Performance-Based Wind Design of Tall Buildings Considering Corner Modification and Inelastic Behavior

Alinejad, Hamidreza; Ahn, Byeonguk; Kang, Thomas H.-K.

doi:10.1061/JSENDH.STENG-13100

Open access

Case Studies

May 14, 2024

Performance-Based Wind Design of Tall Buildings Considering Corner Modification and Inelastic Behavior

Authors: Hamidreza Alinejad https://orcid.org/0000-0002-4616-2131 [email protected], Byeonguk Ahn https://orcid.org/0000-0003-2365-1669 [email protected], and Thomas H.-K. Kang, M.ASCE [email protected]Author Affiliations

Publication: Journal of Structural Engineering

Volume 150, Issue 7

https://doi.org/10.1061/JSENDH.STENG-13100

PDF

Abstract

Design for wind-induced response is one of the critical factors for the design of tall buildings. Aerodynamic treatments such as corner modifications are among the traditional passive solutions for the reduction of wind-induced effects. Another practical solution is the permission of inelastic behavior under extreme wind load to reduce the resonant component of wind load. This approach has received more attention recently in performance-based wind design (PBWD) as an alternative approach for wind design. Moreover, inelastic wind design using a proper wind load reduction factor can significantly facilitate the initial design and makes PBWD more practical. In this study, the efficiency of aerodynamic modification and permission of inelastic behavior in the reduction of wind load and material cost was compared in detail. Three case study buildings with a square-shaped plan and 160 m height were considered, where one building has sharp corners and the others have chamfered and recessed corners as aerodynamic treatment. RC core walls with perimeter moment frames were considered as the structural system of all buildings, and they were designed based on wind load reduction factors of 1 (elastic design) and 2 (inelastic design). Then, the performance of buildings was evaluated according to ASCE prestandard procedure by performing linear and nonlinear time-history analysis using wind load obtained from wind tunnel tests. The results showed that inelastic wind design can be more effective than corner modification in the reduction of wind load; however, the design reinforcement ratio is less and more similar due to minimum requirement. Performance assessment of the building confirmed the adequacy of designed buildings and showed that the inelastic system has acceptable behavior, and there is a large margin of safety against failure for the inelastic building.

Introduction

Design of tall buildings for wind-induced effects is a challenging task for engineers. Some main reasons include facing heavy wind pressure acting on a façade system and significant dynamic-induced vibrations. In addition, tall and slender structures are more vulnerable to aeroelastic effects such as strongly synchronized vibration due to the lock-in phenomenon and excessive deformations under instabilities such as galloping due to negative damping. Besides, there is a concern related to inelastic capacity of the structure if the wind load is larger than the seismic load. Since members should be designed for larger forces, it could adversely impact ductility (Jeong et al. 2021). In practice, there are several solutions to overcome these challenges and mitigate wind-induced vibrations that can be mainly categorized as modification of structural design, utilizing auxiliary damping systems, and aerodynamic treatments (Jafari and Alipour 2021).

In general, the design for wind loads requires careful evaluation of buildings for service and design loads. Design for service load requires evaluating comfort criteria (mainly in terms of limiting induced accelerations) and controlling drift and displacement, while structural stability and strength of members are the main concerns under design load.

Aerodynamic treatment, especially through corner modification, is one of the simplest but most effective approaches that can reduce wind load in both service and design loads. Corner rounding, chamfering, and recession are some of the most practical cases, and their efficiency on reduction of wind load was shown through experimental and numerical simulation (Kwok and Bailey 1987; Tse et al. 2009, 2021; Elshaer et al. 2017; Li et al. 2018, 2023; Lu et al. 2023; Mittal et al. 2019; Sanyal and Dalui 2020; Wang and Zhang 2023). In general, corner chamfering and recession with about 10% cut from the total width of the plan at each edge of each side seems to have the best performance in the reduction of aerodynamic wind loads and corresponding dynamic vibrations.

Wind load for strength design can also be reduced by permission of developing inelastic deformations in the structural elements to increase the dissipation capacity of structures against vibration through hysteretic damping. In this case, an adequate amount of structural ductility should be provided with respect to the maximum expected inelastic deformations. Also, large damage accumulation and the number of cycles with large inelastic amplitude should be carefully evaluated to minimize the risk of ratcheting and low cycle fatigue failures.

One of the main hindrances to using this approach instead of elastic wind design is a lack of knowledge regarding the inelastic behavior of structures subjected to wind load (Tamura et al. 2001). To bridge this gap, many researchers evaluated the inelastic behavior of structures subjected to wind load. Many researches have concentrated on the behavior of inelastic systems using equivalent single-degree-of-freedom models coupled with nonlinear time-history analysis (Vickery 1970; Chen and Davenport 2000; Hong 2004; Gani and Légeron 2012; Judd and Charney 2015; Bezabeh et al. 2020, 2021a, b; Alinejad et al. 2022a, b). These studies were carried out with the main intention to measure damage accumulation and understand its mechanism, estimate ductility demand, and other design criteria related to system-level behavior. In several other research articles, case study buildings were modeled by detailed finite element models, and inelastic behavior was investigated by performing nonlinear time-history analysis. The results of such studies on the inelastic behavior of steel buildings (Tamura et al. 2001; Bakhshi and Nikbakht 2011; Judd and Charney 2016; Mohammadi et al. 2019; Chuang and Spence 2020; Ghaffary and Moustafa 2021; Preetha Hareendran et al. 2022; Huang and Chen 2022) and concrete buildings (Muthukumar et al. 2013; Aswegan et al. 2017; Ghebremariam and Judd 2017; Elezaby and El Damatty 2020; Jeong et al. 2021) revealed acceptable structural performance under wind load.

Furthermore, some experimental research was carried out to examine the low cycle fatigue capacity of structural elements under wind load. Results of experimental tests by Abdullah et al. (2020, 2021, 2022) and Chou et al. (2023) on coupling beams demonstrate a desirable behavior under cyclic wind load.

Substantial development in performance-based wind design (PBWD) procedure provides an appropriate framework to deal with uncertainty in wind-related parameters and assessment of demand and responses to design more reliable structures. Recently, the PBWD procedure has been allowed as an alternative approach for wind design by some standards such as ASCE 7-22 and Korean Design Standard (KDS 41-22). Nonetheless, there are few guidelines and standards that provide detailed procedures to utilize PBWD. The published prestandard for PBWD by ASCE (ASCE 2019) is one of the few available guidelines that provide details related to wind hazard evaluation, performance objectives, acceptance criteria, etc. The prestandard permits a limited inelastic deformation in some structural elements and provides associated acceptance criteria and methods for evaluating nonlinear response. Despite many advantages of PBWD, one of the main barriers to making it practical is related to the time and computational cost of performing nonlinear time-history analysis for evaluating inelastic responses. So, alternative approaches such as methods relying on dynamic shakedown theory, the reduced-order model, and force analogy models were proposed as more efficient approaches to estimate inelastic response under wind load (Tabbuso et al. 2016; Chuang and Spence 2017, 2020; Iancovici et al. 2022; Huang and Chen 2023).

It is worth mentioning that in order to properly address the conflict related to the ductility of tall buildings subjected to significant wind and seismic loads, the same metrics and languages should be used for both hazards in the methodology and analysis tools for performance assessment. This means that a unified risk assessment/design should be utilized within a multihazard framework (Gardoni and LaFave 2016; Suksuwan and Spence 2018; Petrini and Francioli 2022). Wind and earthquake events are considered independent types of multihazards since there is no observed significant correlation between simultaneous occurrences of extreme wind and earthquake loads (Gardoni and LaFave 2016).

Though the former mentioned approaches are very useful for identifying the performance of an existing building, they do not facilitate the design of a new building. In current practice for seismic design, buildings are initially designed for seismic load based on prescribed provisions in the standards (based on response modification factor) and then are evaluated through a performance-based procedure. For this reason, inelastic wind design was proposed as a practical approach for preliminary design, in which the wind load reduction factor is applied to components of elastic wind load for implicit consideration of inelastic response (Elezaby and El Damatty 2020; Bezabeh et al. 2020; Alinejad et al. 2020, 2021; Jeong et al. 2021). It was found that using a wind load reduction factor of around 2 to 3 could substantially reduce the material cost and the design building would have an acceptable performance.

In summary, both inelastic wind design and aerodynamic modification could be very beneficial for the reduction of wind load. However, there is no comparison of their efficiency. Also, further studies are required to expand the insight into the inelastic behavior of buildings subjected to wind load, the performance of buildings designed by inelastic wind design approach, and the development of criteria based on structural systems. In this study, three high-rise case study buildings were carefully designed with consideration of inelastic wind design and corner modification, and their performance is comprehensively compared. The available potential for a combination of aerodynamic modification and inelastic wind design is also investigated. A series of wind tunnel tests was carried out to obtain aerodynamic wind load, and the performance of buildings was examined based on results of linear and nonlinear time-history analysis in accordance with the procedure of the ASCE prestandard.

