ~F1

¿ (t ) can be calculated by pressure integral as follows:

~F1¿ ( t )=∫0

H ~F ( z , t ) ϕ1 ( z ) dz=∑j

~M 1 , j (t ) ϕ1 , j

(5)

where ~F ( z , t ) , ϕ1 and

~M ( t ) are equivalent-static wind loads, mode shape and fluctuating components of the BBM, respectively. Accordingly, RMS of BBM response can be calculated by spectral modal analysis as follows:

σ ~M=(∫0

∞S~M (n )|H 1 (n )|2 dn)1/2

(6)

where S~M ( n ) is generalized power spectral density of the BBM, and |H (n )|2 is the mechanical admittance function of a structure, and given by

[ H (n ) ]2= 1

[1−(n/n0 )2]2+(2 ζn /n0 )2(7)

The mean BBM on a building is given by

M̄=∫0

HF̄ ( z ) zdz

(8)

Finally, the expected extreme BBM response can be calculated as follows:

M̂=∫0

HF̄ ( z ) zdz+gM (∫0

∞S~M (n )|H 1 (n )|2 dn)1 /2

(9a)

=∫0

HF̄ ( z ) zdz+gM σ M (1+ π

41ς 0

χ 0SM ( χ 0)σM

2 )1/2

(9b)

where, χ0 SM ( χ0 )/σM2

is dimensionless power spectral density of the fluctuating BBM, σM is the standard deviation of the BBM. χ0=n0B/U H is reduced frequency, B is characteristic breadth of the building and UH is the mean velocity at the top of the building. The reciprocal of the reduced frequency is the reduced wind velocity, i.e.,

U∗¿ 1χ 0

=UH

n0 B(10)

From eq. (9b), it implies that dynamic responses depend on the reduced wind velocity. The reduced wind velocity in evaluation of RMS of BBM is considered from 2 to 9. This range of reduced wind velocities represents full scale wind speeds between UH = 21 and 100 m/s. The extreme BBM response on the principal building with and without the interfering building was obtained by some assumptions: the fundamental mode shape of the building is set at z/H which is uncoupled and linear. 1st natural frequency of the principal building is set at 0.41Hz, damping ratio is set at ζ=0 .005 and mass of the principal building is 160kg/m3.

The interference effects are commonly expressed in terms of an interference factor (Khanduri et al., 1998). Similarly, to reach some critical conclusions that could be used to improve a design code, Design Interference Factor (DIF) for the extreme BBM responses in along-wind, across-wind and torsional wind directions are suggested to present the interference effects by maximizing the interference factor in the reduced wind velocities and wind directions.

DIFMD (L,T )= maxθ∈ [ 0 ,355 ] [ max

U∗∈ [2,9 ] { M̂D (L,T ) ,with (U *,θ )

M̂D (L,T ) ,without (U *,θ ) }](11)

where M̂D (L,T ) (U *,θ ) is the extreme BBM responses in along-wind, across-wind and torsional wind directions.

3. RESULTS AND DISCUSSION

3.1 Mean interference factors for mean BBM responses

Interference effects on the maximum values of mean BBM responses in along- and across-wind directions for all wind directions are presented and discussed. Figs. 3 shows contours of interference factors (MIFMD) for maximum value of mean BBM response with breadth ratios of an interfering building for all wind directions. In Fig. 3, an interesting observation is that MIFMD with increase in height and breadth ratios tends to increase, i.e., a higher and wider interfering buildings cause larger mean BBM response than that for an isolated building. Particularly for Hr and Br =1.5 as shown in Fig. 3(b) and (d), increases of over 10% in MIFMD occur where an interfering building is located in the regions (X/B, Y/B)=(1.5 3, 0.5 3) for Hr = 1.5, and (1.5 3, 1 3) for Br

= 1.5. Maximum values of MIFMD for Hr = 1 and 1.5 are 1.25 and 1.38, and maximum values of MIFMD for Br = 0.7 and 1.5 are 1.22 and 1.27. Table 2 shows maximum value of MIFMD and critical location for height and breadth ratios. It should be noted that higher and wider interfering buildings can cause higher mean wind loads when an interfering building is placed along (X/B, Y/B) = (1.5, 0 1.5).

1 2 3 4 5 60

1

2

3

4

5

6

X/B

Y/B

1.21.1

1.1

1 2 3 4 5 60

1

2

3

4

5

6

X/B

Y/B

1.3

1.2

1.21.1

1.1

(a) Hr = 1 (b) Hr = 1.5

Symmetry Symmetry

1 2 3 4 5 60

1

2

3

4

5

6

X/B

Y/B

1.21.1

1

1

1

1 2 3 4 5 60

1

2

3

4

5

6

X/B

Y/B

1.2

1.11.1

1.1

(c) Br = 0.7 (d) Br = 1.5

Fig. 3 Contour of mean interference factor for mean BBM responseTable 2 Mean interference factor and most critical location for height and breadth ratios

Height ratio(Hr)

MIFMDLocation(X/B,Y/B)

Breadth ratio(Br)

MIFMDLocation(X/B,Y/B)

0.5 1.08 (2, 1) 0.7 1.22 (1.5, 1)1 1.25 (1.5, 1) 1.5 1.27 (1.5, 1.5)

1.5 1.38 (1.5, 1)

3.2 Envelope interference factors for fluctuating BBM responses

Figs. 4 and 5 show contours of interference factors (EIFMD, EIFML and EIFMT) for maximum value of fluctuating BBM responses in along-wind, across-wind and torsional wind directions with height and breadth ratios of an interfering building for all wind directions. From Fig. 4, EIFMD, EIFML and EIFMT for Hr = 1.5 increased to 1.6, 1.4 and 1.4, respectively, but the critical locations of Hr = 1.5 was different with fluctuating BBM responses in along-wind, across-wind and torsional wind directions.

