LB /VON / 20i T)G£ 03 jo 1 / 03 EFFECTS OF AXIAL SHORTENING OF COLUMN IN TALL BUILDINGS / \ 26 APR 2004 THESIS SUBMITTED TO THE DEPARTMENT OF CIVIL ENGINEERING IN FULFILMENT OF THE REQUIREMENT FOR THE DEGREE OF MASTER OF SCIENCE IN ENGINEERING " "V SR! IW&C ? V ' • : 1« ) * By W. M. V. P. K. Jayasena Supervised By Dr. M. T. R. Jayasinghe V\ W r---f O- / • C^S'-'V6 University of Moratuvva L/A/ Thesis 77706 DEPARTMENT OF CIVIL ENGINEERING UNIVERSITY OF MORATUWA SRI LANKA 1T106 December 2002 77706 DECLARATION I, Wijesooriya Mudiyanselage Vasana Prasanthi Kumari Jayasena, hereby declare that the content of this thesis is the output of original research work carried out over a period of 15 months at the Department of Civil Engineering, University of Moratuwa. Whenever the work done by others was used, it was mentioned appropriately as a reference. .1. ACKNOWLEDGEMENT First, the author wishes to acknowledge the Asian Development Bank for funding this particular research work. Author is immensely grateful to Prof (Mrs) N. Ratnayake (Director, Post Graduate Studies), Prof. Malik Ranasinhge (Dean, Faculty of Engineering, University of Moratuwa) and the Senate Research Committee for the acceptance of the research proposal as a valuable one. Heart full gratitudes is conveyed by the author to the research supervisor, Dr. M.T.R. Jayasinghe, Associate professor, Department of Civil Engineering for his continuous supervision and support given throughout the research period. Thanks are also due to Dr. S.A.S. Kulatilake (Research Coordinator, Department of Civil Engineering) and Dr. A.D.C. Jayanandane (Senior Lecture, Department of Civil Engineering) for their valuable ideas, which helped to make this research a success. Special thanks to Mr. T.M.D. Fernando, fellow research student, for the support given during the period of research. The cooperation given by all other research students in the Building Science Laboratory, Department of Civil Engineering is highly acknowledged by the author. Author also wishes to thank the technical assistants Mr. D. Dishantha and C. Malnayakc for their kind help in various aspects. Whole hearted thanks to my husband for the encouragement given from the beginning of the research. The final acknowledgement is to all others helped in various ways, including the staff members of Computer Laboratory, for completing the work. -11- ABSTRACT Even today, only a very few number of tall buildings are available in Sri Lanka, compared to other countries in the world. However, with the increase in population and due to the limited space availability the latest trend is to spread buildings vertically than laterally. Nowadays, there is a much greater demand for taller buildings relative to the past. After concrete was introduced to construction world, it gained many improvements with in a short time period and because of that concrete buildings spread all over the world. Due to the higher strength ranges that can be achieved by good quality concrete, the section dimensions of members in concrete buildings have reduced drastically in the recent past. The increase in height accompanied with the reduced member sizes formed slender buildings, which require more attention focused on the lateral stability of the building. This problem was however solved by the introduction of various efficient structural forms such as shear walls, shear cores, outriggers, etc. in to the building skeleton. Since the modern tall buildings arc made up of smaller members, the vertical deformation of columns, i.c. axial shortening of columns which was considered as of with minor importance up to then, has now become more critical in high rise buildings. The total shortening contributed by creep and shrinkage of concrete and gravity loads applied on structure became more serious as the height of the structure increases. Damages can occur to structural as well as non structural elements due to differential shortening of these vertical members. The research includes estimation of possible axial shortening of columns in buildings with selected number of storeys. Changes in estimated shortening values were observed with slight modifications to original building configurations. Finally guidelines, which can be used by design engineers at a preliminary design stage and by construction engineers