Research Significance

In the practical promotion of inelastic wind design, a crucial step is to compare its advantages and disadvantages against more traditional solutions, such as aerodynamic modification. This research aims to shed light on the design and behavior of tall buildings equipped with RC core wall systems that face wind load challenges. The focus is on key factors such as design loads and reinforcement ratios, serving as indices for cost-effectiveness comparisons. Additionally, a comprehensive performance assessment of these buildings has been executed, aligning with ASCE prestandard guidelines to confirm the expected behavior. This evaluation goes beyond the standard methods, incorporating extensive linear and nonlinear time-history analyses to provide a more precise understanding of uncertainties in both the load and response in elastic and inelastic regions. By addressing these critical aspects, findings and discussions of this research can contribute to enhancing the current insight into inelastic behavior of tall buildings and confirm effectiveness of inelastic wind design to reduce wind load and material cost with acceptable performance.

Case Study Buildings

Case study buildings are assumed to be reinforced concrete (RC) buildings having 160 m height (40 stories with a height of 4 m) and a square-shaped plan with a width of 40 m. Case 1 has a sharp corner (no aerodynamic modification), while the other two cases have aerodynamic modification at the corners in the form of 10% chamfering (Case 2) and 10% recession (Case 3).

The structural system for all three cases is assumed to be building frame systems with ordinary shear walls, including RC beams (B1–B4) and columns (C1–C3) arranged at the outer sides of plans, main RC core walls (MCW) with RC coupling beams (CB), and interior RC walls, as shown in Fig. 1. The structural layout is designed with the intention that columns and interior walls mainly carry out gravity load, and lateral (seismic and wind) load is mostly transferred to core walls. Among several practical solutions for the structural layout at the modified corner, the layout shown in Fig. 1 was chosen to minimize differences with Case 1 and have a more logical comparison. Since the cantilever girders do not contribute to the lateral resisting system, they are not discussed further in this study. Floors were modeled by shell elements with consideration of rigid diaphragm constraint. Stairs and elevators are not the main structural elements for lateral systems. However, their contribution to vertical load must be considered. For this reason, stairs at each story and elevators only at the roof level were represented by shell elements, and their corresponding loads were applied as uniform loads. Analysis and design were performed by ETABS (CSI 2016).

It was assumed that the modulus of elasticity and compressive strength of concrete material are 30 GPa and 40 MPa, respectively, and steel material is SD500 with the modulus of elasticity and yield strength of 200 GPa and 500 MPa, respectively. Section properties of structural elements are reported in Table 1. The same sections were used for all three models, and the required reinforcement ratio is set as the index for comparison (and design values are reported in the Appendix).

Table 1. Section properties

Structural element	Section	Effective stiffness	Effective in-plane stiffness	Effective out-of-plane stiffness
Column
1st–20th stories	$1,000 mm \times 1,000 mm$	$1.0 E A$ , $0.7 E I_{g}$ , $1.0 G A$	—	—
21st–40th stories	$800 mm \times 800 mm$	$1.0 E A$ , $0.7 E I_{g}$ , $1.0 G A$	—	—
Beam	$600 mm \times 800 mm$ ( $width \times height$ )	$1.0 E A$ , $0.35 E I_{g}$ , $1.0 G A$	—	—
Coupling beam	$900 mm \times 900 mm$ ( $width \times height$ )	$1.0 E A$ , $0.15 E I_{g}$ , $1.0 G A$	—	—
Wall
Main core walls
1st–6th stories	900 mm (thickness)	—	$1.0 E A$ , $0.35 E I_{g}$ , $0.5 G A$	$0.25 E I_{g}$
7th–40th stories	900 mm (thickness)	—	$1.0 E A$ , $0.7 E I_{g}$ , $1.0 G A$	$0.25 E I_{g}$
Interior walls	250 mm (thickness)	—
1st–6th stories	900 mm (thickness)	—	$1.0 E A$ , $0.35 E I_{g}$ , $0.5 G A$	$0.25 E I_{g}$
7th–40th stories	900 mm (thickness)	—	$1.0 E A$ , $0.7 E I_{g}$ , $1.0 G A$	$0.25 E I_{g}$
Slab	210 mm (thickness)	—	Rigid diaphragm	$0.1 E I_{g}$

Note: $E A$ = axial rigidity of gross section; $E I_{g}$ = flexural rigidity of gross section; and $G A$ = shear rigidity of gross section.

The main occupancy of buildings is assumed to be the office. In addition to structural weight (dead load), superimposed dead load (

S D

) and live load (

L

) were assigned as the uniform load for floors (

S D = 2.5 kN / m^{2}

,

L = 3.5 kN / m^{2}

), corridors (

S D = 2.5 kN / m^{2}

,

L = 5 kN / m^{2}

), stairs (

S D = 2 kN / m^{2}

,

L = 5 kN / m^{2}

), roof (

S D = 3 kN / m^{2}

,

L = 3 kN / m^{2}

), and elevators (

S D = 4.5 kN / m^{2}

,

L = 15 kN / m^{2}

). For cantilever parts of Case 2 and Case 3, 1.5 times the office live load was assigned according to KDS 41-22. The mass of the structure was defined as the summation of structural mass and superimposed dead load.

The natural period and frequency of models are reported in Table 2, and corresponding mode shapes are shown in Fig. 2. The first three mode shapes of all three buildings are fully decoupled modes, where the first and second modes are lateral vibrations in the X and Y directions and the third mode is rotational vibration about Z axis. As shown in the figure, the mode shapes of buildings are almost the same and match well with the approximate linear mode shape. Since the natural periods and mode shapes of systems are almost the same, in comparison of the results of Case 1 with Case 2 and Case 3, differences can be directly related to the effect of aerodynamic modification rather than the structural system. In addition, the generalized mass and stiffness of systems based on exact mode shapes and approximate linear mode shapes were calculated, and the difference was less than 3%, which implies that errors related to the assumption of linear mode shape for equivalent static wind load derivation are negligible.

Table 2. Natural period and frequency of structures

Mode	Natural period (s)			Natural frequency (Hz)			Direction
Mode	Case 1	Case 2	Case 3	Case 1	Case 2	Case 3	Direction
1	4.039	3.943	4.012	0.248	0.254	0.249	X
2	4.004	3.909	3.977	0.25	0.256	0.251	Y
3	2.546	2.444	2.487	0.393	0.409	0.402	RZ

Fig. 2. (a) Mode shapes of Case 1; (b) mode shapes of Case 2; (c) mode shapes of Case 3; and (d) comparison of normalized mode shape.

Design Procedure

All buildings were designed for gravity, seismic, and wind loads. Based on KDS 41-22, load combinations reported in Table 3 were used for seismic and wind design.

Table 3. KDS 41-22 design load combination

Load combination	Contents
Gravity loads	$1.4 D$ and $1.2 D + 1.6 L$
Gravity and wind loads	$1.2 D + 1.0 L + 1.0 W$ and $0.9 D + 1.0 W$
Gravity and seismic loads	$1.2 D + 1.0 L + 1.0 E$ and $0.9 D + 1.0 E$

Note: $D$ = dead and super dead load; $L$ = live load; $W$ = wind load; and $E$ = seismic load.

Seismic design was done based on response spectrum analysis by including the first 50 modes of vibration to obtain a modal mass participation ratio of 99% in all directions. The seismic parameters were determined per KDS 41-22, as reported in Table 4. Results of spectrum analysis showed that the combined response for the modal base shear was more than 100% of the equivalent static seismic load, so results were used directly for seismic design. Seismic loads in orthogonal directions are combined based on 100-30 rule along with dead and live loads.

Table 4. KDS 41-22 design seismic parameters

Parameter	Value
Site class	$S_{C}$ ( $\geq 20 m$ depth to bedrock)
$S$ , effective ground acceleration (2,400-year MRI)	0.22 g
$S_{D S}$ , design spectral acceleration at short period	0.54 g
$S_{D 1}$ , design spectral acceleration at 1 s period	0.23 g
$T_{0} = 0.2 S_{D 1} / S_{D S}$ , $T_{S} = S_{D 1} / S_{D S}$ , and $T_{L}$	0.09, 0.43, and 5 (s)
$S_{a}$ , design spectral acceleration (g)	—
$T < T_{0}$	$S_{a} = S_{D S} (0.4 + 0.6 T / T_{0})$
$T_{0} \leq T \leq T_{S}$	$S_{a} = S_{D S}$
$T_{S} \leq T < T_{L}$	$S_{a} = S_{D 1} / T$
$T_{L} \leq T$	$S_{a} = S_{D 1} T_{L} / T^{2}$
$R_{E}$ , response modification factor	5
$I_{E}$ , importance factor	1.2
Damping ratio	5%

Note: $T$ is natural period of structure.

