Wind-Induced Responses and Wind Loads on a Super High-Rise Building with Various Cross-Sections and High Side Ratio—A Case Study

: With the development of construction technology and material, more and more super high-rise buildings will be constructed in the future. In a speciﬁc metropolitan area, super high-rise building with various cross-section and high side ratio have to been designed and constructed due to the size limitation of construction site. This kind of building is also very prone to wind excitations. In this research, wind tunnel tests for a practical case of this kind of building with surrounding buildings were carried out in atmospheric boundary wind tunnel. Equivalent static wind loads (ESWLs), wind-induced responses and wind load distribution on the building were analyzed. In particular, the base overturning moment along the axis with weak lateral stiffness were investigated for bearing capacity limit state design of the building. The results demonstrate that the maximum value of wind-induced base overturning moments and acceleration responses appears at 60 ◦ or 330 ◦ wind directions instead of the orthogonal wind direction, and the aerodynamic interference of surrounding buildings affects the wind pressure distribution on facades of the building. These results and conclusion may be helpful to wind-resistant design of super high-rise buildings with high side ratio.


Introduction
With the rapid development of construction technology and building materials, a growing number of super high-rise buildings have been completed or under construction.The website of Council on Tall Buildings and Urban Habitat (CTBUH, https://www.ctbuh.org/, accessed on 29 November 2022) reports that more than 1300 super high-rise buildings with a height above 200 m have been constructed around the world.On some specific building construction sites, especially in metropolitan cities, super high-rise buildings with various cross-section and high side ratio (ratio of the long side to the short side of the building plan) will be designed and constructed due to size limitation of construction site as shown in Figure 1.These super high-rise buildings, which have low damping and stiffness [1], are very sensitive to wind excitations because the natural frequencies of these buildings nearly correspond with dominant frequencies of wind loads.This may lead to large amplitude wind-induced vibration responses of these buildings [2,3].Therefore, wind-induced responses and wind loads on the super high-rise buildings with various cross-sections and high side ratio need be investigated by wind tunnel tests or numerical simulation method, e.g., method of Computational Fluid Dynamics (CFD).
Current research mainly focuses on the characteristic of wind pressure distribution on two dimensional cross-section of high-rise building and three dimensional high-rise building with maximum value of 5:1 side ratio.Mannini et al. [4] investigated pressure and forces on a stationary two-dimensional cylinder with rectangular 5:1 cross section in the wind tunnel and found that incoming turbulence affects the vortex-shedding mechanism of impinging shear-layer instability.Wang and Gu [5] carried out experimental investigation of Reynolds number effects on two-dimensional rectangular prisms with various side ratios, and their research revealed that the aerodynamic behavior to Reynolds number increases with larger side ratio.Gu et al. [6] further studied the effects of chamfered corners with 1:1~4:1 side ratios on aerodynamic forces of two-dimensional rectangular prisms.The results show that for a side ratio equal to 1:1 and 2:1 prism without chamfered corners, the separated flow does not reattach to the side surfaces.However, for a side ratio equal to 2 rectangular prism with chamfered corners and side ratios equal to 3 and 4 rectangular prisms, flow reattachment on the side surfaces was observed for all of these models.Lin et al. [7] found that side ratio has a profound effect on the mean drag force, but has small effects on root mean square (RMS) drag coefficients.Li et al. [8] proposed an simplified expression to evaluate torsional wind loads of tall buildings with various side ratio from 1:1 to 2:1 by wind tunnel tests.Their results showed that root mean square value of torque coefficients vary the side ratio, and the coefficients is the smallest when side ratio is equal to 1. Huang et al. [9] studied aerodynamic damping of tall buildings with various side ratio from 1:1 to around 3:1. Their results indicated that the aerodynamics damping of the rectangular building with side ratio being greater than 1 tend to be similar to those square building (side ratio equal to 1) in the along-wind direction when reduced wind speed (defined in the cite) less than or equal to 6. Ha [10] formulated an empirical equation of cross-wind fluctuating loads of tall buildings with different side ratios at range of 1:5 to 5:1 and found that the fluctuating force coefficient tends to increase as side ratio increase, and particularly the coefficient shows a gradual increase until side ratio reaches 2.0, but a rapid increase when side ratio exceeds 3.0.Zeng et al. [11] observed the spatial distribution of gust loads on a rectangular prism with 2:1 and 1:2 side ratio by wind tunnel tests and found that when side ratio is equal to 2, the reattachment occurs near downstream of the maximum value point of the fluctuating pressure on the lateral sides.Sanyal and Dalui [12] used numerical method to investigate wind loads and pressures on a Y plan shaped tall building with change in side ratios and drew a conclusion that the horizontal force and overturning moment coefficients increase with the increase in side ratios.Lin et al. [13] estimated crosswind