1

BEHAVIOR AND DESIGN OF FIN WALLS AT THE PERIPHERY OF 1

STRONG CORE WALL STRUCTURE IN HIGH-RISE BUILDINGS 2

3

Taesung Eoma, Su-Min Kangb*, Seung-Yoon Yuc, Jae-Yo Kimd, Dong Kwan Kime 4

5

aDepartment of Architectural Engineering, Dankook Univ., 152 Jukjeon-ro, Gyeonggi-do, 6

Korea, 448-701, Email: tseom@dankook.ac.kr, M: +82-10-3296-9678. 7

bDepartment of Architectural Engineering, Chungbuk National University, Chungdae-ro 1, 8

Seowon-Gu, Cheongju, Chungbuk, Korea, 361-763, *Corresponding Author, Email: 9

kangsm@cbnu.ac.kr, M: +82-10-9208-4116. 10

cDepartment of Architectural Engineering, Chungbuk National University, Chungdae-ro 1, 11

Seowon-Gu, Cheongju, Chungbuk, Korea, 361-763, dbtmddbs3414@naver.com, M: +82-10-12

6674-4180 13

dDepartment of Architectural Engineering, Kwangwoon University, Nowon-gu, Seoul, Korea, 14

139-701, kimjyo@kw.ac.kr, M: +82-10-3215-9437. 15

eDepartment of Architectural Engineering, Cheongju University, Daeseong-ro 298, 16

Cheongwon-gu, Cheongju, Chungbuk, Korea, dkkim@senkuzo.com, M: +82-10-2886-8216. 17

18

Biography: 19

Tae-Sung Eom is an Associate Professor of the department of architectural engineering at 20

Dankook University in South Korea. He received his BE, MS, and PhD in architectural 21

engineering from Seoul National University. His research interests include nonlinear analysis 22

and seismic design of RC structures. 23

2

Su-Min Kang is an assistant professor of the department of architectural engineering at 24

Chungbuk National University in South Korea. He received his BE, MS, and PhD in 25

architectural engineering from Seoul National University. His research interests include 26

earthquake design of reinforced concrete structures. Corresponding author. 27

Seung-Yoon Yu is a graduate student of the department of architectural engineering at 28

Chungbuk National University in South Korea. He received his BE in architectural 29

engineering from Chungbuk National University. His research interests include earthquake 30

design of reinforced concrete structural walls. 31

Jae-Yo Kim is a professor of the department of architectural engineering at Kwangwoon 32

University in South Korea. He received his BE, MS, and PhD in architectural engineering 33

from Seoul National University. His research interests include inelastic FE analysis of 34

reinforced concrete structures and serviceability of RC flat-plate system. 35

Dong Kwan Kim is an assistant professor of the department of architectural engineering at 36

Cheongju University in South Korea. He received his BE, MS, and PhD in architectural 37

engineering from Seoul National University. His research interests include earthquake design 38

of reinforced concrete structures and seismic wave generation for earthquake design. 39

40

Abstract 41

In high-rise buildings, lateral loads, such as wind and seismic loads, are frequently resisted by 42

reinforced concrete (RC) structural walls. Behavior and design of fin walls at the periphery of 43

strong core wall structure in high-rise buildings were not analyzed seriously despite their 44

structural importance. Using elastic design/analysis methodologies for the design of high-rise 45

RC fin walls, it is shown that elicited reinforcement ratios are too high, the economic 46

feasibility and constructability thus becomes worse and the ductile failure mode can not be 47

3

assured. In the present study, the current design process of these fin walls is investigated by 48

analyzing their structural behavior. According to the investigation of the current design and 49

elicited results, high-rise RC fin walls are coupled by beams although they are located on 50

another line and apart from each other, which is main cause of high reinforcement in high-rise 51

RC fin walls. In the present study, a literature review has been conducted to recommend the 52

alternative design method for high-rise RC fin walls under lateral loads, and inelastic analysis 53

has been performed to verify the design method. 54

Keywords: High-rise RC structural walls, Fin walls, Alternative design, Inelastic analysis, 55

Coupling beam, High-rise building design 56

57

1. Introduction 58

In high-rise buildings, lateral loads, such as wind and seismic loads, are frequently resisted by 59

reinforced concrete (RC) structural walls [1~3]. Since RC structural walls have large stiffness 60

and strength, they can control deformation and efficiently assure the strength of the building 61

structure. In the structural design of RC building structures, the RC structural walls are 62

designed as independent single walls (isolated walls) or coupled walls connected by 63

connecting beams which are located closely on a straight line. However, in the high-rise RC 64

building structures, in many cases, the structural RC walls were located on another line and 65

apart from each other, and they are designed generally as independent single walls (isolated 66

walls) without the consideration for their structural behavior. 67

Fig. 1 shows a typical example of a structural system for a 35 story residential building. As 68

shown in Fig. 1, the gravity load is resisted by the RC flat plate slab and the RC column. 69