Wind design (for serviceability and strength design) was done based on the equivalent static wind load (ESWL) obtained from results of wind tunnel tests and Korean Design Standard (KDS 41-22). In accordance with KDS 41-22, 10-min average wind speed with 1-, 50-, and 500-year mean recurrence interval (MRI) should be used for checking comfort, service design, and strength design, respectively. The basic parameters for wind design were determined per KDS 41-22 and are reported in Table 5. Based on the parameters, the target wind speeds (

V_{H}

) for 1-, 50-, and 500-year MRIs are

31.92 m / s

,

51.07 m / s

, and

63.84 m / s

, respectively. The damping ratio of all structures under wind load was assumed to be 1.2% in accordance with ISO 4354 (ISO 2009).

Table 5. KDS 41-22 design wind parameters

Parameter	Value
$V_{0}$ , basic wind speed (500-year MRI)	$42 m / s$
Surface roughness category	C
$K_{z r}$ , mean wind speed profile factor	$0.71 {(z)}^{0.15}$
$K_{z t}$ , topography factor	1.0
$K_{d}$ , wind directionality factor	1.0
$I_{W}$ , importance factor	1.0
Damping ratio^a	1.2%

a

Data from ISO 4354.

Wind Tunnel Test

Aerodynamic wind load was measured on rigid specimens using the high-frequency force balance (HFFB) technique. In accordance with recommendations on appropriate scaling factors (The Wind Engineering Institute of Korea 2010) and conditions of the wind tunnel facility, a geometry length scale factor of 1/600, velocity scale factor of 1/10, and time scale factor of 1/60 were selected. Accordingly, three specimens were manufactured using Balsa wood material as shown in Figs. 3(a and b). The wind speed profile was validated by comparison with that of KDS 41-22 [Fig. 3(c)].

Fig. 3. (a) Dimensions of specimens (unit: mm); (b) manufactured specimens; and (c) vertical profile of mean wind speed and turbulence intensity.

Wind load in KDS 41-22 is based on 600 s (10-min) average load and is equivalent to 10 s in a scaled-down wind tunnel test. For each angle of attack, wind loads were recorded with the sampling frequency of 1,000 Hz for a duration of 120 s (12 repetitions) to obtain stationary results and provide more time histories of aerodynamic load. The results confirmed that aerodynamic load can be effectively reduced by means of corner chamfering and recession, especially for the angle of attack of zero degree, and the efficiency of both modifications is comparable. Both cases reduce the value of power spectral density (PSD) of the across-wind load at the angle of attack of zero degrees (across-wind load type) at vortex shedding frequency (Fig. 4).

Fig. 4. PSD of across-wind overturning moment (angle of attack of zero degree).

Equivalent Static Wind Loads

In current practice for elastic wind design, the equivalent static wind load (ESWL) for along-wind load is calculated based on the concept of the gust-effect factor using either displacement gust load factor (GLF) (Davenport 1967) or base moment gust load factor (MGLF) (Zhou and Kareem 2001). A similar computational procedure to the MGLF method is also used to calculate components of ESWL for across-wind and torsional-wind loads (Tamura et al. 1996). In the inelastic wind design procedure, a wind load reduction factor is applied to the resonant component or total ESWL (Alinejad et al. 2020, 2021; Bezabeh et al. 2020; Elezaby and El Damatty 2020; Jeong et al. 2021). In this study, the wind load reduction factor for resonant component (

R_{W R}

) is used, which results in Eqs. (1)–(3) for ESWLs:

F_{D} = {\bar{F}}_{D} + \sqrt{F_{D B}^{2} + {(F_{D R} / R_{W R})}^{2}} = G {\bar{F}}_{D} where G = 1 + \sqrt{G_{B}^{2} + {(G_{R} / R_{W R})}^{2}}

(1)

F_{L} = {\bar{F}}_{L} + \sqrt{F_{L B}^{2} + {(F_{L R} / R_{W R})}^{2}}

(2)

M_{T} = {\bar{M}}_{T} + \sqrt{M_{T B}^{2} + {(M_{T R} / R_{W R})}^{2}}

(3)

where

F_{D}

,

F_{L}

, and

M_{T}

= ESWLs for along-wind, across-wind, and torsional-wind load at each story, respectively; parameters with over-bar are the mean components; parameters with subscripts “

B

” and “

R

” are background and resonant components, respectively; and

G

= gust-effect factor. Note that

R_{W R}

of 1 results in elastic ESWL.

The following assumptions were considered in the calculation of ESWL for all three specimens. Wind load directionality is neglected, and structures are designed only for the angle of attack of zero degree for along-wind, across-wind, and torsional-wind load, which is expected to have the largest influence on the design of buildings. The normalized vertical distribution of mean along-wind load follows the normalized profile in KDS 41-22. The vertical profile in KDS 41-22 is defined as the difference of pressure coefficient on windward and leeward walls and for square shape plan equals

0.8 k_{z} + 0.5

, where

k_{z}

is the pressure distribution coefficient for vertical profile and is calculated by Eq. (4):

z \leq z_{b} k_{z} = {(z_{b} / H)}^{2 α} z_{b} < z < 0.8 H k_{z} = {(z / H)}^{2 α} z \geq 0.8 H k_{z} = {0.8}^{2 α}

(4)

where for exposure C,

z_{b} = 10 m

and

α = 0.15

. The vertical profile is normalized and adjusted according to the base shear of each specimen.

With an assumption of linear mode shapes, power spectral density (PSD) of base overturning and torsional moments was used to calculate the standard deviation of background and resonant components of ESWL. A mode correction factor equal to 0.6 was applied to the standard deviation of the base torsional moment due to the difference between the assumed linear mode shape and actual uniform distribution [ASCE 49-21 (ASCE 2022b); KDS 41-22 (KDS 2022)]. The peak factor,

g

, for all ESWLs was calculated by peak factor formulation provided by KDS 41-22 [Eq. (5)] with the corresponding natural frequency (

f_{1}

) reported in Table 2:

g = \sqrt{2 \ln (600 f_{1}) + 1.2}

(5)

Peak values of background and resonant overturning moments for along-wind load were calculated as the product of the corresponding standard deviation and the peak factor. Then, components of the gust-effect factor (

G_{B}

and

G_{R}

) for along-wind load were calculated as normalized peak background and resonant overturning moments by mean overturning moment. Finally, the gust-effect factor was multiplied by mean along-wind load to calculate ESWL.

The resonant component of across-wind and torsional-wind load was assumed to be linear. In order to estimate distribution of their mean and background components, the open-access wind tunnel database of Tokyo Polytechnic University (TPU) was used (Tamura 2012). Wind pressure data for a model similar to Case 1 (

height ∶ width ∶ length = 4 ∶ 1 ∶ 1

; power law exponent of velocity profile = 1/6; angle of attack of 0 deg) was extracted. These wind pressures were integrated with respect to their tributary area and center of geometry for each layer of pressure taps to calculate the story forces in the along-wind and across-wind directions [

F_{Y} (z)

and

F_{X} (z)

, respectively] and the story torsional moment (

M_{Z} (z)

), and the normalized coefficients are shown Fig. 5. According to the figure, a uniform distribution was assumed for mean and background components of across-wind and torsional-wind loads. Though the TPU database provides data only for models with sharp corners, the same distribution was assumed for Case 2 and Case 3 for simplification.

Fig. 5. Normalized distribution of story forces and torsional moment. (Data from Tamura 2012.)

All buildings were designed for both service and strength loads; however, wind tunnel tests were performed with consideration of wind speed corresponding to strength design. Thus, the wind tunnel test results were scaled with consideration of geometry length scale and time scale (based on corresponding wind speed for serviceability design) and used to calculate components of ESWL for service load.

R_{W R} = 1

was used for service design and elastic strength design. For inelastic wind design, only

R_{W R} = 2

was used since the wind load for

R_{W R} = 3

and larger was smaller than the service load.

In order to consider the correlation between ESWLs (combination of maximum values), the load case factors in KDS 41-22 (Table 6) were used for both service and strength design. The load case factors in KDS 41-22 are defined by assuming that the along-wind load is not correlated with across-wind and torsional-wind loads and there is no significant coupling between the modes. Based on KDS 41-22, the combination factor for across-wind and torsional-wind loads (

κ

) is defined. Linear interpolation is used for intermediate values of

n_{1} B / V_{H}

.

Table 6. KDS 41-22 load case factors

Load case	$F_{D}$	$F_{L}$	$M_{T}$
1	1	0.4	0.4
2	$0.4 + 0.6 / G$	1	$κ$
3	$0.4 + 0.6 / G$	$κ$	1

Note: $G$ = gust-effect factor; $n_{1}$ = the maximum of natural frequency in across-wind direction and torsional mode; $B$ = building width; $V_{H}$ = wind speed at building height; and $κ$ = combination factor for across-wind and torsional-wind loads (for $n_{1} B / V_{H} = 0.1$ , 0.3, and 0.6, $κ = 0.55$ , 0.55, and 0.65, respectively, and linear interpolation is used for intermediate values of $n_{1} B / V_{H}$ ).