1 2 3 4 5 6 0

1

2

3

4

5

6

X/B

Y/B

1.5 1.4

1.31.2

1.4

1.2

1.3

1.2

1.4

1.5

1.6

1 2 3 4 5 6 0

1

2

3

4

5

6

X/B

Y/B

1.4

0.9

11.1

1.2

1.2

1.1

1.2

1.3

1.3

1.1

1 2 3 4 5 6 0

1

2

3

4

5

6

X/B

Y/B

1.41.1

1.41.2

1.2

1.3

1.2

1.1

1.1

1.21.31.1

1.2

1.2

(a) EIFMD (b) EIFML (c) EIFMT

SymmetrySymmetry

Fig. 4. Contours of envelope interference factor for fluctuating BBM response of Hr = 1.5

1 2 3 4 5 6 0

1

2

3

4

5

6

X/B

Y/B

1.3

1.21.2

1.1

1.1

1

1 2 3 4 5 6 0

1

2

3

4

5

6

X/B

Y/B

0.6

0.7

0.91

1.1 1.1

1

1 2 3 4 5 6 0

1

2

3

4

5

6

X/B

Y/B

0.9

1.1

1

1.21.1

1

1.1

(a) EIFMD (b) EIFML (c) EIFMT

Fig. 5. Contours of envelope interference factor for fluctuating BBM response of Br = 1.5

Furthermore, interfering building of Hr = 1.5 was caused higher fluctuating BBM responses and was influenced over X/B = 6. On the other hand, EIFMD and EIFMT for Br

=1.5 slightly increased as shown in Fig. 5(a) and (c). Notable observation was that there was almost no interference effect on fluctuating BBM responses in across-wind direction as shown in Fig. 5(b).

3.3 Design interference factors for extreme BBM responses

Figs. 6 and 7 show the design interference factors (DIFMD, DIFML and DIFMT) for the extreme BBM responses for height and breadth ratios. It should be noted that distribution of the design interference factors was highly correlated with those of Envelope interference factors. It means that wind-induced interference effects between two tall buildings may be subjected to fluctuating responses rather than the mean response on a tall building as shown in Figs. 4 ~ 7. Another notable observation was that the critical locations of interfering buildings with different height and breadth ratios were somewhat different and depend up on their heights and widths. These results will be useful in estimating approximate structural wind loads on tall buildings in preliminary design.

1 2 3 4 5 6 0

1

2

3

4

5

6

X/B

Y/B

1.51.4

1.31.3

1.2 1.21.1

1.3

1.2

1.1

1.2

1.1

1 2 3 4 5 6 0

1

2

3

4

5

6

X/B

Y/B

1

1.1

1.2

1.31.2

0.8

0.9

1 1.11.1

.

1 2 3 4 5 6 0

1

2

3

4

5

6

X/B

Y/B

1.21.2

1

1.1

11.2

10.9

1.1

1 1.11.3

11

1.2

(a) DIFMD (b) DIFML (c) DIFMT

Fig. 6. Contours of design interference factors for extreme BBM responses of Hr = 1.5

1 2 3 4 5 6 0

1

2

3

4

5

6

X/B

Y/B

1.3

1.2

1.2

1.1

1.1

1

1 2 3 4 5 6 0

1

2

3

4

5

6

X/B

Y/B

0.6

0.7

0.8

0.9

1

1.1

1

1

1 2 3 4 5 6 0

1

2

3

4

5

6

X/B

Y/B

0.9

1

1.11.21

(a) DIFMD (b) DIFML (c) DIFMT

Fig. 7. Contours of design interference factors for extreme BBM responses of Br = 1.54. CONCLUSIONS

The main aim of this study is to tackle the problem of wind-induced interference effects between two tall buildings in order to establish a generalized set of guidelines. Mean and dynamic interference factors between two buildings with height ratios and breath ratios were investigated by a series of deliberate wind tunnel tests. To reach some critical conclusions that could be used to improve a design code, design interference factor for extreme BBM responses was suggested for the assessment of wind-induced interference effects between two tall buildings.

ACKNOWLEDGMENTS

This study was financially supported by the Ministry of Land, Infrastructure and Transport (MOLIT) of the Korea government (code 12 Technology Innovation E09) and Korea Institute of Ocean Science and Technology (PE99421), and the Ministry of Education, Culture, Sports, Science and Technology, Japan, through the Joint Usage / Research Center of Wind Engineering, Tokyo Polytechnic University, 2013-2019. The authors gratefully acknowledge their support.

REFERENCES

Australian / New Zealand Standard (AS/NZS 1170.2: 2002), Part 2: Wind actions, Standards Australia/ Standards New Zealand.

A.C. Khanduri, T. Stathopoulos, C. Bédard (2000), “Generalization of wind-induced interference effects for two buildings”, Wind and Structures, 3(4), 255-266

A.G. Davenport (1967), “Gust loading factors”, J. Struct. Div. ASCE 93(3), pp. 11-34.A. Kareem, Y. Zhou (2003), “Gust loading factor – past, present and future, J. Wind

Eng. Ind. Aerodyn., 91, pp. 1301-1328.

W. Kim, Y. Tamura, A. Yoshida (2015), “Interference effects on aerodynamic wind forces between two buildings”, J. Wind Eng. Ind. Aerodyn., 147, pp. 186-201.

Z.N. Xie, M. Gu (2004), “Mean interference effects among tall buildings”, Engineering Structures 26 (2004) pp. 1173–1183.

Z.N. Xie, M. Gu (2007), “Simplified formulas for evaluation of wind-induced interference effects among three tall buildings”, J. Wind Eng. Ind. Aerodyn., 95, pp. 31-52.