Currently, RC flat plates are used frequently as a slab system since they can decrease the floor 70

height and construction time, and increase space utilization and constructability. As shown in 71

4

Fig. 1(b), the lateral load is frequently resisted by RC structural walls since they have large 72

stiffness and strength owing to their long length. Fig. 2 shows the plan of the building drawn 73

in Fig. 1. As mentioned above, RC structural walls are located in the center of the plan to 74

resist the lateral load. In the plan, some RC structural walls extend from the center to the 75

boundary of the plan, which were called as “Fin walls” (Fin walls indicate planar walls such 76

as W1 ~ W5 which were installed along the perimeter of the rectangular core wall structure, 77

as shown in Fig. 2). These RC structural walls, fin walls, are used frequently to divide the 78

space for architectural design and to control the lateral deflection of the high-rise building 79

because they can enlarge effectively the moment inertia of the building system. Generally 80

they are located on another line and apart from each other, and they are designed as 81

independent single walls without the sufficient consideration for their structural behavior. 82

However, as shown in Table 1, the reinforcement ratio of these RC fin walls at floor B3 83

ranges from 0.59% to 3.38%. In accordance to the current structural design code, such as ACI 84

318-14 [4], the reinforcement ratio of the RC structural walls is limited to 1% when they are 85

not enclosed by transverse ties. Therefore, some of these structural walls violate the 86

requirement prescribed by the design code if they are not enclosed by transverse ties. 87

Furthermore, in the cases where the reinforcement ratio is more than 1%, its value is 88

considered to be too high to assure economic feasibility and constructability. Moreover, the 89

application of the transverse ties to the RC structural walls having more than 1% 90

reinforcement ratio decreases significantly the constructability. And, if the flexural 91

reinforcement in high-rise RC structural walls was placed excessively without the 92

consideration for their structural behavior, it may lead to unexpected brittle shear failure of 93

high-rise RC structural walls. In this study, structural behavior of fin walls installed along the 94

periphery of strong core wall structure in high-rise buildings were studied. Elastic analysis of 95

5

a 35-story high-rise building with core walls and fin walls was performed and the design 96

loads acting on each fin wall such as axial load and bending moment were investigated. 97

Further, flexure-compression design of the fin walls were carried out and the reason why the 98

design results (i.e. reinforcement amounts) significantly differed among the fin walls was then 99

discussed in detail. Based on these investigations, their alternative design method was 100

investigated based on literature review. And this alternative design method was verified using 101

the latest structural analysis method for RC structural wall system. 102

103

2. Investigation on the results from the current design 104

As mentioned above, the values of the flexural reinforcement ratios of RC fin walls that 105

extend from the center to the boundary of the plan are too high (Table 1). In this study, 106

applied loads and strengths of the walls W2 and W3 at floor B3 that yielded the largest 107

flexural reinforcement ratio, were investigated through elastic analyses using the Midas Gen 108

program [5]. Recently, new theories on the structural analysis of beams and plates have been 109

developed to improve accuracy and convergence. Bourada, M., Kaci, A., Houari, M.S.A. and 110

Tounsi, A. (2015) developed a simple and refined trigonometric higher-order beam theory for 111

functionally graded beams [6]. Tounsi et al. (2016) proposed a new 3-unknowns non-112

polynomial plate theory for functionally graded sandwich plate [7]. Hebali et al (2014) 113

developed a new quasi-3D hyperbolic shear deformation theory for functionally graded plates 114

[8]. Bennoun, M., Houari, M.S.A. and Tounsi, A. (2016) devised a novel five variable refined 115

plate theory for functionally graded sandwich plates [9]. Ait Yahia, S., Ait Atmane, H., 116

Houari, M.S.A. and Tounsi, A. (2015) investigated wave propagation in functionally graded 117

plates [10]. Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Anwar Bég, O. 118

(2014) invented an efficient and simple higher order shear and normal deformation theory 119

6

[11]. Houari, M.S.A., Tounsi, A., Bessaim, A., and Mahmoud, S.R. (2016) developed a new 120

simple three-unknown sinusoidal shear deformation theory for functionally graded plates 121

[12]. Mahi, A., Adda Bedia, E.A. and Tounsi, A. (2015) proposed a new hyperbolic shear 122

deformation theory for functionally graded, sandwich and laminated composite plates [13]. 123

