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Series on Innovation in Structures and Construction —Vol. 3 Series Editors: A . S. Elnashai & P. J. Dowling DESIGN OF MODERN HIGHRISE REINFORCED CONCRETE STRUCTURES Editor: Hiroyuki Aoyama irfk Imperial College Press DESIGN OF MODERN HIGHRISE REINFORCED CONCRETE STRUCTURES SERIES ON INNOVATION IN STRUCTURES AND CONSTRUCTION Editors: A. S. Elnashai (University of Illinois at P. J. Dowling (University of Surrey) Urbana-Champaign) Published Vol. 1: Earthquake-Resistant Design of Masonry Buildings by M. Tomazevic Vol. 2: Implications of Recent Earthquakes on Seismic Risk by A. S. Elnashai & S. Antoniou Vol. 3: Design of Modern Highrise Reinforced Concrete Structures by H. Aoyama Series on Innovation in Structures and Construction — Vol. 3 Series Editors: A . S. Elnashai & P. J. D o w l i n g DESIGN OF MODERN HIGHRISE REINFORCED CONCRETE STRUCTURES Editor Hiroyuki Aoyama University of Tokyo, Japan ICP Imperial College Press Published by Imperial College Press 57 Shelton Street Covent Garden London WC2H 9HE Distributed by World Scientific Publishing Co. Pte. Ltd. P O Box 128, Farrer Road, Singapore 912805 USA office: Suite IB, 1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. DESIGN OF MODERN HIGHRISE REINFORCED CONCRETE STRUCTURES Copyright © 2001 by Imperial College Press All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 1-86094-239-3 Printed in Singapore by Uto-Print Preface Reinforced concrete (RC) as construction material has been used for a wide range of building structures throughout the world, owing to its advantages such as versatile architecture application, low construction cost, excellent durability and easy maintenance. However, its use in seismic countries and areas in the world has been limited to lowrise or mediumrise buildings, considering inherent lack of structural safety against earthquakes. In the last several decades, highrise RC buildings finally emerged in Japan, under the increased social need of more advanced types of RC buildings. Such a new type of structures was developed with the tremendous technical efforts for new high strength material, new design method, and new construction method, backed up by vast amount of research accomplishment. A five year national research project, entitled "Development of Advanced Reinforced Concrete Buildings using High Strength Concrete and Reinforcement", was conducted in 1988-1993 by the coalition of many research organizations in Japan with the Building Research Institute of the Ministry of Construction as the central key organization. The major incentive of this national research project was to further promote construction of highrise RC buildings as well as other advanced types of RC structures, by providing new high strength material and new design and construction methods suitable for such material. This national research project was simply referred to "the New RC" project. Now it is more than five years since the conclusion of the New RC project. It is quite clear that the project was successful and effective in finding numerous applications in the practical design and construction of advanced RC structures. This book was written as an effort to disseminate major findings of the project so as to help develop modern RC buildings in seismic countries and areas in the world. It consists of the following nine chapters. In Chapter 1, development and structural features of highrise RC buildings up to the onset of the New RC project are explained. It was the major motivation of the New RC project to develop even taller highrise RC buildings in seismic areas. Methods of seismic design and dynamic response analysis, vi Preface prevalent at the time of New RC project initiation, are also introduced in this chapter. In Chapter 2, the development goal of the New RC project, development organizations and the outline of expected results are mentioned. Chapter 3 is entitled "high strength materials", and describes the development of high strength concrete and reinforcement and their mechanical characteristics. Chapter 4 describes the structural tests of New RC structural members such as beams, columns, walls, and so on, subjected to simulated seismic loading, and the evaluation methods of structural performance of New RC members and assemblies. Chapter 5 is entitled "finite element analysis", and describes the development of nonlinear finite element analysis models for New RC members, examples of analysis that supplement the structural testing of Chapter 4, and the guidelines for nonlinear finite element analysis. Chapter 6 introduces the New RC Structural Design Guidelines, emphasizing the new seismic design method for New RC highrise buildings, which basically consists of evaluation of seismic behavior through time history response analysis and static incremental load (push over) analysis. Also introduced in this chapter are several design examples. Chapter 7 intends to give an introductory explanation of dynamic time history response analysis to readers who are not quite acquainted with this kind of analysis, or to those who have experience in modal analysis or elastic analysis only. Computational models suitable for RC structures, general trends of seismic response of RC structures, and method of numerical analysis are presented. In Chapter 8, outline of a full-scale construction test and the New RC Construction Standard are presented. The construction standard is the compilation of standard specifications for New RC materials, their manufacturing and processing, and various phases of construction works. In the last Chapter 9, feasibility studies on three new types of buildings using high strength materials are mentioned, and highrise buildings utilizing New RC materials that were actually designed and constructed, or under construction, are introduced. Most chapters of this book were authored by persons who acted as secretaries of the relevant committees of the New RC project. This is the reason why relatively few literatures were referred to in each chapter of this book. Preface vii The authors wish that the publication of this book will further promote the dissemination of the results of the New RC project into practice throughout the world, and will also encourage further research on the use of high strength and high performance materials to RC structures. Hiroyuki Aoyama Contents Preface v Chapter 1 RC Highrise Buildings in Seismic Areas Hiroyuki Aoyama 1 1.1. Evolution of RC Highrise Buildings 1.1.1. Historic Background 1.1.2. Technology Examination at the Building Center of Japan 1.1.3. Increase of Highrise RC and the New RC Project 1.2. Structural Planning 1.2.1. Plan of Buildings 1.2.2. Structural Systems 1.2.3. Elevation of Buildings 1.2.4. Typical Structural Members 1.3. Material and Construction 1.3.1. Concrete 1.3.2. Reinforcement 1.3.3. Use of Precast Elements 1.3.4. Preassemblage of Reinforcement Cage 1.3.5. Re-Bar Splices and Anchorage 1.3.6. Concrete Placement 1.3.7. Construction Management 1.4. Seismic Design 1.4.1. Basic Principles 1 1 ix 3 5 7 7 10 12 13 15 15 16 17 18 19 21 21 22 22 x Contents 1.4.2. 1.4.3. 1.4.4. 1.4.5. 1.4.6. Design Criteria and Procedure Design Seismic Loads Required Ultimate Load Carrying Capacity First Phase Design Second Phase Design 1.4.6.1. Calculation of Ultimate Load Carrying Capacity . 1.4.6.2. Ductility of Girders 1.4.6.3. Column Strength and Ductility 1.4.6.4. Beam-column Joints 1.4.6.5. Minimum Requirements 1.4.6.6. Imaginary Accident 1.4.7. Experimental Verification 1.5. Earthquake Response Analysis 1.5.1. Linear Analysis 1.5.2. Nonlinear Lumped Mass Analysis 1.5.3. Nonlinear Frame Analysis 1.5.4. Input Earthquake Motions 1.5.5. Damping 1.5.6. Results of Response Analysis 1.6. For Future Development 1.6.1. Factors Contributed to Highrise RC Development 1.6.2. Need for Higher Strength Materials 23 25 26 26 27 27 28 29 30 30 30 31 32 32 32 33 33 34 36 37 37 38 Chapter 2 The N e w R C Project Hisahiro Hiraishi 40 2.1. 2.2. 2.3. 2.4. 40 41 44 53 53 55 55 56 56 59 Background of the Project Target of the Project Organization for the Project Outline of Results 2.4.1. Development of Materials for High Strength RC 2.4.2. Development of Construction Standard 2.4.3. Development of Structural Performance Evaluation 2.4.4. Development of Structural Design 2.4.5. Feasibility Studies for New RC Buildings 2.5. Dissemination of Results Contents Chapter 3 N e w R C Materials xi 61 Michihiko Abe Hitoshi Shiohara 3.1. High Strength Concrete 3.1.1. Material and Mix of High Strength Concrete 3.1.1.1. Cement 3.1.1.2. Aggregate 3.1.1.3. Chemical Admixtures 3.1.1.4. Mineral Admixtures 3.1.1.5. Mix Design 3.1.2. Properties of High Strength Concrete 3.1.2.1. Workability 3.1.2.2. Standard Test Method for Compressive Strength 3.1.2.3. Mechanical Properties 3.1.2.4. Drying Shrinkage and Creep 3.1.2.5. Durability 3.1.2.6. Fire Resistance 3.2. High Strength Reinforcing Bars 3.2.1. Reinforcement Committee 3.2.2. Advantages and Problems of High Strength Re-bars . . . . 3.2.3. Relationship of New Re-bars to Current JIS 3.2.4. Proposed Standards for High Strength Re-bars 3.2.4.1. General Outlines 3.2.4.2. Specified Yield Strength 3.2.4.3. Strain at Yield Plateau 3.2.4.4. Yield Ratio 3.2.4.5. Elongation and Bendability 3.2.5. Method of Manufacture and Chemical Component 3.2.6. Fire Resistance and Durability 3.2.6.1. Effect of High Temperature 3.2.6.2. Corrosion Resistance 3.2.7. Splice 3.3. Mechanical Properties of Reinforced Concrete 3.3.1. Bond and Anchorage 3.3.1.1. Beam Bar Anchorage in Exterior Joints 3.3.1.2. Bond Anchorage in Interior Joints 61 61 62 64 66 70 71 75 75 76 77 80 82 84 86 86 86 87 88 88 91 91 92 93 93 97 97 99 100 104 104 105 109 xii Contents 3.3.1.3. Flexural Bond Resistance of Beam Bars 3.3.2. Lateral Confinement 3.3.2.1. Stress-strain Relationship of Confined Concrete . 3.3.2.2. Upper Limit of Stress in Lateral Reinforcement . 3.3.2.3. Buckling of Axial Re-bars 3.3.3. Concrete under Plane Stress Condition 3.3.3.1. Biaxial Loading Test of Plain Concrete Plate . . . 3.3.3.2. Tests of Reinforced Concrete Plate under In-plane Shear Ill 113 113 120 121 122 123 124 Chapter 4 N e w R C Structural Elements Takashi Kaminosono 127 4.1. Introduction 4.2. Beams and Columns 4.2.1. Bond-Splitting Failure of Beams after Yielding 4.2.2. Slab Effect on Flexural Behavior of Beams 4.2.3. Deformation Capacity of Columns after Yielding 4.2.4. Columns Subjected to Bidirectional Flexure 4.2.5. Vertical Splitting of Columns under High Axial Compression 4.2.6. Shear Strength of Columns 4.2.7. Shear Strength of Beams 4.3. Walls 4.3.1. Flexural Capacity of Shear-Compression Failure Type Walls 4.3.2. Deformation Capacity of Walls under Bidirectional Loading 4.3.3. Shear Strength of Slender Walls 4.4. Beam-Column Joints 4.4.1. Bond in the Interior Beam-Column Joints 4.4.2. Shear Capacity of 3-D Joints under Bidirectional Loading 4.4.3. Shear Capacity of Exterior Joints 4.4.4. Concrete Strength Difference between First Story Column and Foundation 4.5. Method of Structural Performance Evaluation 4.5.1. Restoring Force Characteristics of Beams 127 128 129 136 141 147 152 156 162 169 170 178 183 189 191 196 203 206 209 209 Contents xiii 4.5.1.1. Initial Stiffness 210 4.5.1.2. Flexural Cracking 210 4.5.1.3. Yield Deflection 211 4.5.1.4. Flexural Strength 214 4.5.1.5. Limiting Deflection 214 4.5.1.6. Equivalent Viscous Damping 214 4.5.2. Deformation Capacity of Columns 215 4.5.2.1. Flexural Compression Failure 215 4.5.2.2. Bond Splitting Along Axial Bars 216 4.5.2.3. Shear Failure in the Hinge Zone after Yielding . . 217 4.5.2.4. Shear Strength of Beams and Columns 219 4.5.3. Flexural Strength of Walls 219 4.5.4. Shear Strength of Beam-Column Joints 221 4.5.5. Connections of First Story Column to Foundation 224 4.5.5.1. Bearing Stress 224 4.5.5.2. Splitting Stress 224 4.5.5.3. Strengthening 225 4.6. Concluding Remarks 225 Chapter 5 Finite Element Analysis Hiroshi Noguchi 227 5.1. Fundamentals of FEM 5.2. FEM and Reinforced Concrete 5.2.1. History of Finite Element Analysis of Reinforced Concrete 5.2.2. Modeling of RC 5.2.2.1. Two-Dimensional Analysis and Three-Dimensional Analysis 5.2.2.2. Modeling of Concrete 5.2.2.3. Modeling of Reinforcement 5.2.2.4. Modeling of Cracks 5.2.2.5. Modeling of Bond between Reinforcement and Concrete 5.3. FEM of RC Members Using High Strength Materials 5.4. Comparative Analysis of RC Members Using High Strength Materials 227 229 229 232 232 232 234 234 234 235 236 xiv 5.5. 5.6. 5.7. 5.8. Contents 5.4.1. Comparative Analysis of Beams, Panels and Shear Walls 5.4.2. Material Constitutive Laws 5.4.2.1. Uniaxial Compressive Stress-Strain Curves of Concrete 5.4.2.2. Compressive Strength Reduction Coefficient of Cracked Concrete 5.4.2.3. Confinement Effect of Concrete 5.4.2.4. Biaxial Effect of Concrete 5.4.2.5. Tension Stiffening Characteristics of Concrete . . 5.4.2.6. Shear Stiffness of a Crack Plane 5.4.2.7. Cracking Strength 5.4.2.8. Stress-Strain Relationship of Reinforcement . . . 5.4.2.9. Dowel Action of Reinforcement 5.4.2.10. Bond Characteristics 5.4.3. Analytical Models and Analytical Results 5.4.3.1. Analysis of Beam Test Specimens 5.4.3.2. Analysis of Panel Specimens 5.4.3.3. Analysis of Shear Walls 5.4.3.4. Conclusions FEM Parametric Analysis of High Strength Beams 5.5.1. Objectives and Methods 5.5.2. The Effect of Shear Reinforcement Ratio 5.5.3. Effects of Concrete Confinement Models with a Constant Value of pw<Jwy 5.5.4. Conclusions FEM Parametric Analysis of High Strength Columns 5.6.1. Objectives and Methods 5.6.2. Analytical Results 5.6.3. Conclusions FEM Parametric Analysis of High Strength Beam-Column Joints 5.7.1. Objectives and Methods 5.7.2. Comparison between Test and Analytical Results 5.7.3. Results of Parametric Analysis 5.7.4. Conclusions FEM Parametric Analysis of High Strength Walls 236 237 237 238 238 239 239 239 240 240 240 240 240 242 242 244 244 246 246 247 248 251 251 251 253 255 255 255 256 256 260 260 Contents xv 5.8.1. Objectives and Methods 5.8.2. Outline of Research 5.8.3. Analytical Results and Discussions 5.9. FEM Parametric Analysis of High Strength Panels 5.9.1. Objectives and Methods 5.9.2. Analytical Results and Summary 260 260 262 265 265 265 Chapter 6 Structural Design Principles Masaomi Teshigawara 271 6.1. Features of New RC Structural Design Guidelines 272 6.1.1. Earthquake Resistant Design in Three Stages 273 6.1.2. Proposal of Design Earthquake Motion 273 6.1.3. Bidirectional and Vertical Earthquake Motions 273 6.1.4. Clarification of Required Safety 274 6.1.5. Variation of Material Strength and Accuracy in Strength Evaluation 274 6.1.6. Structural Design of Foundation and Soil-Structure Interaction 274 6.2. Earthquake Resistant Design Criteria 275 6.2.1. Design Earthquake Intensity 275 6.2.2. Design Drift Limitations 275 6.2.3. Design Criteria 276 6.3. Design Earthquake Motion 279 6.3.1. Characteristics of Earthquake Motion 279 6.3.2. New RC Earthquake Motion 279 6.3.3. Relation to Building Standard Law 280 6.4. Modeling of Structures 281 6.4.1. Modeling of Structures 281 6.4.2. Relation of Model and Earthquake Motion 281 6.4.2.1. Fixed Base Model 281 6.4.2.2. Sway-Rocking Model 282 6.4.2.3. Soil-Foundation-Structure Interaction Model . . . 282 6.5. Restoring Force Characteristics of Members 283 6.5.1. Dependable and Upper Bound Strengths 283 6.5.2. Member Modeling 284 6.5.3. Hysteresis 286 6.6. Direction of Seismic Design 286 xvi Contents 6.6.1. Design Forces in Arbitrary Direction 6.6.2. Bidirectional Earthquake Input 6.6.3. Effect of Vertical Motion 6.7. Foundation Structure 6.8. Design Examples 6.8.1. 60-Story Space Frame Apartment Building 6.8.2. 40-Story Double Tube and Core-in-Tube Office Buildings 6.8.2.1. Double Tube Structure 6.8.2.2. Core-in-Tube Structure 6.8.3. Mediumrise Office Buildings (15-Story Wall-Frame, 15-Story Space Frame, 25-Story Space Frame) 286 289 289 289 291 291 Chapter 7 Earthquake Response Analysis Toshimi Kabeyasawa 315 7.1. Earthquake Response Analysis in Seismic Design 7.2. Structural Model 7.2.1. Three-Dimensional Frame Model 7.2.2. Two-Dimensional Frame Model 7.2.3. Multimass Model 7.2.4. Soil-Structure Model 7.3. Member Models 7.3.1. One-Component Model for Beam 7.3.2. Multiaxial Spring Model for Column 7.3.3. Wall Model 7.4. Nonlinear Response of SDF System 7.4.1. Displacement-Based Design Procedure 7.4.2. Correlation of Nonlinear Response to Linear Response 7.5. Numerical Analysis 7.5.1. Numerical Analysis of Equation of Motion 7.5.2. Release of Unbalanced Force 315 319 319 321 323 324 325 325 328 331 335 335 Chapter 8 Construction of N e w R C Structures Yoshihiro Masuda 345 299 299 305 310 337 341 341 343 Contents 8.1. Introduction 8.2. Full Scale Construction Testing 8.2.1. Objectives 8.2.2. Outline of Construction Testing 8.2.3. Concrete Mix 8.2.4. Reinforcement Construction 8.2.5. Concrete Construction 8.2.5.1. Fresh Concrete 8.2.5.2. Construction of Column Specimens 8.2.5.3. Construction of Frame Specimen 8.2.5.4. Measurement of Internal Temperature 8.2.5.5. Strength Development 8.2.5.6. Observation of Cracks on Frame Specimen . . . . 8.2.6. Conclusion 8.3. Construction Standard for New RC 8.3.1. General Provisions 8.3.2. Reinforcement 8.3.3. Formwork 8.3.4. Concrete 8.3.4.1. General 8.3.4.2. Concrete Quality 8.3.4.3. Material 8.3.4.4. Mix 8.3.4.5. Manufacture of Concrete 8.3.4.6. Placing and Surface Finishing 8.3.4.7. Curing 8.3.4.8. Compressive Strength Inspection Chapter 9 Feasibility Studies and Example Buildings Hideo Fujitani xvii 345 345 345 346 349 354 356 356 357 360 366 366 371 374 375 375 375 376 377 377 377 383 384 386 387 388 388 391 9.1. Feasibility Studies 391 9.1.1. Highrise Flat Slab Buildings 391 9.1.1.1. Highrise Flat Slab Condominium with Core Walls 393 9.1.1.2. Highrise Flat Slab Condominium with Curved Walls399 9.1.2. Megastructures 407 9.1.2.1. OP200 Straight Type 407 9.1.2.2. OP300 Straight Type 408 xviii Contents 9.1.2.3. OP300 Tapered Type 9.1.2.4. BR200 K-brace Type 9.1.2.5. BR200 D-brace Type 9.1.2.6. BR300 X-brace Type 9.1.2.7. Concluding Remarks 9.1.3. A Box Column Structure for Thermal Power Plant 9.2. Example Buildings 410 412 412 414 415 418 424 Index 437 Chapter 1 RC Highrise Buildings in Seismic Areas Hiroyuki Aoyama Department of Architecture, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan E-mail: aoyama-al@kozo.co.jp 1.1. 1.1.1. Evolution of R C Highrise Buildings Historic Background The national research project on development of advanced reinforced concrete buildings using high strength concrete and reinforcement, usually referred to as the "New RC" project and on which basis this book was written, was planned and conducted in 1988-1993 in Japan under the leadership of the Japanese Ministry of Construction. This project was carried out on the background of quick development of highrise RC buildings since about 1975, in order to further promote the development and use of higher strength materials for highrise and other advanced types of RC buildings. This chapter is devoted to the introduction of the background of the New RC project, that is, the development of highrise RC buildings up to the onset of the New RC project in 1988. Reinforced concrete as building material was introduced to Japan around 1905. The first all RC building was a warehouse in Kobe, designed by Naoji Shiraishi, a professor of civil engineering of the University of Tokyo and a member of the Institute of Civil Engineers of the Great Britain, and constructed in 1906. The RC construction became popular in the subsequent years, for it was generally accepted as fire-proof and earthquake-proof construction, in contrast to combustible wooden construction or earthquake-crumbling brick construction. l 2 Design of Modem, High-rise Reinforced Concrete Structures However the RC construction as building structure did not trace a favorable history since then. Regardless of its reputation as an "eternal" architecture, many RC buildings in Tokyo suffered heavy damage in 1923 Kanto earthquake. The behavior of RC in this earthquake disaster was generally inferior to concrete-encased or brick-encased steel buildings. This led to the development of composite steel and reinforced concrete (SRC) construction as a uniquely Japanese type of construction for Mghrise buildings. The traditional RC construction, on the other hand, was limited to buildings whose height did not exceed 20 m. This limitation was not explicitly prescribed in the building code, but was enforced by means of the administrative guidance. Any building taller than, say, seven stories had to be constructed by steel structure or SRC structure. This administrative guidance was carried over to post-war period. In 1950, five years after the end of the World War II, the new Building Standard Law was enforced to replace the old Urban Building Law, but the situation for RC construction was basically unchanged. Around 1980, the situation began to change rapidly. The RC construction was started to be used for taller buildings. This new trend included development of highrise wall-frame construction of 10 to 15 stories and highrise frame construction of 20 stories or higher, both for apartment buildings. The more important of the two developments was the latter, which was initiated by Kajima Construction Co. by completing an 18-story building in Tokyo, the Shiinamachi Apartment, in 1974, followed by another 25-story building also in Tokyo, Sun City G-Blook Apartment, in 1980, as shown in Fig. 1.1. It should be mentioned that all the big Japanese construction companies have (a) Shiinamachi Apartment (b) Sun City G-Building Fig. 1.1. Early examples of RC highrise buildings. RC Higkri.se Buildings in Seismic Areas 3 design sections within the company, and hence the structural design of these buildings was also done by Kajima. The Building Standard Law prescribed provisions for buildings up to 31 m in height in its original version of 1950, which was revised to extend the height limitation to 60 m in 1981. If one wants to build a taller building, its structural design, particularly the seismic design, has had to be subjected to the technical review of the Technical Appraisal Committee for Highrise Buildings of the Building Center of Japan, and subsequently a special permit of the Minister of Construction is issued. For the two Kajima buildings of highrise RC, this review was especially challenging, as it was the first experience for both design engineers and committee members to handle earthquake resistant highrise RC construction. Kajima had conducted an extensive research and development project within the company prior to designing these buildings. It included large-scale structural testing in the laboratory of beams, columns, and subassemblages, computer programs of advanced analysis technique for nonlinear static and dynamic earthquake response, and development of construction technology. With the help of vast experimental and analytical background data, Kajima could obtain technical appraisal for their first highrise RC buildings, leading to the special permission of the Minister of Construction. Kajima subsequently submitted 25- and 30-story apartment buildings for technical appraisal in 1983. Other big construction companies did not allow Kajima alone to go further in highrise RC construction. Taisei Construction Co. and Konoike-gumi Construction Co., among others, submitted similar proposal to the Building Center of Japan. In 1983-1984, it became almost like a violent competition of big construction companies to prepare for submission of highrise RC construction, regardless of the possibility to realize the projected plan. 1.1.2. Technology of Japan Examination at the Building Center The Highrise RC Construction Technology Examination Committee was formed in 1984 in the Building Center of Japan under the chairmanship of Dr. Hiroyuki Aoyama, Professor of the University of Tokyo. The chairman was succeeded by Dr. Yasuhisa Sonobe, Professor of Tsukuba University, in 1986. The purpose of this committee was to control the spontaneous and violent competition of construction companies for highrise RC construction. 4 Design of Modern Highrise Reinforced Concrete Structures In many countries where earthquake is not a potential risk for structural safety of buildings, highrise RC construction as tall as 30 stories is not uncommon. The country of Japan makes a sharp contrast to these countries not only for its high seismic risk, but also for its high level of protection demand against earthquake damage by the society. Under such a condition one would have to be prudent in the development of highrise RC construction. It was deemed insufficient to utilize the experience of highrise steel or SRC construction, and was deemed necessary to solve new problems proper to highrise RC construction. To this end the above-mentioned construction companies established new technologies associated with the design and construction of highrise RC buildings in the course of technical appraisal of the structural design of particular buildings. However this meant a dual object in the conduct of technical appraisal. The applicant of a highrise RC building — the design section of a construction company — had to show design capability for highrise RC construction by the compilation of experimental data, computer programs for nonlinear static and dynamic response analysis, and construction guidelines with practices, and so on, in addition to showing the design and analysis of the building project to be appraised, unless the construction company was a repeater of highrise RC such as Kajima. The Technical Appraisal Committee had to work on materials of the general nature as well as those specifically related to the building in question. Some companies wanted to obtain technical appraisal of a highrise RC building only in order to be recorded. In spite of having no prospect to realize the project, they compiled and submitted the materials of general character showing design capability for highrise RC to the Technical Appraisal Committee. This movement clearly added improper burden to the Committee. The Highrise RC Construction Technology Examination Committee was formed, as mentioned earlier, in 1984 in order to control undue competition of construction companies. It also helped release the Technical Appraisal Committee from the above-mentioned unfair burden. It was reorganized in 1992 as the Highrise RC Construction Technology Guidance Committee under the chairmanship of Dr. Yasuhisa Sonobe. The committee has been chaired by Dr. Shunsuke Otani, Professor of the University of Tokyo, since 1994 up to the present time. The Technology Examination Committee's work is different from that of the Technical Appraisal Committee in that there is no concrete project to RC Highrise Buildings in Seismic Areas 5 be designed and constructed. Instead, applicants submit set of materials to demonstrate their capability to design and construct highrise RC buildings. The materials usually consist of structural design specifications, an imaginary building project designed accordingly, and construction specifications with emphasis on the quality control. Materials are frequently accompanied by reports of laboratory structural tests of RC members, laboratory and field tests of high strength concrete, and operation tests of various stages of construction. The structural design and construction specifications are required to fully reflect results and implications of these tests. One of the most important aspect of the examination is the operation test of the construction of a full-size mock-up, usually one- or two-storied and single- to double-span frame in two directions. Such an operation test is almost mandatory to the applicant, and is carried out in the presence of committee members. The construction operation test has been shown to be quite effective in the reform of understanding of both structural and construction engineers to account for new aspects of highrise RC, such as high viscosity of high strength concrete, preassembling of high strength re-bar cages, responsibility of contractor in the quality control of concrete and form works, separate concreting for columns and floor framing, proper use of concrete buckets, concrete pumps, vibrators, and so on. As an application to the technology examination involves construction technology, majority of applicants are construction companies. A few design firms have so far applied by forming a team with construction companies, or by preparing elaborate construction specifications to be applied to the contractor after bidding is settled. 1.1.3. Increase of Highrise RC and the New RC Project The number of highrise RC buildings is steadily increasing since about 1985. Figure 1.2 shows annual numbers of highrise buildings that passed the technical appraisal of the Building Center of Japan, together with the breakdown into three structural categories of steel, SRC and RC. It is seen the number fluctuates greatly, presumably according to the construction business fluctuation, but the annual number for highrise RC construction shows steady increase since 1987. It is inferred that the increase since 1987 owes to the increase of construction companies that passed the technology examination of the Building Center of Japan, backed up by the beginning of brisk business condition at that time. After the peak of good business of 1990, the ratio of concrete construction 6 Design of Modern Highrise Reinforced Concrete Structures 120 110 100 - ns ®SRC 90 E 80 w 1 • RC 70 - *3 ^ t ° zo 60 50 40 30 20 10 0 - 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 Year Fig. 1.2. Annual highrise construction in Japan. including SRC and RC to the total highrise construction became larger. In the average of recent ten years, steel, SRC and RC occupy approximately 70, 15 and 15 percent of total highrise construction, respectively. The total number of highrise RC at the end of 1997 exceeds 200. In 1987 when the New RC project was proposed at the Building Research Institute of the Ministry of Construction, the immediate arrival of highrise RC boom was quite apparent. The quick development of highrise RC construction owed to many factors, such as large scale structural testing, advanced analysis techniques, and development of construction technology. But the most significant and influential factor was the development of high strength concrete up to 42 MPa and high strength, large size reinforcing bars up to SD 390 D41 bars. The New RC project was an attempt to further promote the development of advanced RC construction in the seismic zones. As mentioned earlier, this national research project, development of advanced RC buildings using high strength concrete and reinforcement in its full name, was conducted as a fiveyear project in 1988-1993 under the leadership of the Japanese Ministry of Construction, with Building Research Institutes as the key organization. It was a very ambitious project to enlarge the scope of RC construction to a new height in the seismic countries such as Japan, probably to 200 m or higher. The technology developed in this project can be regarded as an attractive new technology to enhance the possibility of RC construction. Its influence was spread out to RC construction even before the end of the five-year project. RC Highrise Buildings in Seismic Areas 7 The increase of highrise RC after 1988 in Fig. 1.2 is the result of this influence, at least partly. As will be seen in Chapter 9 of this book, there are already more than 20 highrise RC buildings constructed, or under construction, as the direct result of this New RC project. 1.2. 1.2.1. Structural Planning Plan of Buildings Highrise RC construction is currently used almost exclusively for apartment houses, because of better habitability provided by concrete. Floor plan of these buildings is generally regular, and symmetric with respect to one or two axes. Figure 1.3 shows a typical plan of buildings that were investigated in the technology examination of the Building Center of Japan. This is probably the most regular of the all, but other plans investigated in the technology examination were much alike. The variation employed in those plans included the following; slightly different span numbers in two directions, slightly different span 1200 5000 | II | *" I m °® // • » J 25000 © ® 5000 1200 | I" © © ©,5°° Fig. 1.3. Example of typical floor plan of RC highrise building. 8 Design of Modern Highrise Reinforced Concrete Structures lengths in two directions, varying span lengths in one direction, eliminating one span each at four corners, eliminating one or two central spans at four sides, and having a courtyard at the center. Thus it was apparent that designers of highrise RC buildings gave priority to structural characteristics, at least at the beginning in the stage of technology examination, by shaping the plan as simple as possible within the practicability limit. The span length of the building in Fig. 1.3 is 5 m in both directions. The span length of 5 m is much shorter than comparable SRC or steel buildings, but this was also typical for most of the buildings subjected to technology examination. The short span was adopted in order to limit the axial load on a column, and thereby reduce the seismic force acting on a column. Here lies a possibility for the New RC to liberate the structural constraint, that is, to enlarge the span by adopting higher strength materials. Z9.0 (a)H729 n.a 36.0 (22,-2)X2 (b)H789(32,-4) (c) H444 3B.5 2 .8 (d)H504 (25,-2) («) H425 (30,0) (30,0) (0H495 (29-1) x 33.6 11.3 (g)H309 (25,0) Fig. 1.4. (h)H59S (21.-2JX2 37.6 (i) H505 (30,-2) Key plans of RC highrise buildings. RC Highrise Buildings in Seismic Areas 9 1 1 X 31.8 JZ.l <j)H514 (k)H5B3 (25,-1) (1)H466 (33-2) (30,-1) dampers wall M j y. (m) HB67 - (26, - 2) J- (n)H706 (33,-1) L nH r 3S. ? (o)H5B0 (37,-1) (RC 13 Et±) (p)HB84 Fig. 1.4. (41,-1) (Continued) Figure 1.4 shows sixteen examples of structural key plan of highrise RC buildings actually constructed up to 1991. These drawings show columns and floor girders only, and cantilever balcony slabs are not shown. Floor opening for stairs and elevators are not shown either. X-marks denote courtyards and similar open bays. In the case of actual buildings, somewhat larger variations from the regular plan shown in Fig. 1.3 are apparent. Figures 1.4(a) to (h) are frame buildings without courtyard, (i) to (1) are frame buildings with courtyard, (m) is the 10 Design of Modern Higkri.se Reinforced Concrete Structures one with shear walls in one direction, (n) is a frame building with a special antiseismic device explained in the next section, (o) and (p) are the so-called tube structure buildings also described in the next section. However it will be seen that all buildings are shaped more or less like a tower with 30 m to 40 m in each direction. There is no slab-shaped buildings as contrasted to lowrise to mediumrise apartment buildings. Most buildings are equipped with balconies of continuous cantilever slabs around the periphery of the plan. A few examples have balconies inside the peripheral frame lines. It should be noted that there are no buildings with a structural core. The core system is better suited to office buildings, but not used for apartment houses. As a partial result of the New RC project, Chapter 9 of this book introduces an office building with hybrid structure, consisting of RC core and peripheral steel frames. Such a variation is not found in Fig. 1.4 where all buildings are for dwelling. 1.2.2. Structural Systems Structural systems of highrise RC buildings currently constructed in Japan are classified into three categories; space frame system, space frame with seismic elements, and double-tube system. The space frame system consists of frames with uniform, or nearly uniform, span lengths in two directions. Unlike RC construction in overseas countries, all frames available in the plan are designed as moment resisting frames. This is because of high earthquake resistance required in Japan. By far this type is the most common in highrise RC construction. Figure 1.4 introduces twelve examples of space frame system, (a) to (1). Presence of a courtyard does not make any basic difference to the structural characteristics. What matters is the mixture of frames with variable number of spans. Compared to frames with multiple spans, frames with one or two spans are more susceptible to bending deformations resulting from axial deformation of columns under lateral loading, and it is usually required to analyze such structures by means of threedimensional structural analysis. One important consideration in a building with courtyard is the inplane stiffness of floor slabs as diaphragms. Due to the Japanese taste of enjoying sunshine in the dwellings, stairs and elevators are most often concentrated to the north side of the floor which is disadvantageous in this respect. It is then necessary to pay attention to the diaphragm stiffness at the north side of a RC Highrise Buildings in Seismic Areas 11 courtyard so that the floor slab openings of stairs and elevators will not cause any problem to the rigid slab assumption. The space frame with seismic elements refers to buildings like in Figs. 1.4(m) and (n). The first is the space frame building with shear walls. It is a well established fact that shear walls are quite effective in earthquake resistance, but it is limited to the past experience with lowrise to mediumrise RC buildings. It is believed that shear walls would be effective in highrise construction as well, but its performance would be different from lowrise buildings. The analysis and design of a space frame with shear walls will have to involve more sophisticated nonlinear analysis, static as well as dynamic. Presumably for this reason there are strikingly few examples of this type in the current highrise RC construction. Restriction in the interior architectural design by the presence of wall, and added complication in construction process, may also contribute to discourage the engineers from adopting shear walls. Figure 1.4(m) is one of rare examples of this type of construction where shear walls are provided in one direction only. When shear walls are provided in two directions, the spatial interaction would become more complicated. Challenge to such type of structures depend on engineers' courage. Another example in the space frame with seismic elements category is the building of Fig. 1.4(n). It is a space frame building having two axes of frames in the diagonal directions, with additional seismic dampers made of honeycomb shaped steel plates at several midspan of girders. These steel dampers yield at a small story drift, and absorb seismic energy through their elasto-plastic hysteresis, thereby reducing seismic effect on the RC space frames. It is an application of the so-called "structural control", usually referred to as passive seismic control. The third category in the structural systems is the double-tube system. A tubular structure here means plane frames with relatively short spans arranged into four-sided box. For an apartment building plan with a courtyard, exterior and interior peripheries can be used as this kind of tubes, such as shown in Figs. 1.4(o) and (p), hence they are called double tubes. Span length in the plane frames is usually 3 to 4 m, and the floor between the tubes spans over 10 m or so, which consist of floor slabs with subbeams or slabs with prestressing steel. The most important consideration in the structural design of double tubes is to ensure ductile behavior of short-span girders in the plane frames. Some examples utilize the so-called X-shaped reinforcement in the short girders. 12 Design of Modern Highrise Reinforced 1.2.3. Elevation of Concrete Structures Buildings Buildings for technology examination as well as those for actual construction have a common feature of regular shape in the vertical direction. Abrupt stiffness change between adjacent stories is carefully avoided. The total number of stories varies from 20 to 40 or more, and the story height is about 3 m, which is much smaller than office buildings. The short story height gives advantage in seismic design by reducing column moments for a given lateral load, and the fact that apartment houses do not require larger story height probably lead to the prosperity of current highrise RC construction. The first story above ground is usually occupied by entrance hall and other special purpose spaces, and hence has larger story height of 4 m or more. The aspect ratio, height to width ratio of the building, is less than 4 in all cases. Buildings usually have penthouse, consisting of RC frames with or without wall, or steel frames. Penthouses, containing elevator machinery and roof outlet from stairs, are often located off the center of gravity of typical floors, thus cause eccentricity to the main building body. It is also necessary to pay attention to the stress around the openings in the roof floor from the lateral seismic force of the penthouse. In case steel frames are used for a penthouse, the detail design of the connection to the main building is the point of major consideration. More than 80 percent of highrise RC buildings are built on basement stories. In the stage of technology examination many construction companies avoided basements for the sake of simplicity in structural design, but in actual practice basements are often needed for various architectural purposes. They also provide added safety and stability to seismic performance. The basement is generally provided with thick exterior retaining walls, which also serve as shear walls. Thus it has considerably larger lateral stiffness and strength than stories above ground. Care should be taken to account for possible reversed shear forces in the basement columns. Reversed column shear occurs when the basement story does not drift as much as the first story under lateral loading and first story column base moment is transmitted to the basement column. It contributes to the additional lateral force in the basement in the direction of lateral load, and also induces axial force in the first floor girders. It is also necessary to pay due attention to the transfer of lateral forces in the first floor slabs. In the first story lateral load is distributed more or less uniformly into column shear forces, but in the basement story most of the lateral load (more RC Highrise Buildings in Seismic Areas 13 than 100 percent when reversed shear forces occur in the basement columns) is carried by shear walls. Hence large amount of lateral load has to be transferred to shear walls through the first floor slabs acting as the diaphragm, and the floor slabs should be designed to account for this loading. The foundation of buildings may be directly supported by subsoil if it is firm enough, but in most cases pile foundation has to be employed. The most popular type of pile system is the bearing piles made by cast-in situ concrete, constructed by reverse circulation method or all casing method, or with partial replacement by continuous wall-piles. The foundation of buildings in these cases consists of pile-cap tie girders, strong and stiff enough to ensure monolithic performance of the building as a whole. The basement story shear walls add strength and stiffness to these foundation girders, but they are often reserved in the structural design as a surplus margin of safety. In case of pile foundation, foundation girders must be designed for flexure, shear and axial load considering the reaction to pile-top bending moment. 1.2.4. Typical Structural Members Column section is usually square, with the maximum dimension of about 90 cm at the lower stories above ground. Figure 1.5 shows typical sections of columns. Axial reinforcement ratio is about 2 to 3 percent. To provide effective confinement to the core concrete, construction companies devised various types of lateral reinforcement for the technology examination, but in the more recent years it became a governing trend to use subhoops in the shape of Fig. 1.5(b) consisting of high strength deformed PC steel or flush butt welded (FB) rings. 12-D41 Spiral Hoop Ol6<f>@75 Hoop D16(J)@75 (a) F i g . 1.5. 12-D41 Spiral Hoop Dtf)ll@80 Hoop #<J>11@80 (b) T y p i c a l c o l u m n sections. 14 Design of Modern Highrise Reinforced Concrete Structures To overcome large seismic overturning moment which produces dominating axial forces in the exterior columns in lower stories, additional axial bars (core bars) are frequently located in the central portion of these column sections. Some examples are shown in Fig. 1.6. Girders are of rectangular section with height not greater than 80 cm and with relatively large width of about 60 cm, providing space for four large diameter axial bars in a row, as shown in Fig. 1.7. Four-leg stirrups are generally used. High strength deformed P C steel is often used for stirrups to increase shear resistance. In most cases girders are located below the floor slab, and thus form a T-shaped section with the monolithic slab. But in a few cases wall girders were used in the exterior frames which consisted of girders below the slab and spandrels above the floor connected monolithically into girders of large depth. The prevalent architectural design to provide balconies around the floor plan prohibits the use of wall girders. When and where balconies are J D r i ->, C« cfl n A r-I 880 16-D41+8-D41 J. Hoop S.Hoop 16-D41+8-D41 Hoop DiJ)ll@60 #cj)ll@60 (b) (a) Fig. 1.6. E x t e r n a l c o l u m n s w i t h core bars. J 3 0 c 3 3 3 C W c r D 3 ") J U L C c c r 1. T f 650 650 16-D41 Stirrup DD16-@100 14-D41 Stirrup © D i e - ® 100 Fig. 1.7. T y p i c a l girder sections. 1 RC Highrise Buildings in Seismic Areas 15 not provided, or when they are located inside the peripheral frame lines, wall girders can be used to increase strength and stiffness against lateral load. As mentioned earlier the story height of typical apartment houses is about 3 m. It is then essential to provide horizontal openings penetrating through the girder web for piping and air ducts. These openings must not pose any problem to the fiexural and shear strength of girders. For the practical reinforcement around such openings various prefabricated devices are available in the shape of multiple rings and spirals and so on, which have passed the technical appraisal of the Building Center of Japan. 1.3. 1.3.1. Material and Construction Concrete All highrise RC buildings use concrete with specified strength much higher than ordinary buildings, to cope with large axial forces in the columns. The number of stories is almost completely dictated by the concrete strength in the lowest story, as long as current floor plans and column sections are used. Concrete strength in the first story was either 36 or 42 MPa before 1988 when the New RC project was started. Compared with the concrete used for conventional RC lowrise construction of 21 or 24 MPa, this was already very high. Practical use of such high strength concrete required careful evaluation of construction technology including quality control. After the initiation of the New RC project, some construction companies started the use of even higher strength concrete, such as 48 MPa or in some cases 60 MPa before the results of the project were released. Evidently the New RC project created an atmosphere to welcome high strength material, and encouraged construction companies to develop their own voluntary project towards high strength concrete. It is a common practice to reduce strength in upper stories, with the minimum about 24 MPa. Most of highrise RC buildings are constructed by placing column concrete and that for floor system separately. This was quite a revolution in the Japanese construction practice, as the concrete casting into column and floor system simultaneously has been a common traditional practice for lowrise buildings. VH separate casting (which means casting separately into vertical and horizontal members) was deliberately adopted for highrise construction with the aim of maintaining good quality in the column concrete. 16 Design of Modern Highrise Reinforced Concrete Structures In United States or other countries it is often observed that, in conjunction with the VH separate casting, different concrete strength is specified for columns and floor system, that is, higher strength for column concrete, and lower strength for floor slabs, girders, and beam-column joints. This practice is not used in Japan, and concrete of the same quality is specified for columns and floor system. Use of same concrete strength was probably accepted by most construction companies as a natural consequence from the previous custom of VH simultaneous casting. At the same time it can be also said that, although engineers are well aware of the importance of a good quality beamcolumn joint, they are not very much acquainted with, or not quite confident in, remedies for low strength concrete in a beam-column joint such as in the ACI Building Code. In some cases where lower strength concrete in the floor system is strongly required for construction economy, two types of concrete are used for floor system: same concrete as the column for the beam-column joint and some portion of surrounding girders and slabs, and lower strength concrete for the remainder of floor systems. Of course the construction joint of the two types of concrete in this case has to be treated with a special care. Concrete for the basement and foundation need not be so strong as the first story columns, but it is essential to ensure bearing strength just below the first story column base. Usual practice is to place somewhat stronger concrete than basement or foundation in some top layer portion below the column base. 1.3.2. Reinforcement The use of high strength and large size reinforcing bars is indispensable for highrise RC construction, to ensure seismic strength of the structure. Longitudinal bars up to 41 mm diameter (D41) with 390 MPa yield stress (SD390) are commonly used. After the New RC project was started in 1988, some attempts have been made to use bars with 490 MPa yield stress which had been specified in the Japanese Industrial Standard since several decades ago but had never been used extensively nor had been easily available in market. Lateral reinforcement consists of either D16 bars of 295 MPa steel or high strength deformed PC bars with 1275 MPa yield stress (Ulbon). This also sharply contrasts to the prevalent use of D10 and D13 bars of 295 MPa steel in lowrise buildings. RC Highrise Buildings in Seismic Areas 1.3.3. Use of Precast 17 Elements The use of precast members is advantageous for the efficient construction work with reduced work force. However considering the inevitable use of cast-inplace concrete at some critical portions such as diaphragm or joint of precast members, the extent of precasting in practice has received a divergence of opinions. Various degrees of precast application are spotted in the current practice. On one extreme end are buildings with all members cast-in-place. A popular and modest application is to use precast concrete formwork for composite floor slabs. Upper half of the floor slab is made by cast-in-place concrete to form the diaphragm for seismic loading, and the lower half is formed by precast slabs which also serve as the formwork for fresh concrete. Balcony cantilever slabs are often fully precast with elaborate architectural shape, best suitable for precast concrete construction. The use of precast girders is the next step. Precast girders have concrete up to the soffit of floor slabs in the cover, and the central portion is trough shaped. The upper portion is cast monolithically with the floor diaphragm. Bottom reinforcement is spliced at the beam-column joint or at the midspan, and top reinforcement is carried together with the precast unit and moved later to the prescribed position before concrete for upper portion is cast. It is easier to use precast units in only one of two orthogonal directions of a space frame. No matter precast units are used in one or two directions, it is essential that the units placed first in position must have only one layer of reinforcing bars in the bottom, as shown in Fig. 1.8. Columns are the most difficult to apply precast technique. When they are precast, there are currently available two kinds of technique. One is to use sleeve type splice for vertical bars located at the column bottom, as shown cast-in-situ concrete . n \->\0 <_ A •; \ // ,/ ^ n ,vr (a) X direction 4 (b) Y direction Fig. 1.8. Precast girders with cast-in situ slab. 18 Design of Modern Highrise Reinforced An f, Concrete fl f" Structures Ai 1 | | J | 1 1 } I * ' 1 1\ >J w K in Fig. 1.9, and after placing on the protruded ends of column bars of lower story, sleeves are filled with high strength mortar. Another is to precast column without vertical bars but with sheaths for them at each bar location, around which are placed hoops and subhoops. Individual column bars are welded to those of lower story, and the precast units are lowered while bars are piercing through sheaths, which are later filled with mortar. Centrifugal precasting is sometimes applied to obtain good concrete quality. 1.3.4. Preassemblage of Reinforcement Cage Bars for cast-in-place girders and columns are all preassembled on the ground and hoisted up to the position. This practice assures efficient and accurate bar RC Highrise Buildings in Seismic Areas 19 arrangement. Column bars are often preassembled in case of lowrise buildings also, but preassemblage of girder cage is a unique technique developed for highrise RC. Main girder bar splices are located either at each midspan or every other midspan, and cages in two orthogonal directions are usually fabricated simultaneously. Resulting cage assumes a shape like a cross, a double cross, or a quadrangle. In some instances cages in two directions are assembled separately, but in this case due consideration must be given on how to intersect cages in orthogonal directions. 1.3.5. Re-Bar Splices and Anchorage Lapped splices, commonly used for lowrise construction, may be seen also in highrise construction in seismic areas such as U.S. west coast or New Zealand. However they are never used in highrise RC in Japan. Instead, several methods to splice bars concentrically, butt-to-butt, were developed. Presumably this was the result of structural engineers' fastidiousness not to allow awkward offset of large diameter bars, and of contractors' confidence on the newly developed splice technique. Currently available splicing techniques are classified as follows. (1) Gas butt welding. Hand operated gas butt welding is most popular in lowrise RC construction, but it does not warrant a good quality for large diameter deformed bars used in highrise RC construction. Automatic gas butt welding, in which a microcomputer controls the heat and pressure, was devised by several steel manufacturing companies, for example, Autowelbar by Nippon Steel and Autojointer by Sumitomo Steel, and are more reliable for large diameter bars up to D41. (2) Welding. Ordinary arc welding cannot be used for re-bars. Enclosed welding, where arc from thin wire electrode fills the parallel gap of butt ends of bars while it is enclosed in carbon dioxide gas, was a new technique introduced by steel manufacturing companies such as KEN-method by Kobe Steel and NKE-method by Nippon Kokan. (3) Pressed collar. Mild steel pipe collar is inserted around deformed bars and pressed to make indents around the lugs of the bars. Squeeze joint was developed by Kajima, Takenaka and Okabe, Grip joint by Obayashi, Powergrip by Taisei, TS sleeve joint by Toda and Shimizu. They use slightly different machines to press the collar tight around the re-bars, but the basic principle is same. 20 Design of Modern Highrise Reinforced Concrete Structures (4) Sleeve splices. Steel splice is inserted around bars, similarly to above, but in this case the gap between the sleeve and the bars is filled with mortar or molten metal. NMB splice-sleeve, devised by Japan Splice Sleeve, uses high strength mortar, and Cadweld by Okabe uses molten metal. (5) Screw-deformed bars. There are numbers of deformed bars with screw shaped lugs. They are not machined screw, but are hot-rolled by special rollers. They are named with Japanese word "Neji", meaning screw, as follows: Nejicon by Kobe Steel, Sumineji-bar by Sumitomo Steel, Neji-tekkon by Tokyo Steel, Neji-D-bar by Nippon Steel. These screw-deformed bars can be spliced by a steel coupler with machined or die-cast screw inside. As the hot-rolled screw is quite loose it has to be tightened by lock nuts or grouted with resin or high strength mortar. Different diameter bars can be spliced by using specially manufactured couplers. Above-mentioned variations came out to the market while construction companies were struggling with the technology examination. Recently selection was made to leave in most cases only screw-deformed bars with mortar grouted couplers (neji-grout splice) for cast-in-place construction and splice-sleeves for precast concrete members. The anchorage of girder bars to exterior columns is provided by bend. It had been a Japanese tradition to bend both top and bottom girder bars downward for lowrise RC buildings for a long time, but it is clearly undesirable for seismic construction where alternate horizontal load produces tension in top and bottom bars by turns. Ever since the beginning of highrise RC construction the design engineers succeeded in expelling this bad tradition of bent down bottom bars. Now in all construction sites top bars are bent down and bottom bars bent up. When the size of the beam-column joint does not allow both bars bent into L-shaped anchorage, top and bottom bar anchorage are united to form [/-shaped anchorage. In case of screw-deformed bars anchor plates with screw nuts may be used when the space for anchorage is limited. Exterior beam-stub for beam bar anchorage, as popularly seen in New Zealand, is never used in Japan. Another place where anchorage must be carefully accounted for is the top of the column at the roof. It is difficult to use bent bars for column axial reinforcement. Hence in most cases anchor plates with screw nuts are used. RC Highrise Buildings in Seismic Areas 1.3.6. Concrete 21 Placement As mentioned before, concrete is cast separately into columns and floor system, not with the purpose of using different concrete quality to those members, but in order to produce good quality in column concrete. With the VH separate casting, column concrete is cast prior to the placement of girder reinforcement cage, and by doing so, it is possible to use relatively low slump concrete and compact it with an internal vibrator. In the recent practice high performance water reducer is used as a chemical admixture in the concrete mix, which also has the slump loss reduction effect, and the slump at the casting is made to be about 18 cm or slightly larger. The unit water content is not more than 175 1/m3 in accordance with the definition of high durability concrete. A concrete bucket is commonly used for the placement of column concrete, and placement of concrete not more than about 50 cm deep and compaction by means of an internal vibrator are conducted in turn. Placement of concrete in the floor system is done by a concrete bucket or a concrete pump, and the sequence is first to cast girders up to the slab soffit level, then to cast floor slab concrete. Floor slabs with flat surface throughout the building is the easiest to construct. For architectural purposes it is more desirable to have different levels in different rooms, particularly of apartments. To match the Japanese lifestyle of taking off shoes in the house, entrance and outdoor corridors should be lowered 10 to 15 cm from rooms. Bathroom floor should also be lowered to accommodate Japanese style washing space. In case of highrise apartment this kind of double level floor slabs are more cumbersome to construct in the field, and most contractors build floor slabs as single level flat plate. Space around the entrance hall and bath room are built with raised floor finishing, and living and bed rooms are in the space one step down from there. However when the building is designed by an architectural design firm, the traditional multiple level floor slabs are often specified in the design, to increase the value of the building. This also matches the recent need for barrier-free interior design for coming society of elderly people. 1.3.7. Construction Management The technical review of the Technical Appraisal Committee for Highrise Buildings is related to structural design, and hence in general the construction process is not reviewed as far as steel or SRC buildings are concerned. In case 22 Design of Modern Highrise Reinforced Concrete Structures of highrise RC buildings, on the contrary, a document prescribing the construction planning is required in the review process. This construction planning is prepared jointly by the design section and construction section of the construction company. In the case where the building is designed by an architectural and engineering design firm, a specification to manage the quality control of the contractor is required. The quality control of high strength concrete includes quality control of aggregate, particularly that of its surface water, concrete strength at early ages, casting and compacting, and perfect curing, just to point out a few important items among others. Recent trend shows prevalent use of high performance water reducer, and management age for specified concrete strength longer than 28 days. 1.4. 1.4.1. Seismic Design Basic Principles Seismic design consideration has the priority over other structural design considerations for highrise RC buildings. Hence in this section seismic design is described almost exclusively. The fundamental natural periods of highrise RC buildings ranging from 25 to 30 stories fall in the range of 1.2 to 1.8 seconds. It is possible to make design base shear coefficient lower than lowrise buildings, but the natural period is not long enough to expect a linear response to strong earthquake shaking. It is necessary to absorb earthquake energy through the inelastic deformation, or in other works, through the ductility, of the structure. For this purpose, beam-hinge mechanism, or strong column-weak beam mechanism, shown in Fig. 1.10, is always assumed. Column hinges are allowed at the bottom of the first story and the top of the uppermost story, and at the exterior columns in the tension side of the lower stories. The beam-hinge mechanism is assumed in order to provide large energy dissipating capacity distributed all around the structure. It is not desirable if the above-mentioned collapse mechanical is altered by the presence of nonstructural elements. For this reason all nonstructural elements are insulated from the structure. For example, concrete walls cast monolithically with frames are completely avoided except for those in the basement and designated shear walls in the superstructure. This makes a conspicuous RC Highrise Buildings in Seismic Areas 23 Hinges are allowed at top of uppermost story columns (esp, inner columns). earthquake load Hinges are allowed at the exterior columns in the tension side of lower stories. Hinges are allowed at bottom of all first story columns. Fig. 1.10. Strong column-weak beam mechanism. difference from lowrise construction where concrete walls are rather arbitrarily constructed as needed by architectural reasons. Exterior walls of highrise RC buildings are made of precast or ALC (autoclaved lightweight concrete) panels, and interior walls are also made of ALC or fiber reinforced plaster panels, in both cases installed with allowance to the expected story drift. Precast concrete spandrel walls are sometimes used, with the same care to insulate them from interfering with the structure. 1.4.2. Design Criteria and Procedure Earthquake resistant design criteria are summarized in Table 1.1. Two levels of earthquake ground motions are assumed: level 1, the strongest ground motion that is expected to occur at least once during the lifetime of the building, whose maximum velocity is about 25 cm/s, and level 2, a limiting 24 Design of Modern Highrise Reinforced Concrete Structures Table 1.1. Earthquake resistant design criteria. Seismic hazard level Level 1 Probability of recurrence Maximum ground velocity Maximum ground velocity Once in lifetime 25 cm/s 25 c m / s Concrete cracks but no steel yields less than 1 less than 1 less than 1/200 Member forces Story ductility factor Member ductility factor Story drift angle Level 2 Possible maximum 50 c m / s 50 c m / s Steel yields but no building collapses less than 2 less than 2 less than 1/100 ground motion that may or may not happen but that should be considered in the design, whose maximum velocity is about 50 cm/s. The building's expected behavior is, for the former, level 1, ground motion, that concrete will crack but re-bars remain in the elastic range, and for the latter, level 2, ground motion, that re-bars may yield but ductility factors are limited in order to avoid excessive inelastic deformation leading to the collapse. In addition, the story drift angle is limited to be less than 1/200 under level 1, and 1/100 under level 2, ground motions. These criteria are similar to those for steel or SRC highrise buildings with the height in excess of 60 m. They are not explicitly stipulated in the Building Standard Law. They have been traditionally used in the technical review by the Technical Appraisal Committee for Highrise Buildings of the Building Center of Japan, as a kind of current consensus among structural engineers. The design procedure consists of two phases, which essentially correspond to the two levels in Table 1.1. The first phase design is to protect the "weak link" of the structure, that is, yield hinges under the action of level 1 earthquake. For this purpose, design seismic loads are determined, usually referring to Building Standard Law and preliminary earthquake response analysis, and members are proportioned to carry forces resulting from the design seismic loads. The second phase design is to ensure the assumed mechanism to form under the action of level 2 earthquake. Collapse load associated with the mechanism formation is calculated, and structural members outside yield hinges are proportioned to forces associated with the mechanism formation enhanced by appropriate magnification factors. RC Highrise Buildings in Seismic Areas 25 A series of nonlinear time history earthquake response analysis are performed to confirm the design criteria in Table 1.1. 1.4.3. Design Seismic Loads Current Building Standard Law and its Enforcement Orders provide design seismic loads for buildings up to 60 m in height only. However, it is a common practice for structural engineers to just extrapolate the provisions to obtain design seismic loads for highrise buildings, and modify as needed by a preliminary earthquake response analysis. 0.25 0.2 0.15 0.1 0.05 0 0 0.5 1 1.5 2 2.5 3 Ti=0.02h (a) Fundamental period from code equation 0.25 0.2 0.36/Ti 0.15 0.1 0.18/Ti 0.05 0 0 0.5 1 1.5 2 Ti (x,y direction) 2.5 3 (b) Fundamental period from analysis Fig. 1.11. Relationship between base shear coefficient and fundamental natural period. 26 Design of Modern Highrise Reinforced Concrete Structures Figure 1.11(a) shows the design base shear coefficient of highrise RC buildings against the fundamental natural period from an equation stipulated in the Law, i.e. Ti = 0.02/i (1.1) where h is building height in m. Most design falls above the code curve for second class (intermediate) soil. Figure 1.11(b) shows the design base shear coefficient against calculated elastic fundamental natural period. The range shown by two curves corresponds to most highrise construction in Japan, either steel or SRC construction. It seems highrise RC buildings have slightly lower base shear, as long as they are compared on the basis of elastic natural period. Probably it would be more fair comparison to take natural period based on cracked sections, although it is not a common practice to do so in Japan. 1.4.4. Required Ultimate Load Carrying Capacity Although the Building Standard Law requires, for buildings up to 60 m in height, that ultimate load carrying capacity be calculated and be confirmed to exceed the required ultimate load carrying capacity, it is not necessary for highrise buildings exceeding 60 m in height to conform to this requirement, because dynamic time history earthquake response analysis performed on these buildings substitutes the requirement. To tell the truth, the requirement to check the ultimate load carrying capacity was incorporated into the Building Standard Law as a substitute to earthquake response analysis. In the actual seismic design of highrise RC buildings, calculated yield load of each story is compared with the design seismic load to make sure that the yield load level exceeds at least one and half times the design seismic loads. The yield load corresponds to the lower bound of the ultimate load carrying capacity in the Building Standard Law. The required capacity level of one and half times the design seismic load corresponds to the adoption of structural characteristics factor Ds to be 0.3, the value same as the ductile frames for RC structures in the Law. 1.4.5. First Phase Design The first phase design consists of structural analysis for design loads and proportioning of members. Structural analysis is carried out for permanent RC Highrise Buildings in Seismic Areas 27 loading as well as design seismic loading. Actions on each section of members are found, and reinforcement in each sections determined, much the same way as ordinary structures. Analysis for permanent loading is carried out usually by displacement method by a computer based on the uncracked section, considering only flexural deformation of members. Shear deformation is not considered because it does not influence very much on the stress distribution. Axial deformation of columns is not considered because it sometimes gives unrealistic moment distribution in upper girders. Rigid zones at member ends are not considered because most computer programs currently available do not include subroutines to calculate fixed end moments and forces of members with rigid zones. Analysis for seismic loading in earlier period of highrise RC development was mostly carried out also by displacement method by a computer based on the uncracked section, considering flexural, shear and axial deformation of members, and rigid zones at member ends. The moment redistribution was applied as deemed necessary by designers. In the more recent time designers seem to prefer carrying out nonlinear incremental frame analysis using the amount of reinforcement temporarily determined by preliminary analysis. The method of analysis is same as what is explained in the next subsection. The moment redistribution is an art to account for the stiffness change due to concrete cracking. By doing the redistribution design moments are adjusted to more reasonable distribution. However the way they are redistributed is largely left to the judgment of designs. Furthermore its appropriateness must be demonstrated in the subsequent nonlinear frame analysis, so that no yield hinges would occur under the action of design seismic loads. By conducting nonlinear frame analysis from the beginning, moments are automatically redistributed, and the appropriateness of moment distribution can be proven simultaneously. 1.4.6. 1.4.6.1. Second Phase Design Calculation of Ultimate Load Carrying Capacity The second phase design consists of calculating the ultimate load carrying capacity and associated stress distribution, and to ensure formation of assumed mechanism. The ultimate load carrying capacity may be evaluated by limit analysis. However, nonlinear incremental frame analysis (push-over analysis) is usually performed, which gives not only the ultimate capacity but also the 28 Design of Modern Highrise Reinforced Concrete Structures primary load-displacement relation for each story for use in the dynamic earthquake response analysis. The nonlinear incremental frame analysis must incorporate two kinds of nonlinear models for members. The one is the so-called beam model, which enables us to determine incremental stiffness matrix of a member from the nonlinear stiffness assigned to critical sections at both member ends. Various beam models are available but the one component model, which consists of an elastic member with inelastic rotational springs at both ends, seems to be the most favorite recently. The other nonlinear model is the so-called hysteresis model, or restoring force model, which determines the incremental nonlinear stiffness at each critical section from the load, or deformation, history of that critical section. The static incremental analysis requires only the primary portion of the load-deformation relation, but usually a computer program includes load-deformation relation under reversal of loadings, or hysteresis, so that the same program can also be used for dynamic time history analysis. The primary portion must be determined prior to the analysis by the input data, and designers usually find a cracking point and a yield point for each section by appropriate equations found in the literature, to form trilinear primary curve by connecting them. 1.4.6.2. Ductility of Girders For the calculated member forces associated with the mechanism, ultimate strength of each member is investigated whether the assumed mechanism would be actually formed. This confirmation consists of three steps. The first is to ensure the ductility of girders. Almost all girders are assumed to have yield hinges at both ends. Shear strength of the girders must be sufficient to prevent premature shear failure. At the same time, girder end zones must be designed for yield hinges with sufficient rotation capacity. Bond splitting failure must also be prevented. For the safety evaluation of shear strength, it is necessary to calculate the yield hinge moment with sufficient safety margin. However there is no unified standard for this purpose at present. Designers usually assume steel yield strength of 1.1 times the specified value, consider re-bars within the effective width of slab, and multiply calculated shear force at mechanism by 1.1 or so, but such a procedure may not always be safe enough. Shear strength is evaluated by an empirical equation by Ohno and Arakawa (Ref. 1.1), RC Highrise Buildings in Seismic Areas 29 an equation in the "Design Guidelines Based on Ultimate Strength Concept (Ref. 1.2)", or in case of using high strength lateral reinforcement an equation used at the technical appraisal of that material. Bond splitting is usually checked by the "Design Guidelines Based on Ultimate Strength Concept". On the other hand the rotation capacity of yield hinges is never evaluated quantitatively. It is generally felt that the current design provides sufficient rotation capacity by arranging almost equal amount of top and bottom reinforcement, and also by providing considerable amount of lateral reinforcement in the hinge zone (typically about 0.4 percent or more in terms of web reinforcement ratio). However it is desirable to develop a practical design method for required rotation capacity of yield hinges. 1.4.6.3. Column Strength and Ductility The second step in the confirmation of the mechanism formation is to ensure that columns possess sufficient strength and ductility. Except where yield hinges are expected to occur, such as first story column base or exterior columns on the tension side, columns should be protected against flexure and shear associated with the mechanism formation. A practical problem in this respect is how to determine design forces. Forces determined in the inelastic frame analysis correspond to predetermined load profile, but forces during dynamic excitation are subjected to large fluctuation due to ratio of upper and lower story drift, usually referred to as higher mode effect. Taking a beamcolumn joint, for example, where girders on both sides have already developed yield hinges and hence the flexural moment input to the joint is determined, it is now transferred to the top and bottom column ends. It is the ratio of these column moments that fluctuates by the higher mode effect. Even if the inelastic frame analysis indicates the moment at the base of upper column to be, say, 60 percent of the total girder moment, it can go up to 70 or 80 percent or more during the dynamic response to earthquake motions. Furthermore columns must be protected against forces coming from girders in two directions. There is no unified standard for these aspects. Designers have to employ rather arbitrary magnification factors ranging somewhere from 1.3 to 1.5 to multiply to the forces from inelastic frame analysis. The ductility of columns, on the other hand, must be maintained in the locations where yield hinge formation is expected, which, in turn, requires good confinement of core concrete. It is possible for columns to yield at places 30 Design of Modern Highrise Reinforced Concrete Structures where yield hinges are not expected, owing to unforeseen higher mode effect or biaxial effect. Hence it is a common practice to provide lateral confining reinforcement in all columns throughout the height of the building. 1.4.6.4. Beam-column Joints Prevention of premature joint failure is achieved by restricting shear stress in the joint, and by restricting bond stress along the beam bars passing through the joint. For exterior beam-column joint, beam bar anchorage is checked and is carefully detailed. The provisions proposed in the "Design Guidelines Based on Ultimate Strength Concept" are being applied in many recent designs. 1.4.6.5. Minimum Requirements In addition to above calculations there are number of minimum requirements on axial reinforcement ratio, compression-to-tension reinforcement ratio, lateral reinforcement ratio, anchorage length, and so on, set up voluntarily by structural designers. These minimum requirements are largely based on currently prevalent AIJ Calculation Standard (Ref. 1.3), with some modification toward the more strict direction, that is, toward somewhat increased minimum values. In some cases shear span ratio of column is restricted, but in some other cases this restriction is waived with the argument that the confirmation of collapse mechanism supersedes such restriction. Axial forces in external columns are often restricted by some maximum values in compression as well as in tension. In the compression side the value is usually about (0.600.65) times concrete strength times the gross column area, which is too high to expect ductility in unexpected yield hinge formation unless sufficient lateral confinement is provided. 1.4.6.6. Imaginary Accident Finally an analysis on an imaginary accident is introduced. Highrise RC construction was realized owing to the development of high performance structural members through large size structural testing, development of response analysis techniques for earthquake excitation reflecting the characteristics of structural members, development of construction techniques, and, above all, strong volition of the pioneering construction companies toward the realization of highrise RC buildings. Nevertheless it is true that some uneasiness or distrust was felt in early stages of development of highrise RC compared to, say, RC Highrise Buildings in Seismic Areas 31 steel structures. To demonstrate the safety of concrete highrise and to wipe off unreasonable distrust, analysis was carried out in the process of technology examination by several companies in which an imaginary accident, for example, complete loss of load carrying capacity of one column in the first story, was assumed. The analysis showed that the building could escape the collapse even in such an absurdly severe accident. 1.4.7. Experimental Verification Various parts of a structure, shown in Fig. 1.12, have been tested in the development of highrise RC, particularly in the technology examination process. Tests include girders, columns, beam-column joints, and subassemblages of members. In some cases new ideas of detailing are tested, but in many cases similar structural testing was repeated by different construction companies. This was due to the competitive mind of companies, and some companies found significance of testing in the advancement of consciousness of employees towards the development of a new type of construction. It is strongly desired that each structural testing should have some new ideas on the detailing, or different combination of structural parameters, so that it can contribute to add new knowledge to structural engineering. Structural testing produces experimental restoring force and hysteresis characteristics to which computed ones based on the method in the design m^TYTOY Fig. 1.12. Test specimens of structural members. 32 Design of Modern Highrise Reinforced Concrete Structures process are overlapped and compared. It is necessary to pay attention to the displacement range in this comparison. Testing is usually performed to the destruction of test specimens, and to the unexperienced eyes the hysteresis with the largest displacement amplitude is often the most conspicuous. However the comparison should focus on the range of displacement that is to be practically considered in the design. 