at the time of construction were developed. Keywords: Concrete buildings Axial shortening of columns -in- CONTENTS Declaration Acknowledgement Abstract 1 11 in Contents IV List of Tables x List of Figures xv CHAPTER 1 Introduction 011.1 General 1.2 Objectives 1.3 Methodology 1.4 Main Findings 1.5 An Overview of the Thesis 03 03 04 05 CHAPTER 2 Literature Review 062.1 Analysis of Tall Buildings 2.1.1 Tall Buildings 2.1.1.1 Definition 2.1.1.2 Construction Materials 2.1.2 Lateral Stability of Tall Structures 2.1.2.1 Rigid Frame Structures 2.1.2.2 Shear Wall Structures 2.1.2.3 Wall Frame Structures 2.1.2.4 Outrigger Structures 2.1.3 Computer Analysis of Structures 2.1.3.1 Two Dimensional Modeling 2.1.3.2 Three Dimensional Modeling 06 06 06 07 07 08 10 11 13 14 14 -IV- 142.1.3.3 Reduction Techniques 2.1.3.4 The Analysis Tool - Micro feap PI 2.1.4 Loads on Tall Buildings 2.1.4.1 Dead Loads 2.1.4.2 Live Loads 2.1.4.3 Wind Loads 2.1.4.4 Earthquake Loads 2.2 Axial Shortening of Columns 2.2.1 Contributing Factors for Axial Shortening 2.2.1.1 Creep of Concrete 2.2.1.2 Shrinkage of Concrete 2.2.1.3 Elastic Shortening of Concrete 2.2.2 Effects of Axial Shortening 2.2.2.1 Absolute Shortening 22.2.2 Differential Shortening 2.2.3 Effect of Loading History and Construction Sequence on Axial Shortening of Columns 2.2.4 Available Methods to Estimate Axial Shortening 2.2.4.1 Fintel and Khan’s Method 2.2.4.2 Ghosh’s Method 2.2.4.3 Koutsoukis and Beasley's Method 17 17 18 18 18 19 19 20 20 22 23 23 23 24 26 27 27 28 28 292.3 Summary CHAPTER 3 Estimation of Axial Shortening of Columns 303.1 General 3.2 Comparison of Fintel & Khan’s and Ghosh’s Methods 3.2.1 Shortening due to Creep 3.2.1.1 Creep due to Previous Load Applications 3.2.1.2 Creep due to Subsequent Load Applications 3.2.2 Shortening due to Shrinkage 3.2.2.1 Shrinkage Strain 3.2.2.2 Effect of Member Dimensions 30 32 32 38 39 39 40 -v- 403.2.2.3 Effect of Time Since Placement 3.2.2.4 Effect of Relative Humidity 3.2.2.5 Effect of Reinforcement 3.2.3 Elastic Shortening 3.3 Selection of Creep and Shrinkage Parameters 3.3.1 Method Based on BS5400- Part 4 41 41 42 44 44 443.3.2 The Method Based on AS3600 453.3.3 Recommendation of BS8110-Part 2 3.3.3.1 Estimation of Ultimate Creep 3.3.3.2 Estimation of Ultimate Shrinkage 3.3.4 Method Selected for the Research Study 3.4 Spreadsheet for Estimating Axial Shortening of Columns 3.5 Summary 45 46 47 48 52 CHAPTER 4 Case Study on Tall Buildings 534.1 General 4.2 Planning of Buildings 4.2.1 Planning of 20 Storey Buildings 4.2.1.1 Service Core Arrangement 4.2.1.2 Calculation of Loads 4.2.1.3 Determination of Member Sizes 4.2.2 Summary of Building Data Selected for Case Study 4.2.2.1 Floor Plans 4.2.2.2 Arrangement of Lifts 4.2.2.3 Arrangement of Sanitary Appliances 4.2.2.4 Allocation of Services in the Sendee Core 4.2.2.5 Summary of Loads 4.2.2.6 Summary of Member Dimensions 4.2.2.7 Arrangement of Structural Elements on Plan 4.3 Two Dimensional Modeling of Buildings 4.3.1 10 Storey Building 4.3.1.1 Two Dimensional Model 54 54 55 64 70 75 75 78 78 78 79 84 85 88 88 88 -vi- 884.3.1.2 Materia] Properties 4.3.2 15 Storey Building 4.3.2.1 Two Dimensional Model 4.3.2.2 Material Properties 4.3.3 20 Storey Building 4.3.3.1 Two Dimensional Model 4.3.3.2 Material Properties 4.3.4 25 Storey Building 4.3.4.1 Two Dimensional Model 4.3.4.2 Material Properties 4.3.5 30 Storey Building 4.3.5.1 Two Dimensional Model 4.3.5.2 Material Properties 4.3.6 35 Storey Building 4.3.6.1 Two Dimensional Model 4.3.6.2 Material Properties 4.3.7 40 Storey Building 4.3.7.1 Two Dimensional Model 4.3.7.2 Material Properties 89 89 89 90 90 91 92 92 92 93 93 94 95 95 96 97 97 98 994.4 Results of Analysis 4.5 Estimation of Reinforcement 99 CHAPTER 5 Results 1005.1 General 5.2 Comparison Between Fintel &Khan’s and Ghosh’s Methods 5.3 Absolute Shortening of Columns 5.3.1 Absolute Shortening of Ground Floor Column 5.3.2 Absolute Shortening of 5lh and 10lh Floor Columns 5.4 Differential Shortening of Columns 5.4.1 Differential Shortening With Grade 30 Concrete 5.4.2 Differential Shortening With Grade 40 Concrete 5.4.3 Differential Shortening With Grade 50 Concrete 100 102 102 104 105 106 106 107 -vii- 1075.4.4 Average Differential Shortening ........ 5.4.5 Average Differential Shortening - Complete Results of Case Study 5.4.5.1 Average Differential Shortening Values - Selection 1 ..... 