However, in this study, to investigate the overall behavior of high-rise RC structural wall 124

system in an overall framework and to use commercial program, the Midas Gen program [5] 125

which is FEM program using conventional beam theory was used. 126

In Fig. 3, the P-M relationship curves of walls W2 and W3 at floor B3 are shown as the 127

strength capacity of these wall sections. Moreover, round dots in Fig. 3(b) and 3(c) represent 128

the applied axial load and moment according to load combinations. As shown in Fig. 3(b) and 129

3(c), the flexural reinforcement ratio of walls W2 and W3 was determined based on the load 130

case, including the wind load (W1, W2), which is a common phenomenon in high-rise 131

buildings. Therefore, walls W2 and W3 are designed to resist the wind load as the critical 132

lateral load. In Fig. 3(b) and 3(c), the axial load is proportional to the moment load. This is 133

not a typical feature for isolated RC structural walls in general. In Fig. 4, the axial load 134

applied on walls W2 and W3 was investigated according to the load case. As shown in this 135

figure, the axial load of wall W2 is inversely proportional to that of wall W3. This means that 136

wall W2 and W3 are coupled with each other by the coupling beams, although the two walls 137

are physically located far apart from each other and on another line. 138

As shown in Fig. 4(b), walls W2 and W3 are connected by center walls and coupling beams. 139

Since center walls have relatively large stiffness, the coupling level of walls W2 and W3 may 140

be determined by the stiffness of the coupling beams. To verify this coupling behavior of 141

walls W2 and W3, their strain distribution under the wind load was investigated according to 142

the stiffness of the coupling beams (Fig. 5). In the present study, strain distribution of coupled 143

7

walls under the wind load was calculated by cross-sectional analysis. The cross-sectional 144

analysis was based on the plane hypothesis and the equilibrium condition. The stress-strain 145

relation for the concrete and steel rebar was assumed to be linear because, in the majority of 146

cases, the maximum concrete stress was less than half the concrete strength and the maximum 147

tensile stress of steel rebar was much less than the yield stress. As shown in Fig. 5, the strain 148

distribution of walls W2 and W3 with stronger coupling beams under the wind load shows an 149

increased linearity in the distribution of strain. This means that as the stiffness of the coupling 150

beams becomes large, the walls W2 and W3 will behave as one unified wall. Therefore, the 151

walls W2 and W3 are coupled by the coupling beams although they are located far apart with 152

respect to each other and on another line, and the stiffness of the coupling beams is a key 153

factor that determines the coupling level. 154

As shown in Fig. 6(a), when the walls are coupled by coupling beams, these beams 155

experience large deformation under lateral loads owing to the geometric shape of beams and 156

walls. Because of this large deformation elicited under a lateral load, large shear forces occur 157

in coupling beams. Correspondingly, these forces are then transferred to the coupled walls as 158

an axial load [1]. In the case of high-rise buildings, the number of coupling beams is very 159

large and the axial load that is transferred to the coupled walls is also large. As shown in Fig. 160

6(b), when the wind load is applied from the left direction to the right, the additional axial 161

tensile load owing to the coupling beams is applied to wall W2, and the additional axial 162

compressive load exerted by the coupling beams is applied to wall W3. As shown in Fig. 6(c), 163

when an additional axial tensile load is applied to RC structural walls, the moment capacity of 164

these walls decreases and additional flexural reinforcement is needed to resist the applied 165

moment load. As shown in Fig. 6(d), sometimes, when the additional axial compressive load 166

that is applied is too high, the strength reduction factor for the structural RC walls would be 167

8

decreased. Therefore, in this case, additional flexural reinforcement or high-strength concrete 168

should be used. Accordingly, the high flexural reinforcement ratio of the walls (which extend 169

from the center to the boundary of the plan) is caused by the additional axial load from the 170

coupling of the beams. Moreover, these additional axial loads are relatively very high in value 171

because of the large deformation of the coupling beams, shown in Fig. 6(a). 172

However, the additional axial load from the coupling beam, which is calculated as part of the 173

elastic analysis, is larger than the value elicited from the actual behavior since the strength of 174

the coupling beam is limited by the actual details of the beams [1, 14]. Therefore, 175

consideration of the actual behavior of the coupled wall system can lead to a proposition of a 176

reasonable design of these fin walls. 177

178

3. Actual behavior and reasonable design of coupled fin walls 179

To investigate the actual behavior of the coupled wall system, a literature review and an 180

inelastic analysis was performed. According to Paulay and Priestley [1], the strength of a 181

