Structural analysis of multi-storey buildings

340 Pages·2020·18.672 MB·English

by  K. A. Zalka

STRUCTURAL ANALYSIS

OF MULTI-STOREY

BUILDINGS

STRUCTURAL ANALYSIS

OF MULTI-STOREY

BUILDINGS

Karoly Zalka
Second edition published 2020
by CRC Press
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In memory

of

Lajos Kollár

Contents

Notations xi

1 Introduction 1

2 Individual bracing units: frames, (coupled) shear walls and cores 5

2.1 Deflection analysis of rigid sway-frames under horizontal load 5

2.1.1 Characteristic deformations 6

2.1.2 One-bay, multi-storey frames 7

2.1.3 Extension of the results: multi-bay, multi-storey frames 19

2.1.4 Discussion and special cases 20

2.1.5 Worked example: two-bay, ten-storey frame 23

2.2 Frequency analysis of rigid sway-frames 26

2.2.1 Fundamental frequency 26

2.2.2 Discussion 33

2.2.3 Worked example: three-bay, twenty-five storey frame 34

2.3 Stability analysis of rigid sway-frames 37

2.3.1 A comprehensive method for the stability analysis 38

2.3.2 Worked example: two-bay, twenty-five storey frame 43

2.4 Other types of frame 45

2.4.1 A simple method for the stability analysis 45

2.4.2 Frames on pinned support. Stability analysis 49

2.4.3 Frames with longer columns at ground floor level. Stability analysis 51

2.4.4 Frames with cross-bracing 52

2.4.5 Infilled frames 55

2.4.6 Worked example: fifteen-storey frame with cross-bracing 57

2.5 Coupled shear walls 60

2.5.1 The modified frame model 60

2.5.2 Worked example: three-bay, thirty-storey coupled shear walls 62

2.6 Shear walls 68

2.7 Cores 68

2.7.1 Torsional stiffness characteristics 69

2.7.2 Deflection and rotation under uniformly distributed horizontal load 75

2.7.3 Fundamental frequency 77

2.7.4 Critical load 79

3 Deflection and rotation analysis of buildings under horizontal load 83

3.1 Three-dimensional behaviour 84

3.2 The planar problem: lateral deflection analysis of torsion-free buildings 86

3.2.1 The governing differential equations of the problem 86
viii Structural Analysis of Multi-Storey Buildings
3.2.2 Method “A”: The simple method 89

3.2.3 Method “B”: The more accurate method 92

3.3 The torsional problem 97

3.3.1 Torsional behaviour and basic characteristics 98

3.3.2 Torsional analysis 102

3.3.3 Discusson and special cases 105

3.4 Maximum deflection 108

3.5 Load distribution among the bracing units 109

3.6 The behaviour of buildings under horizontal load 111

3.7 Worked examples 112

3.7.1 Maximum deflection of twenty-eight storey symmetric building 113

3.7.2 Maximum deflection of twenty-eight storey asymmetric building 120

4 Frequency analysis of buildings 127

4.1 Lateral vibration of a system of frames, (coupled) shear walls and cores 128

4.2 Pure torsional vibration 135

4.3 Coupled lateral-torsional vibration 140

4.4 Worked examples 142

4.4.1 Fundamental frequency of twenty-five storey symmetric building 142

4.4.2 Fundamental frequency of twenty-storey asymmetric building 148

5 Stability analysis of buildings 160

5.1 Sway buckling of a system of frames, (coupled) shear walls and cores 161

5.2 Sway buckling: special bracing systems 169

5.2.1 Bracing systems consisting of shear walls only 169

5.2.2 Bracing systems consisting of frames only 170

5.2.3 Shear walls and frames with very high beam/column stiffness ratio 170

5.2.4 Shear walls and frames with very high column/beam stiffness ratio 171

5.3 Pure torsional buckling 172

5.4 Coupled sway-torsional buckling 177

5.5 Concentrated top load 179

5.6 Worked examples 180

5.6.1 Critical load of twenty-storey monosymmetric building 181

5.6.2 Critical load of fifteen-storey asymmetric building 191

6 Global structural analysis 206

6.1 The global critical load ratio 207

6.2 Illustrative example 208

6.3 Practical application No. 1: Illustrative example 211

6.3.1 Basic characteristics 212

6.3.2 Case 1: an unacceptable bracing system arrangement 217

6.3.3 Case 2: a more balanced bracing system arrangement 226

6.3.4 Case 3: an effective bracing system arrangement 235

6.4 Practical application No. 2: Kollár’s classic five-storey building 240

6.4.1 Layout “A”: an open core on the right side of the layout 241

6.4.2 Layout “B”: an open core in the centre of the layout 246

6.4.3 Layout “C”: a partially closed core on the right side of the layout 248

6.4.4 Layout “D”: a partially closed core in the centre of the layout 252

6.5 Practical application No. 3: Ten-storey asymmetric building 254

6.5.1 Stability analysis 256
Contents ix

6.5.2 Maximum deflection 264

6.5.3 Fundamental frequency 270

7 Accuracy and reliability 280

7.1 Basic characteristics of the bracing units 281

7.2 Structural analysis of individual bracing units 285

7.2.1 Maximum deflection 285

7.2.2 Fundamental frequency 287

7.2.3 Critical load 290

7.3 Structural analysis of systems of bracing units 297

7.3.1 Maximum deflection of symmetric, torsion-free bracing systems 297

7.3.2 Maximum deflection of asymmetric bracing systems 301

7.3.3 Fundamental frequency 303

7.3.4 Critical load 304

7.4 Accuracy with the nineteen worked examples 305

Appendix: List of worksheets 307

References 311

Subject index 316

Author index 323