Comparison of Design Forces and Sections

The story force and shear corresponding to the design seismic load were compared in Fig. 6 to those of the service wind load (S) and design wind load (D) for elastic design (

R_{W R} = 1

) and inelastic wind design (

R_{W R} = 2

). Since values for Case 2 and Case 3 are very close to each other, the average values were considered as design load for aerodynamically modified models. It can be seen that the story force and shear under wind load, even for service wind load, are significantly larger than those of seismic load. This large gap between seismic and wind loads requires significantly stronger and stiffer members, which could adversely impact the ductility of the structure. According to the results shown in Fig. 6, both aerodynamic modification and inelastic wind design could effectively reduce this gap.

Fig. 6. Comparison of story force and shear for seismic load with design (D) and service (S) wind loads for Case 1 and aerodynamically modified models (Case 2).

Table 7 reports base shear and overturning moments for different cases and shows how the design is governed by wind load. Both base shear and overturning moment are considerably larger than values under seismic load for all cases. Under service wind load, the design base shear and overturning moment of Case 1 are 1.74 and 1.84 times those of seismic load. Aerodynamic modification reduces these ratios to 1.37 and 1.5, which are significant reductions.

Table 7. Comparison of base shear and overturning moments

Component	Seismic	Case 1			Average of Case 2 and Case 3
Component	Seismic	Service	$R_{W R} = 1$	$R_{W R} = 2$	Service	$R_{W R} = 1$	$R_{W R} = 2$
Base shear (kN)
Along-wind	16,463	28,700 (1.74)	46,100 (2.80)	37,800 (2.30)	21,400 (1.30)	34,300 (2.08)	28,600 (1.74)
Across-wind	16,463	27,700 (1.68)	44,500 (2.70)	25,800 (1.57)	22,500 (1.37)	36,100 (2.19)	20,600 (1.25)
Overturning moment ( $kN \cdot m$ )
Along-wind	1,625,390	2,491,000 (1.53)	3,998,000 (2.46)	3,278,000 (2.02)	1,853,000 (1.14)	2,974,000 (1.83)	2,482,000 (1.53)
Across-wind	1,625,390	2,994,000 (1.84)	4,805,000 (2.96)	2,790,000 (1.72)	2,431,000 (1.50)	3,902,000 (2.40)	2,222,000 (1.37)

Note: Values in parentheses are ratios to the corresponding value for seismic load.

Under design wind load, degrees of reduction of wind load using inelastic wind design and aerodynamic modification are comparable for the along-wind load. Both the base shear and overturning moment for along-wind load can be reduced by around 20% by inelastic wind design and aerodynamic modification. However, the reduction in across-wind load by inelastic wind design is about 40% which is more noticeable than that by aerodynamic modification (about 20%). Based on the results, the combination of aerodynamic modification and inelastic wind design (Case A,

R_{W R} = 2

) is the best option to reduce wind load. For this case, along-wind load and across-wind load can be reduced by about 38% and 54%, respectively.

All buildings were initially designed only for gravity and seismic loads, and the required reinforcement ratio of members is reported in the Appendix. In the second step, members were designed for all loads, including gravity, seismic, and wind loads, and the design reinforcement ratio of members is reported in the Appendix.

Comparing the required reinforcement ratio for seismic and wind loads clearly shows how strongly wind governs the member design. It can be seen that inelastic wind design can significantly reduce the cost due to the less required reinforcement ratio. For instance, the reinforcement ratio of coupling beams was reduced between 28 to 44% by inelastic wind design, which is even more significant than the reduction by aerodynamic modification with

R_{W R} = 1

(about 23 to 26%). Combination of inelastic wind design and aerodynamic modification (Case A,

R_{W R} = 2

) results in a more considerable reduction of about 46% to 58%. A similar trend for the reduction can be seen, less and more, for the moment frame beams and columns. The reduction in the reinforcement ratio of main core walls was almost the same for all cases (about 43%).

Note that the results for the combination of aerodynamic modification and inelastic wind design are presented only to illustrate the available potential. This case will not be further discussed in this paper to have a clearer comparison between aerodynamic modification and inelastic wind design approaches.

Performance-Based Wind Design Procedure

Performance of the designed structures was evaluated based on ASCE prestandard (ASCE 2019) with some modifications.

Performance Objectives and Criteria

Prestandard for PBWD published by ASCE (2019) is used as the primary reference for the assessment of structural performance of case study buildings, with some modifications to be compatible with KDS 41-22, as explained in the following.

The PBWD procedure based on the prestandard requires us to satisfy criteria for three main structural performance objectives of “occupant comfort,” “operational,” and “continuous occupancy (limited interruption)” for the structural system. To be consistent with KDS 41-22, wind speed with 1-, 50-, and 500-year MRI was used to evaluate demands for occupant comfort, operational, and continuous occupancy performance levels. Demands were obtained using linear modal time-history analysis for occupant comfort and operational performance levels and nonlinear time-history analysis for continuous occupancy performance levels.

Since site-specific wind hazard analysis has not been done, the directionality effect was ignored and performance was evaluated only for an angle of attack of 0 deg. The base shear (corresponding to along-wind and across-wind directions) and base torsional moment obtained from the wind tunnel tests were scaled up according to each target wind speed. Then, these loads were distributed according to the same vertical profile as the mean and background components of corresponding ESWLs and were applied to the mass center of each story. A set of 10 time histories of aerodynamic wind load (by splitting the original time histories) was used for each case to consider the uncertainty more accurately, particularly for peak values. A summary of the procedure for performance-based assessment in this study is illustrated in Fig. 7.

Fig. 7. Performance objectives and criteria. (Data from ASCE 2019; KDS 41-22.)

In addition to the assessment mentioned above for the continuous occupancy performance level, which follows Method 1 of ASCE prestandard, one more case was evaluated. Methods 2 and 3 of ASCE prestandard can be used for more comprehensive performance assessment, which adopts complicated stochastic simulation models incorporating the wind load with a wider range of MRI to find the probability distribution of failure. In this study, these methods were not used; however, to be more comprehensive and check the structural safety regarding inelastic wind design, structural behavior was evaluated under wind load with longer MRIs. This can ensure that failure is not probable for MRI close to that of design level (500-year MRI). Two additional series of wind loads with MRIs of 900 years (equivalent MRI for special buildings based on KDS 41-22) and 3,000 years (for special structures in ASCE 7-22) were prepared, and the same procedure for continuous occupancy (criteria, analysis, etc.) was followed for evaluation. The ratio of wind speed with

T

-year return period (

V_{T}

) and wind speed with 500-year return period (

V_{500}

) based on KDS 41-22 can be obtained by Eq. (6):

\frac{V_{T}}{V_{500}} = 0.465 + 0.086 \ln (T)

(6)

Based on the equation, wind speeds with 900-and 3,000-year MRIs are about 5% and 15% larger than those of 500-year, respectively. The annual probability of wind speed with a certain MRI is very closely approximated by 1/MRI for an MRI of longer than 10 years [ASCE 7-22 (ASCE 2022a)]. Accordingly, the values of the annual probability of wind speeds with MRIs of 500, 900, and 3,000 years are 0.20%, 0.11%, and 0.03%, respectively. Therefore, if the structure can meet the acceptance criteria under wind load with an MRI equal to 900 or 3,000 years, it can be concluded that the designed structure (for 500-year MRI) has a large margin of safety against failure.

Nonlinear Modeling Assumptions

Moment frame beams were modeled using two concentrated plastic hinges at member ends. Nonlinear modeling parameters and acceptance criteria were defined based on ASCE 41-17, using the expected strength and Takeda model for hysteretic behavior. Coupling beams for case study buildings have a span to depth ratio of 3.3, which implies that response is mainly due to flexural deformation and shear failure is not expected. Thus, nonlinearity was modeled similarly to beams using concentrated hinges. However, the hysteretic behavior was described by the pivot model to introduce pinching point and unloading stiffness degradation. The hysteretic behavior of coupling beams varies depending on many parameters, such as the span to depth ratio and confinement reinforcement ratio. Here for simplification, only the span to depth ratio, which is the same for all coupling beams of case study buildings, is considered as the main variable for hysteretic behavior, calibrated by experimental results of the HB3-10L-T50 specimen by Xiao et al. (1999), and used for all cases. The assumption would not introduce considerable errors since the expected inelastic deformation under wind load is very small. As shown in Fig. 8(a), the hysteretic behaviors of the experiment and calibrated model match very well.

Fig. 8. (a) Verification of hysteresis model for coupling beam; (b) verification of hysteresis model for shear walls; (c) material model for steel fiber elements (SD500); and (d) material model for concrete fiber elements (C40).

Shear walls and columns are modeled using fiber elements to simulate axial–flexural interaction more accurately. Material properties for concrete and rebars based on expected strength are shown in Figs. 8(c and d). Concrete and degrading hysteretic types were used for concrete and rebars, respectively. The accuracy of the proposed modeling approaches was verified with experimental results of the RW2 specimen by Thomsen and Wallace (1995) for the walls, as shown in Fig. 8(b).