coupled wall system under lateral load can be determined by controlling the strength of 182

individual walls as indicated below: 183

𝑀 = 𝑀1 +𝑀2 + 𝑙𝑆 × 𝑇 (1)

where 𝑀 is the strength of the coupled wall system, 𝑀1(𝑀2) is the strength of the individual 184

wall with additional axial tensile(compressive) load, 𝑇 is the axial load caused by the 185

coupling beams and 𝑙𝑠 is the length between the centroids of the coupled walls (See Fig.7). In 186

the coupled wall system, the shear force generated by the coupling beams was transferred to 187

the axial load of the wall. Generally, as shown in Fig. 7, the shear force (V) generated by the 188

coupling beams is limited by the moment strength of coupling beams (Mb,i) because the beams 189

are designed to yield prior to failure by shear. Therefore, the axial load in the wall base (T) 190

9

can be calculated by summating the shear force of the coupling beams at each story as 191

follows[1]: 192

𝑇 =∑𝑀𝑏,𝑖/2𝑙𝑏

𝑛

𝑖=1

(2)

where 𝑀𝑏,𝑖 is the moment strength of the coupling beams, 𝑙𝑏 is the beam length and 𝑛 is the 193

number of beam. 194

Therefore, the axial load transferred to the walls can be determined from the strength of 195

the coupling beams. According to Paulay and Priestley [1], Paulay [14, 15], and Santhakumar 196

[16], the moment loading of an individual wall in a coupled wall system can be redistributed 197

by maintaining the strength of the system [Eq. (1)]. Therefore, using this design concept, the 198

reinforcement ratio of the wall with an additional axial tensile load can be decreased by 199

sending its moment load to the wall with an additional axial compressive load [1]. 200

Correspondingly, the moment strength capacity of the wall is enlarged owing to the additional 201

axial compressive load. In the present study, in order to verify this moment redistribution 202

method for the coupled wall system and investigate its actual behavior, inelastic analysis was 203

performed. 204

According to Kim et al. [17] and Park and Eom [18], the ultimate behavior of a coupled 205

wall system can be accurately simulated by the longitudinal-and-diagonal-line-element-model 206

(LDLEM) method. The LDLEM method has excellent stability for numerical analysis of 207

structural wall systems because it consists of simple trusses as a macro model as shown in Fig. 208

8. Therefore, in this study, the LDLEM method was adopted for the inelastic analysis of a 209

coupled wall system consisting of a number of structural members. 210

In the LDLEM method, the unit wall between the adjacent floors can be simulated using a 211

simple longitudinal and diagonal truss model (see Fig. 8). The diagonal truss was used to 212

10

represent the shear resisting element and the diagonal truss angle (θc) was defined to be the 213

diagonal crack angle in the web of the RC wall. The diagonal crack angle could be calculated 214

using the modified compression field theory proposed by Vecchio and Collins [19]. Moreover, 215

according to Kim et al. [17], the diagonal truss angle could be simplified to 45° for practical 216

analysis. In this study, the material model of the concrete and steel for a truss element was 217

defined as the stress–strain relationship to reflect the inelastic behavior of the coupled wall 218

system, as shown in Fig. 9. 219

As shown in Fig. 10, the prototype model of the coupled wall system (model A, model B) 220

is selected for the inelastic analysis. Model A is representative model for the typical design 221

result of the coupled wall system under elastic analysis. In this case, a high reinforcement 222

ratio value is assumed for the wall with an additional axial tensile load (𝜌𝑓 = 0.015 ) and a 223

low reinforcement ratio value is assumed for the wall with an additional axial compressive 224

load (𝜌𝑓 = 0.005 ). On the other hand, in the case of model B, the reinforcement ratio of the 225

coupled wall is unified as 𝜌𝑓 = 0.01 and this reinforcement ratio is determined by equalizing 226

the sum of the individual moment strengths of model B to that of model A [𝑀′1 +227

𝑀′2(model B) = 𝑀1 +𝑀2(model A), see Fig.10.]. Except for the reinforcement ratio of the 228

coupled walls, the other design parameters of model A and model B are the same. 229

The LDLEM analysis for model A and model B in Fig. 10 was conducted by using 230

OpenSEES program (PEER 2001[22]). Static pushover analysis was performed by 231

displacement control. The coupling beams in model A and model B were modeled with 232

equivalent beam elements (nonlinear Beam-Column Element of OpenSEES (PEER 2001) 233

with fiber section). And concrete elements resist only compressive force, which structural 234

behavior was determined by material model in Fig 9(a). 235

Using the LDLEM method that simulated the ultimate behavior of the coupled wall system 236