load effects on tall buildings with different side ratios by a machine learning method.The research indicated that as the side ratio is more than critical value, the peak of crosswind force spectra gradually decreases due to the separation shear layer interacts with the trailing edge of bluff body.Lipecki [14] performed wind tunnel tests of two buildings with 2:1 and 4:1 side ratios, respectively, and revealed the effects of side ratios and boundary layer characteristics on mean wind pressure coefficients on these buildings.The result showed that the boundary layer has slightly stronger influence on the coefficient on windward walls than the change in side ratios and dimensions of models.Kim and Kanda [15] investigated the mechanism of aerodynamic force reduction in tall buildings though tapering and set-back cross-section in wind tunnel.They compared aerodynamic forces on tall buildings with 1:1 side ratio with results on building with tampered or set-back cross-section along height.It is concluded that: (1) Tapering or set-back of cross-section can reduce the mean drag force and fluctuating.(2) Reduction ratio increased as tapering ratio of cross-section increases.(3) The set-backed model was more effective to reduce the fluctuating lift force than the tapered model with identical surface area.Liu et al. [16] explored mean, fluctuating and peak wall pressure coefficient distributions on rectangular cross-section high-rise buildings with 0.11~9 side ratios.The results showed that side ratio has significant effects on pressure coefficients on the leeward and side walls of the buildings with side ratios being less than about 4. The largest mean base shear coefficient occurs on the building with side ratio of about 0.67, but decreasing for larger or smaller side ratios.
The most recent studies focus on effects of various cross-section and side ratios (being less than 4:1) on wind pressure distribution on windward, leeward and sideward walls of single high-rise buildings and reveal the mechanism of the effects.A few studies discuss wind-induced responses and ESWLs of super high-rise buildings with various cross-section, which has a maximum value of 4:1 side ratio.In addition, as shown in Figure 1, most super high-rise buildings are always surrounded by other buildings in practical project.Aerodynamic forces on the investigated high-rise building are interfered by surrounding buildings, which further affects the wind-induced responses of the investigated high-rise building.This research extends previous studies to wind loads, wind-induced responses and ESWLs of a surrounded super high-rise building with various cross-section and high side ratio and includes in the following aspects: (1) Wind tunnel tests of a super highrise building with 4.3:1 side ratio as a practical project are carried out in wind tunnel.Current research mainly focuses on the characteristic of wind pressure distribution on two dimensional cross-section of high-rise building and three dimensional high-rise building with maximum value of 5:1 side ratio.Mannini et al. [4] investigated pressure and forces on a stationary two-dimensional cylinder with rectangular 5:1 cross section in the wind tunnel and found that incoming turbulence affects the vortex-shedding mechanism of impinging shear-layer instability.Wang and Gu [5] carried out experimental investigation of Reynolds number effects on two-dimensional rectangular prisms with various side ratios, and their research revealed that the aerodynamic behavior to Reynolds number increases with larger side ratio.Gu et al. [6] further studied the effects of chamfered corners with 1:1~4:1 side ratios on aerodynamic forces of two-dimensional rectangular prisms.The results show that for a side ratio equal to 1:1 and 2:1 prism without chamfered corners, the separated flow does not reattach to the side surfaces.However, for a side ratio equal to 2 rectangular prism with chamfered corners and side ratios equal to 3 and 4 rectangular prisms, flow reattachment on the side surfaces was observed for all of these models.Lin et al. [7] found that side ratio has a profound effect on the mean drag force, but has small effects on root mean square (RMS) drag coefficients.Li et al. [8] proposed an simplified expression to evaluate torsional wind loads of tall buildings with various side ratio from 1:1 to 2:1 by wind tunnel tests.Their results showed that root mean square value of torque coefficients vary the side ratio, and the coefficients is the smallest when side ratio is equal to 1. Huang et al. [9] studied aerodynamic damping of tall buildings with various side ratio from 1:1 to around 3:1. Their results indicated that the aerodynamics damping of the rectangular building with side ratio being greater than 1 tend to be similar to those square building (side ratio equal to 1) in the along-wind direction when reduced wind speed (defined in the cite) less than or equal to 6. Ha [10] formulated an empirical equation of cross-wind fluctuating loads of tall buildings with different side ratios at range of 1:5 to 5:1 and found that the fluctuating force coefficient tends to increase as side ratio increase, and particularly the coefficient shows a gradual increase until side ratio reaches 2.0, but a rapid increase when side ratio exceeds 3.0.Zeng et al. [11] observed the spatial distribution of gust loads on a rectangular prism with 2:1 and 1:2 side ratio by wind tunnel tests and found that when side ratio is equal to 2, the reattachment occurs near downstream of the maximum value point of the fluctuating pressure on the lateral sides.Sanyal and Dalui [12] used numerical method to investigate wind loads and pressures on a Y plan shaped tall building with change in side ratios and drew a conclusion