1.5. 1.5.1. Earthquake Response Analysis Linear Analysis RC structures start cracking at a relatively low level of loading. Hence the elastic linear analysis based on the uncracked section serves little in predicting actual behavior. Linear analysis based on the cracked section is more meaningful, but it has some inherent ambiguity in how to determine the cracked section stiffness and the associated damping. Therefore, nonlinear time history analyses considering cracking and yielding explicitly are conducted in all cases of highrise RC design for both levels 1 and 2 earthquake responses. 1.5.2. Nonlinear Lumped Mass Analysis As a simplified analytical model for nonlinear analysis, a lumped mass shear model is almost exclusively used. The restoring force characteristics of stories are defined by simplifying the load-displacement relation from incremental frame analysis into an equivalent trilinear relation. Degrading trilinear model or Takeda model are used for hysteresis rules under reversal. Shear model is generally regarded as an easy model to analyze, but it also has some drawbacks. For example high mode periods and shapes do not agree with those from more exact models. Story displacement in the inelastic range is apt to concentrate in particular stories while such concentration would not result in using more elaborate models. Member ductility cannot be found from the shear model analysis. Users of this model should be aware of these disadvantages. As a slightly more sophisticated model, a so-called flexural shear model is sometimes used, in which flexural deformation due to overturning moment is separately evaluated and added to the shear deformation which is the frame deformation. The flexural deformation is evaluated on the basis of linear elastic axial deformation of columns. RC Highrise Buildings in Seismic Areas 33 When the building is susceptible to torsional vibration, three-dimensional response analysis must be conducted. For this purpose a dynamic quasithreedimensional model is frequently used, which consists of many shear models, or flexural shear models, corresponding to each planar frame interconnected by rigid floor diaphragms. One of the serious drawbacks of lumped mass models is the lack of ability to predict member ductility factors. Usually member ductility is indirectly evaluated by equating dynamic story drift to the static one in the incremental frame analysis. However, some engineers opt to carry out dynamic frame analysis explained in the next subsection. 1.5.3. Nonlinear Frame Analysis Dynamic nonlinear frame analysis, where inelastic deformation of constituent frame members are directly accounted for in the time history of earthquake response, can compensate all the incompleteness of lumped mass models. Theoretically this analysis is just an extension of static incremental frame analysis into dynamic domain. It is an analysis that requires awfully a lot of computation, but the recent technical advancement of computer hardware enables us to perform such an analysis relatively easily. Recent popularization of excellent software also helps engineers conduct, in their recent design works, nonlinear frame response analysis to a limited number of input earthquake ground motions, that is, to one or two motions that were shown to be most effective to the structure in the lumped mass analysis. It must be pointed out however that frame analysis at present is in most cases limited to planar frames. For the building with torsional vibration, it is ideal to carry out nonlinear space frame analysis, and a few softwares are currently available for this purpose. But it will be some time in future when such analysis becomes a popular design tool to all structural engineers. 1.5.4. Input Earthquake Motions As for the input earthquake ground motions, the Building Center of Japan recommends the use of three or more waveforms in the following three categories for any highrise buildings including RC construction: (1) Well known "standard" motions, e.g. El Centra 1940 NS and Taft 1952 EW. 34 Design of Modern Highrise Reinforced Concrete Structures (2) Records taken at nearby stations, e.g. Tokyo 101 1956 NS for buildings in Tokyo. (3) Records containing relatively long period components, e.g. Hachinohe 1968 NS and EW, Sendai TH 030 1978 NS and EW. In addition to these recorded ground motions, synthetic ground motions are increasingly used recently. Earthquake ground motions are normalized in terms of maximum velocity to the levels as prescribed in Table 1.1 for design criteria. 1.5.5. Damping When time history earthquake response analysis of any kind is conducted, a damping factor is assigned by the analyst. In this regard the present state of the art is definitely incomplete. The type of damping is prescribed in the computer program, and each type of damping requires input data in a form appropriate to the type being used. The analyst must be well aware of the type of damping and its consequence. Among damping types in the linear system, there are external damping where damping matrix is proportional to mass matrix, internal, or viscous, damping where damping matrix is proportional to stiffness matrix, Rayleigh damping where damping matrix is a linear combination of the above two, and Caughey damping where damping matrix is expressed as a series consisting of mass and stiffness matrices. These are, and only these are, types of damping that enable us to decompose the equations of motion into classical normal modes. The modal damping values for higher mode decreases in external damping, while it increases in internal damping. With Rayleigh damping it is possible to assign modal damping values to two arbitrary modes. Caughey damping is the most general in that it makes us possible to assign modal damping values to all modes. In the practical earthquake response analysis internal viscous damping is almost always preferred. When the response goes into nonlinear range due to inelastic strains in the structure, the stiffness matrix is modified in each step to represent incremental, or instantaneous, stiffness. The incremental stiffness in the inelastic range is lower than, but not proportional to, the linear elastic stiffness. If the damping matrix in the linear range is unchanged, it is theoretically not possible to decompose the system into normal modes. But it is easy to imagine that the result of numerical integration would reflect larger effect of damping RC Highrise Buildings in Seismic Areas 35 as incremental stiffness becomes lower and lower. In practice this would result in an underestimation of response. To avoid such an apparent overdamping, use of the internal viscous damping can give us some remedies. The damping matrix in this case can be written as follows. [C] = {2h/u)[K] (1.2) where [C] is the damping matrix, [K] is the stiffness matrix, u is the circular frequency of the first mode, and h is the fraction of damping to the critical damping. If we take the incremental stiffness matrix in each step of inelastic range into the above stiffness matrix, and carry out modal analysis to find the first mode circular frequency w in each step, and construct new damping matrix based on Eq. (1.2) while keeping the value of h constant, then we will end up with a constant fraction of damping throughout the inelastic response time history. The above-mentioned procedure is preferred by relatively few engineers. The reason is that the repeated modal analysis at each step in order only to find the fundamental circular frequency is time consuming. Many engineers prefer, instead, to use the damping matrix of Eq. (1.2) with a constant coefficient to incremental stiffness matrix, that is, a constant (2/i/w) value. Such a procedure is called "damping proportional to incremental stiffness". As a value of constant (2h/ui), they use prescribed first mode damping of, say, 0.03 for h, and fundamental circular frequency in the linear elastic range. By doing so they implicitly assume smaller fraction of damping to critical damping as the incremental stiffness is lowered (roughly speaking, assumed damping is proportional to the square root of the incremental stiffness). This would give a slight overestimation of response, but it can be judged to be on the safe side. When the soil structure interaction or coupling vibration of superstructures and substructures is taken into account in the earthquake response analysis, damping becomes even more complicated. In such cases damping values different from those for superstructure are often assigned to soil or substructure. It is then necessary to find modal damping values which are usually assumed to be proportional to the strain energy of each part in each mode, and construct a Caughey series type damping matrix. The damping proportional to incremental stiffness can no longer be used. Fortunately there are few occasions in the practice where soil structure interaction or coupling vibration would have to be 36 Design of Modern Highrise Reinforced Concrete Structures considered. However in case they must be employed in the response analysis, damping matrix formulation must be conducted following the above theory in each step, no matter how tedious it is. 1.5.6. Results of Response Analysis In the engineering design document the results of response analysis are demonstrated by two series of figures, one each for levels 1 and 2 responses, illustrating the distribution along the building height of maximum story shear, maximum story ductility factor, and so on. Other quantities such as maximum floor acceleration or maximum floor displacement are also plotted in some cases. Plots of maximum response values on the load-displacement curves of stories, ° El Centro 60 50 40 1 I 20 10 0 0 0.2 0.4 0.6 Story drift (%) 0.8 1 Fig. 1.13. Primary curves of story shear vs. story drift with plots of maximum response to earthquake motions. RC Highrise Buildings in Seismic Areas 37 such as in Fig. 1.13, serve as a good guide to demonstrate the degree of inelastic deformation. Quantities such as member ductility factors are often tabulated. As a matter of course all response analyses for the design of highrise RC buildings result within the design critical as set forth in Table 1.1. In many cases, design criteria for story drift angle are found to be the governing criteria. Story ductility factors under level 2 response often fall below 1.0, and member ductility factors remain mostly less than 2.0. 1.6. 1.6.1. For Future Development Factors Contributed to Highrise RC Development So far the recent development of highrise RC construction in 1980's in Japan has been described and discussed in detail. In this section, factors that contributed to this development and some future outlook will be summarized for the conclusion of the chapter. (1) Relatively short-span and low story height realized the reduction of column axial load and seismic forces. At the same time this structural configuration limited the occupancy to residence only. It has been desired to make longer spans even for residential use. (2) Relatively regular plan and elevation eliminated possible disadvantages due to torsional vibration or concentrated story drift along the height of the building. This is mainly the consequence of primitive state of the art of structural engineering and prudence of engineers. Future development of sophisticated analysis techniques will liberate the structural planning to adapt to variety of architectural needs, but at the same time this may end up with structurally unsound buildings in effect. (3) Various types of lateral reinforcement for columns have been developed, particularly in early period, for the confinement of core concrete and shear reinforcement. The means to account for large axial forces, such as core bars, have also been devised. Selection and standardization are already on the way, and it is expected that some kind of guidelines will be compiled in future. (4) Availability of concrete and reinforcement with higher strength than those for conventional lowrise construction was certainly the most important factor to realize highrise construction. Further increase of material strength will liberate the structure from current restrictions. 38 Design of Modern Highrise Reinforced Concrete Structures (5) Advancement of re-bar splicing techniques helped the rationalization of construction. Presently available variety is already subjected to selection to a fewer number of standardized techniques. (6) Use of precast members also helped the rationalization of construction. It is desired to proceed this direction with the overall reasonable judgment to use precasting as needed, together with further improvement of detailing. (7) Design procedure to ensure assumed collapse mechanism by providing strength and ductility to hinge sections and sufficient strength to nonhinge sections has become a popular understanding among structural engineers. It is desirable to establish guidelines such as the "Design Guidelines Based on Ultimate Strength Concept" for highrise construction. (8) Development of analytical procedure for dynamic frame response in the recent years has been targeted to highrise RC buildings. Steel or SRC highrise buildings, which have been analyzed by lumped mass model almost exclusively in the past, are recently being analyzed by more elaborate frame model. Further development of computer software is desired. 1.6.2. Need for Higher Strength Materials As mentioned in the previous subsection, the quick development of highrise RC owed to many factors, but development and use of high strength concrete and high strength, and large size reinforcing bars was evidently the most fundamental factor. High strength concrete with specified compressive strength of 36 to 42 MPa, and high strength large size deformed bars of SD390, D38 or D41 were the two most important factors towards the realization of highrise construction up to 30 stories or more in an intensively seismic country such as Japan. In reviewing the practice of structural design of highrise RC buildings, there were two evident need of advanced structures. One was the increased number of stories. Highrise RC, growing out of lowrise to 20, 30, or 40 stories, would like to reach up to, say, 60 stories, or 200 m in height, which had been realized only by steel structures. Another was the increased span length to accommodate freer architectural plan within current range of story numbers. Either of these two needs would require development and use of even higher strength material. This was the basic motive of the five-year "New RC" national project of 1988-1993, based on which results the following chapters have been written. RC Highrise Buildings in Seismic Areas 39 References 1.1. Ohno, K. and Arakawa, T., A study on the shear resistance of reinforced concrete beams, Trans. Arch. Inst. Japan 66, 10 (1960) (in Japanese). 1.2. Design guidelines for earthquake resistant reinforced concrete buildings based on ultimate strength concept, Arch. Inst. Japan, 1990, p. 340 (in Japanese). 1.3. Standard for structural calculation of reinforced concrete structures, Arch. Inst. Japan, 1991, p. 654 (in Japanese). Chapter 2 The New RC Project Hisahiro Hiraishi Department of Architecture, Meiji University, 1-1-1 Higashimita, Tama-ku, Kawasaki 214-8571, Japan E-mail: hiraishi@isc.meiji.ac.jp 2.1. Background of the Project The background of this national research project is described in detail in the preceding chapter. It will be briefly summarized here. Reinforced concrete (RC) has been widely used for lowrise building construction ranging from two to seven stories because of its excellent fire resistance and durability, low cost, and easy maintenance. However its application to highrise buildings had been suspended in Japan where high seismic hazard called for high degree of protection, because RC was generally regarded as material inherently inferior to steel in ductility. A breakthrough of this obstacle was achieved around 1980 by the improved potential of RC, namely the development of high strength concrete with compressive strength twice as large as the ordinary concrete, development of detailing techniques to ensure ductility of various structural members, development of computer analysis for earthquake response based on sophisticated theories, development of new construction technology, and improvement of quality control techniques. As a result, highrise apartment buildings in the range of 20 to 40 stories were constructed, which gave a favorable prospect to the future RC construction. However at the same time it became apparent that even higher strength concrete and high strength steel to make good use of concrete strength must be developed, in order to widen the scope of application to even higher apartment buildings 40 The New RC Project 41 or to the nonresidential buildings such as offices where architectural demand would require more liberal structural coniguration. Based on this background, the Ministry of Construction of Japan decided to promote a five-year national research project entitled "Development of Advanced Reinforced Concrete Buildings using High Strength Concrete and Reinforcement" (usually referred to as the "New RC"). The project started in 1988 fiscal year, and aimed at producing high strength and high quality concrete of specified strength from 30 to 120 MPa and high strength and high quality steel reinforcing bars with yield strength from 400 to 1200 MPa, and at developing new field of RC buildings by utilizing these materials. 2.2. Target of t h e Project The range of material strength set forth as the target of the New RC project is shown in Fig. 2.1. Horizontal axis shows compressive strength of concrete and vertical axis shows yield strength of steel reinforcement. The small zone denoted "ordinary" corresponds to the range for ordinary RC construction, covering concrete from 18 to 27 MPa and steel from 300 to 400 MPa, and the adjacent small zone denoted "highrise" corresponds to the range for recently developed highrise RC construction, covering concrete from 36-48 MPa and steel same as "ordinary". As seen in the figure currently used materials for ordinary and highrise RC buildings occupy only small zones. )r~^ *" 800 n-2 ; h~ \ n-1 \ // Ordinary , \ : i i 400 I J j r I .3> I III X h ighr se I 30 60 90 Concrete strength (MPa) ! 120 Fig. 2.1. Strength of materials and zones (I, II-l, II-2 and III) for research and development. 42 Design of Modern Highrise Reinforced Concrete Structures In contrast, the ranges of strength in the New RC project are much larger. Concrete from 30 to 120 MPa and steel from 400 to 1200 MPa are included. Comparing the zones for these ranges of material, it is obviously unrealistic to assume that behavior of New RC structures can be understood simply by extrapolating the knowledge of current RC structures. The area in Fig. 2.1 for the New RC was further divided into four zones, namely zones I, II—1, II—2, and III. Structures in these zones were studied by somewhat different tactics. Zone I corresponds to concrete up to 60 MPa and steel up to 700 MPa, which was assumed to be the direct target of the New RC project whose results could be compiled and put into practical use right at the conclusion of the five-year project in 1993. For this zone the extrapolation of the knowledge of current RC structures was thought to be relatively effective. On the contrary zone III corresponds to concrete from 60 to 120 MPa and steel from 700 to 1200 MPa, which was regarded as a future "dream". Basic characteristics of RC would have to be reexamined, and hence the project was not expected to produce much practical results. Basic subjects such as material characteristics and performance under loading of structural elements and members would be the major results for the zone III. Zones II—1 and II—2 are the combination of very high strength material and not-so-high strength material. Such combination would not have much practical significance, hence they were regarded to have secondary importance in the project. It would be relatively easy to use such combination of materials once zones I and III were completely understood. Objectives and corresponding final results of the project are summarized in Table 2.1. The first item was development of high strength materials. This required close cooperation of material engineers, structural engineers who must specify basic requirements, material supplier for cement, mineral and chemical admixtures, and steel manufacturers. The second item was investigation into properties of structural members, particularly framing members for the superstructure, under the action of seismic excitation. Experimental approach by conducting laboratory testing was indispensable in this aspect, but theoretical examination of experimental data was also emphasized in this project. The third item was development of design and construction guidelines. Here the word "guidelines" did not mean a type of guidelines that would specify full details of technology, but it was to give only fundamental considerations on principles for design and construction practice. Such a soft type of guidelines The New RC Project 43 Table 2.1. Objectives of research and development and expected final results. Objectives (1) Development of high strength and high quality materials Expected final results Methods for mix proportion and quality control of concrete (Zone I) Methods for production and use of reinforcement (Zone I) Principles for developing ultra-high strength materials (Zones II and III) (2) Evaluation of basic properties of materials, structural members and frames Methods for evaluation of basic properties of materials (Zones I—III) (3) Development of design and Structural design guidelines (Zone I) construction guidelines Methods for evaluation of basic properties of members and frames (Zones I—III) Earthquake response evaluation guidelines (Zone I) Construction guidelines (Zone I) Development of criteria for structural design, earthquake response evaluation, and construction (Zones II and III) (4) Feasibility study on RC buildings in Zone II—I New type of highrise RC buildings (5) Feasibility study on RC buildings in Zone III New image of RC buildings (super-highrise) (6) Trial design of a highrise boiler building in Zone II—I A structure with steel superbeams and RC box supercolumns was preferred in the worldwide trend towards the performance-based design. The above three items were expected, not only to produce final results as outlined in Table 2.1, but also to throw some light on the current RC technology towards the possible future revisions of specifications and standards. The fourth to sixth items in Table 2.1 were aiming at exploring the feasibility of new type of structures using the New RC material, although they were not essential parts of the project philosophically. It was expected that the New RC project would induce development of new technologies in various related fields, improve potential for international competition of construction industry, and contribute to the activation of the industry. 44 Design of Modern Highrise Reinforced Concrete Structures 2.3. Organization for the Project The Building Research Institute of the Ministry of Construction was in charge of conducting the entire project. Research committees were set up in an organization called Japan Institute for Construction Engineering, to organize people from universities, Housing and Urban Development Corporation, makers of cement, admixtures and steel, and construction companies. The entire organization for the project is shown in Fig. 2.2. Technical Coordination Committee was the center of the committee tree. Research Promotion Committee consisting of representatives from sponsoring companies and Technical Advisory Board consisting of senior researchers of related fields helped the Technical Coordination Committee from financial and technical sides. These three committees were chaired by Dr. Hiroyuki Aoyama, Professor of the University of Tokyo (the affiliation at the time of the five-year project, same in the followings). Under the Technical Coordination Committee five technical committees were set up. Concrete Committee was chaired by Dr. Fuminori Tomosawa, Professor of the University of Tokyo; Reinforcement Committee by Dr. Shiro Morita, Professor of Kyoto University; Structural Element Committee by Dr. Shunsuke Otani, Associate Professor of the University of Tokyo; Structural Design Committee by Dr. Tsuneo Okada, Building Research Institute 9, Building Contractors Society Japan Institute For Construction Engineering Technical Advisory BRI Project \g— Team Technical Coordination Committee Research Promoting Committee _jj Private Organization Housing & Urban Development ! Corporation Cement Admixure ^ Makers Concrete Committee Re inforce m e nt Committee Structural Element Committee Working Working Working Group Structural Design Committee Working Group Construction Manufact ring Committee Working Group AIJ, Universities Fig. 2.2. Organization for research and development. ""*{ Private Organization 1 Private Organization | The New RC Project 45 Table 2.2. Technical Coordination Committee. Position Chairman Vice-chairman Secretary General Secretary Member Administrator Name Aoyama, Hiroyuki Kamimura, Katsuro Okada, Tsuneo Morita, Shiro Murota, Tatsuro Tomosawa, Fuminori Otani, Shunsuke Masuda, Yoshihiro Hiraishi, Hisahiro Hirosawa, Mas aya Murakami, Masaya Sawai, Nobuaki Nishimukou, Kimiyasu Bessho, Satoshi Saida, Kazuo Noto, Hidekatsu Yamamoto, Kouichi Kurumada, Norimitsu Kidokoro, Motoyuki Habu, Hiroharu Takahashi, Yasukazu Yamazaki, Yutaka Nakata, Shinsuke Abe, Michihiko Kaminosono, Takashi Baba, Akio Teshigawara, Masaomi Shiohara, Hitoshi Fujitani, Hideo Kubo, Toshiyuki Akimoto, Toru Mori, Shigeo Ishikawa, Yukio Affiliation* University of Tokyo Utsunomiya University University of Tokyo Kyoto University Building Research Institute University of Tokyo University of Tokyo Building Research Institute Building Research Institute Kogakuin University Chiba University Housing & Urban Develop. Co. Building Contractors Society Kajima Construction Co. Shimizu Construction Co. Steel Makers Club Kobe Steel Co. Cement Association Ministry of Construction Ministry of Construction Building Research Institute Building Research Institute Building Research Institute Building Research Institute Building Research Institute Building Research Institute Building Research Institute Building Research Institute Building Research Institute Japan Institute for Construction Japan Institute for Construction Japan Institute for Construction Japan Institute for Construction Engineering Engineering Engineering Engineering *As of March 31, 1993. Professor of the University of Tokyo; Construction and Manufacturing Committee by Dr. Katsuro Kamimura, Professor of Utsunomiya University. These committees were in charge of making detailed research programs, implementing research works, and integrating research results in five particular fields. Tables 2.2 to 2.9 show the rosters of these eight committees, with due appreciation to the contribution of these committee members which was reflected in this book. Numerous working groups were formed as needed under the five technical committees, but the rosters had to be eliminated here because of the limitation of the space. 46 Design of Modern Highrise Reinforced Concrete Structures Table 2.3. Research Promotion Committee. Position Chairman Name Affiliation* Aoyama, Hiroyuki University of Tokyo Vice-chairman Kamimura, Katsuro Utsunomiya University Secretary Takahashi, Yasukazu Murota, Tatsuro Building Research Institute Building Research Institute Member Okada, Tsuneo Tomosawa, Puminori Morita, Shiro Otani, Shunsuke Hirosawa, Masaya Koizumi, Shinichi Nishimukou, Kimiyasu Takata, Kenjo Moriguchi, Goro Ohmori, Kazuhiro Imazu, Yoshiaki Nakane, Jun Miki, Masahiro Nakae, Shintaro Bessho, Satoshi Kato, Takehiko Ono, Tetsuro Tamura, Ryoji Koitabashi, Michikata Higashiura, Akira Saida, Kazuo Nohmori, Masami Matsumoto, Hiroshi Harasawa, Kenya Heki, Hisashi Mogami, Tatsuo University of Tokyo University of Tokyo Kyoto University University of Tokyo Kogakuin University Housing Urban Develop. Co. Building Construction Society Aoki Construction Co. Asanuma-gumi Construction Co. Ando Construction Co. Ohki Construction Co. Obayashi Construction Co. Ohmotc-gumi Construction Co. Okumura-gumi Construction Co. Kajima Construction Co. Kumagai-gumi Construction Co. Konoike Construction Co. Goyo Construction Co. Sada Construction Co. Sato Kogyo Construction Co. Shimizu Construction Co. Sumitomo Construction Co. Seibu Construction Co. Zenidaka-gumi Construction Co. Daisue Construction Co. Taisei Construction Co. Dainippon-doboku Construction Co. Ano, Shinji Takenaka Construction Co. Sugano, Shunsuke Chizaki Kogyo Construction Co. Ohkawa, Akinori Tekken Construction Co. Morimoto, Hitoshi Takusagawa, Masamitsu Tokai Kogyo Construction Co. Tokyu Construction Co. Yamamoto, Toshihiko Toda Construction Co. Motegi, Yuji Tobishima Construction Co. Nakagawa, Mitsuo J •—.—_ The New RC Project Table 2.3. {Continued) Position BRI Secretary Affiliation* Name Yamanouchi, Jiro Taguchi, Renichi Yanagisawa, Nobufusa Toda, Tetsuo Koga, Kazuya Nishimatsu Construction Co. Nissan Construction Co. Nippon Kokudo Kaihatsu Co. Hazama Construction Co. Haseko Corp. Saitou, Junichi Teraoka, Masaru Wakabayashi, Hajime Maeda, Yasuji Abe, Osamu Endo, Katsuhiko Inaba, Masahiro Noto, Hidekatsu Yamamoto, Koichi Suzuki, Akinobu Kurokawa, Kenjiro Inaoka, Shinya Shimizu, Hideo Kurumada, Norimitsu Uchikawa, Hiroshi Tanaka, Mitsuo Nakano, Kinichi Nagashima, Masahisa Sakai, Masayoshi Takeda, Shigezo Furukawa, Ryutarou Sawamura, Hirotoshi Makino, Yoshihisa Maebana, Tadao Toda, Kazutoshi Kodama, Kazumi Kidokoro, Motoyuki Habu, Hiroharu Hiraishi, Hisahiro Fukuda-gumi Construction Co. Pujita Construction Co. Fudo Construction Co. Maeda Construction Co. Matsumura-gumi Construction Co. Mitsui Construction Co. Mitsubishi Construction Co. Steel Makers Club Kobe Steel Co. Japan Steel Co. NKK Co. Kawasaki Steel Co. Sumitomo Metal Co. Cement Association Onoda Cement Co. Chichibu Cement Co. Osaka Cement Co. Mitsubishi Material Co. NKK Co. Japan Steel Co. Shin-nittetsu Chemical Co. Kawatetsu Kogyo Co. Sumitomo Metal Co. Kobe Steel Co. Chemical Admixture Association Nisso Master Builders Co. Ministry of Construction Ministry of Construction Building Research Institute Masuda, Yoshihiro Abe, Michihiko Kaminosono, Takashi Teshigawara, Masaomi Building Building Building Building Research Research Research Research Institute Institute Institute Institute 47 48 Design of Modern Highrise Reinforced Table 2.3. Position Structures (Continued) Affiliation* Name Shiohara, Hitoshi Pujitani, Hideo Kubo, Toshiyuki Administrator Akimoto, Toru Mori, Shigeo Ishikawa, Yukio Concrete Building Research Institute Building Research Institute Japan Institute for Construction Engineering Japan Institute for Construction Engineering Japan Institute for Construction Engineering Japan Institute for Construction Engineering *As of March 31, 1993. Table 2.4. Technical Advisory Board. Position Name Affiliation* Chairman Aoyama, Hiroyuki University of Tokyo Vice-chairman Kamimura, Katsuro Utsunomiya University Advisor Secretary Umemura, Hajime University of Tokyo Takahashi, Yasukazu Murota, Tatsuro Building Research Institute Building Research Institute Member Shiire, Toyokazu Tomii, Masahide Okada, Tsuneo Ogura, Kouichiro Kasai, Yoshio Kanoh, Yoshikazu Kishitani, Kouichi Sonobe, Yasuhisa Tomosawa, Fuminori Muguruma, Hiroshi Morita, Shiro Yamada, Minoru Watabe, Makoto Otani, Shunsuke Hirosawa, Masaya Kidokoro, Motoyuki Yokota, Mitsuhito Habu, Hiroharu Kanagawa University Kyushu University University of Tokyo Meiji University Nihon University Meiji University Nihon University Tsukuba University University of Tokyo Kyoto University Kyoto University Kansai University Shimizu Construction Co. University of Tokyo Kougakuin University Ministry of Construction Ministry of Construction Ministry of Construction Administrator Kubo, Toshiyuki Akimoto, Toru Japan Institute for Construction Engineering Japan Institute for Construction Engineering *As of March 31, 1993. The New RC Project 49 Table 2.5. Concrete Committee. Position Name Affiliation* Chairman Tomosawa, Fuminori University of Tokyo Secretary Shimizu, Akiyuki Tokyo Science University Abe, Michihiko Building Research Institute Kamata, Eiji Hokkaido University Kawase, Kiyotaka Niigata University Kemi, Torao Daimon, Masaki Tanigawa, Yasuo Matsufuji, Yasunori Kittaka, Yoshinori Ashikaga Institute of Technology Member Noguchi, Takafumi Hamada, Masaru Hisaka, Motoo Nakane, Jun Okamaoto, Kimio Matsuo, Tadashi Izumi, Itoshi Hiraga, Tomoaki Sakai, Masayoshi Kurumada, Norimitsu Kodama, Kazumi Kosuge, Keiichi Suguri, Hideaki Furuta, Hajime Aoki, Hitoshi Masuda, Yoshihiro Hiraishi, Hisahiro Baba, Akio Tanano, Hiroyuki Yasuda, Masayuki Tokyo Institute of Technology Nagoya University Kyushu University Utsunomiya University University of Tokyo Housing & Urban Develop. Co. Materials Testing Center Obayashi Construction Co. Kajima Construction Co. Sato-kogyo Corp. Takenaka Construction Co. Toda Construction Co. NKK Co. Cement Association NMB Co. Denki Kagaku Co. Ministry of Construction Ministry of Construction Ministry of Construction Building Research Institute Building Research Institute Building Research Institute Building Research Institute Building Research Institute Coop. Member Shiraishi, Kiyotaka Shiomi, Itsuo Sudo, Eiji Building Research Institute Building Research Institute Building Research Institute Administrator Japan Institute for Construction Engineering Japan Institute for Construction Engineering Akimoto, Toru Ishikawa, Yukio *As of March 31 1993. 50 Design of Modern Highrise Reinforced Concrete Structures Table 2.6. Reinforcement Committee. Affiliation* Name Position Chairman Morita, Shiro Kyoto University Secretary Noguchi, Hiroshi Shiohara, Hitoshi Chiba University Member Kubota, Toshiyuki Tanaka, Reiji Tanigawa, Yasuo Matsuzaki, Ikuhiro Kinki University Tohoku Institute of Technology Nagoya University Tokyo Science University Wada, Akira Imai, Hiroshi Kaku, Tetsuzo Sakino, Kenji Hayashi, Shizuo Tokyo Institute of Technology Tsukuba University Toyohashi Institute of Technology Kyushu University Tokyo Institute of Technology Tsukuba Technical College Pujisawa, Masami Building Research Institute Kyoto University Shimizu Construction Co. Taisei Construction Co. Takenaka Construction Co. Yamamoto, Toshihiko Tokyu Construction Co. Fujita Construction Co. Teraoka, Masaru Kobe Steel Co. Yamamoto, Koichi New-Japan Steel Co. Suzuki, Akinobu Sumitomo Metal Co. Shimizu, Hideo Ministry of Construction Suguri, Hideaki Ministry of Construction Puruta, Hajime Pujii, Shigeru Inada, Yasuo Hattori, Takashige Sugano, Shunsuke Administrator Aoki, Hitoshi Ministry of Construction Fukushima, Tbshio Masuda, Yoshihiro Hiraishi, Hisahiro Building Research Institute Building Research Institute Building Research Institute Baba, Akio Kato, Hirohito Building Research Institute Building Research Institute Akimoto, Toru Japan Institute for Construction Engineering Japan Institute for Construction Engineering Ishikawa, Yukio *As of March 31, 1993. The New RC Project 51 Table 2.7. Structural Element Committee. Name Position Affiliation* Chairman Otani, Shunsuke University of Tokyo Vice-chairman Watanabe, Pumio Kyoto University Secretary Kaminosono, Takashi Building Research Institute Member Fujitani, Hideo Building Research Institute Ohkubo, Masamichi Kanoh, Yoshikazu Takiguchi, Katsumi Nomura, Setsuro Minami, Koichi Kato, Daisuke Kabeyasawa, Toshimi Joh, Osamu Fujisawa, Masami Ichinose, Toshikatsu Bessho, Satoshi Kato, Takehiko Yoshizaki, Seiji Maeda, Yasuji Kyushu Institute of Design Meiji University Tokyo Institute of Technology Tokyo Science University Fukuyama University Niigata University Yokohama National University Hokkaido University Tsukuba College of Technology Nagoya Industrial University Kajima Construction Co. Kumagai-gumi Construction Co. Taisei Construction Co. Maeda Construction Co. Mitsui Construction Co. Ministry of Construction Ministry of Construction Aoki, Hitoshi Ministry of Construction Nakata, Shinsuke Building Research Institute Hiraishi, Hisahiro Building Research Institute Goto, Tetsuro Building Research Institute Teshigawara, Masaomi Building Research Institute Kato, Hirohito Building Research Institute Endo, Katsuhiko Suguri, Hideaki Tsujikawa, Takao Coop. Member Oka, Kohji Building Research Institute Administrator Japan Institute for Construction Engineering Japan Institute for Construction Engineering Akimoto, Toru Mori, Shigeo *As of March 31, 1993. 52 Design of Modern Highrise Reinforced Concrete Structures Table 2.8. Structural Design Committee. Position Name Affiliation* Chairman Okada, Tsuneo University of Tokyo Vice-chairman Murakami, Masaya Chiba University Secretary Yoshimura, Manabu Member Sugimura, Yoshihiro Matsushima, Yutaka Wada, Akira Akiyama, Hiroshi Hirosawa, Masaya Tohoku University Tsukuba University Kabeyasawa, Toshimi Kanda, J u n Yokohama National University University of Tokyo Nagoya Institute of Technology Hokkaido University Tokyo Metropolitan University Teshigawara, Masaomi Building Research Institute Pujitani, Hideo Building Research Institute Kubo, Tetsuo Takizawa, Haruo Nakano, Yoshiaki Sawai, Nobuaki Izumi, Nobuyuki Yoshioka, Kenzo Abe, Isamu Ono, Tetsuro Saida, Kazuo Yamamoto, Masashi Ishida, Tadashi Toda, Tetsuo Suguri, Hideaki University of Tokyo Housing &; Urban Develop. Co. Toda Construction Co. Obayashi Construction Co. Okumura-gumi Construction Co. Kohnoike-gumi Construction Co. Shimizu Construction Co. Tobishima Construction Co. Nishimatsu Construction Co. Hazama-gumi Construction Co. Ministry of Construction Tsujikawa, Takao Ministry of Construction Aoki, Hitoshi Kitagawa, Yoshikazu Ministry of Construction Yamazaki, Yutaka Building Research Institute Nakata, Shinsuke Building Research Institute Yamanouchi, Hiroyuki Hiraishi, Hisahiro Building Research Institute Coop. Member Igarashi, Haruhito Administrator Tokyo Institute of Technology University of Tokyo Kogakuin University Building Research Institute Building Research Institute Building Research Institute Akimoto, Toru Tokyo Institute for Construction Engineering Mori, Shigeo Tokyo Institute for Construction Engineering •As of March 31, 1993. The New RC Project 53 Table 2.9. Construction and Manufacturing Committee. Position Chairman Vice-chairman Secretary Member Coop. Member Administrator Name Kamimura, Katsuro Morita, Shiro Tomosawa, Fuminori Masuda, Yoshihiro Shiohara, Hitoshi Kemi, Torao Tanaka, Reiji Imai, Hiroshi Shimizu, Akiyuki Fukushi, Isao Nakane, Jun Bessho, Satoshi Okamoto, Kimio Hattori, Takashige Izumi, Itoshi Sugano, Shunsuke Yamamoto, Koichi Abe, Michihiko Hiraishi, Hisahiro Yasuda, Masayuki Nishimura, Susumu Akimoto, Toru Ishikawa, Yukio Affiliation* Utsunomiya University Kyoto University University of Tokyo Building Research Institute Building Research Institute Ashikaga Institute of Technology Tohoku Institute of Technology Tsukuba University Tokyo Science University Housing & Urban Develop. Corp. Obayashi Construction Co. Kajima Construction Co. Kajima Construction Co. Taisei Construction Co. Takenaka Construction Co. Takenaka Constructoin Co. Kobe Steel Co. Building Research Institute Building Research Institute Building Research Institute Building Research Institute Japan Institute for Construction Engineering Japan Institute for Construction Engineering "As of March 31, 1993. In addition, several cooperative research projects were organized between the Building Research Institute and volunteering companies. Figure 2.2 shows these cooperative research projects in the right hand side enclosed by dotted lines. The aim of the cooperative research covered the latter three objectives in Table 2.1, namely various feasibility studies of the New RC structures. Chapter 9 of this book deals with the results of these cooperative research projects. 2.4. 2.4.1. Outline of Results Development of Materials for High Strength RC The first major effort was the development of high strength concrete and steel, together with their test methods and evaluation criteria. Figure 2.3 shows fresh high strength concrete at the slump test. High strength concrete 54 Design of Modem Highrise Reinforced Concrete Structures Fig. 2.3. Concrete after slump test. 160 140 --W/(C+Si)=20% 120 ~ 100 m 80 // -^1- -- -W/(C+Si)=25% t -~W/C=35% W/C=65% V\ — / ,7 V) .7 ' 55 ?/ 60 40 20 0 w V. 1 \ I' 0 0.1 0.2 0.3 0.4 0.5 0.6 Strain (%) Fig. 2.4. Examples of stress-strain relationship of concrete. with compressive strength greater than 40 MPa usually displays viscous iow. Handling of such viscous fresh concrete in the site requires special attention, as explained in Chapters 3 and 8 of this book. Figure 2.4 shows some examples of stress-strain relationship of concrete. Relatively linear ascending portion and steep descending portion are conspicuous characteristics of high strength concrete. Figure 2.5 illustrates stress-strain curve of USD 685 steel with specified yield point of 685 MPa that was newly developed for axial reinforcement, together with commercially available reinforcing bars and prestressing steel. As shown by dotted curves in Fig. 2.5, stress-strain relationships of steel in tension tends to lose yield plateau as yield point gets higher. The newly developed The New RC Project 55 2,000 1,500 ' PC ban (0.86) 5 | New RC USD675(0.77) \ 1,000 • SD590 (0.76) w ' SD390 (0.67) 500 SD295(0.71) "0 5 10 15 Strain (%) 20 25 30 Numbers in { ) indicate yield ratio. Fig. 2.5. Examples of stress-strain relationship of reinforcing bars. USD 685 was a successful attempt to produce high strength steel with well denned yield plateau. 2.4.2. Development of Construction Standard Major achievement in the construction engineering was the development of New RC Construction Standard. It is different from the current JASS (Japan Architectural Standard Specification) in the definition of concrete strength. In order to procure the specified strength in the structure with the maximum reliability, concrete strength in the New RC Construction Standard is defined by the strength of concrete in the structure, to be controlled by the strength development in the structure and in the cylinders under the corresponding curing condition. Essential features of the New RC Construction Standard are introduced in Chapter 8. 2.4.3. Development of Structural Performance Evaluation A set of evaluation methods for structural performance of New RC elements and structural members was developed. Performance of elements here refers to beam bar anchorages to columns, buckling of compression bars, lateral confinement, planar RC panel elements subjected to plane stress conditions, and so on. Performance of structural members means items as indicated below: flexural behavior of beams and columns as influenced by axial load, bond 56 Design of Modern Highrise Reinforced Concrete Structures splitting along axial bars, and shear failure in the hinge zone; flexural and shear strength of walls; shear failure of beam-column joints; and connections of first story columns to foundations. Needless to say that monotonic loading as well as cyclic reversal of loading were considered. These evaluation methods, mostly in the form of equations, were developed primarily through theoretical studies, which were subsequently investigated by experiments for their adequacy and accuracy. In some aspects, however, empirical approaches were indispensable, which was judged appropriate for the complex structural material such as RC. Chapter 4 of this book is devoted to this development of performance evaluation methods. Chapter 5 was written as a plain guide for the readers to the nonlinear finite element analysis for RC elements and members, as it was shown in the New RC project that finite element analysis was such a powerful tool for structural engineering that it should have a wider application in the structural design in future. 2.4.4. Development of Structural Design New RC Structural Design Guidelines was developed mainly for earthquake resistance. It is based on the dynamic time history response analysis to earthquake ground motions with a clear definition of required safety. It is introduced in detail in Chapter 6 of this book. Figure 2.6 illustrates an imaginary building that was designed using the guidelines. It is a sixty-story apartment building, whose detail and structural design are also included in Chapter 6. Chapter 7 was written as an easy introduction to the earthquake response analysis, keeping those readers with no experience or little knowledge on the response analysis in mind. The guidelines were developed for highrise RC buildings, but it will be applicable to RC structures in general, and its philosophy should also be applicable to structures of other material. 2.4.5. Feasibility Studies for New RC Buildings Application feasibility studies were made for materials in Zones II and III in Fig. 2.1. They consist of the following three types of buildings. The first was a highrise flat slab building shown in Fig. 2.7. This building was assumed to be constructed using materials in zone II—I. Flat slab structures The New RC Project 57 Fig. 2.6. Bird's eye view of a 60-story building. Fig. 2.7. Highrise flat plate building utilizing high strength concrete. have significant advantage for dwellings because of no girders protruding below the soffit of ioor slabs, in other words, from the ceilings. However its application in Japan has been quite limited in view of apparent deficit in seismic resistance. This feasibility study aimed at the breakthrough for this type of construction in the seismic areas with the use of high strength materials. It was shown to be quite feasible, and much future development is expected. The second was a series of highrise buildings based on the "megastructure" concept. Figure 2.8 shows an example of such structures with 300 m in height, 58 Design of Modern Highrise Reinforced Concrete Structures Fig. 2.8. Megastructure of 300 m high utilizing high strength materials. I s 4&:> Fig. 2.9. Highrise boiler building of thermal power plant. consisting of five rnegastories each of which contains fifteen stories of substructures inside. Materials in zone III are to be used. The basic idea for this type of structures is that the megastructure constructed by high strength RC can be used for centuries as a kind of infrastructure to the society due to its superior durability and easy maintenance, whikf the substructure is relatively light and easily alterable according to the future change of occupancy or other changes of The New RC Project 59 architectural needs. The feasibility study lead to the trial design of two groups of megastructures, having 200 m or 300 m in height. The third was a new type of thermal power plant boiler building shown in Fig. 2.9, consisting of four huge RC box columns housing a vertical boiler inside, suspended from the steel grid girders that connect top of four columns at the height of 100 m. Materials in zone II—1 were assumed. Laboratory experiment was conducted for a portion of box columns, and it was also shown that this type of structure was quite feasible by the use of New RC materials. 2.5. Dissemination of Results Bulky reports were compiled each year during the New RC Project of 19881993 by the research committees shown in Fig. 2.2, and disseminated to all parties involved in the project. Major findings were condensed into short summary papers and reported at the Annual Conventions of the Architectural Institute of Japan in each year. Occasional introductions at international meetings were also made (Refs. 2.1-2.3). In addition, seminars were organized each year for audiences from participating universities and construction companies. In October 1994, the Concrete Journal published 55-page articles in Japanese covering all features of the project (Ref. 2.4). Some portions of the results have already been in use in the construction of highrise concrete buildings. Standards for performance evaluation or design and construction guidelines have been partially incorporated into existing standards and guidelines. It is expected that such practical use of results of the New RC Project will increase. Objects of the feasibility studies, namely highrise flat slab buildings, highrise megastructure buildings, and thermal power plant boiler buildings, will be constructed eventually. It is deemed necessary that following items have to be attended appropriately in the near future. (1) JIS (Japanese Industrial Standards) for newly developed reinforcing steel with 685 MPa yield strength. (2) Incorporation of standard specification for high strength and superhigh strength concrete into existing standard specification and design standards. (3) Popularization of high strength and superhigh strength ready mixed concrete. (4) Acceptance and authorization of New RC design and construction guidelines at the Technical Appraisal Committee for Highrise Buildings of the Building Center of Japan. 60 Design of Modern Highrise Reinforced Concrete Structures T h e major contents of this book except C h a p t e r 7 are t h e translation of a report published by Building Research I n s t i t u t e in M a r c h 2001 (Ref. 2 - 5 ) . References 2.1. Aoyama, H., Murota, T., Hiraishi, H. and Bessho, S., Development of advance reinforced concrete buildings with high-strength and high-quality materials, Proc. Tenth World Conference on Earthquake Engineering, Madrid, Vol. 6, July 1992, pp. 3365-3370. 2.2. Aoyama, H., Recent Development in seismic design of reinforced concrete buildings in Japan, Bulletin of the New Zealand National Society for Earthquake Engineering, 24(4), December 1991, pp. 333-340. 2.3. Aoyama, H. and Murota, T., Development of new reinforced concrete structures, Eleventh World Conference on Earthquake Engineering, Acapulco, Mexico, June 23-28, 1995. 2.4. Murota, T. et al., Feature articles on new reinforced concrete structures (in Japanese), Part I-VII, Concrete J. 32(10), October 1994, pp. 5-61. 2.5. Aoyama, H. et al., Development of advanced reinforced concrete buildings using high-strength concrete and reinforcement, Report No. 139, Buildings Research Institute, March 2001. Chapter 3 New RC Materials Michihiko Abe Department of Architecture, Kogakuin University 1-24-2 Nishi-Shinjuku, Shinjuku-ku, Tokyo 163-8677, Japan E-mail: abe@cc.kogakuin.ac.jp Hitoshi Shiohara Department of Architecture, University of Tokyo 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan E-mail: shiohara@sake.t.u-tokyo.ac.jp 3.1. High Strength Concrete Chapter 3 of this book is devoted to the description of high strength and high quality materials developed for the New RC project. The first section deals with the development and properties of high strength concrete, achieved by the effort of the Concrete Committee under the chairmanship of Dr. F. Tomosawa, Professor of the University of Tokyo. 3.1.1. Material and Mix of High Strength Concrete In order to obtain high strength of concrete, three methods are available in general. The first is to increase the strength of the binder, the second is to select aggregate with high strength, and the third is to improve the bond at the interface of aggregate and binder (Refs. 3.1 and 3.2). Among them, the most popularly adopted is the first method. This is because of the fact that the binder strength of concrete in the ordinary strength range is smaller than the strength of aggregate, hence the strength of 61 62 Design of Modern Highrise Reinforced Concrete Structures concrete is dictated by that of binder. The increase of binder strength requires the cement and mineral admixtures suitable for high strength, and reduction of water-binder ratio as the most effective means in terms of mix design. This is a well-known fact by the classical name of "water-cement ratio" theory. In addition, to maintain workability of concrete within the practical limit without increasing the unit water content while keeping the low water-binder ratio, that is, without increasing the unit binder content, it is necessary to develop chemical admixtures with high capability of dispersing cement and mineral admixtures. The increase of binder strength naturally results in producing concrete whose strength is strongly affected by the aggregate strength. Hence the selection of aggregate suitable for high strength concrete becomes an important issue. Finally, it is an established fact (Ref. 3.3) that the concrete strength depends microscopically on the structure of the transition zone between aggregate and binder. For the strength improvement of the transition zone, not only the reduction of water-binder ratio but also the use of mineral admixtures with ultrafine particle such as silica fume was found to be effective. Based on these general considerations for high strength of concrete, this subsection presents research accomplishment on the development of cement, chemical and mineral admixtures, and the selection of aggregate, both suitable for high strength, and achievement on the mix proportioning method of high strength concrete. 3.1.1.1. Cement A series of experiment was carried out in the New RC project with the aim of developing the cement suited for high strength concrete and of developing the quality standard of such cement, leading to test results as summarized below. Compressive strength of mortar with water-cement ratio of 25 to 65 percent was studied using ordinary, high-early strength, moderate heat, and type B blast furnace slag portland cement. As shown in Fig. 3.1, mortar strength is affected by cement type for water-cement ratio greater than 30 percent, but the difference is small for water-cement ratio of 25 percent. The figure also shows mortar strength for type B fly ash cement and for ordinary portland cement with silica fume, which resulted in lower strength even at the water-cement ratio of 25 percent. New RC Materials 63 Ordinary Portland ceaent High-early-strength Portland ceaent Moderate heat Portland cement Type B blast furnace ceaent Type B fly-ash ceaent OPC with silica fume Age'-28 days 25 30 35 40 50 later-ceaent ratio (%) Fig. 3.1. ratio. Strength of mortar with various cement types in the range of low water-cement 130 120 - ^ 1 1 10 ^>- o O ° o 9 l d»1* ° O>0 • * • 90 Jeo 70 i 40 I 60 I 80 I I 100 Percentage of base cement (%) Fig. 3.2. Relationship between base cement percentage in particle size distribution controlled cement and mortar strength. Setting and compressive strength tests were conducted of mortar with water-cement ratio of 30 percent and sand-cement ratio of 1.4, using ordinary, high-early strength, moderate heat, and type B blast furnace slag portland cement of various makers. High strength could be obtained by any cement, but the correlation between mortar strength and cement strength by JIS (Japanese 64 Design of Modern Highrise Reinforced Concrete Structures Industrial Standard) method was not observed. This indicates that JIS may not be sufficient as a quality standard of cement for high strength concrete. The fluidity of mortar and concrete using commercially available cement is greatly impaired when the water-cement ratio is low. To increase the fluidity of mortar with low water-cement ratio, particle size distribution controlled cement was manufactured on trial, by replacing part of ordinary portland cement by pulverized matter such as coarse particle portland cement or finely ground limestone. Tests of mortar and concrete were conducted using this particle size distribution controlled cement, and mortar with good fluidity (flow value of 200 mm) was obtained even with water-cement ratio of 20 percent or less. The fluidity of concrete using this cement at the water-cement ratio of 20 percent was also excellent, and as shown in Fig. 3.2, compressive strength of more than 100 MPa was achieved for the new cement with 60 to 80 percent base cement (40 to 20 percent replacement). Quality standards for cement to be used for concrete between 36 MPa and 60 MPa were developed, which will be explained in Chapter 8. 3.1.1.2. Aggregate The relationship between the quality of high strength concrete and the quality of aggregate was studied experimentally, to establish method for selection of aggregate suitable for high strength concrete. Major findings were as follows. Assuming that concrete is a two-element system of matrix (mortar) and coarse aggregate, and that mortar is another two-element system of matrix (cement paste) and fine aggregate, strength variation of concrete and mortar was studied by varying the amount of aggregate from various places while keeping the matrix quality constant. Figure 3.3 shows results for concrete. For both water-cement ratio of 25 percent and 35 percent, concrete was made using four different kinds of coarse aggregate, which are marked O, T, K and D. Compression tests were made at the age of 28 days. With the increase of unit coarse aggregate content of K or D, compressive strength decreased almost linearly, while it remained more or less constant with the increase of good quality aggregate such as O or T. Thus it is clear that coarse aggregate with inferior quality affects the strength of high strength concrete remarkably. Figure 3.4 shows a similar results as above for mortar. Using nine different kinds of sand of varying sand-cement ratio while keeping the water-cement ratio constant at 25 percent, mortar strength was tested at ages of 7 or 28 days. The compressive strength showed tendency to decrease as sand New RC Materials 65 Unit coarse aggregate content (!/•*) 0 1 200 400 i 600 100 ° i i 200 400 600 80 00 S\. NX ^"& • Hortar oo 60 Nof-O A T 80 ^v vK 40 OD (b) W/C = 35 X (a) f/C = 25 % Fig. 3.3. Relationship between unit coarse aggregate content and compressive strength of concrete using various kinds of coarse aggregate (O, T, K and D). Sand-ceoent r a t i o 120 0.5 1.0 1.5 2.0 T 1 r W/C=25% 110 ^^ 100 Age^ 28 days Si 90 •M SO I 80 to « S B3 OA1 70 - « A 2 ©A3 ©A4 OB • C i D vE OF D | 90 80 70 N A 60 Fig. 3.4. Relationship between sand-cement ratio and compressive strength of mortar using various kinds of sand ( A 1 ~ F ) . 66 Design of Modern Highrise Reinforced 8r~ Concrete W=160kg/m', Structures Drying p e r i o d s months Sfc... 20 22.5 25 25N 30 20 22.5 25 25N 30 w/B (%) 20 22.5 25 25N 30 Andesite Limestone Hard Sandstone Pig. 3.5. Effect of kinds of coarse aggregate on the drying shrinkage of concrete. content increases for all kinds of sand used, but the decreasing trend was more conspicuous for some sand, for example with marks D and E. A study into the effect of aggregate size, shape, and unit coarse aggregate content on the compressive strength was conducted. No effect was found of aggregate size and aggregate content on the concrete strength, but angular shape was found to be advantageous for high strength. Crushed hard sandstone, limestone, and andesite aggregates with BS (British Standard) crushing value of 15 to 20 were used for high strength concrete of 100 to 120 MPa compressive strength, to investigate Young's modulus at 28-day age and drying shrinkage at 6-month age. Limestone concrete showed higher Young's modulus of about 50 GPa compared to about 40 GPa of hard sandstone or andesite concrete. Drying shrinkage was also smaller for limestone concrete as shown in Fig. 3.5, which illustrates shrinkage strain after 6 months of drying period for concrete using three kinds of coarse aggregate and water-cement ratio ranging from 20 to 30 percent while keeping the unit water content of 160 kg/m 3 constant. All concrete except for 25N used the cement with 15 percent replacement by silica fume for the binder. High strength concrete with 120 MPa strength can be made by using selected aggregate, both coarse and fine, and the fluidity can be improved by using fine aggregate with adjusted fineness, i.e. by removing very fine component from the fine aggregate. 3.1.1.3. Chemical Admixtures Various commercially available as well as newly developed chemical admixtures, generally known as air-entraining and high-range water-reducing agents, New RC Materials 67 were compared in a series of unified tests. Concrete with four grades of compressive strength were considered. They were 40 MPa at water-cement ratio of 40 percent, 60 MPa at water-cement ratio of 30 percent, 80 MPa at waterbinder ratio of 25 percent of both plain concrete and concrete mixed with silica fume or ground granulated blast furnace slag, and 100 MPa at water-binder ratio of 22 percent of concrete mixed with silica fume or ground granulated blast furnace slag. Items such as relationship between unit water content and admixture addition ratio to achieve the target slump or air content, time variation of slump, setting time, compressive strength, drying shrinkage, and freezethaw resistance, were studied. As an example, the case of 60 MPa concrete at water-cement ratio of 30 percent is illustrated below. Figure 3.6 shows change with time of slump of concrete using various brands of chemical admixtures. Unit water content of 165 kg/m 3 was kept content, and air content was in the range of 3 to 4 percent. Some brands, e.g. marks A and G, showed larger slump loss with time than other brands. Figure 3.7 shows range of setting time of concrete with unit water content of 165 kg/m 3 and 150 kg/m 3 using the same ten brands of chemical admixtures as above. Some brands showed very long setting time, particularly when the unit water content was low. The drying shrinkage strain of concrete using certain brands of admixture was also found to be longer. L_J 0 1 15 i 30 I 60 i 90 Time (min) Fig. 3.6. Change with time of concrete slump using various brands of air-entraining and high-range water-reducing agents. 68 Design of Modern Highrise Reinforced Concrete Structures 1250 Z l W=165kg/m3 H i W = 150kg/m 3 1000 •S 1 W/C=30% 750 D I EH 500 250 S A B _L C D E _L F 151 ri G H I Brand of admixtures Fig. 3.7. Setting time of concrete using various brands of air-entraining and high-range water-reducing agents. 120 100 W/C=3Q% • W=165kg/m\ M W=165kg/m\ W& W=150kg/m 3 , H I W=150kg/m 3 , Air=3~4X Air=2 % Air=3~4 X *ir=2 * I d e n o t e s r a n g e of max and min 80 20 4 [W 60 40 rfi T if" i I ll 28 i 91 Age (days) Fig. 3.8. Compressive strength of high strength concrete using various brands of airentraining and high-range water-reducing agents. New RC Materials 69 Nevertheless, compressive strength of concrete was satisfactory for all brands of admixtures. Figure 3.8 shows compressive strength for four different combination of unit water content and air content at five different ages. Watercement ratio of 30 percent was kept constant, aiming at compressive strength of 60 MPa. As can be seen in the figure, the target strength was more than satisfied at the age of 28 days. It was even cleared at 7 days in this test. The cases of higher strength concrete indicated the significance of air entrainment on the freeze-thaw resistance. Figure 3.9 is the results of freezing and thawing test of 80 MPa concrete with water-cement ratio of 25 percent, indicating the relationship of spacing factor and durability factor, which is the relative value of dynamic modulus of elasticity at the end of freezing and thawing test. For plain concrete without mineral admixture with air of 3 to 4 percent and plain concrete with ground granulated blast furnace slag, no reduction of durability factor was observed. However, plain concrete with low air content and plain concrete with silica fume showed inferior durability. Based on these unified tests, quality standard and usage guideline for chemical admixtures for 60 MPa high strength concrete were developed. Test data for higher strength concrete were not compiled into practical form as above at the present stage, but they are believed to throw some light into the future advancement of the concrete research. O • Q A Mineral admixture ; not mixed : not mixed : silica fume ; blast furnace slag • V«» L < c 4 ^ ^ c g ^ 100 D D £- a 60 OO 1. ^ Q ! 3 air content ^2 % 3~4 % <J2 % ^2 % D a ° J 0.1 I I 0.3 I I I o I I I I I 0.5 0.7 0.9 1.1 Spacing factor (mm) I I 1.3 I l_ 1.5 Fig. 3.9. Durability factor and spacing factor of concrete using various brands of airentraining and high-range water-reducing agents. 70 Design of Modern Highrise Reinforced Concrete Structures 3.1.1.4. Mineral Admixtures Mineral admixtures for high strength concrete are to replace a part of cement and form a part of binder. Admixtures such as silica fume, fly ash fume, ground granulated blast furnace slag, and etringite type special admixture were considered. Fly ash fume is obtained by processing fly ash at high temperature, thereby evaporating silicon dioxide whose boiling temperature is relatively low among substances in the fly ash, and then coagulating it at the lowered temperature for collection. Etringite was used to be known as cement bacillus, but the etringite type special admixture is a kind of mineral admixture mainly consisting of Type 2 anhydrous gypsum, with the aim of growing hardened binder body with fine structure by utilizing the growth of needle-shaped crystal of etringite (formed by the reaction of aluminate in the cement and gypsum). Followings are major findings of unified tests for mineral admixtures. Fluidity and compressive strength of cement paste, mortar and concrete were tested using silica fume or fly ash fume whose specific surface area was modified to range of 260 000 to 700 000 cm 2 /g. It was found that replacement of 10 to 15 percent of silica fume or fly ash fume lead to the maximum compressive strength. Greater specific surface area of fly ash fume resulted in the increase of strength. Workability, strength development and freeze-thaw resistance of mortar and concrete were studied using ground granulated blast furnace slag with specific surface area of 6000, 8000 and 10 000 cm 2 /g. The strength development was slow at low temperature, but strength was improved when the specific surface area was greater. Strength development of concrete with low water-binder ratio was measured where the binder consisted of three components of cement, ground granulated blast furnace slag, and silica fume or fly ash fume. The concrete with the three components showed greater increase of strength at long term than two component concrete. Properties of concrete with etringite type special admixture were investigated, and it was shown that increase of compressive strength of about 15 MPa was obtained by adding this admixture. Figure 3.10 shows the effect of curing condition on this kind of concrete, in terms of compressive strength at 28 and 91 days under four different curing conditions, i.e. exposed to air after 2, 4, 7, or 28 days of wet curing either in the form or under standard curing condition. Strength of cylinders under standard curing condition is shown in all four groups as a common reference. An exception in this figure is the leftmost group New RC Materials 0 0 Strip at 2d tin, sealed Strip at 2d. then standard-cured I Strip at 2d standard-cured 1(3 Strip at 2d standard-cured 2d than air-cured Strip at 2d then air-cured 71 5d than aircured Strip at 4d then air-cured fU Strip at 7d than air-cured 2 Strip at 2d standard-cured 25dthen air-cured • Strip at 28d than ail-cured 130 120 I 110 S ioo 90 80 70 (w/ad. ) (w/out ad.) (w/ad. ) (w/out ad. ) (w/ad.) (»/out ad. ) (w/ad.) (w/out ad.) Fig. 3.10. Effect of curing condition on the compressive strength of concrete using etringite type special admixture. where strength of sealed cylinders is shown, which was happened to be similar to that under standard curing. In each group strengths with and without etringite type admixture are compared. For all four curing conditions, strength increase due to addition of the admixture is clearly seen. Furthermore, this admixture improves the strength development in the concrete exposed in the air. Concrete with this admixture revealed strength comparable or even better strength compared to standard curing even after 4 or 7 days of wet curing condition. These mineral admixtures are very important for high strength concrete, especially in excess of 60 MPa, and the individual special features must be carefully considered in their practical use. 3.1.1.5. Mix Design Aiming at developing specification for mix design of high strength concrete of 60 to 80 MPa specified strength, procedure to determine water-cement ratio or 72 Design of Modern Highrise Reinforced Concrete Structures water-binder ratio, unit water content, unit bulk volume of coarse aggregate, and dosage of chemical admixtures was studied to achieve the required average (proportioning) strength, air content and slump or slump flow. Major findings are summarized below. In order to find relationship between required average strength and watercement ratio or water-binder ratio, and relationship between unit water content or dosage of chemical admixture and workability, tests were made on the various concrete properties in the range of water-binder ratio of 15 to 40 percent and unit water content of 145 to 175 kg/m 3 , using air-entraining and high-range water-reducing agent, silica fume and ground granulated blast furnace slag 8000. For the same slump or slump flow of fresh concrete, it was found that flow speed of concrete was faster, hence the workability was better, when silica fume was used or when unit water content was increased. Furthermore, as shown in Fig. 3.11, compressive strength at ages of 7, 28 and 91 days increased in proportion to binder-water ratio in the range of water-binder ratio of 25 percent or more, but for lower water-cement ratio compressive strength did not increase with the increase of binder-water ratio. As shown in the figure, concrete with ordinary portland cement (OPC) showed the strength at 28 days of about 100 MPa, and concrete with silica fume replacement of 15 percent (OPC + SF) and concrete with ground granulated blast furnace slag 8000 replacement of 30 percent (OPC -I- BS) showed the strength at 28 days of about 120 MPa, both more or less constant for different binder-water ratio above 4. 140 j£^ 120 xfe* S1" I 80 •B 60 \ .,—& <?/ o* / OPC OPC+SF 0PC+8S Age=7 days Age-28 days Age=91 days /a / I 40 4 _1_ 5 I I Binder-water ratio I J I L 40 30 25 22.5 20 18.2 16.7 15 Water-binder ratio (X) Fig. 3.11. Relationship between water-binder ratio and compressive strength. New RC Materials 73 Relationship between concrete mix and various properties was studied of 60 MPa concrete with water-cement ratio of 30 percent and slump 21 cm, and of 80 MPa concrete with water-binder ratio of 25 percent and slump 25 cm. Figure 3.12 indicates setting time of 60 MPa concrete with the same 1000 W7C=30% slunp=2] ca 800 n D" 600 S 400 m final setting I |~1 initial setting ] j right after sizing 200 Q " ^ ] 90 iin, after ailing I ; aortar J I I 140 160 180 200 Unit water content ( k g / m 3 ) Fig. 3.12. Relationship between unit water content and setting time. V//C = 30%, slu»p=21 en standard curing 28 days 100 (2 95 -S-^(1.9%> Jl.5%) 90 l(1.2%) 85 80 >(1.0%) Numbers in parentheses indicate dosage of admixture 75 1 1 I I I I I L_ 130 140 150 160 170 180 190 200 210 Unit water content ( k g / m * ) Fig. 3.13. Relationship between unit water content and compressive strength. 74 Design of Modern Highrise Reinforced 140 Concrete Structures Water-binder ratio:25% Age:28 days ja 130 a. ~120 110 W=160kg/m 3 W=200kg/m 3 100 90 0 I _L _L _L _L _L 10 20 30 40 50 60 70 Replacement ratio by mineral admixture (%) Fig. 3.14. Relationship between replacement ratio of O P C by mineral admixture and compressive strength. water-cement ratio but different unit water content, showing longer setting time for smaller unit water content. To keep the water-cement ratio constant while reducing unit water content, one must reduce the paste content, and to keep the slump constant one has to use large amount of chemical admixture leading to higher viscosity. This is the reason for longer setting time for smaller unit water content in the figure. On the other hand, as shown in Fig. 3.13, concrete with larger unit water content showed smaller compressive strength even under constant water-cement ratio. Figure 3.14 is for 80 MPa concrete where silica fume or ground granulated blast furnace slag 8000 is used as mineral admixture. This figure shows the compressive strength for different replacement ratio of mineral admixture, and it can be seen that silica fume replacement of 10 percent and blast furnace slag replacement of 30 to 50 percent resulted in maximum strength, for any of the unit water content considered. Appropriate unit bulk volume of coarse aggregate can be determined corresponding to the slump or slump-flow value referring to the mix design for unified tests of chemical admixtures and other available sources. Based on the above-mentioned studies, a general procedure of mix calculation is organized as shown by a flow chart in Fig. 3.15. Detail of proposed New RC Materials 75 start of mix calculation x establish conditions for determining designed mix proportioning strength •lump air content determine replacement ratio of mineral admixture determine unit determine water-cement coarse aggregate (water-binder) ratio volume I calculate unit cement (binder) content determine unit water content calculate unit determine dosage of coarse aggregate chemical admixture calculate unit fine aggregate content end of calculation Fig. 3.15. General procedure of mix calculation. numerical values for constituent materials and mix elements can be found in Chapter 8. 3.1.2. 3.1.2.1. Properties of High Strength Concrete Workability High strength concrete generally has high viscosity, and hence high segregation resistance even for large slump. On the other hand pumping efficiency is low despite large slump. Thus it can be concluded that the slump may not be a good measure of workability for high strength concrete. A study was therefore conducted to establish a new index to evaluate workability of high strength concrete by examining its rheological characteristics. A conclusion was that use of rheology constants themselves, such as plastic viscosity or yield value, is more desirable than the direct use of various consistency test results. Figure 3.16 shows that rheology constants can be obtained from the combined results of slump test and ASTM flow test. It was also shown that casting performance 76 Design of Modern Highrise Reinforced Concrete Structures 600 For high strength concrete 500 400 ? £ 300 o & I200 J 100 "0 J 1 J_ I 400 800 1200 1600 Yield value r i (P») Fig. 3.16. tests. Estimation of rheology constants from the combination of current consistency of fresh concrete in the form could be analyzed by viscoplastic divided space element method using rheology constants. Thus the use of rheology constants leads to a good prediction of casting performance of high strength concrete. 3.1.2.2. Standard Test Method for Compressive Strength Aiming at a proposal of standard test method for the compressive strength of high strength concrete, various factors that would affect the compression test results were examined. They are as follows: characteristics of testing machines such as stiffness or swivel detail, loading speed, end surface treatment of cylinder by grinding or capping, shape and size of cylinder and its dry or moist condition at testing, manufacture of cylinder such as forms or method of compaction, and so on. Figure 3.17 shows results of compression test of four kinds of concrete by 16 testing machines (A through P). Some testing machines show consistently low values. It may be the consequence of calibration problem, but it may also be resulted from some difference in some of the above-mentioned influencing factors. New RC Materials 130 120 110 10 77 F,=80 (MPa) 2 ° § f | •1 3 90 80 70 60 I 50 j 40 30 20 10 ° A B C D E F G H I J K L~M~N 0 P Testing machines Fig. 3.17. Effect of testing machines on the compressive strength. Based on these studies, a proposal for making compression test cylinders was made based on JIS A 1132, and that for test method for compressive strength was made based on JIS A 1108. As for end surface treatment, unbonded capping method was developed which does not require any specific end surface finishing. Effect of rubber pad quality and hardness, and that of steel frame diameter was examined by comparing the test results with machine-ground cylinders. For chloroprene rubber pads, increase of compressive strength was observed with the increase of rubber hardness in case of high strength concrete. For polyurethane or NBR pads, compressive strength dropped with the increase of rubber hardness when the diameter of steel frame was large. In both cases many cylinders reached the compression failure accompanied by end chipping or vertical splitting. In conclusion, conditions of unbonded capping that would give equivalent compressive strength and failure mode to machine-ground cylinders were presented. 3.1.2.3. Mechanical Properties Stress-strain relationship, Young's modulus, and failure characteristics of high strength concrete, basic mechanical properties of confined concrete, and tensile strength were the major items of the series of investigations into mechanical properties of high strength concrete. Results are summarized below. 78 Design of Modern Highrise Reinforced 2000 4000 6000 Strain (X10~*) (a) Kent & Park Concrete 2000 4000 6000 Strain (X10"') (b) Falitia & Shah Structures 2000 4000 6000 Strain (X10 - *) (e) Muguriuzut 2000 4000 6000 Strain (X10-«) (d) Popovics Fig. 3.18. Comparison between measured (full lines) and calculated (dashed lines) stressstrain curves. Coarse aggregate content — Max.size a/n3) (nn> 5000| -o 0 ^ 200-20 D 400-20 • 400-15 5, *. 400-10 5 4 500 ! i 4 000 3S0O 55 3 000 - 2 500 20 Fig. 3.19. 60 100 Compressive strength (MPa) 140 Influence of coarse aggregate on strain at compressive strength. There are several proposals for the stress-strain relationship of high strength concrete, and some of them represent the test results quite accurately as shown in Fig. 3.18. One problem is the estimation of the strain associated with the maximum stress, which increases gradually as the compressive strength increases, but the trend differs for different coarse aggregate. Furthermore Fig. 3.19 shows the different interdependence of strain at maximum stress on New RC Materials Compressive strength (MPa) (a) Without considering ki, k2 and y variations • X <N A X A • °• '*> + \ 40000 + sa . J*^ l':'^f5e , 50000 x v r . c • " A ' RC Equation E-; 3500X1^ xk,,x T/2.4)ix(aJ SO)"1 [MPa] (k, kj=i, T=2.4) *z 3 -Oa : * o <? *• * o * ' A River O ivel H Calcine Bauxite • Cnishe< Graywacke •^ Crushed Cobble c a O Cnished Quartzile d Cnished Basalt D Crashed Limestone • Crashed Ctaystone T3 O Crushe Andesite + Lightw ght Coarse Ag regale V Blast F nace Slag X Lightw ght Fine + Co se Aggregate a 00 "60 ,-° / A T3 40 60 80 100 120 Compressive strength (MPa) (b) Considering ki, k2 and y variations Fig. 3.20. Relationship between compressive strength and Young's modulus. 79 80 Design of Modern Highrise Reinforced Concrete Structures the compressive strength for different coarse aggregate content or maximum aggregate size. Thus it would be necessary for a stress-strain model to incorporate coarse aggregate related parameters, and further study is needed in this regard. Available test data of compression test of cylinders were collected to investigate the relationship between Young's modulus and compressive strength of high strength concrete. Figure 3.20(a) shows the straight results. In the figure, the Architectural Institute of Japan (AIJ) equation, which is basically the same as the American Concrete Institute (ACI) equation, is shown in the range of concrete strength less than 36 MPa, in which mass of unit volume 7 is put equal to 2.3 t / m 3 . A new equation developed in the New RC project is shown in the range of concrete strength greater than 36 MPa, with the constant mass of unit volume 7 of 2.4 t / m 3 . The new equation is different from the AIJ equation in that the exponent to mass of unit volume is 2.0, the exponent to compressive strength is 1/3, and that two coefficients fci and &2 are introduced to account for the type of coarse aggregate and mineral admixture. In Fig. 3.20(a), it is clear that the data for lightweight aggregate concrete fall far below that for normal weight concrete, indicating the significance of the term for mass of unit volume. Figure 3.20(b) shows the modified Young's modulus taking into account not only the mass of unit volume but also two coefficients k\ and kz. The scatter of data becomes much smaller than the previous figure, indicating the effectiveness of the New RC equation in predicting the Young's modulus of high strength concrete of wide variety. The detail for coefficients fci and fo can be found in Chapter 8. Effect of confinement was observed similar to the normal strength concrete, but the confining effect decreased as height-diameter ratio of the specimen increased, and the effect was not influenced by the aggregate type. Effect of confinement is further discussed in Sec. 3.3 of this chapter. 