11

(model A and model B), the relationship of the total moment capacity at the base and the drift 237

at the roof was investigated, as shown in Fig. 11. According to Fig. 11, model A and model B 238

show almost the same behavior under a lateral load. The structural performances (stiffness, 239

strength and deformability) of the coupled wall systems before/after the moment 240

redistribution are almost identical. Therefore, the moment redistribution concept [1, 14, 16] 241

for the effective design of the coupled fin walls in high-rise buildings was verified through 242

LDLEM analysis method. Particularly, the high reinforcement ratio of the walls with an 243

additional axial tensile load can be reduced when the moment redistribution concept is used as 244

Paulay and Priestley proposed [1]. If the structural design was performed according to elastic 245

analysis, the flexural reinforcement might be placed such as the pattern of Model A, where 246

the amount of flexural reinforcement in tension-side wall is larger than that of Model B. If 247

lateral load in the opposite direction is applied, the existing compression-side wall will 248

become tension-side wall and the amount of flexural reinforcement will increase. As a result, 249

in the structural design based on the elastic analysis, the amount of the flexural reinforcement 250

is determined by the amount of the flexural reinforcement of the tension-side wall. And 251

according to the result of the analysis of the model B, the design by the elastic analysis has a 252

greater flexural performance than the flexural performance required for the design load. These 253

design results decrease the economic feasibility and constructability. Moreover, excessive 254

flexural performance of high-rise RC structural walls may lead to their unexpected brittle 255

shear failure. Therefore, to assure structural safety and economic feasibility, the use of 256

moment redistribution method should be considered seriously. However, further studies are 257

still required to verify the moment redistribution concept under various design parameters and 258

to identify the limitations of this method. 259

260

12

4. Conclusions 261

In high-rise buildings, lateral loads, such as wind and seismic loads, are frequently resisted by 262

RC structural walls since they have a large stiffness and strength. In the high-rise RC building 263

structures, in many cases, the structural RC walls were located on another line and apart from 264

each other, and they are designed generally as independent single walls (isolated walls) 265

without the consideration for their structural behavior. Especially, behavior and design of fin 266

walls at the periphery of strong core wall structure in high-rise buildings were not analyzed 267

seriously despite their structural importance. Sometimes, these RC fin walls, which extend 268

from the center to the boundary of the plan, have a large reinforcement ratio that is more than 269

1%. Such a value cannot assure economic feasibility and constructability. In the present study, 270

the current design process of these fin walls is investigated, and inelastic analysis and 271

literature review is performed to study the actual behavior of these RC fin walls, and to 272

recommend the alternative design method for them. According to the investigation of the 273

current design and elicited results, the walls, which are located far apart from each other and 274

which are connected by center walls and beams on another line, are coupled by the beams. 275

Therefore, owing to the large deformation of the coupling beams under the lateral load, large 276

shear forces occur in coupling beams that are subsequently transferred to the coupled walls as 277

an axial load. Moreover, in the case of high-rise buildings, the number of coupling beams is 278

very large and the axial load that is transferred to the coupled walls is also large. These 279

additional axial forces result in a significant reinforcement of the coupled walls. However, the 280

additional axial load from the coupling beam, which is calculated using the current elastic 281

analysis, is larger than that elicited actually since the strength of the coupling beam is limited 282

by the actual detail of the beams. Accordingly, the high-rise RC fin walls, which are located 283

far apart from each other and which are connected by center walls and beams on another line 284

13

should be designed as coupled wall system instead of isolated walls. 285

In the present study, the moment redistribution method is introduced as alternative design 286

method for high-rise RC fin wall system through a literature review. And it was verified by 287

the inelastic analysis using the LDLEM method which was newly-developed and specialized 288

structural analysis method for RC wall systems. According to the results of the inelastic 289

analysis and the literature review, the moment redistribution concept can be used for the 290

effective design of the RC fin walls in high-rise buildings. Particularly, by using the moment 291

redistribution concept, the high reinforcement ratio of the walls with additional axial tensile 292

load can be reduced and the unexpected shear failure of high-rise RC structural systems can 293

be avoided by protecting their excessive flexural performance. However, further studies are 294

still required to verify the moment redistribution concept under various design parameters and 295

to identify the limitations of this method. 296

297

Acknowledgement 298

This work was supported by the research grants of the National Research Foundation of 299

Korea (NRF) (No. 2015R1C1A1A01053471 and Code R-2015-00441 [Mid-career Research 300

Program]). The authors are grateful to the authorities for their support. 301

302

Reference 303

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Buildings”, John Wiley & Sons, New York (1992). 305