Wind Tunnel Tests of a Super High-Rise Building with a High Side Ratio
The super high-rise building with various cross-section, located in a China coastal city, has 32 stories, with a height of 132.4 m, as shown in Figure 2a,b.The cross-section size of the lower part of the building is shown in Figure 3; it indicates that the cross section has 4.3:1 side ratio.For the sake of analyzing wind pressure distribution characteristics, the four façades on the buildings are defined as façade A, B, C and D in Figure 3.The mass and lateral distributions along height of the building are important factors for estimating structural dynamic characteristics i.e., natural frequencies and vibration modes.The mass including dead and live loads of each floor are obtained from the finite element model and their distribution variation with height has been shown in Figure 4a.Likewise, the lateral stiffness of each floor also can be extracted from the finite element model.Due to lateral stiffness along the y-axis being smaller than that along the x-axis, the wind-induced responses along the y-axis are probably larger than that of the x-axis, so that only the lateral stiffness along y-axis is presented in Figure 4b.The mass and lateral stiffness of each floor can form the mass matrix and the stiffness matrix of the building, then the dynamic characteristics of the high-rise building such as natural frequencies can be estimated.The first natural frequency along y-axis of the building is 0.26 Hz.
The synchronous multi-point pressure wind tunnel tests of the high-rise building were carried out in the boundary layer wind tunnel laboratory of Shantou University.Length, width and height of the main test section of the wind tunnel is 20 m, 3 m and 2 m, respectively [17].The geometric scale ratio of the model to prototype of the building is set as 1:200.The reference wind pressure of the building location is 1.13 kPa (wind speed of 42.5 m/s) corresponding to 50-year return period.The wind speed of wind tunnel tests is set as 10.5 m/s, and the ratio of wind speed for wind tunnel tests to prototype is 1:4.0.The time ratio of approximately 1:56 is derived by geometric scale and wind speed ratios.Electronic scanning valves made by Scanivalve Inc. (Liberty Lake, WA, USA) are used to measure fluctuating pressure on the building model.A total of 13 measure layers (419 measure taps) are distributed on the surface along the height of the building.The layer L of measure taps are arranged as shown in Figure 5.The time histories of pressure data for every pressure tap were sampled at a frequency of 312.5 Hz, with a total sampling duration of 65 s.The test model is mounted on a 2.4 m diameter turn-table in the test section of the wind tunnel to simulate wind directions.Thirty-six wind directions are considered at an interval of 10 • during the tests, and wind direction β ranges from 0 • to 350 • along the counterclockwise direction as shown in Figures 2a and 3.According to Load Code for the Design of Building Structures (GB50009-2012) [18], D category of urban terrain is simulated by the combination of spires and cubic elements in front of the test section as shown in Figure 6a.For the D category terrain, the profiles of mean wind velocity and turbulence intensity are presented in Figure 6b.In Figure 6b, α equal to 0.3 is the value of power-law exponent for the mean wind velocity profile.H and U represent any specific height and the corresponding wind speed, respectively.H r and U r are the reference height and corresponding wind speed, respectively.I U represents the turbulence intensity.The synchronous multi-point pressure wind tunnel tests of the high-rise building were carried out in the boundary layer wind tunnel laboratory of Shantou University Length, width and height of the main test section of the wind tunnel is 20 m, 3 m and 2 m respectively [17].The geometric scale ratio of the model to prototype of the building is se as 1:200.The reference wind pressure of the building location is 1.13 kPa (wind speed of 42.5 m/s) corresponding to 50-year return period.The wind speed of wind tunnel tests is set as 10.5 m/s, and the ratio of wind speed for wind tunnel tests to prototype is 1:4.0.The time ratio of approximately 1:56 is derived by geometric scale and wind speed ratios.Elec tronic scanning valves made by Scanivalve Inc. (Liberty Lake, WA, USA) are used to measure fluctuating pressure on the building model.A total of 13 measure layers (419 measure taps) are distributed on the surface along the height of the building.The layer L of measure taps are arranged as shown in Figure 5.The time histories of pressure data for every pressure tap were sampled at a frequency of 312.5 Hz, with a total sampling duration of 65 s.The test model is mounted on a 2.4 m diameter turn-table in the test section of the wind tunnel to simulate wind directions.Thirty-six wind directions are considered at an interval of 10° during the tests, and wind direction β ranges from 0° to 350° along the counterclockwise direction as shown in Figures 2a and 3.According to Load Code for the Design of Building Structures (GB50009-2012) [18], D category of urban terrain is simulated by the combination of spires and cubic elements in front of the test section as shown in Figure 6a.For the D category terrain, the profiles of mean wind velocity and turbulence intensity are presented in Figure 6b.In Figure 6b, α equal to 0.3 is the value of power-law exponent for the mean wind velocity profile.H and U represent any specific height and the corresponding wind speed, respectively.Hr and Ur are the reference height and corre sponding wind speed, respectively.IU represents the turbulence intensity.The synchronous multi-point pressure wind tunnel tests of the high-rise building were carried out in the boundary layer wind tunnel laboratory of Shantou University.Length, width and height of the main test section of the wind tunnel is 20 m, 3 m and 2 m, respectively [17].The geometric scale ratio of the model to prototype of the building is set as 1:200.The reference wind pressure of the building location is 1.13 kPa (wind speed of 42.5 m/s) corresponding to 50-year return period.The wind speed of wind tunnel tests is set as 10.5 m/s, and the ratio of wind speed for wind tunnel tests to prototype is 1:4.0.The time ratio of approximately 1:56 is derived by geometric scale and wind speed ratios.Electronic scanning valves made by Scanivalve Inc. (Liberty Lake, WA, USA) are used to measure fluctuating pressure on the building model.A total of 13 measure layers (419 measure taps) are distributed on the surface along the height of the building.The layer L of measure taps are arranged as shown in Figure 5.The time histories of pressure data for every pressure tap were sampled at a frequency of 312.5 Hz, with a total sampling duration of 65 s.The test model is mounted on a 2.4 m diameter turn-table in the test section of the wind tunnel to simulate wind directions.Thirty-six wind directions are considered at an interval of 10° during the tests, and wind direction β ranges from 0° to 350° along the counterclockwise direction as shown in Figures 2a and 3.According to Load Code for the Design of Building Structures (GB50009-2012) [18], D category of urban terrain is simulated by the combination of spires and cubic elements in front of the test section as shown in Figure 6a.For the D category terrain, the profiles of mean wind velocity and turbulence intensity are presented in Figure 6b.In Figure 6b, α equal to 0.3 is the value of power-law exponent for the mean wind velocity profile.H and U represent any specific height and the corresponding wind speed, respectively.Hr and Ur are the reference height and corresponding wind speed, respectively.IU represents the turbulence intensity.