The same stiffness modification factors presented in Table 1 were used in the nonlinear model, with the following exceptions. No stiffness modification factor was used for the flexural stiffness of columns and walls since the stiffness is directly calculated based on the introduced strain–stress model for each fiber.

Fast nonlinear analysis (FNA) method was used for performing nonlinear time history analysis to evaluate continuous occupancy performance objectives. FNA is a very efficient method for dynamic analysis of large-scale models and is more accurate where the level of inelastic behavior is not very large (Wilson 2002), which is consistent with expected conditions for the inelastic behavior of buildings under wind load.

Performance-Based Assessment

This section presents the analysis results and performance assessment of case study buildings for each performance objective.

Occupancy Comfort and Operational Performance Levels

Time histories of acceleration at the center of the roof of case study buildings for one of the time histories are shown in Fig. 9 for along-wind and across-wind directions, respectively.

Fig. 9. Time history of acceleration at roof center in along-wind and across-wind directions for wind load with 1-year MRI.

The ensemble average and coefficient of variation (C.O.V.) of maximum acceleration at the roof level of case study buildings for 1-year MRI wind speed are reported in Table 8. Acceleration in torsion (equivalent translational acceleration) is defined as

r A_{Z}

, where

r

is the distance from the center of torsion to the objective point (corner point in this study) and

A_{Z}

is the angular acceleration of the torsional vibration [ISO 10137 (ISO 2007)]. The results are presented independently of the value of

R_{W R}

, because the initial stiffness and consequently demand for both cases are the same.

Table 8. Maximum acceleration at roof level for 1-year MRI wind speed

Building	Ensemble average ( $m / s^{2}$ )			C.O.V. (%)
Building	Along	Across	Torsion	Along	Across	Torsion
Case 1	0.054	0.110	0.003	16.51	18.32	12.63
Case 2	0.049	0.079	0.002	21.11	20.73	11.94
Case 3	0.040	0.083	0.002	20.97	21.17	12.18

Note: $1 m / s^{2} = 100 milli - g$ .

Based on the results, aerodynamic modification is very effective in reducing acceleration. Accelerations in along-wind, across-wind, and torsional-wind of Case 2 are about 72%, 91%, and 73% of Case 1, respectively.

Accelerations in along-wind, across-wind, and torsional-wind directions of Case 3 are about 75%, 74%, and 84% of Case 1, respectively. Since the maximum acceleration is in the across-wind direction, it can be said that the efficiencies of both Case 2 and Case 3 are comparable, and aerodynamic modification can reduce acceleration by about 25%. The ensemble average of peak accelerations is compared with the frequency-dependent acceleration limits of the prestandard for 1-year MRI and office occupancy, as shown in Fig. 10. According to the results, the value of demand acceleration is smaller than the limits, and acceptance criteria for occupant comfort performance level are met for the buildings.

Fig. 10. Comparison of peak acceleration and acceptance criteria.

The ensemble average and coefficient of variation (C.O.V.) of maximum displacement at the roof level of case study buildings for 50-year MRI wind speed are reported in Table 9. Note that results are presented independently of the value of

R_{W R}

, because the initial stiffness and consequently demand for both cases are the same.

Table 9. Maximum displacements at the roof level for 50-year MRI wind speed

Building	Ensemble average (mm)		C.O.V. (%)
Building	Along	Across	Along	Across
Case 1	183	195	6.67	18.01
Case 2	131	157	9.88	17.91
Case 3	122	158	10.35	12.16

Based on the results, aerodynamic modification is very effective in reducing displacement, as well. Maximum displacement in the along-wind and across-wind directions of Case 2 is about 81% and 72% of Case 1. Maximum displacements in the along-wind and across-wind directions of Case 3 are about 81% and 67% of Case 1, respectively. In comparison with Case 1, the maximum displacement under along-wind load for both Case 2 and Case 3 is about 19% smaller. Under across-wind load, the maximum displacements of Case 2 and Case 3 are about 28% and 33% smaller than those of Case 1, respectively. Thus, the efficiencies of both Case 2 and Case 3 are comparable as the difference is not significant (about 5%). Since the maximum displacement is in the across-wind direction, it can be said that aerodynamic modification can reduce maximum displacement by around 30%.

In accordance with the prestandard, the peak displacement should be less than 320 to 400 mm (

H / 400

to

H / 500

). So, the maximum displacements of buildings (Table 9) are less than the limits. Also, strength limits (

DCR < 1

) were satisfied during the design procedure, since service wind loads were included in the load combination. Therefore, all acceptance criteria for operational performance levels for buildings are satisfied.

Continuous Occupancy Performance Level

The story force and shear for Case 1 based on nonlinear time-history analysis (NTHA) at the moment of the minimum and maximum overturning moment in along-wind and across-wind directions are compared with design values in Fig. 11. Since values at the minimum overturning moment in the along-wind direction were very small, they are not depicted in the figure. It can be seen that the results by NTHA are very close to those of design values based on ESWL. The differences between design along-wind forces and results by NTHA are due to the assumed distribution for the resonant component of ESWL (similar to the mean component). The ensemble average of story force and shear for case study buildings are compared in Fig. 12(a). It can be seen that the results for Case 1 with

R_{W R} = 1

and

R_{W R} = 2

are almost the same, and the difference is less than 1%. The reason lies in the fact that there is a difference between some influential factors in the initial design procedure and performance assessment. In the design procedure, specified material properties and strength reduction factors of less than 1 were used. Meanwhile for time-history analysis, expected strength and strength reduction factor equal to 1 were used. The difference results in a larger initial yield strength of the structures than expected values from the initial design. Thus, the structures remain almost elastic, which implies that dynamic properties will not significantly change, and induced dynamic loads remain the same in both structures. In comparison of the aerodynamically modified model (Case A, average of Case 2 and Case 3) with Case 1, forces in the across-wind direction of Case A are a little smaller, and forces in the along-wind direction are comparable.

Fig. 11. Comparison of story shears and forces at the maximum overturning moment with design values (Case 1, $R_{W R} = 1$ ): (a) along-wind; and (b) across-wind.

Fig. 12. Comparison of ensemble averages: (a) story force and shear; and (b) story displacement and drifts.

The maximum overturning moment and base shear of case study buildings in along-wind and across-wind directions are reported in Table 10. In comparison with Case 1 with

R_{W R} = 1

, responses of Case 1 with

R_{W R} = 2

are a little larger in the along-wind direction and smaller in the across-wind direction.

Table 10. Maximum base shear (

V

) and overturning moment (

M

)

Buildings	Along-wind		Across-wind
Buildings	$V$ (kN)	$M$ ( $kN \cdot m$ )	$V$ (kN)	$M$ ( $kN \cdot m$ )
Case 1 ( $R_{W R} = 1$ )	42,000 (7.82%)	4,015,000 (8.87%)	41,000 (11.32%)	4,381,000 (12.86%)
Case 1 ( $R_{W R} = 2$ )	42,000 (7.81%)	4,019,000 (8.84%)	41,000 (11.46%)	4,370,000 (13.05%)
Average of Case 2 and Case 3 ( $R_{W R} = 1$ )	42,000 (8.94%)	3,930,000 (10.33%)	36,000 (15.85%)	3,810,000 (17.70%)

Note: Values in parentheses are C.O.V. of the parameter.

Since some elements in Case 1 with

R_{W R} = 2

yielded, the natural frequency decreases a bit and demand increases. Because the structure experiences full cyclic deformation due to a small mean value in the across-wind direction, total damping increases by hysteretic damping. Demand is a consequence of both effects, and for the case study building the reduction effect by hysteretic damping is more dominant, resulting in the smaller demand.

In the along-wind direction, deformations are not in a full cyclic form due to the large mean value, and hysteretic damping does not contribute to the total damping of the system. However, damping increases through unidirectional plastic deformation. For this building, the amplifying effect is more dominant, which results in the larger demand. However, the differences between the two structures in both along-wind and across-wind directions are negligible.

The difference between Case 1 and Case A in the along-wind direction is not significant (about 2%); however, Case A has about 13% smaller responses in the across-wind direction.

The C.O.V. of responses for Case 1 with

R_{W R} = 1

and

R_{W R} = 2

is about 8% to 13%, though the values for Case 1 with

R_{W R} = 2

in the across-wind direction are about 1% larger due to inelastic behavior. The C.O.V. of responses for Case A is about 14% to 40% larger than Case 1. Notwithstanding is that the values of C.O.V. of all cases are relatively small, which confirms that the uncertainty in the ensemble average of peak values is quite reliable.

Ensemble averages of maximum story displacement and drift are compared in Fig. 12(b). Since minimum values for along-wind direction are small, they are not shown in the figure.

It can be seen that the maximum drifts or displacements of Case 1 with

R_{W R} = 1

and

R_{W R} = 2

are almost the same in both the along-wind and across-wind directions. The ensemble average of maximum story displacement (and story drift) in the along-wind and across-wind directions are 210 mm (0.172%) and 234 mm (0.190%), respectively. For aerodynamically modified models, the ensemble average of maximum story displacements or story drifts in both the along-wind and across-wind directions are almost the same as 203 mm (0.167%). Compared to Case 1, the ensemble average of maximum story displacement, as well as story drift, of Case A in the along-wind and across-wind directions is around 3% and 13% smaller, respectively.