[2] Taranath B. S. “Reinforced Concrete Design of Tall Buildings”, CRC Press, london 306

(2009). 307

[3] Kaltakci, M.Y., Arslan, M.H. and Yavuz, G., “Effect of Internal and External Shear Wall 308

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Engineering; Vol. 17, No.4, pp. 312-323 (2010). 310

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American Concrete Institute, Farmington Hills. MI (2014). 312

[5] Midasit, http://www.midasit.com. 313

[6] Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A., “A new simple shear and normal 314

deformations theory for functionally graded beams”, Steel and Composite Structures, 315

18(2), pp. 409 – 423 (2015). 316

[7] Tounsi, A., Houari, M.S.A. and Bessaim, A. , “A new 3-unknowns non-polynomial plate 317

theory for buckling and vibration of functionally graded sandwich plate”, Struct. Eng. 318

Mech., Int. J., 60(4), pp.547 – 565 (2016). 319

[8] Hebali, H. Tounsi, A., Houari, M.S.A. Bessaim, A and Bedia, E.A.A, “New quasi-3D 320

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functionally graded plates”, ASCE J. Engineering Mechanics, 140(2), pp. 374 – 383 322

(2014). 323

[9] Bennoun, M., Houari, M.S.A. and Tounsi, A., “A novel five variable refined plate theory 324

for vibration analysis of functionally graded sandwich plates”, Mechanics of Advanced 325

Materials and Structures, 23(4), pp. 423 – 431 (2016). 326

[10] Ait Yahia, S., Ait Atmane, H., Houari, M.S.A. and Tounsi, A., “Wave propagation in 327

functionally graded plates with porosities using various higher-order shear deformation 328

plate theories”, Structural Engineering and Mechanics, 53(6), pp. 1143 – 1165 (2015). 329

[11] Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Anwar Bég, O., "An 330

efficient and simple higher order shear and normal deformation theory for functionally 331

graded material (FGM) plates”, Composites: Part B, 60, pp. 274–283 (2014). 332

15

[12] Houari, M.S.A., Tounsi, A., Bessaim, A. and Mahmoud, S.R., "A new simple three-333

unknown sinusoidal shear deformation theory for functionally graded plates", Steel and 334

Composite Structures, 22(2), pp. 257 – 276 (2016). 335

[13] Mahi, A., Adda Bedia, E.A. and Tounsi, A., "A new hyperbolic shear deformation theory 336

for bending and free vibration analysis of isotropic, functionally graded, sandwich and 337

laminated composite plates”, Applied Mathematical Modelling, 39, pp. 2489–2508 (2015). 338

[14] Paulay, T. “Seismic Design in Reinforced Concrete-The State of The Art in New 339

Zealand”, Proceeding of 9th World Conference on Earthquake Engineering, Tokyo, Japan 340

(1988). 341

[15] Paulay, T. “ The Philosophy and Application of Capacity Design”’ Scientia Iranica, 342

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[16] Santhakumar, A.R. “The Ductility of Coupled Shear Wall”, PhD thesis, University of 344

Canterbury, Chrischurch, New Zealand (1974). 345

[17] Kim, D. K., Eom, T. S., Lim, Y. J., Lee, H. S. and Park, H. G. “Macro model for 346

nonlinear analysis of reinforced concrete walls”, Journal of the Korea Concrete Institute, 347

Vol. 23, No. 5, pp. 569-579, (in Korean) (2011). 348

[18] Park, H. G. and Eom, T. S. “Truss model for nonlinear snalysis of RC members subject 349

to cyclic loading”, Journal of Structural Engineering, Vol. 133, No. 10, pp. 1351-1363 350

(2007). 351

[19] Vecchio, F. J. and Collins, M. P. “The modified compression-field theory for reinforced 352

concrete elements subjected to shear”, ACI Structural Journal, Vol. 83, No.22, pp. 219-353

231 (1986). 354

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16

[21] Menegotto, M., and Pinto, P. E. “Method of analysis for cyclically loaded reinforced 357

concrete plane frames including changes in geometry and non-elastic behavior of elements 358

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Figure list 380

Fig. 1 Typical example of structural system for high-rise residential buildings 381

Fig. 2 Structural plan 382

Fig. 3 Applied load and strength of the wall W2 and W3 at floor B3 383

Fig. 4 Axial load applied to the wall W2 and W3 at floor B3 according to each load 384

combination 385

Fig. 5 Strain distribution of wall W2 and W3 under the wind load according to the stiffness of 386

the coupling beam 387

Fig. 6 Increase of flexural reinforcement of coupled walls owing to additional axial loading 388