Theory on Wind-Induced Response of High-Rise Building
The differential equation of the building under wind excitations can be written as [19] M ..
where M, C and K are mass, damping and stiffness matrix of the building, respectively.y(t) and P(t) are the dynamic displacement and the fluctuating wind load vector, respectively.The elastic restoring force can be expressed as where Φ and q(t) are the modal matrix and the modal coordinate vector, respectively.Λ is the frequency matrix, which is a diagonal matrix.The ith diagonal element in frequency matrix is square of the ith natural frequency ω i 2 .The arbitrary responses r(t) can be calculated by the restoring forces as where A is the matrix of influence coefficients.The covariance matrix C r of the response vector, the covariance matrix C rp between the response vector and the load vector can be respectively expressed as where C p is the covariance matrix of the elastic restoring force p(t), which can be written as The root mean square of the ith response r i (t) is where A i is the ith row vector of A. Thus, the maximum responses caused by fluctuating wind is where g is the peak factor, p f,eq is the vector of ESWL corresponding to the maximum responses.
Substitute Equations ( 2) and ( 6) into Equation ( 9), ESWLs corresponding to the maximum responses caused by the fluctuating wind can be derived as follows: where C q is the covariance matrix of the modal response.It can be calculated by the modal response power spectrum matrix S q (n): where S q (n) and S P (n) represent power spectral density matrix of modal responses and fluctuating wind excitations, respectively.H(n) and H * (n) are the frequency responses function matrix and its conjugate matrix, respectively.The peak factor g can be estimated by the expression presented by Davenport [20]: where T w is the duration of the selected observation sample and η is the effective structural response frequency, which can be taken equal to the first natural frequency of the structure in Hz [21].Consequently, the total ESWLs on each floor of the structure p ESWL is equal to the sum of the mean wind load and the ESWLs caused by the fluctuating wind:

ESWLs of the High-Rise Building
As mentioned in the Section 2, the lateral stiffness of the building along y-axis is less than that along x-axis; the wind-induced responses and ESWLs along y-axis are highly concerned by structural engineers during bearing capacity limit state design of the building.The displacement response of the top floor along y-axis is taken as the equivalent objective to estimate ESWLs and overturning moments of the building.The ESWLs along the y-axis at each wind direction can be calculated based on wind tunnel datum and the theory in Section 3.1.The overturning moments around x-axis are further evaluated by integral calculus of ESWLs and height of the building.The Figure 7a,b show the variation of overturning moments M x with different wind directions corresponding to 100-and 50-year return period, respectively.The mean, maximum and minimum values of the overturning moment are corresponding to equivalent objectives of mean, maximum and minimum top displacement responses, respectively, along the y-axis of the building.It is evident that the mean values of the overturning moment M x are positive at these wind directions from 0 • to 180 • , and negative at other wind directions.The mean value of M x reach to zero at the two wind directions of 0 • and 180 • .The two directions of the wind flow are perpendicular to the direction of the x-axis; therefore, the energy of vortex shedding for the building with high side ratio was reduced due to the shear-layer-edge interaction so that the wind loads acting on the x-axis direction are small and cancel each other out partly [7].The absolute values of mean M x at these wind directions from 0 • to 180 • are not the same as that at the wind directions of 180 • ~360 • .It is attributed to aerodynamic interference of surrounding buildings as shown in Figure 6a. Figure 7 indicates that M x reaches to the maximum value 1439.2MN•m at wind direction of 60 • , and the minimum value −1388.6MN•m appears at wind direction of 330 • .Structural engineers usually concern these worst working cases, e.g., 60 • and 330 • wind directions during wind-resistant design of the super high-rise buildings.Hence, ESWLs at the two wind directions are presented as shown in Figure 8.
Figure 8a,b show ESWLs along the y-axis for 100-year and 50-year return period at wind directions of 60 • and 330 • , respectively.The distribution of ESWLs at wind direction of 60 • in Figure 8a indicates that absolute values of ESWLs exceed 600 kN at the height ranging from 15 m to 120 m for the 100-year return period.However, at the top and bottom of the building, absolute values of ESWL are less than 400 kN.This is attributed to the wind speed being very low due to these factors of mean wind speed profile and aerodynamic interference of the surrounding buildings at the bottom, and the mass of the building has lower weight at the top than that of other height.The absolute ESWLs at wind direction of 330 • in Figure 8b are less than that at wind direction of 60 • in Figure 8a.It may be ascribed to the shielding effects of the surrounding building I (blue color building in Figure 6a), which is located at the front of the investigated building at wind direction of 330 • and is taller than the investigated building.
wind speed being very low due to these factors of mean wind speed profile and aerodynamic interference of the surrounding buildings at the bottom, and the mass of the building has lower weight at the top than that of other height.The absolute ESWLs at wind direction of 330° in Figure 8b are less than that at wind direction of 60° in Figure 8a.It may be ascribed to the shielding effects of the surrounding building I (blue color building in Figure 6a), which is located at the front of the investigated building at wind direction of 330° and is taller than the investigated building.