The C.O.V. of ensemble average of maximum story displacement or drift is quite small, confirming that the uncertainty in the ensemble average of peak values is relatively low; i.e., the results are reliable (9% to 11% for Case 1 with

R_{W R} = 1

; 9% to 12% for Case 1 with

R_{W R} = 2

; 13 to 19% for Case A with

R_{W R} = 1

). In addition to the peak drift value, residual drift was measured for Case 1 with

R_{W R} = 2

. Since the defined ramp-down part at the end of time history is quite long (about 100 s), residual drift was defined as the value at the last increment of each time-history analysis, and the absolute values are shown in Fig. 13.

Fig. 13. Residual story displacement and drift (Case 1, $R_{W R} = 1$ ): (a) along-wind; and (b) across-wind.

Since the C.O.V. of the ensemble average of residual drift is very large in this case, the maximum values in the along-wind and across-wind directions (14 and 60 mm, respectively) are considered for conservatism. Based on the suggested allowable value of drift by the prestandard, the peak displacement should be less than 533 to 800 mm (

H / 200

to

H / 300

). In addition, residual displacement at the roof level and each story should not be more than 160 mm (

H / 1,000

). Therefore, acceptance criteria for both transient and residual drifts are satisfied in all cases.

No plastic deformation was observed in any building members designed with

R_{W R} = 1

. Since all members of Case 1 with

R_{W R} = 1

and Case A with

R_{W R} = 1

remain elastic, the demand capacity ratio (DCR) for all members is less than 1, and strength limits are satisfied.

Several coupling beams of Case 1 with

R_{W R} = 2

experienced small inelastic deformations, as shown in Fig. 14(a), and all other members remain elastic. It can be seen that maximum plastic rotations in the across-wind direction are relatively larger than those in the along-wind direction. Only a few elements yield in the along-wind direction, while many elements yield in the across-wind direction. The force-displacement curve of the most critical element is shown in Fig. 14(b). As shown in the figure, elements in the along-wind direction almost remain elastic, and maximum inelastic deformation is very small.

Fig. 14. (a) Maximum plastic rotation in coupling beams; and (b) moment-rotation curve of critical coupling beams (Case-1, $R_{W R} = 2$ ).

Based on the results, all coupling beams are in immediate occupancy level. The plastic deformation in both directions is very small and comparable with the reported values by Aswegan et al. (2017) and Jeong et al. (2021).

According to the ASCE prestandard, to limit the risk of low cycle fatigue failure, the number of cycles with inelastic strain at 1.5 times section yield should be limited to about 10 cycles. The section yield of coupling beams varies between about 0.4% and 0.7%, and the corresponding inelastic rotation at 1.5 times section yield is in the range of 0.2% to 0.45%. These values are close to the acceptance criteria of coupling beams in ASCE 41-17 for immediate occupancy performance objective (0.5% to 0.6%). According to the results in Fig. 14, plastic rotations are much smaller than the limit value of 0.2% to 0.45%. It can be concluded that failure due to low cycle fatigue is not expected. Based on the above evaluations, all acceptance criteria for continuous occupancy performance objectives are met for all three case study buildings.

Safety Evaluation

The intention for the proposed enhanced continuous occupancy objectives is to ensure those acceptance criteria for continuous occupancy objectives can be satisfied under wind load with relatively larger MRI. For this reason, first, the story force and shear, as well as maximum (transient and residual) drift and displacement, of Case 1 with

R_{W R} = 2

for different MRIs are compared.

The overturning moments in the along-wind and across-wind directions for MRI of 900 years are about 14% and 11%, respectively, larger than those of MRI of 500 years. Overturning moments in the along-wind and across-wind directions for MRI of 3,000 years are about 35% and 50%, respectively, larger than those of MRI of 500 years. Therefore, if the system satisfies the criteria under these significantly larger wind loads, it implies that there is a large margin of safety under design wind load with MRI of 500 years.

Based on the results, both maximum and residual story displacement and drift increase with the MRI significantly, especially in the across-wind direction. However, the maximum values are still considerably smaller than the limit of 533 to 800 mm (

H / 200

to

H / 300

) for maximum transient drift and 160 mm (

H / 1,000

) for residual drift. This evaluation implies that there is a large margin against the acceptance criteria for transient and residual drifts.

The force-displacement curve of some critical coupling beams for different MRIs is shown in Fig. 15. It can be seen that more elements yield by increasing wind load and maximum plastic rotation is significantly increased, especially in across-wind directions. The amount of increasing the plastic rotation in the along-wind direction is considerably smaller than the across-wind direction.

Fig. 15. Comparison of the moment-rotation curve of critical coupling beams for different MRIs (Case-1, $R_{W R} = 2$ ).

Maximum plastic rotations of coupling beams for MRI of 500, 900, and 3,000 years are shown in Fig. 16. Because of the large C.O.V. of maximum plastic rotation, the maximum case among the 10 time series for each MRI is shown in the figure and was considered for comparison. Based on the results, both the number of yield elements and the maximum plastic rotation increase considerably by MRI. Furthermore, the difference in the across-wind direction is more significant. According to results, plastic rotations even for MRI of 3,000 years are much smaller than the limit value of 0.2% to 0.45%, and it can be concluded that failure due to low cycle fatigue is not much expected.

Fig. 16. Comparison of maximum plastic rotation in coupling beams for different MRIs (Case 1, $R_{W R} = 2$ ).

Since all acceptance criteria for continuous occupancy objectives are satisfied for MRIs of 900 and 3,000 years, which have significantly smaller annual probability, it can be concluded that there is a large margin of safety against failure mechanism.

Comparison of Aerodynamic Modification and Inelastic Wind Design Approaches

The performance assessment in the preceding sections showed that examined case study buildings could satisfy all acceptance criteria for immediate occupancy, operational, and continuous occupancy performance objectives of the ASCE prestandard. Seismic performance could be significantly improved using either aerodynamic modification or inelastic wind design with

R_{W R} = 2

. Through the PBWD procedure, it was shown that the maximum drifts of Case 1 with

R_{W R} = 1

and 2 were almost the same with similar C.O.V. Inelastic deformation in Case 1 with

R_{W R} = 2

is very small with a large margin of safety against failure. Because of very small inelastic deformations, the natural frequency of the system is not that much changed, and consequently demands remained almost the same. The performance of Case A was quite similar to that of Case 1 in the along-wind direction; however, the maximum drift in the across-wind direction was about 13% smaller. Required design sections for both Case A and Case 1 with

R_{W R} = 2

were similar.

However, the aerodynamic modification requires losing some part of the plan area and special treatment for corner parts. On the other hand, there can be extra costs after an extreme wind event for retrofitting Case 1 with

R_{W R} = 2

due to inelastic deformation. Based on the above discussion, the total cost for the aerodynamically modified model can be considered as the summation of construction material cost and the price of the reduced part of the plan at the corners. Similarly, the total cost for Case 1 with

R_{W R} = 2

can be considered as the summation of construction material cost and extra cost for retrofitting after an extreme wind event.

In this study, the same number of structural elements and member sizes are considered for both models. In addition, the reinforcement ratio for both models is comparable. If the required special treatment for the corner part of aerodynamic model is ignored, the construction material cost is almost the same. The retrofitting cost and price of the area depend on the conditions and regions. If the retrofitting cost and price of the area are similar, the total cost is very similar. To sum up, it can be concluded that the pros and cons of aerodynamic modification and inelastic wind design are comparable and eventually lead to almost the same performance.

Summary and Conclusion

In this paper, inelastic wind design and aerodynamic modification, in the forms of corner chamfering and recession, were applied to three case study buildings as two practical remedies for reduction of wind loads. Case 1 has sharp corners, Case 2 has 10% chamfered corners, and Case 3 has 10% recessed corners. Buildings were designed for both seismic and wind loads to show how dominantly elastic wind load governs the member design.

For this reason, loads and design reinforcement ratios were compared, and it was shown that aerodynamic modification and inelastic wind design could effectively reduce the wind load and required reinforcement ratio. Based on the results, the base shear and overturning moment of Case 1 under service load were 1.74 and 1.84 times that of seismic load, respectively. Aerodynamic modification reduced these ratios to 1.37 and 1.5. For the design level of load, wind load was reduced by about 20% using inelastic wind design and aerodynamic modification. However, the reduction in across-wind load by inelastic wind design was about 40%, which is more noticeable than the reduction by aerodynamic modification (about 20%). Inelastic wind design can significantly reduce the cost due to the less required reinforcement ratio. In the case of coupling beams, the reinforcement ratio was reduced by 30% to 40% through inelastic wind design, which is even more significant than the reduction by aerodynamic modification with

R_{W R} = 1

. The results of the performance assessment procedure showed that the designed buildings can meet the corresponding acceptance criteria and support that both aerodynamic modification and inelastic wind design approaches can be effectively used in practice. For continuous occupancy performance, the maximum drifts of Case 1 with

R_{W R} = 1

and 2 were almost the same. Inelastic deformation in Case 1 with

R_{W R} = 2

was very small with a large margin of safety against low cycle fatigue failure. The performance of the aerodynamically modified model was quite similar to Case 1 in the along-wind direction, but the maximum drift in the across-wind direction was about 13% smaller.