Fig. 7 Strength of coupled wall system [1] 389

Fig. 8 Longitudinal-and-diagonal-line-element-model (LDLEM) for the simulation of the 390

actual behavior of a coupled wall system [17] 391

Fig. 9 Material model 392

Fig. 10 Coupled wall model for inelastic analysis 393

Fig. 11 Result of inelastic analysis 394

395

Table list 396

Table 1 Reinforcement detail of RC structural walls 397

398

399

400

401

402

403

404

18

405

Fig. 1 Typical example of structural system for high-rise residential buildings 406

407

408

409

Fig. 2 Structural plan 410

411

Thirty-five stories

Three basement level

RC structure

a. RC Flat-plate

b. RC Structural wall

c. RC Column

Location : Seoul, Korea

(a) 35 stories residential building (b) Lateral load resisting system

RC Structural wall RC Flat-plate + Column

(C) Gravity load resisting system

W2W3

W1

W4 W5

19

412

Fig. 3 Applied load and strength of the wall W2 and W3 at floor B3 413

414

415

416

417

Fig. 4 Axial load applied to the wall W2 and W3 at floor B3 according to each load 418

combination 419

W2 W3

W2 H : 8.15m, T=0.3m, D25@100 (3.38%)

f’c=30MPa, fy=600MPa

-60000

-40000

-20000

0

20000

40000

60000

80000

100000

120000

-150000 -100000 -50000 0 50000 100000 150000A

xia

l lo

ad

(k

N)

Bending moment (kN-m)

1.2D+1.0L-1.3W1

1.2D+1.0L-1.3W2

0.9D-1.3W1

0.9D+1.3W1

1.2D+1.0L+1.3W1

-60000

-40000

-20000

0

20000

40000

60000

80000

100000

-150000 -100000 -50000 0 50000 100000 150000

Ax

ial

loa

d (

kN

)

Bending moment (kN-m)

0.9D+1.3W1

1.2D+1.0L+1.3W1

1.2D+1.0L-1.3W1

0.9D-1.3W1

W2 H : 7.65m, T=0.3m, D22@100 (2.58%)

f’c=30MPa, fy=600MPa

(a) Building plan (b) Applied load and capacity of wall (W2) (c) Applied load and capacity of wall (W3)

(a) Axial load to W2

-30,000

0

30,000

60,000

0 10 20 30 40 50 60 70 80

W2 벽체 축력

W3 벽체 축력

Load Combination

Axia

l lo

ad(k

N)

1.2D+1.0L+1.3W1

1.2D+1.0L-1.3W1 0.9D+1.3W1 0.9D-1.3W1

(a) Applied load and load combination (b) Axial load applied to wall W2 and W3 at B3

Lateral load

- Earthquake load(E:Rx,Ry)

- Wind load (W)

Gravity load

- Dead load(D)

- Live load (L)

- Snow load (S)

(b) Axial load to W3

No. Load combination1 1.4D2 1.2D + 1.6L3 1.2D + 1.3W1 + 1.0L4 1.2D + 1.3W2 + 1.0L5 1.2D + 1.3W3 + 1.0L6 1.2D - 1.3W1 + 1.0L7 1.2D - 1.3W2 + 1.0L::

::

78

0.9D -1.0(1.0(1.14)[RY(RS)-

RY(ES)]-0.3(1.45)[RX(RS)+RX(ES)])

(C) Axial load applied to wall W2 and W3 at B3 according to each load combination

(a) Axial load to W2

(b) Axial load to W3

Coupling beam

20

420

Fig. 5 Strain distribution of wall W2 and W3 under the wind load according to the stiffness of 421

the coupling beam 422

423

WindLoad

WindLoad

(a) Strain distribution of W2 and W3 with existing coupling beams under the wind load

(b) Strain distribution of W2 and W3 with stronger coupling beams under the wind load

existing coupling beams: 0.6ⅹ0.5 (depth ⅹ thickness, m)

strong coupling beams: 2.4ⅹ0.5 (depth ⅹ thickness, m)

0.00025

-0.00025

030th floor

0.00025

-0.00025

020th floor

0.0005

-0.0005

0

10th floor

B3 floor

0.001

-0.001

0

W2 W3

W2 W3

0.00025

-0.00025

030th floor

0.00025

-0.00025

020th floor

0.0005

-0.0005

0

10th floor

B3 floor

0.001

-0.001

0

21

424

Fig. 6 Increase of flexural reinforcement of coupled walls owing to additional axial loading 425

426

427

Fig. 7 Strength of coupled wall system [1] 428

(a) Deformation of coupling beam (b) Axial load applied to wall W2 and W3 at B3

(1) Axial load to W2

(2) Axial load to W3

(c) Flexural rebar increase of wall

with tensional load

‘ ‘ ‘

‘

θ

P(a

xia

l lo

ad)

Com

p.