Wind-Induced Acceleration Responses of the High-Rise Building
Building occupant comfort serviceability criteria is assessed by wind-induced acceleration responses.According to the Equation ( 1) and wind tunnel test datum, wind-induced acceleration responses are estimated to evaluate occupant comfort of the super high-rise building.Figure 9 shows the variation of peak wind-induced acceleration responses of the top floor with wind directions corresponding to 10-year return period, and limitation values of 15.3 milli-g and 19.3 milli-g in standard and code (JGJ3-2010 and ISO wind speed being very low due to these factors of mean wind speed profile and aerodynamic interference of the surrounding buildings at the bottom, and the mass of the building has lower weight at the top than that of other height.The absolute ESWLs at wind direction of 330° in Figure 8b are less than that at wind direction of 60° in Figure 8a.It may be ascribed to the shielding effects of the surrounding building I (blue color building in Figure 6a), which is located at the front of the investigated building at wind direction of 330° and is taller than the investigated building.

Wind-Induced Acceleration Responses of the High-Rise Building
Building occupant comfort serviceability criteria is assessed by wind-induced acceleration responses.According to the Equation ( 1) and wind tunnel test datum, wind-induced acceleration responses are estimated to evaluate occupant comfort of the super high-rise building.Figure 9 shows the variation of peak wind-induced acceleration responses of the top floor with wind directions corresponding to 10-year return period, and limitation values of 15.3 milli-g and 19.3 milli-g in standard and code (JGJ3-2010 and ISO

Wind-Induced Acceleration Responses of the High-Rise Building
Building occupant comfort serviceability criteria is assessed by wind-induced acceleration responses.According to the Equation ( 1) and wind tunnel test datum, wind-induced acceleration responses are estimated to evaluate occupant comfort of the super high-rise building.Figure 9 shows the variation of peak wind-induced acceleration responses of the top floor with wind directions corresponding to 10-year return period, and limitation values of 15.3 milli-g and 19.3 milli-g in standard and code (JGJ3-2010 and ISO 10137, respectively) [22,23].It can be observed that the maximum value of peak acceleration is 21.3 milli-g, and it occurs at wind direction of 330 • .Peak wind-induced acceleration responses at some wind directions, such as 330 • and 340 • exceed the limitation value to satisfy comfort requirements in Technical Code for Concrete Structure of High-rise Buildings (JGJ3-2010) [22].Therefore, the reduction in reference wind pressure at some wind directions are considered on the basis of weather data from meteorological station of building location to decrease wind-induced acceleration responses of the building.The peak acceleration considering the basis of weather data in Figure 9 can be obtained, which has the maximum value of 14.9 milli-g corresponding to 330 • , less than the limitation value of 15.3 milli-g in JGJ3-2010 for the buildings used as apartments.The code of ISO 10137 [23] uses the root mean square (RMS) of acceleration as the comfort limit standard corresponding to 5-year return period.The prescribed values in the code of ISO need to be converted in order to obtain the peak acceleration limitation corresponding to 10-year return period.As a result, the prescribed value in ISO 10137 is equal to 19.3 milli-g, which has been drawn in Figure 9.
responses at some wind directions, such as 330° and 340° exceed the limitation value to satisfy comfort requirements in Technical Code for Concrete Structure of High-rise Buildings (JGJ3-2010) [22].Therefore, the reduction in reference wind pressure at some wind directions are considered on the basis of weather data from meteorological station of building location to decrease wind-induced acceleration responses of the building.The peak acceleration considering the basis of weather data in Figure 9 can be obtained, which has the maximum value of 14.9 milli-g corresponding to 330°, less than the limitation value of 15.3 milli-g in JGJ3-2010 for the buildings used as apartments.The code of ISO 10137 [23] uses the root mean square (RMS) of acceleration as the comfort limit standard corresponding to 5-year return period.The prescribed values in the code of ISO need to be converted in order to obtain the peak acceleration limitation corresponding to 10-year return period.As a result, the prescribed value in ISO 10137 is equal to 19.3 milli-g, which has been drawn in Figure 9.