5.4.5.2 Average Differential Shortening Values - Selection 2...... 5.4.5.3 Average Differential Shortening Values - Selection 3...... 5.5 Effect of Relative Humidity ........ 5.5.1 Absolute Shortening ........ 5.5.2 Differential Shortening ........ 5.6 Effect of Construction Rate ........ 5.6.1 Shortening of 10th Floor Supports ........ 5.6.2 Shortening of 15th Floor Supports ........ 5.6.3 Combined Effect of Construction Rate and Relative Humidity........ 5.7 Effect of Construction Sequence ........ 5.7.1 Wall Leading the Frame ........ 5.7.1.1 Differential Shortening With Grade 30 Concrete ........ 5.7.1.2 Differential Shortening With Grade 40 Concrete ....... 5.7.1.3 Differential Shortening With Grade 50 Concrete ....... 5.7.1.4 Average Differential Shortening ........ 5.7.2 Frame Leading the Wall ........ 5.7.2.1 Differential Shortening With Grade 30 Concrete ........ 5.7.2.2 Differential Shortening With Grade 40 Concrete ........ 5.7.2.3 Differential Shortening With Grade 50 Concrete ........ 5.7.2.4 Average Differential Shortening ........ 5.8 Effects of Axial Shortening ........ 5.8.1 Axial Stresses in Masonry Walls ........ 5.8.2 Additional Moments in Beams ........ 108 108 108 108 109 109 111 113 113 113 114 115 115 116 116 116 117 117 117 118 118 118 119 119 120 CHAPTER 6 Discussion of Results 1226.1 General ....... 6.2 Absolute Shortening of Columns ....... 6.2.1 Effect of Grade of Concrete on Absolute Shortening ....... 6.2.2 Effect of Cross Sectional Area of Column on Absolute Shortening 122 122 124 -Vlll- 1266.2.3 Effect of Number of Storeys in the Building on Absolute Shortening 6.2.4 Effect of Delay in Partition Construction ......... 6.2.5 Problems due to Absolute Shortening ......... 6.2.6 Solutions for Absolute Shortening ......... 6.3 Differential Shortening between Adjacent Members ......... 6.3.1 Effect of Grade of Concrete ......... 6.3.2 Effect of Number of Storeys in the Building ......... 6.3.3 Problems due to Differential Shortening ......... 6.3.4 Solutions for Differential Shortening ......... 6.4 Effect of Relative Humidity ......... 6.4.1 Absolute Shortening ......... 6.4.2 Differential Shortening ......... 6.5 Effect of Construction Rate ......... 6.6 Effect of Construction Sequence ......... 6.6.1 Simultaneous Construction of Wall and Frame ......... 6.6.2 Wall Leading the Frame by 5 Storeys ......... 6.6.3 Frame Leading the Wall by 5 Storeys ......... 128 128 129 129 129 130 134 134 135 135 136 138 139 139 140 140 1426.7 Summary CHAPTER 7 Conclusions and Guidelines 1437.1 Conclusions 7.1.1 Absolute Shortening 7.1.2 Differential Shortening 7.1.3 Construction Rate 7.1.4 Construction Sequence 143 144 145 145 1457.2 Guidelines 1467.3 Future Work 147• References 149• Appendix A • Appendix B 166 -IX- LIST OF TABLES CHAPTER 3 Comparison of specific creep of concrete3.1 CHAPTER 4 4.1 Wind forces along the height of the 20 storey building 4.2 Arrangement of lifts in the building selected for the case study 4.3 Arrangement of sanitary appliances in the building selected for the case study 4.4 Space allocation for services in the service core 4.5 Wind loads along the height of each building 4.6 Bending moment at the base of each building due to wind loads 4.7 Earthquake loads on buildings selected for the case study 4.8 Comparison of wind and earthquake loads on buildings 4.9 Shear force distribution from bottom to top of each building due to earthquake loads 4.10 Bending moment at the base of each building due to earthquake loads 4.11 Base moments in each building due to wind and earthquake loads 4.12 Dimensions of members selected for buildings 4.13 Material properties adopted in the analysis of 10 storey building 4.14 Material properties adopted in the analysis of 15 storey building 4.15 Material properties adopted in the analysis of 20 storey building 4.16 Material properties adopted in the analysis of 25 storey building 4.17 Material properties adopted in the analysis of 30 storey building 4.18 Material properties adopted in the analysis of 35 storey building 4.19 Material properties adopted in the analysis of 40 storey building 4.20 Section variation of columns from top to bottom of each building CHAPTER 5 Comparison of shortening of 5lh, 10th and 15lh storey supports in the 