Though the required design reinforcement of both aerodynamic modification and Case 1 with

R_{W R} = 2

was similar, the aerodynamic modification requires losing some part of the plan area and special treatment for corner parts. Thus, it can be concluded that the advantages and disadvantages of aerodynamic modification and inelastic wind design are comparable for the case study buildings.

Appendix. Design Reinforcement Ratio

The design reinforcement ratio of members is reported in Tables 11–14. There is room for further optimization of members.

Table 11. Design reinforcing bar ratio for seismic load (Cases 1, 2, and 3)

Story	Moment frame beams												Moment frame columns						Coupling beams		Main core walls
	B1			B2			B3			B4			C1		C2		C3		Coupling beams		Main core walls
	$ρ_{b}$	$ρ_{t}$	$ρ_{v}$	$ρ_{b}$	$ρ_{t}$	$ρ_{v}$	$ρ_{b}$	$ρ_{t}$	$ρ_{v}$	$ρ_{b}$	$ρ_{t}$	$ρ_{v}$	$ρ$	$ρ_{v}$	$ρ$	$ρ_{v}$	$ρ$	$ρ_{v}$	$ρ_{b} = ρ_{t}$	$ρ_{v}$	$ρ_{v e r}$	$ρ_{h o r}$
1–4	0.18	0.27	0.08	0.18	0.31	0.08	0.18	0.40	0.08	0.18	0.40	0.08	2.57	0.14	2.57	0.14	1.03	0.14	0.31	0.08	0.16	0.28
5–8	0.18	0.31	0.08	0.18	0.36	0.08	0.22	0.45	0.08	0.22	0.45	0.08	2.03	0.14	2.03	0.14	1.03	0.14	0.34	0.08	0.16	0.28
9–12	0.18	0.31	0.08	0.18	0.36	0.08	0.27	0.50	0.08	0.22	0.50	0.08	1.03	0.14	2.03	0.14	1.03	0.14	0.34	0.08	0.16	0.28
13–16	0.18	0.31	0.08	0.18	0.36	0.08	0.27	0.59	0.08	0.27	0.54	0.08	1.03	0.14	1.03	0.14	1.03	0.14	0.34	0.08	0.16	0.28
17–20	0.18	0.31	0.08	0.18	0.36	0.08	0.27	0.59	0.08	0.27	0.59	0.08	1.03	0.14	1.03	0.14	1.03	0.14	0.34	0.08	0.16	0.28
21–24	0.18	0.31	0.08	0.18	0.36	0.08	0.31	0.68	0.08	0.31	0.68	0.08	1.07	0.12	1.07	0.12	1.07	0.12	0.34	0.08	0.16	0.28
25–28	0.18	0.31	0.08	0.18	0.36	0.08	0.36	0.78	0.08	0.36	0.73	0.08	1.07	0.12	1.07	0.12	1.07	0.12	0.34	0.08	0.16	0.28
29–32	0.18	0.31	0.08	0.18	0.36	0.08	0.36	0.78	0.08	0.36	0.78	0.08	1.07	0.12	1.07	0.12	1.07	0.12	0.34	0.08	0.16	0.28
33–36	0.18	0.31	0.08	0.18	0.36	0.08	0.36	0.82	0.08	0.36	0.78	0.08	1.07	0.12	1.07	0.12	1.07	0.12	0.34	0.08	0.16	0.28
37–40	0.18	0.31	0.08	0.18	0.36	0.08	0.36	0.82	0.08	0.36	0.78	0.08	1.07	0.12	1.07	0.12	1.07	0.12	0.34	0.08	0.16	0.28

Table 12. Design reinforcing bar ratio (%) of moment frame beams for wind and seismic loads

Story	Case 1						Cases 2 and 3
	$R_{W R} = 1$			$R_{W R} = 2$			$R_{W R} = 1$			$R_{W R} = 2$
	$ρ_{b}$	$ρ_{t}$	$ρ_{v}$	$ρ_{b}$	$ρ_{t}$	$ρ_{v}$	$ρ_{b}$	$ρ_{t}$	$ρ_{v}$	$ρ_{b}$	$ρ_{t}$	$ρ_{v}$
	B1
1–4	0.27	0.36	0.08	0.18	0.36	0.08	0.18	0.36	0.08	0.18	0.36	0.08
5–8	0.31	0.45	0.08	0.22	0.36	0.08	0.27	0.40	0.08	0.18	0.36	0.08
9–12	0.36	0.50	0.08	0.22	0.36	0.08	0.27	0.40	0.08	0.18	0.36	0.08
13–16	0.36	0.50	0.08	0.22	0.36	0.08	0.27	0.40	0.08	0.18	0.36	0.08
17–20	0.36	0.50	0.08	0.22	0.36	0.08	0.27	0.40	0.08	0.18	0.36	0.08
21–24	0.36	0.50	0.08	0.22	0.36	0.08	0.27	0.40	0.08	0.18	0.36	0.08
25–28	0.31	0.45	0.08	0.22	0.36	0.08	0.27	0.40	0.08	0.18	0.36	0.08
29–32	0.27	0.45	0.08	0.18	0.36	0.08	0.22	0.36	0.08	0.18	0.36	0.08
33–36	0.27	0.40	0.08	0.18	0.36	0.08	0.27	0.40	0.08	0.18	0.36	0.08
37–40	0.22	0.40	0.08	0.18	0.36	0.08	0.22	0.36	0.08	0.18	0.36	0.08
	B2
1–4	0.27	0.40	0.08	0.22	0.36	0.08	0.22	0.36	0.08	0.18	0.31	0.08
5–8	0.36	0.50	0.08	0.27	0.40	0.08	0.31	0.36	0.08	0.18	0.36	0.08
9–12	0.36	0.54	0.08	0.27	0.45	0.08	0.31	0.36	0.08	0.18	0.36	0.08
13–16	0.36	0.59	0.08	0.27	0.45	0.08	0.31	0.36	0.08	0.18	0.36	0.08
17–20	0.36	0.59	0.08	0.27	0.45	0.08	0.31	0.36	0.08	0.18	0.36	0.08
21–24	0.36	0.59	0.08	0.27	0.45	0.08	0.22	0.36	0.08	0.18	0.36	0.08
25–28	0.36	0.59	0.08	0.27	0.45	0.08	0.22	0.36	0.08	0.18	0.36	0.08
29–32	0.36	0.54	0.08	0.27	0.45	0.08	0.18	0.36	0.08	0.18	0.36	0.08
33–36	0.31	0.54	0.08	0.27	0.40	0.08	0.18	0.36	0.08	0.18	0.36	0.08
37–40	0.31	0.50	0.08	0.22	0.40	0.08	0.18	0.36	0.08	0.18	0.36	0.08
	B3
1–4	0.31	0.73	0.08	0.27	0.59	0.08	0.31	0.63	0.08	0.22	0.50	0.08
5–8	0.36	0.92	0.08	0.31	0.68	0.08	0.36	0.78	0.08	0.27	0.59	0.08
9–12	0.36	0.99	0.08	0.36	0.78	0.08	0.36	0.92	0.08	0.31	0.68	0.08
13–16	0.40	1.05	0.08	0.36	0.82	0.08	0.36	0.92	0.08	0.31	0.73	0.08
17–20	0.40	1.05	0.08	0.36	0.87	0.08	0.36	0.99	0.08	0.36	0.73	0.08
21–24	0.40	1.12	0.08	0.36	0.92	0.08	0.36	0.99	0.08	0.36	0.82	0.08
25–28	0.40	1.12	0.08	0.36	0.92	0.08	0.36	0.99	0.08	0.36	0.82	0.08
29–32	0.40	1.12	0.08	0.36	0.92	0.08	0.36	0.99	0.08	0.36	0.87	0.08
33–36	0.40	1.12	0.08	0.36	0.92	0.08	0.36	0.99	0.08	0.36	0.87	0.08
37–40	0.40	1.12	0.08	0.36	0.92	0.08	0.36	0.99	0.08	0.36	0.87	0.08
	B4
1–4	0.36	0.73	0.08	0.27	0.59	0.08	0.36	0.54	0.08	0.22	0.40	0.08
5–8	0.40	0.92	0.08	0.31	0.68	0.08	0.40	0.68	0.08	0.31	0.50	0.08
9–12	0.45	1.11	0.08	0.36	0.78	0.08	0.40	0.82	0.08	0.31	0.59	0.08
13–16	0.45	1.12	0.10	0.36	0.87	0.08	0.40	0.87	0.08	0.31	0.63	0.08
17–20	0.50	1.19	0.12	0.36	0.92	0.08	0.36	0.87	0.08	0.31	0.68	0.08
21–24	0.45	1.19	0.12	0.36	0.92	0.08	0.36	0.92	0.08	0.36	0.73	0.08
25–28	0.45	1.19	0.12	0.36	0.99	0.08	0.36	0.92	0.08	0.36	0.78	0.08
29–32	0.45	1.19	0.12	0.36	0.99	0.08	0.36	0.92	0.08	0.36	0.78	0.08
33–36	0.45	1.19	0.12	0.36	0.99	0.08	0.36	0.92	0.08	0.36	0.82	0.08
37–40	0.40	1.19	0.12	0.36	0.99	0.08	0.36	0.92	0.08	0.36	0.82	0.08