Mean wind Pressure Distribution on the High-Rise Building
The time history of the wind pressure coefficient of the ith measuring tap on the surface of the model can be obtained from the wind tunnel test mentioned in Section 2: where pi(t) is the transient wind pressure measured from the ith measuring tap.p0 and p∞ are the total pressure and static pressure measured at the reference height, respectively.Mean values of wind pressure coefficients are respectively written as where T represents the period of sample.Mean wind pressure can be calculated by the mean values of wind pressure coefficients Cpi,mean

Wind Pressure on the Building Mean wind Pressure Distribution on the High-Rise Building
The time history of the wind pressure coefficient of the ith measuring tap on the surface of the model can be obtained from the wind tunnel test mentioned in Section 2: where p i (t) is the transient wind pressure measured from the ith measuring tap.p 0 and p ∞ are the total pressure and static pressure measured at the reference height, respectively.Mean values of wind pressure coefficients are respectively written as where T represents the period of sample.Mean wind pressure can be calculated by the mean values of wind pressure coefficients C pi,mean where ρ is the density of air and V pro,mean is the mean wind speed at the reference height of the prototype building.Mean wind pressure on the surface of prototype building can be calculated by the corresponding wind pressure coefficients.Figure 10 shows the location of surrounding buildings.The variation of mean wind pressure (MWP) of some typical pressure measurement taps on the Lth pressure measurement layer (as shown in Figure 5) with 36 wind directions is shown in Figure 11. Figure 11 indicates that the MWP of the pressure measurement taps of L4 and L5 are negative, which correspond to suction pressures, at all of 36 wind directions, and approach to the maximum value of suction pressure −1.2 kPa around 60 • wind direction.L4 and L5 at 0 • , 180 • and 90 • wind directions are, respectively, on the side and leeward surface.MWP of L4 and L5 at the above three wind directions is suction pressure due to effects of vortex shedding and wake flow.L4 and L5 at 270 • wind direction are on the windward surface.However, MWP of the two pressure taps are still suction pressure.This is attributed to aerodynamic interference of the surrounding building I (as shown in Figure 10), and the windward surface of the investigated building is located in the wake flow of the surrounding building.The authors of [24] drew the same conclusion that windward wall of the investigated building appears negative pressure when the upstream surrounding high-rise building is located in a close proximity of the investigated building.Figure 11b-d show pressure variation of L11, L12, L19, L20, L24 and L25 taps with wind directions.As shown in Figure 11b-d, positive pressure of the six pressure measurement taps occurs around 0 • , 90 • and 180 • wind direction, respectively, when these taps are on the windward surface of the building.
urement taps on the L th pressure measurement layer (as shown in Figure 5) with 36 wind directions is shown in Figure 11. Figure 11 indicates that the MWP of the pressure meas urement taps of L4 and L5 are negative, which correspond to suction pressures, at all o 36 wind directions, and approach to the maximum value of suction pressure −1.2 kPa around 60° wind direction.L4 and L5 at 0°, 180° and 90° wind directions are, respectively on the side and leeward surface.MWP of L4 and L5 at the above three wind directions i suction pressure due to effects of vortex shedding and wake flow.L4 and L5 at 270° wind direction are on the windward surface.However, MWP of the two pressure taps are stil suction pressure.This is attributed to aerodynamic interference of the surrounding build ing I (as shown in Figure 10), and the windward surface of the investigated building i located in the wake flow of the surrounding building.The authors of [24] drew the same conclusion that windward wall of the investigated building appears negative pressure when the upstream surrounding high-rise building is located in a close proximity of the investigated building.Figure 11b-d show pressure variation of L11, L12, L19, L20, L24 and L25 taps with wind directions.As shown in Figure 11b-d, positive pressure of the six pressure measurement taps occurs around 0°, 90° and 180° wind direction, respectively when these taps are on the windward surface of the building.In order to study the distribution of mean wind pressure on the cross section of the high-rise building, Figure 12a-d present variation of mean pressure distribution on the layer L with wind directions of 0 • , 90 • , 180 • and 270 • , respectively.Figure 12a-c indicate that mean wind pressure on the windward line (red line) is positive value at 0 • , 90 • and 180 • wind direction, whereas negative pressure appears on the windward line owing to the aerodynamic interference of surrounding building I at 270 • wind direction as shown in Figure 12d.Figure 12a-d show the absolute value of mean wind pressure on the leading edge of side line is larger than that on the rear side owing to flow separation on the leading edge.For example, the suction pressure along the side line decrease from −1.16 to −0.55 kPa in Figure 12a at 0 • wind direction.It is worth noting that unlike the case of a rectangular building, whose side surface is subjected to negative pressure, the side line (orange line) on the corner exposes to negative pressure in Figure 12a.The same phenomenon appears in the reference [25,26].This phenomenon is attributed to the flow of wind after striking the red surface with 0.38 kPa pressure is reversed and leads to the positive pressure of 0.17 and 0.32 kPa on the rear part of the orange line.Figure 12a-d present that the negative wind pressure on the leeward line (the opposite side of red line) are approximate uniform, whereas the absolute values of suction pressure around −0.4 and −0.3 kPa on leeward line for high side ratio (as shown in Figure 12a,c) is smaller than that of the wind pressure around −0.8 and −0.7 kPa on low side ratio (as shown in Figure 12b,d).This may be attributed to the effects of vortex shedding and reattachment on wake flow.The distribution pattern of the wind pressure on the leeward line is consistent with result of single building with different side ratios in the reference [16].In order to study the distribution of mean wind pressure on the cross section of the high-rise building, Figure 12a-d present variation of mean pressure distribution on the layer L with wind directions of 0°, 90°, 180° and 270°, respectively.Figure 12a-c indicate that mean wind pressure on the windward line (red line) is positive value at 0°, 90° and 180° wind direction, whereas negative pressure appears on the windward line owing to the aerodynamic interference of surrounding building I at 270° wind direction as shown in Figure 12d.Figure 12a-d show the absolute value of mean wind pressure on the leading edge of side line is larger than that on the rear side owing to flow separation on the leading edge.For example, the suction pressure along the side line decrease from −1.16 to −0.55 kPa in Figure 12a at 0° wind direction.It is worth noting that unlike the case of a rectangular building, whose side surface is subjected to negative pressure, the side line (orange line) on the corner exposes to negative pressure in Figure 12a.The same phenomenon appears in the reference [25,26].This phenomenon is attributed to the flow of wind after striking the red surface with 0.38 kPa pressure is reversed and leads to the positive pressure of 0.17 and 0.32 kPa on the rear part of the orange line.Figure 12a-d present that the negative wind pressure on the leeward line (the opposite side of red line) are approximate uniform, whereas the absolute values of suction pressure around −0.4 and −0.3 kPa on leeward line for high side ratio (as shown in Figure 12a,c) is smaller than that of the wind pressure around −0.8 and −0.7 kPa on low side ratio (as shown in Figure 12b,d).This may be attributed to the effects of vortex shedding and reattachment on wake flow.The distribution pattern of the wind pressure on the leeward line is consistent with result of single building with different side ratios in the reference [16].To investigate the distribution characteristics of mean wind pressure along height of the high-rise building, Figures 13 and 14 give the contour map of the distribution of mean wind pressure on the facade of the building at 90° and 270° wind direction, respectively.Figure 13a indicates that the right part of the facade A is subjected to negative wind pressure, and the absolute value of the negative wind pressure approach to the maximum value at upside of the building.The top right corner on the façade A is exposed to positive wind pressure owing to the façade being not parallel to incoming wind flow.To investigate the distribution characteristics of mean wind pressure along height of the high-rise building, Figures 13 and 14 give the contour map of the distribution of mean wind pressure on the facade of the building at 90 • and 270 • wind direction, respectively.Figure 13a indicates that the right part of the facade A is subjected to negative wind pressure, and the absolute value of the negative wind pressure approach to the maximum value at upside of the building.The top right corner on the façade A is exposed to positive wind pressure owing to the façade being not parallel to incoming wind flow.Figure 13b shows that most of the windward facade expose to positive mean wind pressure, and the biggest value of mean wind pressure occurs on the upper part of the wind ward facade.Due to the aerodynamic interference effects of surrounding building II on the investigated building, the lower right part of the windward surface of the building is subjected to negative wind pressure.The other side's façade, as shown in Figure 13c, and leeward façade, as shown in Figure 13d, are immersed in negative wind pressure.
(c) (d) To investigate the distribution characteristics of mean wind pressure along height of the high-rise building, Figures 13 and 14 give the contour map of the distribution of mean wind pressure on the facade of the building at 90° and 270° wind direction, respectively.Figure 13a indicates that the right part of the facade A is subjected to negative wind pressure, and the absolute value of the negative wind pressure approach to the maximum value at upside of the building.The top right corner on the façade A is exposed to positive wind pressure owing to the façade being not parallel to incoming wind flow.Figure 13b shows that most of the windward facade expose to positive mean wind pressure, and the biggest value of mean wind pressure occurs on the upper part of the wind ward facade.Due to the aerodynamic interference effects of surrounding building II on the investigated building, the lower right part of the windward surface of the building is subjected to negative wind pressure.The other side's façade, as shown in Figure 13c, and leeward façade, as shown in Figure 13d, are immersed in negative wind pressure.