3.1.2.4. Drying Shrinkage and Creep Research projects aiming at long term behavior of high strength concrete such as drying shrinkage and creep characteristics produced following results. From mix tests and unified tests for chemical admixtures, it was found that drying shrinkage of high strength concrete is strongly influenced by the rock type of aggregate, water-binder ratio, and dosage of chemical admixture. Figure 3.21 shows variation of drying shrinkage strain with respect to New RC Materials 81 10W=170kg/m s X 8l_ g '* fil— H ° Sandstone I 10 15 20 25 30 35 40 45 Water-binder ratio (%) 50 Fig. 3.21. Relationship between water-binder ratio and drying shrinkage. 10 2 8 x 'I 6 V=4.10 + 0.90^(n=30) 2 0 — X _L J_ _L 1.0 2.0 3.0 4.0 5.0 Dosage of admixture (% to cement) Fig. 3.22. Relationship between dosage of chemical admixture and drying shrinkage strain. water-binder ratio for two rock types of coarse aggregate. When hard sandstone is used, drying shrinkage increased in proportion to water-binder ratio, but for river gravel it remained high regardless of water-binder ratio. Figure 3.22 shows that drying shrinkage increases when the dosage of chemical admixture is increased. Within the examined test data, unit water content was not found to be influential on the drying shrinkage. Shrinkage cracks were tested based on the proposed JIS of drying shrinkage crack test method. It was found that high strength concrete develops large shrinkage strain at relatively early age, and shrinkage cracks appear in early days. Figure 3.23 shows the age at crack appearance for various water-cement 82 Design of Modern Highrise Reinforced Concrete SR S R » • SR 40 A A ~ 1 20 •3 _ • 1 10 ~ • A A o A A 5— 0 O o era = 15 • l-6mm • A o _ S 25 Confining plate thickness o * 2.0mm - 2.4mm : 2.9mm SR '. Shrinkage reducing agent SRa o» S R SR - o CO nee (day ~ 35 Structures • A* 1 1 1 1 40 45 50 55 Water--cement ratio (%) i i 25 30 i 35 1 60 Fig. 3.23. Age of shrinkage crack appearance. ratio. With the use of confining plate thickness 2 mm or greater, crack age increased almost proportional to water-cement ratio. The use of shrinkage reducing agent was found to be effective in delaying the shrinkage crack appearance as shown by marks SR in the figure. Compressive creep test was conducted using concrete with water-cement ratio of 25 to 60 percent in the form of plain concrete columns varying from 20 cm square section to 60 cm square section as well as 10 cm diameter and 20 cm high cylinders. Free shrinkage strain and creep strain tended to be smaller for higher compressive strength of concrete. For 60 MPa concrete smaller creep strain was observed for larger column sections, but creep of 100 MPa concrete did not depend on section size. 3.1.2.5. Durability In order to evaluate durability of high strength concrete, frost resistance and alkali-aggregate reaction was tested, leading to the following findings. Freezing-thawing test as specified in ASTM C666 Method A, in-water freezing and in-water thawing method, was conducted for concrete with water-cement ratio of 28 to 55 percent, air content of 2 to 5 percent, and with various curing conditions, as shown in Fig. 3.24. This is the case of concrete using andesite and river gravel combined for coarse aggregate. From the figure it can be seen that the effect of low water-cement ratio on the New RC Materials <»>W/C=28% (b)w/C=32% (dw/C=37% (d)w/C = 45% (e) w / C == 5 5 % - / Fig. 3.24. 83 / / / f Jp JF Curing conditions • • • • a 2yra. sir exposed £r • -A 8 week* inair • — • 2 weeks in water o — O 4 weeks in water Relationship between air content and durability factor after different curing. freeze-thaw resistance is as high as the entrained air, and a clear difference can be seen between water-cement ratio of 28 percent (Fig. 3.24(a)) and 37 percent (Fig. 3.24(c)). However even in case of concrete with water-cement ratio of 28 percent some deterioration can be observed in freeze-thaw resistance after being exposed two years in the outdoor air (dotted line in Fig. 3.24(a)). Although low water-cement ratio was effective under moist curing conditions, it did not compensate for the low air entrainment under dry condition. Thus it was concluded that certain air content was necessary for frost resistance even for high strength concrete. The entrained air has conspicuous effect also in preventing frost damage at early ages, and so it is recommended to insure air content of at least 3.5 percent at concrete casting. For concrete with air content of 3.5 percent or more, the minimum curing time to prevent frost damage at early ages is up to the age at which compressive strength of 3.2 MPa is obtained. Concrete expansion due to alkali-aggregate reaction was measured by the Japan Concrete Institute (JCI) concrete bar method for high strength concrete with unit cement content of 650 kg/m 3 and water-cement ratio of 26 or 36 percent, and for normal strength concrete with unit cement content of 350 kg/m 3 and water-cement ratio of 56 percent both using reactive or nonreactive aggregate and varying alkali content by adding varying amount of sodium hydrate. Figure 3.25 shows the case of reactive aggregate both for normal and high strength concrete. It is seen that expansion due to alkaliaggregate reaction depends not on the concrete strength, but on the alkali content in the concrete. High strength cannot prevent expansion due to alkaliaggregate reaction. On the other hand, nonreactive aggregate under normal usage has little possibility of producing harmful expansion when used for high strength concrete within usual condition. It was also confirmed that an appropriate replacement of cement with mineral admixtures such as ground 84 Design of Modern Highrise Reinforced Concrete Structures 0.10 Alkali addition (kg/m3) • 1.8 * 2.4 • 3.0 • 3.6 J g 0.05 I 0 0.5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Age (months) (a) Normal strength concrete, unit cement content 350 kg/m3 0.10 a I 0.05 & 0 J_I I I 0.5 1 2 3 1 1 I I I I I I 1 I L 4 5 6 7 8 9 10 11 12 13 14 Age (months) (b) High strength concrete, unit cement content 650 kg/m3 Fig. 3.25. Comparison of expansion due to alkali-aggregate reaction of normal and high strength concrete using reactive aggregate. granulated blast furnace slag, silica fume or fly ash fume in case of high strength concrete was effective in preventing alkali-aggregate reaction just as in case of normal strength concrete. 3.1.2.6. Fire Resistance To evaluate fire resistance of high strength concrete, explosive fracture under varying heating speed was examined of 10 cm by 20 cm cylinder of concrete with water-cement ratio of 25 to 65 percent and unit water content of 140 to 200 kg/m 3 . Explosive failure occurred most often to concrete with the lowest water-cement ratio of 25 percent. In another heating test of 15 cm by 30 cm cylinders of concrete with varying kind of coarse aggregate and moisture content of concrete, it was found that the moisture content had dominant influence on the fire resistance, and concrete with moisture content less than 3.5 percent did not explode even with the water-cement ratio of 25 percent. New RC Materials 1100 85 - Lengths outside parentheses indicate depths of measuring point w / c : 60% _^_ ] 1000 W/C.35% IV/C:259S(*) QO02--* " t _-.-•" -^1'." ^+»^ II ^0*~' 900 § 800 6005 500 s 400 300 1/ / ^ " I / i&m***^ 200 100 90 120 150 180 Time after start of heating (min) Fig. 3.26. Measured interior temperature of concrete during fire resistance test. Fire resistance test of 50 cm concrete cube specimens was conducted at two months age of natural drying condition, and specimens with water-cement ratio of 35 percent did not explode but those with water-cement ratio of 25 percent exploded. But the same kind of specimens after one-year exposed in the outdoor air under rain shelter showed much milder behavior in the fire resistance test. Figure 3.26 shows measured time history of internal temperature during the fire resistance test at two months age. In the figure results for three different water-cement ratio, i.e. 60, 35 and 25 percent, are shown. The specimen with 25 percent water-cement ratio showed violent explosion and temperature measurement is shown only for reference. It is seen that watercement ratio has little influence on the temperature rise, and it can be concluded that 2 to 4 cm cover is necessary for three-hour fire resistance, in order to keep the steel temperature of a reinforced concrete member below 500 degree Celsius. Also from the fact that temperature rise did not depend on watercement ratio, it can be inferred that the heat conductivity of high strength concrete is similar to that of normal strength concrete. 86 Design of Modern Highrise Reinforced Concrete Structures 3.2. High Strength Reinforcing Bars Compared with recent global effort to develop high strength concrete, studies toward the development and practical application of high strength reinforcing bars (re-bars) seem to be meager. In the New RC Project, development and use of high strength re-bars was regarded as an essential factor to extract the maximum potential ability of high strength concrete. 3.2.1. Reinforcement Committee At the time when the New RC research project was initiated in 1988, Japan Industrial Standard (JIS) for reinforcing bars had included SD490 with specified yield point of 490 MPa as the re-bar with the highest strength, and no stronger re-bars were available to researchers who wanted to use high strength re-bars in the experiment of high strength concrete members. The Reinforcement Committee of the New RC project, under the chairmanship of Dr. Shiro Morita, Professor of Kyoto University, tackled the task of trial manufacture of high strength re-bars that were not specified in the current standards, with the full cooperation of steel manufactures participating in the project. Proposals for standards of following re-bars were presented to the committee: USD685A and 685B for axial reinforcement of beams and columns expected to form yield hinges, USD980 for axial reinforcement of nonyielding beams and columns, USD785 and USD1275 for lateral reinforcement of beams and columns to provide lateral confinement and shear resistance. It was confirmed that re-bars conforming to all these proposed standards could be actually manufactured. The Reinforcement Committee also conducted experimental studies into fundamental mechanical characteristics, such as bond and anchorage, concrete confining effect, and constitutive equations, of reinforced concrete members using various combination of high strength materials. Results of these experiments were compiled into proposals for evaluation of mechanical properties of high strength reinforced concrete (Ref. 3.4). This portion of the work of Reinforcement Committee will be presented in the next Sec. 3.3. 3.2.2. Advantages and Problems of High Strength Re-bars Some merits of high strength re-bars in the structural members are summarized below. New RC Materials 87 (1) Higher member strength or reduction of steel amount can be achieved. (2) When reduction of member section is attempted by using high strength concrete, reinforcement congestion can be avoided by the use of high strength re-bars leading to easier construction practice and quality control. (3) Application of high strength re-bars as lateral reinforcement can improve the brittle behavior of high strength concrete, and enlarge the scope of application of high strength concrete. On the other hand, there were problems that needed to be solved to realize high strength re-bars, such as the following. (1) Currently available high strength steel such as prestressing bars or strands for prestressed concrete has no distinct yield plateau and small plastic elongation before reaching fracture. This would lead to poor performance in reinforcement fabrication if re-bars were made of such steel. Also it would lead to poor behavior as a structural member, particularly of earthquake resistant structures where large plastic deformation is expected to occur. (2) For structural members dictated by cracking or deflection limit states, high strength re-bars cannot contribute to the reduction of steel amount. For members dictated by flexural strength, i.e. ultimate limit state, high strength re-bars can reduce steel amount, but stress transfer to concrete such as bond and anchorage is not improved by increasing steel strength, which would result in increased bond or anchorage length leading to congestion and difficulty of re-bar arrangement in the construction. It was thus necessary to determine new standard specification of high strength re-bars to ensure above-mentioned merits while solving above problems, and to trial manufacture re-bars conforming to the new standard. 3.2.3. Relationship of New Re-bars to Current JIS Current Japan Industrial Standard (JIS) specifies 6 kinds of re-bar grades in JIS G 3112 (Steel bars for reinforced concrete) and JIS G 3117 (Rerolled steel bars for reinforced concrete), namely SD245, SD295A, SD295B, SD345, SD390 and SD490. For steel tendons for prestressed concrete, JIS G 3536 for PC wires and strands and JIS G 3109 for P C bars are available. Specified strength of PC tendons cover the range of 780 MPa to 1785 MPa, and steel of this high strength has already been put into practical use, which is however different from the use of re-bars in reinforced concrete. Figure 3.27 shows stress-strain curves in tensile tests of re-bars and PC tendons of different grades. Dotted 88 Design of Modern Highrise Reinforced Concrete Structures PC strand (0.89) NewRC USD1275 , -- - - PC wire (0.85) PC deformed bar (0.86) ' NewRC USD980 (0,88) | 1,000 " NewRC USD780 (0.84) ^NewRC USD685 (0.77) • SD590 Equivalent (0.76) • ^ . ^ SD490(0.72) " SD390 (0.67) SD295 (0.71) Numbers in ( ) denote yieid ratio I 15 I 20 25 Fig. 3.27. Stress-strain relationships of steel with different strength. lines show curves for currently available steel and full lines show those for newly manufactured re-bars in the New RC project. It is clear from the figure that currently available re-bars including PC tendons generally show smaller or no yield plateau and smaller fracture strain as the strength is increased. The lower strength axial re-bar developed in the New RC project, USD685, show clear yield plateau despite its relatively high strength, while the higher strength axial re-bar, USD980, does not. Re-bars developed for lateral reinforcement, USD780 and USD1275, show similar trend as other P C tendons of similar strength, but with larger fracture strain. 3.2.4. 3.2.4.1. Proposed Standards for High Strength Re-bars General Outlines Draft proposal of standards for five kinds of high strength re-bars, USD685A, USD685B, USD980, USD785 and USD1275, were presented to the Reinforcement Committee in the last year of the 5-year project. The full text of these proposed standards was not published for five years after the conclusion of the project conforming to the cooperatives research contract, that is, until March, 1998. New RC Materials 89 The specified values in these proposed standards were all confirmed to be sufficiently manufacturable by trial manufacture during five years of the New RC project. Thus these standards are accompanied with good amount of practical experience. At present these new brands of re-bars do not necessarily circulate in the market, but they should be available to order to the steel manufactures who participated in the New RC project. Table 3.1 summarizes the required mechanical properties of five kinds of new re-bars. First three columns, USD685A, USD685B and USD980, are rebars that can be used for axial reinforcement of beams and columns. They are included in the Proposed Standard for High Strength Deformed Bars for Reinforced Concrete, and cover the diameter range from D10 to D51 as shown in Table 3.2. Last two columns of Table 3.1, USD785 and USD1275 are to be used exclusively for lateral reinforcement such as lateral confinement or shear reinforcement. They are included in the Proposed Standard for High Strength Deformed Bars for Lateral Reinforcement, and Table 3.3 shows the diameter ranges for bars of these two grades. The new name of USD was adopted to clarify that the nature of these Standards is not an official standard of general nature but is a kind of selfimposed standard with the strength range exceeding that of current JIS, although it follows the JIS requirements in regard to shape and size of bars. Current JIS G 3112 specifies SD490 as the strongest re-bar for reinforced concrete, and USD685A is the weakest re-bar specified in the new Standards, leaving a large gap of yield strength in between to which no standard exists. This is the consequence of concentrated and efficient effort for trial manufacture of new re-bars in the New RC project, where manufacture of USD685 was one of the most immediate target. As shown partly in Table 3.2, re-bar diameters and other dimensions, and shape of surface deformation of USD685 and USD980 follow the specifications in the current JIS G 3112, Deformed Bars for Reinforced Concrete. On the other hand, specifications for USD785 and USD1275 are made to match those of PC tendon manufacturing companies who have already acquired special permission of Construction Minister to practically manufacture re-bars of corresponding strength for lateral reinforcement. The requirement for surface deformation is more liberal compared to JIS G 3112, because it is generally accepted that bond requirement for lateral reinforcement need not be as strict as for axial reinforcement. 90 Design of Modern Highrise Reinforced Concrete Structures Table 3.1. Required mechanical properties of high strength re-bars. Grade of steel Yield stress* (MPa) 1 USD685A USD685B USD980 USD785 USD1275 685-785 685-755 980 and above 785 and above 1275 and above 930 and above 1420 and above Tensile strength (MPa) not specified Strain at yield plateau* 2 1.4% and above Fracture strain 10% and above Yield ratio 85% and below Inner radius for 90° bending* 3 not specified 7% and above 80% and below 90% and below 2d 7% and above not specified 1.5d 2.5d S6-S13 H6-H13 id D10-D51 Range of diameter 8% and above Surface deformation similar to JIS G 3112 indent or groove Major use axial reinforcement for beams and columns lateral reinforcement %1 Yield stress is taken as 0.2% offset stress in case clear yielding is not observed. * 2 See Fig. 3.28 for definition of strain at yield plateau. * 3 "d" iindicates nominal diameter of the bar. Table 3.2. Dimensions and unit mass of USD685 and USD980. Grade USD685A USD685B USD980 Mark Nominal diameter mm Nominal area mm2 Nominal perimeter mm Unit mass kg/m D10 D13 D16 D19 D22 D25 D29 D32 D35 D38 D41 D51 9.53 12.7 15.9 19.1 22.2 25.4 28.6 31.8 34.9 38.1 41.3 50.8 71.33 126.7 198.6 286.5 387.1 506.7 642.4 794.2 955.6 1140 1340 2027 30 40 50 60 70 80 90 100 110 120 130 160 0.560 0.995 1.56 2.25 3.04 3.98 5.04 6.23 7.51 8.95 10.5 15.9 New RC Materials 91 Table 3.3. Dimensions and unit mass of USD785 and USD1275. Grade USD785 USD1275 3.2.4.2. Nominal diameter mm Nominal area mm 2 Nominal perimeter mm Unit mass kg/m S6 S8 S10 S13 6.35 7.94 9.53 12.7 31.67 49.51 71.33 126.7 20 25 30 40 0.249 0.389 0.560 0.995 H6 H7 H9 Hll H13 6.4 7.4 9.2 11.0 13.0 30.0 40.0 64.0 90.0 125.0 20 23 29 35 41 0.236 0.314 0.502 0.707 0.981 Mark Specified Yield Strength A clear yield plateau is the most desirable feature of axial reinforcement in the yield hinges. As USD685 is to be used in this situation, both upper and lower bounds of yield stress are specified in the proposed Standard. The difference between upper and lower bounds is 100 MPa for USD685A, and 70 MPa for USD685B. The narrower interval allows the structural engineer more accurate estimation of flexural yield strength leading to smaller magnification of required strength of nonyielding members. On the other hand, manufacture of USD685B would require more stringent quality control, possibly resulting in higher cost, compared with USD685A. It is up to the decision of structural engineers in future which one of USD685A or USD685B would be favored. USD980, ultrahigh strength bars to be used in nonyielding members, and USD785 and USD1275 both for lateral reinforcement, have the specified values of lower bound of yield stress only. These kinds of steel usually show no distinct yield plateau, and yield stress is defined by 0.2 percent offset stress as in the current Standard. 3.2.4.3. Strain at Yield Plateau A new concept of strain at yield plateau is introduced in the specifications for USD685A and USD685B. It is the strain at the end of yield plateau, or in other words, strain at the start of strain hardening. As shown in Fig. 3.28, it is defined as the strain at which upper bound of yield stress is exceeded. As shown 92 Design of Modern Highrise Reinforced Concrete Structures Stress Tensile Strength y.l e .. Strain at yield plateau is taken as strain at which upper bound yield stress is exceeded Point /, ' ' Upper bound yield stress Lower bound yield stress 0 ,"- M Yield H 0.2% s t r a i n : Stain at yield plateau (2 1.4%) • Strain Fig. 3.28. Stress-strain relationship of USD685. in Table 3.1, this value is specified not to be smaller than 1.4 percent for both USD685A and USD685B. This requirement is expected to ensure prescribed amount of yield plateau in the stress-strain relationship, by avoiding the onset of strain hardening and accompanied strength increase of structural members within certain range of deformation after re-bar yielding. This type of behavior is believed to be useful for the structural engineers to ensure the occurrence of intended collapse mechanism. 3.2.4.4. Yield Ratio Yield ratio of steel is defined as the ratio of measured yield stress to measured tensile strength. Lower the yield ratio, larger is the increase of stress after yielding due to strain hardening. As may be read in Fig. 3.27 where yield ratios are shown in parentheses, yield ratio of ordinary re-bars such as SD295 or SD345 is low, around 0.7, but it increases as the yield strength gets higher. It was found in the process of trial manufacture that yield ratio of high strength re-bars could go up to almost 1.0 depending on the manufacture method. Yield ratio has been an important consideration for steel structures since long ago, but it has received little attention in case of reinforced concrete as a potential source of inferior behavior. However in the New RC project structural tests were conducted to demonstrate the possibility of strain concentration and fracture of bars when steel with yield ratio as high as almost 1.0 is used. Hence provisions for upper limit of yield ratio were introduced to re-bars that are New RC Materials 93 expected to be used as axial reinforcement. As shown in Table 3.1, values of limiting yield ratio for USD685A and USD685B are 85 percent and 80 percent, respectively, while that for USD980 is 95 percent. These requirements of yield ratio serve to specify the minimum value of tensile strength in effect. Hence tensile strength is not specified in Table 3.1. 3.2.4.5. Elongation and Bendability Elongation of re-bars at fracture is desirable to be as large as possible, for easier bending process without bar fracture, but loss in elongation capacity is unavoidable as tensile strength increases. As shown in Table 3.1, 10 percent for USD685A and USD685B and 7 percent for USD980 are the specified minimum values of fracture strain. Bendability of deformed re-bars is affected by the shape of surface deformation, and in general re-bars with screw shaped lugs are unfavorable to ordinary lateral lugs in bending process. Table 3.1 specifies inner radius of 90 degree bend to be twice bar diameter for USD685A and USD685B, and four times bar diameter for USD980. For lateral reinforcement of USD785 and USD1275, elongation of 8 percent and 7 percent, and inner radius at 90 degree bend of 1.5 times and 2.5 times bar diameter, are insured respectively. Strain age hardening, which means that a bar tends to harden and becomes susceptible to fracture with age after receiving processing strain, is sometimes observed depending on the type of steel. To see whether this effect is observed in case of high strength re-bars, tensile tests were conducted of specimens of D32 screw-deformed bars of USD685 manufactured by component adjustment and hot rolling (as roll), first subjected to tensile prestrain of 10 percent, then subjected to accelerated ageing of one hour at 100 degree Celsius in the electric furnace. It was confirmed no strain age hardening was observed in case of D32 bars of USD685 manufactured by component adjustment and hot rolling (as roll). 3.2.5. Method of Manufacture and Chemical Component Steel manufacturers who participated in the New RC project made trial manufacture of re-bars conforming to the target performance by adopting two methods: the first one was by component adjustment and hot rolling (as roll) including on-line heat treatment in the rolling process, and another one was off-line heat treatment after completion of rolling. As stated previously, the New RC project adopted four grades of high strength steel as its aim of 94 Design of Modern Highrise Reinforced Concrete Structures development, all of which are required high degree of ductility in addition to high strength. In principle, three methods are conceivable to make high strength re-bars: addition of strengthening chemical elements, cold work, and heat treatment. However, a careful process design is necessary for each of these methods corresponding to employed equipment. Adopted methods of manufacture for each of four grades are summarized below. USD685A and USD685B: Since required yield plateau strain is large, and also required yield ratio is low, cold work is not suitable as it leads to unclear yield point and reduced ultimate strain. Re-bars of this grade can be manufactured either by addition of strengthening chemical elements or by heat treatment. Addition of one or several kinds of strengthening chemical elements to molten steel results in higher strength due to atomic size effect (solid melting or replacement) or crystallization effect. Higher yield stress and strain can be achieved by finer crystalline particles. By adding Al, Ti, or Nb at the steel manufacture, and by heating and hot roll, fine crystalline particles of austenite can be obtained. On the other hand, heat treatment of quenching and tempering can be employed to the ordinary medium carbon steel with addition of chemical elements effective for quenching. In either of these methods, amount of impure elements that affect mechanical properties must be carefully controlled. USD980: This steel is high strength but required yield ratio is relatively high. Hence commercially available P C steel manufacturing technology of JIS G 3109 "PC bars" can be applied. First deformed bars are manufactured by adding chemical elements effective for heat treatment or cold work. Then heat treatment of quenching and tempering is conducted, or cold work by 10 percent stretching and subsequent brewing are applied, in order to secure high strength and ductility. USD785: This steel is for small diameter bars to be used as lateral reinforcement. It can be manufactured by addition of strengthening chemical elements and by on-line heat treatment at the time of hot rolling consisting of air-cooling to quench during hot roll followed by tempering automatically by remaining heat. USD1275: This steel is also for small diameter bars to be used as lateral reinforcement. It can be manufactured by methods specified in the current JIS G 3536 "PC steel wires and PC strands" or JIS G 3109 "PC steel bars". Some products were already available commercially at the time of New RC project. New RC Materials 95 Table 3.4. Trial manufactured USD685B. Size Mechanical properties Chemical component (% by weight) C Si Add D13 0.33 0.41 strengthening D22 0.32 0.41 elements D32 0.32 0.99 D41 0.32 0.99 Mn P S 0.75 0.70 1.58 1.55 0.007 0.010 0.006 0.009 0.004 0.001 0.002 0.004 Bending Yield Tensile JYield ElonPoint strength ratio gation (MPa) (MPa) (*) (MPa) 726 696 710 702 1111 i Method of manufacture 0.80 0.79 0.79 0.78 19 14 18 17 745 734 731 732 good good good good ] *stress at e = 1.4%. (a) (b) (c) (A) Fig. 3.29. (a) Tensile test of re-bar. (b) An example of stress-strain curve, (c) Microscopic structure, (d) Bending test. A part of results of trial manufacture is introduced herein. Table 3.4 is the chemical components and mechanical properties of USD685B re-bars of four different sizes. It will be seen that all bars conform to requirements in Table 3.1. Figures 3.29(a) and (b) show tensile test of re-bar and an example of stressstrain curve. Figure 3.29(c) shows microscope structure, and Fig. 3.29(d) shows results of 90 degree bending test. These are examples of trial manufacture 96 Design of Modern Highrise Reinforced Concrete Structures (b) Alternate reversal of loading Fig. 3.30. Stress-strain curves under reversal of loading. illustrating the possibility to make products of USD685B conforming to the proposed Standard. Figure 3.30 shows two examples of stress-strain curves under reversal of loading, (a) into one-way increase into tension, and (b) in alternative increase into both tension and compression. It will be seen that Bauschinger effect and strain hardening of the new steel are similar to those of currently used steel re-bars. High-stress fatigue test, carried out assuming cyclic earthquake or wind loading, showed that for USD685, stress amplitude directly affected the fatigue strength. For stress amplitude of 0.98 and 0.93 times the specified yield strength, the number of cycle to failure changed from 6000 to 10 000. USD980 has higher yield ratio than USD685, and hence test stress was high. It appeared that the number of cycle to failure was affected more by the shape of surface deformation than the stress amplitude. New RC Materials 97 In case of design of structures susceptible to fatigue condition, it would be necessary to carry out fatigue test assuming the actual design condition to which high strength re-bars are exposed, considering the possibility of the influence of shape of surface deformation. 3.2.6. Fire Resistance and Durability 3.2.6.1. Effect of High Temperature Mechanical properties of steel changes when the steel is exposed to high temperature of fire. Figure 3.31 shows yield stress and tensile strength at room 1400 1 USD980 l 1200 1000 1 S 800 o S3 600 | /USD785 1 7,, "•! | ' USD685A S..1 < r—+ ..„ ' **' USD685B _ 1 Vi ^USD345 "" 400 200 0 „ Room 400 500 600 700 800 temperature Temperature in degree Celcius (a) Yield stress after heating and cooling 1400 XUSD980 / 1200 1000 J 1 800 600 400 i m w \ L SD685A 5D685 3 \1 x 1- 1 • ^ / • N 1 1 ^ USD345 200 0 Room 400 500 600 700 800 temperature Temperature in degree Celcius (a) Tensile stress after heating and cooling Fig. 3.31. Yield stress and tensile strength after exposed t o high temperature. 98 Design of Modern Highrise Reinforced Concrete Structures temperature of USD685A, USD685B and USD980 for axial reinforcement, USD785 for lateral reinforcement, and SD345 for comparison, after exposed to high temperature ranging from 400 to 800 degree Celsius. It is seen from the figure that both yield point and tensile strength of axial bar USD685 and lateral bar USD785 starts dropping at heating of 700 degree Celsius, and the 1400 1200 1000 e Room 200 300 400 500 temperature Temperature in degree Celcius 600 (a) Yield stress at high temperature 1400 US D980 1200 z_ US3685A 1000 £ US 3685B'-..' 800 s SD345 V W 600 400 \ \ 200 0 Room 200 300 400 500 temperature Temperature in degree Celcius 600 (b) Tensile strength at high temperature Fig. 3.32. Yield stress and tensile strength at high temperature. New RC Materials 99 reduction rate is slightly greater than SD345, and that yield point and tensile strength of USD980 which was made by off-line heat treatment starts dropping at heating of 600 degree Celsius. Up to 500 degree Celsius, which is the highest temperature expected in case of fire, there is no mechanical property change of high strength re-bars similarly to currently used SD345 steel. Figure 3.32 shows yield stress and tensile strength tested while being heated in the electric furnace up to the designated temperature. There is a general trend of larger reduction of yield stress and tensile strength for higher strength steel, but minimum remaining tensile strength of about 200 MPa can be insured at 600 degree Celsius for any grades of steel including SD345. 3.2.6.2. Corrosion Resistance When different metals touch in the corrosive environment, the metal on electrically base side tends to corrode due to difference of ionization. Furthermore, high strength re-bars contain many special chemical elements compared to ordinary steel. Considering the possibility of mixed use of high strength and ordinary strength bars, corrosion tests were conducted of steel in contact as well as isolated in the solution of sodium chloride and calcium hydroxide to simulate the environment in fresh concrete. Tests consisted of three items. The first was isolated immersion test, to observe and measure rust appearance, corrosion loss of mass, and corrosion hole depth, during 30 days of immersion at 25 degree Celsius. The second was measurement of electrochemical natural potential, to determine inertness-break voltage by measuring natural potential and anode polarization (re-bar in corrosion side). The third was measurement of coupling current between different grade steel, tested as shown in Fig. 3.33. 9 91 . solution of sodium ~~"- -x specimens chloride and calcium hydroxide of pH 10-12 j—r~^ I Fig. 3.33. Measurement of electric current between different grade steel. 100 Design of Modern Highrise Reinforced Concrete Structures After equilibrium in 30 days of immersion, coupling current was measured and corrosion area ratio and corrosion speed were calculated. SD345, USD685 and USD980 bars were used as specimens. It was found that corrosion resistance of isolated specimens of high strength steel was similar to currently available ordinary strength steel. Corrosion due to different metal touch tended to occur on the lower strength steel while higher strength steel is corrosion-proofed. However the speed of corrosion in the pH 12 environment was in the range of 0.001 to 0.019 mm per year, so it was very small and was on the same order as the corrosion of isolated bodies. 3.2.7. Splice Current reinforced concrete construction employs various splicing methods of re-bars, such as lap splice, gas butt welding, arc welding, and mechanical splices. As high strength bars of USD685 are manufactured by addition of strengthening chemical elements and controlled hot rolling or heat treatment, gas butt welding or arc welding are not suitable. Metal crystalline structure is apt to change in the heat-affected zone of these splices, which results in reduced strength. Hence mechanical splices are more desirable for high strength re-bars. Among them, the most advantageous would be the use of deformed bars with screw type surface deformation, spliced with screw coupler with grouting. This kind of coupling does not require special skill of technicians, and is relatively easy to keep good quality control, hence is most practically feasible. Screw coupler splices are currently available for screw type deformed bars up to SD490 steel. They use steel couplers with female screw on the internal face conforming to the screw shaped surface deformation of bars. After the coupler is installed to connect bar ends, grout material is injected through the hole at the center of the coupler. Both organic grout of epoxy resin and inorganic grout of cementitious material are available. Applicability to USD685 high strength re-bars was investigated of this type of screw coupler splices. Both epoxy grout splices and inorganic grout splices were applied to D19, D22, D25, D32, D35, D38 and D41 bars, and three kinds of tension tests, specified in the bar splice performance acceptance criteria (1982) of the Building Center of Japan, were carried out. (1) One-way loading test. As shown in Fig. 3.34, specimen is first loaded up to 0.95 times the specified yield stress and unloaded to 0.02 times the yield. Secant moduli at 0.70 times, and at 0.95 times, the yield stress are New RC Materials 101 Splice specimen 0.95 c,o- Base metal re-bar 0.70 <T,0- CTy0: specified tensile yield strength of base metal re-bar 0.02 o y 0 Strain Bar slip Fig. 3.34. One-way loading test. Base metal re-bar Splice specimen Strain 0.50 o,„ bar slip Fig. 3.35. Cyclic test in the elastic range. measured. Offset strain at 0.02 times the yield, corresponding to bar slip, is also measured. Then it is loaded all the way up to failure to determine maximum strength. (2) Cyclic test in the elastic range. As shown in Fig. 3.35, load is reversed 20 times between 0.95 times the yield in tension and 0.50 times the yield in compression, and then increased in tension to the point of failure. Stiffness in the first and twentieth cycles is measured and the ratio is calculated. Slippage in 20 cycles is also determined as shown. 102 Design of Modern Highrise Reinforced Concrete Structures Base metal re-bar Splice specimen Repeated 4 cycles 8 0.50 c,,, Strain -0.25 CT, -0.50 a. Bar slip Fig. 3.36. Cyclic test in the plastic range. (3) Cyclic test in the plastic range. As shown in Fig. 3.36, load is reversed four times between twice the yield strain in tension and 0.5 times the yield stress in compression, and then increased in tension to the point of failure. Slippage is determined from the fourth loop as shown in the figure. Criteria of acceptance for these tests of high strength re-bars have not been established, so the criteria for ordinary re-bars were simply extrapolated to match the strength of USD685. It was shown that all splice specimens broke in base metal, and that the splices possessed the capacity corresponding to Class A splices specified by the Ministry of Construction. Lapped splices are not likely to be used in the New RC buildings, because bars in New RC buildings are mostly large diameter bars, and either prefabricated cages or precast members would be used in practice. Hence no investigation was conducted in the New RC project into the performance of lapped splices. Splices were also tested in the structural tests. Figure 3.37 shows a specimen of cantilever beam having splices of axial bars at the critical section. The purpose of this test was to see whether splices induce strain concentration at the critical section. High strength re-bars have relatively high yield ratio, which may lead to strain concentration at the section of first yield without allowing the plastic hinge zone to expand, particularly of flexural members with low steel percentage. This trend may be exaggerated by the presence of bar splices. Hence structural tests of specimens as in Fig. 3.37 were conducted using steel with yield ratio of 90 percent and 75 percent, with or without bar splices. New RC Materials coupler Loading Point I Negative spiral $ 6 0 8 0 dia.100 . length 650 Fig. 3.37. Test specimen for beams using re-bars with different yield ratio. 250 1 ! i .=• V/VMS 150 -50 -100 -150 -200 -750 _ - JAM : R90 100 50 w KJCn^r - - • (YJ-rmzh bar breakage*—*'' Mf\^gp -20 A a. X • i i " "• .4 , . , . . . ) . . . t t . » .-. Icy : Her r i - .. . _ 0 20 Deflection (mm) (a) Yield ratio 90% without splice -20 0 Deflection (mm) (a) Yield ratio 75% with splice Fig. 3.38. Load-deflection curves of beams using re-bars with different yield ratio. 103 104 Design of Modern Highrise Reinforced Concrete Structures Figure 3.38 shows load deflection relations of two specimens, (a) yield ratio of 90 percent without splices, and (b) yield ratio of 75 percent with splices. Marks indicate points corresponding to particular bar strain. It can be seen that higher yield ratio results in smaller deflection at a given bar strain, meaning that strain is more concentrated in case of higher yield ratio. Although not shown in the figure, trend of the specimen of 90 percent yield ratio with splices was quite similar to Fig. 3.38(a), hence the presence of splices did not accelerate the strain concentration even in case of yield ratio of 90 percent. However, as shown in Fig. 3.38(a), bars broke in tension in the reversal of loading at an amplitude of 5 percent in terms of deflection angle. Bars also broke in the same specimen with splices. This test results form the basis of yield ratio limitation in the mechanical property specification of high strength reinforcing bars. 3.3. Mechanical Properties of Reinforced Concrete When a new kind of material is introduced to reinforced concrete construction, a set of structural tests of members, such as beams, columns, and walls, is usually carried out in the laboratory. In the course of New RC research project, this kind of structural testing was also considered to be an essential part of research, and Structural Element Committee was organized for this purpose. At the same time, emphasis was placed on an effort to clarify fundamental mechanical characteristics of reinforced concrete as a composite structural material, and this was included in a part of assignment to the Reinforcement Committee. Subjects such as bond and anchorage in the structure, confining effect of lateral reinforcement, and behavior of high strength concrete under biaxial stress condition, were investigated. These subjects form a kind of boundary field between materials research and structural research. It was expected that the emphasis on research into this kind of fundamental mechanical characteristics would help deeper understanding of the behavior of New RC structural elements and subsequently that of whole structure. 3.3.1. Bond and Anchorage Reinforced concrete is a composite structural material consisting of concrete and reinforcement, and hence concrete and re-bars must behave in an integrated manner, to be provided by bond and anchorage. Above basic requirement applies to the New RC material with high strength as a matter of course. Bond and anchorage capacity must be increased along with the increase New RC Materials 105 in steel stress, because similar bar arrangement as conventional reinforced concrete is expected in New RC structures. Under the action of bending and shear, axial bars in beams and columns are subjected to flexural bond. Structural members used for building construction usually have relatively thin concrete cover around axial bars, and bond stress tends to trigger splitting failure of cover concrete. Bond resistance mechanism against splitting failure consists of resistance of surrounding concrete and resistance of lateral reinforcement. On the other hand, beams and columns in a moment resisting frame structure must transfer forces in each other members through beam column joints. Bond resistance of bars passing through joints, or anchorage of bars by bending within joints must be activated. Thus flexural bond resistance of beams and bar anchorage in beam-column joints received major attention. Experimental data using concrete with compressive strength of 60 MPa and above or using re-bars with yield strength of 700 MPa and above did not exist here and abroad, and so extensive testing was organized in the New RC project. It was concluded that combination of high strength materials makes it possible to provide satisfactory bond and anchorage within practical range of detailing. Research works toward beam bar anchorage in the exterior and interior beam-column joints and flexural bond development of beam bars will be introduced below. 3.3.1.1. Beam Bar Anchorage in Exterior Joints Exterior columns usually receive beam bars anchored into beam-column joints by 90 degree bend or 180 degree bend (U-bend) occasionally. The anchorage resistance consists of those of straight lead portion, bend portion, and end-tail portion. Most of anchorage resistance is provided through the bearing at the bend. Tests were conducted using the specimens shown in Fig. 3.39, simulating an exterior column between midheight of adjacent stories and having only one Fig. 3.39. Test specimens for bar anchorage of exterior joint (No. 10). 106 Design of Modern Highrise Reinforced Concrete Structures pg/T~ No. 1 - 3 sr. No. 9 a-na -^ ' »T—r ,a. P'°'«l • D25 40° No. 10, 11 Fig. 3.40. ar DIP 100 D23 , h- i -I No. 12 Column sections (Nos. 1-12) for exterior joint anchorage test. layer of bars on one side of beam in tension. Compression force of concrete on the other side of beam was simulated by the reaction force of bar tension. Figure 3.40 shows the variation of column size and beam bar arrangement for 12 specimens. Three kinds of concrete strength, 40, 80 and 120 MPa, were used. There were another series of 12 specimens with D19 bars anchored with various bent radius, variety of concrete strength, and various amount of lateral reinforcement. The anchorage failure occurs as the bearing failure at the bend provided that bond capacity at the end-tail portion is sufficient. When the side concrete cover is small, the bearing failure is combined with the splitting failure of side concrete cover. When the straight lead length is small, the failure takes New RC Materials 107 a form of cone-type pull out failure of concrete. Parameters associated with the anchorage strength includes concrete strength, bend radius, side concrete cover, spacing of beam bars, bend position, bend direction, projected horizontal length of embedment, lateral reinforcement, bend bar diameter and so on. It is generally assumed that anchorage strength is proportional to the square root of concrete strength. However in the experimental study the anchorage strength tended to hit its ceiling when concrete strength reached 100 MPa. Anchorage strength of specimens without lateral reinforcement was increased by 30 to 50 percent by the addition of lateral reinforcement. The lead length, which is the length of the straight portion of the bar up to the beginning of bend, was found to have a definite effect on the anchorage strength. Insufficient lead length resulted in large drop of anchorage strength. From these experiment, following anchorage strength equation was proposed fd = 100kik2k3k4kckhksy/aB (3.1) where fd is anchorage bar stress in MPa, <TB is compressive strength of concrete in MPa, fci is a coefficient for type of concrete, to be taken as 1.0 for ordinary aggregate concrete and 0.85 for lightweight aggregate concrete, k2 is a coefficient to consider lower anchorage strength for high strength concrete, to be equal to 1.0 for aB not greater than 40 MPa and k2 = ( a s / 4 0 ) - 1 / 6 (3.2) for ab in excess of 40 MPa, £3 is a coefficient to take into account the direction of bend in the joint, to be taken as 1.0 for inward bend in normal practice and as 0.7 for outward bend in case of bottom beam bar bent down in traditional Japanese practice (bad practice), k4 is a coefficient for the bend radius r relative to bar diameter db, expressed as follows k4 = 0.1(r/db) + 0 . 7 ^ 1.15, (3.3) kc is a coefficient for the effect of side concrete cover c relative to bar diameter db, expressed as follows kc = 0.1(c/db) + 0 . 4 3 ^ 1.0, (3.4) kh is a coefficient for the lead length ldh relative to bar diameter db, expressed by kh = O.Q38(ldh/db) + 0.544 ^ 1.15 , (3.5) 108 Design of Modern Higkri.se Reinforced Concrete Structures and ks is a coefficient for lateral reinforcement diameter d3 relative to anchored bar diameter db, expressed by ks = 1 + 2/3 -(ds/di,)2 ^1.4. (3.6) Equation (3.1) is applicable to concrete strength from 21 to 120 MPa, steel yield strength from 295 to 685 MPa, and bar diameter from D13 to D38. The design should also observe following minimum requirements. (1) Projected embedment length should not be less than 8 bar diameter and 15 cm. (2) The bend should start from a position beyond the central axis of the member to which the bar is anchored. (3) The end-tail portion of a 180 degree bend should be more than 4 bar diameter and 6 cm. (4) The end-tail portion of a 90 degree bend should be more than 10 bar diameter. Table 3.5 shows the necessary projected embedment length for various combination of steel grade and concrete strength. In the table, d denotes bar diameter, and upper figures are for the case where lateral reinforcement is not considered, and lower figures are for the case where lateral reinforcement is considered which must cover entire anchorage zone of lead length, bend and tail length, and at least two lateral bars must cross the inscribed circle Table 3.5. Necessary minimum lead length of 90 degree bent anchorage (d denotes bar diameter). Concrete strength (MPa) Steel grade SD295 SD345 24 30 36 42 60 80 100 14d 10.5d lid 13.5d 14d 10.5d 14d 9d 8d 11.5d 8.5d 15.5d 11.5d 8d 8d lOd 8d 13.5d 10 — — — — 14.5d 8d 8d 8d 8d 13.5d 8d 15.5d 11.5d 8d 8d 8d 8d 10.5d 8d 12.5d 9d 8d 8d 8d 8d 8d 8d 10.5d 8d 16d 13.5d — 13.3d SD390 SD490 — — — — — — USD685 Upper figures: Lateral reinforcement not considered. Lower figures: Lateral reinforcement considered (see text). New RC Materials 109 of the bend. Blanks in the table indicate combinations of material where bar anchorage cannot be made under the prescribed conditions. In these cases anchorage strength must be calculated, and it is necessary to pay further attention to increase concrete cover and to provide greater amount of lateral reinforcement. 3.3.1.2. Bond Anchorage in Interior Joints Anchorage of beam bars passing through an interior column depends on the column size. If the column section is sufficiently large, beam bar slip in the joint is small, and hence the hysteresis of members connected to the joint is stable with a large hysteretic area. In this case the shear resistance of joints is provided partly by the truss mechanism, thus the shear resistance is also enhanced. On the other hand, if the column section is insufficient, beam bar slip and pull-out displacement increase, and hence the hysteresis of members shows inverted S shape with a small hysteretic area. Insufficient beam bar anchorage also results in reduced compression bar effect of beam section and hence loss of ultimate strength and ductility. Shear resistance of joint in this case depends on the arch, or strut, mechanism only. The beam bar bond through the beamcolumn joint thus becomes an important issue in the seismic design. Tests were conducted using specimens as shown in Fig. 3.41. A part of interior column having only one beam bar passing through it was fabricated, and one end of the bar was pulled while the other end was pushed simultaneously using the set-up as shown while a constant axial load was applied on the column. Figure 3.42 shows detail of the representative specimens. In tie down strap horizontal support pin Unit: mm Fig. 3.41. Test set-up for bar development of interior joint. 110 Design of Modern Highrise Reinforced Concrete Structures 8 (a) S-series (b) L-series Fig. 3.42. Detail of interior joint specimens. total, 13 specimens were tested, including concrete strength ranging from 40 to 120 MPa, bar yield point from 345 to 785 MPa, and bar diameter from D19 to D35. As the result of these tests, following equation was proposed for the local bond strength within the core of interior beam-column joint = 2.3(0.86 + 0.84<7 0 /<7B)B/d 6 (a B /36.4) 2 / 3 (3.7) where T„ is local bond strength in the joint core in MPa, erg is concrete strength in MPa, <TQ 1S average normal stress in the joint in MPa, B is unit column width obtained as total column width divided by number of beam bars, and db is diameter of beam bars passing through the joint. Using this equation, bar diameter column depth ratio necessary for beam bar development was expressed as shown below 2/3 (k/he £ 1.34(1.0 + <To/<TB)((Td fry) (3.8) where hc is column depth and ay is steel yield point in MPa, and other notations are same as in Eq. (3.7). For beam axial re-bars going through interior column joint of moment resisting frames designed for beam yielding mechanism, the minimum column depth hc can be obtained from Eq. (3.8) using specified concrete strength and steel yield strength. Table 3.6 shows necessary minimum column size thus obtained, where d denotes beam bar diameter. Upper and lower figures New RC Materials 111 Table 3.6. Necessary minimum column depth at interior joints with through beam bars (d denotes bar diagram). Concrete strength (MPa) Steel grade SD295 SD345 SD390 SD490 USD685 24 30 36 40 60 80 100 23.0d 19.5d 26.7d 23.4d 30.5d 26.6d 38.2d 33.4d 53.4d 46.8 19.7d 17.3d 23.1d 20.2d 26.3d 23. Id 32.9d 28.8d 46.0d 40.3d 17.5d 15.3d 20.4d 17.9d 23.3d 20.4d 29.2d 25.5d 40.8d 35.7d 15.8d 13.8d 18.4d 16.1d 21.0d 18.4d 26.3d 23.0d 36.8d 32.2d 12.4d 10.9d 14.5d 12.8d 16.6d 14.5d 20.7d 18.2d 29.0d 25.4d 10.3d 9.0d 12.0d 10.5d 13.7d 12.0d 17.1d 15.0d 24.0d 21.0d 8.9d 7.8d 11.9d 10.4d 11.8d 10.4d 14.8d 12.9d 20.7d 18. Id Upper figures: Column compressive stress = <TB/6. Lower figures: Column compressive stress = <TB/3. correspond to column compression stress of one-sixth and one-third the concrete strength, respectively. The table is based on the assumption that tension and compression yield would take place simultaneously at both faces of the column, and the unit column width per one beam bar is greater than 6 times the bar diameter. It should be noted that the use of high strength steel inevitably involve longer projected embedment length and larger column size, and the combined use of high strength concrete only partly compensates because the tensile strength does not increase in proportion to the compressive strength. 3.3.1.3. Flexural Bond Resistance of Beam Bars Beams and column in the moment resisting frames are subjected to bending and shear under the action of horizontal load. Axial reinforcement in these members are subjected to flexural bond. In order to expand the scope of application of existing equation as in AIJ Design Guidelines (Ref. 3.5) to New RC material, two series of bond tests were carried out. The one was simple beam bending tests of 36 specimens with various combination of test parameters, with end supports provided through the openings in the web in order to avoid conflict against bond splitting of axial bars in tension. The other series was numerous tests of pull-out specimens for bond resistance, with both concentric as well as eccentric bar arrangement. 112 Design of Modern Highrise Reinforced Concrete Structures As the result of these testing, following equation was proposed for bond strength for design of beam and column axial bars except for top reinforcement in beams rbu = [0.053 + 0.126i + lOknPtvb/iNdb^y/aS (3.9) where rbu is bond strength of axial bars in MPa, CTB is concrete strength in MPa, bi is a coefficient for the effect of concrete between axial bars, expressed as follows bi = (b- Ndb)/Ndb, (3.10) kn is a coefficient for the effect of substirrups or subhoops within the peripheral web reinforcement, expressed as follows fcn = 1.0 + 0 . 8 5 ( n - 2 ) / i V , (3.11) pw is web reinforcement ratio defined as follows Pw = Ast/{bs). (3.12) In all of above equations, b is width of member, N is number of axial bars, db is nominal diameter of axial bars, n is number of vertical legs in one set of web reinforcement, Ast is total cross sectional area of vertical legs in one set of web reinforcement, and s is spacing of web reinforcement. Equation (3.9) is applicable to the case where sufficient amount of web reinforcement is provided, such as pwawy ^ 0Al5^/aE (3.13) where awy is yield strength of web reinforcement in MPa and other notations are same as above. If web reinforcement does not satisfy Eq. (3.13), S/O~B in Eq. (3.9) must be replaced by pwawy/0.415. For the top bars in beams where bond resistance is usually lower, a coefficient fco is multiplied to obtain bond strength. fco is defined as follows fco = 0.80 = 0.7143 + 0.002857 aB for aB ^ 30 MPa for 30 MPa < aB ^ 100 MPa. This means that fco is 0.80 for 30 MPa concrete and 1.0 for 100 MPa concrete, and straight interporation is applied in between. Equation (3.9) is generally applicable to cases with web reinforcement ratio between 0.2 and 1.2 percent, and concrete strength between 30 and 100 MPa. New RC Materials 3.3.2. 113 Lateral Confinement High strength concrete is used in the building structure to cope with high axial compressive stress in the vertical members, both from gravity load and from the overturning moment due to lateral load. Consequently higher strength is desired as the building height increases. On the other hand, high strength concrete inherently shows brittle behavior after reaching its maximum compressive strength. Lateral confinement using high strength steel is thought to be an effective countermeasure to compensate for rapid decrease in the descending branch of stress-strain relationship of high strength concrete. At the time of New RC project, however, very few experimental data were available on the confining characteristics of high strength concrete over 50 MPa. An extensive testing of short columns of high strength concrete with high strength lateral reinforcement was therefore conducted under concentric compression to investigate the improving effect of lateral confinement on the stress-strain relationship of confined concrete. 3.3.2.1. Stress-strain Relationship of Confined Concrete Figures 3.43 and 3.44 show typical short column specimens with circular or square cross-sections subjected to concentric compression. Columns were provided with axial reinforcement of 620 MPa D13 bars. Lateral reinforcement consisted of 1130 MPa D6 bars. Dotted lines indicate perimeter of specimens Fig. 3.43. Typical circular short column specimen. 114 Design of Modern Highrise Reinforced Concrete Structures Unit: mm Fig. 3.44. Typical square short column specimen. 6000 5000 -4000 \ i 3000 "°"Y ^^, 2000 "^- , CUD CC«T>» ! ' \ CHS1L \ 1 KIM. V \ •31 < i 1000 j.. w i t h cover- • CHBOL ' ^ * ^ 0, iiiiS ^^--^-4^-... 2 3 4 5 axial strains (%) (a) Circular columns, 40 MPa concrete 6000 5000 4000 3000 - i — ^ _ N 1000 1 I •i CCJOIIH 2000 CN20KH 1" 0 ; . i . j ._ i j CC40HH ] CMOMH --„-.-i-^--- -,-J--. 2 3 4 5 axial strains (%) (b) Circular columns, 80 MPa concrete Fig. 3.45. Load vs. axial strain of circular columns. New RC Materials 6000 J.. . - — - j 115 _ "* 5000 5 ifr^l 4000 S 3000 r 2000 •*-»„ "-»-. SCML "^"^Cl*"' t swot • ^ " • - . SCtOL with cover-t- 1000 0 2 3 4 5 axial strains (%) (a) Square columns, 40 MPa concrete I 6000 1 5000 1 //' § 4000 1 3000 1— ••->- ..s&z^^^: •-./::-- _. 2000 .. 1000 0 9 ays* **' 0 1 2 3 4 axial strains (%) 5 6 (b) Square columns, 80 MPa concrete Fig. 3.46. Load vs. axial strain of square columns. without concrete cover. Figures 3.45 and 3.46 show load-axial strain relationship of some specimens. Upper figures are for specimens with 40 MPa concrete, and lower ones for specimens with 80 MPa concrete. In the figure, specimen marks like CC20L indicate the following. The first letter is C or S, corresponding to circular or square column. The second letter is C or N, indicating specimens with concrete cover or no cover. In the figure they are illustrated by full lines or dashed lines, respectively. Two following digits show the spacing of lateral reinforcement consisting of D6 high strength bars. The last letter L or MH correspond to concrete strength, L for low, 40 MPa concrete, MH for medium high 80 MPa concrete. Although not shown, medium strength concrete 60 MPa and high strength concrete 120 MPa were also tested. From these figures, it is clear that lateral confinement is quite effective in improving the otherwise brittle behavior of concrete after reaching the maximum stress. Concrete cover has almost no effect after the maximum stress of plain concrete as it spalls off easily at the strain of around 0.2 percent. Stressstrain relationship of confined concrete can be determined from these figures by subtracting the force carried by axial reinforcement. 116 Design of Modern Highrise Reinforced Concrete Structures Using these test data as well as other existing data of concrete with passive confinement using specimens not smaller than 20 cm in diameter of circle or side of square cross-section, following stress-strain relationship was proposed ac _ AX + (D-l)X* a'B 1 + (A-2)X + DX* [6 Li>) - where ac is compressive stress in concrete, <r'B is maximum stress of confined concrete as explained later, X is normalized strain defined by X = ec/ec0 (3.16) where sc is compressive strain in concrete and SCQ is strain associated with maximum stress a'B as explained later, A is a constant representing the initial elastic modulus of concrete and is defined by A = Ecec0/(TB (3.17) where Ec is Young's modulus of concrete. D in Eq. (3.15) is another constant to define the shape of stress-strain curve, to be explained later. The form of Eq. (3.15) was originally proposed by Sargin et al. (Ref. 3.6). For this equation, maximum stress of confined concrete a'B, strain associated with maximum stress eco, and constant D must be defined. The maximum stress of confined concrete, a'B, is expressed as follows a'B = flCFB + KPhCTy (3.18) where as is compressive strength of plain concrete cylinder, /i is a constant according to shape of column section and is taken to be 0.8 for circular section and 1.0 for square or rectangular section, ph is volumetric ratio of lateral reinforcement to confined concrete taken to the center lines of peripheral lateral reinforcement, ay is yield strength of lateral reinforcement which should not exceed 700 MPa for straight lateral reinforcement, and K is a constant depending on column section expressed as shown below. For circular section K = kc(l - s/2Dc)2 kc = 2.09 (3.19) For square or rectangular section K = ks{d"/C){l - s/2Dc) ks = 11.5 (3.20) New RC Materials 117 where d" is nominal diameter of lateral reinforcement, C is effective lateral support span of lateral reinforcement, s is spacing of lateral reinforcement, Dc is center-to-center distance of peripheral lateral reinforcement within the section (diameter of circular hoop for circular column). The strain associated with the maximum stress, £co, was assumed to be obtained by multiplying that of plain concrete by a constant which is a function of strength magnification factor K K = ^ = l +^ ^ (3.21) In case of K < 1.5 = 0.93(<7 B ) 1/4 10- 3 {1 + 4.7(A- - 1)} (3.22) = 0.93(<7 B ) 1/4 1(T 3 {3.35 + 20(K - 1.5)} (3.23) £c0 In case of K ^ 1.5 £c0 where the concrete strength is <TB in MPa. The basic equation for eco of unconfined concrete owes to Popovics (Ref. 3.7) and the multiplier is due to Sun et al. (Ref. 3.8). Finally, the constant D in Eq. (3.15) was determined to fit the measured stress-strain curves as follows D = 1.5 - 1.71 x l(T 2 cr B + 1.6y/{K - 1)CT B /23 (3.24) where the constant in front of square root, 1.6, may be increased to 2.4 in case lateral confinement is provided by steel pipe. The strength magnification factor K should be obtained by Eq. (3.21). Figure 3.47 shows the relationship between measured compressive strength of confined concrete a'B and lateral pressure oy exerted by lateral confinement for circular columns. Both axes are normalized by plain concrete strength OB • Lateral pressure aT is defined as follows <?r = -Ph(Ty(l - s/2Dc)2 . Also shown in the figure are three straight lines. Richart equation is <J'B = 0 . 8 5 < T B +4.1oy. (3.25) 118 Design of Modern Highrise Reinforced Concrete 0.0 0.1 0.2 0.3 Structures 0.4 0.5 0.6 aJaB Fig. 3.47. Strength of confined concrete vs. lateral pressure for circular columns. An equation developed in the Building Research Institute in an earlier stage of the project is a'B = 0.72 aB + 4.61 ar. The best fit to all test data was found to be a'B = 0 . 8 0 C T B + 4.18OV from which Eq. (3.19) was derived. Figure 3.48 shows the relationship between measured compressive strength of confined concrete a'B and lateral pressure index are for square columns. Both axes are also normalized by concrete strength OB- In case of square sections, lateral pressure cannot be reasonably defined, and so an index representing the degree of lateral confinement are was defined as are = {d"/C){\ - s/2Dc)phcjy . (3.26) The straight line in the figure is a'B — 1.0 &B + 11.5 erre from which Eq. (3.20) was obtained. Figure 3.49 illustrates measured and calculated stress-strain curves for various column sections with various amount of lateral reinforcement. It will be seen that theoretical model based on Eq. (3.15) can reasonably simulate the behavior of confined concrete under compression. New RC Materials Matter ol Data:186 Maan v a l u e : . . 0 0 Standard error: 0.13 3.5 119 a=1.00 bet 1.57 r-0.87 3.0 2.5 B BQ O 2.8 CO "0 . 1.5 • t.B • a B • • > • • • La-1- " • " I I I J - • U.LWJU-1- B.S i.« a.84 a.i a.as a.aa 11 I t A 1 U . J . e.la B. XI <Va B Fig. 3.48. Strength of confined concrete vs. lateral pressure index for square columns. 1 S. | 60 •'"j^5""" f^TTJL 1i SN25L| r ; 1 J • £ 0 / I j •] SC25MJ SN25M1 \ \ ""-r^--4^ • ; V "-».^ ' 1 2 3 4 5 : 6 0 1 2 : 1—sc50L| 'J SN50U 3 : 4 : 5 6 "0 1 2 : I—SCSOM] , | SN50M| -^---pK^ 3 4 I 60 \ y 0 1 ; 'r 2 3 1 j 4 ! : _; 5 6 0 1 2 3 4 5 6 0 I 0.2 0.4 0.6 m : 1—SCSOLI ;.^—SNWy, CTOMI reoMf. 0.8 I -SNBOHI Im 60 ^T^SSa^^j 20 0 30 2 3 Strain (%) 4 5 6 / * S s s f e a == ^s 1 ^ °0 1 2 s s = 3 Strain (%) =^ 4 -_: 5 6 6 ,y \ 'I....!.... ""7 "'^p^^^s^^ 5 : E-SN23LI j "f SC25HI SN25H[ 0.2 0.4 0.6 0.8 Strain (%) Fig. 3.49. Measured and calculated stress-strain curves of confined concrete. 1 120 Design of Modern Highrise Reinforced Concrete 3.3.2.2. Structures Upper Limit of Stress in Lateral Reinforcement The effect of lateral reinforcement may have a limit when high strength steel is used for lateral re-bars. For lateral reinforcement in the shape of square hoops and subhoops, yielding of lateral reinforcement with very high strength was not observed even at the maximum compressive strength was reached. The yield stress to calculate confined strength of concrete by Eq. (3.18) should thus be limited to avoid unsafe estimate. Looking into test data a tentative proposal was made to limit the yield strength in Eq. (3.18) to 700 MPa in case of straight lateral reinforcement, as stated earlier. On the other hand, circular lateral reinforcement was almost always shown to yield in the tests, and the calculated confined strength using yield stress of lateral reinforcement did not overshoot most of the time. Hence yield stress up to 1100 MPa, which is the upper limit in the test, may be utilized in the calculation. Uniaxial compression test of large size square column specimens was also conducted to confirm the results obtained from test of smaller size specimens. As shown in Fig. 3.50, column section was assumed to be 500 mm square, approximately two-thirds the actual column section, and concrete cover was removed to have the exterior diameter of 470 mm. Column height was 1300 mm. Four specimens were tested, among which three had same hoop spacing of 58 mm with different hoop diameter of D8, D10, or D13, resulting in three different amount of lateral reinforcement ratio. The fourth one had 15 120 470 ,85 i 85 30 120 \\5 -15 m52 & 40 ~0| 470 85 "30 120 ^ s= •15 500 | Unit: mm C9712 Fig. 3.50. Section of large-scale columns under uniaxial compression. New RC Materials 0 10 20 30 40 121 50 Axial deformation (mm) Numbers in parentheses indicate lateral reinforcement ratio in % Fig. 3.51. Load-deformation of large-scale columns under uniaxial compression. smaller hoop spacing of 42 mm with D8 bars, resulting in equal lateral reinforcement ratio as the second specimen. Figure 3.51 compares load vs. axial compressive deformation. As amount of lateral reinforcement increases, maximum load shows modest increase, while improvement of brittleness in the falling branch is conspicuous. Two specimens with same lateral reinforcement but different hoop spacing showed almost identical result. The applicability of aforementioned stress-strain model was satisfactory in general, including the assumed upper limit of lateral bar stress of 700 MPa, but there was a trend that lateral confinement was more effective for smaller size columns. 3.3.2.3. Buckling of Axial Re-bars A limited number of concentric compression tests of square columns were conducted to examine effect of lateral reinforcement in possibly preventing the buckling of axial reinforcement. Figure 3.52 shows one of 24 specimens. Test parameters were axial bar diameter, tie diameter and tie spacing. Slits were provided between loading stub and test zone with core concrete without cover, in order to transfer compression force through axial bars only. Buckling of bars was observed after yielding in compression for all specimens. Even the largest tie spacing of 8 bar diameter in the test was sufficient to produce compression yielding before buckling took place. Hence the maximum load was always determined by the yield strength of axial reinforcement, 122 Design of Modern High-rise Reinforced Concrete Structures styroform to make a slit in concrete o oV//////Mr test zone with core concrete only 3 JJ(///////XJ( loading stub Fig. 3.52. styroform to make a slit in concrete Column specimens to examine buckling of axial bars. and tie spacing had no effect. On the other hand, vertical displacement at maximum load was affected greatly by the tie spacing. It increased to 1.2 or 2.2 times by reducing tie spacing to 6 or 4 bar diameter, respectively, from 8 bar diameters. Tie spacing of 8 bar diameter was judged to be insufficient to secure deformation capability. A minimum tie spacing of 6 bar diameter is tentatively recommended for high strength axial reinforcement. Buckling could not be prevented by increasing tie bar strength, but higher strength seemed to prevent rapid decrease of compression capacity after buckling. 3.3.3. Concrete, under Plane Stress Condition Finite element method (FEM) in the inelastic range became recently a popular and useful analytical tool for researchers of reinforced concrete. It was considered to be an effective method to fill up gaps between experimental data in the New RC project, as the number of laboratory test specimens had always to be limited because of financial reasons. As FEM was to be used extensively New RC Materials 123 in the New RC project, constitutive equations of high strength concrete under biaxial compression was vitally needed. 3.3.3.1. Biaxial Loading Test of Plain Concrete Plate Tests were conducted using plain concrete plate of 200 mm square with 50 mm thickness, the same size as those tested by Kupfer et aL (Ref. 3.9). Concrete with compressive strength ranging from 60 to 65 MPa was used. Biaxial compression load was applied, as shown in Fig. 3.53, through three layers of telon sheet and cup grease to avoid deformation confinement due to friction on the loading surface. Figure 3.54 shows comparison of the failure criterion of 62 MPa concrete for various stress ratio 0*2/^l- Also shown in the figure is the failure criterion of 30 MPa concrete, expressed by the full line curves. For high strength concrete, the ultimate strength for each stress ratio exceeded uniaxial compressive strength, and it became largest, 37.5 percent greater than uniaxial strength, for stress ratio between 0.2 and 0.52. When stress ratio a%l<J\ was equal to 1, on the other hand, strength increase over uniaxial strength was only 2.5 percent. Thus the trend of strength increase due to biaxial compression for high strength concrete is different from that for normal strength concrete. A new equation for failure criterion of high strength concrete derived from the test is the following. Fig. 3.53. Biaxial loading method for plain concrete plate. 124 Design of Modern Highrise Reinforced Concrete Structures -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 Fig. 3.54. Failure criterion of high strength concrete under biaxial compression. For -0.83 ^cn/U^O 307!/7co)(<Tl/'fee + 1) - 2(<7 1 // c o + 1) = 0 . (3.27) For -1.025 S cri/fco < -0.83 (ai/fco) + [ptlfco) + 2-041 = 0 (3.28) where <j\ and cr2 are principal stresses in compression under plane stress condition and are interchangeable, and fco is the uniaxial compressive strength of the plate. 3.3.3.2. Tests of Reinforced Concrete Plate under In-plane Shear Figure 3.55 shows a reinforced concrete plate specimen subjected to in-plane pure shear loading. Twelve specimens, 600 mm square and 80 mm thick, with doubly orthogonal reinforcement, were made using 40, 70 and 100 MPa concrete, and tested under pure shear loading to examine the effect of concrete strength, reinforcement ratio, steel yield strength, and unequal steel amount in two directions, on the ultimate strength, cracking, stress-strain relationship and mode of failure. New RC Materials 125 Fig. 3.55. Specimen of reinforced concrete plate subjected to in-plane shear. Cracking stress was approximately 0 . 3 V / O B where OB is compressive strength in MPa. With the increase of reinforcement the shear strength increased while deformation capacity was reduced. When the amount of reinforcement exceeded certain value concrete started to crush, and ultimate strength increased more slowly with the increase of reinforcement. For higher strength concrete, the tension stiffening was decreased, and effective strength of concrete was also reduced, down to about 0.35 to 0.4 for 100 MPa concrete. These test data are useful for the calibration of FEM softwares. In the course of New RC project, standard formulation of constitutive equations for high strength concrete and high strength steel, including confined concrete, was compiled as a guideline for FEM users. This guideline will be explained in Chapter 5 of this book. References 3.1. Nagataki, S., Research on high strength concrete and its application (in Japanese), Proc. Japan Concrete Institute Annual Convention 10(1), 1988, pp. 61-68. 3.2. Fukuzawa, K., High strength concrete (in Japanese), Mod. Concrete Technol. Ser., Sankaido, 8, 1987, p. 93. 3.3. Uchiyama, H., Toshisuke, H. and Daisuke, S., Evaluation of transition zone thickness of hardened mortar and concrete and relationship between transition 126 3.4. 3.5. 3.6. 3.7. 3.8. 3.9. Design of Modern Highrise Reinforced Concrete Structures zone thickness and compressive strength (in Japanese), Trans. Japan Concrete Institute 4(2), 1993, pp. 1-8. Morita, S. and Hitoshi, S., Development of high strength mild steel deformed bars for high performance reinforced concrete structural members, Proc, 11th World Conference on Earthquake Engineering, Paper No. 1742, Acapulco, Mexico, 1996. Design guidelines for earthquake resistant reinforced concrete buildings based on ultimate strength concept (in Japanese), Arch. Inst. Japan, November 1990, p. 340. Sargin, M., Ghosh, S.K. and Handa, V.K., Effect of lateral reinforcement upon the strength and deformation properties of concrete, Mag. Concrete Res. 23, June 1971, pp. 99-100. Popovics, S., Numerical approach to complete stress-strain curve of concrete, Cement Concrete Res. 3, 1973, pp. 583-599. Sun, Y. and Sakino, K., Flexural behavior of reinforced concrete columns confined in square steel tube, Proc. 10th World Conference on Earthquake Engineering, Madrid, Spain, 1992, pp. 4365-4370. Kupfer, H. and Hilsdorf, H.K., Behavior of concrete under biaxial stresses, ACI J. 66(8), August 1969, pp. 656-666. Chapter 4 New R C Structural Elements Takashi Kaminosono Associate Director, Codes and Evaluation Research Center, Building Research Institute, Ministry of Land, Infrastructure and Transport, 1 Tachihara, Tsukuba, ttarahi 305-0802, Japan E-mail: kamino@kenken.go.jp 4.1. Introduction The purpose of the Structural Element Committee of the New RC research project was to develop method to evaluate the mechanical performance of structural elements including joints made of high strength concrete and high strength steel, and to propose method to design structural elements for the required performance. Emphasis was placed on the development of evaluation method of structural performance based on rational and logical procedure as much as possible. Existing theories and analytical methods for structural elements made of ordinary strength materials were adopted as the basis of evaluation methods for high strength elements, and experimental works were carried out in order to calibrate theoretical or analytical predictions. Parametric test program based on "design of experiment" approach was avoided as much as possible not to increase the number of specimens and accompanying budgetary burdens. Sections 4.2 to 4.4 of this chapter present results of major experimental programs on beams and columns, walls, and beam-column joints, respectively. Beams and columns here refer to structural members consisting a moment resisting frame. Beams in a moment resisting frame are often called girders 127 128 Design of Modern Highrise Reinforced Concrete Structures in order to distinguish them from floor subbeams, but the word beam is used throughout this chapter. Columns always refer to those in the moment resisting frame, and vertical posts to support gravity load only are excluded. Walls here mean the so-called shear walls to resist lateral load due to earthquake loading. Since such structural walls resist overturning moment in addition to shear force, and structural behavior of such walls is not necessarily governed by shear force, particularly in case of walls in highrise buildings, the simple word wall is used in this chapter. Beam-column joints are not independent elements but they are in fact part of columns in the moment resisting frame. Because of importance of this portion of a frame in resisting lateral load, this part receives particular attention in the recent decades. It is sometimes called as beam-column connection, girder to column joint, girder to column connection, or in some case joint panel. In this chapter, beam-column joint is used throughout. Finally, Sec. 4.5 of this chapter summarizes the work of the Structural Element Committee in a form readily applicable to the practical design, for flexural and shear behavior of beams, combined axial, flexural and shear behavior of columns and walls, and shear and anchorage behavior of beamcolumn joints. 4.2. B e a m s and Columns A limited amount of experimental data were available at the time of the New RC project as to the structural behavior of beams and columns made of high strength materials. Many test programs were organized by the members of Structural Element Committee to clarify various uncertainties in the art of structural performance evaluation. Seven representative test programs are briefly presented in the following subsections. They are as follows. (1) Bond-splitting failure of beams after yielding. (2) Slab effect on flexural behavior of beams. (3) Deformation capacity of columns after yielding. (4) Columns subjected to bidirectional flexure. (5) Vertical splitting of columns under high axial compression. (6) Shear strength of columns. (7) Shear strength of beams. New RC Structural Elements 4.2.1. Bond-Splitting Failure of Beams after 129 Yielding When beams and columns of a moment resisting frame are subjected to antisymmetric bending, the shear force in a member causes bond stress around axial bars to develop tension at one end while developing compression at the other end of the member. This bond stress tends to produce bond-splitting cracks around the axial bars, and ultimately bond-splitting failure as shown in Fig. 4.1. Bond-splitting failure may occur to beams as well as columns, and is more apt to occur to members with short span, or more precisely, small span-to-bar diameter ratio. It can be prevented if dependable bond strength is evaluated, but experimental data of bond-splitting failure and related behavior of beams with high strength material were not available at the time of the New RC project. The study in this section was conducted using beam specimens made of 80 MPa concrete and USD685 re-bars subjected to cyclic reversal of antisymmetric bending. It aimed at (1) examining the relationship between results of Reinforcement Committee on bond-splitting failure (see Chapter 3) and Fig. 4.1. Typical bond-splitting failure of a beam. 130 Design of Modern Highrise Reinforced Concrete 500 Structures 1080/2 Fig. 4.2. Beam specimen details (Specimen No. 1). actual bond-splitting behavior of beams, (2) investigating the effect of double layer reinforcement and span-to-depth ratio (shear span ratio) of beams, and (3) clarifying the relationship between deformation capacity after yielding of beams and bond deterioration. Six beam specimens were prepared. Figure 4.2 shows a representative specimen No. 1. Beams had loading stubs at both ends, and were subjected to antisymmetric flexure-shear without axial loading. Figure 4.3 shows sections of all six specimens. Since the clear span of 1080 mm is same, the span-to-depth ratio is 3 for No. 3, 6 for No. 4, and 4 for all other specimens. Shear reinforcement is 0.39 percent for Nos. 1, 3 and 4, and 0.62 percent for Nos. 2, 5 and 6. The specimen No. 1 is the basic one, and No. 2 is to see the effect of increased lateral reinforcement. Numbers 3 and 4 are for the effect of different span-todepth ratio, and Nos. 5 and 6 are for the effect of double layer reinforcement and different amount of re-bars at top and bottom of the section. Concrete strength at the testing was 83 MPa in compression and 3.0 MPa in splitting tension. Loading was applied through a BRI-type loading rig frequently used in Japan for testing of columns. It gives a specimen the forced antisymmetric deformation by keeping the two loading stubs in parallel position, while moving one of them laterally in cyclic reversal. Lateral deformation at deflection angle of 0.5, 1, 2, 3 and 5 percent was applied two times each before loading to the final failure. New RC Structural Elements 131 Fig. 4.3. Section of beam specimens. Table 4.1 summarizes observed load and associated deflection at flexural cracking, shear cracking, flexural yielding, maximum strength, and critical deformation. Flexural cracks and shear cracks were observed with naked eyes, and two data in Table 4.1 correspond to the cracks at left and right ends of specimens. Flexural yielding was determined by a sudden break of load deflection curves endorsed by re-bar strain measurement at the critical sections. In case of double layer reinforcement yielding of second layer was confirmed in determining this point. The load at flexural yielding was 1.04 to 1.12 times the calculated values of flexural strength (AIJ formula). Critical deflection was defined as the deflection at which the envelope of the load deflection curve reached down to 80 percent of the maximum load. Final failure mode of all six specimens was same. It was bond failure after flexural yielding. Figure 4.4 compares the load deflection envelope curves of all six specimens, where the load was normalized by the yield load Py. Figure 4.5 is similar to Fig. 4.4 except that the deflection was also normalized with respect to the yield Design of Modern Highrise Reinforced Concrete Structures s • 3 S | »H co m O to oo in co m -*r to m I N OS I N CN CO CO r- t- m oo oo to rH r-t i—i i-t <N ( N 1—( i-H I N CN CO <N in CN O TP tO O T-4 m to TP "^ IN tO 00 bOS OS OS X CN I N <N CO M CN m oo t- b- .2SE t- s rj* TP 00 rH rH O «-t o* SN Tf X 6| CO os m ^ i-t i © ' CO i> , iri to ' Load aS 3 £ E ^ 0? ? >" •O 1: 3 •—* lex iel E £ U* _* of -—s rac s 00 lO lO IC OS TP r H TP ( N CN CO OS b- rH T—1 1-H <N IN r H CS rH OS O I N r-t 00 TP to oo OS i—1 to to OS to m in m <N CO ( N CN TP I > : OS OS hX ( N CS CN co ( N CN i n CO t> O CN CO b - CO (N l O OS T P i n TP i - i <N O CO 00 r H TP m O X CO OS CO CN tO rH r H CN O CO (O O <N CO rI N r"* t-H OS CO CO i-l rH 00 Tl* rH i-t O CO C I CO CO to co b- (N t> rH CN CO x m CN I N tear C) in 1-1 m °> CO <N OS 2 JC to t - to t - 2S n" (X) t© TP rH ,-—« h J_ J! U to co -—> H r H <N tO t - O rH OS ( N to x I> to rf* 00 rH rH ^ o O to os m to oo o ^ m co os to co r r TP O TP CO as as m b- m CO O rH b- b- rH O X X f-i TP" X in OS co i n X in os t> r- 05 <N 00 X I N <N X OS O O --• O o o Tf O X lO CO t 00 CN - H OS OS X o o mm o o r H r-t to TP U u o o o o o o m r-t r H TP OS r H o <N i-t to to in to o ^ "? m m in <N TP TP in m to I-H o ^p Tp oo O -3* OS OS o o CO CO rH O CN T H a 3 •—. t-- m OS t O rH V-+ TP tf OS CO Q0 CO •q* CO t O CO CO m to os to m m rH 00 O TP co m o o CO OS o r p CO J£ ft. c Spec ime 132 0 V a c -. CO •"* 0 Q) a c CN 0 0) a c CO *•** '- 0 , Qi a c TP o <u a c lO O V a c to 0 0 0 0 o o Z Z Z Z Z z New RC Structural 1.5 1.0 0 133 fH%: O—O NOI -A—A N02 Q — • N03 0.5 _ 0 — Q N04 £ Elements #—m Nos A — • N06 -0.5 -1.0 1 1 1 1 1 1 -1.5 - 8 - 6 - 4 - 2 0 2 4 6 8 Deflection angle 5/l(%) Fig. 4.4. Normalized load vs. deflection angle. 