Table 13. Design reinforcing bar ratio (%) of moment frame columns for wind and seismic loads

Story	Case 1				Cases 2 and 3
	$R_{W R} = 1$		$R_{W R} = 2$		$R_{W R} = 1$		$R_{W R} = 2$
	$ρ$	$ρ_{v}$	$ρ$	$ρ_{v}$	$ρ$	$ρ_{v}$	$ρ$	$ρ_{v}$
	C1
1–4	2.57	0.14	2.57	0.14	2.57	0.14	2.57	0.14
5–8	2.57	0.14	2.57	0.14	2.57	0.14	2.03	0.14
9–12	2.03	0.14	1.15	0.14	1.15	0.14	1.03	0.14
13–16	1.03	0.14	1.03	0.14	1.03	0.14	1.03	0.14
17–20	1.03	0.14	1.03	0.14	1.03	0.14	1.03	0.14
21–24	1.07	0.12	1.07	0.12	1.07	0.12	1.07	0.12
25–28	1.07	0.12	1.07	0.12	1.07	0.12	1.07	0.12
29–32	1.07	0.12	1.07	0.12	1.07	0.12	1.07	0.12
33–36	1.07	0.12	1.07	0.12	1.07	0.12	1.07	0.12
37–40	1.07	0.12	1.07	0.12	1.07	0.12	1.07	0.12
	C2
1–4	2.57	0.14	2.57	0.14	2.57	0.14	2.57	0.14
5–8	2.57	0.14	2.57	0.14	2.57	0.14	2.03	0.14
9–12	2.03	0.14	2.03	0.14	2.03	0.14	2.03	0.14
13–16	2.03	0.14	1.03	0.14	1.03	0.14	1.03	0.14
17–20	1.03	0.14	1.03	0.14	1.03	0.14	1.03	0.14
21–24	1.07	0.12	1.07	0.12	1.07	0.12	1.07	0.12
25–28	1.07	0.12	1.07	0.12	1.07	0.12	1.07	0.12
29–32	1.07	0.12	1.07	0.12	1.07	0.12	1.07	0.12
33–36	1.07	0.12	1.07	0.12	1.07	0.12	1.07	0.12
37–40	1.07	0.12	1.07	0.12	1.07	0.12	1.07	0.12
	C3
1–4	2.57	0.14	2.57	0.14	2.57	0.14	2.57	0.14
5–8	2.03	0.14	2.03	0.14	2.03	0.14	2.03	0.14
9–12	1.03	0.14	1.03	0.14	2.03	0.14	1.03	0.14
13–16	1.03	0.14	1.03	0.14	1.03	0.14	1.03	0.14
17–20	1.03	0.14	1.03	0.14	1.03	0.14	1.03	0.14
21–24	1.07	0.12	1.07	0.12	1.07	0.12	1.07	0.12
25–28	1.07	0.12	1.07	0.12	1.07	0.12	1.07	0.12
29–32	1.07	0.12	1.07	0.12	1.07	0.12	1.07	0.12
33–36	1.07	0.12	1.07	0.12	1.07	0.12	1.07	0.12
37–40	1.07	0.12	1.07	0.12	1.07	0.12	1.07	0.12

Table 14. Design reinforcing bar ratio (%) of coupling beams and main core walls for wind and seismic loads

Story	Coupling beams: Case 1				Coupling beams: Cases 2 and 3				Main core walls: Case 1				Main core walls: Cases 2 and 3
	$R_{W R} = 1$		$R_{W R} = 2$		$R_{W R} = 1$		$R_{W R} = 2$		$R_{W R} = 1$		$R_{W R} = 2$		$R_{W R} = 1$		$R_{W R} = 2$
	$ρ_{b} = ρ_{t}$	$ρ_{v}$	$ρ_{b} = ρ_{t}$	$ρ_{v}$	$ρ_{b} = ρ_{t}$	$ρ_{v}$	$ρ_{b} = ρ_{t}$	$ρ_{v}$	$ρ_{v e r}$	$ρ_{h o r}$	$ρ_{v e r}$	$ρ_{h o r}$	$ρ_{v e r}$	$ρ_{h o r}$	$ρ_{v e r}$	$ρ_{h o r}$
1–4	0.85	0.44	0.61	0.28	0.65	0.44	0.46	0.16	0.28	0.28	0.16	0.28	0.28	0.28	0.16	0.28
5–8	1.53	0.88	1.01	0.88	1.13	0.88	0.73	0.44	0.28	0.28	0.16	0.28	0.28	0.28	0.16	0.28
9–12	1.58	0.88	1.05	0.88	1.20	0.88	0.73	0.44	0.28	0.28	0.16	0.28	0.16	0.28	0.16	0.28
13–16	1.58	0.88	1.05	0.88	1.20	0.88	0.73	0.44	0.28	0.28	0.16	0.28	0.16	0.28	0.16	0.28
17–20	1.58	0.88	0.97	0.88	1.20	0.88	0.69	0.44	0.28	0.28	0.16	0.28	0.16	0.28	0.16	0.28
21–24	1.47	0.88	0.85	0.88	1.09	0.88	0.61	0.28	0.28	0.28	0.16	0.28	0.16	0.28	0.16	0.28
25–28	1.26	0.88	0.75	0.44	0.97	0.88	0.53	0.28	0.16	0.28	0.16	0.28	0.16	0.28	0.16	0.28
29–32	1.09	0.88	0.61	0.44	0.83	0.88	0.46	0.16	0.16	0.28	0.16	0.28	0.16	0.28	0.16	0.28
33–36	0.89	0.44	0.53	0.28	0.69	0.44	0.46	0.16	0.16	0.28	0.16	0.28	0.16	0.28	0.16	0.28
37–40	0.75	0.44	0.46	0.28	0.57	0.28	0.34	0.08	0.16	0.28	0.16	0.28	0.16	0.28	0.16	0.28

Data Availability Statement

All data, models, and code generated or used during the study appear in the published article.

Acknowledgments

The research described in this paper was financially supported by the National Research Foundation of Korea (NRF) (No. 2021R1A5A1032433) and the Institute of Construction and Environmental Engineering at Seoul National University. The discussion of Dr. Seung Yong Jeong on the ETABS modeling and Prof. Ki-Pyo You on the wind tunnel testing was greatly appreciated. The views expressed herein are those of the authors, and do not necessarily represent those of the sponsor or discussors.

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Information & Authors

Information

Published In

Journal of Structural Engineering

Volume 150 • Issue 7 • July 2024

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This work is made available under the terms of the Creative Commons Attribution 4.0 International license, https://creativecommons.org/licenses/by/4.0/.

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Received: Aug 12, 2023

Accepted: Jan 22, 2024

Published online: May 14, 2024

Published in print: Jul 1, 2024

Discussion open until: Oct 14, 2024

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Hamidreza Alinejad https://orcid.org/0000-0002-4616-2131 [email protected]

Postdoctoral Researcher, Institute of Engineering Research, Seoul National Univ., 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Korea. ORCID: https://orcid.org/0000-0002-4616-2131. Email: [email protected]

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Byeonguk Ahn https://orcid.org/0000-0003-2365-1669 [email protected]

Ph.D. Student, Dept. of Architecture and Architectural Engineering, Seoul National Univ., 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Korea. ORCID: https://orcid.org/0000-0003-2365-1669. Email: [email protected]

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Thomas H.-K. Kang, M.ASCE [email protected]

Professor, Dept. of Architecture and Architectural Engineering and Institute of Engineering Research, Seoul National Univ., 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Korea (corresponding author). Email: [email protected]

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Abstract

Introduction

Research Significance

Case Study Buildings

Design Procedure

Wind Tunnel Test

Equivalent Static Wind Loads

Comparison of Design Forces and Sections

Performance-Based Wind Design Procedure

Performance Objectives and Criteria

Nonlinear Modeling Assumptions

Performance-Based Assessment

Occupancy Comfort and Operational Performance Levels

Continuous Occupancy Performance Level

Safety Evaluation

Comparison of Aerodynamic Modification and Inelastic Wind Design Approaches

Summary and Conclusion

Appendix. Design Reinforcement Ratio

Data Availability Statement

Acknowledgments

References

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