Conclusions
In this paper, the wind pressure on surface of the high-rise building with various cross-section and high side ratio are measured through wind tunnel tests.Based on data of wind tunnel tests and theory of structural dynamics, the ESWLs and the base overturning moment Mx are estimated, and the peak wind-induced acceleration responses is evaluated along each wind direction.The mean wind pressure distribution on four facades of the building is investigated and compared with results of single high-rise building with rectangular-plan.The main conclusions are as follows.
(1) For a super high-rise building with high side ratio, the base overturning moment along the axis with weak lateral stiffness are concerned by structural engineering for bearing capacity limit state design of the building.Unlike a single high-rise building, absolute values of wind-induced base overturning moments Mx is not symmetric with respect to 180° wind directions owing to aerodynamic interference of surrounding buildings.The maximum value of Mx appears at 60° and 330° wind directions instead of 0° and 90° wind directions; (2) The peak wind-induced acceleration response occurs at 330° wind direction, and is decreased after considering the reduction in reference wind pressure on the basis of weather data around 330° wind direction; (3) For mean wind pressure distribution on the high-rise building with various crosssection and high side ratio, the characteristics of wind pressure on some facades are consistent with previous reference at specific wind direction, for example, wind pressure on some facades in Figure 12.The surrounding buildings have an important impact on the