1.5 T I 1.0 0.5 0 -0.5 -1.0 -1.5 -8 AJ _L _L -4.0 -2.0 0 2.0 Ductility factor 6/Sy I _L 4.0 6.0 Fig. 4.5. Normalized load vs. ductility factor. deflection 6y. Average of positive and negative values in Table 4.1 was taken for this purpose. In these figures the specimen No. 2 with larger amount of web reinforcement shows better behavior than the specimen No. 1, indicating the improved bond by lateral reinforcement retarded the strength reduction and contributed to greater energy dissipation. Specimens Nos. 3, 1 and 4 are the series with different beam depth, and they result in smaller deformability for smaller beam depth. This tendency is more pronounced when the deformability is expressed by the ductility factor. Comparing Nos. 5 and 6 with double layer reinforcement with No. 2 with single layer reinforcement, double layer clearly affects the deformability of the member. It would be necessary to account for greater margin of bond safety to the double layer re-bar arrangement. In Fig. 4.6, critical deflection angle and bond index are plotted for all specimens plus five other specimens from pilot testing in BEL Critical deflection 134 Design of Modern Highrise Reinforced Concrete 2.0 i — r 1.5 : Nos "I- Structures • J O! N 0 4 io *joi . r iCD: N02_. ND6 0.5 [~| 0 BRI pilot tests ' • < ' 2 6 4 J 8 L 10 12 critical deflection angle Rso<%) Fig. 4.6. Bond index vs. critical deflection angle. angle is the deflection angle at which the envelope of the load deflection curve reached down to 80 percent of the maximum load. Bond index is the design bond stress divided by the bond-splitting strength, i.e. inverse of the safety factor for bond. Design bond stress is obtained by assuming a re-bar in tension yielding at one end and in compression yielding at the other end, and effective bond length of clear span minus effective beam depth is taken considering inclined cracking in the tension zone. Bond strength was calculated based on the paper by Kaku et al. (Ref. 4.1), which is similar to the bond strength equation introduced in Sec. 4.5. From the plotting it can be seen that the critical deflection becomes larger for lower bond index. Bond index has been used as an index of inelastic defomability of beams and columns failing in bond-splitting in the ordinary material strength range, and Fig. 4.6 indicates that the bond index can also be used for the same purpose for high strength material. Figure 4.7 is a similar plotting as Fig. 4.6 except that the critical ductility is plotted on the abscissa. Critical ductility is the critical deflection divided by the yield deflection. Although the trend is not very clear, low bond index New RC Structural 2.0 T T Elements 135 1 — b Nfc>3 D O INOl 1.5 TKHf -i D 1 I O. LO 1.0 D N02 N05O • NCH5 0.5 D I BRI pilot teata J l__ 4 6 l8_ i10 12 critical ductility \Uo Fig. 4.7. Bond index vs. critical ductility. generally associates with large critical ductility, except for specimens Nos. 4-6. These are the specimen with small beam depth or those with double layer rebars. The fact that these specimens showed inferior deformability should be duly considered. Conclusions from this test series were as follows. (1) Bond index, as defined by the ratio of design bond stress to the bondsplitting strength, can be a measure of deformability of beams made of high strength materials failing in bond-splitting in the repeated reversal of loading after yielding. If bond index less than 1.0 is secured for a beam, excessive deterioration of deformability in the inelastic range can be avoided. (2) When re-bars are arranged in two layers, bond stress around the outer layer bars accelerates the bond-splitting crack around the inner layer bars, leading to early deterioration in the deformability. (3) A beam with large depth has larger bond index owing to the increase in design bond stress, but deformability of the member is not so much affected as the beam with small depth. 136 Design of Modern Highrise Reinforced 4.2.2. Slab Effect on Flexural Concrete Behavior Structures of Beams Floor slabs, cast monolithically with beam, act not only as a horizontal diaphragm for the building, but also as a flange to the beam in flexure. At a section of the beam where it is subjected to positive bending, the floor slab is in compression and concrete in the floor slab cooperates with that of beam in compression. At a section where it is subjected to negative bending, the floor slab is in tension and slab concrete will crack, but re-bars in the floor slab cooperate with beam axial bars in tension. In both cases, not the entire width of the slab, but certain effective width of the slab, plays the cooperating role. The purpose of the current study was to investigate whether the existing knowledge on the slab effect on flexural behavior of beams, such as initial and inelastic stiffness, yield and ultimate strength, and so on, using ordinary anchor plate (PL-9) — s. r2-DCS<SI50 I::::::::::;::: V 5 500 • ' r- * • I — I) 4-D1.3 § IV)I S / 1 270 S 3 1080 I 300 t -D6@135 i r ^ -D6@145 «* 8~ i 500 WW unto Fig. 4.8. | 300 D e t a i l of s p e c i m e n B S 0 1 . Mil MO I New RC Structured Elements 137 strength material, is applicable to members made of high strength material. Five cantilever beams with floor slabs and one beam without slab of about one third scale were tested. Figure 4.8 shows the detail of a representative specimen of BS01. Beam section is 200 mm by 270 mm with effective depth of 243 mm, and floor slab thickness is 50 mm and width is 1000 mm on one side. The left end of the specimen was bolted to the reaction wall, and a reversed cyclic load was applied in such a way that a point 810 mm away from the critical section of the cantilever is the point of contraflexure. Thus the shear span ratio M/VD is 3.0. Specimen BS01 was made of 70 MPa concrete whose actual strength at testing was 58.4 MPa and Young's modulus 27.0 GPa. Beam axial re-bars were grade USD685 D13 bars with yield point 714 MPa and tensile strength 950 MPa. Stirrups were grade USD980 D6 bars with yield point 978 MPa and tensile strength 1141 MPa. Slab bars were ordinary grade SD295 D6 bars with yield point 346 MPa and tensile strength 527 MPa. Other specimens involved variations of test parameters. BS02 had high strength slab reinforcement of grade USD980 bars. BS03 had slab concrete with ordinary strength of 30 MPa, whose actual strength was 28.8 MPa and Young's modulus 29.8 GPa. BS04 was similar to BS01 except that it had fewer slab distributing bars (perpendicular to beam) of D6 at 255 mm on centers. BS05 had no floor slab. BS06 was a short specimen with 800 mm clear span, and loaded to produce shear span ratio of M/VD = 1.8. Figure 4.9 shows load-deflection curves of three specimens; BS01, prototype specimen, BS02, specimen with high strength slab bars, and BS05, specimen without floor slab. Deflection was measured at the point of contraflexure. Downward load and deflection associated with negative bending in the usual sense at the critical section were taken positive. BS01 had flexural cracks in the slab at load 32.3 kN at which point the deflection angle was about 0.12 percent, and beam bars yielded at the deflection angle of about 1.5 percent as shown in Fig. 4.9(a). Positive load did not increase after beam bar yielding. In the negative direction where the floor slab was in compression, yield load was much lower. Figure 4.10 shows final crack pattern of BS01 specimen. Full lines and dotted lines indicate cracks due to positive loading and negative loading, respecitively. Compared with BS01, BS02 showed much higher yield load, and the load continued to increase after beam bar yielding until the deflection angle reached about 5 percent as shown in Fig. 4.9(b). The behavior in the negative direction 138 Design of Modern Highrise Reinforced Concrete Structures -20 0 20 deflection (mm) (a) BS01- prototype 300 B S 0 2 ; /Beam bar yielding 200 Flexural cracking. 100 -200 -60 300 -40 20 0 20 deflection (mm) (b) BS02- high strength slab bars BS05 ; 200 100 ' 60 _-Beam bar yielding Flexural cracking _ 0^P' 0 I I -100 -200-60 -40 -20 0 [ • 20 41 deflection (mm) (c) BS05- without slab Fig. 4.9. Load-deflection curves. was very similar to BS01. BS05 specimen without floor slab had smaller initial stiffness, and smaller cracking and yield loads as shown in Fig. 4.9(c), which were similar to those in the negative direction of BS01 or BS02. BS03 with ordinary strength concrete in the slab, and BS04 with fewer number of slab distributing bars, showed quite similar behavior as BS01. BS06 with short New RC Structural Elements 139 R=l/20 Fig. 4.10. Crack pattern of BS01. shear span showed similar behavior as BS01, if the deflection was expressed in terms of deflection angle (deflection of the point of contraflexure divided by the distance to the point). Initial stiffness, inelastic secant stiffness at yielding, and cracking load in the positive direction were calculated assuming three kinds of slab effective width, and compared with the measured or observed values in the test in Fig. 4.11. Initial stiffness was calculated considering elastic uncracked flexural and shear deformations based on the effective span length assuming the fixed end at one quarter the beam depth away from the critical section. Inelastic stiffness at yielding was obtained by multiplying ay, yield stiffness reduction factor originated by S. Sugano (Ref. 4.2), to the above-mentioned initial stiffness ay = (0.043 + 1.64npt + QMZa/D){d/D)2 (4.1) where ay : yield stiffness reduction ratio n : modular ratio of steel to concrete Pt • tensile reinforcement ratio to be obtained as tensile re-bar area divided by uncracked concrete area 140 Design of Modern Highrise Reinforced Concrete 2.22.0- • initial stiffness 4- yield stiffness <^> cracking load $ 1.6| l A •a u5»>- a O O 0.0 o •v 2 0.8§ 0.6. n 8" 0.4 0.2 Structures D ba=0.1L • 1 1 9 + D ba=0.3L -i P.. P.. fi ba=0.5L r~ 1 1 2 3 4 specimen No. Fig. 4.11. Comparison of measured vs. calculated values of initial stiffness, yield stiffness and cracking load. a : shear span length (M/V) which is same as the distance to the point of contraflexure D : beam depth d : effective beam depth to the centroid of tensile reinforcement. Cracking strength in Fig. 4.11 was calculated by the theory of elasticity assuming tensile strength of concrete as follows cat = Q.hl^B (4.2) where cat : tensile strength of concrete (MPa) <JB '• compressive strength of concrete (MPa). In Fig. 4.11, effective width was assumed in three ways, i.e. beam width plus twice the cooperating slab width ba, where cooperating slab width ba was taken to be 0.1L, 0.3L, and 0.5L (L: distance to the point of contraflexure). As seen, initial stiffness is best estimated by ba = 0.1L, yield stiffness by ba = 0.3L, and cracking strength by ba = 0.5L. Yield load and ultimate load was also calculated and compared with test results in the positive direction in Fig. 4.12. Entire slab width was assumed to be effective in these calculations, and the moment lever arm in the critical section was approximated by 7/8 times effective depth for yield load, and 0.9 times effective depth for ultimate load. As seen in Fig. 4.12, the assumption of entire width to be effective is a good approximation, slightly on the safe side. Itemized conclusions are as follows New RC Structural Elements 141 0 yield load 1.8- + ultimate load 1.61.41.2- D + 6 ? S a 0.80.60.4- v— without slab 0.2" full width o.o- "'!"" - _\ - specimen No. Fig. 4.12. Comparison of measured vs. calculated values of yield load and ultimate load. (1) High strength of slab re-bars contributes to the beam strength under negative bending (slab in tension). (2) High strength of slab concrete does not contribute to the beam strength. (3) Amount of slab distributing bars (bars perpendicular to the beam axis) has no effect on the beam strength. (4) Slab effective width based on cooperating width on one side of beam of 0.1L, 0.3L and 0.5L, appears to predict well the initial stiffness, yield stiffness, and cracking strength, respectively, under negative bending (slab in tension). (5) In calculating yield load and ultimate load under negative bending, effective slab width may be assumed to be equal to the entire width. 4.2.3. Deformation Capacity of Columns after Yielding The most frequently observed failure of columns in earthquake damage used to be the premature shear failure before flexural yielding. As structural engineers became aware of the necessity of preventing premature shear failure by providing shear resistance to cover shear demand corresponding to mechanism formation, this type of failure seems to decrease in recent earthquake disasters. On the other hand, experimental research works conducted in 1970's and 1980's demonstrated the possibility of shear failure of columns in the inelastic post-yield reversal. In this case the column once reaches the flexural yielding without premature shear failure, but it finally fails in shear in the reversal of post-yield deformation amplitude. This phenomenon has been gradually understood as the reduction of shear strength with respect to inelastic deformation. Shear strength of a member is not a unique constant value to the 142 Design of Modern Highrise Reinforced Concrete Structures member, but it is a function of inelastic deformation, or in other words, a function of ductility factor of the member. Even though shear strength at a small deformation exceeds the shear force associated with the flexural yielding, it keeps dropping while the flexural shear remains more or less constant as the inelastic deformation increases. Eventually shear strength and shear demand would meet, and this determines the end of the inelastic deformation. The above-mentioned concept has been incorporated in the recent design guidelines in Japan (Ref. 4.3). Shear strength is expressed by an equation based on the truss model and arch (or strut) model concept, where the reduction of shear strength is empirically expressed by reduction of effective concrete strength and variation of concrete strut inclination angle of the truss with respect to inelastic deformation. The empirical expressions were confirmed by available test results of beams and columns, but majority of them were from test specimens of ordinary strength materials. The experimental program of this section was organized to find the applicability of the guideline equation to high strength RC columns, and also to examine the effect of axial load on the deformation capacity and effect of reinforcement details on the resistance to vertical splitting failure of columns. 1300 300 i MI n n « v i Specimen S6. S7 9 Specimen S8, S9. S10 Fig. 4.13. Column test specimens. New RC Structural Elements 143 Five specimens, marked S6 through S10, will be introduced here. Figure 4.13 shows the detail of specimens. S6 and S7 are 300 mm square columns with the height of 900 mm, hence the shear span ratio of 1.5. S8, S9 and S10 are 250 mm square columns with the height of 1000 mm, hence the shear span ratio of 2.0. Concrete strength is 80 MPa (measured strength ranged from 75 to 77 MPa), axial reinforcement yield point is 396 MPa for all specimens, and lateral reinforcement yield point is 1260 MPa for S6 and S7, and 874 MPa for S8, S9 and S10. Axial load was kept constant for all specimens except for S7. In terms of axial load ratio 77 as defined below 77 = N/(AgaB) (4.3) where N : axial load Ag : gross sectional area as '• concrete strength, 77 was 0.50 for S6, and 0.15, 0.35, and 0.50 for S8, S9, and S10. Specimen S7 was subjected to constant compression of 77 = 0.50 in terms of axial load ratio when the lateral loading was positive (same as S6), and no axial load was applied when loaded to negative direction. Loading set-up of Fig. 4.14 was used. Axial load was supplied by a 2000 tonnes structural testing machine, while lateral load was given by a horizontal oil jack through an L-shaped rig which was kept in parallel position to the test bed by means of a pair of auxiliary oil jacks. Fig. 4.14. Test set up for a column specimen. 144 Design of Modern Highrise Reinforced Concrete l/200rad. l/100rad l/50rad. Structures S9 1/lOOrad. S10 l/100rad. Fig. 4.15. Cracking of specimens at maximum load. Horizontal loading was controlled by the deformation angle which is the lateral displacement divided by clear height of column. Two cycles each at 0.25, 0.50, 1.0 and 2.0 percent of deflection angle were applied before loaded to the final failure. Figure 4.15 shows cracking of specimens at the stage of maximum loading. In all specimens axial bars yielded in compression first, and maximum load was reached by the crushing of concrete in the compression side. Since S6 reached its maximum load at a very early stage, it shows some flexural cracks and vertical cracks along the central axial bar only. These vertical cracks joined the cracks in the end compression zone in the later loading stage, and formed the diagonal cracking zone. This was quite similar to S7 except that the diagonal crack formed under positive loading only. S8 reached its maximum in the 2 percent cycle, while S9 and S10 reached the maximum in the 1 percent cycle. S10 had some vertical cracks at the maximum load. Figure 4.16 shows lateral load vs. lateral deformation angle relationship for all specimens. Calculated ultimate load was exceeded by tests for all specimens. Deterioration after attaining maximum load was more pronounced for S6 than S7 in the positive direction, which was essentially loaded into positive direction only because the negative loading on S7 had little effect on its ultimate capacity. Comparing S8, S9 and S10, it is clear that axial load level had controlling effect on the behavior after maximum load, and higher the axial load, smaller the deformation capacity. Deterioration due to high axial compression was also endorsed by the measurement of axial deformation. For low axial load of S7 in the negative New RC Structural Elements SB il=0.5 •:• \---jf •2 1 0 1 2 3 deformation angle (%) (a)S6, 17 = 0.50 ••"•• S7 600 n=o.o. 5 400 3 ral load i. a-200 -« -400 P)"-^ J ~ Xtt'wl' •////// 2 !i W J\ / fS\ \ L~*r /J/! \ | } i | -600 •800 • 2 - 1 0 1 2 3 4 deformation angle (.%) (b)S7, 7j = O.MXpos.) 0.0 (neg) •""• 400 2 ss n-o. 15 = a <S 200 ^ ^ ^ 3 VJ^L-^^ JeS-H' ! o ed •§-200 •400 ==£! ^I^fe * 1 1... • 3 - 2 - 1 0 1 2 3 deformation angle (%) 4 (c)S8, 7j = 0.15 Fig. 4.16. Load-deformation curves. 145 146 Design of Modern Highrise Reinforced Concrete 400 Structures S9 n - o . 35 2 200 i::::::t:::.T 0 'A/~~. ft: 200 400 •4 -3 1 -2 _i*~*^ f 0 i 4- '") 3 4 5 -•-?" ••-: ; — • ? — —j ? 4 5 1 2 6 deformation angle (%) (d)S9, 7) = 0.35 400 I S10 n=o. 5 200 / / 200 •} ]— - 2 - 1 0 1 2 •:•••• 400 !":>$» •4 -3 3 6 deformation angle (%) (e)S10, 7| = 0.50 Fig. 4.16. (Continued) direction and S8, axial deformation was negative (elongation), while contraction was more rapidly accumulated in case of higher axial compression. Measurement of lateral re-bar strain indicated that no lateral reinforcement yielded up to the failure of the specimen. For S8 and S9 that did not develop diagonal cracks the strain of hoops at the midheight zone was small, but for other specimens strain at midheight was larger than the strain at yield hinge zones which was not influenced by the axial load. As the direct results of testing, following conclusions can be stated. (1) Compared to constant axial load, specimen with varying axial load with the same maximum value showed better deformability. (2) Higher the level of axial compression, smaller was the deformation capacity of columns with shear span ratio of 2.0. (3) Columns with shear span ratio of 1.5 had vertical cracks which may lead to vertical splitting failure. The slender column under high axial load also had some vertical cracks, but not so extensive as in case of short columns. New RC Structural Elements 147 The more important contribution of these test results was that they were used, together with other test series, to develop shear strength equation for high strength RC members as a function of inelastic deformation. This will be explained in Sec. 4.5. 4.2.4. Columns Subjected to Bidirectional Flexure Columns in a space (three-dimensional) moment resisting frame are subjected to bidirectional flexure and shear by horizontal earthquake motions in addition to vertical axial loading due to gravity load. When the level of axial load is not so high and the column behavior is controlled by yielding of axial re-bars, columns are quite stable even under bidirectional flexure, and the behavior can be analyzed by simple models such as the one based on the plasticity theory. When, however, the column is a lower story column of a highrise building and the column behavior is more directly covered by the concrete in compression, bidirectional flexure gives a more severe condition to the column than the unidirectional flexure, and inelastic deformation capacity of the column is apt to be impaired. There have been some studies on this kind of behavior of columns made of ordinary strength material. The study introduced in this section involves tests of high strength columns subjected to high axial load and bidirectional bending, and aims at establishing the criteria for axial load limitation in the column design. The test program consists of testing four identical columns shown in Fig. 4.17. Column section is 250 mm square and 1250 mm high. Concrete with compressive strength of 90 MPa and axial and lateral reinforcement with yield strength of 714 MPa and 1000 MPa, respectively, were used. Specimens were placed in a loading set-up shown in Fig. 4.18, and loaded axially and horizontally in two directions. Type of horizontal loading, loading path, and level of axial load were the test parameters, and the specimen mark expressed these test parameters as shown in Table 4.2. The first letter S or C corresponds to the type of loading. S is for antisymmetric loading with the point of contraflexure at midheight of column, and so the shear span ratio is 2.5. C is for cantilever loading with the point of contraflexure at the soffit of upper stub, and the shear span ratio is 5.0. The second letter A or B refers to the loading path. A is for unidirectional loading in NS direction only, and load was cyclically reversed twice each at deformation angles of 0.125, 0.25, 0.5, 1.0, 1.5, 2.0 and 3.0 percent before 148 Design of Modern Highrise Reinforced Concrete Structures I 323 I 250 I 325 I Fig. 4.17. Column specimen for bidirectional loading test. Fig. 4.18. Test set-up for bidirectional loading. increased to final fracture. B is for bidirectional loading into directions, and the two deformation paths shown in Fig. 4.19 alternatively at each deformation angle as in the unidirectional last two digits corresponds to the axial load ratio rj as defined NS and EW were applied loading. The by Eq. (4.3). New RC Structural Elements 149 Table 4.2. Column specimens under bidirectional loading. Axial Load Specimen Type of Loading M/VD SA35 antisymmetric 2.5 Loading Path Load N (kN) Ratio 85.4 1870 unidirectional 0.35 CA35 89.2 1950 CB35 cantilever Concrete Strength <TB (MPa) 5.0 bidirectional 3470 CB60 0.60 92.5 * : r, = N/(AgcB) Ag = gross sectional area Cycle No M L — m '•' ' R i --«£- Cycle No.2 7 V i E V Fig. 4.19. Displacement path in bidirectional loading test. The value of 77 was 0.35 for the first three specimens and 0.60 for the fourth specimen. Figure 4.20 shows shear force vs. deformation (drift) angle and axial shortening vs. deformation angle relationship for specimens SA35 and CA35, both subjected to unidirectional loading. SA35 was loaded while keeping the upper and lower stubs in parallel position to produce antisymmetric bending in the column. Flexural cracks were formed in the 0.25 percent cycle, and corner concrete crushing was found in the 0.5 percent cycle. Compression re-bars yielded at 0.7 percent deformation, maximum load was reached at 1.0 percent, 150 Design of Modern Highrise Reinforced Concrete 400i 1 1 1 1 1 Structures r NS drift angle (%) (a) Specimen SA35 NS drift angle (%) (b) Specimen CA35 Fig. 4.20. Shear force vs. drift angle and axial shortening vs. drift angle. and a vertical splitting crack was formed along the central re-bars at the second negative cycle of 1.5 percent, as noted in Fig. 4.20(a). The specimen did not pick up load beyond 60 percent of maximum load in the following 2 percent deformation cycles, probably due to this vertical splitting crack. Axial shortening started to become conspicuous at 2.5 percent deformation, and increased quite rapidly after 3 percent to the final stage where axial load could not be carried. CA35 was loaded so that the point of zero moment coincided with the top of the column clear height, hence the shear force associated with the same moment at column bottom was half as much of the specimen SA35. The shear force in Fig. 4.20(b) is much smaller than Fig. 4.20(a) for this reason. Flexural cracks appeared in the 0.5 percent deformation cycle, and corner concrete started to crush in the 1.0 percent cycle. Maximum load was reached at 1.5 percent deformation and axial shortening started to increase after 2.5 percent loading to the final failure. In the 3 percent deformation cycle a lateral reinforcement broke, and axial load could not be carried after this point. Figure 4.21 shows shear force vs. deformation (drift) angle relationship in EW and NS directions, and axial shortening vs. NS deformation angle relationship, for specimens CB35 and CB60 specimens, both subjected to bidirectional New RC Structural 300 200 i 1 1 400 — | CE35 100 o i , _L •300 •400 j i $ 11 u r — -+~ -•w 0 "•~**- -100 i -200 i * l 100 -+-J •100 •200 200 151 i — i — i — .. CB60 300 ii i 400 —1 Elements -300 i I .. -400 - 2 - 1 0 1 2 EW drift angle (%) 400 ~ -s 300 z a 200 a S 100 •S S o £•a -loo a -2oo T i i 1 0 1 2 EW drift angle (%) 1 i 1 ; CB60 ' i, ~~^-i.Mi y i i !- ; ] '*~i—L. 1 -300 axial shortening (mm) _. •2 1 0 1 NS drift angle (%) ..* -,, , i i \ i ' ' r — i • ! 1 i 1 - ! - 2 - 1 0 1 2 NS drift angle (%) (a) Specimen CB35 (b) Specimen CB60 Fig. 4.21. Shear force vs. drift angle in E W and NS directions and axial shortening vs. NS drift angle. loading. CB35 showed flexural cracks in the 0.25 percent deformation cycle and corner concrete crushing in the 0.5 percent cycle. In the 1 percent cycle crushing and axial shortening became more pronounced, and in the 1.5 percent cycle cover concrete spalled off all around the periphery of the critical section. Testing concluded in 2 percent cycle where axial load could not be maintained. In Fig. 4.21(a), effect of previous deformation in the perpendicular direction is clearly seen. For example in the second 1 percent cycle to the EW negative direction, the load was very low due to the previous loading in the NS direction. Axial shortening accumulated as the result of inelastic loading into any directions, that is, more rapidly than the companion specimen CA35 under unidirectional loading. 152 Design of Modern Highrise Reinforced Concrete Structures CB60, subjected to very high axial compression, started to crush at corners even at the initial 0.125 percent deformation cycle, and re-bar compression yielding was noticed in the 0.25 percent cycle. In the 0.5 percent cycle flexural cracking appeared, and maximum load was reached. Axial shortening increased rapidly in this cycle, almost to the level of 1.5 percent cycle of CB35 specimen, and the specimen CB60 failed violently when only three quarter of 0.5 percent cycle was completed, accompanied by breaking of lateral reinforcement. Buckling of four corner bars was confirmed after the testing. The observed behavior as described above is believed to be a valuable objective for analytical studies, and also an effective evidence in establishing the criteria for axial load limitation. Particularly important conclusion from this point of view is, first, that high axial load whose ratio to A9(TB is 0.6 produces compression failure at a relatively small drift angle of 0.5 percent under bidirectional forced deformation, and second, that axial shortening is more pronounced under bidirectional loading compared to columns under unidirectional loading. 4.2.5. Vertical Splitting of Columns High Axial Compression under In the previous Sec. 4.2.4, one of four column specimens, SA35, showed a vertical splitting crack at the second cycle of deformation angle amplitude of 1.5 percent. It was a specimen subjected to antisymmetric bending. The vertical crack appeared along the plane of central axial reinforcement placed at a perpendicular location to the loading direction, and caused drastic loss of load carrying capacity of the column. After the conclusion of the loading test the specimen was cut along the loading direction, and internal crack distribution was examined, to find that the vertical splitting crack extended to the central portion of the section, and that it virtually divided the specimen into two pieces vertically. This kind of vertical splitting crack had been observed in past experiments, but the phenomenon had not been completely explained. A study was conducted therefore to give some more lights to the mechanism of formation of this kind of vertical splitting crack, and to the expected strength of columns against this cracking, utilizing available test results as well. Figure 4.22(a) shows idealized deformation of a column in which yield hinges have formed at both ends and splitting crack has appeared along the New RC Structural Elements 153 Fig. 4.22. Idealized deformation and assumed forces. center line. The column is subjected to axial load N and tensile yield force in the section is T, hence the compression resultant is N + T acting at the compression side of the yield hinge. Q is the column shear force. The forces acting in the tensile hinge zone may be expressed as in Fig. 4.22(b), where A T denotes bond forces along the tensile reinforcement, Tw is the resultant of forces in the lateral reinforcement, and Cp is the resultant of compression forces in the concrete struts, all in the tensile hinge zone. If we assume AT is zero considering that concrete cover in the hinge zone has spalled off all around the section due to cyclic reversal of loading, the resultant of Tw and Cp must be zero from the equilibrium of the tensile hinge zone. Then we obtain simplified assumption of forces shown in Fig. 4.22(c), before formation of the splitting crack. Thus we define forces acting along the potential splitting crack plane of a column in antisymmetric bending to be, as shown in Fig. 4.23(a), shear force N + 2T and normal force Q. Splitting crack plane has the area of column height minus depth D times the width of core concrete as shown in Fig. 4.23(b). Then the average shear stress acting on the potential crack plane can be expressed by the following equation TS = (N + 2T)/AC where TS : the average shear stress N + 2T : shear force acting on the plane (4.4) 154 Design of Modern Highrise Reinforced Concrete Structures T V Q N+2T'^ - \ J "t\: D 5 ,N+2T \7////7/W////\ \W///W///A Q N+2T • potential si "»potei cracking plane cracl T— W/////////////A |N+T (a) Assumed model with forces (b) Assumed section of splitting crack Fig. 4.23. Assumed model and crack section. Ac : area of crack plane as explained above. In case of cantilever type bending of previous subsection, this equation has to be modified appropriately. The splitting crack strength of the vertical plane may be expressed by the combination of concrete term and normal force term. They are assumed as follows Tsu = ay/cTB~ + P(Q/AC + p) (4.5) where splitting crack strength concrete compressive strength column shear force Q area of crack plane Ac confining stress of concrete from lateral reinforcement P a, 13 numerical coefficents. The first term on the right hand side corresponds to shear cracking strength of plane concrete expressed as to be proportional to the square root of compressive strength, and the coefficient a may be assumed to be about 1.8 which gives shear strength of 30 to 40 percent of compressive strength to the ordinary strength concrete. The second term has a form of normal stress acting on the plane multiplied by a friction coefficient /?. Friction coefficient of a concrete crack may involve aggregate interlock, and (5 may be assumed as high as 1.0. As to the confining stress p from lateral reinforcement, it is a well known OB New RC Structural Elements O • 2.0 - 155 ' No sub-hoops, uncracked I No sub-hoops, cracked /^v * Sub-hoops, uncracked J)L * Sub-hoops, cracked 1.0 CB60 — SA35 O ^ O CA35^CB35 0 5r"03 X 0.4 X _L 0.5 0.6 axial load ratio Fig. 4.24. Splitting crack stress vs. axial load ratio. observed fact that lateral confining stress is high in the hinge zones but it is low outside the hinge zones including point of contraflexure. Hence we may assume p = 0. Figure 4.24 shows relationship between splitting crack stress vs. axial load ratio for specimens in the previous subsection as well as other existing data. Splitting crack stress is the average shear stress of Eq. (4.4), and it is normalized by the splitting crack strength of Eq. (4.5), where a = 1.8, /3 = 1.0 and p = 0 were assumed. Axial load ratio is same as Eq. (4.3). Plotted in Fig. 4.24 are specimens without or with subhoops, which correspond to circle or triangle marks in the figure. Specimens that formed vertical splitting crack are marked black, while those that did not form crack are marked white. It is clear that columns tend to form vertical splitting cracks when r s approaches or exceeds r s u , and whether the column is provided with subhoops or not does not make much difference. Also the axial load ratio is irrelevant as long as it is incorporated in the form of Eq. (4.4). Needless to say that the area Ac in Eq. (4.4) depends on the column height, and TS becomes larger for shorter columns. On the other hand, r s is small for cantilever type columns in the preceding subsections. 156 Design of Modern Highrise Reinforced Concrete Structures It may be concluded that the mechanism of the formation of vertical splitting crack may be explained by the proposed model of Fig. 4.23 and Eqs. (4.4) and (4.5), however crude it is. 4.2.6. Shear Strength of Columns Shear strength of beams and columns of a moment resisting frame plays double roles, one in the pre-yield (elastic) range and another in the post-yield (inelastic) range. For members in which yield hinges are not expected to occur, premature shear failure must be prevented. For this purpose it only suffices to equate the shear force associated with the formation of yield mechanism to the shear strength of the member in the elastic range, i.e. shear strength at the pre-yield shear failure, which may be referred to as "elastic" shear strength. On the other hand, for members in which yield hinges are expected to occur, hinge rotation corresponding to the maximum anticipated deformation must be ensured. According to the recent knowledge of shear strength in the inelastic range as explained in Sec. 4.2.3, shear strength of a member is not a unique constant but is a decreasing function of the inelastic deformation of yield hinge. It is necessary to find out shear strength corresponding to the required inelastic Fig. 4.25. Shape and size of column specimen. New RC Structural Elements 157 deformation, which may be termed as "inelastic" shear strength. By equating the shear force associated with the formation of yield mechanism to this inelastic shear strength, inelastic deformation corresponding to the inelastic shear strength is ensured to occur to the member. The study in this subsection is related to the elastic shear strength of columns of high strength RC, while the one in the next subsection is related to the inelastic shear strength of beams of high strength RC. Experimental program of columns involve eight column specimens made of 60 MPa concrete, as shown in Fig. 4.25. Column section is 300 mm square and clear height is 900 mm. Figure 4.26 shows two sections of column, reinforced laterally with D6 or D10 bars, both fabricated into closed form by flush-butt welding. Axial re-bars are USD685 12-D19 bars with actual yield strength of 757 MPa, while lateral re-bars of two different grades, SD345 and SBPR 785/930 are used. Table 4.3 lists parameters for eight column specimens, and actual yield strength of lateral reinforcement are shown. As seen in Table 4.3, major testing parameters are axial load ratio, with the definition of Eq. (4.3), of 1/6 and 1/3, -i—i—^- =q .. W_Jm_L_<m._m v J I i - ^ - < N •to-i—ff dDh=et 40 I 70 J40 ! 40! 70 140 3S_ (a) Using D10 lateral bars 4 1—I—I ^ (b) Using D6 lateral bars Fig. 4.26. Section of column specimen. 158 Design of Modern Highrise Reinforced Concrete Structures Table 4.3. Column specimens for shear strength test. Specimen Axial Load Ratio 6-1 6-2 6-3 6-4 3-1 3-2 3-3 3-4 Lateral Bar (%) (MPa) (MPa) 1/6 D6 D10 D6 D10 0.53 1.19 0.53 1.19 402 409 931 1091 2.13 4.87 4.93 12.98 1/3 D6 D10 D6 D10 0.53 1.19 0.53 1.19 402 409 931 1091 2.13 4.87 4.93 12.98 Pv, Pw: lateral reinforcement ratio (%) awy: yield strength of lateral reinforcement (MPa) and amount and yield strength of lateral reinforcement. Compressive strength of concrete at the testing age was 73.5 MPa, and tensile strength was 4.9 MPa. All columns were tested under constant axial load and incremental reversal of lateral load while keeping the top and bottom stubs of column in the parallel position. Actual axial load was 1100 kN and 1950 kN for two levels of axial load ratio. Figure 4.27 indicates lateral load (column shear) vs. deformation angle relationship of four columns tested under axial load ratio of 1/3 (more exactly it was 0.30), together with points of flexural and diagonal cracking and maximum load. Lines of P-delta effect and computed strengths, as explained later, are also shown. General appearance of load-deformation curves of other four specimens under axial load ratio of 1/6 was quite similar to these four columns. All specimens first showed flexural cracks at the critical sections, followed by diagonal cracks in the central portion. Load at cracking was affected by the axial load ratio. Flexural cracks appeared for axial load ratio of 1/6 at 225-275 kN, and for 1/3 at 350-425 kN. Diagonal cracks appeared for axial load ratio of 1/6 at 350-390 kN, and for 1/3 at 475-500 kN. The increase of cracking loads due to axial load was in good accordance with the analysis based on fundamental theory of strength of materials. All specimens failed in shear before formation of flexural yield hinges. However the failure mode was significantly affected by the lateral reinforcement strength denoted by pw • awy as listed in Table 4.3. When the lateral reinforcement strength is low, columns failed in a typical shear failure, but those with high lateral reinforcement strength failed in bond-splitting failure New RC Structural Elements 159 in the flexural compression zones. Deformations at the maximum load and at the failure were slightly larger for higher lateral reinforcement strength. Axial load ratio did not affect the mode of failure. Table 4.4 lists measured and calculated maximum loads. Looking at measured loads, it is clear that axial load ratio has relatively small influence; the maximum load is more significantly influenced by the amount of lateral 1000 800 600 400 2 & 200 a> M o u jS -200 tn -400 -600 -800 -2 1000 1 0 1 2 3 deformation angle (%) (a) Specimen 3-1 4 5 6 4 5 6 800 600 200 <8 0 she 400 1^ c5 -200 -400 -600 -800 - 2 - 1 0 1 2 3 deformation angle (%) (b) Specimen 3-2 Note: V : flexural crack, T : diagonal crack, Fig. 4.27. M: max. load L o a d - d e f o r m a t i o n c u r v e s for four c o l u m n s p e c i m e n s failing in s h e a r . 160 Design of Modern Highrise Reinforced 10001 ; Concrete Structures deformation angle (%) (c) Specimen 3 3 1 i ; deformation angle (%) (d) Specimen 3-4 Note: V: flexural crack, T: diagonal crack, M: max. load Pig. 4.27. (Continued) reinforcement and its yield strength. In terms of lateral reinforcement strength, Pw • &Wy, it is interesting to note that the second and the third specimen in each axial load group, provided with approximately same amount of pw • awy, showed different maximum load. The second specimen with large amount of weak re-bars is always stronger than the third specimen with small amount of strong steel. This fact will be investigated in the more general study of Sec. 4.5. New RC Structural Elements 161 Table 4.4. Comparison of measured vs. calculated max. load. Calculated Measured Specimen Max. Load Q(kN) 6-1 6-2 6-3 6-4 3-1 3-2 3-3 3-4 Flex. Strength QF (kN) Shear Strength Qs (kN) Bond Strength QB (kN) 465.0 665.5 570.0 704.5 787.8 321.6 507.3 510.0 649.0 851.9 919.1 816.8 926.3 532.0 706.5 585.0 744.0 898.3 321.6 507.3 510.0 649.0 851.9 919.1 816.8 926.3 Table 4.4 also lists various calculated values of the column strength. Flexural strength was obtained by ordinary ultimate strength theory, and it was much greater than measured strength for all specimens. Shear strength calculated by the ultimate strength guidelines (Ref. 4.3) was found to be on the safe side for all specimens, particularly so for those with low yield strength lateral re-bars. Bond strength in Table 4.4 was calculated by Fujii-Morita equation which is the original form of bond strength equation in Sec. 4.5. Calculated bond strength was much higher than observed maximum load, indicating that the observed bond-splitting failure in the flexural compression zone was different from the bond-splitting failure along the axial bars in entire column length. Figure 4.28 shows relationship between maximum load and lateral reinforcement strength or axial load. The ordinate shows maximum load Q, and positive abscissa shows lateral reinforcement strength pw • awy and negative abscissa indicates axial load N. Open circles and squares denote observed values, while flexural, shear and bond strengths as listed in Table 4.4 are shown by variety of lines. Flexural strength QF is not a function of pw -awy, and shear strength Qs is not a function of N. Bond strength QB is shown only on the right hand side. Also entered is another shear strength prediction Q's, calculated by a theory by Wakabayashi and Minami (Ref. 4.4), which is more complicated than the ultimate strength guidelines (Ref. 4.3) as it considers effect of axial load also. When the observed values are compared with calculated lines, it can be concluded that Qs estimates the shear strength generally on the safe side without reflecting the effect of axial load, and that Q's estimates the shear strength on the unsafe side, though reflecting duly the effect of axial load. 162 Design of Modern Highrise Reinforced Concrete I l l 3000 2000 1000 axial load N (kN) I 0 Structures I 5.0 l I 10.0 15.0 pw • or wy(MPa) Fig. 4.28. Relationship between max. load Q and lateral reinforcement strength pw • o-wy or axial load N. Summarizing the findings from this experiment, one might note as follows. (1) Shear strength of columns with 60 MPa concrete increases with pw • awy but not in proportion to it. (2) For the same amount of pw • awy, it appears that greater pw is more advantageous than higher awy. (3) Prediction by ultimate strength guidelines is on the safe side, and axial load effect, though small, is not reflected. Wakabayashi-Minami theory accounts for the axial load correctly, but overestimates the test results in general. 4.2.7. Shear Strength of Beams In a preliminary investigation of the New RC project it became clear that the shear strength of a beam made of high strength concrete up to 120 MPa can be estimated fairly accurately by the equation in AIJ guidelines (Ref. 4.3), if the effective compressive strength of concrete is appropriately evaluated. Effective compressive strength for pre-yield shear strength, or "elastic" shear strength, of high strength concrete may be evaluated by an equation proposed by CEB, as explained later. On the other hand, beams in a building are mostly designed as New RC Structural Elements 163 yielding members, and appropriate ductility is ensured by considering "inelastic" shear strength which is a decreasing function with respect to the inelastic deformation. The equation in AIJ guidelines is provided with two decreasing elements for this purpose; one is the inclination angle of concrete struts in the truss mechanism, and another is the effective compressive strength of concrete. The study introduced in this subsection was conducted with the aim of establishing a unified expression of effective compressive strength of concrete for elastic as well as inelastic shear strength of beams made of high strength concrete. In order to evaluate the effective compressive strength continuously from elastic to inelastic range, four beam specimens were tested under flexural shear, with the same sectional dimensions, same shear reinforcement, same concrete, and with the only difference in yield strength and amount of axial reinforcement. As shown in Fig. 4.29, specimens have section of 150 mm by 300 mm, and the first specimen BE-1 has top and bottom axial re-bars of 5-D16 SD980 steel (actual yield point was 970 MPa). Other three specimens have top and bottom axial re-bars of 4-D16, with different yield strength; BE-2 is provided with SD980 steel same as above, BE-3 with SD685 steel (actual yield point was 654 MPa), BE-4 with SD 390 steel (actual yield point was 424 MPa). Shear reinforcement of four specimens are identical, consisting of four legs of closed 2400 Reflection measuring point specimen BE-1 ^-5-Dl6 Fig. 4.29. Dimension and reinforcement of beam specimens. 164 Design of Modern Highrise Reinforced Concrete Structures stirrups of D6 SD295 bars (actual yield point was 337 MPa) spaced at 70 mm, with shear reinforcement ratio of 1.22 percent. Concrete with nominal strength of 60 MPa was used for all specimens, whose actual strength was 69.3 MPa. Beams were loaded in a test rig in such a way that the point of contraflexure came to a point shown in Fig. 4.29, i.e. 600 mm from the critical section at the left end of 900 mm clear span. Under this loading the shear span ratio was 2.0, and a yield hinge would form at the left end only. Deflection of the point of contraflexure was measured relative to the fixed left stub of the specimen. Figure 4.30 shows load-deflection curves for four specimens. Specimen BE-1 with the largest flexural strength, shown in Fig. 4.30(a), had shear cracks at rotation angle 0.5% 1% 1.5% 2% 15 -10 -5 0 5 deflection (mm) (a) Specimen BE-1 rotation angle 0.5% 1% 1.5% 2% Xl' Kll^'l' 1 -5 0 5 deflection (mm) (b) Specimen BE-2 Fig. 4.30. Load-deflection curves for beam specimens. New RC Structural rotation angle 0,5% .1% L 5 % 2 % 300 i i -30 ii 165 4% i ) i •i i | i i i i -20 10 0 10 deflection (mm) (c) Specimen BE-3 20 rotation angle 0.5% 1% 1.5% 2% 200 100 Elements - J. j. i : : 30 4% \lT£j^Cliit' i wFriJr-4 mffltf^^uL^i f&jhr—_^/ z M « "8E-4 T jo ! 100 u i j . 1 1 i i i i i i i i i -200 -30 -20 10 0 10 deflection (mm) 20 30 (d) Specimen BE-4 Fig. 4.30. {Continued) the load of about 70 kN, then reached the maximum load at the deflection angle of 1 percent which was much lower than the calculated flexural capacity of 387 kN. After the deflection angle of 1.5 percent was exceeded, the load dropped quite rapidly without forming a yield hinge. Specimen BE-2 in Fig. 4.30(b) also had shear cracks at about the same time as BE-1, and the load at 0.5 percent deflection angle, axial re-bars being in the elastic range, was much smaller than BE-1, owing to smaller stiffness resulting from smaller amount of reinforcement. The load was kept increasing up to 1.5 percent deflection, barely lower than the calculated flexural capacity of 314 kN. After the first cycle of 2 percent deflection, the load dropped quite abruptly without forming a yield hinge. 166 Design of Modern Highrise Reinforced Concrete Structures Contrary to above, specimens BE-3 and BE-4 in Figs. 4.30(c) and (d), respectively, reached the flexural capacity although they also had shear cracks at about the same time as above specimens. BE-3 in Fig. 4.30(c) experienced the axial re-bar yielding at 1 percent deflection under the load almost equal to calculated flexural capacity of 212 kN, and the load was kept going up until 2 percent deflection angle, and after that load was decreased gradually. Note that the scale on both axes of Figs. 4.30(c) and (d) is different from those of Figs. 4.30(a) and (b). Rapid load drop after 4 percent deflection occurred due to bond failure of top axial reinforcement. BE-4 with the weakest steel showed yielding at 0.5 percent deflection and reached the maximum load that exceeded the calculated flexural capacity of 137 kN. The load did not drop up to the deflection angle of 4 percent as shown in Fig. 4.30(d). The shear strength equation of AIJ Guidelines (Ref. 4.3) is shown below. Here the shear strength is expressed by the sum of forces carried by a truss mechanism and an arch (or a strut) mechanism Vu = bjtPwPwy cot <j> + tan 0(1 - (3)bDvaB/2 tan 9 = y/(L/D)2 + 1 -L/D f3 = (1 + cot 2 $)pw<rwyl{vaB) (4.6) (4.7) (4.8) where <JB • compressive strength of concrete awy : yield strength of web reinforcement (to be taken 25<TB if awy exceeds 25a B) b : width of the member jt : distance between top and bottom axial re-bars D : total depth of the member L : clear span of the member pw : web reinforcement ratio (pwawy should be taken to be equal to VCB/2 if it exceeds vas/2) 8 : angle of concrete strut in the arch (strut) mechanism (3 : the ratio of compressive stress in the concrete strut of truss mechanism to the effective concrete strength. The coefficient v is the coefficient for the effective compressive strength of concrete and is expressed as follows. Before yielding, it is a constant equal to New RC Structural Elements 167 the basic value VQ v = VQ = 0.7 - <TB/200 (<JB in MPa) (4.9) and after yielding it is a function of hinge rotation angle Rp v = (1.0 - 1 5 i ? p ) i / 0 ^ 0.25i/0 • (4.10) The angle 0 represents angle of concrete strut in the truss mechanism, and cot <j> is determined as the minimum of the following three equations before yielding cot(£ = 2.0 (4.11) cot«£ = j t / ( D t a n 6 0 (4.12) COt<f) — yv<TB/(Pw<Twy) - 1 - 0 (4-13) and after yielding, Eq. (4.11) is replaced by a function of hinge rotation angle Rp as follows cot</> = 2 . 0 - 5 0 i ? p Z 1-0. (4.14) Among the above equations, effective concrete strength van from Eq. (4.9) may not be applicable to high strength concrete, and the following equation by CEB was found to be applicable to high strength concrete up to 120 MPa in the various existing studies v0oB = 1.7c7fl/3 (aB in MPa). (4.15) For the current shear test specimens, effective concrete strength vaB and truss strut angle cot<^> were evaluated from Eqs. (4.10) through (4.14) using measured hinge rotation angle Rp, and potential shear strength was calculated by Eq. (4.6). As to the basic value of effective strength, Eq. (4.15) was used instead of Eq. (4.9). Hinge rotation angle Rp was determined from the deformation measurement of hinge zone of 300 mm from the critical section as shown in Fig. 4.29. Figure 4.31 shows the results of above analysis for two specimens, BE-1 and BE-4. The upper half shows shear force-deflection envelope curve and calculated shear strength based on measured Rp. For BE-1 in Fig. 4.31(a), calculated shear strength is in good agreement with the tested shear strength, and for BE-4 in Fig. 4.31(b), the specimen did not reach the shear strength 168 Design of Modern Highrise Reinforced Concrete Structures shear strength from measured Rp 6 8 Defkction(mm) 10 | 12 14 measured Rp (a) Specimen BE-1 shear strength from measured Rp Deflection(mm) angle <J> from measured Rp (b) Specimen BE-4 Fig. 4.31. Evaluation of hinge ductility. even at the deflection of 24 mm, or 4 percent in deflection angle. The lower half of the figures shows measured Rp by full lines with respect to the left ordinate, and angle 0 determined from this Rp by broken lines with respect to the right ordinate. It is seen that the angle (j> starts at 26.5 degrees (cot</> = 2.0) and increases to about 30 degrees (cot(/> = 1.73) in case of BE-1 which failed in shear, while it goes up to 45 degrees (cot <j> = 1.0) in case of BE-4 which formed a yield hinge and deformed up to 4 percent deflection. New RC Structural Elements 169 Prom the tests and analysis of this investigation, it was confirmed that the shear design of ductile members can be achieved with sufficient accuracy, by the use of effective concrete compressive strength reduction in the AIJ guidelines combined with the basic effective strength as defined by Eq. (4.15). Strictly speaking, however, the use of hinge rotation angle for Rp as the measure of inelastic deformation may be criticized. Inelastic deformation should theoretically be measured after the formation of a plastic hinge, and therefore Rp should be determined accordingly. This subject should be further studied in future. 4.3. Walls When high strength materials such as those developed in the New RC project are utilized in the building construction, size of structural members may become smaller than ordinary buildings, leading to insufficient rigidity against lateral forces. Use of structural walls may be an effective countermeasure in such cases for the addition of rigidity. At the same time a multistory structural wall in a moment resisting frame is also effective in equalizing the story drift distribution and in avoiding the formation of single story collapse mechanism. A series of experimental and analytical studies were conducted in the New RC project into the flexural behavior and shear strength of multistory structural walls. Following three subjects are introduced in this section as the representative achievement. (1) Flexural capacity of shear compression failure type walls. (2) Deformation capacity of walls under bidirectional loading. (3) Shear strength of slender walls. Throughout this book, the word "shear wall" is avoided as much as possible. A multistory structural wall in a moment resisting frame tends to be a slender wall, and it behaves more like a flexural member than a bracing member against lateral shear. Sometimes a word "flexural wall" is needed in order to distinguish this type of wall from a squat wall in lowrise buildings (Ref. 4.6). In this book, however, a simple word "wall", or a "structural wall", is preferred. This choice of wording does not imply negligence of the importance of wall shear strength. On the contrary, shear strength of a "flexural wall" is a very important design issue as discussed elsewhere (Refs. 4.6, 4.7 and 4.8) and also in Chapter 6 of this book. 170 Design of Modern Highrise Reinforced 4.3.1. Flexural Capacity Type Walls Concrete Structures of Shear-Compression Failure Structural walls made of high strength reinforced concrete were tested under static reversal of lateral load to produce shear-compression failure in the wall plate nearly simultaneously with flexural yielding, with the objective of examining design method for shear strength and flexural deformability. Four wall specimens will be introduced here. They are about a quarter scale single span dumbbell type section walls with the same dimension, shown in Fig. 4.32. Center-to-center span of 1.5 m, column size 200 mm square, wall thickness 80 mm, and wall clear height 3.0 m are all common to four specimens. Variables are column axial bars and wall !5cJ20oi 1300 I200J150 2000 Fig. 4.32. Detail of wall specimens. New RC Structural Elements 171 Table 4.5. List of wall specimens. Column Specimen Axial Bars USD685 (P9%) NW-3 12-D10 (2.14) NW-4 NW-5 16-D10 (2.85) NW-6 12-D13 (3.81) Wall Spiral Hoop USD1275 (Pw%) Subhoop* USD1275 (Pw%) 2-5</> @40 (0.49) 2-50 @ 40 (0.49) Vert. & Horiz. USD785 (Ps%) 1-D6® 150 (0.27) 2-D6® 150 (0.53) 'arranged in the lower half (1500 mm) only reinforcement as shown in Table 4.5. Grade of re-bars is also shown in the table. Concrete with the specified strength of 60 MPa was used, but actual strength ranged from 56 to 68 MPa. Actual re-bar yield strength was as follows; D13, 740 MPa, D10, 727 MPa, D6, 768 MPa, and 50, 1258 MPa. Walls were tested under constant axial load and reversal of lateral load. Axial load on NW-3 and NW-5 was 1600 kN to produce average normal stress of 8.7 MPa, and on NW-4 and NW-6 it was slightly lower, 1400 kN for the stress of 7.6 MPa. Lateral load was applied at the level of lower surface of top girder, i.e. 3.0 m above the critical section at the wall base, to maintain the shear span ratio of 2.0 with respect to center-to-center wall span of 1500 mm. Figure 4.33 shows load vs. deflection relationship for four specimens. Figure 4.34 illustrates specimens after completion of testing. All specimens had flexural cracks on the tension side column and wall base at the deflection angle of 0.25 percent. Flexural shear cracks and shear cracks were formed subsequently, and criss-cross network of diagonal cracks as seen in Fig. 4.34 covered the wall under the loading up to 0.75 percent of deflection. Hysteresis loops up to this stage were quite similar for four specimens, assuming an S shape with small energy absorption area. Yielding of column axial bars was observed in all specimens at the deflection between 0.75 and 1 percent. Specimen NW-3 shown in Fig. 4.33(a) started to lose strength in the second cycle of 1 percent, and web wall plate crushed in the third cycle accompanied by breakage of wall horizontal re-bars. Specimen NW-4 in Fig. 4.33(b) started to crush at web wall plate in the positive 1 percent cycle, and a large central portion of wall crushed in the negative 1 percent cycle accompanied by wall re-bar breakage. Specimen NW-5 in Fig. 4.33(c) with greater amount of wall reinforcement sustained loading up to 1.5 percent, and failed by crushing in the 172 Design of Modern Highrise Reinforced Concrete Structures -0.5 0 0.5 rotation angle (%) (a) Specimen NW-3 -0.5 0 0.5 rotation angle (%) (b) Specimen NW-4 Fig. 4.33. Load-deflection curves of walls. New RC Structural Elements 1 ! ; : ' yielding nf column main bar ! 1 yielding of wall bar ' maximum shear force shear crack t " flexural crack / \ y/j^0^ • / web; crushing 4- j 1 i Speclaen NW-5 -2.0 -1.5 -1.0 -0.5 0 0.5 rotation angle (%) 1.0 2.0 1.5 (c) Specimen NW-5 yielding of column main bar -2.0 -0.5 0 0.5 rotation angle (%) (d) Specimen NW-6 Fig. 4.33. (Continued) force 1.0 1.5 2.0 173 174 Design of Modern Highrise Reinforced Concrete Structures central and lower portion of wall without re-bar breakage. Specimen NW-6 in Fig. 4.33(d) was quite similar to NW-5 up to 1 percent deflection, but the lower portion of wall crushed abruptly at 1.3 percent deflection. No re-bar breakage was observed. In analyzing the test results, the shear strength equation of walls given in AIJ Guidelines (Ref. 4.3) was used. It is similar to Eq. (4.6), the one for beams and columns introduced in Sec. 4.2.7, except that confining effect of dumbbell type columns to the wall plate is taken into account. It is introduced below. The shear strength is expressed by the sum of shear force carried by a truss mechanism and shear force carried by an arch (or a strut) mechanism as follows Vu = tlbpwawy cot<j> + tan 0(1 - (3)tlavaBl2 tan 6 = V(VU 2 + 1 - h/la (4-16) (4.17) New RC Structural Elements 175 j8 = (1 + cot 2 <j>)pwaWyl(vaB) where (TB <7wy t lb, la h pw (4.18) '• compressive strength of concrete : yield strength of wall reinforcement (not to exceed 400 MPa) : thickness of web wall plate • effective length of wall assumed in the truss and arch mechanisms and explained later : height of wall to be taken equal to the height of the story being considered : wall reinforcement ratio (pwawy should be taken to be equal to VCTB/2 if it exceeds V<JB /2) 0 0 : angle of concrete strut in the arch (strut) mechanism : the ratio of compressive stress in the concrete strut of truss mechanism to the effective concrete strength. The coefficient v is the coefficient for the effective compressive strength of concrete and expressed as follows. Before yielding, it is a constant equal to the basic value vQ as given by Eq. (4.9), and after yielding, it is a function of deflection angle of wall R as follows v = u0 for R ^ 0.005 v = (1.2 - 40R)v0 for 0.005 ^ R < 0.02 v = 0.4i/0 for 0.02 ^ R. (4.19) Similar to the previous case of beams and columns, Eq. (4.15) replaces Eq. (4.9) in case of high strength concrete. The angle <f> represents angle of concrete strut in the truss mechanism, and unlike the previous equation for beams and columns, cot cj> for walls is assumed to be cotcj) = 1.0 at all times. Effective wall length la and lb are determined as follows. It is the sum of center-to-center span of dumbbell columns of a wall lw plus a bonus considering the confining effect of columns A/ a or A/;,. la = lw + AZ0 (4.20) lb = lw + Mb (4.21) A/ 0 = Ace/t for Ace ^ tDc ) Ala = (Dc + ^/AceDc/t)/2 for Ace > tDc (4.22) 176 Design of Modern Highrise Reinforced Concrete Structures Alb = Ace/t for Ace ^ tDc Alb = Dc for Ace > tDc. (4.23) In these equations, Dc is depth of a dumbbell column, and Ace is effective area of a dumbbell column to be determined from Ace = AC- Nce/crB ^ 3tDc (4.24) where Ac : area of a dumbbell column Nce : axial force on a column in the compression side at the deflection associated with the ultimate limit state. The above equations imply that the effective column area Ace is reduced from Ac with the increase of axial force, and once Ace is not greater than wall thickness times column depth tDc, Ace itself is considered in calculating the bonus wall length A/ a and Alb- When Ace is greater than tDc, Alt, for truss mechanism is taken to be the column depth, making the effective wall length lb in Eq. (4.21) equal to the outside measurement of a dumbbell wall. Ala in this case for arch mechanism expressed by Eq. (4.22) makes the effective wall length la in Eq. (4.20) longer than the outside length. Confining effect of a dumbbell column is thus positively taken into account in the shear strength equation of Eq. (4.16). Figure 4.35 shows relationship of observed ultimate load and calculated shear strength for six specimens including two pilot test specimens not described above, where both axes are normalized by calculated fiexural strength. If the abscissa is less than 1.0, the specimen should fail in shear, and the observed strength should be approximated by the calculated shear strength. If the abscissa is greater than 1.0, the specimen should fail in flexure, and the ordinate should be about 1.0. As seen in Fig. 4.35, six specimens follow this rule in principle. In calculating the shear strength from Eq. (4.16), values of cotcj) = 1 . 0 and cot<f> = 1 . 5 were used, and it was found that the latter gave more accurate estimation of shear strength. Figure 4.36 is the result of investigation into deformability of walls. The abscissa is cumulative deformation capacity, defined as the total of absolute values of deflection up to the point of load drop to 80 percent of maximum. Since the loading history to all specimens is identical, it is possible to correlate cumulative deformation to the maximum deflection as shown by vertical chain or broken lines. The ordinate was determined as follows. First the shear force New RC Structural Elements 177 2.0 f S 1.5 cot ^ =1.5| n "53 JiW-2 Nf-1 * ^ 1.0& 0.5 0 0.5 1.0 1.5 2.0 shear strength(cal) / flexural atrength(cal) Fig. 4.35. Measured and calculated strength of walls. associated with the calculated flexural capacity was determined. Then effective concrete strength necessary to produce calculated shear strength equal to the above flexural shear was found. Finally the ratio of effective concrete strength thus determined to the one from Eq. (4.15) was obtained, and plotted against the cumulative deformation experienced by each specimen. A clear relationship is seen, that smaller the effective strength, larger the cumulative deformation. This implies that a similar approach as the Guidelines (Ref. 4.3) is possible for the deformation capacity procurement. The broken line in Fig. 4.36 shows the effective concrete strength determined from Eq. (4.19). Conclusions from this investigation may be summarized as follows. (1) All specimens finally failed more or less in a brittle manner either by web wall crushing or wall bar breakage, but dumpbell columns were stable and were able to carry axial load even after the failure. (2) Shear strength can be evaluated by AIJ guidelines with a slight modification. (3) Cumulative deformation capacity of walls increases as the effective concrete strength necessary for flexural shear decreases. 178 Design of Modern Highrise Reinforced Concrete 2.0 i (l) 1.5 : ! (2) j (3) • (4) Structures ' i (5) (6) cot^»l. 5 i i i •! I i 1.0 i NW-6 : " • • • . ! '•j... NWJ3 i j i 0.5 0.1 i. i •'• i i j j i i 0.2 NW-2 •U!"H i ®NI-1 i 0.3 0.4 0.5 0.6 cumulative deformation capacity(rad.) note: (1)&(2) 1.0H : 1st and 2nd cycles (3)&<4) 1.5% : 1st and 2nd cycles (5)&(6) 2.0S : lat and 2nd cycles Fig. 4.36. Effective concrete strength coefficient and cumulative deformation capacity. 4.3.2. Deformation Bidirectional Capacity of Walls Loading under A multistory wall in a space moment resisting frame may yield under the inplane lateral load, and it may also be subjected to reversal of out-of-plane lateral load. Flexural yielding causes the wall to stand on one column in the compression side only, imposing high level of axial compression on that column. Under the action of out-of-plane loading, the column must behave as an independent column under high compression, possibly leading to failure at relatively small deformation. Thus it is possible that the deformation capacity of a wall would be smaller under bidirectional loading. An elaborate experimental program was implemented in the New RC project to test structural walls under bidirectional loading. Four specimens were tested. They were about a quarter scale dumbbell type walls, taken from a lower portion of multistory wall, as shown in Fig. 4.37. Center-to-center span of 1.5 m, column size 200 mm square, wall thickness 80 mm, and wall New RC Structural Elements MWTypc 179 PType Fig. 4.37. Detail of wall specimens. clear height 2.0 m are all common to four specimens. Concrete with specified strength of 60 M P a , D10 re-bars for column axial reinforcement with yield strength of 865 M P a , a n d D6 re-bars for wall reinforcement a n d column lateral reinforcement with yield strength of 826 M P a , were used throughout. Gross column reinforcement ratio was 2.14 percent, and wall reinforcement ratio was 0.80 percent. 180 Design of Modern Highrise Reinforced Concrete Structures Table 4.6. List of walls under bidirectional loading. Specimen Column Spiral Column Subhoop Axial Load Ratio N 2A0aB M35X 2-D6® 60 M35H P35H M30H D6@ 60 Loading Path 1800 in-plane 0.35 1960 0.30 1500 — 2-D6® 60 Axial Load N kN 1900 bidirectional Table 4.6 lists variables for four specimens. The first letter M or P denotes difference in the column lateral reinforcement. Peripheral spiral of D6 at 60 mm is common to four specimens whose web reinforcement ratio was 0.53 percent, but those with mark M had additional subhoops of 2-D6 at 60 mm in two directions, making the web reinforcement ratio to a doubled value. P is a specimen without subhoops. The next two digits in the specimen mark refer to the axial load level. In terms of axial stress with respect to column area, it was either 35 or 30 percent of concrete strength. As the actual concrete strength fluctuated between 62.6 and 70.0 MPa, amount of axial load on each specimen is shown in Table 4.6, which was kept constant during the testing using four vertical actuators. The average normal stress on the gross wall and column area was 9.8 to 10.7 MPa for the first three specimens and 8.2 MPa for the last specimen. The last letter X or H in the specimen mark corresponds to the type of loading. M35X was subjected to reversal of in-plane horizontal loading. The load was applied in such a way that the shear span (critical moment divided by shear force) would be 3.0 m, or shear span ratio with respect to center-tocenter span of 2.0. Since the wall is 2.75 m high to the top surface of top loading girder, additional moment was produced by a pair of vertical actuators simultaneously with the loading from horizontal actuators. Other three specimens with the letter H are subjected to bidirectional loading as shown schematically in Fig. 4.38. In-plane loading was similar to M35X. Out-of-plane loading was made so that the wall (actually two side columns) would be in an antisymmetric bending. For this purpose another pair of vertical actuators were activated to apply top moment simultaneously with horizontal loading. The behavior of M35X was quite similar to NW-3 in the previous section, with somewhat greater deformation capacity. This is quite understandable New RC Structural ©© Elements ®<D 2.1 t "© ®<D ©1 ©® Fig. 4.38. Bidirectional loading path. Kx(S). starting of yielding of •column main bar M3 6H -5 t 5 6 z (mm) (b) Out-of-plane loading of M35H Fig. 4.39. Load-deflection curves of walls under bidirectional loading. 181 182 Design of Modern Highrise Reinforced Concrete •2.0 1200 1 •1.0 j 1.0 —t 1 calculated Qmu 800 - Structures starting of yielding column main bar **M « 2.0 1 I stf2£~ (\ f... 400 - \ S failure yielding of all L column main; bars •400 ••••j 800 1200 -41 i i i -3* -1« -It • P-3 6-H i « i tl H JO ixbtun) (c) In-plane loading of P35H •1.0 0 1.0 T- -2.0 150 T" 41 Ry<*) 2.0 T • starting'ofyieWiitgof column main bar 100 - failure 8 -50 yielding of all olumn main bars -100 P3B+» 150 II -IS -(0 -S I v _l_ 5 _L- II IS 20 6x(mm) (d) Out-of-plane loading of P35H Fig. 4.39. (Continued) when one sees that the cross section, column reinforcement and level of axial load are similar, with the only difference being the increased wall re-bars in M35X. After sustaining 2 cycles at 1.5 percent deflection, shear compression failure of web wall plate took place at 1.8 percent deflection, leading to a sudden loss of lateral resistance. Figure 4.39 shows load-deflection relationship of two specimens, M35H and P35H, subjected to the bidirectional loading of Fig. 4.38. M35H failed, after sustaining 1 cycle of 1.5 percent deflection, by the shear compression failure New RC Structural Elements 183 of web wall plate at second 1.5 percent deflection. P35H had fewer column confining re-bars, and failed in the first 1.5 percent deflection cycle, also by the shear compression failure of wall. M30H with lower axial struss was similar to M35H, except that it failed in a similar way after sustaining 2 cycles of 1.5 percent deflection. The load-deflection relationship of four specimens was quite stable in general before the onset of the failure. As shown in Fig. 4.39, load at the peak in-plane deflection dropped due to the effect of out-of-plane load reversal. Similar load drop in the out-of-plane direction is not observed, as the in-plane loading was applied when the out-of-plane deflection was zero, and only a V-notch was formed near the ordinate of the out-of-plane hysteresis. Except for this kind of load drop, effect of bidirectional loading was not conspicuous in Fig. 4.39. The bidirectional effect was more clearly seen in the axial strain measurement. Figure 4.40 is a plot of axial strain of a column and nearby wall at the conclusion of out-of-plane loading cycles. For all specimens, compressive strain of column increases as the horizontal drift of the wall increases, and furthermore in case of specimens under bidirectional loading, the column strain increases in the second out-of-plane cycle. On the contrary the wall compressive strain does not increase rapidly while the horizontal drift remains within 1 percent deflection. It is inferred that the sudden wall strain increase at 1.5 percent of M35H and P35H was caused by the high compressive strain of columns at the previous 1 percent deflection. Damage of columns due to out-of-plane loading should have caused the transfer of axial load to the wall plate, thus accelerated the shear compression failure. To conclude this section, major findings from this experiment were as follows: (1) Deformation capacity of walls under bidirectional loading was smaller than those under unidirectional loading. (2) Deformation capacity loss was more remarkable for higher axial stress or poorer column confinement. (3) Deformation capacity loss of wall should be the consequence of the progress of column axial strain. 4.3.3. Shear Strength of Slender Walls The experimental study introduced in this section deals with the ultimate shear strength of structural walls made of high strength materials under static 184 Design of Modern Highrise Reinforced Concrete Structures 1.50 1.25 l * • - * MW5H 1 '"&•-• A M30H [ ,- o— a P3SH i / 0.5 1.0 1.5 deflection angle (%) (a) Column compressive strain 2.0 1.50 1 it—fr A—A D—d 1.00J- «•••'•'••<• O—6 | 0.50 1.25 f 3 °-75 WR5H I U30H T P35B \ M35H ""]' M35X I 0.25 0 0.6 1.0 1.5 deflection angle (%) 2.0 (b) Wall compressive strain Fig. 4.40. Column and wall compressive strain at various wall drift. reversal of horizontal load. Emphasis was placed on the study to investigate the applicability of shear strength equation of AIJ Guidelines (Ref. 4.3). In particular, the coefficient for the effective compressive strength of concrete, the angle of concrete strut in the struss mechanism, upper and lower limits of reinforcement were the major points of interest. Eight specimens were tested. They were all dumbbell type section walls, designed to fail in shear prior to flexural yielding. The wall shape was very similar to Fig. 4.37. Columns on both sides of wall were 200 mm square, 1.5 m New RC Structural Elements 185 Table 4.7. Parameters of wall specimens for shear. Specimen No. Nominal Concrete Strength (MPa) 1 2 60 Wall Re-bars 2000 72.9 77.6 Wall Re-bar Ratio 1% 2-D6® 400 0.20 2-D6® 230 0.35 2-D6® 150 0.53 2-U6.4® 122 0.62 2-D6® 80 1.00 2-D6® 55 1.45 SD785 3000 2.00 75.6 60 Arrangement 1.33 105.5 78.2 6 8 Shear Span Ratio 72.2 73.2 100 5 7 Wall Height (mm) 66.4 3 4 Actual Concrete Strength (MPa) SD1275 2000 1.33 SD785 center-to-center span, and the wall thickness was 80 mm. Wall height was 2.0 m from the foundation surface to the soffit of loading beam, where the horizontal load was centered to make the shear span ratio of 1.33, except for one specimen, No. 5, whose height was 3.0 m to make the shear span ratio of 2.0. Nominal concrete strength was 60 MPa except for one specimen, No. 4, which was made of 100 MPa concrete, but actual compressive strength varied as shown in Table 4.7. Each of dumbbell columns was heavily reinforced with 16-D13 bars of SD785 grade, whose yield strength was 1029 MPa. Columns also had large amount of confining re-bars, made of D6 spirals of SD1275 grade at 50 mm on centers and the equal amount of subhoops. The amount of wall re-bars was a major variable as shown in Table 4.7. SD785 D6 bars had yield point of 808 MPa, and SD1275 U6.4 bars used for the specimen No. 6 had yield point of 1448 MPa. Specimens were loaded vertically on top of each column with a constant axial load of 800 kN or 1330 kN, corresponding to one third the nominal concrete strength in terms of column compressive stress (not considering wall area), and horizontally under cyclic reversal with increasing amplitude. The process of failure was almost common to all specimens. Figure 4.41 shows envelopes of load-deflect ion curves for all specimens. Shear cracks appeared on wall panels at deflection angle of 0.07 to 0.11 percent, and fiexural cracks appeared on tension side columns at 0.06 to 0.14 percent. Shear 186 Design of Modern Highrise Reinforced Concrete (ForNo.5) (For others)-2.0 -1.0 -1.5 -0.5 -1.0 Structures Rotation Angle (%) 0 0.5 -0.5 0 0.5 1.0 r 1.0 1.5 2.0 Fig. 4.41. Envelopes of load-deflection curves. cracks extended, and their number increased, up to the deflection angle of 0.5 percent, to cover almost entire area of wall panels. By this time, cracks were seen between compression strut of wall and side column, and wall re-bars yielded in case of specimens with wall re-bar ratio not greater than 0.53 percent, i.e. specimens Nos. 1-5. At 0.75 percent deflection cycle compression strut of all specimens with shear span ratio of 1.33 failed by crushing, accompanied by a sudden loss of lateral load. Axial reinforcement of columns never yielded, as the measured strain in tension side columns was about 40 percent of yield strain. Specimen No. 5 with shear span ratio of 2.0 followed the similar process up to the deflection angle of 0.5 percent. Large shear cracks along diagonals of the panel formed at 0.75 percent cycle. After that, cracking between compression strut and side column extended, and compression struts crushed at the peak of 1.0 percent cycle. Column bar strain in tension at the maximum load was about 60 percent of yield strain. Figure 4.42 shows sketch of typical specimens after completion of the testing. Hysteresis of load vs. deflection relationship before shear compression failure was S-shaped, very much like those in Figs. 4.33 or 4.39, with even smaller hysteretic area. New RC Structural (a) Specimen No. 3 Elements 187 (b) Specimen No. 5 Fig. 4.42. Final crack pattern of typical wall specimens. iHW-1 0.5 1.0 l.S calc. Vu/calc. Vf (a) Assuming cot* =1.0 tO "0 0.S 1.0 . 1.5 calc. Vii / calc. Vf 2.0 (b) Assuming cot 4> =1.5 Fig. 4.43. Measured vs. calculated wall strength {Vu: shear strength, Vf. flexural strength). Measured maximum load is now compared with calculated flexural and shear strengths. Flexural strength was calculated by an approximate equation as shown below. Vf = Mu=Ag Mu/hw (4.25) 188 Design of Modern Highrise Reinforced Concrete Structures where : flexural strength in shear : flexural strength in moment fiyj : wall height (shear span) : center-to-center span of columns f-w A A : gross sectional area of column and wall axial bars y ? ^tvy : yield stress of column and wall axial bars N : total axial load on the wall. Shear strength was calculated using Eq. (4.16), using Eq. (4.15) instead of Eq. (4.9) for effective compressive strength of concrete. It was confirmed in this test series also that the use of Eq. (4.15) improves the shear strength evaluation over the use of Eq. (4.9). Another point of concern for the shear strength calculation was the value of cot<f> to be used in Eq. (4.16). As it was discussed in Sec. 4.3.1, use of cot<j) = 1.0 did not lead to a satisfactory agreement compared to the use of cot</> = 1.5. For the current test series, it was found that cot <j) should assume a higher value, say cot <j> = 2.0, for specimens with small wall reinforcement ratio such as Nos. 1-2, and cot<j> = 1 . 