20 storey building Comparison of shortening of 5lh, 10lh and 15lh storey supports in the 40 storey building Shortening of ground floor column after certain time periods 5.1 5.2 5.3 -x- Shortening of 5lh floor column after certain time periods Shortening of 10th floor column after certain time periods Differential shortening between a column and a wall in different buildings (Grade 30 concrete - simultaneous construction) Differential shortening between a column and a wall in different buildings (Grade 40 concrete - simultaneous construction) Differential shortening between a column and a wall in different buildings (Grade 50 concrete - simultaneous construction) Average differential shortening between a column and a wall in different buildings (simultaneous construction) 5.10 Average differential shortening between a column and a wall (Selection 1) 5.11 Average differential shortening between a column and a wall (Selection 2) 5.12 Average differential shortening between a column and a wall (Selection 3) 5.13 Absolute shortening of ground floor column from the moment of casting 5.14 Absolute shortening of ground floor column three months after casting 5.15 Absolute shortening of ground floor column six months after casting 5.16 Differential shortening along the height of each building with 40% relative humidity 5.17 Differential shortening along the height of each building with 60% relative humidity 5.18 Differential shortening along the height of each building with 80% relative humidity 5.19 Shortening of 10lh floor support with different construction rates 5.20 Shortening of 15th floor support with different construction rates 5.21 Percentage reduction in shortening with rate of construction at different relative humidities 5.22 Differential shortening between a column and a wall in different buildings (Grade 30 concrete - wall leading frame) 5.23 Differential shortening between a column and a wall in different buildings (Grade 40 concrete - wall leading frame) 5.24 Differential shortening between a column and a wall in different buildings (Grade 50 concrete - wall leading frame) 5.25 Average differential shortening between a column and a wall in different buildings (wall leading frame) 5.4 5.5 5.6 5.7 5.8 5.9 -xi- Differential shortening between a column and a wall in different buildings (Grade 30 concrete - frame leading wall) Differential shortening between a column and a wall in different buildings (Grade 40 concrete - frame leading wall) Differential shortening between a column and a wall in different buildings (Grade 50 concrete - frame leading wall) Average differential shortening between a column and a wall in different buildings (frame leading wall) Stresses in masonry walls in ground floor Additional moments in beams due to differential shortening between wall and column (simultaneous construction) Additional moments in beams due to differential shortening between wall and column (wall leading frame) Additional moments in beams due to differential shortening between wall and column (frame leading wall) 5.26 5.27 5.28 5.29 5.30 5.31 5.32 5.33 CHAPTER 6 Variation of absolute shortening with grade of concrete Variation of absolute shortening with column cross sectional area Variation of absolute shortening with number of storeys in the building Variation of differential shortening between a wall and an adjacent column with grade of concrete M/bh2 due to additional moments generated in connecting beams (simultaneous construction) M/bh2 due to additional moments generated in connecting beams (wall leading the frame) M/bh2 due to additional moments generated in connecting beams (frame leading wall) Differential shortening between wall and frame at different storey levels (simultaneous construction) Differential shortening between wall and frame at different storey levels (wall leading the frame) Differential shortening between wall and frame at different storey levels (frame leading wall) 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 -xii- APPENDIX A Member forces in a selected column in the 10 storey building Member forces in a selected column in the 15 storey building Member forces in a selected column in the 20 storey building Member forces in a selected column in the 25 storey building Member forces in a selected column in the 30 storey building