Conclusions
In this paper, the wind pressure on the surface of the high-rise building with various cross-section and high side ratio are measured through wind tunnel tests.Based on data of wind tunnel tests and theory of structural dynamics, the ESWLs and the base overturning moment M x are estimated, and the peak wind-induced acceleration responses is evaluated along each wind direction.The mean wind pressure distribution on four facades of the building is investigated and compared with results of single high-rise building with rectangular-plan.The main conclusions are as follows.
(1) For a super high-rise building with high side ratio, the base overturning moment along the axis with weak lateral stiffness are concerned by structural engineering for bearing capacity limit state design of the building.Unlike a single high-rise building, absolute values of wind-induced base overturning moments M x is not symmetric with respect to 180 • wind directions owing to aerodynamic interference of surrounding buildings.The maximum value of M x appears at 60 • and 330 • wind directions instead of 0 • and 90 • wind directions; (2) The peak wind-induced acceleration response occurs at 330 • wind direction, and is decreased after considering the reduction in reference wind pressure on the basis of weather data around 330 • wind direction;

Figure 1 .
Figure 1.Size limitation of the construction site.

Figure 2 .
Figure 2. Schematic diagram of the building: (a) the axonometric sketch of the building; (b) t dimensions of the elevation along y-axis and z-axis.

Figure 3 .
Figure 3. Size of the cross-section of the building.

Figure 2 .Figure 2 .
Figure 2. Schematic diagram of the building: (a) the axonometric sketch of the building; (b) the main dimensions of the elevation along y-axis and z-axis.

Figure 3 .
Figure 3. Size of the cross-section of the building.

Figure 3 .
Figure 3. Size of the cross-section of the building.

Figure 3 .
Figure 3. Size of the cross-section of the building.

Figure 4 .
Figure 4. Mass and lateral stiffness distribution along height of the building: (a) mass; (b) lateral stiffness along the y-axis.Figure 4. Mass and lateral stiffness distribution along height of the building: (a) mass; (b) lateral stiffness along the y-axis.

Figure 4 .
Figure 4. Mass and lateral stiffness distribution along height of the building: (a) mass; (b) lateral stiffness along the y-axis.Figure 4. Mass and lateral stiffness distribution along height of the building: (a) mass; (b) lateral stiffness along the y-axis.

Figure 5 .Figure 5 .
Figure 5.The measuring taps on the layer L.

Figure 5 .Figure 6 .
Figure 5.The measuring taps on the layer L.

Figure 7 .
Figure 7.The overturning moments around the x-axis corresponding to: (a) 100-year return period; (b) 50-year return period.

Figure 9 .
Figure 9. Variation of peak acceleration on the top floor with wind directions ranging from 0° to 350°.

Figure 9 .
Figure 9. Variation of peak acceleration on the top floor with wind directions ranging from 0 • to 350 • .

Figure 11 .
Figure 11.Mean wind pressure (MWP) of the measuring points on the layer L at the wind directions from 0° to 350°: (a) L4 and L5 on facade D; (b) L11 and L12 on facade A; (c) L19 and L20 on facade B; (d) L24 and L25 on facade C.

Figure 11 .Figure 12 .
Figure 11.Mean wind pressure (MWP) of the measuring points on the layer L at the wind directions from 0 • to 350 • : (a) L4 and L5 on facade D; (b) L11 and L12 on facade A; (c) L19 and L20 on facade B; (d) L24 and L25 on facade C. Buildings 2023, 13, x FOR PEER REVIEW 12 of 15

Figure
Figure 14a-d respectively present mean wind pressure on the façade A~D at 270° wind direction.Both the side façade A in Figure 14a and leeward façade B in Figure 14b are subjected to negative wind pressure.A large proportion of area on the other side façade C in Figure 14c and the windward façade D in Figure 14d are exposed to negative pressure, and positive wind pressure appears on the edge of the two facades due to the aerodynamic interference of surrounding building I at 270° wind direction.

Figure
Figure 14a-d respectively present mean wind pressure on the façade A~D at 270 • wind direction.Both the side façade A in Figure 14a and leeward façade B in Figure 14b are subjected to negative wind pressure.A large proportion of area on the other side façade C in Figure 14c and the windward façade D in Figure 14d are exposed to negative pressure, and positive wind pressure appears on the edge of the two facades due to the aerodynamic interference of surrounding building I at 270 • wind direction.

FigureFigure 14 .
Figure 14a-d respectively present mean wind pressure on the façade A~D at 270° wind direction.Both the side façade A in Figure 14a and leeward façade B in Figure 14b are subjected to negative wind pressure.A large proportion of area on the other side façade C in Figure 14c and the windward façade D in Figure 14d are exposed to negative pressure, and positive wind pressure appears on the edge of the two facades due to the aerodynamic interference of surrounding building I at 270° wind direction.