0 gave a good agreement to specimens with large wall reinforcement ratio such as Nos. 7 and 8. Figure 4.43 shows comparison of measured VmEtx/calc. Vj vs. calc. V u /calc. Vf for two cases of cot<£ = 1.0 and cot</> — 1.5. It also shows plots for specimens in Sec. 4.3.1 failing in flexural shear. Use of c o t 0 = 1.5 in Fig. 4.43(b) may be preferred for the overall accuracy, but for practical purposes use of cot</> = 1.0 in Fig. 4.43(a) will be justified for the safe side estimation of shear strength. It will be noted in Fig. 4.43(a) that the shear strength of specimens Nos. 6 and 8 was underestimated even by the use of cot cj> — 1.0. Horizontal wall bars (shear reinforcement) of those specimens, as well as those of specimen No. 7, did not yield, and the assumption of wall bar yielding in Eq. (4.16) was not applicable. This gives implications as to the upper limit of wall reinforcement. As stated in Sec 4.3.1, pwawy in Eq. (4.16) is to be limited to the value of UCTB/2. However, specimen Nos. 6-8 did not show wall bar yielding nevertheless the value of pwawy (8.1 to 11.7 MPa) did not exceed vaB/2 (14.9 to 15.5 MPa). Nevertheless, shear strength of two of these specimens were underestimated. A more stringent upper limit than I/CTB/2 will be necessary in practice. To summarize the investigation reported in this section, followings may be stated. Vf Mu New RC Structural Elements 189 (1) Restoring force characteristics of walls of high strength material shows S shaped hysteresis with small energy absorption, and specimens with shear span ratio of 1.33 failed in shear compression failure of struts at 0.75 percent deflection angle, while the one with shear span ratio of 2.0 failed in the same manner at 1.0 percent deflection. (2) Wall horizontal bars yielded in case of specimens with wall reinforcement ratio not greater than 0.53 percent, while those with greater reinforcement ratio did not show yielding. (3) The shear strength equation proposed in AIJ Guidelines was found to be satisfactorily accurate with the use of Eq. (4.15) for effective compressive strength of concrete and value of cot cf> greater than 1.0 (say 1.5). However for practical purposes use of cot<^> = 1 . 0 gives a safer estimate. (4) When the amount of wall reinforcement is very high either by the use of very high strength steel or by providing heavy amount, its effectiveness is reduced, and a more stringent upper bound than AIJ guidelines will be necessary. 4.4. B e a m - C o l u m n Joints A beam-column joint refers to the portion of a column within the intersection of connected beams. This is a relatively new area to receive attention of researchers and engineers working on the seismic behavior of reinforced concrete structures. Basically there are two aspects of its behavior that give influence to the overall behavior of a frame. First is its deformation in the elastic range. As long as we visualize beams and columns of a frame as linear flexural elements based on the Bernoulli-Euler hypothesis (plane section remains plane), end portions of an element lying within the beam-column joint do not deform, because the second moment of section of those end portions is infinitely large. However if we idealize beams and columns with end rigid zones corresponding to beam-column joints and assume only the clear span portion is deformable, we will definitely end up with an overestimation of frame stiffness. Beam-column joints are subjected to extensive shear stress and deform, even in the elastic range, considerably to render the frame more flexible. There are three methods available to take the effect of beam-column joint deformation into account. The first method is to shorten the rigid zones and 190 Design of Modern Highrise Reinforced Concrete Structures to make the deformable portion longer than the clear span. The effect of joint deformation is then indirectly taken into consideration. This method is a standard method of analysis in the AIJ Calculation Standard (Ref. 4.9), and is so prevalent in Japan that the word rigid zone usually refers to this method of analysis. With the use of this method, however, the ends of rigid zones do not coincide with the critical sections which are usually located at the surface of intersecting members. This leads to some difficulties at the analysis in the inelastic range. The second method to consider beam-column joint deformation is not to shorten the rigid zones but to reduce the second moment of section of deformable portion in the clear span. A formula for such effective second moment of section is available in the AIJ Guidelines (Ref. 4.3). This is also to consider the effect of joint deformation implicitly. The third method is to consider the joint shear deformation explicitly in the frame analysis. This is the most perfect method from theoretical point of view, and it is possible to accommodate inelastic joint deformation as well. Needless to say it requires more sophisticated theory of structural analysis and corresponding software for computers. The second aspect of beam-column joint behavior that influences the overall frame behavior is its inelastic deformation which may possibly lead to premature joint failure. Particularly with the use of high strength materials and with the inherent reduction of member size, beam-column joints of New RC frames are apt to be subjected to higher shear stress. Bond stress of re-bars passing through a joint, or being anchored in a joint, will also increase by the increased tensile strength of re-bars. High shear stress or bond stress may lead to shear or bond failure, and even if they do not, they will definitely lead to large shear strain in the joint or increased slip deformation due to pull out of re-bars, thus ultimately to reduced overall stiffness and increased earthquake response deformation. It is this second aspect of beam-column joint behavior that was studied in this section. Following four subjects are discussed, with, the aim of establishing ways to evaluate shear strength and stiffness of joints, to prevent bond and anchorage failure, and to estimate bar ship deformation. (1) Bond in the interior joints. (2) Shear capacity of 3-D joints under bidirectional loading. (3) Shear capacity of exterior joints. (4) Concrete strength difference between first story column and foundation. New RC Structural 4.4.1. Bond in the Interior Beam-Column Elements 191 Joints Under the action of horizontal load, a reinforced concrete frame is expected to form a beam yielding mechanism, where yield hinges form on both sides of a beam-column joint. To develop full yield strength as well as deformability, beam bars passing through the joint have to be well anchored by means of bond stress within the joint. When the bond strength is not sufficient, bars would start slipping leading to reduced strength and increased deformation, thus to impaired energy absorption. The AIJ Guidelines (Ref. 4.3) provides a design method to preserve good bond by limiting bond stress to a certain level. However, its application to beam-column joints with high strength materials has not been justified experimentally. The study reported herein aims at investigation into bond deterioration and related behaviors of beam bars passing through the joint after beam yielding. Specimens are cruciform beam column subassemblages of about one third scale as shown in Fig. 4.44. Story height measured between points of contraflexure of upper and lower columns is 1470 mm, and beam span measured between midspans of adjacent beams is 2700 mm. Column section is 300 mm square, and beam section is 200 mm by 300 mm. Table 4.8 lists bar arrangement of members. As it will be noted in the table, these specimens use Fig. 4.44. Beam-column joint specimen (MKJ-1). 192 Design of Modern Highrise Reinforced Concrete Structures Table 4.8. Interior joint specimens. Specimen MXJ-1 MKJ-2 MKJ-3 MKJ-4 top bars bottom bars 2-D19 2-D19 3-D19 3-D19 2-D22 2-D19 3-D22 2-D22 stirrups 2-D6® 90 Pw = 0.36% 2-D6® 60 Pw = 0.53% 2-D6® 50 Pw = 0.46% 2-D6® 50 Pw = 0.63% Beam Column Joint axial bars 12-D10 12-D16 12-D13 12-D19 hoops 2-D6® 80 Pw = 0.27% 2-D6® 50 Pw = 0.43% 2-D6® 65 Pw = 0.33% 2-D6® 40 Pw = 0.53% hoops 4-D6 x 3 sets @ 50 Pw = 0.54% Concrete Strength aB (MPa) Joint Shear Stress at Beam Yielding Tjy (MPa) Beam Bar Bond Index \x 100.4 86.0 12.4 8.2 5.37 13.4 9.5 5.54 relatively large size beam bars. Material used for beam bars is SD685 steel with yield point ranging from 757 MPa to 786 MPa. Concrete strength is shown in Table 4.8. Beam bar diameter is directly related to bond behavior as follows. An index for beam bar bond /x is defined by M = 2T//V5I = (db/Dc)(ay/^). (4.26) Thus fi is twice the bond stress at beam yielding r / divided by square root of concrete strength ag, and is expressed as the above equation by the product of ratio of bar diameterrf;,to column depth Dc and ratio of beam bar yield strength ay to square root of concrete strength erg. This relationship can be easily obtained when the bond stress 17 is calculated assuming that the beam bar stress difference at both column surfaces is equal to twice the yield stress. The value of beam bar bond index /i recommended by AIJ Guidelines is 4.0 or less for good bond, but the /x value calculated for specimens MKJ-1 to MKJ-4 is more than 5 as shown in the bottom line of Table 4.8, which means that these specimens would exhibit poor bond behavior after beam yielding. Columns are sufficiently reinforced to prevent premature yielding. Major parameters for four specimens are concrete strength and joint shear New RC Structural Elements 193 stress at beam yielding as shown in Table 4.8. Joint shear stress at beam yielding is either about 10 percent or 15 percent of concrete strength, which is low enough for us to anticipate no joint shear failure prior to beam yielding. Specimens were loaded first by the column axial load with axial stress of about 10 percent the concrete strength, which was kept constant during the test, and then loaded at beam ends antisymmetrically to simulate lateral loading, which was cyclically reversed at the story drift angle of 0.5, 1, 2, 3 and 4 percent, twice each. All specimens showed beam yielding in the 2 percent cycle, and reached the maximum load in the subsequent 3 percent cycle. Concrete cover at beam ends crushed, and partially spalled, towards the end of testing. Beam-column joint had extensive diagonal cracking, and the percentage of joint deformation in the story drift gradually increased up to about 20 percent at the maximum load. This is an indication of the failure mode usually referred to as "joint failure after beam yielding". Figure 4.45 shows story shear vs. story drift relationship of MKJ-1 overlapped with the skeleton curves of the other three specimens. The hysteresis loop of four specimens was similarly S shaped, with relatively small energy absorption, but it was most pronounced in the case of specimen MKJ-1. The maximum load was dictated by beam yielding, and so it was larger for MKJ-4, -SO -40 ->» 0 70 40 story drift (mm) Fig. 4.45. Story shear vs. story drift relationship. 60 194 Design of Modern Highrise Reinforced Concrete LJ 2 0.5% 3 ^_,4 LJ> Structures I_, 8 l_J0 1% 4% 2% 3% cycle No. and drift angle Fig. 4.46. Equivalent viscous damping factor. 2, 3 and 1 in that order. They are all in good agreement with theoretical prediction. For all specimens bond slip of beam bars was clearly observed, leading to an added beam deformation. Although the percentage of joint deformation in the story drift increased as stated before, the percentage of beam deformation including the effect of bond slip was dominating, more than 50 percent even at the end of loading for all specimens. To investigate the effect of beam bar bond deterioration on the hysteresis characteristics, Fig. 4.46 shows equivalent viscous damping factor heq in each cycle for four specimens. Equivalent viscous damping factor heq is denned as follows, h,e q 1 AA 2TT E A e 1 AA 2TT P m a x • S„ (4.27) where AA is the energy absorption in one cycle, i.e. area of a hysteretic loop, £A e is sum of elastic potential energy to the positive maximum and to the negative maximum, to be calculated as half the product of maximum load P ma x and the deformation 5maK associated with the P m a x - This heq is an indication of energy absorbing capacity in the inelastic reversed loading cycle. The AIJ Guidelines postulates that heq of 10 percent at 2 percent drift constitutes the limit of bond deterioration, and on that basis recommends bond index // of Eq. (4.26) less than 4.0 experimentally. As shown in Table 4.8, the current New RC Structural Elements 195 specimens had bond index fi greater than 5.0, and hence bond deterioration was anticipated from the beginning. Figure 4.46 shows that except for the first cycle of MKJ-1, all specimens showed /ieq less than 10 percent at 2 percent cycle, or in other words, poor bond behavior in terms of energy absorption. At the same time, however, it has to be mentioned that bond failure is not a brittle failure as, and the hysteresis is more stable than, the shear failure due to diagonal compression of concrete. Figure 4.47 is plotting of bond index n and the inverse of joint failure index J - 1 of the current specimens as well as many existing test results. The joint failure index J will be explained in more detail in the next subsection and also in Sec. 4.5.5. The ordinate of Fig. 4.47 roughly corresponds to the inverse of J so it is denoted as J - 1 , which, due to its early stage of development, is defined differently from the next subsection as follows r _i 1 J~ = beDbvaB (4.28) ^at(Ty where be is effective width of beam-column joint taken as the average width of beam and column, Db is beam depth, VOB is effective concrete strength for shear in Eq. (4.9), at is tensile bar area of beam, <ry is yield stress of beam bars, 1 <S 3.2 4.8 6.4 bond index |i Fig. 4.47. Discrimination of failure mode. 196 Design of Modern Highrise Reinforced Concrete Structures and I! is for the sum of left and right beams of a joint. J - 1 is an indication of concrete strength relative to the joint shear stress at beam yielding. It was expected that J~l less than 1.0 would result in premature joint shear failure, while J - 1 greater than 1.0 would probably lead to beam yielding. Looking at Fig. 4.47, however, it is clear that the limit for joint shear failure is not J - 1 = 1.0, but it goes up gradually as bond index fi increases. This leads us to a modification in the definition of J index as explained in the next subsection. Also, there are large number of specimens failing in B-J mode (joint failure after beam yielding) above the limiting line. The four specimens, plotted by double circles in Fig. 4.47, lie at abscissa of about 5.0 and at ordinate above 1.8, in the area where there were almost no previous specimens. Because of relatively high value of J"1, none of them failed by premature joint shear failure. But all of them had progressive joint failure after beam yielding, and in particular, even MKJ-1 and MKJ-3 with J-1 value as high as 2.5 or 2.8 showed joint failure in the later stage. This may be attributed to, first, the compressive stress concentration to concrete strut in the joint due to bond deterioration, and secondly, the lowered coefficient v for effective compressive strength of high strength concrete. In conclusion, we may state the following. (1) Beam column joint with bond index [h greater than 4.0 showed poor bond behavior in terms of hysteresis shape and energy absorbing capacity. Equivalent viscous damping factor at 2 percent drift cycle was less than 10 percent. (2) Although joint shear stress level was low to enable beam yielding prior to joint failure, shear deterioration of joint was progressed after beam yielding, due possibly to beam bar bond deterioration and high strength of concrete. (3) The joint failure index J should take into account the effect of bond index /x, in order to be more effective in predicting the mode of failure of a beam-column joint. 4.4.2. Shear Capacity of 3-D Joints Bidirectional Loading under A beam-column joint of a moment resisting space frame receives beams coming from three or four directions to be connected to the column. The research project reported herein consists of testing of such realistic beam-column New RC Structural Elements 197 joints subjected to bidirectional (north-south and east-west) lateral loading. Emphasis was placed whether the joint failure index J developed for planar frame beam-column joint is applicable to 3-D joints. Both interior and exterior joints, one each of about one third scale, was tested. Specimens were designed so that the joint shear failure would occur simultaneously with beam yielding. The joint failure index J, briefly introduced in the preceding section, was greatly improved to take many related factors into account. It is now defined as follows beDbaia2V(TB where T,atay is same as in Eq. (4.28), the sum of yield force of beam tensile bars, be, D;, and VOB are same as in Eq. (4.28), effective concrete beam-column joint width, beam depth, effective concrete strength for shear in Eq. (4.9), respectively. a.\ is a coefficient to consider the reduction of effective strength VOB when high strength steel is used, expressed as follows c*i = 1 - 0.1(<7j, - 350)/350 . (4.30) a.2 is another coefficient to consider effect of lateral confinement to the joint expressed as follows a 2 = 1 + 0.6lpway/(TB (4.31) where pw is lateral reinforcement ratio of the joint in the section parallel to the loading direction, and if the joint has perpendicular beams on both sides, axial bars in these beams can be added to the joint hoops in calculating pw, and ay and OB are steel yield point and concrete strength, respectively. Finally a in Eq. (4.29) is a coefficient to consider the effect of joint bond index p, as defined by Eq. (4.26), to be expressed as follows a =0 for p < 3.2 a = (fj.- 3.2)/3.2 for 3.2 < /j. < 6.4 a = 1 for /u > 6.4. (4.32) This equation is a direct reflection of the trend in Fig. 4.47. The value of J index is same as in Eq. (4.28) for good bond (except for a\ and 02), but is doubled for very poor bond, a is also taken to be 1.0 for exterior beam-column joint. 198 Design of Modern Highrise Reinforced Concrete 4 Structures g $ 1200 I 1200 2700 1Z W 2 note: exterior joint specimen (J-13) lacks the hatched portion (b) Plan view Fig. 4.48. Interior beam-column joint specimen (J-12). The value of J index less than 1.0 would correspond to beam yielding prior to joint shear failure, and J value greater than 1.0 would correspond to premature joint shear failure. The 3-D beam-column joint specimens in this subsection were designed aiming at J equals 1.0. Figure 4.48 shows side and plan views of interior beam-column joint specimen J-12. Figure 4.49 shows cross section of column and beams. Column is 300 mm square and beams are 240 mm by 320 mm, and floor slab is 60 mm thick, reinforced with D6 bars at 150 mm on centers in two directions. The exterior beam-column joint specimen J-13 is similar to J-12, except it lacks the New RC Structural 30 J2L Ml 40 40 40 n—i ii r w f— 7^ 30 n—«r • \ i 4 3-D6«» 199 3Q| i—n .,.,..-,. 30-016 Elements 30 60 40 40 100 40 a 60 30 (a) column section 240 *o.«o /I, I 4 J*L o.f?. 4 9 | *<» I I 40 40 40 40 4Q 40 I I I I I l\ • .(•)• < 10-D13 10-D13 /2-D6»J0 160 320 • • » 2-D6®50 4 r - ^ M o - i D13 10-D13 160 320 » » » * (b) EW beam section (c) NS beam section note • exterior joint specimen (J-13) lacks bars in parentheses Fig. 4.49. Member sections of interior joint specimen (J-12). hatched portion of Fig. 4.48(b), and the bars in parentheses of Figs. 4.49(b) and (c). EW beam bars of specimen J-13 are U-shape anchored in the beamcolumn joint. Concrete strength is 61.5 MPa for both specimens, and yield points of beams bars (USD685), column bars (USD980), lateral reinforcement (USD780), and slab bars (SD345), are 725 MPa, 993 MPa, 816 MPa and 345 MPa, respectively. Nominal joint shear stress at beam yielding considering 200 Design of Modern Highrise Reinforced Concrete Structures slab bar contribution to the beam strength is 35 percent and 22 percent of concrete strength for J-12 and J-13, respectively. The interior joint specimen J-12 was first loaded by a constant column axial load of 1620 kN to produce compressive stress of 30 percent the concrete strength. The exterior joint specimen J-13 was loaded by 810 kN axial load, and it was varied in proportion to the column shear force in the EW direction in such a way that N — AP + 810 (kN) where N is axial load and P is column shear force, in the range between 150 kN and 1620 kN. Bidirectional horizontal loads were applied indirectly as vertical loads at beam end, where beam end deflections at both ends were kept the same at all times, and story drift was controlled in a four-leaved clover shape as shown in Fig. 4.50. Numbers in circle indicate cycle numbers, thus each pair of two leaves was repeated twice before going into the next pair of other two leaves. Figure 4.51 shows two examples of load deflection curves. Figure 4.51(a) shows NS direction of J-12, where, as shown in the previous Fig. 4.50(a), the load was always first applied and unloaded in this direction, followed by loading and unloading in the EW direction. Large drops after each peak of load deflection curves correspond to loading in the EW direction, and a steep valleys near the vertical axis correspond to unloading in the EW direction. Similarly, Fig. 4.51(b) shows EW direction of J-13, where the load was always first applied and unloaded in this direction. Because there is only one beam in this direction, the load is much lower than J-12. Otherwise the trend in 1 ^ 4 (z>® * - T3 >> u o m •rH - 1 " -• I UX2> ~ .—i _ ) - 1 6 43 T3 >> O s-i \ r ,©(D 2 T ®@ l z _ ^ -3-3 -5 1 ffl 0 •l± J" o (5)(6) ®@ 0 a "1 @® W -4 1 I 1 1 1 I 1 1 _l 1 - 4 - 3 - 2 - 1 0 1 2 3 ,4 NS direction story drift (%) 5 I I I I I I !_ - 4 - 3 - 2 - 1 0 1 2 3 4 5 NS direction story drift (%) (b) Exterior joint J-13 (a) Interior joint J-12 Fig. 4.50. Story drift history of beam-column joint specimens. New RC Structural 200 £ 3 0) A IB ! -80 -60 -40 -20 0 20 40 60 SO 40 60 80 NS story drift (mm) (a) J-12, NS direction -80 -60 -40 -20 0 20 EW story drift (mm) (b) J-13, E W direction Fig. 4.51. Story shear vs. story drift relations. Elements 201 202 Design of Modern Highrise Reinforced Concrete Structures the load deflection relation is similar to Fig. 4.51(a). Due to above-mentioned bidirectional effect, hysteresis loops are fatter than those under unidirectional loading. Beam bars in the first layer of tension side of J-12 yielded either in the 2 percent or 3 percent drift cycle. In most cases yielding of beam bars in the second layer occured immediately after that. Beam bars in the first as well as the second layer of J-13 yielded mostly in the 2 percent drift cycle. Yielding of column bars was never observed. Corners of beam-column joint had extensive crushing and spalling, and although the damage of joint concrete could not be directly observed, it was concluded that the joints of both specimens failed in the 3 percent drift cycle or later, from the loss of strength in Fig. 4.51 and also from the joint deformation measurement. Thus both specimens failed in the B-J mode, joint shear failure after beam yielding. Figure 4.52 shows history of joint shear stress divided by concrete strength. The general trend of history is similar to that of column shear. An interesting point is that the shear stress in one direction decreases, after reaching its maximum in that direction, under the loading in perpendiculur direction. The maximum shear stress is 0.37CTB for NS direction of J-12, and 0.20<7B for EW direction of J-13. Theses figures are much higher than those usually observed in planar beam-column joint specimens. EW direction of J-12 was 0.36CTB, quite similar to NS direction. However NS direction of J-13 reached only to 0.27(Ts. J-13 was an interior joint in the NS direction, and this low value of J3%.drift 2%.4rift -«. M . «-•.1.1-1.1-1.1 • 1.1 1.1 I. J •. i (. J I. M . 4-1. J-l. 1-1. I I Fig. 4.52. •. I •. I ». 1 I. 4 •. S Tns/OTB Xns / GB (a) J-12 (b)J-13 History of joint shear stress. New RC Structural Elements 203 maximum shear stress indicates the significance of lack of beam member in the perpendicular direction, and possibly the adverse effect of bidirectional loading. In conclusion, we can summarize as follows. (1) The maximum shear strength of 3-D beam-column joints is higher than 2-D (planar) joints due to the presence of perpendicular beams and slab effect. (2) Joint shear stress in one direction decreases, after reaching its maximum in that direction, under the loading in perpendicular direction. (3) Design of a 3-D beam-column joint for joint failure index J equals 1.0 was shown to be adequate to prevent premature joint shear failure prior to beam yielding. 4.4.3. Shear Capacity of Exterior Joints Exterior joint here refers to the beam-column joint at the end of multiple span beams, where the beam and column form a sideways-laid T shape subassemblage. The specimen J-13 in the previous subsection is a typical exterior joint in the EW direction. The objective of this subsection is to investigate the shear strength of exterior joints constructed by high strength materials. As the majority of test data on shear strength of interior as well as exterior beamcolumn joints are based on planar specimens without perpendicular beams and floor slabs, tests in this subsection also employ planar beam column subassemblages. Figure 4.53 shows the detail of specimens. Specimens are about one third scale, with 250 mm square column and 200 mm by 250 mm beam. There are four specimens in this test series, J8, J9, J12 and J13. Apart from difference in material strength, they have different joint lateral reinforcement and beam bar embedment length. Table 4.9 lists concrete strength, shear flexure strength ratio which is ratio of joint shear strength to the joint shear stress at beam flexural yielding, joint lateral reinforcement ratio, and embedment length (horizontal projection) to beam bar diameter ratio. From the second column of the table it can be inferred that specimens J8 and J9 would fail in joint shear while specimens J12 and J13 would fail in beam flexural yielding. Specimens were placed on the test bed as the column in flat position and the beam in upright position, and beam end was loaded horizontally in the cyclic reversal of increasing amplitude. Column was lightly loaded by axial force only to keep the specimens in a stable position. 204 Design of Modern Highrise Reinforced Concrete Structures 1600 Fig. 4.53. Exterior joint specimen details. Table 4.9. Exterior joint specimens. Specimen (1) Concrete Strength O-B (MPa) (2) Shear Flexure Strength Ratio (3) Joint Lateral Reinforcement Ratio Ratio Pj% (4) Embedment Length Beam Bar Diameter Ratio J8 54.8 1.02 0.2 16.5 J9 50.3 0.90 0.6 12.0 J12 85.4 1.39 J13 81.0 1.34 j 0.2 16.5 0.6 16.5 Figure 4.54 shows plottings of the most important test results of joint shear strength vs. concrete strength together with results of some previous test specimens. J8 failed in joint shear simultaneously with the yielding of first layer beam reinforcement, and all specimens failing in joint shear (J mode) are New RC Structural Elements 0 20.0 40.0 60.0 80.0 concrete strength OB (MPa) 205 100.0 Fig. 4.54. Joint shear stress and concrete strength. plotted in Fig. 4.54 with circles (black and white for positive and negative maximum, respectively). J9 is a specimen with small embedment length of 156 mm compared to 215 mm of other specimens, and it failed in anchorage failure (Ja mode) with splitting cracks along beam bars, and its strength is plotted with triangles together with another specimen in the same failure mode. J12 and J13 failed in beam flexural yielding followed by joint shear failure, and all specimens failing in this mode (B-J mode or B-Ja mode) are plotted in Fig. 4.54 with squares. Figure 4.54 also shows the relationships of test results with AIJ recommendation for external joint (4.3) Tju = 0.18crs (4.33) TJU = 1 . 1 7 v ^ i (4.34) and ACI corner joint Eq. (4.9) where TjU : joint shear strength in MPa <JB : concrete strength in MPa. It will be seen that Eq. (4.33) underestimates joint shear strength in medium concrete strength range but approximates well in high strength range, 206 Design of Modern Highrise Reinforced Concrete Structures of those specimens failing in J mode. Equation (4.34), on the other hand, is a good approximation of the lower limit of all specimens including Ja mode and B-J mode. The regression analysis of only those specimens in J mode resulted in the following expression rju = 0.86cr%655 (4.35) where Tju and (JB are in MPa. Although data are not shown here, bond and anchorage capacity of double layer beam bars were studied utilizing strain measurement, and it was concluded that the anchorage capacity of the second layer is greatly reduced due possibly to the concrete distress around the first layer. This fact should be somehow taken into account for the detailing in practical structural design. 4.4.4. Concrete Strength Difference Column and Foundation between First Story This subsection deals with a somewhat different subject of beam-column joint. It deals with the joint between first story column and footing beams. Foundation of highrise reinforced concrete buildings usually consists of a grid of very large footing beams, several meters deep and more than a meter wide, no matter whether it is supported by piles or directly by hard subsoil. Such grid of large size footing beams is deemed necessary for rigidity and strength to transmit stresses in the superstructure induced by lateral forces to the substructure of piles or subsoil. Because of large amount of concrete used in footing beams, it is quite common to specify lower concrete strength to footing beams, compared to the first story column where the highest strength within the building is usually specified. It is this strength difference and its consequences that was the concern of the research project in this subsection. Figure 4.55 shows shapes of compression test specimens. Shaded portion represents lower part of first story column with 60 MPa concrete, and the column size is 100 mm square, reinforced appropriately. White portion is a part of footing beam grid, in cruciform, T-shape or L-shape, with 20 MPa concrete. Footing beams are either 100 mm wide, same as the column, or 150 mm wide, 50 percent wider than the column, and appropriately reinforced. Under the action of monotonic vertical loading, specimens with cruciform footing beams failed in the column, while those with T- or L-shaped footing New RC Structural "Tllf QaXMPa) Elements |60(MPa) Fig. 4.55. Compression test specimens of column-footing beam joint. + 10 at 450 kN L10at30kN T10at30kN FaceC FaceB ', Face A FaceB 4' FaceB * X X - \ * ; *'* % Face A Face A I \_ % % Face C FaceB 1 FaceB Face A FaceB Face A Fig. 4.56. Principal strains on the side face of footing beams. 207 208 Design of Modern Highrise Reinforced Concrete Structures beams failed in the footing beam portion, at about 83 or 63 percent of cruciform specimens, respectively. From the measurement of principal strains at the side faces of footing beams shown in Fig. 4.56, it is inferred that load path in the footing beam is different between cruciform, T-shaped, or L-shaped footing beams. As shown by the hatch in the plan view sketches, a cruciform beam grid receives the load at a relatively large area, while a T-shaped beam receives mainly by beams in the continuous direction, and an L-shaped beam receives at a relatively small zone near the corner. Furthermore specimens as shown in Fig. 4.57 were made using 60 MPa concrete in the column and 60 MPa or 20 MPa concrete in the footing, and horizontal load was applied at the column top to produce flexural failure at the column base. As seen in the figure, crushing failure was more spread out into the footing in case of weak footing concrete, and the maximum load was 26.7 kN and 23.6 kN, or in other words, weak footing specimen could sustain 88 percent of load for strong footing specimen. However the load deflection relationship was quite similar. Thus it can be concluded that the concrete strength difference between first story column and foundation may not be a problem for interior column, even when the strength difference is as much as threefold. For exterior or corner columns, it is possible that partial collapse of foundation may happen even AJL (a) 60 MPa column and 60 MPa footing (b) 60 MPa column and 20 MPa footing Fig. 4.57. Column-footing beam specimen after failure. New RC Structural Elements 209 under axial loading, and a careful check of bearing strength of foundation is mandatory in the practical design. The prevalent practice of using higher strength concrete in the upper half of footing beam depth would help reduce the problem discussed herein. 4.5. M e t h o d of Structural Performance Evaluation 4.5.1. Restoring Force Characteristics of Beams Frame structures of buildings usually assume weak-beam and strong-column type collapse mechanism, where yield hinges would form at the first story column bases and beam ends of all upper floors. The restoring force characteristics of beams would dictate the overall behavior of frames under earthquake excitation, and therefore it must be accurately evaluated in the design. In the New RC project, experimental force displacement relationship was supposed to be idealized as shown in Fig. 4.58. It may be clear from the figure how to construct trilinear idealization of an experimental curve. Firstly, a point corresponding to the first cracking is determined from the initial stiffness and observed crack load. Secondly, measured yield load is confirmed at maximum strength or the load at 2 percent drift angle, and a load corresponding to the three quarters along the way from maximum load or load at 2% drift angle yielding S7 eQ, y~cQbc) +cQbc ^ 01 V*^ \ idealized Q' 8 experimental Q- 6 o cQo —y cracking c<y»< deformation Fig. 4.58. Idealized force-deformation relationship. 210 Design of Modern Highrise Reinforced Concrete Structures 300.0 I 2 rectangular D T-beams • rectangular (New RC) • T-beams (New RC) 0 200.0 3 .§ 100.0 o. 100.0 200.0 calculated values (MN/m) 300.0 Fig. 4.59. Experimental vs. calculated initial stiffness. cracking to yielding is determined. A point marked "A" is found for this load, and a straight line connecting the crack point and point "A" and its extension is drawn to find the deformation at yielding. Characteristic points of this method are that the yield load corresponds to ultimate flexural load carrying capacity, and that the stiffness after yield is zero. How to determine each parameter in Fig. 4.58 will follow. 4.5.1.1. Initial Stiffness Initial uncracked stiffness is calculated considering flexural and shear deformation of members. Figure 4.59 shows relationship of observed vs. calculated initial stiffness, considering rigid zones at the ends of each member as specified in the Calculation Standards of Reinforced Concrete Structures of AIJ (Ref. 4.3). 4.5.1.2. Flexural Cracking Cracking moment is calculated from the tensile strength of concrete and the equivalent section modulus including effect of reinforcement. Either splitting tensile strength or 0.56 times the square root of concrete strength in MPa may be used as tensile strength. Figure 4.60 shows the relationship of observed vs. calculated cracking load of beams where the tensile strength was evaluated by the latter method. Large scatter is conspicuous as it is inherent to phenomena like cracking, but it will be agreed that the calculated values generally New RC Structural Elements 211 98 & 78 CO <u J3 1 59 73 c 2 39 0 rectangular Q T-beams • rectangular (New RC) • T-beams (New RC) 0* 0 i 1 i i i 20 39 59 78 98 C a l c u l a t e d v a l u e s (kN) Fig. 4.60. Experimental vs. calculated cracking load. shoot the average of observed values, and no different trends are seen between previous tests and New RC tests. 4.5.1.3. Yield Deflection Figure 4.61 shows experimental values of yield deflection of New RC beams as contrasted to those of conventional RC beams. New RC beams with high strength material clearly show greater yield deflection. This is due, first, to larger yield strain of high strength steel, and secondly, due to increased pullout displacement of beam bars from columns or loading stubs, and increased yield hinge length, inherent to relatively poor bond behavior of high strength concrete. In terms of yield stiffness reduction factor, however, the commonly used Sugano's equation may be applied to New RC members. Yield stiffness reduction factor is defined as the ratio of secant modulus at yield point of RC members to the initial uncracked stiffness, and is expressed based on a statistical survey as follows ay = (0.043 + 1.64npt + 0.043a/D + 0.33?7o)(d/D)2 where ay : yield stiffness reduction factor n : Young's modulus ratio of steel and concrete Pt : tensile reinforcement ratio bared on gross concrete section (4.36) 212 Design of Modern Highrise Reinforced Concrete Structures 2.0 j I 1.5 - I: 1.0 30 Q T-beams • rectangular (New RC) • T-beams (New RC) _L _J_ 50 concrete (a) Relation to 40 2.0 r- t O rectangular 0.5 0 I • °a _L 60 70 80 90 strength (MPa) concrete strength • 1.5 O 1.0 O O * 0.5 0 300 a O rectangular • T-beams • rectangular (New RC) • T-beams (New RC) -L. 400 500 600 700 steel yield point(MPa) 800 (b) Relation to steel strength Fig. 4 61. Experimental yield deformation and material strength. a : shear s p a n length determined from t h e ratio of m a x i m u m bending m o m e n t t o t h e m a x i m u m shear force D : d e p t h of t h e m e m b e r 770 : axial stress ratio determined from the axial stress considering concrete area only divided by t h e concrete s t r e n g t h (rjo = 0 for beams) New RC Structural Elements 213 0.4 r O D • • rectangular T-beams rectangular (New RC) T-beams (New RC) 0.1 0.2 0.3 calculated values (a) Exp. vs. calc. values 3.0r O D • • 2.0 1.0 Al. -cS= x; j _ 30 rectangular T-beams rectangular (New RC) T-beams (New RC) _i_ 90 50 60 70 80 concrete strength (MPa) (b) Accuracy vs. concrete strength 40 Fig. 4.62. Yield stiffness reduction factor. d : effective depth of the member i.e. depth from the most compressive fiber to the centroid of tensile reinforcement. Figure 4.62 is the comparison of experimental values of yield stiffness reduction factor to the values from Eq. (4.36). Although large scatter is seen, it may be concluded that Sugano's equation is equally effective to the New RC beams as those of conventional material. 214 Design of Modern Highrise Reinforced Concrete 4.5.1.4. Structures Flexural Strength Flexural strength of a beam may be obtained by one of the following three methods. The first is to use approximate equation given by the Building Center of Japan (Ref. 4.7) Mu = 0.9Zat<Tyd where Mu at ay d S : : : : : (4.37) is flexural ultimate moment of a beam is tensile reinforcement area is yield strength of tensile reinforcement is effective depth of the beam to the tensile reinforcement is for different tensile reinforcement groups. The second method is to conduct theoretical analysis assuming rectangular stress block of American Concrete Institute, and ultimate compressive strain of 0.3 percent. The third method is to use stress block proposed by the high strength steel committee of New RC project, and ultimate compressive strain of 0.3 percent, same as the ACI method. It was shown that the difference between results of the second and third methods was small, and they predicted the observed flexural strength of both rectangular and tee beams reasonably well, provided for the latter that the entire slab width is taken effective. The approximate equation in the first method gave approximately 10 percent smaller values both for rectangular and tee beams, even for the latter if the entire slab width is taken. 4.5.1.5. Limiting Deflection In order to avoid shear failure in the yield hinge zone, and to secure the plastic hinge rotation capacity, it was found necessary to follow the same procedure as will be described later for columns. 4.5.1.6. Equivalent Viscous Damping Flexural deformation usually dominates the beam deformation. For such beams it was shown that the equivalent viscous damping at yielding is about 5 to 10 percent, and it increases as deformation gets larger. It was about 10 to 15 percent at the drift angle of 2 percent. New RC Structural Elements 215 Thus it was concluded that the restoring force characteristics of New RC beams can be formulated generally by the same methods as the conventional beams. However in case where a more precise idealization is required by the analysis software such as separation of flexural and shear deformations, it will be necessary to refer to the original research data. 4.5.2. Deformation Capacity of Columns Columns subjected to lateral load usually retain deformation capacity of more than 2 percent when tensile reinforcement yields first. However, it is usually reduced to smaller values when the column is subjected to flexural compression failure due to high axial load, to bond splitting failure along axial reinforcement, or to shear failure in the yield hinge zone. Followings are the studies leading to evaluation of deformation capacity of columns. 4.5.2.1. Flexural Compression Failure Columns subjected to high compression fail first by crushing of cover concrete, but thereafter the core concrete, confined by compression axial reinforcement and lateral reinforcement, starts carrying compressive stress, up to certain limiting deformation. Equation (4.38) was proposed to evaluate this limiting deformation in terms of drift angle Ru = (0.5 - N/Acfc)/7 ^ 0.04 f'c = Fc + CaPwawy Ca = 4.41a/3(l - 1.24s/D) where Ru N Ac f'c Fc pw Ca (4.38a) (4.38b) (4.38c) : limiting drift angle : axial force : core area : core concrete strength expressed by Eq. (4.38b) : concrete strength to be taken 0.85 times the cylinder strength '• hoop reinforcement ratio : yield strength of hoop reinforcement : a coefficient to reflect the effect of hoop arrangement detail, expressed by Eq. (4.38c) 216 Design of Modern Highrise Reinforced Concrete Structures a,/3: correction factors for number of interior tie legs s : hoop spacing D : column depth. Equation (4.38a) was originally developed for columns of ordinary strength material as an equation to express lower bound of limiting deformation in terms of axial stress relative to core concrete strength. According to Eq. (4.38a), Ru is constantly 4 percent for axial stress ratio less than 0.22, and is linearly reduced for greater axial stress ratio up to 0.5 where Ry, becomes zero. It was shown that Eq. (4.38a) is readily applicable to New RC columns if core concrete strength is expressed by Eqs. (4.38b) and (4.38c). 4.5.2.2. Bond Splitting Along Axial Bars In order to evaluate the deformation capacity as limited by the bond splitting along axial reinforcement, it is reasonable to use the bond index, which is the ratio of working bond stress to the ultimate bond strength. As to the working bond stress, Eq. (4.39) was proposed (Ref. 4.3) where the effective bond length along the member is reduced with the increase of axial load Tf = 2o-ydb/(4Lb) (4.39a) Lb = L - (1 + 7)d (4.39b) 7 = aN/{Ago-B) ^1.0 (a = 3) (4.39c) where Tf : working bond stress cry : yield stress of axial reinforcement db : diameter of axial reinforcement Lb : effective bond length expressed by Eq. (4.39b) L : clear length of a member d : effective depth of a member 7 : a coefficient for axial effect, expressed by Eq. (4.39c) N : axial load Ag : gross area of a member CTB : concrete strength. As to the ultimate bond strength, there are several proposals such as literature (Refs. 4.8-4.10). Based on the literature (Ref. 4.9), the bond index was New RC Structural Elements 2.00 1.50 | r o • •% 217 X= 0.149 —0.1677 X= 0.149 - 0 . 1 1 4 7 Column Beam 1.00 a 0.50 0 j 2.5 5 7.5 10 limiting deflection (%) Fig. 4.63. Bond index and limiting deflection. calculated and related to observed limiting deformation in Fig. 4.63. As seen the scattering of test data is very large. Two straight lines in the figure are regresseion lines for the average and lower limit. However, it will be more practical to show the upper limit of bond index to ensure certain deformation limit such as 2 percent. 4.5.2.3. Shear Failure in the Hinge Zone after Yielding Equation (4.40) was proposed in the New RC project as an equation to evaluate limiting deformation of a yield hinge dictated by the shear failure after yielding. It is similar to the shear strength equation in the AIJ Ultimate Strength Design Guidelines (Ref. 4.7), which was introduced in Sec. 4.2.7, except for the following three points: effective strength of concrete, crack inclination angle, and limiting value for lateral reinforcement yield strength K = bjtPwCwy cot <j> + t a n # ( l - /3)bDt/crB/2 (4.40) where tan0 = y/(L/D)2 + 1- L/D 13 = (1+ cot 2 <$>)Vv>awyl{vaB) • (4.41) (4.42) In the case of calculating /3 value only, cot <j> value outside the hinge zone and value inside the hinge zone are used. 218 Design of Modern Highrise Reinforced Concrete Structures In the above equations, Vu : ltimate shear force b : member width D : member depth jt : distance between axial reinforcement (in case of multilayer section, distance between plastic centroids of axial reinforcement) L : clear length of member 9 : inclination angle of strut in the arch (strut) mechanism, to be determined from Eq. (4.41) /3 : concrete stress in truss mechanism relative to effective strength 4> : crack inclination angle to be explained later v : effective concrete strength factor in the hinge zone, to be explained later pw : lateral reinforcement ratio, and pwawy should not exceed I/CTB/2 awy : lateral reinforcement yield strength as : concrete compressive strength. The coefficient v, effective concrete strength factor in the hinge zone, is expressed by Eq. (4.43) which is same as Eq. (4.10) in Sec. 4.2.7, but i/0 is modified from Eq. (4.15) to consider the axial load level as in Eq. (4.44) v = (1.0 - 15i?p)z/0 ^ 0.25^0 i/0 = 1.7(1 + 2n)/a~1/3 (4.43) (4.44) where Rp : plastic hinge rotation of yield hinge i/0 : effective concrete strength factor outside hinge zone n : axial load ratio [n = N/Agas)The angle 4> roughly corresponds to crack inclination, but more precisely it represents angle of concrete strut in the truss mechanism, and cot <f> is determined as the minimum of the following three equations, where Eq. (4.45) is different from Eq. (4.14) cot <j) = 2.0 - 3n - 50RP (4.45) c o t 0 = j t /(£>tan0) cot <f> = Jtyas/iPw^wy) (4.46) - 1-0 • (4-47) iVetu RC Structural Elements 8 r 219 / / XI £ " / o CI / a a, / / ^L ° / o 0 <n=£l/6 A. l / 6 < n £ l / 3 a l/3<n£l/2 I 0 2 -I 1— 4 6 calculated drift (%) » Fig. 4.64. Comparison of experimental and calculated limiting deformation. Finally the limiting value of awy is modified from 25<TB to 125^V0(TBUsing the above equations and equating the flexural capacity of a yield hinge to the shear strength, limiting deformation Rp associated with shear failure after yielding was inversely calculated. Figure 4.64 shows the observed limiting deformation in the tests and calculated values. It is seen that calculated values are lower than test values, hence the limiting deformation can be estimated on the safe side. 4.5.2.4. Shear Strength of Beams and Columns Equation (4.40) can also be applied to members not expected to produce yield hinges. In this case hinge rotation angle Rp must be put to 0. Then Eq. (4.43) gives v = u0, and cot<f> = 2.0 — 3n from Eq. (4.45). Figure 4.65 shows the relationship of observed shear strength of New RC members and those calculated by Eq. (4.40), both normalized by the calculated flexural strength. It is seen that Eq. (4.40) gives highly dependable evaluation of shear strength, particularly for high strength concrete. 4.5.3. Flexural Strength of Walls As it was shown in Sec. 4.3.1, load deformation curves of flexural walls do not generally have a clear and well defined yield point. However, when all the column bars in the tension side column yields, it is seen that the overall load deformation curve comes to a general yield point. The load at this point was 220 Design of Modern Highrise Reinforced Concrete Structures 1.0- > 5 0 0 0.5 1.0 1.5 2.0 2.5 3.0 Q,/Qj Fig. 4.65. Accuracy of shear strength equation. defined as flexural yield strength of a wall in the New RC project, and it was investigated separately from the ultimate strength. Assuming plane wall section to remain plane, the yield strength can be calculated by a simple theory, for the condition where all tensile column bars yielded. For ordinarily proportioned wall sections, however, Eq. (4.48) may be used as a practical approximation My = {0.8Ty + 0.2Twy + 0.5iV(l n = n)}L N/{(Aw+HAc)aB} (4.48) (4.49) where yield moment of wall tensile force of all axial bars in the tension side column tensile force of all vertical wall bars J-wy N : axial force acting on the wall n : normalized normal stress of the wall : wall area Aw : column area : concrete strength L : total length of wall. Ultimate flexural strength, on the other hand, corresponds to the maximum load carried by a wall failing in flexure. It can also be calculated by a simple theory based on the same assumption as above, for the condition that the most compressive fiber strain reaches 0.3 percent. For ordinarily proportioned wall sections, Eq. (4.50) may be used Mu = {0.9Ty + 0ATwy + 0.5AT(l -n)}L. (4.50) Where Mu is the ultimate moment of wall and other notations are same to New RC Structural 2000 Elements 221 / a : New RC specimens / o : other specimens ju / 1500 •a a •i IOOO 500 500 1000 1500 calculated load (kN) 2 000 Fig. 4.66. Tested and calculated values of ultimate flexural strength of walls. those in Eqs. (4.48) and (4.49). Figure 4.66 shows the favorable comparison between observed and calculated flexural strength of New RC walls and other existing test results. 4.5.4. Shear Strength of Beam-Column Joints As it is possible to make column sections of a New RC buildings smaller than those of ordinary material, beam-column joints become the critical portion in a frame in horizontal resistance. The design method proposed in New RC project is based on the lower bound theorem of plasticity theory. Figure 4.67 shows an example of formation of stress field within and around an interior beam-column joint. Using strut and tie concept, this stress field is constructed in such a way that equilibrium of force is satisfied and no internal force violates the yield criterion. Such a stress field is called statically admissible stress field. Assuming that beam and column bars are infinitely strong, story shear force is obtained from the lower bound theorem of plasticity theory. In Fig. 4.67, a is a coefficient for the bond characteristics of beam bars passing through the joint. If the bond is good, a = 0, and if the bond is very poor, a = 1. For the condition of the load Pi at right beam end to be maximum, we obtain D_ bvdB ~2 (4.51) 222 Design of Modern Highrise Reinforced Concrete Structures Fig. 4.67. Statically admissible stress fields of a beam-column joint. and for the condition of the load P2 at left beam end to be maximum, we obtain Ti + aT2 bv<TB D 2 (4.52) where 7i and T2 are forces as shown, b is width of beam-column joint, VOB is effective compressive strength of concrete, and D is the beam depth. As illustrated in Fig. 4.67, the depth of beam struts is thus half the beam depth. The story shear thus obtained for Fig. 4.67 is now compared with the storyshear corresponding to beam yielding. If the story shear from Fig. 4.67 is greater, the joint shear failure could not happen. A similar strut and tie model can be constructed for an exterior beam-column joint. The effective compressive strength of concrete proposed in the CEB Model Code 90 (Ref. 4.11) was found to be applicable to high strength concrete in Japan. Furthermore, adverse effect of high strength steel to joint shear strength and favorable effect of beams in the orthogonal direction were observed. These are incorporated in the following Eq. (4.53). An index J to evaluate the possible joint shear failure was derived in the Sec. 4.4.2, but it was improved into the following form in view of all available data, and is to be used in the design in such a way that beam bars should New RC Structural Elements 223 satisfy the condition shown in the following equation '-fet'+'-x" (453) ' where Eat : total tensile reinforcement area of beams to be anchored in the joint (Ty : yield strength of beam bars D : beam depth 6 eq : effective width of beam-column joint to be taken as average of beam width and column width VOB '• effective concrete strength as shown below a : bond coefficient, as shown below. The effective concrete strength is expressed as follows VOB = aia2 • 1.7<4/3 (4.54) where as is concrete strength in MPa. Thus it is basically similar to CEB Model Code 90, but is now modified by two multipliers, a\ and a2- The first multiplier ot\ is for the joint strength reduction due to high strength beam bars, and is expressed as follows ai = l-0.18S^p (4.55) where ay is yield stress of beam bars in MPa. Thus a = 1 for SD345, and it reduces to a = 0.82 for SD685. Another multiplier a2 is for the strength enhancement due to beams in the orthogonal direction, and is expressed as follows a2 = 1 + KWW+P&V (4.56) OB where K Pw awy Pg aty <JB : enhancement factor due to confinement, to be taken as K = 1.6 : lateral reinforcement ratio within the joint : yield strength of lateral reinforcement : total axial bar area in orthogonal beams divided by beam area '• yield strength of orthogonal beam bars • concrete strength. 224 Design of Modern Highrise Reinforced Concrete Structures The bond coefficient a is formulated as shown below. For exterior joints, a is always 1 a = 0 for n ^ 3 a = (u - 3)/3 for 3 < n ^ 6 ) a — 1 for fj, > 6 (4.57) db (4.58) y/&B Dc where /x oy OB db Dc : bond index : yield strength of beam bars in MPa '• concrete strength in MPa • beam bar diameter : column depth. Minimum requirement for joint lateral reinforcement is set forth for both interior and exterior joints as 0.2 percent of lateral reinforcement ratio. 4.5.5. Connections of First Story Column to Foundation The effect of high strength first story column on the bearing capacity of foundation made of not-so-strong concrete is discussed in some detail in Sec. 4.4.4. Based on the testing reported therein and also based on the engineering judgment, a set of design recommendations were developed. 4.5.5.1. Bearing Stress Interior columns sitting on the continuous footing beams with width larger than column size should be safe, but exterior and corner column sitting on Tor L-shaped footing beams should be checked for bearing strength of footing beams. 4.5.5.2. Splitting Stress Local compression on the footing beams would produce splitting tensile stress in the directions perpendicular to the bearing stress. Design for this stress may follow the provisions for prestressed concrete structures at the bearing zones of PC steel anchorage. New RC Structural Elements 225 4.5.5.3. Strengthening Footing beams may be strengthened by increased width, exterior beam stub of about one-third the beam depth, steel reinforcement as in PC steel anchorage, or by increasing the concrete strength at least in the upper part of footing beams. 4.6. Concluding Remarks In this chapter, the author tried to present the scope of the Structural Element Committee of the New RC research project. Major portions of this chapter, from Sees. 4.2-4.4, were devoted to presentation of representative experimental programs on beams and columns, walls, and beam-column joints. It was attempted to summarize each experimental program on the entire basis covering several years of its conduct, but the emphasis had to be placed on the results of the last year of the project for which complete reports were presented to the BRI from the individual investigators. Section 4.5 summarizes the entire work in a form readily applicable to the structural design of buildings, although it still does not assume a form of guidelines. As the result of the effort of the Structural Element Committee to place an emphasis on the development of structural performance evaluation based on rational and logical procedure, each conclusion in Sec. 4.5 may be applied to wide range of circumstances on the rational basis. Wider scope of application was always sought, but some problems had to be left without reaching thorough understanding, such as yield deflection, limiting deflection, and effect of bidirectional loading. It is expected that continued research effort should be given to these problems after the conclusion of the New RC project. References 4.1. Kaku, T. et al., A proposal of bond splitting strength equation of reinforced concrete members including high strength materials, Proceedings, Japan Concrete Institute 3(1), January 1992, pp. 97-108 (in Japanese). 4.2. Architectural Institute of Japan, Standard for Structural Calculation of Reinforced Concrete Structures, 1993, p. 654 (in Japanese). 4.3. Architectural Institute of Japan, Design Guidelines for Earthquake Resistant Reinforced Concrete Buildings Based on Ultimate Strength Concept, 1990, p. 340 (in Japanese). 226 Design of Modern Highrise Reinforced Concrete Structures 4.4. Wakabayashi, M. and Minami, K., On the shear strength of structural concrete members, Annual Report of Disaster Prevention Institute, Kyoto University, No. 24B-1, April 1981, pp. 245-277 (in Japanese). 4.5. Aoyama, H., Earthquake resistant design of reinforced concrete frame building with "flexural" walls, J. Faculty Eng., University of Tokyo (B) X X X I X ( 2 ) , 1987, pp. 87-109. 4.6. Otani, S., Kabeyasawa, T., Shiohara, H. and Aoyama, H., Analysis of the Full Scale Seven-Story Reinforced Concrete Test Structure, Earthquake Effects on Reinforced Concrete Structures, US-Japan Research, American Concrete Institute, SP-84, 1985, pp. 203-239. 4.7. Building Center of Japan, Guidelines for structural calculation under the building standard law, July 1991, p. 367 (in Japanese). 4.8. Murakami, Y. and Kato, D., Ductility of reinforced concrete columns using high strength materials, Annual Convention Speech Summary, Architectural Institute of Japan, September 1991, pp. 213-214 (in Japanese). 4.9. Kaku, T., Zhang, J., Kumagai, S. and Iizuka, S., Bond splitting strength of reinforced concrete beams with high strength concrete, Proceedings, Japan Concrete Institute 13(2), June 1991, pp. 163-168 (in Japanese). 4.10. Maeda, M., Otani, S. and Aoyama, H., A proposal of a formula for bond splitting strength of reinforced concrete members, Proc. Struct. Eng. Symp., Architectural Institute of Japan, V. 38B, March 1992, pp. 293-306 (in Japanese). 4.11. Comite Euro-International du Beton, CEB-FIP Model Code 1990, First Draft, Bulletin d'Information, No. 195 and 196, Lausanne, March 1990. Chapter 5 Finite Element Analysis Hiroshi Noguchi Department of Architecture, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan E-mail: noguchi©archi.ta.chiba-u.ac.jp 5.1. Fundamentals of F E M The finite element method (FEM) was first proposed in the middle of 1950's by researchers of aircraft structural mechanics in Europe and North America. Subsequently energetic research and development were undertaken on "matrix structural analysis". International competition on the space development gave impetus to this movement, and the Boeing Corporation developed the displacement method of structural analysis in which displacements are taken to be unknown and analysis was formulated using energy principle which was convenient for analyzing complicated structures. This technique was formulated in the form of matrix, and its clearness was suitable for computer handling (Refs. 5.1-5.3). Before long this method was introduced to other disciplines of structural engineering such as civil engineering, architecture, shipbuilding and mechanical engineering with the support of surprising development of computers. The FEM is a method to express systematically and uniformly the calculation procedure of structural engineering in practical analysis and design by mathematical language of matrix algebra. The computer can understand this language perfectly, and it has enabled us to deal with very complicated and large structural calculation in short time. 227 228 Design of Modern Highrise Reinforced Concrete Structures Grid points Boundary C (i, y+Ay) Deferential approximation {x+Ax.y) 3f . f(x+Ax, y)-f(x, Bx~~ Jx y) ' 3 / . _ f(x, y+Jy)-f(x, dy~ Ay y) Fig. 5.1. Finite difference method (Ref. 5.4). Boundary C Finite element Finite element Approximation Fig. 5.2. Finite element method (Ref. 5.4). The FEM can be easily understood, as Miyoshi explained (Ref. 5.4), in contrast with the finite difference method. The finite difference method is a method to solve the governing equation for an object by the finite difference representation on the lattice points in the area D, as shown in Fig. 5.1. On the other hand, the FEM is a method to approximate an object with infinite degrees of freedom of deformation by an aggregate of many elements with finite degrees of freedom, as shown in Fig. 5.2. The element that has finite degree of freedom is called "Finite Element", because it has a finite size. In the FEM, the governing equation is rewritten for an aggregate of elements, which becomes simultaneous linear equations. In comparison, it is clear that the finite difference method solves a physically exact governing equation by the mathematical approximation of the finite difference, and the FEM obtains a mathematically exact solution of governing equation physically approximated by finite elements. Various types of finite elements have been proposed in order to express an object as an aggregate of finite elements, and to adapt the shape of the element to the object problem. They are as follows: Finite Element Analysis 229 (1) Two-dimensional problem: triangular element, quadrilateral element, etc. (2) Shell problem: triangular plate element, quadrilateral plate element, etc. (3) Three-dimensional problem: tetrahedral element, hexahedral element, etc. (4) Axial-symmetric problem: triangular ring element, quadrilateral ring element, etc. The FEM is mathematically based on the variation analysis of partial differential equations. It can be applied to any phenomena governed by partial differential equations including fluid, heat conduction and electromagnetism. It is now a powerful means to analyze what is called migration phenomenon theory in aeromechanics, heat transfer, electromagnetism and reaction engineering. The main reason why the FEM has been used so widely in various areas is its generality, capable of solving any shaped object under any arbitrary boundary conditions, and also observing deformation distribution and detailed state of stress. The principle of the FEM is described in detail in the literature (Ref. 5.3), etc. 5.2. 5.2.1. F E M and Reinforced Concrete History of Finite Element Reinforced Concrete Analysis of A reinforced concrete (RC) is a composite structure that consists of steel reinforcement and concrete with different material properties. A basic characteristic of RC is that concrete, weak in tension, is reinforced by steel reinforcement, which is strong in tension. RC behaves as a composite structure under load, but when cracks are generated in concrete, it shows complicated nonlinear behavior in which the superposition is not generally applicable as in case of linear behavior. The main phenomena after cracking are bond action between reinforcement and concrete, aggregate interlock along the crack interface, dowel action by the local bending of reinforcement crossing cracks and compressive deterioration of cracked concrete. Since the FEM has been developed initially for isotropic continuous material, its application to RC structures was extremely difficult, as it 230 Design of Modern Highrise Reinforced Concrete Structures becomes discontinuous after cracking. The first application of the FEM to RC was a crack analysis of RC beams by Scordelis and Ngo in 1967 (Ref. 5.5). They represented concrete and reinforcement separately using different sets of finite elements. Their models for cracking and bond slip could simulate physical phenomena splendidly. They investigated the propagation of shear cracking and the subsequent role of shear reinforcement in detail. It was unique that they could trace in detail the change of internal stress condition with load that had been difficult to observe in the physical experiment. This research gave a significant effect on the subsequent researches on RC. Isohata and Takiguchi published papers on the application of FEM to RC shear problems in 1971. The research on the FEM analysis of RC structures in 1970's and 1980's was oriented, first, towards the formulation of constitutive laws for the modeling of material behavior of RC, and second, the application of FEM to clarify nonlinear behavior of RC members. The IABSE Colloquiums held in Delft, the Netherlands in 1981 (Ref. 5.6) was the first international conference in this area. Modeling of the material behavior of RC was discussed, and it was concluded that a future problem was to fill up the gap between FEM researchers and experimental researchers. A committee on the shear strength of RC structures was established under the chairmanship of Okamura, the University of Tokyo in Japan Concrete Institute (JCI), from 1981 to 1984. The shear problem, an important problem in the earthquake-resistant design, was discussed from the viewpoints of macroscopic models and microscopic FEM models. Publication of test data of selected test specimens for the verification of analytical models was a significant activity of the committee. It can be said that the research in this field was drastically advanced by the systematic research activities mainly by young committee members in only four years (Ref. 5.7). In 1983, an international blind competition for the analytical prediction of behavior of RC panels was managed by Collins at the University of Toronto. The experimental result was suppressed from disclosure during the analysis, and FEM researchers were asked to attend the competition and to submit analysis corresponding to the experiment. But many FEM researchers failed to predict the behavior with sufficient accuracy. Applicants with better prediction had confirmed the concrete compressive deterioration characteristics by their own biaxial tests before the analysis. Many analytical researchers of RC learned from this international competition that it is important to carry out basic experiments for the modeling and to evaluate the reliability of analytical Finite Element Analysis 231 models. This experience was succeeded by the integrated research supported by the Ministry of Education Grant-in-Aids for Scientific Research, "Basic experiment on accuracy improvement of FEM analysis of RC structures and development of analytical models", from 1986 to 1989, represented by Morita of Kyoto University. A cooperative research group mainly composed of young researchers made lively discussions overcoming academic clique. The research fruits were presented in one session of the ASCE Structures Congress and also in the Tokyo seminar in 1989. The Tokyo seminar was very successful with more than 200 participants (Ref. 5.8). The first US-Japan seminar on the FEM analysis of RC structures was held in Tokyo in 1985, and analytical models for applying FEM to RC structures (RCFEM) were discussed. It was characteristic for the US side to introduce the concept of fracture mechanics in their research reports. Aoyama and Noguchi reported future prospects of RCFEM. They indicated the necessity of the direct application of FEM to the practical design and the application of FEM to the development of macroscopic models and design equations as future research goals (Refs. 5.9 and 5.10). In JCI committee on "FEM analysis and design method of RC structures" under the chairmanship of Noguchi of Chiba University from 1986 to 1988, future problems indicated in the above US-Japan seminar were made to be activity goals. A design practitioner group published "Guideline on the application of FEM analysis to RC design" (Ref. 5.11). A researcher group verified the validity of previously proposed shear strength equations and macroscopic models of RC members by FEM analysis, aiming at the development of rational macroscopic models and design equations. A calculation method of shear strength derived from a macroscopic model was adopted in the Architectural Institute of Japan ultimate strength design guidelines, based on the activities of the above-mentioned JCI committee (Ref. 5.12). The second US-Japan seminar on the FEM analysis of the RC structure was held in Columbia University, New York in 1991, and Japanese basic and systematic research on the application of RCFEM to development and design of new structures was introduced. A gap between FEM analytical researchers, experimental researchers and practical designers was discussed. Shirai reported on a detailed questionnaire results on the application of nonlinear FEM analysis to practical design, collected from design practitioners of thirteen construction companies in Japan. His report represented the characteristics of the Japanese research (Ref. 5.13). 232 Design of Modern Highriae Reinforced Concrete Structures Over three years from 1992 to 1995, the integrated research on "Reconstruction of the shear design method of reinforced concrete structures by extremely precise FEM analysis" was carried out, represented by Noguchi of Chiba University and supported by the Ministry of Education Grant-in-Aids for Scientific Research. This was a cooperative research based on previous researches and by young generation researchers standing aloof from academic clique. The emphasis was placed on the application of the FEM analysis on the shear design of RC structures by making full use of basic researches. 5.2.2. Modeling of RC When the FEM is applied to RC structures, it is necessary to consider the form that is easy to express characteristics of reinforced concrete structures with FEM (Refs. 5.14 and 5.15). 5.2.2.1. Two-Dimensional Analysis and Three-Dimensional Analysis In previous FEM analysis, two-dimensional analysis that assumes plane stress state or plane strain state is widely used except for special structures like nuclear pressure vessels. It has been applied not only to structures such as shear walls with explicit plane stress condition but also to beams, columns and beam-column joints, which do not necessarily exhibit plane stress or plane strain conditions. By progress of research on the constitutive laws and advance in computer hardware such as workstations, three-dimensional analysis has come to be gradually used. Three-dimensional stress flow is generated in a RC member subjected to two-directional input load, beam-column joints with lateral beams, concrete column confined with steel plates or lateral reinforcing bars, and footings. In these members, three-dimensional analysis is desirable for representing more realistic state of stress and deformation. 5.2.2.2. Modeling of Concrete When Scordelis and Ngo applied the FEM to RC beams in 1967 for the first time, the model of a beam shown in Figs. 5.3-5.5 was used. It was twodimensional analysis, and the plane stress condition was assumed. The concrete was made to have a unit thickness except for reinforcement position. Reinforcing steel was idealized into plane elements, and concrete elements overlapping steel elements were modified to have reduced thickness. Finite Element Analysis 233 UNIT ., WIDTH - 4 / ^ ^",-if" -AV&&0 Fig. 5.3. Analytical model for RC simple beam (Ref. 5.5). Normal direction to crack surfaces t Node Parallel direction to crack surfaces The same coordinate before cracking Fig. 5.4. Crack linkage element (Ref. 5.14). Zero stiffness normal to cracks (a) Discrete Crack Model (b) Smeared Crack Model Fig. 5.5. Crack models (Ref. 5.14). Though concrete is a composite material composed of aggregate, sand and cement, it is usually handled as a uniform material like steel in the FEM analysis. In the two-dimensional analysis, triangle and quadrilateral elements are usually used. In the three-dimensional analysis, a layered shell element is often used, dividing the concrete into the thickness direction. This element can represent reinforcement layers. It is also possible to consider crack 234 Design of Modern Highrise Reinforced Concrete Structures propagation and concrete compressive failure by stiffness evaluation for each layer. However, out-of-plane shear deformation cannot be considered. 5.2.2.3. Modeling of Reinforcement In the analytical example of Fig. 5.3, the reinforcement was expressed like a long column of a plane material. It was overlaid with a concrete layer, and connected by a link element that expressed bond behavior. According to the type of analysis, reinforcing bars can be represented by one of the following elements: a bar element like a truss or a beam, a layer in a shell element, a plane and a hexahedron solid. A reinforcement layer or a truss element is usually used, as the effect of bending stiffness and dowel action of a reinforcing bar is not so large. 5.2.2.4. Modeling of Cracks In the analytical example of Fig. 5.3, concrete cracks were closely set in advance to actual locations between elements. This expression method is called a discrete crack model. Concrete nodes on both sides of crack surfaces are connected by a crack link element that consists of two orthogonal springs, as shown in Fig. 5.4. A large value is given to the spring stiffness before the crack opens. After cracking, the spring stiffness in the orthogonal direction is set to zero, and the spring in the parallel direction is used to express shear transfer across the crack plane. The unique feature of the discrete crack model is that the crack width can be evaluated. It is effective when a small number of cracks will open like in case of shear tension failure of a beam with small amount of lateral reinforcement. On the other hand, a smeared crack model handles the concrete as an orthogonal material with zero stiffness normal to crack directions in an element as shown in Fig. 5.4. In the smeared crack model, cracks are distributed uniformly in one direction in the element. It is not necessary to set a crack path before the analysis like discrete crack model. It is easy to divide an RC element into finite elements by using this model, and it is suitable for elements with many cracks widely distributed, such as a shear wall. However, spacing and width of cracks cannot be evaluated. 5.2.2.5. Modeling of Bond between Reinforcement and Concrete Unless we can assume a perfect bond between reinforcement and concrete, it is necessary to express bond slip in the FEM model. For the expression of Finite Element Analysis 235 bond, there are two ways. In the analytical example of Fig. 5.3, the bond slip is represented by a bond link element with two orthogonal springs between nodes of reinforcement and concrete, as shown in Fig. 5.3. The spring stiffness along the longitudinal direction of reinforcement represents the bond characteristics, determined from bond stress and slip relationship. Characteristics of dowel action of reinforcement are represented by the spring stiffness normal to the longitudinal direction. Another method is the tension-stiffening model. This model assumes that concrete can carry some tensile stress caused by bond after cracking. This method is used for members like shear walls in which reinforcing bars are arranged uniformly and bond slip is relatively small. 5.3. F E M of R C Members Using High Strength Materials RC structural members using high strength materials were analyzed using nonlinear FEM by members of a Working Group of Constitutive Equations and FEM chaired by Noguchi of Chiba University in the Reinforcement Committee of the New RC project. Most of object specimens in the analysis were tested by Structural Element Committee of the project. Principal research fruits in the Working Group on Constitutive Equations and FEM are introduced below. The modeling of RC using high strength materials was established from the basic tests performed in the New RC project. These analytical models were installed into several FEM programs including a common program, "FIERCM". Principal members of RC buildings, such as panels, shear walls, beams, columns and beam-column joints, were analyzed systematically by the working group members using FEM programs, including the common program. Analytical results gave generally reasonable agreement with the test results, and future research items were pointed out. From the systematic FEM parametric analysis, effects of major parameters on the shear strength were investigated and the applicability of design and experimental equations was discussed. Constitutive models for the FEM analysis of high strength RC structures were derived from the basic systematic experiment that had been carried out in the FEM WG. The main items of the investigation in this study were as follows: (1) Modeling of nonlinear constitutive laws of high strength materials and its implementation to FEM programs, including a common program. 236 Design of Modern Highrise Reinforced (2) (3) (4) (5) Concrete Structures The FEM analytical program, "FIERCM", which was developed by Collins, Stevens and Uzumeri of the University of Toronto (Ref. 5.16), was modified for high strength materials and used as a common program. Original FEM programs developed in several universities, institutes and construction corporations were used for the comparison and verification. RC members using high strength and ordinary strength materials were analyzed using several FEM programs. The reliability of the programs was investigated from the comparative analysis. Shear strength and deformation of RC members using high strength materials were investigated by FEM parametric analysis using several programs including the common program. Application of FEM analysis to the structural design of New RC building structures. A large-scale box column of a New RC boiler building in a steam power plant using high strength materials was analyzed (see Chapter 9). A guideline was compiled for the nonlinear FEM analysis of RC members using high strength materials. This guideline gives instructions for the nonlinear FEM analysis of RC members with high strength materials especially for design engineers and experimental researchers. In this chapter, (2) and (3) above are introduced. Details of (1), (4) and (5) are introduced in (Refs. 5.17 and 5.18). 5.4. Comparative Analysis of R C Members Using High Strength Materials 5.4.1. Comparative Analysis Shear Walls of Beams, Panels and Comparative FEM analysis of RC beams, panels and shear walls was carried out using several FEM computer programs including a common program, "FIERCM" developed by Stevens (Ref. 5.16) in order to verify the constitutive laws for RC using high strength materials. Total number of analyzed specimens was 48: Beams: 20 specimens: ordinary strength: 4 specimens, high strength: 16 specimens Ordinary strength: JCI selection test specimens Finite Element Analysis 237 High strength: New RC test specimens Series PB and Series B tested by Kyoto University. Series ASB tested by Chiba University. Panels: 12 specimens: high strength: 12 specimens High strength: New RC test specimens tested by Hazama Corporation. Shear walls: 16 specimens: ordinary strength: 2 specimens, high strength: 14 specimens Ordinary strength: JCI selection test specimens High strength: New RC test specimens Series NW tested by Yokohama National University From Specimens Nos. 1 to 8 tested by Nihon Kokudo Kaihatsu Corporation and Meiji University. 5.4.2. Material Constitutive Laws The constitutive laws used for the FEM analysis of RC using high strength materials are outlined below. 5.4.2.1. Uniaxial Compressive Stress-Strain Curves of Concrete A uniaxial compressive stress-strain curve of high strength concrete is shown schematically in Fig. 5.6 as compared with ordinary strength concrete. The ascending curve of ordinary strength concrete decreases its stiffness from about 25 to 33 percent of the maximum strength, and it becomes a parabolic curve. The ascending curve of high strength concrete is kept linear and its stiffness degradation is small up to about 90 to 95 percent of the maximum strength. StressCCooprcssivc) iligh-strcnglh Compressive strength Ordinary strength iffeninu lension-stiffening ^ I s . S t " ' n at conpressive strenjlh TensiIc strength Fig. 5.6. StrainCComprcssive) Stress-strain relationships of concrete. 238 Design of Modern Highrise Reinforced Concrete Structures The negative gradient after the maximum strength is large, and the strength finally decreases to the stress near the ultimate stress of the ordinary strength concrete. The Fafitis and Shah Model (Ref. 5.21) which expresses these features well has been often used in the analysis. The compression test result of a concrete cylinder is used for the uniaxial compressive strength. 