Member forces in a selected column in the 35 storey building Member forces in a selected column in the 40 storey building Member forces in a selected wall in the 10 storey building Member forces in a selected wall in the 15 storey building Member forces in a selected wall in the 20 storey building Member forces in a selected wall in the 25 storey building Member forces in a selected wall in the 30 storey building Member forces in a selected wall in the 35 storey building Member forces in a selected wall in the 40 storey building A-l A-2 A-3 A-4 A-5 A-6 A-7 A-8 A-9 A-10 A-l 1 A-12 A-13 A-14 APPENDIX 13 Reinforcement for the selected column in the 10 storey building (Selection l) Reinforcement for the selected column in the 10 storey building (Selection 2) Reinforcement for the selected column in the 10 storey building (Selection 3) Reinforcement for the selected column in the 15 storey building (Selection 1) Reinforcement for the selected column in the 15 storey building (Selection 2) Reinforcement for the selected column in the 15 storey building (Selection 3) Reinforcement for the selected column in the 20 storey building (Selection 1) Reinforcement for the selected column in the 20 storey building (Selection 2) Reinforcement for the selected column in the 20 storey building (Selection 3) Reinforcement for the selected column in the 25 storey building (Selection 1) Reinforcement for the selected column in the 25 storey building (Selection 2) Reinforcement for the selected column in the 25 storey building (Selection 3) Reinforcement for the selected column in the 30 storey building (Selection 1) Reinforcement for the selected column in the 30 storey building (Selection 2) Reinforcement for the selected column in the 30 storey building (Selection 3) Reinforcement for the selected column in the 35 storey building (Selection 1) Reinforcement for the selected column in the 35 storey building (Selection 2) B-l B-2 B-3 B-4 B-5 B-6 B-7 B-8 B-9 B-10 B-l 1 B-12 B-13 B-14 B-15 B-16 B-17 -Xlll- Reinforcement for the selected column in the 35 storey building (Selection 3) Reinforcement for the selected column in the 40 storey building (Selection 1) Reinforcement for the selected column in the 40 storey building (Selection 2) Reinforcement for the selected column in the 40 storey building (Selection 3) Reinforcement for the selected wall in the 10 storey building (Selection 1) Reinforcement for the selected wall in the 10 storey building (Selection 2) Reinforcement for the selected wall in the 10 storey building (Selection 3) Reinforcement for the selected wall in the 15 storey building (Selection 1) Reinforcement for the selected wall in the 15 storey building (Selection 2) Reinforcement for the selected wall in the 15 storey building (Selection 3) Reinforcement for the selected wall in the 20 storey building (Selection 1) Reinforcement for the selected wall in the 20 storey building (Selection 2) Reinforcement for the selected wall in the 20 storey building (Selection 3) Reinforcement for the selected wall in the 25 storey building (Selection 1) Reinforcement for the selected wall in the 25 storey building (Selection 2) Reinforcement for the selected wall in the 25 storey building (Selection 3) Reinforcement for the selected wall in the 30 storey building (Selection 1) Reinforcement for the selected wall in the 30 storey building (Selection 2) Reinforcement for the selected wall in the 30 storey building (Selection 3) Reinforcement for the selected wall in the 35 storey building (Selection 1) Reinforcement for the selected wall in the 35 storey building (Selection 2) Reinforcement for the selected wall in the 35 storey building (Selection 3) Reinforcement for the selected wall in the 40 storey building (Selection 1) Reinforcement for the selected wall in the 40 storey building (Selection 2) Reinforcement for the selected wall in the 40 storey building (Selection 3) B-18 B-19 B-20 B-21 B-22 B-23 B-24 B-25 B-26 B-27 B-28 B-29 B-30 B-31 B-32 B-33 B-3 4 B-35 B-3 6 B-37 B-38 B-39 B-40 B-41 B-42 -xiv- LIST OF FIGURES CHAPTER 2 2.1 Deflected shape of a rigid frame structure Shear wall structures Deflected shape of wall frame structures Variation of horizontal deflection, bending moment & shear force along the height of a wall frame structure Outrigger structures Outrigger