Ten..

M

P

Axial load by

lateral load

Axial load by

lateral load

Axial load by

gravity load

Axial load by

gravity load

W2

W3

M

W2

OK

Increase of flexural re-bar

for strength compliment

(d) Decrease of strength reduction factor of wall with compressive load

Decrease of strength

reduction factor

0 002. t

.085

0 005.

065. Comp.-

controlled

sections

Tension-

controlled

sectionsNG

=( ′

)

Strength

decrease

1M

2M

TT

sl

MV

BMD

ibM ,

ibM ,

bl

∑⇒∴≤n

i bib

b

iblMT

l

MV

1= ,

,2/=

2

M

22

429

Fig. 8 Longitudinal-and-diagonal-line-element-model (LDLEM) for the simulation of the 430

actual behavior of a coupled wall system [17] 431

432

433

434

435

(a) Stress-strain relation for concrete [20] (b) Stress-strain relation for concrete [21] 436

Fig. 9 Material model 437

438

wh

4v

Dimensionless rigid beam

Longitudinal truss element (concrete & re-bar)

Diagonal truss element (concrete)

Tributary areas of longitudinal concrete and re-bar elements A

4u

dcA

mh

ml

b

ls wA bs lc lsA bs A

s

Longitudinal element A

dcA

Web concrete

ccosdc w w cA h b

dcAwh

Concrete stress for positive loading

cc

ml

3v

3u

1v

1u

2v

2u

Re-bar ratiosb bw

c

wh

Concrete stress for negative loading

Definition of web depthwh

wh

c

( cos )/dc w w cA h b n

3n

(a) Longitudinal-and-Diagonal-Line-Element-Model (LDLEM) element

(b) Tributary areas of concrete and re-bar

of each longitudinal uniaxial element

(c) Diaongal concrete strut of wall web concrete

Single set of X-type diagonal concrete struts

( cot )/( 1)d w m cs h l n

ml

(d) Multiple sets of X-type

diagonal concrete struts

ds ds

(a) Stress-strain relation for concrete (b) Stress-strain relation for steel reinforcement

compressive strength of concrete

strain corresponding to concrete strength

secant elastic modulus of concrete

yield strength of steel

:0Cf

:0Cε

:0CE

:yf

23

439

440

Fig. 10 Coupled wall model for inelastic analysis 441

442

2nd

8th

7th

6th

5th

4th

3rd

1st

(a) Coupled wall model A ( (tension wall), (compression wall)) 015.0=fρ 005.0=fρ

2nd

8th

7th

6th

5th

4th

3rd

1st

(b) Coupled wall mode B ( (tension wall), (compression wall)) 010.0=fρ 010.0=fρ

Wall ①

Wall ②

)156.0=( '

1 cg fAPM

)244.0=( '

2 cg fAPM

Wall ①, Wall ②

)156.0=( ' '

1 cg fAPM

)244.0=( ' '

2 cg fAPM

′ + ′ ( ) = + ( )

■ f’c=30MPa, fy=400MPa, Story height=3.1m, Wall thickness=0.3m

■ Beam width-depth = 0.3m-0.5m, Flexural reinforcement ratio of beam = 1%

■ Constant axial load at the base =0.2Agf’c

015.0=fρ

5m 2m 5m

Wall ① Wall ②

005.0=fρ

Inelastic beam-

column element

010.0=fρ

5m 2m 5m

010.0=fρ

Wall ① Wall ②

Inelastic beam-

column element

24

443

Fig. 11 Result of inelastic analysis 444

445

446

447

448

449

450

451

452

453

454

455

456

457

458

459

460

461

462

463

464

25

Table 1 Reinforcement detail of RC structural walls 465

Wall List (at floor B3)

f'c=30 MPa, fy=500 MPa (under D13), fy=600 MPa (over D16)

Wall Story

Thickness

(mm)

Vertical

Reinforcement

Horizontal

Reinforcement

W1 B3F-B2F 300 D22 at 100 (2.58%) D10 at 150

W2 B3F-B1F 300 D25 at 100 (3.38%) D13 at 200

W3 B3F-B1F 300 D22 at 100 (2.58%) D10 at 130

W4 B3F-B2F 300 D13 at 150 (0.59%) D10 at 190

W5 B3F-B2F 300 D16 at 125 (1.07%) D10 at 190

466