5.4.2.2. Compressive Strength Reduction Coefficient of Cracked Concrete After shear cracking, as shown in Fig. 5.7, the compressive strength reduction coefficient of cracked concrete reaches 0.4 for high strength concrete in contrast to 0.6 for ordinary strength concrete. The reduction of the compressive strength is more remarkable for high strength concrete than for ordinary strength concrete. This was confirmed from the basic experiment by Ohkubo and Noguchi (Ref. 5.22) and Sumi et al. (Ref. 5.23). 5.4.2.3. Confinement Effect of Concrete The Kent-Park equation (Refs. 5.32 and 5.23) and Sakino equation (Ref. 5.24) proposed by the confined concrete working group of the New RC Reinforcement Committee have been often used. Though these models were developed for flexural analysis, they are also applied to the analysis involving flexural shear behavior. As for high strength concrete, the confinement cannot be very much expected unless high strength steel is used for lateral reinforcement. Principal tensile strain / Strain at compressive strength Fig. 5.7. Compressive reduction factors of cracked high strength concrete. Finite Element g i / g -1.6 -1.1 -(.2 -1.0 Analysis 239 i »0/-i -0.6 -0.6 -0.« -0.2 0.0 Fig. 5.8. Biaxial failure criteria of high strength concrete. 5.4.2.4. Biaxial Effect of Concrete The basic experiment (Ref. 5.25) by the FEM working group of New RC Reinforcement Committee is referred. The shape of yielding surface of high strength concrete for biaxial loading differs from ordinary strength concrete as shown in Fig. 5.8, and a new formula was proposed. The strength increase under biaxial stress state with equal magnitude seems to be small in the case of high strength concrete. 5.4.2.5. Tension Stiffening Characteristics of Concrete The tension stiffening characteristics are used to express the contribution of concrete between cracks to carry some tensile force by bond. There is a model considering the remarkable decrease of tensile stress in the case of high strength concrete, especially panels with high reinforcement ratio. 5.4.2.6. Shear Stiffness of a Crack Plane The crack of high strength concrete often penetrates through the aggregate. This happens due to the strength balance between the matrix and the aggregate. In this case, the shear stiffness of the crack plane becomes very small. But the shear force can be transferred over a crack plane by the macroscopic 240 Design of Modern Highrise Reinforced Concrete Structures zigzag-shaped crack even in case of high strength concrete. Models where the shear stiffness decreases with the increase of the crack width or the concrete strain normal to the crack are used like the Al-Mahadi Model (Ref. 5.26). 5.4.2.7. Cracking Strength Cracking strength of high strength concrete does not increase as much as ordinary strength concrete as the compressive strength increases, and it tends to approach a certain maximum value. The splitting strength is often used for the uniaxial tensile strength for beams, columns and beam-column joints. But the splitting strength becomes a little too large to be used as tensile strength for panels and shear walls with thin thickness, hence a function of compressive strength (such as 0.3^/CTB : OB in MPa) is often used. 5.4.2.8. Stress-Strain Relationship of Reinforcement The characteristics of high strength reinforcement are not particularly considered, because its elasto-plastic behavior, observed in the tension test, can be easily idealized into a model. 5.4.2.9. Dowel Action of Reinforcement It is similar to the ordinary strength reinforcement. 5.4.2.10. Bond Characteristics Referring to the research results of bond and anchorage WG in the New RC Reinforcement Committee (Ref. 5.23), the bond characteristics of high strength concrete are taken into account appropriately. 5.4.3. Analytical Models and Analytical Results Analytical finite element meshes, maximum shear strengths, failure modes, load-deflection curves and cracking patterns are shown in Figs. 5.9, 5.10 and 5.11 from representative analytical results of beams, panels and shear walls, respectively. Finite Element Analysis 241 S P M I M U S tor u t l r t i t .' it hi A* ill -!*. Ar- a) Finite Element Idealization Failure mode shear strength Flexural yielding Experimental result 730kN Shioharas model 684kN 655 kN Naganuma's model Flexural compression failure Uchida.s model-1 Shear compression failure 427kN Uchida's model-2 607kN Shear compression failure(edge) b)Comparisons of Analytical Results with Test Results of Beam PB4 B 00 700 E x x r i M n U l result -Shjohara's oodcl - K a i a n u u ' t Bodel Uchida's sodel -1 100 Uchida's oodcl-2 c) Load-Displacement Relationships 10.0 IS.O Displacement (mm) P3-U d) Crack Pattern (PB-4 at Maximum Strength) Fig. 5.9. Finite element idealization and analytical results of New RC beam, PB4 tested by F. Watanabe. 242 Design of Modern Highrise Reinforced Concrete Structures 5.4.3.1. Analysis of Beam Test Specimens In the analysis of four specimens in the beam test, PB series, and six specimens in the beam test, B series using high strength concrete in the New RC project, the analytical stiffness corresponds to the test results as shown by an example in Fig. 5.9. The analytical strength is generally lower than the test results. Higher values of tested strength are attributed to the details of specimens, e.g. the spacing of shear reinforcement is 50 mm and relatively dense with high confinement on the core concrete. High confinement on the core concrete is also given by heavy longitudinal reinforcement. The analytical reduction factor of the compressive strength of cracked concrete is based on the previous panel test, but the strength does not seem to decrease in beams or columns with a relatively large width as compared to the thin panels. As for the shear transfer mechanism through a crack plane, the Al-Mahaidi equation based on the deep beam test is often used. But it is considered that the contribution of the dowel action of reinforcement is relatively large in the case of these specimens with large amount of longitudinal reinforcement and shear reinforcement. The shear transfer characteristics denned by a function of crack width or strain normal to the crack direction like the Al-Mahaidi equation may underestimate the strength. 5.4.3.2. Analysis of Panel Specimens Eleven panel specimens with high strength concrete were analyzed. Analytical results were compared with each other as well as with experimental results in terms of shear stress-shear strain curves. Figure 5.10 shows an example of comparison of a test with analyses by Noguchi, Shirai, Naganuma, Sumi and Takagi. There is not a large difference in general, though there is some difference between the models in the behavior right after the initial cracking. There is scattering in the maximum shear strength by each analysis, and the strength was evaluated generally high. In the case of failure mode where yielding of reinforcement takes place prior to compressive failure of concrete, the effect of modeling of stress-strain curve of reinforcement appears quite clearly in the analytical results. This is particularly true in case of a simple stress condition like a panel. Therefore, when the stress-strain curve of high strength reinforcement is different from the ordinary strength steel, a model considering the steel test result is preferred over simple models such as a bilinear model. Finite Element Analysis 243 A panel is idealized as a single eleacnt. a) Finite Element Idealization b)Comparisons ol Analytical Results with Test Results of Panel 8-8-8 Experimental result Noguchi's model Shirai's model-1 Shirai's model-2 Shirai's model-3 Shirai's model-4 Shirai's model 5 Naganuma's model-1 Sumi's modet-1 Sumi's model-2 Takagi's model Shear strength Failure mode 9.62MPa 9.37MPa 10.2MPa I0.2MPa 10.2MPa Cut off reinforcement Cut off reinforcement 11.2MPa 10.2MPa 11.0MPa 10.4MPa 10.4MPa 9.02MPa Yielding of reinforcement Cut off reinforcement Cut off reinforcement CO I— cfl CD -C W 1.0 2.0 Shear Strain (%) c) Shear Stress-Shear Strain Fig. 5.10. Finite element idealization and analytical results of New RC panel 8-8-8 tested by K. Sumi of Hazama Corporation. 244 Design of Modern Highrise Reinforced Concrete Structures In the case of failure mode where concrete compressive failure occurs before steel yielding, there is a scatter among analyses using different evaluation of compressive reduction factor. From the comparison between the analytical and test results of specimens with concrete strength of 100 MPa and 70 MPa, the analytical results using the modified equation of Stevens (Ref. 5.16) considering concrete strength, shown as Shirai's model-1 in Fig. 5.10, gave a better agreement with the test results than the analysis using the original equation of Stevens where the compressive reduction factor was given only as the function of tensile principal strain. In the case of specimens with different reinforcement ratios between longitudinal and lateral re-bars, there is difference in the analytical results using different modeling of the shear transfer characteristics of crack planes. In the Stevens model, the maximum shear strength was overestimated, and there is high possibility that the shear transfer effects of the crack planes were overestimated in his model. 5.4.3.3. Analysis of Shear Walls Two specimens were analyzed for ordinary strength concrete and fourteen specimens were analyzed for high strength concrete. In the NW series including both ordinary strength concrete and high strength concrete, the maximum shear strength was grasped well by each analysis as shown in Fig. 5.11. Although the stiffness tended to be higher, the load-displacement curves were well simulated up to the ultimate stage. The analytical initial stiffness of the specimens Nos. 1 to 8 gave a good agreement with the test results, but the stiffness after cracking and the maximum strength were overestimated as compared with the test results. The pattern of the load-deflection curves could simulate the test results. Considering that the experimental failure mode was flexural compressive failure, it is inferred that the input value of the concrete compressive strength was too high. 5.4.3.4. Conclusions RC structural members using high strength material were analyzed by FEM, and the comparison and verification of the material constitutive law were carried out. The comparison between the test results and analytical results revealed that few analytical cases gave a perfect agreement of stiffness and maximum strength. There is also a scatter among analytical results due to Finite Element r ( M i l i u m .7S i : — i - Analysis 245 A\-VT ~7\7 <> a) Shirai's model d) Crack Pattern (NW-1 at Maximum Strength) b)Comparisons of Analytical Results with Test Results of Shear Wall NW-1 Shear strength Failure mode 1063KN Flexural failure Experimental results Noguchi's model Flexural yielding failure 1113KN Shirai's model-3 1013KN . Compressive failure at the bottom of compression Naganuma's model-1 1016KN columns after flexural yielding Compressive failure at shear wall Takagi's model 999KN after column flexural yealding 1500 500 Experimental result Noguchi' 5 sodel — Shirai's model-3 Naganuaa' s Bodel-I Tafcagi" s node] 0.0 20.0 40.0 60.0 WSPLACEMEMT (mm) c) Load-Displacement Relationships Fig. 5.11. Finite element idealization and analytical results of New RC shear wall, NW-1 tested by T . Kabeyasawa. 246 Design of Modern Highrise Reinforced Concrete Structures the different material constitutive laws, and no material constitutive laws were found to be definitely applicable. But there are some analyses that gave good agreement with the test results for the load-deflection curves and the maximum strength. Therefore, it is expected that a more reliable simulation of RC members using high strength materials can be achieved by the accumulation of research on the material constitutive laws. 5.5. 5.5.1. F E M Parametric Analysis of High Strength Beams Objectives and Methods FEM parametric analysis of RC beams using high strength materials was performed with the ratio and strength of shear reinforcement as parameters. Effect of shear reinforcement on the shear behavior of beams was studied. The target specimens were five RC beams, ASB-1, -2, -3, -4 and -6 (section: B x D = 200 mm x 300 mm, shear span to depth ratio: a/D = 2.33) with high strength materials tested by Noguchi and Amemiya (Ref. 5.28). The shear reinforcement ratios were determined according to AIJ Guideline (Ref. 5.29) using a concrete strength reduction factor in the draft of CEB Model Code 90 (Ref. 5.31). The specimens were analyzed by the FEM program developed by Noguchi Laboratory of Chiba University. The constitutive laws are explained in detail in Ref. 5.26. The Sakino's equation (Ref. 5.24) was used for the descending portion of stress-strain curves of concrete after the peak, and the proposed equation by | 1 Concrete element Hoop element o Bond linkage element 1 I Nj [ \ } t t >r£ i — —' ' ' Tested zone —' I | Z00 ) Fig. 5.12. gaO | 220 i | 210 | 150 | 150 11Q0| 100|100)5^ Finite element idealization of beam. Finite Element Analysis 247 Noguchi and Ihzuka (Ref. 5.27) was used for the compressive reduction factor of cracked concrete. The finite element idealization of the specimen is shown in Fig. 5.12. One half of the specimen was analyzed considering symmetry around a point. A linearly varying quadrilateral element with eight nodes was used for concrete. A linear bar element was used for reinforcement, and shear reinforcement was represented by uniformly distributed layered elements. 5.5.2. The Effect of Shear Reinforcement Ratio The analytical shear force-displacement curves are shown in Fig. 5.13. Here, the amount of beam longitudinal reinforcement was assumed to be large enough to avoid flexural yielding based on the specimen ASB-3. The failure mode was brittle shear tension failure with a remarkable shear crack opening and yielding of shear reinforcement in the case of low ratios like pw = 0, 0.3, and 0.6 percent. The failure mode changed into shear compression failure without yielding of shear reinforcement when the shear reinforcement ratio exceeds 1.2 percent. The compression zone at the beam end and the compression strut failed in compression. As the shear reinforcement ratio becomes greater than pw = 2.4 percent, the ultimate shear strength did not increase so much and had a tendency to reach a peak. The analytical shear strength and shear reinforcement ratio relationships are shown in Fig. 5.14, compared with the calculated results by AIJ Guideline using several compression strength reduction factors: AIJ equation (Ref. 5.29), Unit:% P*= 2.-4 P*= 1.8 Pw» 1.2 ?1P 0 . 8 Put* 0.634 Pl»= 0.3 P«r» 0.0 0 2.5 5.0 7.5 10.0 12.5 15.0 Relative Displacement (mm) Fig. 5.13. Shear force-relative displacement relationships. 248 Design of Modern Highrise Reinforced Concrete Structures Reinforcement not yielded £^F Reinforcement yielded O Large amount of main bars O ASB-3 *-— Ichinose equation 0.5 — CEB equation — AIJ equation 1.0 1.5 2.0 2.5 3.0 Lateral reinforccDent ratio Fig. 5.14. Ultimate shear strength-shear reinforcement ratios relationships. ASB-2. \ £ 30 \ H o d i f i e d Kent-Park model (Net RC Sakino's model" \T loon IOOOO —! nooo Strain (p.) Fig. 5.15. Differences of compressive stress-strain relationships by two models. Ichinose's equation (Ref. 5.30), CEB equation (Ref. 5.31). It is indicated that the analytical results are located between AIJ and CEB equations. 5.5.3. Effects of Concrete Confinement Constant Value of p Twy Models with a FEM parametric analysis was carried out by setting the value of pwawy (pw: shear reinforcement ratio, awy: yielding strength of shear reinforcement) at a constant value for the specimen ASB-2. The New RC Sakino's Model (Ref. 5.24) and the modified Kent-Park Model (Refs. 5.32 and 5.33) were used for the confinement effects on the stress-strain curves by shear reinforcement. The difference of both stress-strain curves is shown in Fig. 5.15. The difference is seen for the strain at the peak and the descending curve. Finite Element Analysis 249 The parameters of analysis using New RC Sakino's Model are shown in Table 5.1. Concrete stress-strain curves by Sakino's Model are shown in Fig. 5.16. There is small difference in the strain at the peak when the amount of confining reinforcement is varied. The shear force-relative displacement curves Table 5.1. Parameters in Sakino model. Pw • (Twj = 3.39 M P a Pw (%) 0.2 0.317 0.6 1.2 trwj (MPa) Concrete Peak Strain (/*) 1697 1069 566 283 7840 8630 8850 9100 Pw=0.317%~Pw=1.2% Strain ( u ) Fig. 5.16. Stress-strain curves by Sakino model. 450 400 350 Pw=1 2% _ • 300 / #5?T'" PL- 2 200 a \ . \ \ =w=0.6% Pw=p.317% tii I '50 Pw=0.2% /' 1 i i 100 50 0 5 10 15 20 Displacement Cmm) Fig. 5.17. Shear force-relative displacement by Sakino model. 250 Design of Modern Highrise Reinforced Concrete Structures Table 5.2. Parameters in modified Kent-Park model. Pw • <rwj = 3.39 M P a Pw (%) 0.2 0.317 0.4 1.5 0.6 1.2 o-Wj (MPa) Concrete Peak Strain (/x) 1697 1069 848 679 566 283 9251 15 732 21173 28505 36 993 102 271 P.. 1.2% P.»0.6% P . . 0.5% o 5000 woo \m 20000 Strain ( / O Fig. 5.18. Stress-strain curves by modified Kent-Park model. 450 i I j Pw=0.6% 400 —^—' ' Pw= 350 s0@~ ? 300 f 250 S 2 °0 ^""r^T"" j I j 0 i Pw=0.2% 5 150 | L I 100 0 i.5%- v -- — «=0.317% a> 50 0 / < | rw-( Pw=0.4% i i s ! 19 1 1 ' 1 15 ! 20 ! 25 30 Di splaceaent (am ) Fig. 5.19. Shear force-relative displacement by modified Kent-Park model. Finite Element Analysis 251 are shown in Fig. 5.17. Although the stiffness is higher as pw increases, the maximum strength is not changed very much. The parameters of analysis using modified Kent-Park Model are shown in Table 5.2. Concrete stress-strain curves by the modified Kent-Park Model are shown in Fig. 5.18. The strain at the peak does not change very much, but the slope of descending curves does, when the amount of confined steel is varied. The shear force-relative displacement curves are shown in Fig. 5.19. Although there is small difference in the stiffness, the ultimate shear strengths were different. As the yielding strength of shear reinforcement was lower and the shear reinforcement ratio was larger, the ultimate shear strength was larger. It is inferred that the concrete strain at the compression failure, which become larger for larger pw as shown in Fig. 5.18, gave an effect on the ultimate shear strength. 5.5.4. Conclusions Although the ultimate shear strength increased according to the increase of the shear reinforcement ratio, pw, it gradually approaches to a peak value when the shear reinforcement ratio becomes very high. From the parametric analysis, it was shown that the ultimate shear strength increased as pw increased even though pwcrwy was kept the same. This trend can be attributed to the greater confinement effects provided by the greater geometrical ratio, not the mechanical ratio, of shear reinforcement. Some difference was seen in the confinement effect from the different modeling of concrete in the analysis. 5.6. 5.6.1. F E M Parametric Analysis of High Strength Columns Objectives and Methods FEM parametric analysis of RC columns using high strength materials was performed with shear reinforcement ratio and axial force ratio as parameters. Effect of parameters on the shear behavior of columns was studied. Noguchi et al. in Chiba University analyzed column specimens using their original FEM program. The objective specimens were based on those tested also by Noguchi et al. Parameters were shear reinforcement ratio: pw = 0.3, 0.6, 1.2, 1.8 percent and axial stress ratio: n = N/CNU = 0, 0.05, 0.1, 0.15, 0.3, 252 Design of Modern Highrise Reinforced Concrete Structures 0.45, 0.6, 0.75 where CNU is axial strength including longitudinal reinforcement. Material properties are shown in Table 5.3, and the finite element idealization is shown in Fig. 5.20. Table 5.3. Material properties. Reinforcement ary (MPa) Es (MPa) Main bar Shear reinforcement* 2.19 x 10 5 721 3360 5 847 6670 en (MPa) Ccu (MPa) 56.5 3.60 2250 2.14 x 10 Concrete Ec (MPa) 3.76 x 10 4 tO.2% offset °\ liiuniiii i"T~~ 1.2SP I b . 1 k.. . i _ . — 3 2.25P 44 r* < — ><—- Concrete element — Hoop element Q Bondlink 2.25P A -L- A 3 miMitiit Fig. 5.20. Finite element idealization. Finite Element Analysis 253 (kN) 500 300 200 100 0 • • n-0 n-«. 1 . n-8.7 J. n—•-3 — . — n=J. 4 j. n =«. S _ L : " n-0.1 j.... n - » . 1 .. | n-l.t __ „ . ! . . . 400 o T"1 1 i^i- ft'' \*' /--''T|-— .._ X...C.1 P _l_ 40 20 (mm) (a) Pw*0.3 % 60 6 (mm) (b) P w = 0 . 6 % (kN) (KN) 500 T ,..,, 1 400 400 " 300 o 200 3 fS ''• -"" -/'•;-"'-;f T - /•* i 0 i • l-'~-~yi-~ j- 100 /=-'" ! « r ' 5 (mm) (c) Pw=1 .2% 0 M;3S fO''A''.-'"" i 200 ^ 100 300 fi^^=-r. 6 (mm) (d) P w = 1 . B % Fig. 5.21. Shear force-deflection relationships. 5.6.2. Analytical Results The shear force-deflection curves are shown for each shear reinforcement ratio in Fig. 5.21 from (a) to (d). For every shear reinforcement ratio the increased initial stiffness, shear cracking strength and maximum strength were observed when the axial force ratio was increased. But the drift at the maximum strength tends to decrease for greater axial force ratio. The analytical shear strength-axial stress ratio relationships are shown in Fig. 5.22 with a parameter of shear reinforcement ratio as compared with the test results. Zhang et al. (Ref. 5.35) reported that the increase of shear strength due to the increase of axial stress ratio was more remarkable for lower shear reinforcement ratio. But his tests and analysis were carried out for RC columns with ordinary strength materials. In our case of high strength columns, however, the shear strength increase due to the axial stress ratio increase was observed for any shear reinforcement ratio. As seen in Fig. 5.22, the shear strength increased almost parallel with the axial stress ratio increase. The analytical results gave reasonable agreement with the test results for this 254 Design of Modern Highrise Reinforced Concrete Structures Axial force r a t i o n 0. 15 0.3 = 400, £asflj(%) ca200 ~l Analytical Experimental 0 0.1 O P»=0.6(%) OPW-1.2(%) MM -0.1 OPw=0.3(%) 0.2 0.3 _1_ 0.4 £ Pw=1,8(%) 0.S 0.6 0.7 0.8 0.9 Axial force ratio n Pig. 5.22. Shear strength-axial force ratio relationships. 0.6 0.9 1.2 1.5 Shear reinforcement ratio p« (%)• Fig. 5.23. Shear strength-shear reinforcement ratio relationships. tendency. This difference between Zhang el al. and ours is considered to be the result of different assumptions on the confinement effect of shear reinforcement on the core concrete. The confinement effect was not considered in the Zhang's analysis, while the confinement effect was considered with the modified KentPark equation (Refs. 5.32 and 5.33) in our analysis. Figure 5.22 also indicated that the shear strength deceased under high axial force ratio when the shear reinforcement ratio was small, but no decrease was observed under high axial force ratio for high shear reinforcement ratio. The analytical shear strength-shear reinforcement ratio relationships are shown in Fig. 5.23 with a parameter of axial stress ratio. It indicates that Finite Element Analysis 255 a similar increase of shear strength was observed with the increase of shear reinforcement ratio. Though the increase of shear strength became a little blunt in case of high axial stress ratio, this tendency was not so remarkable as that reported for the ordinary strength concrete. 5.6.3. Conclusions Increases of initial stiffness, shear cracking strength and maximum strength were observed when the axial force ratio was increased. The drift at the maximum strength had a tendency to decrease with the increase of axial force ratio. The increase of shear strength due to the increase of axial force ratio was similar for any shear reinforcement ratio. This trend is considered to be the result of the confinement effect on the core concrete by the shear reinforcement. 5.7. 5.7.1. F E M Parametric Analysis of High Strength Beam-Column Joints Objectives and Methods FEM parametric analysis of RC beam-column joints using high strength materials was performed with the parameters of concrete strength and joint lateral reinforcement. From the analytical results, verification of the guideline equation and the previous design equation of ultimate joint shear strength was discussed. The effects of concrete strength and joint lateral reinforcement on the joint shear strength were also investigated. A two-dimensional nonlinear FEM program with the constitutive laws of high strength materials was used for the analysis. The Ihzuka's equation (Ref. 5.26) was used for the compressive strength reduction factor of concrete. The Fafitis and Shah's Model represented the linear property of the ascending curves of high strength concrete. The modified Kent-Park's Model was used for the confinement effects of lateral reinforcement on the core concrete (Refs. 5.32 and 5.33). The bond link elements composed of two orthogonal springs were used to represent bond between longitudinal bars and concrete. The bond stress-bond slip relationships were determined from the test results. One half of the specimen was analyzed considering the symmetry around a point. After a constant axial loading was applied at the top of the column, lateral displacement control was used. 256 Design of Modern Highrise Reinforced Concrete Structures In order to verify the analytical model, the AT series beam-column joint specimens tested by Takezaki and Noguchi (Ref. 5.36) were analyzed and compared with the test results. The analytical story shear force-story displacement relationships gave reasonable agreement with the test results, for four specimens of AT series including two failure modes, i.e. joint failure and beam flexural yielding. 5.7.2. Comparison between Test and Analytical Results Specimens in the AT series are shown in Table 5.4. As for the material properties, the yielding strength of beam main bars was 556 MPa, the yielding strength of joint lateral reinforcement was 804 MPa and concrete compressive strength was 80.5 MPa. Analytical results of the story shear force-story drift curves are shown with the test results in Fig. 5.24. The analytical initial stiffness, crack propagation, and the stiffness degradation by the yielding of beam main bars gave good agreement with the test results. But after the beam yielding, the displacement increased without strength decay under monotonic loading in the analysis. It was different from the test results where the strength decay was observed after the peak under reversed cyclic loading. The maximum strength and the associated story drift were a little larger than the test results. 5.7.3. Results of Parametric Analysis Beam-column joints were parametrically analyzed for the shear reinforcement ratios, pw = 0, 0.09, 0.18, 0.36, 0.54, 0.9, 1.2, 2.4 percent and concrete strength Table 5.4. Specimens. Specimen Beam AT-2 AT-3 AT-4 AT-5 Main bar 6-D13 8-D13 10-D13 Stirrup D 2-D10® 150 Pw = 0.47% D 2-D10® 100 Pw = 0.71% • 2-D10® 80 Pw = 0.89% Joint lateral reinforcement Joint shear stress at beam yielding, r py (MPa) • 4-D6 x 3® 50 Pw = 0.47% 8.92 = 0.15 Fc 11.9 = 0.20 Fc D 2-D6 x 2@ 60 Pw = 0.18% 14.9 = 0.25 Fc Finite Element Analysis 300 p" 1 ~~ i Analytical Experimental 1 257 * [ •••' i^l. - A T - 2 1 4t it 10 9 20 Story Drift (mm) Fig. 5.24. Story shear-relative displacement relationships. 300 5 200 ;100- Fig. 5.25. Story shear force-story drift relationships. aB = 21, 36, 51, 65, 80, 100, 120 MPa, by Noguchi and Takezaki using their original FEM program. The basic specimen was the specimen AT-4. Effects of joint shear reinforcement ratios and concrete compressive strength were studied. In the parametric analysis, the amount of beam main bars was deliberately increased to avoid beam flexural yielding prior to the joint shear failure. The analytical story shear force-story drift relationships for different shear reinforcement ratios are shown in Fig. 5.25. Although the initial stiffness was almost the same, the maximum strength was reached earlier when the shear reinforcement ratio was lower. Subsequent strength decay also became larger. 258 Design of Modern Highrise Reinforced Concrete Structures -O— 0. 5 I. 0 1. 5 2. 0 Lateral reinforcement rations (%) Fig. 5.26. Joint shear stress-lateral reinforcement ratio relationships. Constant ratio of beam main bare (AT-4) 300 Unit: MPa Fc=20.6 '^ Fc=35.3 Fc=53.9 Fc=78.4 Fc=98.1 Fc=118 20 30 40 SO Story drift (mm) Fig. 5.27. Story shear force-story drift relationships. The analytical joint shear strength-joint shear reinforcement ratio relationships are shown in Fig. 5.26. The joint shear strength increased remarkably from pw = 0 to 0.36 percent and nearly reached the maximum strength at pw — 0.54 percent. Even when the shear reinforcement ratio was very large like pw = 2.4 percent, the strength remained almost the same. The analytical story shear force-story drift relationships for different concrete strength are shown in Figs. 5.27 and 5.28. The beam main bar ratio was kept constant in Fig. 5.27. On the other hand, the beam main bar ratio was increased in Fig. 5.28 for ultrahigh strength concrete such as 100 MPa or 120 MPa in order to maintain the joint shear failure mode. It is seen the initial stiffness tends to increase as the concrete strength increases. In the case of the constant beam main bar ratio, the increase of joint shear strength was remarkable up to 80 MPa of concrete strength, but afterward the Finite Element Analysis 259 Story drift (mm) Fig. 5.28. Story shear force-story drift relationships. Fig. 5.29. Joint shear stress-concrete strength relationships. strength came to a peak owing to the change of failure mode from joint shear failure to the beam flexural yielding. In the case of the joint shear failure type by increasing beam main bars ratio, the strength increase did not stop even in ultrahigh strength concrete like 100 MPa and 120 MPa. The analytical joint maximum shear stress-concrete strength relationships are shown in Fig. 5.29 comparing with test results. The analytical joint maximum shear stress did not increase in proportion to concrete compressive strength, erg, but it increased in proportion to the square root of as- Most of test results of specimens failing in joint shear failure were distributed just above the curve of 1.9 x (the square root of as) as shown in Fig. 5.29. 260 Design of Modern Highrise Reinforced Concrete Structures 5.7.4. Conclusions The analytical joint shear strength increased remarkably from pw = 0 to 0.36 percent and nearly reached the maximum strength at pw = 0.54 percent. Even for higher shear reinforcement ratio such as pw = 2.4 percent, no strength increase was observed. The analytical joint maximum shear stress did not increase in proportion to concrete compressive strength, CTB, but increased in proportion of the square root or two-thirds power of <JB5.8. 5.8.1. F E M Parametric Analysis of High Strength Walls Objectives and Methods The constitutive law model was proposed not only for ordinary strength but also for high strength concrete by the FEM WG in the New RC project. These constitutive laws were installed into the nonlinear FEM program (FIERCM) (Ref. 5.16) in which Stevens et al. had installed the constitutive law model for ordinary strength materials only. The resulted program was called "modified FIERCM" (Ref. 5.37). It was applied to high strength shear walls tested by the Structural Element Committee. The accuracy of the ultimate shear strength was investigated by comparing analysis with tests. Then, parametric analysis was carried out by the modified FIERCM in order to complement the region between test results. Finally, parametric analysis was carried out using previously available macroscopic models, empirical formula and design equations of shear strength. The applicability and problems in applying these equations to high strength shear walls were investigated. 5.8.2. Outline of Research In order to verify the accuracy of the modified FIERCM, six specimens in NW series tested at Yokohama National University (Refs. 5.38 and 5.39) and eight specimens in NO series (Ref. 5.40) tested by the JDC Corporation and Meiji University were analyzed. The analytical and experimental ultimate shear strength was compared. Next, the test specimens of NO series were selected as the object of parametric analysis. The specimen No. 3 was made to be the reference specimen. Dimensions and material properties of the test specimens are respectively shown in Tables 5.5 and 5.6. Finite Element Analysis 261 Table 5.5. Specimens. Wall Columns Concrete Specimen strength (MPa) No. Main bars SD 80 b x D (mm) (ft) Ties SD 130 spiral (P™) Width x Length (mm) Height (mm) [M/Q • D] Top 1/2 60 2-D6® 40 (0.80%) 3 4 ft (%) 2-D6® 400 (0.20) 1 2 Reinforcement 100 200 X 200 5 2-D6® 230 (0.35) 2000 [1.33] 2-D6® 150 (0.53) 16-D13 (5.08%) 2-D6® 150 (0.53) Bottom 1/2 800 x 1300 3000 [2.00] 2-D6® 150 (0.53) 20000 [1.33] 2-U6.4® 122 [SD 130] (0.62) 2-D6® 80 (1.00) 2-D6® 55 (1.45) 2-D6® 50 (0.64%) 6 60 7 8 Table 5.6. Material properties. (a) Concrete Days Strength (MPa) Young Modulus (10 5 MPa) No. 1 49 65.1 — No. 2 70 70.8 2.99 No. 3 60 71.8 2.99 No. 4 95 103.5 3.58 No. 5 101 76.7 3.01 No. 6 94 74.1 2.86 No. 7 70 71.5 3.03 No. 8 66 76.1 3.08 Specimen 262 Design of Modern Highrise Reinforced Concrete Structures Table 5.6. (Continued) (b) Reinforcement Main bars Grade Diameter Yield strength (MPa) Yield strain (xl0~6) Tensile strength (MPa) Young modulus (105MPa) Wall SD785 SD1275 D6 808 1448 6187 8928 1015 1529 1.89 2.05 Column SD785 D13 1028 7205 1132 1.94 1422 8637 1532 2.10 1422 9003 1512 1.98 Column tie Column subtie SD1275 D6 Following four parameters were investigated in this study. (1) (2) (3) (4) Concrete compressive strength: as = 20 to 100 MPa. Wall reinforcement ratio: pw = 0.2 to 1.45 percent. Column main bar ratio: pg = 1.5 to 6.25 percent. Shear span ratio: hw/L = 0.875 to 2.063. Material properties and dimensions except for the parameters were identical to No. 3 specimen. The previous macroscopic model: the Shohara and Kato's Model (Ref. 5.41), the empirical equation: Hirosawa's equation (Ref. 5.42) and the design equation: the AIJ Guideline (Ref. 5.43) were applied to the above shear walls in the parametric analysis. By comparing the results from these equations and the FEM analysis, the applicability and problems were investigated. 5.8.3. Analytical Results and Discussions The comparison of tests and FEM analysis on NW and NO series specimens are shown in Fig. 5.30. The accuracy of the FEM analysis was good within 5 percent for NW series and within 12 percent for NO series. However, the FEM analytical results tended to overestimate a little the ultimate shear strength of NO series. The effect of concrete compressive strength on the ultimate shear strength is shown in Fig. 5.31. In the AIJ Guideline Eq. (1), the Nielsen equation: v — o,7 - (7^/200 (Ref. 5.29) was used for the effectiveness factor v of concrete. In the AIJ Guideline Eq. (2), the CEB equation: v = 1.7 x o~B (Ref. 5.31) was used. In the AIJ Guideline Eq. (3), the modified CEB equation Finite Element Analysis 1 1 1 '' r — 1 ! _!, i | 263 j * i T?-""T~ ~2f~ "T ~T " \a NW series l°_ NO sene ' ' < 9 i i to 12 14 Analytical with FIERCM(MPa) Fig. 5.30. Comparisons between experimental and F E M analytical values. Q A Experimental RERCM ^ - - — ^ Shinohara-Kato model 7 — 7 Hirosawa's equation O " " ' 0 AUGuidelineeq-1 0 0 AU Guideline eq.-2 0 0 AU Guideline eq.-3 ,,•' 0 20 40 60 80 100 120 Concrete strength (MPa) Fig. 5.31. The effects of concrete strength. (v = 1.7 x <r B 1/3 > 0.5) was used. The AU Guideline Eq. (3) expressed the effect of concrete strength the most appropriately. In the meantime, as the concrete strength increased, the calculated value by the AU Guideline Eq. (1) tended to underestimate compared to the test results and the FEM analytical results. The effect of pw x say (pw: wall reinforcement ratio, say: yielding strength of wall reinforcement) on the shear strength is shown in Fig. 5.32. In the range of the examined pw x 3ay values, every design equation tends to overestimate the effect of wall reinforcement according to the increase of pw x say compared with the test results. It is concluded that the assumption of truss mechanism angle in the AIJ Guideline equation, cot <f> = 1, needs more consideration in case of high strength material. 264 Design of Modern Highrise Reinforced Concrete Structures 16 14 12 10 8 6 0—0 4—* FEBCM 4 «—~ 4 » "V 0" * "Q 0" * "0 0***0 2 0 3 6 STWnohara-Kato model Hrrouwataquation AU GuidWn* *q.-i AU GukMlna aq.-J AUQuklallrw>q.-3 g 12 15 Amount of lateral reinforcement p* • s c>{MPa) Fig. 5.32. The effects of s 14 Q ft * ™SCM A JZ • Q " o> c 2 12 10 r--—:A •V ~ 7 •"*"*• 0 0 0 0 pWs&y Experimental Shinohara-Kato mods) Hirasavra's equation AU Guideline eq.-1 AU Guideline eq.-2 AU Guideline eq.-3 _,.. 3.0 4.5 5.0 7.5 Column reinforcement ratio (%) Fig. 5.33. The effects of column main bar ratios. -fflQ. 14 «. S 12 °v JC n) c 03 S ,;>C\_, 10 6 0—0 ft—ft 4—A 7-"7 o—a 0— -0 0-—0 Experimental $.•;•."."."°••^!^*^^^--Xlu»- —*1 Shinohara-Kato model Hirosawa's equation AU Guideline eq.-1 AU Guideline eq.-2 AU Guideline eq.-3 0.5 Fig. 5.34. 1.1 Hi ""*""*— , *»——..., 0 ^, • ' 1.5 2.0 2-5 Shear span ratio (rWL) The effects of shear span ratios. Finite Element Analysis 265 The effect of column main bar ratio on the ultimate shear strength is shown in Fig. 5.33. The calculated results of the AIJ Guideline Eq. (3) gave the best agreement with test results. Although the increase of ultimate shear strength according to the increase of main bars ratio was observed in the FEM analysis, the effect of main bars ratio is not considered in the AIJ Guideline equation. The Hirosawa's equation represented this effect very well. Finally, the effect of shear span ratio on the ultimate shear strength is shown in Fig. 5.34. The AIJ Guideline Eq. (3) and the Hirosawa's equation grasped the tendency of the test results and FEM analysis. The AIJ Guideline Eq. (3) gave the best agreement with test results. 5.9. 5.9.1. F E M Parametric Analysis of High Strength Panels Objectives and Methods FEM parametric analysis was performed on parameters that had not been included in RC panel tests in the New RC project. Parameters in the analysis were reinforcement arrangement methods, uniaxial compressive stress and bidirectional axial compressive stresses. The list of specimens is shown in Table 5.7, respectively. The failure mode in the test was concrete shear failure. The following common basic conditions were applied to all specimens in this analysis. (1) Concrete compressive strength:CTB= 70 MPa. (2) Crack strength: acr: 0.3 times square root of <j&. (3) Tension stiffening characteristics: Stevens equation (Ref. 5.1) was applied. (4) Compressive stress-strain relationships of concrete: For the ascending curve the Fafitis-Shah Model (Ref. 5.6) was applied, and for the descending curve the Shirai equation (Ref. 5.37) was applied. (5) Compressive strength reduction factors of concrete after cracking: Shiohara Model (Ref. 5.37) was applied. 5.9.2. Analytical Results and Summary The analytical shear stress-shear strain relationships are shown in Figs. 5.355.37. The ultimate shear strengths are shown in Table 5.7. From Fig. 5.35, it 266 Design of Modern Highrise Reinforced Concrete ra u a. 2£ lo 0) Structures T^^wmm / / / rf' \S 0.005 0.010 Shear Strain 0.015 Fig. 5.35. Analytical results of a series with variation of combination of pt and *...,•• i say. -05 o a 1 1 t 2 i •—"y ft - 0 . 3 <r B ir it h , . - ' • • - -^r.— / -0 ^ \~/r 0.005 0.010 Shear Strain 0.015 Fig. 5.34. Analytical results of a series with variation of axial stress ratios. 'r-OSa, • j f f <o u 0- 5 55 / ,'-^"sj..—.,— ^ . . . . - • " / 1 1 s" /' / "if—:CL 0 01 0.005 0.010 Shear Strain Fig. 5.37. 0.015 Analytical results of a series with variation of bidirectional axial stress ratios. Finite Element Analysis 267 Table 5.7. Specimens and maximum strength. Max. Strength MPa Specimen t <— I 1 t •4-t— ~v I 1 t <*— r A ^ 4— a-1 SD980,p, = 2.0% 15.14 a-2 SD490,/7, = 4.0% 17.94 a-3 SD295,p, = 6.6% 19.34 b-1 Axial force, none 15.14 b-2 Axial force, 0.1 oB 16.17 b-3 Axial force, 0.3 Ofl 18.11 b-4 Axial force, 0.6 o 8 19.87 c-1 Axial force, none 15.14 c-2 Axial force, 0.1 aB 17.48 c-3 Axial force, 0.3 ofl 24.17 c-4 Axial force, 0.6 o"B 33.87 is indicated t h a t t h e stiffness after cracking a n d t h e u l t i m a t e shear s t r e n g t h increased according to t h e increase of reinforcement ratio, pt, even when pt x (s<Ty'- yielding s t r e n g t h of the reinforcement) was kept constant. From soy Figs. 5.36 a n d 5.37, it is seen t h a t t h e axial compressive stresses, uniaxial or biaxial, contributed t o t h e increase of cracking strength a n d ultimate shear strength. T h e effect was more remarkable for biaxial compressive stresses t h a n uniaxial compressive stress. References 5.1. Washizu, K. ed., Finite Element Method Handbook, Part 1: Basic Edition, Baifukan, September 1981, p. 443 (in Japanese). 5.2. Togawa, H., Introduction of Finite Element Method, Series 1 of Basic and Application of FEM, Baifukan, November 1981, p. 324 (in Japanese). 5.3. Zienkiewicz, O.C., The Finite Element Method, Third Edition, McGraw Hill Book Company Ltd., 1977. 5.4. Miyoshi, T, Introduction to FEM, Revised Edition, Baifukan, December 1994, p. 255 (in Japanese). 5.5. Ngo, D. and Scordelis, A.C., Finite element analysis of reinforced concrete beams, ACI J. 64(3), March 1967, pp. 152-163. 5.6. IABSE, Advanced mechanics of reinforced concrete, Reports of IABSE Colloquium, No. Delft, 1981. 268 Design of Modern Highrise Reinforced Concrete Structures 5.7. Research committee on shear strength of RC structures, Reports of JCI Colloquium on Analytical Studies on Shear Problems of RC Structures, Japan Concrete Institute, JCI-C1, June 1982 (in Japanese). 5.8. Morita, S. (Representative Researcher), Basic test and development of analytical models necessary for development of prediction accuracy of F E M analysis of RC structures, Research Reports of the Grant-in-Aid, the Ministry of Education, March 1989 (in Japanese). 5.9. Finite element analysis of reinforced concrete structures, Proc. US-Japan Seminar, Tokyo, May 1985, published from ASCE, 1986. 5.10. Aoyama, H. and Noguchi, H., Future prospects for finite element analysis of reinforced concrete structures, Proc. US-Japan Seminar, Tokyo, May 1985, published from ASCE, 1986, pp. 667-681. 5.11. Research committee on F E M analysis and design method of RC structures, Guideline on the Application of FEM to Design of Concrete Structures, Japan Concrete Institute, JCI-C16, March 1989 (in Japanese). 5.12. Research committee on FEM analysis and design method of RC structures, Reports of the Analytical Studies on Macroscopic Models and FEM Microscopic Models of RC Shear Walls, Japan Concrete Institute, JCI-18, 1989 (in Japanese). 5.13. Finite element analysis of reinforced concrete structures II, Proc. Int. Workshop, New York, June 1991, published from ASCE, 1993. 5.14. Naganuma, K., Analytical model of concrete structures, FEM analysis as a design method of concrete structures, Part 4, Concrete J. 30(8), 1992 (in Japanese), pp. 81-86. 5.15. Shirai, N., Concrete structures and FEM analysis, FEM analysis as a design method of concrete structures, Part 3, Concrete J. 30(6), 1992, pp. 86-93 (in Japanese). 5.16. Stevens, N.J. et al., Analytical Modeling of Reinforced Concrete Subjected to Monotonic and Reversed Loadings, Pub. No. 87-1, University of Toronto, January 1987. 5.17. Constitutive equations and FEM WG in the sub-committee on high strength reinforcement, Research Reports, Kokudo Kaihatsu Technical Research Center, March 1993, p. 207 (in Japanese). 5.18. Suzuki, N., Guideline for nonlinear FEM analysis of RC structures, Parts 1 and 2, FEM analysis as a design method of concrete structures, Concrete J. 31(8), 1993, pp. 78-83; 31(9), 1993, pp. 76-81 (in Japanese). 5.19. Structural performance sub-committee in the New RC project, Research Reports, Kokudo Kaihatsu Technical Research Center, March 1992 (in Japanese). 5.20. Research committee on shear strength of RC structures, Reports of the 2nd JCI Colloquium on Analytical Studies on Shear Problems of RC Structures, Test Data of the Specimens for Verification of Analytical Models, Japan Concrete Institute, JCI-C6, October 1983, p. 54 (in Japanese). Finite Element Analysis 269 5.21. Fafitis, A. and Shah, S.P., Lateral reinforcement for high strength concrete columns, ACI J. 1985, pp. 213-232. 5.22. Ohkubo, M., Hamada, S. and Noguchi, H., Basic test on compressive deterioration characteristics of cracked concrete under seismic loading, Proc. JCI Colloquium, JCI-C18, October 1992, pp. 17-22 (in Japanese). 5.23. Summary reports on New RC research projects, Kokudo Kaihatsu Technical Research Center, March 1992 (in Japanese). 5.24. Sakino, K., Mechanical Characteristics of confined concrete, Research Reports of Sub-Committee on High Strength Reinforcement, Kokudo Kaihatsu Technical Research Center, March 1992 (in Japanese). 5.25. Ohkubo, M., Matsudo, M. and Noguchi, H., Experimental study on failure criterion of ultrahigh strength concrete under biaxial compressive stresses, Proc. AIJ Ann. Convention, Structure 2, October 1990, pp. 635-638, and September 1991, pp. 473-476 (in Japanese). 5.26. Noguchi, H. and Zhang, A., Analytical study on the effects of axial force on the shear strength of RC columns, Proc. JCI 13(2), 1991, pp. 381-384 (in Japanese). 5.27. Ihzuka, T., Study on Constitutive equations and FEM analysis of reinforced concrete using from ordinary to high strength materials, Doctoral Thesis of Chiba University, 1992 (in Japanese). 5.28. Amemiya, A., Experimental study on shear behavior of ultrahigh strength beams, Proc. AIJ Ann. Convention, Structure 2, October 1991 (in Japanese). 5.29. Architectural Institute of Japan, Design guideline for earthquake resistant reinforced concrete buildings based on ultimate strength concept, 1990, p. 340 (in Japanese). 5.30. Ichinose, T., Shear design method of reinforced concrete members considering deformation capacity, Trans. AIJ, 1990 (in Japanese). 5.31. Comite Euro-International Du Beton, CEB-FIP model code for concrete structures, 1988. 5.32. Kent, D.C. and Park, R., Flexural members with confined concrete, Proc. ASCE 97(ST7), 1971, pp. 1969-1990. 5.33. Park, R., Priestly, M.J.N, and Gill W.D., Ductility of square confined concrete columns, Proc. ASCE 108(ST4), April 1982. 5.34. Nimura, A., Seo, M. and Noguchi, H., Study on behavior of reinforced concrete columns using high strength materials, Proc. AIJ Ann. Convention, Structure 2, August 1992, pp. 627-630 (in Japanese). 5.35. Zhang, A., Nonlinear analysis of shear behavior of reinforced concrete members, Doctoral Thesis of Chiba University, 1991 (in Japanese). 5.36. Abe, M., Takezaki, S. and Noguchi, H., Study on development of high strength reinforcement, Parts 10 and 11, Proc. AIJ Ann. Convention, Structure 2, 1992, pp. 513-516 (in Japanese). 5.37. Shirai, N., Noguchi, H. and Shiohara, H., Study on constitutive laws of reinforced concrete element using ordinary and high strength materials, Parts 1 and 2, Proc. AIJ Ann. Convention, Structure 2, August 1992, pp. 1051-1054. 270 Design of Modern Highrise Reinforced Concrete Structures 5.38. Kabeyasawa, T. et al., Restoring force characteristics of reinforced concrete shear walls with the flexural yielding using high strength materials, Parts 1 and 2, Proc. AIJ Ann. Convention, Structure 2, October 1990, pp. 607-610. 5.39. Kabeyasawa, T. and Kuramaoto, H. et al., Loading test of high strength reinforced concrete shear walls with large shear span ratios, Trans. JCI Ann. Convention 14(2), 1992, pp. 819-824 (in Japanese). 5.40. Kano, Y. and Yanagisawa, N., Study on the shear strength, Summary Reports on New RC Research Projects, Kokudo Kaihatsu Technical Research Center, March 1992, pp. 3.3.35-3.3.40 (in Japanese). 5.41. Shohara, R., Shirai, N. and Noguchi, H., Comparisons of macroscopic models of reinforced concrete shear walls with test results, Reports of Panel Discussion on Macroscopic Models and FEM Microscopic Models of RC Shear Walls, JCI-C11, JCI, January 1988, pp. 41-60 and 97-102 (in Japanese). 5.42. Hirosawa, M., Strength and ductility of reinforced concrete members, Research Reports of Building, Promotion Association of Building Research, 76, March 1977 (in Japanese). Chapter 6 Structural Design Principles Masaomi Teshigawara Head, Structure Division, Department of Structural Engineering, Building Research Institute, Ministry of Land, Infrastructure and Transport, 1 Tachihara, Tsukuba, Ibaraki 305-0802, Japan E-mail: teshi@kenken.go.jp The Structural Design Committee of the New RC research project compiled as its outcome "the structural design guideline for New RC buildings". In this chapter, basic ideas and principles of this design guideline will be explained. Although the title of this chapter refers to the structural design in general, this chapter is entirely devoted to the seismic design. This limited scope is due to the following two reasons. First, the New RC research project, on the results of which this book is based, is concentrated on the seismic behavior and seismic design of RC structures with high strength materials. Secondly, it is usually regarded that the use of high strength concrete and steel does not necessarily improve the behavior under vertical loading, except, at most, for possible reduction of elastic deflection. The use of high strength materials in the vertical load design does not warrant a merit. As far as seismic design is concerned, it is possible and necessary to take full advantage of high strength. For RC buildings with ordinary strength materials, the recent trend of seismic design, particularly of lowrise to mediumrise buildings, is to assume weak-beam strong-column type collapse mechanism. Highrise buildings, on the other hand, tend to receive significant influence of higher modes, and many beams do not necessarily yield within the design seismic deformation limit. Design forces are calculated, not based on the assumed mechanism, but based on the earthquake response analysis. 271 272 Design of Modern Highrise Reinforced Concrete Structures The use of high strength material, particularly that of high strength steel, amplifies this trend. The yield deflection of members with such material becomes larger, about twice as much as that of ordinary material. Highrise buildings with high strength members would not produce much beam yield hinges within the design seismic deformation limit. In this situation the design based on the collapse mechanism is not realistic, and it is mandatory to use earthquake response analysis for the design. Hence a completely new seismic design method was developed for New RC structures. This chapter explains background and characteristics of this design method in the following order. Section 6.1 introduces the main features of the proposed design method. Section 6.2 is on the seismic design criteria in three stages. Section 6.3 features simulated earthquake motions specifically developed for new RC structures. Sections 6.4 and 6.5 discuss the modeling of structures for response analysis and restoring force characteristics of structural members. Section 6.6 again discusses the earthquake motions, particularly on the effect of bidirectional horizontal motions and that of vertical motions. Section 6.7 is devoted to foundation design, and the last, Sec. 6.8 introduces several buildings ranging from 15 to 60 stories designed in detail using New RC material. 6.1. Features of N e w RC Structural Design Guidelines The structural design guideline for New RC buildings was a proposal of a method of structural design for highrise and ultrahighrise buildings utilizing high strength materials within the strength range that would be used in practice in the near future. This guideline does not assume a style of specifications on detailed procedures of structural member proportioning. Rather it aims at basic principles to establish required performance of a building and method to evaluate behavior of a building to be designed. The design of a structure involves various kinds of external loading. However Japanese RC buildings are usually governed by seismic design considerations. For this reason the proposed guideline deals mainly with the seismic design. Design for permanent loading including dead and live loads, design for wind loading, for snow loading, temperature changes, creep and shrinkage, are not dealt with in the guideline. It is assumed that usual structural design method for these loadings would be applied equally to New RC buildings. Six specific features of the guideline are introduced below. Structural Design Principles 6.1.1. 273 Earthquake Resistant Design in Three Stages The guideline proposes seismic safety investigation by means of dynamic and static analyses in three stages, namely, levels 1 and 2, and post-level 2. For level 1 earthquake motion which would happen once in the lifetime of the building, serviceability should be maintained. For level 2 earthquake motion which may be the possible maximum motion to the structure, safety against collapse should be maintained. For the post-level 2 stage, the structure should still maintain suitable collapse mechanism and lateral load-carrying capacity. The adoption of the first two stages may be easily understood. The third stage was added by the following reason. Due to structural material characteristics, strength and deformability of structural members inherently show certain variation (scatter) around their mean values. This variation can be incorporated into design procedure, though not quite completely. However, the variation of earthquake motion or that of earthquake response arising from the idealization procedure of analytical models cannot be fully accounted for in the first two stages. The third stage was added in an attempt to answer to this uneasiness. Thus it may be regarded as a temporary measure reflecting the current state-of-the-art of seismic design. When a more reasonable approach to take all kinds of uncertainties into account is established for seismic design, the third stage may become unnecessary. 6.1.2. Proposal of Design Earthquake Motion The guideline includes a proposal of earthquake motion that should be used in the design of New RC structures. This proposal was made as an attempt to rationalize the currently prevalent use of available strong ground motion records such as El Centro 1940 or Hachinohe 1968. Earthquake ground motion levels to be considered in the structural design, characteristics of motion and method to produce simulated motion are proposed. 6.1.3. Bidirectional and Vertical Earthquake Motions As a part of above-mentioned rationalization, three-dimensional earthquake motions are considered. Thus earthquake ground motion levels and characteristics of motion are proposed not only for one component of horizontal motion, but also for bidirectional horizontal motions. Also some mention is made on the method to consider vertical motions. 274 Design of Modern Highrise Reinforced Concrete Structures However at the present state-of-the-art of earthquake response analysis, it is not practical to consider three dimentional motions explicitly. Hence it is recommended to use unidirectional ground motion applied to the building in any directions. Also a method to consider the effect of vertical ground motion in the static analysis is introduced. 6.1.4. Clarification of Required Safety The safety of a structure under level 1 and 2 earthquake motions and at the post-level 2 stage is specified in the material level and member level. In addition, the overall structural stability is investigated in the post-level 2 stage. In this way the required safety levels are explicitly specified for all three stages. 6.1.5. Variation of Material Strength in Strength Evaluation and Accuracy The concept of dependable and upper bound strengths was introduced to consider the variation of material strength and accuracy of strength evaluation equations. The restoring force characteristics of overall structure and internal forces for member design are to be calculated considering these two levels of strength. This will simplify the probability estimation of assumed performance. 6.1.6. Structural Design of Foundation Soil-Structure Interaction and Soil-structure interaction and superstructure-substructure interaction are to be considered in the design of foundation and evaluation of earthquake input to the superstructure. These features are quite general in nature, and the basic concept of the guideline is believed to be applicable not only to New RC structures but also to other concrete or steel structures. Owing to the limited time of the project, however, there are many subject not thoroughly investigated. It is thus quite natural to assume that much works would have to be done before such application becomes practical. Even in the direct application of this guideline to New RC structures, sound judgment of structural engineers would be required at every turn of structural design, as it was the basic concept that was emphasized in the development of the guideline. Structural Design Principles 6.2. 6.2.1. 275 Earthquake Resistant Design Criteria Design Earthquake Intensity As was previously introduced, two levels of intensity are used for design earthquake motion. Level 1 earthquake motion is the largest earthquake motion expected to occur once during the lifetime of a building, and corresponds to earthquake motion of a return period of approximately 100 years. Level 2 earthquake motion is the largest earthquake motion that is possible to occur at a site, and corresponds to earthquake motion of a return period of approximately 400 years. For an assumed building lifetime of 100 years, the probability of earthquake intensity exceeding the design level is 60 percent for level 1 and 20 percent for level 2 earthquake motions, respectively. In general, the intensity of a level 1 motion should be approximately equal to 0.4 times the intensity of a level 2 motion. 6.2.2. Design Drift Limitations Seismic response of a structure is controlled by the story drift and the structural drift. The story drift is denned as lateral story deflection divided by story height. The structural drift is denned as lateral deflection at the centroid of lateral force distribution profile divided by the height of that point. Roughly speaking the structural drift is defined at the two-thirds height of the building. Three limiting drift levels are identified in the guideline. They are serviceability drift limit, response drift limit, and design drift limit. The serviceability drift limit is defined in terms of story drift, and is used to control structural and nonstructural damage. The response drift limit is defined in terms of structural drift, and is intended to control the deformation under the possible strongest intensity earthquake motions. The design drift limit is also defined in terms of structural drift, and is used to examine the deformation at yield hinge regions and to determine design forces in nonyield hinge regions under the probable largest response deformation considering uncertainties. The serviceability and response drift limits may be selected by a structural engineer, but should not exceed 1/200 (0.5 percent) and 1/120 (0.83 percent), respectively. The response drift limit may be determined considering the extent of damage that can be repaired, and significance of P-5 effect on structural response especially in a highrise building. The design drift limit is defined as 276 Design of Modern Highrise Reinforced Concrete Structures a structural drift at which the work done by static lateral loads becomes two times that at the response drift limit. 6.2.3. Design Criteria The earthquake resistant design criteria are expressed as the combination of design earthquake intensity and design drift limitations, as shown in Table 6.1. A structure must satisfy serviceability performance criteria for level 1 earthquake motions. The serviceability is examined by nonlinear earthquake response analysis. The serviceability criteria are: (1) story drift in any story should be less than the serviceability drift limit, (2) no structural members should, in principle, develop yielding, and (3) nonstructural elements should not be damaged. A structure must also satisfy safety performance criteria for level 2 earthquake motions. Safety criteria are examined by the nonlinear earthquake response analysis. The structure is assumed to exert some nonlinear behavior associated with yielding of re-bars under the action of level 2 earthquake motion, but to remain in the range of stable deformation without load-carrying capacity drop. To achieve this end, the safety criteria for the response analysis Table 6.1. Design criteria for earthquake motion. Stage Drift Level 1 Earthquake (1) Story drift < serviceability drift limit Level 2 Earthquake (1) Structural drift < response drift limit (2) Story drift < 1.5 x response drift limit Post-level 2 Stage Structural drift = design drift limit Note: servicealibity drift limit ^ 0.5% response drift limit ^ 0.83% Members (2) No yielding in structural members (3) No damage of nonstructural elements (3) Yielding is permitted but no resistance reduction (1) Yield hinge rotation < deformability limit (2) No unexpected yield hinges (3) No brittle failure (4) Base shear coefficient > 0.25RtZ Structural Design Principles 277 are set forth as follows: (1) maximum structural drift should be less than the response drift limit, (2) maximum story drift in any story should be less than 1.5 times the above limit. As to the state of the members (3) yielding is permitted but no resistance reduction is allowed. But in reality the force and deformation of each member at this stage is not examined, because it is inferred that the check for the post-level 2 stage would automatically cover the safety criteria for the members. For the level 2 and post-level 2 stages, safety performance is examined also by static (pushover) analysis. Figure 6.1 shows the idea of static analysis in conjunction with level 2 and post-level 2 stages. As shown, it is possible to draw force vs. deformation relationship in two ways, one based on the dependable material strength, and another based on the upper bound material strength. It is customary to perform dynamic as well as static analyses on the basis of the former one, i.e. based on the dependable strength. In case of dynamic analysis it usually gives larger response, hence a safe side solution. The earthquake response fluctuates due to uncertainties in earthquake motion itself and restoring force characteristics of the structure. Hence it is essential to carry out response analysis for several cases in order to estimate, at least approximately, the distribution of the response as shown in Fig. 6.1. The response drift limit should correspond to the upper limit of such distribution. Considering the possibility of further increase of response due to uncertainties in the earthquake level and any unforeseen factors, design drift limit is Force distribution of earthquake response (force) force-drift relation based on upper bound strength design force for members Co fe 0.25 force-drift relation based on dependable strength distribution of earthquake response (drift) Drift response limit lower bound of deformation capacity design limit distribution of deformation capacity evaluation Fig. 6.1. Seismic design concept. 278 Design of Modern Highrise Reinforced Concrete Structures defined at a larger deformation range as shown in Fig. 6.1. Results of static analysis at this level should be used to check the safety criteria as follows: (1) yield hinges must remain within their deformation limit, (2) the locations where yield hinges are not expected to occur should not develop yielding, (3) brittle failure, such as shear failure or bond splitting failure, should not take place, and (4) lateral resistance in terms of base shear coefficient should be larger than some prescribed value. The first one enables us to ascertain that the design drift limit lies at the lower limit of deformability of members. The purpose of second and third ones is obvious, but it is necessary in principle to carry out this check based on the forces associated with the upper bound material strength, i.e. broken line in Fig. 6.1. It would be practical to estimate these forces approximately by magnifying the forces associated with dependable strength with an appropriate coefficient. The fourth one above, i.e. required amount of lateral resistance, was introduced for the continuity with the highrise RC buildings currently designed and constructed in Japan. Philosophically, dynamic and static design criteria without the fourth one should suffice to secure the safety against level 2 earthquakes and post-level 2 stage. The required lateral resistance is a measure to compare the safety level with the current structures. The recommended value is 0.25RtZ in terms of base shear coefficient where Rt is dynamic characteristics factor and Z is zoning factor. Figure 6.2 shows the ultimate base shear coefficient of New RC trial designs and those of current highrise RC buildings. For current RC buildings, ultimate base shear coefficients were estimated approximately by multiplying the design base shear coefficients by 1.5 to 1.7. It is seen that the required lateral resistance of New RC buildings is about the same as that of recently constructed highrise RC buildings. 0.5- 4 I °- 8 °-3 CO _g 0.2 w 0.36/T \ 0 24/r \ • New RC buildings (for ultimate strength) A existing RC buildings (for allowable stress) •* existing RC buildings (for ultimate strength) 0.18/7\ ft H^ 0) 3 o.i 0 0 Fig. 6.2. 1 2 3 fundamental period (sec) 1. Base shear coefficient of highrise RC buildings. Structural Design Principles 279 6.3. Design Earthquake Motion 6.3.1. Characteristics of Earthquake Motion The design earthquake motion is directly used in the response analysis for levels 1 and 2 criteria checking. Hence it is of utmost importance for the design of New RC buildings. Design earthquake motion should be determined considering seismicity of the site and ground conditions. The guideline proposes the spectral characteristics covering period range up to 10 seconds, and it recommends that the simulated ground motion developed from this spectrum should be used simultaneously with the currently used strong motion records. The use of multiple earthquake motions should enable us to get an idea of response distributions as shown in Fig. 6.1. 6.3.2. New RC Earthquake Motion Proposal for level 2 motion was made in the form of response spectrum as shown in Fig. 6.3. This motion was assumed on the exposed engineering bedrock 0.02 0.05 0.10 0.50 1.00 5.00 10.00 20.00 Period (sec) Fig. 6.3. Design response spectrum on exposed engineering bedrock (damping = 0.05). 280 Design of Modern Highrise Reinforced Concrete Structures on which the building is to be supported. The engineering bedrock roughly corresponds to an earth stratum with the shear wave velocity not less than 400 m/sec. This spectrum was developed from studies of earthquake motion prediction assuming an earthquake of magnitude 7.9, similar to the Great Kanto Earthquake, which struck Tokyo and Yokohama area in 1923. The intensity of earthquake ground motion of this spectrum was found to be comparable to, or slightly stronger than, the earthquake intensity commonly used in the highrise building design as level 2 earthquake. The design earthquake motion for level 1 is assumed to be 40 percent of the above level 2 motion. This was derived from the study concerning the return period of two levels of earthquake motion, 100 years for level 1 and 400 years for level 2. The exceedance probability of earthquake intensity for a 100 year lifetime building is approximately 60 percent for level 1 and 20 percent for level 2, respectively. 6.3.3. Relation to Building Standard Law Figure 6.4 shows the acceleration response spectrum of the design earthquake in terms of dynamic characteristics factor Rt, comparing with those in the Building Standard Law for three classes of subsoil. The latter is denned only up to about 2 seconds to cover buildings not taller than 60 m in height, but it is extrapolated to 8 seconds in Fig. 6.4. It is seen that the design earthquake motion denned on the exposed engineering bedrock is similar to that of class 1 soil in the Building Standard Law. class 1 soil (hard) class 2 soil (others) class 3 soil (soft) s design response spectrum for New RC 1 ! period (sec) Fig. 6.4. .Rt curves in Building Standard Law vs. design response spectrum for New RC. Structural Design Principles 6.4. 281 Modeling of Structures 6.4.1. Modeling of Structures In the practical design, it is convenient to analyze a building by different models according to the different methods of analysis. Each model must be idealized from the prototype building in a way that the objective of the particular analysis can be achieved. Static analysis should be carried out based on an appropriate frame model, preferably a space frame model, taking into account the nonlinear mechanical properties of constituent members. Dynamic analysis is performed basically in order to investigate the drift during earthquake excitation. Hence it is not always necessary to be done by a frame model. Provided that the nonlinear characteristics of members are adequately reflected, simple mass and spring model may be used. For this purpose a usual procedure is to perform static incremental (push-over) analysis first, and idealize the story shear vs. story drift relations into appropriate polylinear spring. It is recommended, however, to carry out at least one case of dynamic response analysis using frame model, preferably for earthquake motion that produces the largest response to mass and spring model. This would clarify problems that are associated with the use of simpler model, if any. 6.4.2. Relation of Model and Earthquake Motion The guideline specifies design earthquake motions at the exposed engineering bedrock. Unless the building is directly supported by such bedrock, certain modeling techniques must be employed to reflect the foundation condition. Typical examples of modeling a structure including the soil effect are shown below. 6.4.2.1. Fixed Base Model This is a building model of the case in which the ground can be regarded as being sufficiently stiff compared to the superstructure and foundation. When the foundation is constructed directly on the engineering bedrock, the standard earthquake motion defined on the exposed engineering bedrock (2 x E{) can be directly given as the input ground motion (see Fig. 6.5(a)). When the engineering bedrock is covered by surface layers and the foundation is constructed 282 Design of Modern Highrise Reinforced Concrete design motion Structures 2^Ei : input motion . t engineering bedrock . t seismological bedrock (a) model on engineering bedrock - 2-Eo : input motion t surface layers . , free surface Ei t engineering bedrock (ascending wave) (b) model on surface layers Fig. 6.5. Input motion for fixed base or sway-rocking model. on top of the surface layers, input ground motion is determined considering amplifying characteristics of the surface layers. In this case, the ascending wave (E\) from the engineering bedrock is used as the input to the surface layers, and the response wave of the free surface (2 x EQ) is calculated, which is used as the input to the building (see Fig. 6.5(b)). 6.4.2.2. Sway-Rocking Model The lateral and vertical stiffness of piles and soil under the structure is represented by sway and rocking springs. The stiffness of soil springs may be determined by an elastic analysis. The definition of the input ground motion is same as the fixed base model. Depending on whether the building is constructed on the engineering bedrock or on the surface layers, either 2 x £ i wave or 2 x E0 wave is used as input to the sway-rocking model. 6.4.2.3. Soil-Foundation-Structure Interaction Model The superstructure, basement, foundation structure and the surrounding soil above the engineering bedrock are idealized into an interaction model. Various methods of analysis are available, such as finite element method, grid model, discrete model such as Penzien model, and thin layer element method. When the bottom of the soil portion is fixed on the engineering bedrock as shown in Fig. 6.6(a), the input ground motion should be evaluated as the sum of ascending and descending waves ( £ 2 + F 2 ) obtained from the wave Structural Design Principles E2: ascending wave F2: descending wave free surface surface layers t I engineering bedrock F2 Ez(=Ei) -7777777777777777777777777777777777777E1+F1: input motion (a) Model with fixed base E2: ascending wave F2: descending wave design motion 2- E1 #_ 1 free surface engineering bedrock R(=E1) 2- E1: input motion (b) Model with viscous boundary Fig. 6.6. Input motion for soil-foundation-structure interaction models. transmission analysis of surface layers subjected to the input of ascending wave Ei (— E\ in this case, i.e. half the design earthquake motion). When the bottom of the soil portion is idealized by a viscous boundary as shown in Fig. 6.6(b), the design earthquake motion (2 x E{) is directly used as the input to the boundary. If the bottom of model soil does not correspond to the engineering bedrock, free surface response at the model bottom (2 x E0) is obtained by wave transmission analysis, and is used as input ground motion to the model in Fig. 6.6(a) or (b). 6.5. 6.5.1. Restoring Force Characteristics of Members Dependable and Upper Bound Strengths The guideline suggests to define dependable and upper bound strengths of members considering scattering of material properties and uncertainties involved in the equations for strength, stiffness, and deformation calculation. 284 Design of Modern Highrise Reinforced Concrete Table 6.2. factors. Structures Probability of nonexceedance and strength modification Probability of Nonexceedance 4> 4> For Column For Beam 7 For Column 7 For Beam 90% 1.01 0.97 1.49 1.11 95% 0.94 0.95 1.55 1.13 99% 0.81 0.92 1.68 1.16 99.9% 0.67 0.88 1.83 1.20 tp: strength modification factor for dependable strength 7: strength modification factor for upper bound strength The restoring force characteristics is then determined for each strengths. In determining the dependable and upper bound strengths, a probability of nonexceedance of 0.90 is used on a statistical basis of experimental data. If ratios of the observed to the calculated strength are assumed to take a normal distribution, the dependable and upper bound strengths of a member is estimated as follows from the calculated resistance R based on the average material strength, average ratio AR of the observed to the calculated strength, and coefficient of variation COV of the ratios: Dependable strength = R x AR x (1.0 - 1.28 x COV) = R x <j> Upper bound strength = R x AR x (1.0 + 1.28 x COV) = R x 7. Table 6.2 shows the ratios <p and 7 for various nonexceedance probability for columns and girders. The dependable strength must be used for all members, when response drift of a structure is examined in the earthquake response analysis under level 1 or 2 earthquake motions, and when lateral force resisting capacity of a structure available at the design drift limit is examined in the static analysis. The upper bound strength is assumed at the location of prescribed yield hinges in the static analysis when design actions are determined for regions other than prescribed yield hinges or when the brittle failure of a member is examined. 6.5.2. Member Modeling The stiffness of a reinforced concrete member may be assumed to change at cracking and yielding. Yielding here refers to the point at which the stiffness degrades significantly under monotonically increasing force. It does not Structural Design Principles 285 necessarily correspond to the first yield of the material that constitutes the member. The guideline suggests to use average values for the initial stiffness and cracking moment. Variation of yield strength between dependable and upper bound strengths is idealized as shown in Figs. 6.7 and 6.8 for columns and beams, respectively. This is based on the general trend of these members in the testing. For columns, the yield deformation does not change appreciably with yield strength. Hence it is reasonable to obtain the yield deformation from average yield strength and average yield stiffness, and assume dependable and upper bound yield points at the same deformation as shown in Fig. 6.7. On the other hand, yield deformation of beams increase almost linearly with the increase of yield strength. Hence after obtaining the average yield point from average yield strength and average yield stiffness, dependable and upper force yield strength (upper found) - . . / yield strength (average) yield strength (dependable) crack strength (average) yield stiffness (average) deformation yield deformation (dependable, upper found) Fig. 6.7. Restoring force characteristics for columns. yield strength (upper found) yield strength (dependable) crack strength (average) deformation yield deformation (dependable) yield deformation (upper found) Fig. 6.8. Restoring force characteristics for girders. 286 Design of Modern Highrise Reinforced Concrete Structures 1 "" 'oS 8oB° -2 0 2 drift angle R (%) Fig. 6.9. Equivalent viscous damping factor of a New RC test specimen (example). bound yield points are determined on the second slope combining crack point and average yield point, as shown in Fig. 6.8. 6.5.3. Hysteresis Hysteretic characteristics must be properly selected to account for the hysteretic energy dissipation of members. An assumption of too large hysteretic area results overestimation of energy absorption, which leads to underestimation of response deformation. Commonly adopted simple nonlinear hysteretic models, such as bilinear or trilinear models, inherently possess this tendency and so their use should be limited in practice. A more complicated model, such as Takeda model or degrading trilinear model, is recommended. The degree of hysteretic energy dissipation is best represented by the equivalent viscous damping factor. Figure 6.9 is an example of beam test data showing equivalent viscous damping and deformation. Such data should be useful in determining hysteretic model. 6.6. 6.6.1. Direction of Seismic Design Design Forces in Arbitrary Direction Needless to say that there is no definite direction in an earthquake ground motion, and a building should be safe against earthquake motions coming from Structural Design Principles 287 any directions. Bidirectional horizontal earthquake motions develop varying axial force in a corner column significantly larger than a uniaxial earthquake motion due to the overlapped overturning effect, and also develop simultaneous bidirectional bending moments and shears in the column. The guideline requires that the safety of a structure should be examined for uniaxial horizontal earthquake motions and uniaxial horizontal static forces, but occurring in all possible directions. In ordinary frame buildings of rectangular plan, it usually suffices to design longitudinal and transverse directions plus one oblique direction, usually taken at 45 degrees. In most cases, longitudinal and transverse directions are dictated by deformation criteria, while the oblique direction is dictated by strength criteria. The reason is as follows. In a two-way moment resisting frame system, suppose that the horizontal force resisting characteristics are comparable in the two principal directions, and also suppose that horizontal forces in the oblique direction develop the overall yield mechanism by forming yield hinges at all girder ends and at the base of the first story columns. Then under the oblique loading the columns develop shear force and bending moment square root of two times larger than those in a principal direction. The axial force in a corner column is doubled. This is an extreme case, but in general column shear, bending moment and axial force at a drift beyond yielding are larger when loaded in an oblique direction. On the other hand, earthquake response to the same uniaxial ground motion is smaller in the oblique direction than in the principal directions due to the above-mentioned strength enhancement. For a beam yielding frame, restoring force characteristics for loading in any direction can be obtained by superposing restoring force characteristics for loading in principal directions. In Fig. 6.10, drifts 5X and Sy in the principal directions are shown in the first quadrant, and the force P and drift 5 relations in two directions are shown in the second and fourth quadrants. Although they are shown by elasto-plastic models for simplicity, they can be any restoring force model. The third quadrant shows the force on the vertical members. Therefore, the force corresponding to any deformation can be found by combining forces in two principal directions. In the first quadrant the zone surrounded by x- and y-ax.es and the curve BCG corresponds to the force in the vertical members not greater than Pym, the yield force in y-direction, and it is denoted as Zone I. In the third quadrant it is the zone within the circle with radius OB. In the first quadrant the hatched area to the upper right of point D is the zone corresponding to the yielding in 288 Design of Modern Highrise Reinforced Concrete Structures yielding in Y-direction only II yielding in X-direction only p. S in X-direction I : Zone for column shear force ^ P ym II: Other than zone I and III III: Zone for yielding of both X and Y frames H : Any drift point in zone III Fig. 6.10. Force and deformations, yielding conditions in X and Y directions. two directions, and denoted as Zone III. In the third quadrant it is represented by the point D in case of elasto-plastic restoring force models in two principal directions, and the force in the vertical members is the largest. The zone in the first quadrant between Zones I and III is denoted as Zone II, and is the zone where the force in vertical members exceed Pym, but frames in two directions are either both elastic or only one of them yielding. The force in vertical members falls in zone BCD in the third quadrant. By the way the force in the vertical members is represented by the length of a vector in the third quadrant. So the maximum shear can be found as the point of tangency to a circle with center at point O. Similarly, the maximum axial force is given as the direct sum of those in two principal directions. Hence a similar diagram as Fig. 6.10 may be drawn for axial forces, and a straight line in the third quadrant with minus 45 degrees gradient represents a constant axial force resultant. If one decides to design his structure in the Zone III in Fig. 6.10, or in other words, to design for simultaneous beam yielding mechanism in two directions, no more problems would arise as to the strength of vertical members. However this may result in an overdesign, particularly for highrise buildings for which Structural Design Principles 289 the guideline was drafted, where large inelastic deformation is not expected to occur. In our case, it may be more reasonable and also practical to design vertical members in the Zones I or II corresponding to the drift expected under level 2 earthquakes. 