structure with belt girders Symmetric and asymmetric structures Horizontally lumped equivalent model Vertically lumped equivalent model 2.10 Creep and shrinkage of concrete 2.11 Chart proposed by Hickey (1968) to predict specific creep of concrete 2.12 Rotated partition due to differential shortening of adjacent members 2.13 Flexible partition details 2.14 Buckling of cladding skin 2.15 Potation of shelf angles 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 CHAPTER 3 Schematic diagram of a tall building 3.2 Chart proposed by Hickey (1968) to predict specific creep of concrete 3.3 Variation of with age at loading (Khan’s method) 3.4 Variation of CRla with age at loading (Ghosh’s method) 3.5 Variation of Xc with volume to surface area ratio 3.6 Variation of creep coefficient with time 3.7 Variation of Xs with volume to surface area ratio 3.8 Variation of shrinkage with relative humidity 3.9 Effect of relative humidity, age of loading and section thickness upon creep factor 3.10 Drying shrinkage of normal weight concrete 3.11 Spread sheet used for calculations 3.1 - xv - Input data for estimating shortening of ground floor column, as displayed in the spreadsheet Output sheetl- contribution of ground floor column to total shortening of 5lh floor support Output sheet2- contribution of ground floor column to total shortening of 5lh floor (with the effect of reinforcement) Output sheet 1- Contribution of columns 1 to 5, to total shortening of 5lh floor support Output sheet 2- Contribution of each column to total shortening of 5lh floor (with the effect of reinforcement) 3.12 3.13 3.14 3.15 3.16 CHAPTER 4 Proposed floor plan for 20 storey building 4.2 Arrangement of lifts in 20 storey building 4.3 Beam and column layout of 20 storey building 4.4 Arrangement of service core from 1st to 12th storey 4.5 Arrangement of service core from 13lh to 20th storey 4.6 Arrangement of structural elements in the 20 storey building 4.7 Exaggerated view at A (load transfer from slab to beam) 4.8 Proposed floor plan for 10 storey building 4.9 Proposed floor plan for 15 storey building 4.10 Proposed floor plan for 25 storey building 4.11 Proposed floor plan for 30 storey building 4.12 Proposed floor plan for 35 storey building 4.13 Proposed floor plan for 40 storey building 4.14 Earthquake force distribution along a building 4.15 Arrangement of structural elements in the 10 storey building 4.16 Arrangement of structural elements in the 15 storey building 4.17 Arrangement of structural elements in the 25 storey building 4.18 Arrangement of structural elements in the 30 storey building 4.19 Arrangement of structural elements in the 35 storey building 4.20 Arrangement of structural elements in the 40 storey building 4.21 Two dimensional model of 10 storey building 4.22 Two dimensional model of 15 storey building 4.1 - xvi - 4.23 Two dimensional model of 20 storey building 4.24 Two dimensional model of 25 storey building 4.25 Two dimensional model of 30 storey building 4.26 Two dimensional model of 35 storey building 4.27 Two dimensional model of 40 storey building CHAPTER 5 Shortening of 5th, 10lh and 15th storey supports in the 20 storey building Shortening of 5th, 10th and 15th storey supports in the 40 storey building Graph of percentage reduction of shortening of slab supports with construction rate 5.1 5.2 5.3 CHAPTER 6 Effect of grade of concrete on absolute shortening Effect of column dimensions on absolute shortening Rate of change in absolute shortening with the number of storeys Differential shortening at 5th floor level (RH=60%) Differential shortening at 10th floor level (RH=60%) Differential shortening at 15th floor level (RH=60%) Differential shortening at 20th floor level (RH=60%) Differential shortening at 25lh floor level (RH=60%) Differential shortening at 30lh floor level (RH=60%) Differential shortening at different floor levels (RH=60%) Differential shortening at 5th floor level Differential shortening at 10th floor level Differential shortening at 15th floor level Differential shortening at 20lh floor level Differential shortening at 25lh floor level Differential shortening at 30th floor level Variation of percentage reduction of shortening with different construction rates 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11 6.12 6.13 6.14 6.15 6.16 6.17 - XVII -