6.6.2. Bidirectional Earthquake Input As mentioned earlier the motion only in one direction is assumed to act on a structure in any horizontal direction, and it is not in general necessary to consider simultaneous action of bidirectional earthquake input. However, in a case where, e.g. an appreciable amount of eccentricity exists in the structure, bidirectional response analysis will be required. If a bidirectional earthquake motion is desired in the practical design, the amplitude of a motion in the minor principal direction may be assumed to be two thirds of that in the major principal direction. 6.6.3. Effect of Vertical Motion The effect of vertical ground motion is believed to be more important in a taller building. As the height increases, the fundamental natural period becomes longer, and horizontal acceleration becomes relatively small. On the other hand the vertical acceleration is not reduced, and in some cases it may be amplified due to vertical response of the structure. Thus, the vertical to horizontal acceleration ratio will be larger for taller buildings. The guideline recommends to increase the axial force in the lower story columns under gravity loading by 20 percent to account for the effect of vertical ground motion. This was derived from an estimate of maximum vertical ground acceleration of 10 percent of gravity acceleration, amplification factor of 3.0, and nonconcurrency of the maximum horizontal overturning response and maximum vertical acceleration response. 6.7. Foundation Structure Same design criteria as the superstructure should be applied to the substructure, namely, design criteria for level 1 earthquake motion, dynamic design criteria for level 2 earthquake motion, and static design criteria for post-level 2 stage will have to be satisfied. However, in practice, the level 2 investigation can 290 Design of Modern Highrise Reinforced Concrete Structures be replaced by those in post-level 2 stage, i.e. investigation at design drift limit. Hence the foundation design criteria can be expressed at level 1 earthquake and post-level 2 stage, in terms of bearing capacity and lateral resistance. Of course the bearing capacity under permanent loading must satisfy usual design criteria for foundation. Table 6.3 summarizes the design criteria for bearing capacity. The foundation structure must satisfy these criteria under permanent loading, seismic loading at level 1 earthquake, and seismic loading corresponding to design drift limit. Table 6.4 shows the design criteria for lateral resistance of foundation, particularly that of piles. The foundation structure including foundation beams, pile caps and piles must satisfy these criteria. Table 6.3. Design criteria for bearing capacity of foundations. Stage Working Force Settlement Uplift Force on Piles Permanent Loading less than allowable bearing stress for permanent loading no harmful effect on superstructure less than Wv Level 1 Earthquake less than allowable bearing stress for temporary loading no harmful effect on superstructure less than 2 T u / 3 + Wp Post-level 2 (Design Drift Limit) less than ultimate bearing stress (denned as load at settlement of 10% of pile diameter) no excessive inclination or deformation to superstructure less than Tu + Wp Wp: weight of the pile considering buoyancy Tu: ultimate pullout resistance Table 6.4. Design criteria for lateral resistance of foundation. Stage Level 1 Earthquake Post-level 2 (Design Drift Limit) Criteria Comments All members remain elastic. Lateral deflection should be checked when it affects the superstructure. Partial yielding is permitted, but not reduction of total lateral resistance. Permissible lateral deflections limit may be selected by the engineer. Structural Design Principles 291 6.8. Design Examples Six buildings from the following three categories were selected for the trial structural design following the proposed structural design guideline for New RC buildings. (1) 60-story space frame structure for highrise apartment building. (2) 40-story double tube structure and core-in-tube structure for highrise office buildings. (3) 15-story space frame structure, 15-story wall and frame structure, and 25-story space frame structure for mediumrise office buildings. These buildings were subjected to the trial structural design with the aim of investigating the effectiveness of the structural design guideline. In particular, the 60-story space frame apartment building was studied in order to show an example of super-highrise structural design utilizing high strength concrete and reinforcement according to the structural design guideline. Study of two tube structures, i.e. 40-story double tube and core-in-tube office buildings, was conducted to explore the possibility of application of New RC material to highrise office buildings, and also to expose any problems that may arise in the application of structural design guideline to tube structures. In the trial design of three mediumrise office buildings, possibility of space frame or wall and frame structures applied to this kind of buildings was explored with the use of New RC materials. 6.8.1. 60-Story Space Frame Apartment Building This example structural design was prepared for the illustration of a structure that could be designed by using New RC materials in the Zone I as shown in Chap. 2 (Fig. 2.1). It is a 60-story apartment building as shown in Fig. 6.11, with a regular space frame structure of 5.7 m span in two ways. The typical floor plan is shown in Fig. 6.12. The width of the building as measured at the centerto-center of exterior columns is 34.2 m. Figure 6.13 shows the frame elevation. With the height of the building to the top girder of 175.6 m, the aspect ratio is 5.1, which means that the building is a considerably slender structure. This building shape was not resulted from any particular architectural study, but was arbitrarily selected from the structural design point of view. As a building in the Zone I of Fig. 2.1, concrete with compressive strength of 60 MPa is used from the first story to 41st floor, and 51 MPa concrete is used in 41st story and above. Axial reinforcement in the columns and girders 292 Design of Modern Highrise Reinforced Concrete Structures Fig. 6.11. Bird's eye view of 60-story apartment building. T storage T HQ {JB|B]B|BJ ], 5 700,|,5700 |,5700 [ 5700J 5700 [ 5 700 1500 1500 37 200 Fig. 6.12. Typical floor plan. is USD685B steel, while their lateral reinforcement is USD785, and floor slab reinforcement is SD295A. Columns are all square sections, with the dimension of 1000 mm in the first ten stories decreasing to 750 mm in the top ten stories. Girders have rectangular sections ranging from 450 mm by 900 mm to 400 mm by 700 mm. Their dimensions and re-bar arrangement are shown in Table 6.5. Structural §f | Save height Design Principles 175 6m VRF v5oP = V40F = = z V20F X o V2F V1F Fig. 6.13. Typical frame elevation. 1 293 294 Design of Modern Highrise Reinforced Concrete Structures Table 6.5. Section of members (60-story frame). Interior Columns Story Corner Columns Section Axial Bars Hoops Section Axial Bars (core bars) Hoops 60-51 750 X 750 12-D25 4-D10® 150 750 X 750 12-D29 4-D10® 150 50-41 750 X 750 12-D29 4-D10® 150 750 X 750 12-D32 4-D10® 150 40-31 800 X 800 12-D29 4-D10® 150 800 X 800 12-D35 4-D10® 150 30-21 850 X 850 12-D29 4-D13® 150 850 X 850 16-D35 (+4-D38) 4-D13® 150 20-11 900 X 900 12-D29 4-D13® 150 900 X 900 16-D38 (+8-D38) 4-D13® 150 10-2 1000 X 1000 12-D32 4-D13® 100 1000 X 1000 16-D41 +8-D41 4-D13® 100 1 1000 X 1000 12-D32 4-D13® 100 1000 X 1000 16-D41 (+8-D41) 4-D13® 100 Interior Girders Floor Exterior Girders Section Top & Bot. Bars Stirrups Section Top & Bot. Bars Stirrups RF-57F 400 x 700 4-D19 2-D13® 150 400 X 700 4-D19 2-D10® 100 56F-52F 400 x 700 4-D25 2-D13® 100 400 X 700 4-D19 2-D10® 100 51F-47F 400 X 700 4-D29 2-D13® 100 400 X 700 4-D22 2-D10® 100 46F-42F 400 X 700 4-D29 2-D13® 100 400 X 700 4-D22 2-D10® 100 41F-32F 400 X 750 4-D25 +2-D22 2-D13® 100 400 X 750 4-D22 2-D10® 100 31F-22F 400 X 750 4-D29 +2-D22 4-D13® 150 400 X 750 4-D22 2-D10® 100 21F-12F 450 X 750 4-D29 +2-D29 4-D13® 150 450 X 750 4-D29 2-D13® 100 11F-3F 450 X 750 4-D29 +2-D29 4-D13® 150 450 X 750 4-D29 +2-D22 4-D13® 150 2F 450 X 900 4-D29 +2-D19 4-D13® 150 450 X 900 4-D29 +2-D19 4-D13® 150 Figure 6.14 shows the structural design flow that was adopted specifically for the design of this building. The structural design guideline shows the necessary seismic design criteria and means to achieve the required criteria, but not the detailed procedure to determine structural member sections. It is the responsibility of structural engineers to establish structural design flow such as Structural Design Principles 295 structural planning assume member section & Co (base shear coef.) •—I | establish lateral load profile ] response spectrum & SRSS I I member force analysis for re-bar arrangement equiv. linear 3-D analysis | assume re-bar arrangement | | prelim, static 3-D nonlinear analysis | — \ prelim, earthquake response analysis | Input waves: standard waves 1 ^ ' & New RC wave establish member sections, re-bar arrangement & Co establish serviceability drift limit (R=1/200) establish response drift limit (R=1/140) CB =0.0629, T. =3.82 sec establish design drift limit (R=1/90) prelim, calculation ~| member strength (dependable & upper bound) i s : analysis static 3-D nonlinear confirm that work done at design drift limit exceeds twice that at response drift limit earthquake response analysis 1. mass-spring system (flexural shear model) 2. planar frame model confirm member strength for actions at design drift limit , + | confirm seismic design criteria design of foundations L check tor wind load confirm structural drift lies w/in design drift limit safety against overturning and contact pressure of ground | compare with seismic load ( END ) Fig. 6.14. Flow diagram of structural design. Fig. 6.14. In this case an equivalent linear three-dimensional analysis was first performed to make a preliminary assumptions of member sections and re-bar arrangement, and then preliminary static three-dimensional nonlinear analysis and earthquake response analysis were conducted to establish member sections and re-bar arrangement, to be subjected to the main structural design analysis. This preliminary design flow may be substituted by any other approach, as long as they are reasonable in deriving suitable member sections and re-bar arrangement. Figure 6.15 shows the design story shear force as determined by the response spectrum and SRSS (square root of sum of squares) method, and ultimate load carrying capacity as determined by an approximate analysis (node moment distribution method). Also shown for comparison is a story shear distribution determined by the Ai distribution of the Building Standard Law with the same 296 Design of Modern Highrise Reinforced Concrete Structures story 50 50 A i-distribution ultimate load carrying capacity (approx. analysis) 40 30 20 10 0 0 20 40 60 80 story shear (MN) Fig. 6.15. Design story shear force and ultimate load carrying capacity based on dependable strength. base shear as the design value. Compared to Ai distribution, the design shear by SRSS is smaller in general, except for upper stories around 50th story. The ultimate load carrying capacity exceeds the design story shear by a relatively large margin in most stories, showing that the assumed member sections in Table 6.5 was somewhat "overdesigned". A partial reason for this is the influence of sensitivity of response displacement to the yield deformation and strength distribution of stories. Also the change of fiexural strength evaluation from approximate analysis to a more precise analysis contributed in increased ultimate capacity. It is possible to re-adjust the member section assumptions in Table 6.5 to reduce the ultimate capacity and thereby realize a more economical structure. Figure 6.16 shows load-deflection curves in terms of base shear and structural drift. Loadings into X direction and 45 degrees direction are shown. They are similar in the elastic range, and the load in 45 degrees direction is greater after cracking, with almost same secant slope. The structure did not reach the mechanism even at the design drift limit of 1/90 (1233 mm), and hence the analysis based on the dependable strength and that on the upper limit strength Structural Design Principles 297 70 60 50- I 40 20- 10- 0 0.25 0.50 0.75 1.00 1.25 1.50 structural drift (m) Fig. 6.16. Base shear vs. structural drift relationship. do not make appreciable difference (Fig. 6.16 is the one based on the upper bound strength). The load at the design drift limit is about 10 percent greater in 45 degrees direction than in X direction, which is much lower than about 40 percent increase estimated from the superpositon of load in X and Y directions. This is due to the fact that few yield hinges were developed in the loading up to the design drift limit, and also to the fact that stiffness of columns under 45 degrees flexure and axial stiffness were much more reduced than in the X direction. Maximum response story shear and story drift are plotted in Figs. 6.17 and 6.18, respectively. Story shear and story drift under static loading at the design drift limit are also shown. Although the response values from frame response analysis were plotted in these figures, they were quite similar to the results of mass-and-spring models. At the centroid of lateral load profile located at the 39th floor, the maximum response deflection was 598 mm, or in terms of structural drift angle it was 1/190 (0.53 percent). This is smaller than the response drift limit of 1/140 (0.71 percent). The maximum story drift of 25.5 mm occurred in the 42nd story, or in terms of story drift angle it was 1/110 (0.91 percent). This falls within 1.5 times the response drift limit of 1/93 (1.07 percent). The maximum response story shears were smaller than the story shear at design drift limit, and they were approximately same as those 298 Design of Modem Highrwe Reinforced Concrete Structures 20 40 story shear (MN) Fig. 6.17. Maximum response story shear (level 2, X direction). at design drift limit drift angle {%) Fig. 6.18. Maximum response drift angle (level 2, X direction). at response drift limit. Although not shown in the figures, maximum response overturning moment was found to be less than the overturning moment by static analysis at the response drift limit. In concluding this design example of 60-story apartment building, it may be mentioned that, although the span length of 5.7 m and column size of 1 m Structural Design Principles 299 in lower stories may be disappointing for architectural planning, this example clearly demonstrated that an apartment building of 60 stories could be constructed in a seismic zone using New RC materials. If 60 MPa concrete is replaced by 100 MPa concrete, span length and column size would become more realistic. 6.8.2. 40-Story Double Tube and Office Buildings Core-in-Tu.be These design examples of highrise office buildings were studied in order to expose any problems in structural and seismic design procedures that may be found in the application of structural design guideline to highrise tube structures utilizing New RC materials. 6.8.2.1. Double Tube Structure The building is a 40-story office building with the typical floor plan shown in Fig. 6.19. Exterior tube consists of 48 m square frames with uniform 4 m span, having aspect ratio of 3.4. The interior tube composing an architectural core is 16 m square with the same 4 m span. Figure 6.20 shows the elevation of an exterior frame. This building is to be designed using high strength materials in Zone III. Concrete from 1st story columns to 16th floor has compressive strength of 90 MPa, that from 16th story columns to 31st floor 78 MPa, and that from 31st story columns to roof floor 63 MPa. USD785 steel is to be used i " ',' ii ii ii •' •• I'l I'l I'l l'l II—TT 4.MOxl?=48.00(l (!) Fig. 6.19. Typical floor plan. " y 300 Design of Modern Highrise Reinforced Concrete Structures .-__- - - i CO j n 4U OT o O CD - 000'9 , © 48.000 GL , 6.000 Fig. 6.20. Exterior frame elevation. as axial reinforcement of columns and girders and USD980 steel for lateral reinforcement. Table 6.6 shows dimensions and axial re-bars of columns and girders. In the process of seismic design, somewhat different approaches were adopted for this building compared to those recommended in the structural design guideline. They are summarized in Table 6.7. These differences were resulted from the difference in time of works towards the structural design guideline and the design examples. It is believed that none of these differences give essential effect on the structural design of the example building. Figures 6.21 and 6.22 show the maximum response story shear and story drift, respectively, obtained by the frame response analysis. From the response analysis for various input waveforms, result for two synthetic motions (New HA and New RAN) are plotted in Fig. 6.21, and those only for the former motion are plotted in Fig. 6.22. These synthetic motions conform to the design response spectrum in Fig. 6.3, with the only difference being the phase spectrum used in the synthesis of simulated earthquake motions (the former used the phase spectrum of Hachinohe 1968 NS record, while the latter used a random phase Structural Design Principles 301 Table 6.6. Section of members (double tube). Interior T u b e Exterior T u b e Corner Column Side C o l u m n section re-bars* section re-bars section re-bars section re-bars 36-40 750 X750 12-D25 750 X750 12-D25 800 X800 12-D25 800 X800 12-D25 31-35 750 X800 12-D25 750 X800 12-D25 800 X900 12-D25 800 X900 12-D25 26-30 800 X800 16-D32 800 X800 16-D32 900 X900 12-D29 900 X900 12-D29 16-25 800 x850 16-D32 800 X850 16-D32 900 X1000 12-D29 900 X1000 12-D29 4-15 850 X800 16-D32 (+8-D32) 850 X850 16-D32 1000 X1000 12-D29 1000 X1000 12-D29 1-3 850 X850 16-D32 (+8-D32) 850 X850 16-D32 1100 xllOO 16-D32 1000 X1000 16-D32 Story Side C o l u m n Corner Column Exterior T u b e Floor Interior T u b e G i r d e r s Section T o p & Bot. Bars G i r d e r s Section T o p & Bot. Bars 36F-RF 750 X 800 5-D32 750 X 800 3-D32 32F-35F 750 X 800 6-D32 750 X 800 4-D32 29F-31F 800 x 800 7-D32 800 X 800 5-D32 17F-28F 800 x 800 8-D32 800 x 800 6-D32 13F-16F 850 X 800 4-D35 + 4-D32 850 X 800 4-D35 + 3-D32 2F-12F 850 x 800 8-D35 850 x 800 8-D35 * Re-bars in ( ) i n d i c a t e core b a r s . distribution). In general, the New HA wave gave the largest response to the structure. From the response analysis it was found that the maximum structural drift at the centroid of lateral load profile (located at the 30th floor) was 1/184 (0.54 percent) under the action of New HA wave, which is less than 1/120 (0.83 percent) as stipulated in Table 6.1. Also it was found that the maximum story drift occurred at the 32nd story under New HA wave, and its value was 1/108 (0.93 percent) which is less than 1/80 (1.25 percent) as set forth in Table 6.1. The response drift limit for this building was selected to be 1/156 (0.64 percent) so that the maximum story drift of 1/108 (0.93 percent) lies below 1.5 times the response drift limit. Also the design drift limit for 302 Design of Modern Highrise Reinforced Concrete Structures Table 6.7. Comparison of design guideline and this building (double tube). Item Structure Design Guideline Double Tube Building Material Strength Zone I Zone III Material Constants proposed formula ACI formula Direction of E Q Motion any direction (ID) principal direction (force enhancement for 45° direction) Structure Model space frame model (in principle) pseudo 3-D model Soils and Foundation interaction or coupled model (in principle) 1st column base fixed Static Lateral Force Profile appropriate distribution Aj distribution Mechanism at Design Drift Limit dependable strength of hinges dependable strength of hinges Member Force at Design Drift Limit upper bound strength of hinges magnify by 1.15 Allowance of Member Strength not less than design forces confrim on interaction diagrams Check for Level 1 E Q no yield hinges confrim by frame response analysis Check for Level 2 E Q deformation capacity of members confrim by frame response analysis this building was selected, from the static elasto-plastic (pushover) analysis mentioned later, to be 1 percent so as not to violate design criteria for strength and strain energy absorption. Figure 6.21 shows also plots of story shears from static analysis corresponding to the response structural drift of 1/184 (0.54 percent) and that corresponding to the above-mentioned design drift limit of 1 percent. It is seen that dynamic response values exceed the static value at the same structural drift, but they do not exceed the static values at the design drift limit. Figure 6.22 shows, in addition to the two above, the story drift from the static analysis at the response drift limit of 1/156 (0.64 percent). Like the story shear in Fig. 6.21, dynamic response drifts exceed the static value at the same structural drift, and they even exceed the static values at the response drift limit particularly in the upper stories, but they lie within the static values at the design drift limit. Structural Design Principles 303 story l at design drift limit of 1% l at response drift of NEW HA wave response for NEW HA wave -I response for NEW RAN wave 10 20 30 40 50 60 70 story shear (MN) Fig. 6.21. Maximum response story shear (level 2, X direction). story at design drift limit of 1 % y. at response drift of -* r~ New HA wave at response drift limit of 0.64% response for New HA wave 10 20 30 40 story drift (mm) Fig. 6.22. Maximum response story drift (level 2, X direction). The frame response analysis also gave informations on the member ductility factors. It was found that yield hinges form only in the interior tube girders under the action of level 2 earthquake motion, and the maximum ductility factor of 1.08 was recorded at the 36th floor girder. Figure 6.23 shows the axial force-moment interaction diagrams of first story corner columns with the plots of working force and moment at permanent loading and seismic loading. Point 1 in the figure is for permanent (vertical) loading, points 2 and 3 are for lateral loading corresponding to positive and 304 Design of Modern Highrise Reinforced Concrete Structures 80 100 60 80 4(positive 45°) N 40 I z _ 4 ( p ositive 45°) 3~ > 20 i 4 ^(positive d.d.i.) 1 / i 1 (permanent) 2 4 f5 i \ ) / fJ z 60 ~t ' 1 (permanent) 20 M(MN-m) 10 5(negative 45°) (a) corner column, exterior tube Fig. 6.23. 2(positive d.d.l.)\ 40 3(negative d.d.l.) 0 3 (negative d.d.l.) -20 |- ^ p ^ l 5(negative 45°) 10 |15 20 5 M (MN • m) -20 (b) corner column, interior tube Interaction diagrams of corner columns and design actions. negative design drift limits, zones marked 4 and 5 are for the loading into 45 degrees direction. The last ones were estimated as follows: bending moment in 45 degrees direction will increase by a factor between 1 and y/2, and axial force due to 45 degrees direction loading will increase by a factor between y/2 and 2 multiplied by 0.8 which is the overturning moment reduction factor. Thus rectangular zones indicate the range of internal force variation under the 45 degrees loading. Comparing those with the interaction curves, corner columns of both exterior and interior tubes do not have sufficient reinforcement under axial tension and bending. No feedback to the structural design was undertaken, although such adjustment of re-bars may be necessary in the practical design. Alternately, an analysis taking the tensile yielding of corner column into account may be required. Girders were checked for the shear and bond strengths under the loading at the design drift limit. In some girders shear strength was not sufficient, and lateral reinforcement was appropriately changed to accommodate enough shear strength. From the example structural design of a highrise double tube structure as outlined above, it appears that a more reasonable design would result for the Zone III structures, not by determining the design drift limit unconditionally, but by relating it to the response drift limit in such a way that it would reflect Structural Design Principles 305 dynamic characteristics of the structure. Another conclusion was that the use of high strength steel was meritorious for external tube corner columns where tensile force dominates under oblique loading. The merit of high strength concrete has been established in case of columns under high axial compression. In general there are always columns dominated by high tension and high compression, hence the use of both high strength concrete and high strength steel in good balance will be required for the advancement of RC construction. 6.8.2.2. Core-in-Tube Structure The second example of highrise office building is a 40-story building with the typical floor plan shown in Fig. 6.24. Exterior tube consists of 48 m square frames with 4 m span, and interior tube is now replaced by a structural core walls. Figure 6.25 shows the frame elevation. This building is also to be designed using Zone III material. Concrete strength from 1st story column to 11th floor is 90 MPa, from 11th story column to 21st floor is 80 MPa, from 21st story column to 31st floor is 70 MPa, from 31st story column to roof floor is 60 MPa. USD980 rebar for column and girder bars, not available at present despite the New RC project, is to be used from the first story columns to the 26th floor girders, and USD785 is used in the upper stories. USD980 reinforcement is also used for lateral reinforcement. Table 6.8 shows the dimensions and axial re-bars of columns and girders. It will be seen that members are considerably smaller than the previous example of double tube structure. 16000 f?i) 16000 48000 Gl G1 Gl Gl (V5) 16000 Gl Gl G1 G2 (YI) Ct C2 C2 C2 C3 C4 C4 C4 C3 @ Fig. 6.24. Typical floor plan. (X13) 306 Design of Modern Highrise Reinforced Concrete (a) Y1 frame Fig. 6.25. Structures (b) Y5 frame Frame elevations. Similar to the previous one, this example was also designed by slightly different design procedures compared to those recommended in the structural design guideline. They are compared in Table 6.9. It will be found that the design procedure for this building is similar, but not identical, to the previous example of double tube building. It is believed also that none of the differences to the structural design guideline cause essential effect on the structural design of this example building. Figure 6.26 illustrates force-deflection curves in terms of loading step and structural drift at the centroid of lateral load profile both in X direction and 45 degrees direction. The design drift limit is taken at 1/114 (0.88 percent) in X direction and 1/128 (0.78 percent) in 45 degrees direction. The drift at the Structural Design Principles Table 6.8. Section of members (core-in-tube). Material Exterior T u b e Story 31-40 Concrete Steel section re-bars* section re-bars (MPa) (Mpa) 800 X 800 12-D25 800 X 800 12-D25 60 800 12-D29 70 800 Side C o l u m n Corner C o l u m n 26-30 800 X 800 12-D29 800 X 800 21-25 800 X 800 12-D29 800 X 800 12-D29 70 1000 11-20 800 X 800 16-D29 800 X 800 12-D29 80 1000 12-D32 90 1000 1-10 800 X 800 800 X 800 16-D32 (+4-D32) Material Girders Floor Concrete Steel re-bars (MPa) (Mpa) C o r e coupling Exterior t u b e section re-bars section 37-R 600 X 800 5-D29 600 X 800 4-D29 60 800 32-36 600 X 800 6-D29 600 X 800 6-D29 60 800 27-31 600 X 800 7-D29 600 X 800 4-D32 +2-D29 70 800 22-26 600 X 800 6-D29 600 X 800 4-D32 +2-D29 70 1000 12-21 600 X 800 7-D29 600 X 800 6-D32 80 1000 2-11 600 X 800 7-D29 600 X 800 6-D32 90 1000 Wall Story Column Portion Material Wall P o r t i o n Concrete Steel section re-bars* thick re-bars (MPa) (Mpa) 31-40 800 X 800 12-D25 800 2-D16@ 200 60 800 26-30 800 X 800 12-D25 800 2-D16® 200 70 800 21-25 800 x 800 12-D25 800 2-D16® 200 70 1000 11-20 800 X 800 12-D25 800 2-D16<9 200 80 1000 9-10 800 x 800 12-D25 800 2-D16® 200 90 1000 7-8 800 X 800 12-D29 800 2-D16® 200 90 1000 5-6 800 X 800 16-D29 800 2-D16® 200 90 1000 3-4 800 X 800 16-D32 800 2-D16® 200 90 1000 1-2 800 X 800 16-D32 (+8-D32) 800 2-D16® 200 90 1000 * R e - b a r s in ( ) indicate core b a r s . 307 308 Design of Modern Highrise Reinforced Concrete Structures Table 6.9. Comparison of design guideline and this building (core-in-tube). Item Structure Design Guideline Tube-in-Core Building Material Strength Zone I Zone III Material Constants proposed formula ACI formula Direction of E Q Motion any direction (ID) principal direction (45° directions) Structure Model space frame model (in principle) static: nonlinear space frame dynamic: mass-spring model Soils and Foundation interaction or coupled model (in principle) 1st column base fixed Static Lateral Force Profile appropriate distribution based on preliminary response analysis Mechanism at Design Drift Limit dependable strength of hinges dependable strength of hinges Member Force at Design Drift Limit upper bound trength of hinges dependable strength x l . 1 5 except t h a t axial force xl.O Allowance of Member Strength not less t h a n upper bound strength at hinges illustration by 3-D interaction diagrams (Mn-My-N) Check for Level 1 E Q no yield hinges confirm by mass-spring response analysis Check for Level 2 E Q deformation capacity of members confrim by mass-spring response analysis step design drift limit ot>oV response drift limit ^rf>° I 50 step 0.3125R1Z 40 j £ r 30 |! 0.25RK l 0 design drift limit response drift limit]** o.3i25Rtz o.25Rtz, v 40 30 20 20 10 50 ~ff r !| i i 0.2 i i i 0.4 (a) X direction loading ill 0.6 10 1/114 i i 0.8 i\l 1/128 0 1.0 structural drift (m) (b) 45° direction loading structural drift (m) Fig. 6.26. Loading step vs. structural drift relationship. Structural Design Principles 309 first story where column hinging is expected is 1/408 (0.25 percent) under X direction loading and 1/605 (0.17 percent) under 45 degrees direction loading. The largest deflection angle of tube girders is 1/175 (0.57 percent) at 40th floor and 1/185 (0.54 percent) at 26th floor, and that of coupling girders is 1/81 (1.23 percent) at 11th floor and 1/127 (0.79 percent) at 7th floor, for X direction loading and 45 degrees direction loading, respectively. Figure 6.27 shows the maximum response story shear for X direction response and 45 degrees direction response. Two kinds of input earthquake motion were considered, i.e. New HA and New RAN waves as explained before. The response story shear is in general greater for 45 degrees direction input, and in some stories it is even greater than the story shear at design drift limit. Figure 6.28 shows the maximum response story drift for X direction response and 45 degrees direction response. Results for two input waves as above are plotted. Similarly to the response story shear, the response story drift is generally greater for 45 degrees direction input, and it even supersedes the story drift from the static analysis at the design drift limit. It will be seen that design criteria were not satisfied by the 45 degrees direction response, both in terms of story shear and story drift. This was caused by too conservative definition of the design drift limit in 45 degrees direction which had been determined referring to the preliminary analysis in X direction. Also the slight difference in the models of preliminary analysis 0 30 60 90 0 30 60 story shear(MN) story shear(MN) (a) X direction input (b) 45° direction input Fig. 6.27. Maximum response story shear. 90 310 Design of Modern Highrise Reinforced Concrete Structures response drift limit x1.5 16 30 story drift (mm) 15 30 storage drift (mm) (a) X direction (b) 45° direction Fig. 6.28. Maximum response story drift. and main analysis caused the increased response. It is inferred that all design criteria can be satisfied by defining the design drift limit in 45 degrees direction to a larger value. Thus the example design of a 40-story core-in-tube office building indicated that such a building is feasible by using Zone III high strength materials and following the structural design guideline, although some reexamination is needed to the illustrated example in some parts of the seismic design and analysis. 6.8.3. Mediumrise Office Buildings (15-Story Wall-Frame, 15-Story Space Frame, 25-Story Space Frame) Three office buildings raging from 15 to 25 stories were designed to study the feasibility of New RC structures in the mediumrise buildings. When the structure is equipped with walls, it is possible to determine a small value to the design drift limit, then to reduce the framing member sections even to the extent that they are dictated by the vertical loading, thus the advantage of Zone III high strength material (80 MPa concrete and SD685 re-bars) can be fully utilized. In case of space frame structures where Zone I high strength material (60 MPa concrete and SD685 re-bars) are used, the reduced member size to take full advantage of Zone I material was explored. Structural Design Principles 311 Three buildings have common plan of center core type office building. Figure 6.29 shows the floor plan of 15-story wall-frame building (WF15). In case of 15-story or 25-story space frame buildings (F15 or F25), the plan lacks the exterior transverse walls and interior longitudinal walls. The buildings have 12 m and 9 m spans in the transverse direction, and 6.5 m uniform spans in the longitudinal direction. Table 6.10 summarizes major parameters of the three buildings. Figure 6.30 shows the elevation of transverse frames. The standard story height is 4 m, and the building height is 60.6 m for 15-story and 100.5 m © © ( D C © ® © ® ® Fig. 6.29. Typical floor plan of W F 1 5 building. Table 6.10. Structural systems and material. Buildings WF15 F15 F25 wall-frame space frame space frame No. of Stories (basement) 15(+1) 15(+1) 25(+l) Concrete Strength 80MPa 60MPa 60MPa Steel Grade (main bars) USD685 USD685 USD685 Steel Grade (lateral bars) USD785 USD785 USD785 Max. Column Size 800 x 800 900 x 900 1000 x 1000 Max. Grider Size 400 x 900 550 x 1000 650 x 1000 Structural System Max. Wall Thickness 400 ~ _ 312 Design of Modern Highrise Reinforced Concrete Structures A 12.00 B | 9.00 | C 12.00 D I ~ii—ir A I B 12.00 C I 9.00 I 12.00 D | I 9.00 C I 12.00 D I ZE W20 |W20 W20 "ll ~llW20 |W20 "~1|W20 W20 uc ||W20~ W20 ~ll ||W20~ |W20 "I I IIW20~ |W20 X W20 IW20 IW20 ZE "1IW20 |W20 ~I|W20 IW20 |W20 |W20 ~1| |[W20~ "llwgo W20 (b)F15 Fig. 6.30. Frame elevations. for 25-story. Figure 6.31 summarizes the typical cross section of framing members. It will be clear that WF15 consists of beams and columns with relatively small sections, while F15 and F25 employ members as large as, or even greater than, those in the 60-story apartment buildings. Results of static nonlinear (push-over) analysis, shown in Fig. 6.32, clearly illustrates the structural characteristics of wall-frame structure and space frame structure. WF15 is very stiff up to relatively high load, and the story drift is almost constant through the building height. F15 and F25 show ordinary trilinear type of load-deflection relation, and there is a trend of large story drift occurring in the intermediate stories. The design drift limits were determined as 1/104 (0.96 percent) for WF15, and 1/85 (1.18 percent) for F15 and F25. Figure 6.33 illustrates relationship between story drift at design drift limit and axial load ratio of first story columns. Axial load ratio is defined as the Structural Design Principles 313 Fig. 6.31. Typical member sections of mediumrise buildings. axial load divided by gross concrete area and concrete strength. Encircled plots correspond to WF15, where the plots with large drift are for the transverse direction, and those with small drift are for the longitudinal and oblique directions. Straight lines indicate the prediction proposed by the literature (Report from the ductility subcommittee, Architectural Institute of Japan, 1992). The axial load ratio of frame structures (F15 and F25) falls below the line that dictates the limiting drift angle. The columns in WF15 are the wall-side column of dumbbell shaped shear walls, and hence it is subjected to a large fluctuation of axial load. However it is seen that the axial load ratio of these columns does not exceed the limit to allow 1 percent drift. To conclude the example design of three mediumrise office buildings, the feasibility by such buildings using New RC high strength materials was established. At the same time the validity of the structural design guideline was proved with some minor modifications as to the definition of response and design drift limits. In the practical design of medium to highrise buildings in general, axial load on the columns would be the subject for the most significant design consideration. 314 Design of Modern Highrise Reinforced 0 25 (a)WF15 Concrete 50 Structures 75 100 story drift (mm) (C0=0.29)_ 0 25 50 (b) F15 75 100 0 (c) F25 story drift (mm) Fig. 6.32. 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 25 50 75 100 story drift (mm) Story shear vs. story drift of three buildings. (variable axial load) prediction by literature / "—•+ {constant axial p load) • d * c2 O C4 longitudinal and oblique directions transverse direction First story drift augle (%) Fig. 6.33. Story drift at design drift limit and axial load ratio of first story columns. Chapter 7 Earthquake Response Analysis Toshimi Kabeyasawa Earthquake Research Institute, University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan E-mail: kabe@eri.u-tokyo.ac.jp 7.1. Earthquake Response Analysis in Seismic Design Earthquake response analysis is an art to simulate the behavior of a structure subject to an earthquake ground motion based on dynamics and a mathematical model. In this chapter, recent trends in the methods of the earthquake response analysis are introduced. Various methods of earthquake response analysis have been developed and improved during these thirty years. Development, improvement and verification of accuracy for the response analysis methods have been major research themes in earthquake engineering, such as methods for numerical calculation procedure, structural modeling and hysteresis modeling. Earthquake response analyses of damaged structures or idealized structures have been carried out using accelerograms of strong motions which were recorded during past major earthquakes. Typical or general results of the earthquake response analyses have been interpreted theoretically and reflected on the revision of the requirements in the traditional seismic design codes. Rapid progress in the research field as well as in computer technology enabled engineers to use the earthquake response analysis as a tool in practical seismic design to estimate responses of structures to design earthquake motions. The earthquake response analysis has been applied to particular seismic design of special structures, such as highrise buildings and nuclear power 315 316 Design of Modern Highrise Reinforced Concrete Structures plants, in addition to traditional design based on elastic structural analyses under equivalent static loading. The earthquake response analysis is useful to estimate nonlinear and dynamic responses of the designed structures including local behavior, such as member forces, interstory displacements and local deformations, so as to verify the serviceability or the safety performance based on actually expected behavior of the structure during the earthquake. Available methods of earthquake response analysis in design analysis essentially depend on how the design earthquake motion is expressed or assumed as the input information. If the earthquake is given as a deterministic timehistory of motion at the base, for example, based on past accelerograms at other sites, the hysteretic response of the modeled structure can be calculated by numerical step-by-step procedure, which is called as "time-history response analysis". The method is useful to estimate nonlinear responses of the structure. However, it is still difficult to simulate the deterministic time-history of a future earthquake motion at the construction site. Therefore, the earthquake response analysis has not yet been established as a standard tool in the requirements of seismic design codes. On the other hand, if the design earthquake is given by an elastic response spectrum or Fourier spectrum as commonly adopted in recent design codes, the maximum responses of any elastic system can be estimated by "modal analysis". The maximum response can definitely be determined for each fundamental mode and the maximum responses can be estimated by the superposition of all dominant modes, for example, by means of square root of sum of squares. However, if the response of a structure exceeds the elastic limit, nonlinear response must be estimated from the elastic response spectrum. This is nothing but so-called "equivalent linearization", which correlates nonlinear responses with linear response spectrum. If the design motion is given by the elastic response spectrum and the nonlinear displacement response is used as design criteria, a rational theoretical background on the linearization is essential in the development of design code. Even though the earthquake is specified by the elastic response spectrum, another way of calculating nonlinear response is to perform time-history response analysis under an artificial motion, which is synthesized so that its response spectrum be fitted to the specified target spectrum. However, the response spectrum is only smoothed from past earthquakes and not general for the future earthquake on the site, and the essential time-history characteristics are assumed in the synthesis of the artificial motion, such as, in terms of "envelope Earthquake Response Analysis 317 curve" or "phase spectrum". Therefore, nonlinear time-history response could be different under different motions with the same elastic response spectrum. A rational theory is needed to explain the nonlinear response based on the expected characteristics of the earthquake motion at the site. Another possible method, by which a rational time-history for the design motion could be given, is to simulate the strong motion on site based on the model of the earthquake source function. The methodology for the simulation of the strong motion is rapidly in progress by the recent research in the field, and has been verified through the simulation of recent near-source earthquakes, such as 1994 Northridge earthquake and 1995 Hyogoken-Nanbu Earthquake. As for the earthquake that recently occurred anywhere in the world, the source parameters of the earthquake can be determined by the global network of hypersensitive observation. The detailed source function, including heterogeneous rupture process of the fault called "asperity" can also be determined based on the strong motion records near the source. These are so-called "inversion analyses" of the source rupture process. Based on these determined parameters, the time-history of other sites can be simulated as wave propagation based on the model of underground structures. However, the structural model of underground is still difficult to be identified because the data are not enough except for the limited areas. Moreover, there are no means to determine the source function for future earthquakes. Therefore, it is still very difficult to give the earthquake motion rationally as a design motion expected on the site. It should be noted that the result of a time-history analysis, especially the absolute maximum of the response value, is peculiar to the analytical case, which is susceptible to the assumption on the characteristics of the input earthquake motion. The variety of the results must be understood in relation with the assumptions, and the performance criteria in design code must be adopted considering the variety of the response. However, a rational method is still difficult. Therefore, recently proposed performance-based design methods using nonlinear displacement criteria adopt "push-over analysis" as a standard design tool to estimate nonlinear response, which is a nonlinear static analysis under assumed lateral load distribution. The nonlinear response point on the calculated load-deformation relation is estimated deterministically from specified linear response spectrum, namely by an equivalent linearization procedure. However, the time-history analysis is still useful in design, if engineers or structural designers understand the assumptions and the possible errors 318 Design of Modern Highrise Reinforced Concrete Structures properly. The designer can imagine the detailed dynamic behavior in general even from several cases under the particular motions. These are, for example, inelastic displacement responses, member deformations and member forces due to higher modes, which cannot be simulated by the static analysis. These results give useful information to reinforce judgment in design. On the other hand, if an engineer or a researcher performs nonlinear response analysis using a commercial computer program without knowledge of the analytical methods, the program could be so-called "black box" for the user so that their results might be believed as deterministic behavior. In order to reflect the results of the earthquake response analysis properly on seismic design, it will be indispensable for the structural designer to understand the methods and the assumptions at least conceptually. It is more preferable that they understand the correlation between the assumptions and the results in the analysis generally, based on the rational theoretical background. Or it is recommended that deterministic dynamic analyses should be carried out for as many cases as possible by varying probabilistic parameters of the structure as well as of the earthquake motion. Various types of structural models are selected and used for nonlinear timehistory analysis. Models may be classified mainly by essential difference in the degrees of freedom. The model, or the number of degrees of freedom, should be selected carefully considering the objective of the analysis. Sophistication or use of complicated model to no purpose is not only useless but also sometimes misunderstanding on the contrary in practical design, because it makes difficult to correlate results with assumptions. Therefore, it is important to select an appropriate and simple model to match the purpose of the analysis. Here, the minimum unit elements in the most detailed structural model are supposed to be "members" of the building structure, such as beams, columns and walls. More detailed model is also available for time-history response analysis, such as "finite element model", in which each member is divided further into small elements. The nonlinear modeling for the finite element analysis is described in Chapter 5. The constitutive law in the finite element model, especially under cyclic loading, is still under investigation, and its application to time-history analysis of a whole building might be too sophisticated as a standard practical design procedure. Earthquake Response Analysis 319 7.2. Structural Model 7.2.1. Three-Dimensional Frame Model If a building structure is idealized as exactly as it is for the nonlinear timehistory analysis or push-over analysis in practical design, the structural model will be a three-dimensional frame model. As an example, seven-story reinforced concrete building, shown in Fig. 7.1 will be modeled as illustrated in Fig. 7.2. The nodes, where the displacement and force vectors are denned and calculated, are located at the joints of beams and columns in the model. Each node has six degrees of freedom and a mass and second moment of inertia concentrated from the tributary area of the node as shown in Fig. 7.3. Columns, beams, walls and slabs are idealized using "member models", which give constitutive relations among these nodes. The nonlinear relations under cyclic loading path are idealized as "hysteresis models". Shear deformation M • • — pi •- • T i w — • • pi • =jp Fig. 7.1. Plan of an example seven-story reinforced concrete building with shear walls. Fig. 7.2. Three-dimensional model for the example building structures. 320 Design of Modern Highrise Reinforced Concrete Structures Fig. 7.3. Beam and column model with axial deformations. in the beam-column joint panel is often considered in addition. Otherwise, the panel zones are expressed with equivalent rigid zone lengths at the ends of beams and columns. Stiffness of foundation or soil may be considered using springs which are fixed to the ground, where the earthquake motion is supposed to input. The number of degrees-of-freedom N$0f in above model is 6 x Nn, where Nn is the number of nodes. For the example building in Figs. 7.1 and 7.2, where number of floors are eight and number of the nodes in a floor are twelve, Nn = 8 x 12 and Ndoi = 6 x 8 x 12 = 576. A three-dimensional model has independent displacements at each node and we can consider any type of behavior. However, this model is too complicated in most cases of practical design analysis, because some components of member deformations can be neglected, for example, in-plane shear deformation of slab as well as axial deformation of beam. Because of the difficulties in modeling, verification and numerical calculation, the three-dimensional model has not yet used even in the most sophisticated design practice. Instead, the horizontal translational and rotational degrees-of-freedom of each node are often reduced to one in a floor by assuming in-plane-rigid floor slab, as shown in Fig. 7.4. Vertical displacement is considered at each node, while the horizontal displacement at each node can be expressed using the two displacements at the center of mass and overall rotation of a floor. In this case, JVdof = 3 x JVn + 3 x JV/, where Nf is number of floors, therefore JVdof = 3 x 8 x 1 2 + 3 x 8 = 312, which becomes almost one-half of the previous model. The actions in columns and walls can change, between the two models with and without consideration of axial deformation in beams, especially in Earthquake Response Analysis 321 Fig. 7.4. Assumption of in-plane rigid slab. inelastic region of beam yielding structures. However, the verification by the test, in which shear distribution in the columns and walls are measured, was not enough in the past. Moreover, the distributions are affected by the redistribution among the change of inelastic stiffness during the response. Evaluation of the errors due to the assumption of in-plane-rigid slab as well as modeling of slab with nonlinear in-plane deformation need be investigated further. The effects should be taken into account by the judgment of engineers at present. The response analyses with the three-dimensional models, even with the assumption of in-plane-rigid slab, are especially useful to simulate the responses with three-dimensional effects. These are, for example, (a) displacement in a frame due to the torsional response in the structures with eccentric distributions of stiffness or mass, (b) axial force in the corner column or shear and moment in the internal column under the earthquake motion in two directions or in skewed direction, and (c) stress distribution at the base of the members with effective transverse members, such as fiber stress in the wall base with L-shaped horizontal sections. Otherwise, two-dimensional plane frame models in the following section will be also available for design analyses. 2.2.2. Two-Dimensional Frame Model If the structure has a symmetric plan and torsional response is expected to be small, the three-dimensional model may be reduced into a two-dimensional plane frame model in each principal direction as shown in Fig. 7.5. The model connects all the plane frames in one principal direction by assuming the identical horizontal displacement in a floor. 322 Design of Modern Highrise Reinforced Concrete Structures In the example of Fig. 7.1, where the two outer frames with wall are supposed to be identical, these two frames may be modeled as one frame with doubled stiffness, strength and weight. Axial deformation in the beam member model is neglected in this case. Vertical displacement and rotation is considered at each node and the horizontal displacement is identical at each floor. In this case, JVdof = 2 x iVn 4- JV/} where Nf is number of stories, therefore iVdof = 2 x 8 x 8 + 8 = 136. The number of degrees of freedom can be reduced about one-fourth compared to the three-dimensional model. In the plane frame model, two-dimensional member models are used for beams and columns as shown in Fig. 7.6. Usually axial deformation is neglected in beam but considered in column using one-component model shown in Fig. 7.6(a). The axial deformation in the beam may also be included into Fig. 7.5. Two-dimensional frame model for building structures. -gf—jn—g£ •©• (a) One-component model m m <S> mmm (b) Multi-Spring model Fig. 7.6. Beam and column models in two-dimensional frame model. Earthquake Response Analysis 323 the plane frame model by considering independent horizontal displacement at each node and using the multispring model, as shown in Fig. 7.6(b). Detailed description of the member models are given in Sec. 7.3. 7.2.3. Multimass Model In the early age of application of nonlinear response analysis to the practical design of highrise buildings in Japan, equivalent multimass model shown in Fig. 7.7 has been most frequently used. The reduction of the frame model to a multimass model is based on the static push-over analysis by the frame model as above or more simplified model. The characteristic of the nonlinear spring, which is the force-deformation relation, is idealized based on story-shear vs. interstory drift relations obtained from the push-over analysis. Simplified method based on inelastic story stiffness of columns and beams are also available to determine the relations. Especially for the analysis of highrise buildings, not only shear spring but also rotational spring must be located in every story to simulate an overall flexural deformation of the building due to axial deformation of columns or bending deformation of wall, as shown in Fig. 7.8. The degrees-of-freedom of the model is the number of story Nf. The model is simple and the required amount of calculation and storage can be very much efficiently reduced from the frame model. If the properties of the nonlinear springs are determined properly, the responses calculated by the multimass model would be in fair agreement with the Fig. 7.7. Multimass system. 324 Design of Modern Highrwe Reinforced Concrete Structures Fig. 7.8. Shear and rotational springs. responses calculated by the frame model, on condition that the first mode responses are dominant and within moderately inelastic displacement range. In case that the higher mode response is dominant or the response is in well plastic range, calculated responses could be different from those by the frame model. Another disadvantage of this model is that the responses of the members such as inelastic deformations or internal forces cannot be calculated. The inelastic deformation of the members may be estimated from the push-over analysis, for example, at the corresponding interstory displacement. On the other hand, the member forces in the columns and walls including the effects of the higher mode responses cannot be evaluated directly from the push-over analysis. The effect of the higher mode responses on the moment and shear forces in columns and walls, which is called dynamic magnilcation, should be taken into account in design of these members in addition to the static calculation by the push-over analysis.7,4 However, the multimass model is still useful in practical design, because the responses of highrise buildings to design earthquake motion are relatively small in Japan and the buildings are designed to ensure the beam-yielding mechanism so that the first mode response would be dominant. 7.2.4. Soil-Structure Model In the recent revision of Japanese Building Standard, a new procedure was adopted for the verification of seismic performance in addition to traditional design requirement. One of the innovative features in seismic design procedure is that safety performance is to be verified by the limit states criteria defined using inelastic displacement response and deformation capacity of the structure. Another is that the standard design earthquake is specified as the elastic Earthquake Response Analysis 325 Fig. 7.9. Soil-structure model for response analysis. response spectrum at the engineering bedrock. Amplification by the surface soil should be calculated for each construction site. Simple method is available for this calculation, while soil-structure model, shown in Fig. 7.9, may be used as a sophisticated design tool. The soil-structure model is not being used frequently even for the special design procedure for highrise buildings, because the rocking deformation is relatively small and the design motion is defined at the base of the structure. The model will be useful in the future to estimate (a) amplification of input earthquake by the surface soil, (b) input energy loss due to deformation or viscosity of soil, and (c) action of piles induced by the response of soil shear deformation. 7.3. 7.3.1. M e m b e r Models One-Component Model for Beam One-component model shown in Fig. 7.10 has been used most popularly for the member model of beams and columns (Ref. 7.1). The model has an elastic line element with two inelastic rotational springs at the two ends. Usually rigid zones are added outside the inelastic springs to express the depth of intersecting members. A nonlinear shear spring is also placed in the midspan of the elastic line element, when nonlinear shear deformation should be considered independently to flexural deformation. When the model is used for column, a nonlinear axial spring may also be introduced into the elastic line element. According to the notations in Fig. 7.10, stiffness matrix of the model can be formulated as the inversion of the flexibility matrix as follows. The flexibility matrix [F], which gives the constitutive relation between the moments and 326 Design of Modern Highrise Reinforced Concrete Structures relative rotational deformations at the ends of the springs, can be based on the serial flexibility of these springs and elastic line elements, as Eq. (7.1). Then the relation is transformed into the global coordinate in terms of force and displacement vectors at the two nodes, by the use of compatibility matrix [H] considering the rigid zones and translational displacement, as Eq. (7.2). If the inelastic stiffness or the yielding deformation is determined properly, then the model gives a fair simulation of nonlinear structural behavior. Takeda hysteresis model (Ref. 7.2), as shown in Fig. 7.11 is most widely used to give the moment-rotation relation of the model. The yield stiffness of beam or column may be determined by an empirical equation. To determine the flexibility of Fig. 7.10. One-component model for beam. Fig. 7.11. Takeda hysteresis model. Earthquake Response Analysis 327 nonlinear spring at one end, inelastic curvature distribution must be assumed along the member. Usually antisymmetric curvature distribution is used to formulate the flexibility matrix. However, the verification of the one-component model is not enough, especially on the member forces of members in a frame structure, because the member forces are not measured in the tests. The calculated member forces could be different mainly because of the inelastic axial elongation of the beam, which has verified experimentally recently by a few test result (Ref. 7.3). The model is basically applicable only in unidirectional bending, and interaction of biaxial bending cannot be considered. The effects of varying axial force on the bending stiffness, cracking and yield strength are also important. Practically, the effect can approximately be considered by the predetermined hysteresis relations based on the predicted varying axial force level, because the prediction is not so difficult for building structures consisting of regular frames. However, the effects cannot be taken into account in general by the one-component model. [F] A05 Ami 2/o + /i+3 Amo -fo+9 ' Ami A7B2 Api Ami -fo + 9 2f0 + f2+g (7.1) ( A6X > = [H\T\FY\H\ < A62 (7.2) Avi I Ap2 J lAz/ 2 ) where \H\ — 1 J JO 1 1-A!-A2 1-A2 A2 l/l -l/l 1-Ai l/l -l/l (i _ Al _ A 2 ; / T7T7 6EI and / 1 , f-i : flexibility of nonlinear spring g : flexibility of shear spring. 328 Design of Modern Highrise Reinforced Concrete Structures 7.3.2. Multiaxial Spring Model for Column To reproduce the behavior of flexural and axial deformation of column element representing the interaction among bidirectional bending moments and axial load, multiaxial spring model, called MS model, has been developed and used (Ref. 7.5). The MS model has a line element and two multiaxial spring elements (MS element) at the column-ends, as shown in Fig. 7.12. The MS element consists of a number of uniaxial springs, at least four springs. The spring deformation conforms to the plane section assumption or linear strain distribution at a section. There are then two internal nodes between the line element and the MS elements. The line element is elastic in flexural behavior and axial deformation. It may include inelastic shear deformation represented by shear spring or a shear element. The number of springs in MS element depends on material properties, section shape and size, and reinforcing bar arrangement. For a reinforced concrete member, steel springs may be placed at the location of reinforcing steel bar center point, and concrete springs may be placed at the center of portions properly divided into for example, 2 x 2, 3 x 3, 4 x 4, or more. The number l-spring X, IW do (a) Column with MS element i fa,d0 j '"J" -y (b) MS element and the forces and displacements (positive) Fig. 7.12. Column member model by MS model. Earthquake Response Analysis 329 of springs in MS element may affect the accuracy in simulating the column force-deformation relation. Calibration and reliability examination is given in Ref. 7.6. If the cover concrete is modeled separately, the different hysteresis models may be used for the cover concrete and the confined core concrete. The MS element has elasto-plastic flexibility under moment and axial force but is rigid to shear force. The flexibility of a small portion, namely called as "plastic zone" of the column is assigned to the spring as its initial flexibility, as shown in Fig. 7.13. In that case, the spring initial stiffness and strengthdisplacement are simply calculated as K^ — • ^ i (for ith spring) fc — acAi, dc — ec • r]Lo Fsy - asyAi, dsy - £sy • r/Lo (for concrete) (f° r steel) where K\, is initial stiffness of ith spring, Ei is the material young's modulus, Ai is the spring governed area, and TJLQ is the length of assumed plastic zone. <jc, £ c are the concrete material compression strength and corresponding strain, and asy, esy are the steel material yielding stress and strain. Empirically, rjLo may be taken as D/2 or O.lLo, where Lo is the column clear length, and D is the depth of the column cross section. The plastic zone length riL0 can be selected by the user of analytical program. Different mathematical formula from above based on the curvature at the two ends and distribution along the member is also available. Trilinear curves may be used to represent the force-deformation relation of steel and concrete springs shown in Fig. 7.14. The relations between tensile force and averaged strain of steel covered with concrete degrade before yielding due to cracking and bond deterioration. To allow for such stiffness degradation, the stiffness of the steel spring is reduced at a point lower than yielding. It is roughly determined by magnifying yielding displacement of the spring by the , Assumed plastic zone, i]Lo -XL Column deformable part i Lo Fig. 7.13. Assumed plastic zone for determining spring initial stiffness. 330 Design of Modern Highrise Reinforced Concrete Structures *-D City (a) Steel spring fc-OcAi dc=sc-rjLo *-D (b) Concrete spring Fig. 7.14. Skeleton curve of spring force-displacement relations. factor of 1 . 0 + ^ ^ ° h0/D ko,D>1.0 (7.3) ho/D < 1.0 1.0 where ho is the shear span, and D is the depth of the cross section of the column. To balance the initial stiffness of the line element and two MS elements, a flexibility reduction factor is considered for the line element to make total initial flexibility approximately equal to the original column member. The initial rotational flexibility 5sr and axial flexibility <5s0 of the MS element (to its section centroid) can be calculated as T) • Lp osr ZEiAiY? T)- Lp $s0 = ZEtAi ^ T] • Lp ~ 0.9EI _ Tj- Lp ~~ EA (7.4) Earthquake Response Analysis 331 where EI is the initial flexural stiffness of original column section around concerned axis, and EA is the initial axial stiffness of the column. Using flexibility reduction factors 71, 72, 70, the bending and axial flexibility of the line element can be expressed as A) 3EI L0 6EI 7I [*L] = 5o = ^x u 6EI It must be „ „ , , > , or 71 > 0.5 ZEI 6EI I2L0 3EI (70>0) J - Including the flexibility of MS elements, the total bending flexibility of a column in unidirection is given by U l\Lp 3EI 6EI Lo 3EI 3EI U 6EI EA V- LO 0.9EI Lp 6EI LQ 6EI I2L0 n- Lo 0.9EI1 3EI V LQ •yoLo T}- L0 EA ' EA ' EA (7.5) (7.6) That gives the following flexibility reduction factors 71 > 0.5, 72 > 0.5 (for r) > 0.15) = 72 = 1.0 - ^ (for rj < 0.15) 7l (for T] > 0.5) 2r, (for rj < 0.5) That is, the initial stiffness may not be balanced if the plastic hinge zone parameter 77 is over certain value. Stiffness matrix can be transformed into the relation between nodal displacements and nodal forces as in the same way as shown for the one component model. 7.3.3. Wall Model In the architectural design point of view, a wall is an element used to partition the space, which may be either structural or nonstructural. A typical structural wall in Japan, which is called as "shear wall", is dumbbell shaped section with two boundary columns, as shown in Fig. 7.15(a). In this case, a wall can clearly 332 Design of Modern Highrise Reinforced Concrete Structures i • i 1 1 r r i * • • • • • • • • • • < • - 1 1 t i t u j i » « « (a) Wall with boundary columns » W I M • » « • • 1 > 1—• • II I (b) Wall with confined regions i » p;—p:—TBI 7m • • (c) Wall-type column Fig. 7.15. Horizontal sections of wall. be differentiated from "columns". However, a wall may be designed without boundary columns, as shown in Fig. 7.15(b). Instead, the boundary regions are designed with sufficient confinement to ensure flexural ductility. Further, the horizontal section of a vertical member could be with thick and short depth as shown in Fig. 7.15(c), which may be called as either of wall-type column or column-type wall. In this case, it is difficult to define the boundary between column and wall. The only difference between the wall and the column is the shape of the horizontal section. Analytical models for the column may be used for a wall member, especially for slender wall. However, it may be preferable to use a special model for wall member, which is different from the member model for the column, because the characteristics of walls are generally different in the following points: (1) The ratio of shear deformation to flexural deformation of the wall is relatively large. Not only flexural mode of failure but also shear failure need be considered in design and analysis. (2) The wall member consists of different elements, i.e. wall panel, boundary columns and beams. The behavior is affected by their composite actions. (3) Nonlinear axial elongation of the tensile boundary column is not negligibly small but is much larger than that of the compressive boundary column. Earthquake Response Analysis 333 (4) Stiffness of wall is relatively large in a frame and greatly affects the results of overall structural analysis. (5) Moment distribution is not antisymmetric in a story and depends on the structures. Here, various macroscopic member models for walls are introduced. Finite element model is not included, although it will also be one of practical models in the future. Above characteristic behavior is simulated by models in which several nonlinear springs or line elements are used. For the multistory wall, linear strain distribution at horizontal section is usually assumed using rigid beams, though axial elongation of the boundary beam is important in some cases. As shown in Fig. 7.16(a), one component model for column with flexural, shear and axial springs can be used as a simple model for wall members. The overall behavior of the wall can be simulated well if the nonlinear characteristics of the springs are determined appropriately. However, movement of centroid of strain in nonlinear range, i.e. larger axial elongation in tension side, is not considered in this model, because the rotation occurs around the center line. Therefore, for example, the analysis by this model does not express the difference of ductility of connecting beams on tension side and compression side. The so-called fiber model, shown in Fig. 7.16(b), by which the flexural curvature distribution along the wall height is intended to be simulated as rigorously as possible, has been used not only for walls but also for beams and columns (Ref. 7.7). However, the model does not express nonlinear shear deformation or bond deterioration so that theoretical model does not simulate the experimental behavior, though the model requires relatively large number of degrees-of-freedom. Therefore, it is not so rational for frame analysis to use many fiber slices. To consider the larger inelastic axial elongation on the tensile side, three vertical line element model (Ref. 7.8), as shown in Fig. 7.16(c) has often been used as a practical model. The boundary columns are idealized using line element with nonlinear axial spring, which give flexural rigidity under symmetric bending moment. The panel element is idealized by one-component model with nonlinear flexural, shear and axial springs at the base. The central line element is intended to give shear and flexural rigidity under antisymmetric bending moment. Flexural spring must be evaluated so as to separate the effects of boundary columns and panel. To separate the effects more clearly, flexural spring is removed and only shear and flexural springs are used in 334 Design of Modern Highrise Reinforced Concrete Structures (a) One-component model (b) Fiber model (c) TVELM model (d) MVELM model (e) M-S model (f) Truss model (g) Panel and boundary element model Fig. 7.16. Various wall models. another model (Ref. 7.9), as shown in Fig. 7.16(d). This model, which may be called as multiple vertical line element model, is equivalent to the fiber model of one layer. The MS model for column is also useful for walls as shown in Fig. 7.16(e). This model is especially useful under biaxial bending. The method to release the unbalanced force is important in this model. The truss model, shown in Fig. 7.16(f), which has been used for a model in elastic analysis, is also used for nonlinear analysis. The stiffness of each element is to be given so as to give equivalent stiffness of the whole section, which is easy in elastic range. The model is developed to meet with the resistance mechanism of truss and arch model for the evaluation of ultimate shear strength. However, it is a little difficult to determine the inelastic stiffness rationally, especially of Earthquake Response Analysis 335 tensile truss element. More complicated model with additional truss element, shown with dotted lines in the figure, has also been proposed. Based on the constitutive law for two-dimensional reinforced concrete element for FEM analysis (Refs. 7.10 and 7.11), a simple model for the wall is also proposed, as shown in Fig. 7.16(g), which simulate shear and flexural behavior very well. Further study is needed to verify the stability of the model in numerical calculation to apply the method to practical design analysis. The wall model need be sophisticated further for frame analysis on the following points: (1) Axial deformation of beam with slab must be idealized. (2) Column axial property must be idealized with the effect of confinement. (3) Simple but rational 2-D constitutive model need be developed, especially under cyclic loading. (4) 3-D model need be developed, under skewed loading. (5) Modelling of irregular walls should be developed. 7.4. 7.4.1. Nonlinear Response of SDF S y s t e m Displacement-Based Design Procedure A displacement-based seismic design procedure has been adopted by recently revised Japanese Building Code in addition to the traditional design procedure. Instead of time-history response analysis, static push-over analysis for equivalent linearization is supposed to be the standard design tool to calculate nonlinear displacement response of a building structure. Nonlinear and dynamic response of a structure as multi-degree-of-freedom (MDF) system is evaluated based on the response of a reduced single-degree-of-freedom (SDF) system, the dynamic response of which is estimated from an equivalent linearization. A standard procedure may be as follows: (1) Push-over analysis is performed to obtain lateral load-displacement relations of the MDF structure. (2) The load-displacement relations of the MDF structure are reduced into those of the equivalent SDF system assuming a constant basic mode shape, for example, the elastic fundamental mode shape. (3) Linear response spectrum of the design earthquake is specified for the levels of the design earthquake motions with corresponding damping ratios. 336 Design of Modern Highrise Reinforced Concrete Structures (4) On the load-displacement relations of the SDF system, response displacement is determined at the elongated equivalent period, Tm, which corresponds to the equivalent linear stiffness at the maximum response in the nonlinear region. (5) Member deformations or strains can be calculated from push-over analysis at the corresponding displacement determined by the SDF response. (6) Serviceability, damage control or ultimate limit state criteria are deined and selected for each member using inelastic deformations, which are verified to be larger than the responses with appropriate degrees of reliability, or safety factors. (7) Member forces, especially shear in nonyielding members, such as columns and walls, are magnified from the values in the push-over analysis superposing the static force and higher mode forces. (8) Shear capacity is verified to be larger than the maximum response at the ultimate limit with appropriate degrees of reliability. Maximum response displacement of the structure as a multi-degree-offreedom (MDF) system can be estimated with reduced equivalent single-degreeof-freedom (SDF) system, shown in Fig. 7.17, as follows. MDF equation of motion is expressed as [M]{x} + [C}{±} + {/} = - [ M ] { e } * 0 (7.7) where [M): mass matrix, {x}, {x}: relative acceleration and velocity vectors, [C]: mass-proportional damping matrix (= 2/io;[M]), 2huj; constant, if u) is taken as a frequency of the first mode, then the damping coefficient h is supposed to be defined to the frequency, and {/}: restoring force vector, {e}: unit matrix. The above equation of motion for a multi-degree-of-freedom system can m Fig. 7.17. One-mass (single-degree-of-freedom) system. Earthquake Response Analysis 337 be reduced to the following equation of motion for an equivalent SDF system by assuming a dominant basic mode of {x} — {u}/3xe and {/} = as xe + 2hujxe + fe = -XQ [M]{u}Pfe, (7.8) where xe: equivalent displacement and fe: equivalent force, and, /3 — \U}T{M}{U\ : participation factor. In the frame structure, the assumed mode shape, especially of the force vector, is very sensitive to the displacement response in well inelastic range, and the effect of higher modes of response should be considered carefully. However, these effects are expected to be small within small inelastic ductility level. The elastic first mode may be assumed for {«} in the following estimation. Push-over analysis is carried out under the first mode force for the system, from which nonlinear relations between the equivalent force fe and displacement xe are obtained. The skeleton curve may be idealized as a trilinear skeleton so that the strain energy is equivalent. The hysteretic damping in relation to the ductility is based on the Takeda model as is used in the beam model in MDF analysis. SDF response, the maximum equivalent displacement, can be determined based on the response spectrum as is described in the following section. 7.4.2. Correlation of Nonlinear Linear Response Response to To estimate nonlinear response of SDF system from linear response spectrum, that is, equivalent linearization (Ref. 7.12), a simple procedure, called "capacity-demand diagram method" has become popular recently (Ref. 7.13). The method is especially useful in graphical presentation of equivalent linearization on linear response spectrum based on push-over analysis. As an example of an earthquake record and response of SDF system, an accelerogram recorded at Kobe Meteorological Observatory (KMO) during the 1995 Hyogoken-Nanbu earthquake is shown in Fig. 7.18. Calculated timehistory of the displacement response of a nonlinear system to the accelerogram at KMO is shown in Fig. 7.19. The hysteresis rule is "Takeda model", which represents the nonlinear behavior of reinforced concrete structures with trilinear initial skeleton and degrading unloading stiffness. The period of the structure calculated using the yielding stiffness is one second. The yield strength 338 Design of Modern Highrise Reinforced Concrete Structures Fig. 7.18. Time-history of accelerogram recorded at Kobe Meteorological Laboratory during 1995 Hyogoken-Nanbu Earthquake (KOB). LIII1G ISj Fig. 7.19. Displacement time-history response of a nonlinear system with Takeda-hysteresis model to the input acceleration of KOB. M -0.4 -0.2 0 0.2 Disp. (m) Fig. 7.20. Hysteretic response of the nonlinear system with Takeda-hysteresis model to the input acceleration of KOB. of the system is selected so that the maximum displacement response would reach the ductility factor of four, where the ductility factor is denned as the ratio of the maximum displacement to the yielding displacement. The calculated hysteretic response of the system is shown in Fig. 7.20. By the time-history analysis, not only the maximum response but also hysteretic behavior of the system can be simulated in detail. The elastic response spectrum of the acceleration, velocity and displacement for the accelerogram (KMO) is given in Fig. 7.21 for the system with Earthquake 4000 Response Analysis 339 0% 5% 10% 15% 20% 25% 32000 -' < !/5 0 1 2 3 4 5 4 5 4 5 T (sec.) 600 - ^ 400 o "Z 200 0 1 2 3 T (sec.) 100 I 50 0 1 2 3 T (sec.) Fig. 7.21. Elastic response spectra of accelerogram recorded at Kobe Meteorological Laboratory during 1995 Hyogoken-Nanbu Earthquake (KOB). damping coefficients of 0, 0.05, 0.10, 0.15, 0.20 and 0.25. The spectrum expresses the maximum response of the system with corresponding fundamental period during all the time-history. The time-history displacement response of an elastic system with the fundamental period of 2.0 second and the damping coefficient of 0.20 is shown in Fig. 7.22. The waveform is similar to that of the nonlinear system in Fig. 7.19. The fundamental period defined using the secant stiffness of the nonlinear system from the origin to the attained maximum displacement response is 2.0 second in this case, because the maximum ductility factor is four, which means that the secant stiffness is one-fourth of the yielding stiffness. The viscous damping coefficient of 0.20 corresponds to the hysteretic damping of Takeda model with the maximum amplitude of ductility factor four in stationary cyclic load reversal. 340 Design of Modern Highrise Reinforced Concrete Structures 20 time (s) Fig. 7.22. Displacement time-history response of an equivalent linear system for t h e nonlinear system with Takeda model. 20 15 3 10 5 h=5% h=10% h=15% h=20% h=25% ^l W6 j r » \ '// Z^^S<g 0.2 Estimatedfromequivalent linearization 1 )i ; / » ,- w. 't v >Sj 0 $ ) *• _ 0.4 Disp. (m) Fig. 7.23. Equivalent linearization of the nonlinear response on acceleration-displacement response (capacity-demand) diagram. Using the capacity-demand diagram, or acceleration-displacement (Sa-Sd) response spectrum format, above correspondence of the nonlinear response to linear spectrum can be expressed as shown in Fig. 7.23. The quadrant of the calculated nonlinear hysteretic response is plotted for the direction of the absolute maximum response on the Sa-Sd response spectrum. The response by equivalent linearization may be estimated simply as the crossing point of the envelope of the hysteresis and the spectrum curve with the corresponding damping coefficient 0.20, shown with shaded circle in the figure. The estimate by the diagram is fairly close to the calculated maximum from nonlinear response analysis. This is an example in case of which a relatively good correlation is observed between nonlinear response and linear response by the simplest equivalent linearization. However, the correspondence by this simple method is not always good like this case, because the response is not stationary under the actual earthquake motion. In another case, shown in Fig. 7.24, the nonlinear response Earthquake 10 Response Analysis 341 20 time (s) (a) Nonlinear time-history response 0.2 0.1 0 -0.1 -0.2 | ' T=1.0sh=0.20' 1 —~~J Mf*""*** : ' 10 20 time (s) (b) Equivalent linear response -0.2-0.1 0 0.1 0.2 Disp. (m) 0.2 0.4 Disp. (m) (c) Hysteretic response Fig. 7.24. Equivalent linearization for another system (Ty = 0.5, Te = 1.0 second). is smaller because the displacement response in the opposite direction is small. In other words, the maximum response is induced suddenly to one direction within relatively short time. In this case, equivalent period is shorter than the secant stiffness to the maximum displacement. A rational linearization is still needed, which formulates the equivalent period and equivalent damping for any nonlinear system generally based on the fundamental characteristics of earthquake motions. 7.5. 7.5.1. Numerical Analysis Numerical Analysis of Equation of Motion To calculate the responses step-by-step numerically, a common mathematical formula is available to all the models, although stiffness matrices are different 342 Design of Modern Highrise Reinforced Concrete Structures depending on the structural modeling. Instantaneous stiffness matrix is formulated using tangent stiffness of the structure at one step, and the status at the next time step can be definitely determined by assuming that: (1) the stiffness of the structure is constant during the small incremental time step of calculation, and (2) input acceleration or response acceleration is linearly changed during short time step. Time step should be short enough to satisfy these assumptions for stable numerical procedure. However, if the time increment is made small and the number of degreesof-freedom of the model is large, the calculation time and memory storage become large. Therefore, time-history analysis need be efficient to meet practical purpose. From this point of view, an appropriate numerical calculation technique is still required, especially for analyses in a practical design. To integrate the equation of motion (Eq. 7.8) by a numerical procedure, it is rewritten into the incremental form as follows, (Eq. 7.10) for ith step and (Eq. 7.11) for the next (i + l)th step [M]{x}i + [C\i-i{±} + {fh [M]{x}i+1 + [C\i{x}i+1 + [K\i{Ax}\+1 + {fh = -[M){e}x0i = -[M}{e}x0i+1 (7.9) (7.10) where, for the equation of (i + l)th step, [M] : mass matrix {x}i+i : relative acceleration vector [C]i : damping matrix {x}i : velocity vector [k]i : instaneous stiffness matrix {Ax}* + 1 : incremental displacement vector {f}i : restoring force vector {e} : unit vector XQi : input base acceleration. In a frequently used numerical procedure, called N e w m a r k ' s /?-method, t h e following relations are assumed {Az}* + 1 = At{x}i + At2 (\ ~ /?) {*h + 0{x}i+i { i } i + 1 = {xh + At[(l - 7){*} i + 7{*}i+i] • (7.11) (7-12) The parameters (3 and 7 express the change of the acceleration vector during the integration time from ith step to (i + l)th step, by which accuracy and Earthquake Response Analysis 343 stability of numerical integration is selected. Prom Eqs. (7.11)—(7.13), three unknown vectors, incremental displacement, velocity and acceleration vectors at (i + l)th step, can be determined. 7.5.2. Release of Unbalanced Force In the numerical calculation procedure as above, the instantaneous stiffness matrix during the integration time step At is assumed to be constant. In other words, the assumed load-deformation relationship is piecewise linear corresponding to the prescribed time step. However, the load-deformation of any member passes through the stiffness interruption point of the hysteresis model, where the member stiffness changes during the time-step. In this case, unbalance of external force and internal force due to the stiffness change is inevitable. In the dynamic time-history analysis, the error accumulates with numbers of cyclic hysteresis paths to some extent, which should not be neglected, even though the unbalance in one step is small. The numerical calculation technique is important for the development of a computer program, which eliminates the error by applying the fictitious external force from the node to the member. In case of using the Multiaxial Spring (MS) model described in 7.3.2, this problem is especially important. The column idealized by MS model has three elements, a line element with two MS elements at its ends. In nonlinear analysis stiffness changes occurred in any element may cause force unbalances among the elements. Therefore, numerical iteration method is needed in some cases to find out a set of force increment against a set of given displacement increment for the three elements to satisfy the equilibrium condition. If the damping matrix is assumed to be proportional to stiffness matrix, the unbalanced force must also be released for the damping term. References 7.1. Giberson, M.F., Two nonlinear beams with definition of ductility, ASCE J. Struct. Div. 95(ST2), 1969, pp. 137-157. 7.2. Takeda, T., Sozen, M.A. and Nielsen, N.N., Reinforced concrete response to simulated earthquake, ASCE J. Struct. Div. 96(ST12), 1970, pp. 2557-2573. 7.3. Teshigawara, M., Sugaya, K., Kato M. and Nishiyama, I., Experimental study on overall seismic behavior of 12-story coupled shear wall, J. Struct. Construct. Eng. Trans. AIJ, 1997, pp. 149-156 (in Japanese). 344 Design of Modern Highrise Reinforced Concrete Structures 7.4. Kabeyasawa, T., Evaluation of column and wall actions in the ultimate-state design of reinforced concrete structures, Proc. Ninth World Conference on Earthquake Engineering V I I I , 1988, pp. 699-704. 7.5. Li, K.-N. and Otani, S., Multi-spring model for 3-dimensional analysis of RC members, J. Struct. Eng. Mech. 1(1), 1993, pp. 17-30. 7.6. Li, K.-N. and Kubo, T., Reviewing the multi-spring model and fiber model, Proc. 10th Japan Earthquake Engineering Symposium 2, 1998, pp. 2369-2374. 7.7. Takanayagi, T. and Schnobrich, W.C., Computed behavior of reinforced concrete coupled shear walls, Civil Eng. Stud. Struct. Res. Ser. 434, University of Illinois, Urbana, 1976. 7.8. Kabeyasawa, T., Shiohara, T., Otani, S. and Aoyama, H., Analysis of the fullscale seven-story reinforced concrete test structure, J. Fac. Eng., University of Tokyo X X X V I I ( 2 ) , 1983, pp. 431-478. 7.9. Vulcano, A. and Bertero, V.V., Analytical models for predicting the lateral response of RC shear walls, Report No. UCB/EERC-87/19, Berkeley. 7.10. Committee on the Safety of Nuclear Installations, OECD-NEA, Comparison Report-SSWISP, OECD-NEA SSWISP Short Reports, Second Workshop on Seismic Shear Wall International Standard Problem, Yokohama, April 1996. 7.11. Okamura, H. and Maekawa, K., Nonlinear Analysis and Constitutive Models of Reinforced Concrete, Gihodo-Shuppan, 1991. 7.12. Shibata, A. and Sozen M.A., Substitute structure method for seismic design in RC, ASCE J. Struct. Div. 102(ST1), 1976, pp. 1-18. 7.13. Freeman, S.A., Prediction of response of concrete buildings to severe earthquake motion, Publication SP-55, ACI, 1978, pp. 589-605. Chapter 8 Construction of New RC Structures Yoshihiro Masuda Department of Architecture, Utsunomiya University, 1-1-2 Yoto, Utsunomiya, Tochigi 321-8585, Japan E-mail: masuday@cc.utsunomiya-u.ac.jp 8.1. Introduction High strength concrete and high strength steel have considerably different physical properties compared to ordinary strength concrete and steel. Hence construction of New RC structures cannot be made by the same construction method as that for ordinary RC structures of low strength materials. The High Strength Concrete Committee and the Construction and Manufacturing Committee of the New RC project carried out various series of indoor tests and a full scale construction test using high strength concrete and steel, and investigated material, mix, manufacture, construction and management in order to realize structures with prescribed quality. A new construction standard was developed for the construction utilizing high strength concrete and high strength steel, based on these testing and also on the construction standard of private companies for the current highrise RC buildings. In this chapter, the full scale construction testing and the New RC construction standard are introduced. 8.2. 8.2.1. Full Scale Construction Testing Objectives The objectives of the full scale construction testing are, first, to actually construct a full scale structure consisting of typical member sections selected from 345 346 Design of Modern Highrise Reinforced Concrete Structures 1200 1000 11-2 - III Construction testing "TO" ^ 800 1 to I 400 V / t 11-1 \ 1 !;-Xu,RC\ M 200 -r . Current [ highrise 0 0 30 60 90 Concrete strength (MPa) 120 Fig. 8.1. Material strength zoning for New RC project and material for construction testing. a 60-story building that was trial designed in the project, to ascertain that required quality of structural concrete is obtained, and at the same time to point out problems in construction if any, and ultimately to provide background data for the development of the New RC construction standard including results of current construction techniques. Figure 8.1 indicates the relationship of material strength zoning and construction tests. Material strength zoning is same as in Chapter 2. According to strength of concrete and steel, four zones are defined. Two circles denote material strength combinations of full scale construction testing. It will be seen that construction testing was performed using material combinations corresponding to Zones I and II—1. 8.2.2. Outline of Construction Testing The structure to be constructed is a frame specimen shown in Fig. 8.2. It represents a part of lower stories of a highrise building designed in the New RC project, consisting of single bays in X and Y directions with 6 m span length, and two stories with 2.9 m story height. A half portion of four-column structure is open frame, and another half is frame with shear wall with 300 mm thickness. In addition, five isolated column specimens, 850 mm square crosssection and 2900 mm high, were also constructed. Table 8.1 shows combination of specimens and construction methods. Construction site was located in the Building Research Institute of the Ministry of Construction, Tsukuba City, Ibaraki. Testing was conducted in the period from September to November, 1991. Construction of New RC Structures ©- i i M Mf^T M 500 347 M I Wall "f~"W Wall -J..-I Wall 300 850 850 ©- o ^4, 1500 »::::Q1:: 58o~ ^r I 3rd floor 1500 I 3000 I 3000 9000 (a) Column (b) Frame Fig. 8.2. Construction test specimens. | 1500 I" " Two kinds of high strength concrete were used. One was 60 MPa specified design strength without using mineral admixture, and another was 100 MPa specified design strength using silica fume as mineral admixture. Four kinds of control cylinders were manufactured for each of two kinds of concrete. They were cured in water on site, seal-cured on site, standard-cured, and drilled cores. Control age was either 28 days or 91 days. 348 Design of Modern Highrise Reinforced Concrete Structures Table 8.1. Specimens and method of construction. Specimen Member Strength (MPa) Slump Column No. 1 column 25 60 Curing internal vibrator monolithic form 1 day sheet 6 days monolithic form 1 day plywood Al Zone steel column, girder, slab, joint 25 steel form 3 days internal vibrator sheet 4 days for girders, slabs, and steel columns form vibrator for plywood form VH walls separation 7 days plywood plywood B Zone C Zone column Frame 2 story plywood steel Column No. 5 A2 Zone Consolidation VH plywood separation 100 Column No. 4 Frame 1 story Placing steel Column No. 2 Column No. 3 Form D Zone column wall CD Zone girder, slab, joint 60 21 Slump target was set at 21 cm or 25 cm. As chemical admixture to realize this slump, high range AE water reducing agents from two manufacturers were used. Axial reinforcement in columns and girders was high strength large diameter deformed bars of SD685 D41 and D35. Formwork consists of steel forms or plywood forms, with partial use of transparent forms. Two kinds of concrete casting method were used. One was VH separate casting, i.e. to cast column and wall (vertical) concrete first before girder and slab re-bars are brought in, then place girder and slab cages and cast (horizontal) concrete. The other one was monolithic casting, i.e. place all reinforcement first including girder and slab bars, then cast concrete in column and wall as well as girder and slab in one operation. In this case concrete in vertical members is cast through girder and slab bars. Compaction was made in principle by means of internal (spud) vibrators with sufficient time, but a part of concrete was compacted with external vibrators while the use of internal vibrator was eliminated. Two kinds of curing method were employed. One was to leave formwork for seven days in place to give sufficient curing. Another was to remove formwork Construction of New RC Structures 349 Fig. 8.3. Column specimens. Fig. 8.4. FVame specimen. the next day or three days later, then wrap exposed concrete by polyethylene sheets until the seventh day. Concrete mix was determined by trial mix conducted in the laboratory as well as that using actual plant machinery. Figures 8.3 and 8.4 show an isolated column specimen and the frame specimen at the conclusion of construction, respectively. 8.2.3. Concrete Mix The concrete mix used for the full scale construction testing was determined, after laboratory test mixes, by manufacturing high strength concrete in the 350 Design of Modern Highrise Reinforced Concrete Structures plant actually used for the concreting, which would satisfy needed workability of the construction job. Materials used for concrete was as follows. Cement was ordinary portland cement with specific weight of 3.16. Silica fume for 100 MPa concrete had specific weight of 2.20 and specific surface area of 200 000 cm 2 /g. Fine aggregate was 7:3 mixture by weight, of land sand from Kashima with saturated and surface-dried specific weight of 2.62 and water absorption rate of 1.25 percent, and crushed limestone sand with saturated and surface-dried specific weight of 2.69 and water absorption rate of 1.66 percent. Coarse aggregate was crushed hard sandstone gravel from Iwase with saturated and surface-dried specific weight of 2.66, water absorption rate of 0.59 percent and percentage of absolute volume of 61.1 percent. Chemical admixture was high range AE water reducing agent and following three kinds were used: A was polycarbonate acid chain used for 60 MPa concrete, B was amino-sulphonate acid chain used for 60 MPa concrete, and C was also amino-sulfonate acid chain used for 100 MPa concrete. Table 8.2 shows concrete mix for both 100 MPa and 60 MPa concrete for column specimens, and two kinds of mix for 60 MPa concrete for the frame specimen. Mix was conducted in a forced double-spindle mixer of 3.0 m 3 capacity, with the procedures illustrated in Fig. 8.5. Fresh concrete tests and manufacture of concrete cylinders were carried out at the ready-mixed concrete plant and the construction site. Fresh concrete tests consisted of slump test, slump flow test, air content measurement, and L-type flow test (conducted only on site). Table 8.2. Mix proportioning. Unit mass ( K g / m 3 ) Strength Slump Air W/C f.a.r.* (MPa) (cm) (%) (%) (%) W C SF Si s2 G Column No. 1, 2, 3 100 25 2 20 39.6 160 720 80 414 177 910 Column No. 4, 5 60 25 4 27 44.1 165 611 — 499 214 910 Frame 1 story 60 25 4 27 44.1 165 611 — 499 214 910 60 21 4 27 44.0 165 611 — 453 194 976 Specimen Frame 2 story *fine aggregate ratio Construction of New RC Structures 351 Mixing procedure for 60MPa concrete c+s w, Ad G 30sec.10sec. 150sec. 10sec. 90sec. rotate stop rotate stop rotate -*—Mixer Mixing procedure for 10OMPa concrete C+S+SP W, Ad G I I I I II 30sec.10sec. stop rotate stop t 150sec rotate II I 10sec. 90sec. stop rotate -a— Mixer Fig. 8.5. Procedure of concrete mixing. Compression tests of cylinders (100 mm diameter and 200 mm high) were performed on 7, 28 and 91 days of age. Table 8.3 shows the mix of tested fresh concrete and result of fresh concrete tests. The time for transportation from the plant to the site was about 30 minutes. Mix Nos. 1 and 6 showed segregation of paste and coarse aggregate at the unloading on site, although the segregation was not noticeable when the concrete was shipped from the plant. The slump flow of these two concrete mix exceeded 70 cm at the shipment, and it was inferred that the unit water content was too high. Except for mix Nos. 1 and 6, concrete with 25 cm slump revealed very little time dependent change of slump and air content. Concrete with slump of 21 cm or less showed slump loss of 1 to 2 cm and slump flow loss of about 10 cm, although air content did not show any definite change. Concrete with 18 cm slump had poor fluidity, and construction difficulty was anticipated with the use of this concrete. Table 8.4 summarizes the compression test results of concrete cylinders at three ages. Almost no difference was observed between the strength of concrete at the plant (shipment) and on site (unloading). Figure 8.6 shows the relationship of slump and compressive strength or amount of high range AE water reducing agent for both plant test and laboratory test. In both cases, amount of chemical admixture increased as slump increased. The compressive strength at 91 days also increased as slump increased, which was attributed to the amount of chemical admixture. Figure 8.7 shows the relationship of binder-water ratio and compressive strength at 28 days from plant tests and laboratory tests for 60 MPa concrete r-< o o <-t Ol co t~ Oi O O O o I—t O l O) to .—i co i - Ol »—1 O) CO CO I * - CO o i-H T f T — 1 I - 1 - b - CO CO c o Ol Tf -* • * in Ol CO CO i n ho 1 1 1 I fc. co 1 1 1 I 1 1 1 o ~H t—» r-H CO CO CO CO CO CO CO O £> 1 in in io i n in in a s CO CO CO CO CO o in m i n i n CN CO CO t - CO Tl" O 0 0 CN *3> T f TJ- CO >tf o o CN CN • * •* o> CO M~^ o o o o o CO CO CO in in m o o y r n 00 i n lO m CN CN CN CN ^ 4 IO CN o in in m CN CN CN ~' ^- (^ ^ bt in CN CM CN CN CN CN CN CN O CN CN CN X S 2 i—i CM CO TP i n CO 1- 00 X. *c0 PL, V. s c IS o © »C CO N o w M >n i n m co i n i n CN CN CN I N l O CO co CO I N ( N H o d d q co m in co « d o i ^ >o co 0 0 CN CO ITO ( N (N in H 00 in iq TP cq o CN CO O Is- ^ CO N CO O TJ d CN H N CN W c£) d oo i o CN CN H CN o oo p co CN i n CN CN CN p q p p p o q CO CO CO 1 ^ N CO CN CN CN CN CN CN t-I cd b^ CN CN CN Tf CO CO T p in q o o Slump (cm) o o Plant (shipment) O ^H o CO O CN CO i n c o CO i n o s ^ 3 5 CO O to in o f—t a> Mix CJ o co in 1 Strength > S J 2 ~-~- o CO Temperature * O •* Air Content * • * • Slump Flow (cm) —1 • p o O CO CO CO * ^6? o i o i - s oo CS ( N I N M o Slump (cm) £ o CO CO t - t - 00 (%) it Mass *—' p to M 1 lC CO CN CO CN CO CN CN H CO CO o d d O in in CO 0 0 l O I O l C 0 0 N CO CO T f CO S H b- CO 0 0 •«* W in m CO CO O w m CO 0 0 ifl I O W O i n CN i n H d N CN CN CN CN CN CN H CN co Tf o CD m co o m co co i n CN CN CN b- CO OS 100 en segregation y-t segregation CN (%) r-t Temperature (°C) 05 i-H Air Content m i—i Note r H i—i t-f O 6 r— i n ^ H O ! i—i Structures Slump Flow (cm) o CN Concrete Site (unloading) t- 1008 (%) Che mical Admixture Design of Modern Highrise Reinforced Construction of New RC Structures 353 and 100 MPa concrete. Plant tests correspond well with laboratory tests for 100 MPa concrete, but plant tests for 60 MPa concrete was much lower than laboratory tests, which may be attributed to the surface water of fine aggregate and wash water remainder in mixer cars. The concrete mix to be used in the construction testing was finally determined for the following three kinds of concrete, considering the construct ability as the top priority: Table 8.4. Compressive strength. Site (unloading) Plant (shipment) Strength (MPa) Mix No. 7 days 28 days 91 days 7 days 28 days 91 days 60 1 2 3 4 5 6 44.1 62.2 74.0 74.2 69.3 54.4 55.0 69.0 85.8 89.3 81.6 61.8 58.4 88.6 95.8 98.1 92.4 70.5 45.9 62.9 76.0 73.1 73.1 59.9 54.1 70.1 81.6 82.4 80.3 65.9 57.6 83.9 101.9 99.1 95.7 77.9 100 7 8 9 90.6 86.2 96.4 115.7 109.2 123.8 125.6 109.2 135.7 93.6 86.1 97.6 112.2 115.1 122.0 137.9 123.0 135.6 Plant test 3.0 g <2.0 w/c -. 27% IV: 165kg/m3 Laboratory test W/C: 30% IV: 163, 164ltg/m3 CD t_ 11.0 < 0.0 _ 110 CL §- 90 n 91days 0 28days Hfl 7days p 70 50 18 21 25 18 Slump (cm) 21 25 Fig. 8.6. Relationship of slump and compressive strength or amount of chemical admixture. 354 Design of Modern Highrise Reinforced Concrete 60MPa concrete 130 120 ^110 £100 - Lab. test S 90 c o> 80 £ 70 03 Structures 100MPa concrete O -X - o _ 60 50 - ^ Lab. test O: Plant test J- 0~Z 2.5 1 3.0 1 3.5 1 4.0 "C 3.5 i i i 4.0 4.5 5.0 BAN I 35 Fig. 8.7. I I I I 30 27 25 25 W/B (%) i i 22 20 Relationship of binder-water ratio and compressive strength. (1) 60 MPa concrete with target 28-day strength of 80 MPa, water-cement ratio 27 percent, water content 165 kg/m 3 , slump 25 cm, admixture A or B (notation: 60-27-25-A or -B). (2) 60 MPa concrete with target 28-day strength of 80 MPa, water-cement ratio 27 percent, water content 165 kg/m 3 , slump 21 cm, admixture A (notation: 60-27-21-A). (3) 100 MPa concrete with target 28-day strength of 120 MPa, watercement ratio 20 percent, water content 160 kg/m 3 , slump 25 cm, admixture C (notation: 100-20-25-C). 8.2.4. Reinforcement Construction Reinforcing bars used in the full scale construction test were as follows. For column bars, USD685 D41 bars with screw-type deformation were used. For beam bars, USD685 D35 bars with screw-type deformation were used, with U-type bent anchorage at the exterior column-ends. For wall and slab bars, USD685 D16 and D13 bars with ordinary deformation were used, respectively. Column hoops were SD290 D16 bars with ordinary deformation, built into closed form by flush butt welding. Beam stirrups were SD785 D13 bars with ordinary deformation, also built into closed form by flush butt welding. Thus high strength steel was used throughout except for column hoops where ordinary grade steel was adopted in order to accommodate welding joints. Construction of New RC Structures 355 Fabrication of reinforcing bars was carried out after careful examination of fitting by detailed re-bar work drawings and re-bar assembling drawings. This was necessary for re-bar fabrication with congestion such as this test structure. As a result of detailed examination, the work precision requirements for each re-bar element could be made more stringent than current JASS 5 as shown below, except for the length of wall and slab bars. Precision of length of column and girder axial bars was plus zero and minus 10 mm. In case of U-bend girder bars with inner bend diameter of 4 times bar diameter, length from bar end to the exterior surface of vertical portion and length between exterior surface of horizontal portions must also be plus zero and minus 10 mm. Length of wall and slab bars must be plus or minus 20 mm. Hoops and stirrups with 90 degrees bend and/or 180 degrees hook with inner bend diameter of 4 times Fig. 8.8. Election of girder cage. Fig. 8.9. Corner column to girder joint. 356 Design of Modern Highrise Reinforced Concrete Structures bar diameter, length between exterior surface of parallel portions, lengthwise as well as crosswise, must be plus or minus 3 mm. Reinforcement cages for columns and beams were prefabricated firmly on the ground. Column cages of one story high and girder cages of double-cross shape were made as one unit of prefabrication, and erected into the designated positions using a truck crane. Figure 8.8 shows erection of a girder unit. Column bar splices were located 300 mm above floor slabs except for core bars, which were spliced 800 mm above floor slabs, i.e. 500 mm above the splices of periphery column bars. Column and girder bars were spliced mechanically by screw-type coupler joints. Figure 8.9 shows the view of corner column to girder joint while election. 8.2.5. Concrete Construction 8.2.5.1. Fresh Concrete Fresh concrete tests were performed at the shipment from plant and at the unloading on site for 60 MPa concrete of full scale test structure, in order to investigate its performance and quality. Figure 8.10 shows slump, slump flow and air content measured at the shipment and unloading. The slump at these occasions was almost same, and its actual value for 25 cm slump concrete was within minus 2.0 cm and plus 1.2 cm range, while the value for 21 cm slump concrete was somewhat higher, within minus 1.0 cm and plus 4.0 cm range. The slump flow and air content showed j£ Q : Slump 0 ^ : S l u m p f l o w I 4 0 A A u 2 1 0 A A 4 A A A A A Black: Unloading 1 J A J J A A A * fl fi J * E „ ^ o. 30 a. 0 A White : Shipment ~ & O " 70-H- o D 1 | 1 4 —1 Li 1— 3 a 1 1 j o 5 a o o 3 ; * ' • a —i 5 ^ ' A £ 2. ^ A : Air content a o • a • 1 1 1 1 i— D 1 D D 1 o a ° ! *n ! * n l D 1 ' 1 1 a a 1 1 2 50 g a. 30 | 1 3 4 5 6 7 1 2 3 1 2 3 4 5 No. of agitator truk Column Column Frame (Monolithic) Frame (Vertical) Frame (Horizontal) 100-20-25-C 60-27-25-B 60-27-25-A 60-27-21-A Fig. 8.10. Variation with time of slump, slump flow and air content. Construction y=5.265x-74.622 r=0.956 y=7.912x-139.072 1=0.907 of New RC Structures 357 y=4.952x-68.205 1=0.933 Fig. 8.11. Relationship between slump and slump flow. general decrease from shipment to unloading. The variation of air content was less than 1 percent. Figure 8.11 shows relationship between slump and slump flow. Although they showed some correlation, it often happened that concrete with similar slump had considerably different flow values. It was deemed appropriate to evaluate workability of concrete by slump flow, rather than slump, in case of high strength concrete. 8.2.5.2. Construction of Column Specimens Casting of concrete was done by concrete pump truck with a boom of 22.4 m having maximum outlet capacity of 65 m 3 /hr. Figure 8.12 shows the sequence of column concrete casting schematically. In case of VH separate casting, the flexible hose at the end of concrete pipe was lowered to the bottom of form, through girder and column re-bar cages, and it was raised in accordance with the rise of concrete surface up to the height of girder soffit (2150 mm). The upper H portion concrete was placed 4 hours 20 minutes after completion of V portion casting. In case of monolithic casting, concrete was dropped from the top of girder level through girder re-bar cages, and was cast all the way to the top of the column. Rate of casting was 25 m 3 /hr, and casting and compacting operation was carried out continuously. Figure 8.13 shows a view of concrete placement in a column. Curing for all column specimens was same, i.e. formwork was remained in place for 1-day, and after formwork removal, columns were wrapped by vinyl sheet. 358 Design of Modern Highrwe Reinforced Concrete Structures Figure 8.14 shows distribution along height of concrete strength obtained from test of drilled core specimens. Shown here are data of two columns using 100 MPa concrete and different method of casting, but fluctuation of concrete strength along height was similar for VH separate casting and monolithic vibrator <£43mm,120Q0VPW! m vibrator vibrator o o o u o r 850 Q oo — o ° / • 20 sec. per one layer, one point 8 Construction joint Horizontal portion 750 Vertical portion 2150 J @ JL o4 ^vibrator Monolithic casting I ® I ^vibrator VH separate casting Fig. 8.12. Sequence of column concrete casting. Fig. 8.13. Concrete casting of a column. Construction 3000 of New RC Structures 359 A No.2 playwood —VH sparate casting • No.3 playwood — monolithic casting 10OMPa concrete 2000 1000 \ 70 Fig. 8.14. 80 90 100 110 120 Core strength (MPa) 130 140 Distribution along height of concrete strength. 3000 r- 10OMPa concrete 2000 • o A A 1000 0.5 1 No.1 No.1 No.2 No.2 steel (core surface) steel (ext. surface) plywood (core surface) plywood (ext. surface) 1.5 Bubble area rate (%) Fig. 8.15. Distribution along height of surface bubbles. casting. The maximum strength difference along height was 9.7 MPa, or about 10 percent of specified strength. Figure 8.15 shows distribution along height of surface bubbles observed externally and on the core cylinder surfaces. Plotted values on the abscissa are bubble area rate in percent, defined as total bubble area divided by total surface area times 100. This figure shows data of two columns using 100 MPa concrete placed by VH separate casting, using different form material. Bubble area rate 360 Design of Modern Highrise Reinforced Concrete Structures 0.0 -0.2 . . -0.4 $ h -OR Col. No.3(100MPa) Col. No.5 (60MPa) ? ett <B -0.8 w -1.0 -1.2 0 4 8 Time (hr) 12 16 Fig. 8.16. Settlement of concrete upper surface. was greater for steel form than plywood form, and also greater in the upper portion of the column. In general more bubbles were found on core cylinder surface than external surface of the column, but there were no honeycombs and so concrete filling was judged good. Settlement of concrete upper surface after casting was measured as shown in Fig. 8.16. The maximum value was about 0.9 mm, and considering the column height of 2900 mm it was judged very small, much smaller than ordinary strength concrete. Settlement was concluded in about 1.5 hours for all concrete mixes, and hence it was made clear that H portion concrete of VH separate casting could be placed 1.5 hours after casting V portion (column) concrete. 8.2.5.3. Construction of Frame Specimen Figure 8.17 shows a view of concrete casting of a wall. Due to its limiting dimension, concrete casting to walls is the one that requires utmost attention in the practice. Figure 8.18 shows the flow of wall concrete in the form of a wall in the first story. As shown in the figure, wall concrete was placed in two operations, each followed by vibration from a form vibrator. Figure 8.19 shows concrete casting into girders and floor slabs of the third floor. Concrete placed in girders was compacted by a high frequency rod-type vibrator inserted into fresh concrete at 40 cm spacing along girder axis from a point 20 cm away from the girder end, with 10 seconds of vibration at each location. Fresh concrete in the columns and column girder joints was compacted at four corners of formwork by 20 second each of vibration. Conveying speed of concrete was 25 m 3 /hr. Construction of New RC Structures 361 Fig. 8.17. Concrete casting of a wall. Placing sequence (B zone, 1st layer) ©-(D-KD-^©~»form vibrator © © Placing sequence (B zone, 2nd layer) (CD: after form vibration) ^®-*®-*i)-*i)-^#-*(D)--*©--»forrn vibrator Fig. 8.18. Flow of wall concrete in the form. Material segregation of concrete was not noticeable in columns and walls even when concrete was dropped from the top of girder re-bar cages. Conveying speed of 25m3/hr was appropriate for placing, compacting and leveling operations of column and wall concrete, but it was found that higher conveying speed such as 35 or 50 m 3 /hr was too fast to make satisfactory 362 Design of Modern Highrise Reinforced Concrete Structures Fig. 8.19. Concrete casting of girders and floor slabs- Fig. 8.20. General view of construction work. placing, compacting and leveling operations. Figure 8.20 shows a general view of construction work in progress. Concrete conveying by concrete pump was measured for high strength concrete of 60 MPa, water-cement ratio of 27 percent and slump 21 cm, used for the third floor girders and floor slabs. The concrete pump was an IHI IFF 85B machine which is lateral single action double spindle hydraulic piston type, with maximum conveying speed of 65 m 3 /hr, theoretical conveying pressure of 7.36 MPa, cylinder size 195 mm diameter and 1400 mm long, hopper capacity 0.45 m3, boom pipe of three-step hydraulic operated bending, conveying pipe diameter 125A, and maximum above-ground height 20.7 m. The reduced horizontal length of conveying pipe that corresponds to conveying load of the boom pipe was taken to be 180 m. Construction of New RC Structures 363 Figure 8.21 shows relationship of theoretical conveying speed and theoretical conveying pressure and actual values. As shown the concrete pumping operation was carried out with a sufficient margin. However the conveying load of high strength concrete was found to be 2 to 3 times the ordinary strength concrete of same slump of 21 cm shown in the concrete pump guidelines (Ref. 8.5), due mainly to the large viscosity of high strength concrete. Figure 8.22 shows the relationship between theoretical conveying pressure and slump change or slump flow change rate before and after conveying. Slump flow change rate is defined as the ratio of the slump flow change before and after conveying to the slump flow before conveying expressed in percent. The slump dropped by 4 to 7.5 cm by conveying, and the slump flow dropped by 8.2 to 15.5 cm making the change rate of 21 to 36 percent. The slump loss and slump flow loss was greater for higher conveying pressure. The air content, on the other hand, increased by 0.1 to 0.5 percent by conveying. Figure 8.23 shows the sequence of construction of the frame specimen, together with locations of concrete core boring after the completion of construction. Concrete in girders and floor slubs of second and third floors was cast, first, in the construction Zone B, and subsequently in the Zone A 60 to 180 minutes later. The construction joint between the two zones was made using lath mesh and air tubes. The high frequency rod-type vibrator used for concrete compaction was not inserted into the preceding concrete. Comparing lath mesh and air tubes for the construction joint, it was found that the latter, Conveying limit O 1st truck o 2nd truck S= 7 A 4th truck v 5th truck .Conveying pressure for high strength concrete from ref. (8.4) ?5 b 3 a V6A A Conveying pressure for ordinary strength concrete, slump 21cm from ref. (8.5) a 1 - 0 10 20 30 40 50 60 70 Theoretical conveying speed (rrr/hr) Fig. 8.21. Relationship of theoretical conveying speed and pressure. 364 Design of Modern Highrise Reinforced Concrete Structures o Slump loss (SI) A Slump flow change rate (7;) (numeral) indicates slump flow change (cm) 37.5 2.9 / °>8 A 35 ?7 32.5 7) = - 1 1 . 7 H (r=0.94) / A r^AT * AT X A 30 / 27.5 / / r f A/ \ ?5 17.5P/' ! c/\ 0 25 y \° 22.5 Sl= -7.62+5.2P(r=0.91) 20 I I I I I 17.5 §1 551.75 2 2.25 2.5 2.75 3 3.25 Theoretical conveying pressure P (MPa) Fig. 8.22. Relationship of theoretical conveying pressure and slump loss or slump flow change rate. Construction joint ', Column 7T I O slab core (J girder core ESggcolumn core ! t::j: ®Girder 1 ZoneB preceding Wall-^ concrete placement i< Zone A following concrete placement _ \ J _ _(k *~' • 6 j + T ar.vx ©1500 I ir Fig. 8.23. Sequence of construction of frame specimen and location of core boring. Construction of New RC Structures 365 air tubes, was easier to install, but on its removal the preceding concrete had to stay up by itself that requires more than 120 minutes after completion of Zone B to commence the Zone A concreting. On the other hand, metal lath mesh need not be removed, so the construction time can be shortened, but it requires more work to install. The sequence of concrete casting of columns was as follows. First, the second story column concrete was cast up to the soffit of third floor girders, and upper concrete was cast 8 days later to the top surface of the third floor slabs. Column construction joint in Zone A was treated on the next day of column casting by wire brush to remove laitance, and by subsequent water washing. Construction joint in Zone B was not treated. Concrete surface finishing and initial curing method was examined by applying different methods of tamping, metal trowel finishing, and whether or not applying water spraying. Figure 8.24 shows combination of finishing and curing conditions applied to the second floor slab. It was found that concrete with 21 cm slump was harder to finish compared to 25 cm slump concrete. Surface finishing work generally required larger amount of time and labor because of high viscosity compared to ordinary strength concrete. Figure 8.25 shows a view of floor slab casting and finishing. Water spraying of 100 to 200 ml per i f?V- i H-irj.r 2nd floor B zone 1 st finishing tamping water spraying troweling 2nd finishing water spraying Ehr 10min after start of casting 0- 1 J j rh _ "I tf.T~~- j 2nd floor A zone 1st finishing tamping no spraying I i 2nd finishing none '" I '' • |_J j Fig. 8.24. L_^ | I j I ! L Combination of finishing and curing conditions of second floor slab. 366 Design of Modern Highrise Reinforced Concrete Structures Fig. 8.25. Floor slab casting and finishing. m 2 of floor was effective for plaster's work. The level of surface finishing varied by the method of leveling, and the best accuracy of plus or minus 0.2 mm was obtained by metal trowel finishing. 8.2.5.4. Measurement of Internal Temperature Table 8.5 shows the results of internal concrete temperature measurement at representative locations of the frame specimen. Figure 8.26 illustrates temperature history of first story columns at the central axis or at a corner of the section. The lower half of the figure shows the temperature difference between the corner and the center column section. The table and the figure indicate that concrete in any location reached its maximum temperature 14 to 15 hours after casting, and returned to the external air temperature after 4 or 5 days. Temperature in girders and walls was also about 70 degrees Celsius at its maximum in case of first story where monolithic casting was employed, which is about the same as column concrete. 8.2.5.5. Strength Development Development of concrete strength was examined from various points of view. Figure 8.27 shows relationship between cylinder strength standard-cured in water at age of 28 days and core strength at age of 91 days. The dotted line Y = X indicates the equal strength. For 60 MPa concrete, the core strength was lower than standard-cured cylinder strength by 0 to 18.0 MPa, with the average 13.0 MPa. This corresponds to 75 to 100 percent of standard-cured cylinder strength. For 100 MPa concrete, core strength was about 87 percent of standard-cured cylinder strength. Construction of New RC Structures 367 Table 8.5. Internal temperature measurement. Specimen Column Frame Member No. No. No. No. No. Point 1 2 3 4 5 (°C) Time of Max. Temp. (h) Temp. Rise Per Cement (°C /10 kg) 26.0 26.0 29.0 28.0 28.0 74.3 76.6 74.5 70.0 72.7 14.0 15.0 15.0 14.0 14.0 0.67 0.70 0.63 0.69 0.73 24.0 73.2 69.2 75.5 70.5 15.0 16.0 17.0 18.0 0.81 0.74 0.84 0.76 14.0 15.0 17.0 18.0 0.83 0.73 0.87 0.80 Temp. at Casting (°C) Max. Temp. 1st story column 1 2 3 4 2nd story column 1 2 3 4 23.0 73.6 67.9 76.0 72.0 2nd floor girder 1 2 24.0 70.2 74.5 14.0 15.0 0.76 0.83 3rd floor girder 1 2 22.0 63.7 68.1 14.0 13.0 0.68 0.75 1st story wall 1 2 24.0 72.5 70.1 13.0 14.0 0.79 0.75 2nd story wall 1 2 23.0 65.3 64.7 14.0 14.0 0.69 0.69 2nd floor slab 24.0 48.4 15.0 0.40 3rd floor slab 22.0 41.3 14.0 0.32 Figure 8.28 shows relationship between cylinder strength cured in water on site at age of 28 days and core strength at age of 91 days. The difference was smaller than the previous figure, but for 60 MPa concrete, the core strength was lower than on-site water-cured cylinder strength by 0 to 16.0 MPa, with the average of 9.8 MPa. This corresponds to 80 to 100 percent of on-site watercured cylinder strength. For 100 MPa concrete, core strength was about 93 percent of on-site water-cured cylinder strength. From this data it was judged difficult to adopt cylinders cured in water on site for the strength control of concrete in the structure. Design of Modern Highrise Reinforced Column A1 Column A2 Column C1 70 60 50 Column A1 center Column A2 center C) 40 30 IU ?n a b 1- Structures Form Curing removal Member 80 -I Concrete HI III 368 Column C1 center Column A1 come Column A2 corner 10 Column C1 corner 0 -10 -20 A ' \ • // \ -30 ^ , ,.. Temprature difference r Column C1 . . btw. center and comer Column A2 -40 0 1 2 3 4 5 J I 6 7 Elapsed time (dav) Fig. 8.26. T e m p e r a t u r e history of first story columns. • Isolated column OColumn in frame D Wall A Girder A Floor slab J I I 70 80 90 I 1 0 0 1 1 0 1 2 0 130 140 Standard-cured 2 8 d a y cylinder strength (MPa) Fig. 8.27. Relationship between s t a n d a r d - c u r e d cylinder s t r e n g t h and core s t r e n g t h . Figure 8.29 shows relationship between cylinder strength cured in seal on site at age of 28 days and core strength at age of 91 days. The on-site seal- cured cylinder strength was closer to the core strength than standard-cured or on-site water-cured cylinders, but it was still higher than core strength by - 4 . 0 to 10 MPa with the average of 4.8 MPa. Construction 120 of New RC Structures 369 r 110 Y=1.04X-12.9 (r=0.93) 1100 I so CD en <D ,S Y=0.8X 80 • Isolated column OColumn in frame O Wall A Girder A Floor slab 70 o O 60 50 50 60 70 80 90 100 110 120 On-site water-cured 28day cylinder strength (MPa) Fig. 8.28. Relationship between on-site water-cured cylinder strength and core strength. 120 / y Y=0. Y=0.950X-0.79 95) 110 Q_ 5 100 ? 90 CD 80 Core 91 c ,' Y=0.85X 70 60 50 • Isolated column O Column in frame D Wall A Girder A Floor slab ' ' ' 50 60 70 80 90 100 110 120 On-site seal-cured 28day cylinder strength (MPa) Fig. 8.29. Relationship between on-site seal-cured cylinder strength and core strength. In general the structural concrete strength is denned as the compressive strength that emerged in concrete in the structure. The Building Standard Law in Japan defines it by the compressive strength at age of 28 days of onsite water-cured cylinders, core strength at age of 91 days of age, or strength of cylinders under similar curing condition. Among them, the last one, i.e. cylinders under similar curing condition as cores means cylinders seal-cured on site. 370 Design of Modern Highrise Reinforced Concrete Structures For this reason, the strength control of concrete in the structure has been traditionally executed by on-site seal-cured cylinders. However, for New RC structures the proposed standard specification defines the structural concrete strength by core strength at age of 91 days, and recommends that the concrete mix be determined so that the structural concrete strength satisfies the specified strength in design, and that quality control of concrete be done accordingly. As shown above, the control cylinders of three kinds in this full scale construction testing, i.e. standard-cured in water, on-site cured in water, and onsite seal-cured, all showed greater strength than the core strength. For 60 MPa concrete, the average core strength was 70.6 MPa which was more than satisfactory for specified strength. On the other hand, the strength of control cylinders was 85.0 MPa for standard-cured cylinders, 83.0 MPa for on-site water-cured cylinders, and 80.0 MPa for on-site seal-cured cylinders. It is considered possible for concrete up to 60 MPa to control the strength by means of control cylinders, and to determine proportioning strength by adding surcharge to the specified strength. If the proportioning strength F2s is determined by the following equation, F2S = FC + S + Ka (8.1) where Fc : specified strength S : strength difference between standard-cured cylinders at 28 days and structural concrete a : standard deviation K : a coefficient for the increase of proportioning strength and further if the strength of structural concrete is controlled by the standardcured cylinders at age of 28 days, then taking the adjustment S of abovementioned 13.0 MPa and standard deviation a of 5.6 MPa (or 2a of 11.2 MPa) we obtain F2S = 84.2 MPa for Fc = 60 MPa. For 60 MPa concrete used in the full scale construction testing the average value of standard-cured cylinder strength was 89.8 MPa, hence it can be inferred that the proportioning strength of Eq. (8.1) and above-mentioned quality control method are applicable to 60 MPa concrete. On the other hand, the same Eq. (8.1), if applied to 100 MPa concrete, gives necessary proportioning strength of F28 = 129.9 MPa, because the adjustment S is 14.7 MPa and twice the standard deviation 2a is 15.2 MPa. However the Construction of New RC Structures 371 average value of standard-cured cylinder strength was 122.9 MPa, which was lower than the necessary proportioning strength. Thus the control method of 100 MPa concrete is left for future studies. 8.2.5.6. Observation of Cracks on Frame Specimen Surface cracks of the frame specimen was observed by naked eyes, and their location, shape, and the observed dates were recorded. Crack width and length were measured using crack scales. Crack observation was started on the next day of concrete placement for floor slabs, and it was commenced right after the form removal for columns, walls and girders, until the age of 41 to 57 days. Figure 8.30 shows cracks on the second floor slab. There were 21 cracks on this floor slabs among which 14 cracks were observed already on the next day of concrete placement. Crack width was mostly about 0.08 to 0.10 mm. The location where many cracks concentrated was along line 1 girder that had no wall underneath, and around A-l column. As indicated in Fig. 8.24, no water spraying was done in this area at the surface finishing, which should have affected to produce these surface cracks. 1500 3000 <4* Fig. 8.30. 3000 -i- 1500 rH Cracks on the second floor slab. Design of Modern Highrise Reinforced Concrete Structures (A) Line exterion side \ J 1 (i)Line exterion side 1 / X' \ /' \ i O 7 |S70| 1 I \ /' 2900 \ | JO g O 2150 \ /' X / \ / \ o 1 ^ 372 • J=t 1500 I © " 3000 3000 9000 I 1500 ® ©Line exterion side Fig. 8.31. Cracks on the walls and girders. Construction of New RC Structures 373 Cracks were not observed on columns. Figure 8.31 shows cracks observed on wall and girder surfaces. Table 8.6 summarizes crack appearance on the first story walls and second floor girders that were cast monolithically, and Table 8.7 shows cracks on the second story walls and third floor girders constructed by V-H separate concrete casting. The age at which cracks were found was shown in the table, while the formwork removal time and curing condition were shown in the footnote. When cracks were found on both front and back sides it was judged to be a through crack, and average length and width were entered in these tables. In the lower rows of Tables 8.6 and 8.7, total crack length, and crack width on the walls and girders, and their sums are shown. Number of cracks found on the monolithic wall and girder was 10, while that on the VH separate cast wall and girder was 14. Total length of cracks at the first observation was 855 cm for monolithic, and 945 cm for VH separate. Total width of cracks at the first Table 8.6. Cracks in the first story (monolithic casting). Line Member Age of Cracking (day) Length Initial (cm) Length Final (cm) Width Initial (mm) Width Final (mm) Penetration A (west) girder 19 60 60 0.15 0.30 yes wall 4 19 4 215 180 200 215 190 200 0.14 0.10 0.12 0.25 0.22 0.25 yes yes yes girder 4 4 10 20 30 30 0.02 0.04 0.02 0.04 no yes — — — — — 40 20 40 20 0.06 0.02 0.06 0.02 yes no — — — — — 50 60 50 60 0.08 0.12 0.10 0.17 yes yes wall 595 605 0.36 0.72 girder 260 290 0.47 0.71 total 855 895 0.83 1.43 B (east) wall 1 (north) girder 7 57 wall 2 (south) Total girder 7 7 Note: Forms remained in place for 3 days, while shoring below girders remained for 19 days. No curing was applied after form removal, expect for line 1 wall which was cured for 4 days. 374 Design of Modern Highrise Reinforced Concrete Structures Table 8.7. Cracks in the second story (VH separate casting). Line Member Age of Cracking (day) Length Initial (cm) Length Final (cm) Width Initial (mm) Width Final (mm) Penetration A (west) girder 4 50 50 0.17 0.20 yes wall 3 3 3 7 150 130 60 55 170 150 140 170 0.12 0.11 0.11 0.12 0.17 0.15 0.17 0.20 yes yes yes yes girder 4 4 4 50 55 50 50 55 50 0.03 0.06 0.06 0.04 0.08 0.06 yes yes yes wall 7 100 135 0.10 0.17 yes girder 4 4 55 10 55 10 0.09 0.01 0.09 0.01 yes no wall 3 80 140 0.07 0.17 yes girder 4 4 50 50 50 50 0.05 0.06 0.07 0.10 yes yes wall 575 905 0.60 1.03 girder 370 370 0.53 0.65 total 945 1275 1.13 1.68 B (east) 1 (north) 2 (south) Total Note: Forms remained in place for 3 days except for line 1 wall where forms remained for 7 days. Shoring below girders remained for 6 days. No curing was applied after form removal. observation was 0.83 mm for monolithic and 1.13 mm for VH separate, and further the total crack width at the final stage was 1.43 mm and 1.68 mm, respectively. Thus, regardless of walls and girders, fewer number of shorter and thinner cracks were observed for monolithic casting, and the reverse for VH separate casting. 8.2.6. Conclusion The full scale construction testing clearly revealed the possibility of practical construction of 60 MPa concrete with assured quality. Some problems were left for future study for 100 MPa concrete, however, this testing gave prospects of its practical construction. The results of the full scale testing was fully incorporated into the construction standard introduced in the next section. Construction of New RC Structures 375 This construction testing was carried out at the Building Research Institute with the cooperation of academic members of the Construction and Manufacturing Committee chaired by Professor K. Kamimura, and also the cooperation of companies represented by the members of the Research Promotion Committee listed in Table 2.3 of Chapter 2. Actual construction work of reinforcement was carried out by Sato Komuten Co., and manufacture of high strength concrete was done by the Tsukuba Factory of Chichibu Ready-mix Concrete Company. 8.3. 8.3.1. Construction Standard for N e w R C General Provisions A new construction standard specification for the construction using high strength concrete and high strength steel was developed by the High Strength Concrete Committee and Construction and Manufacturing Committee of the New RC project. It was intended to cover the concrete strength range between 36 and 120 MPa and reinforcement with yield strength range between 390 and 1275 MPa. Concrete construction using up to 36 MPa concrete and reinforcement work using up to 390 MPa steel may depend on the current JASS (Japan Architectural Standard Specification). Followings are the description of only the very basic features of the new construction standard. 8.3.2. Reinforcement Axial reinforcement of girders and columns, and structural wall reinforcement, shall conform to USD685A, USD685B, or USD980 of the New RC reinforcement standard developed in the New RC project, and lateral reinforcement of girders and columns shall conform to USD785 or USD1275 of the New RC lateral reinforcement standard, also developed in the New RC project. USD685A, USD685B and USD980 are re-bars of general use that can be applied to axial reinforcement of framing members and structural walls, and its diameter range and shape of surface deformation are same as the standing JIS G 3112, with nominal diameter from D10 to D51. USD785 and USD1275 are re-bars that can only be used for shear reinforcement or confining reinforcement, with sizes and quality standard same as those already in practical use. Chapter 3 already elaborated on these high strength reinforcement. In the fabrication of reinforcement, attention should be paid on the fact that high strength steel generally possesses inferior elongation capacity compared 376 Design of Modern Highrise Reinforced Concrete Structures to ordinary strength steel, leading to inferior bendability. It is hence stipulated that shape of standard hook and bend radius shall be determined by the structural designer. Bars shall be bent, in principle, in the air temperature, however in case of need for heated bend for smaller bend radius, careful consultation with the structural designer is required accompanied by advanced bend test and complete specification of temperature condition and work procedure. The allowance of fabrication is determined from the accuracy of splices and accuracy required in the cage fabrication. Mechanical splices are prevalently used, hence the allowance for axial bars is taken more strictly than the current JASS. Cage prefabrication is recommended throughout the standard, as this can eliminate undesirable possibility of reverse bend at the time of bar election. As to the quality control, necessary items of inspection, time and frequency of inspection, and acceptance criteria are shown for reception on site of reinforcing bars, processing of bars and manufacture of re-bar cages, and splices. 8.3.3. Formwork Formwork is required to perform the following roles. First, it should have sufficient strength and rigidity to maintain its original position during concrete placement and compaction, without producing harmful displacement, deflection or lateral deformation. Second, it should be manufactured with sufficient accuracy to produce the structure with prescribed positions and sizes within the prescribed tolerances, without giving detrimental influence on the finishing, uniformity and strength of concrete. Thirdly, it should serve as effective means of initial curing until forms are removed. These are basically same as ordinary strength concrete. Hence, the requirements for formwork are quite similar to those in current JASS. Some particular features of the New RC standard are the followings. Firstly, provisions for formwork left permanently with the structure are included. Secondly, provisions for formwork as a part of permanent structure, such as precast composite floor slab elements, are developed. Thirdly, higher lateral pressure on formwork is specified considering low yield value of fresh concrete. Although high strength concrete is highly viscous, its yield value is low and lateral pressure does not decrease from the static liquid pressure. Hence the next equation is specified to calculate lateral pressure P = W0Hg (8.2) Construction of New RC Structures 377 where P : lateral pressure on the form (Pa) Wo : unit mass per volume of concrete (kg/m 3 ) H : head of fresh concrete (m) g : gravity acceleration (m/s 2 ). Finally, longer period before form removal is specified compared to ordinary strength concrete. For column, wall and girder sides, forms should remain in place until concrete strength reaches 8 MPa instead of 5 MPa. The period before removal of girder and floor slab shoring is same as the current JASS. 8.3.4. 8.3.4.1. Concrete General Concrete with specified design strength between 36 MPa and 60 MPa is dealt with in full detail herein. Concrete exceeding 60 MPa and up to 120 MPa in strength should be treated along with this standard in principle but after preliminary laboratory and construction tests in order to ascertain that the built structure would possess required quality. 8.3.4.2. Concrete Quality 8.3.4.2.1. Slump Slump of concrete between 36 MPa and 50 MPa shall be not more than 21 cm, and for concrete between 50 MPa and 60 MPa slump shall be not more than 23 cm or slump flow not more than 50 cm. If segregation resistance has been confirmed to allow larger slump flow, corresponding slump flow may be specified, but in no case it shall exceed 65 cm. 8.3.4.2.2. Compressive strength Compressive strength of structural concrete shall be defined by the 91-day strength of concrete core bored from the structure, and the strength control shall be made by testing concrete cylinders cured under conditions that would reasonably represent the condition of structural concrete. Strength control 378 Design of Modern Highrise Reinforced Concrete 28-day strength; of standard-cured Structures n-day strength of seal-cured on site 28-djay strength of water-cured on site • Strength development in structure (core) - Strength development of standard-cured i — Strength development of watericured on site : Strength development of seal-cured on site (same as core) 20 28 40 60 80 91 100 (n^91) Age (days) (a) Normal strength concrete (JASS 5) S (adjust to structural concrete) Jin-day strength of temperature-history-cured with structural concrete * Strength development in structure (core) ' Strength development of standard-cured Strength development of watericured on site Strength development of temperature-history-cured with structural concrete (same as core) J 0 20 28 i 40 l_ 60 80 91 100 Age (days) (b) High strength concrete (New RC) Fig. 8.32. Concept of concrete strength development in structure. Construction of New RC Structures 379 criteria shall be based on 5 percent badness ratio. The condition to reasonably represent that of structural concrete may be satisfied by temperature history chasing curing or simplified adiabatic curing, and it is possible to estimate the structural concrete strength from cylinder testing of standard curing if the correction factor has been established beforehand by construction tests. Figure 8.32 illustrates the concept of strength development of concrete under various curing conditions. Figure 8.32(a) shows the concept of strength development of normal strength concrete, currently specified by the Building Standard Law and adopted in the standard specification JASS 5 or JASS 5N. Concrete strength to be controlled is that in the structure, and it is assumed to be represented by the core strength at the age of quality control. This strength is approximated by one of two methods. Firstly, it is approximated either by 28-day strength of water-cured cylinders on site, or by n-day strength of seal-cured cylinders on site. For the former the proportioning strength F28 is obtained by F2& = FC + T + Ka (8.3) F2s = FC + Tn+Ka (8.4) and for the latter where Fc : specified concrete strength T : correction factor for temperature at age of 28 days (difference of standard-cured 28-day strength and water-cured on-site 28-day strength) T n : correction factor for temperature at age of n days (difference of standard-cured 28-day strength and seal-cured on-site ra-day strength) K : a factor to multiply standard deviation o : standard deviation and judgment on the cylinder test result X is based on X ^ Fc. The second method of approximation, not shown in Fig. 8.32(a), is to evaluate the structural concrete strength from the AT-day standard-cured cylinder strength minus temperature correction factor T/v, which is defined as the correction for mean anticipated curing temperature (difference of standard-cured TV-day strength and strength at N days of specimens cured with mean curing temperature). 380 Design of Modern Highrise Reinforced Concrete Structures In this case, the proportioning strength is found as FN = FC+TN+ Ka (8.5) and judgment on the test result X is based on X }?. FC + TN. SO much for the case of ordinary strength concrete. In the course of laboratory and full scale construction testing it was found that the on-site water-cured cylinders were inappropriate to represent concrete strength in large section members such as columns made of high strength concrete of 60 MPa or higher. It was also found that on-site seal-cured specimens were inappropriate to represent core strength of concrete. For these reasons the structural concrete strength for the New RC was defined by the 91-day core strength, and Fig. 8.32(b) illustrates the concept of strength development of high strength concrete. The black dot in Fig. 8.32(b) shows the core strength at age of 91 days. Like the ordinary strength concrete, this strength is approximated by one of two methods. Firstly, it is assumed to be equal to the strength of temperature history chasing-cured cylinders at age of n days, then the proportioning strength Fn is given by Fn = Fc + P + Ka (8.6) where P : correction factor for the temperature history (difference of standardcured n-day strength and temperature history chasing-cured n-day strength — not shown in the figure) and judgment on the cylinder test result X is based on X ^ Fc. The second method is to evaluate the structural concrete strength from the n-day standardcured cylinder strength minus correction factor S, which is defined as the correction factor for structural concrete strength development (difference of standard-cured n-day strength and 91-day strength of core specimens or equivalent). In this case the proportioning strength Fn is given by Fn=Fe + S + K<r (8.7) and judgment on the test result is done by X ^ Fc + S. These approaches for high strength concrete were adopted considering the early development of structural concrete strength as illustrated in Fig. 8.32(b) due to high cement content and large sectional area of New RC members. Construction of New RC Structures 381 8.3.4.2.3. Young's modulus Young's modulus of concrete is an important parameter to describe seismic performance of New RC structures, and so it is recommended to establish the value prior to structural design by trial mix using available material for concrete. An equation shown in Chapter 3 was developed for the New RC concrete to cover wide range of concrete strength and material variety, which is the following E = 33 500 x fci x fc2 x (7/2.4) 2 x ( < T B / 6 0 ) 1 / 3 (8.8) where E : CTB 7 : fci : k2 : Young's modulus of concrete in MPa : compressive strength of concrete in MPa specific weight of concrete a coefficient for the effect of coarse aggregate type a coefficient for the effect of mineral admixture. The coefficient fci is to be taken as follows: fci = 1.2 for crushed limestone and burnt be auxite fci = 0.95 for crushed liparite, crushed andesite, crushed basalt, crushed clay stone, and crushed boulder fci = 1 . 0 for all other coarse aggregate and the coefficient fc2 is to be taken as follows: fc2 = 0.95 for silica fume, fly ash fume and ground granulated blast furnace slag fc2 = 1.0 for the case where no mineral admixture is used. Some representative values are given in the construction standard, but they are best to be determined by tests at each job site. 8.3.4.2.4. Durability and fire resistance The durability requirement for high strength concrete is summarized into the following six items: (1) Chloride content in the concrete shall be less than 0.20 kg/m 3 by the amount of chloride ion. (2) Concrete shall be free of alkali-aggregate reaction. 382 Design of Modern Highrise Reinforced Concrete Structures (3) Neutralization resistance of concrete shall be tested by the accelerated neutralization test method shown by the Recommendation for Design and Construction Practice of High Durability Concrete by the Architectural Institute of Japan (Ref. 8.6), and the resulted neutralization depth shall be less than 20 mm. (4) Drying shrinkage rate of concrete shall be less than the value that would trigger cracks in the structural members harmful from durability point of view. (5) Hydration heat of concrete shall be less than the value that would trigger cracks in the structural members harmful from durability point of view. (6) The durability index for concrete subjected to possible frost damage shall be more than 80 at 300 cycles. In general tests for the durability takes long time. Hence tests using actual material or proportioning cannot catch up the construction job, and available past records must be utilized in the judgment of durability. Concrete with water-cement ratio of 40 percent or less does not show neutralization, but for concrete with water-cement ratio greater than 40 percent shows the progress of neutralization, and its examination is necessary. The accelerated neutralization test quoted here was carried out under the condition of 20 degrees Celsius, 60 percent relative humidity, 5 percent carbon dioxide concentration, and 6 months of accelerated neutralization. Specified neutralization depth of 20 mm was determined considering the building life time of 100 years, so that neutralization remains in the concrete cover at the exterior surface, and in the zone 20 mm inside the concrete cover at the interior surface, in 100 years of time. For drying shrinkage rate, JASS5 for high durability concrete specifies the value of 6 x 1 0 - 4 , but it was found difficult to meet this requirement. Hence the drying shrinkage rate of 7 x 1 0 - 4 specified in the Recommendation for Design and Construction Practice of High Durability Concrete (Ref. 8.6) is taken here as the target value, and care should be taken for cracking when this value is exceeded. Fire resistance of high strength concrete is regarded to be somewhat inferior to the ordinary strength concrete, due to fine structure of high strength concrete which would retard drying of concrete interior, leading to possible explosion in case of fire. For this reason, a provision of fire resistance was included in this construction standard, stating that harmful deformation, failure or drop out during fire should be prevented. Construction of New RC Structures 383 Experiments in the New RC project presented the following conclusions: (1) Internal temperature distribution during fire of high strength concrete is similar to that of ordinary strength concrete, and so high strength concrete can resist fire in the same way as ordinary strength concrete unless harmful deformation, failure or drop out do not take place. (2) Concrete with low water-cement ratio is apt to explode when subjected to fire. However room drying or forced drying is effective in controlling the explosion. 8.3.4.2.5. Concrete cover Concrete cover to the reinforcement can be made smaller for high strength concrete if its fine structure and high durability is considered effective in resisting the neutralization and osmosis of chloride ions. However crack appearance and fire resistance requirements may prohibit the reduction of coverage. This leads to the conclusion that same cover as in the current JASS 5 is specified in the New RC construction standard. 8.3.4.3. Material Cement shall conform to the New RC standard "the Quality Standard of Cement for High Strength Concrete", and details are specified separately for JlS-compatible cement and for others separately. JlS-compatible cement shall satisfy, in addition to all requirements in JIS, the strength requirement that the compressive strength at age of 28 days of water-cement ratio 30 percent mortar with adequate high range AE water reducer exceeds 55 MPa, and the compressive strength at age of 91 days exceeds 60 MPa. JlS-incompatible cement includes low heat portland cement and fineness adjusted cement that was developed during the New RC project, and they shall satisfy the strength requirement that the compressive strength at 28 days of water-cement ratio 30 percent mortar with adequate high range AE water reducer exceeds 50 MPa, and the strength at 91 days exceeds 60 MPa. For coarse and fine aggregate, it is necessary to produce not only required strength of concrete but also required Young's modulus. Hence they must be tested prior to construction even if they conform to the class I of JASS 5-1975. As to alkali-aggregate reaction, material judged as innocuous by test shall be used, as high strength concrete usually has higher unit cement content and hence it contains higher amount of alkali substance. 384 Design of Modern Highrise Reinforced Concrete Structures For water the requirements are same as J ASS 5-1993, and no recycled water shall be used. Chemical admixture to be used in high strength concrete is high range AE water reducing agent, and its quality is specified in the standard. There are also quality standards issued from the Architectural Institute of Japan or Housing and Urban Development Corporation. Mineral admixture such as silica fume or ground granulated blast furnace slag need not be used for high strength concrete up to 60 MPa. These and other mineral admixtures must be used for high strength concrete in excess of 60 MPa. Manufacture of 60 MPa concrete becomes easier when these mineral admixtures are used. The construction standard includes quality standards for silica fume, fly ash fume, ground granulated blast furnace slag, and etringite type special admixture. 8.3.4.4. Mix The proportioning strength for high strength concrete is represented by the standard-cured cylinder tests at control age between 28 and 91 days, and is expressed by the following equations Fn ^ Fc + S0 + Ka0 Fn ^ 0.9(FC + S0) + 3<T0 (8.9) (8-10) where Fn : proportioning strength at control age of n days Fc : specified design strength So : strength difference at age of n days between standard-cured cylinders and estimated compressive strength of structural concrete strength control cylinders (To : standard deviation of strength of structural concrete strength control cylinders, to be taken as one tenth of (Fc + So) if tests are not performed K : a coefficient corresponding to the permissible badness ratio of structural concrete strength control cylinders, usually in the range of 2 to 2.5. The water-binder ratio is determined so that the target strength for proportioning is obtained, and the approximate range is shown in Table 8.8. The Construction of New RC Structures 385 unit binder content of more than 350 kg/m 3 is recommended, as it is necessary to provide such amount to obtain good workability, resistance to segregation, and durability. The unit water content of less than 175 kg/m 3 is recommended, and it should be determined so that excessive use of chemical admixture is avoided. Table 8.9 summarizes the approximate range of unit water content for each water-binder ratio, determined based on the test results of New RC. The amount of chemical admixture is determined to obtain required consistency of concrete in terms of slump or slump flow, based on the recommended standard amount. Excessive use may lead to segregation of materials, retardation of setting, or large drying shrinkage. Too meager use may result in large slump loss during construction. Table 8.8. Specified design strength, proportioning strength and water-cement ratio. Specified Design Strength (MPa) Proportioning Strength (required mean strength) (Mpa) Water-Cement Ratio (water-binder ratio) (%) 18~24 27~36 39~48 54~60 80 100 120 24 ~ 30 33 ~ 4 5 48~60 70~85 100 ~ 110 120 ~ 130 140 ~ 150 50 ~ 65% 40 ~ 50% 30 ~ 40% 25 ~ 30% 20 ~ 25% 20 ~ 22% <20% Table 8.9. Unit water content. Water-Binder Ratio (%) 45 30~40 25 22 Unit Water Content ( k g / m 3 ) 165 160 155 150 ~ ~ ~ ~ 175 170 165 160 Table 8.10. Bulk volume of coarse aggregate. Slump (cm) Bulk Volume of Coarse Aggregate Per Unit Volume of Concrete ( m 3 / m 3 ) 18 21 23 0.60 ~ 0.64 0.59 ~ 0.63 0.58 ~ 0.62 386 Design of Modern Highrise Reinforced Concrete Structures To determine aggregate content, either unit bulk volume of coarse aggregate or fine aggregate ratio may be used as the basic parameter, but for large slump concrete, it is customary to use unit bulk volume of coarse aggregate as the basic parameter in order to maintain certain amount of coarse aggregate. There is a trend for unit bulk volume of coarse aggregate to decrease with slump increase, and to increase with lower water-cement ratio and with the use of higher dispersing agent. This trend is applicable to high strength concrete, but the standard value of unit bulk volume of coarse aggregate cannot be determined from water-binder ratio or slump (or slump flow). Table 8.9 shows recommended approximate range for various slump values. The entrained air may be between 2 and 4.5 percent, except when freezing is expected the largest value of above is taken. 8.3.4.5. Manufacture of Concrete High strength concrete is always manufactured in a ready-mixed concrete plant having past experience of producing high strength concrete or having sufficient production capability. Necessary conditions of such plant are JIS accredited plant, stationing of a licenced chief concrete engineer, and location from construction site within 120 minutes of transportation and placing time. In principle a single concrete plant should be selected. Before placing an order for ready-mixed concrete, trial mix should be made and detailed quality and manufacturing specifications must be established, covering: (1) (2) (3) (4) (5) Kind and quality of cement. Kind and quality of aggregate. Kind and quality of admixtures. Method of proportioning of concrete. Method of mixing (order of material input, mixing time and mixing volume). (6) Transportation route and time of concrete. (7) Inspection of ready-mixed concrete at unloading. Concrete manufacturing equipments may be same as those in ordinary ready-mixed concrete plant, but storage and management of material must be made more carefully as the quality of high strength concrete is more susceptible to variation of material than ordinary strength concrete. High strength concrete requires longer mixing time due to its high viscosity resulting from low Construction of New RC Structures 387 water-cement ratio and high unit cement content. Proper mixing time may be effectively determined from the electric current measurement of the concrete mixer. Transportation time within 90 minutes is recommended between shipment and unloading. Inspection at the plant by general contractor must be made as needed, in order to ascertain that manufacturer is executing quality control items specified in JIS A 5308 and also items particularly specified for the job. The inspector should reserve the right to refuse the shipment of fresh concrete that would not satisfy inspections at the unloading on site. Inspection of fresh concrete on site must follow the details shown in the construction standard, as to inspection items, test method, time, frequency and lot size of inspection, judgment criteria, and countermeasures in case of failure in the inspection. Slump and air content measurement must be made on all up to the fifth concrete mixers, because it is possible that the plant start mixing initially without getting hold of the real aggregate condition. Frequency of tests thereafter is determined based on the assumption that perfect quality control is being executed in the plant, hence it is necessary for the general contractor to get in touch with information on the plant operation. 8.3.4.6. Placing and Surface Finishing Placing and consolidation of fresh concrete must follow detailed planning made prior to the construction. Work zones, placing sequence, and placing rate must be appropriately determined, concrete carrying devices, consolidation devices, and laborers must be appropriately arranged, and measures against sudden rain or sudden stop of concrete supply must be determined in advance. Time interval between placing must be tested in order not to cause unexpected cold joints, as the surface of high strength concrete tends to develop thin membrane of stiff substance attributable to low water-cement ratio. Both vertical-horizontal separate placing and monolithic placing are possible, and one of them is selected with due consideration of reinforcement congestion. Concrete transportation is made by bucket or concrete pump. In case of pump, an equipment with sufficient conveying pressure must be selected as the conveying load of high strength concrete is much higher than ordinary strength concrete. Before concrete placement, reinforcement cages, formwork, and embedded hardwares must be inspected, and cleaning, water spraying and arrangement 388 Design of Modern Highrise Reinforced Concrete Structures of concrete placement devices must be properly done. Re-bars outside the concreting zone must be covered to avoid staining by splash. Concrete placing is executed from working platform, scaffold board, or walking board arranged not to disturb re-bar cages or formwork. Consolidation is made by internal (spud) vibrators placed within 60 cm of distance, in the column, wall, as well as girder concrete. Construction joints are placed near the midspan of girders and slabs, and girder soffit and slab top of columns and walls. Metal laths, wood sticks, or air fences are used for horizontal construction joints. Joints are cleaned to remove laitance and weak concrete to expose healthy concrete, and sprayed before concrete casting. Surface finishing of high strength concrete is more difficult than ordinary strength concrete due to its high viscosity. It is important to level off the surface at the time of placing and consolidation. Bleeding seldom happens to high strength concrete, and the surface tends to dry out. Spraying water after surface finishing is effective to prevent excessive drying and cracking. 8.3.4.7. Curing Moist curing by water spraying, curing mats or membrane curant must be made after placing, for the period of at least 2 days (until 3 days of age) for 50 to 60 MPa concrete, at least 3 days (until 4 days of age) for 40 to 50 MPa concrete, at least 4 days (until 5 days of age) for 27 to 40 MPa concrete, and 7 days for up to 27 MPa concrete. If sheathing is removed before these days, concrete surface must be kept moist until above ages by appropriate methods such as water spraying, curing mats or membrane curant. Curing temperature must be specified for cold weather concreting to avoid initial freezing, and to enhance development of required strength at the specified control age. Harmful vibration or loading must be avoided before concrete hardens sufficiently, and construction work on unhardened concrete must be restricted. 8.3.4.8. Compressive Strength Inspection Compressive strength of concrete being used is tested by standard-cured cylinders at specified control age with the purpose of confirming potential concrete strength, but at the same time with the purpose to see whether concrete is being manufactured under a stable condition. For this reason, inspection Construction of New RC Structures 389 is made for each lot of concrete quantity for one-day operation, and three tests per lot is required. In case concrete quantity for one-day operation exceeds 300 m 3 , at least one test per 100 m 3 is required, but if the concrete quantity for one-day operation does not reach 30 m 3 , one lot can cover two days of concrete placing. Acceptance criteria for compressive strength are following two equations XN^FC Xmin^0.9(Fc + S 0 +(K- + S0) -^j *o (8.11) (8.12) where XN '• Average of compressive strength of one lot N tests Xmm : Minimum of compressive strength of one lot N tests Fc + SQ : specified strength Fc : specified design strength So : difference between compressive strength of standard-cured cylinders at control age and estimated compressive strength of structural concrete strength control cylinders K : normal deviation of compressive strength of structural concrete strength control cylinders for permissible badness ratio Ka : normal deviation for producer risk N : number of test for one lot <TO : standard deviation of compressive strength of structural concrete strength control cylinders. This inspection method is based on the scheme that the producer risk becomes a when N specimens are tested out of concrete population with known standard deviation of a0 and badness probability of P for the specified strength. Usually N is taken to be 3, badness probability is 5 percent (K = 1.64), and producer risk is 10 percent (Ka = 1.282). Compressive strength of structural concrete must be tested to confirm that concrete in each part of structure satisfied the specified design strength. Frequency of inspection is made equal, in principle, to the above tests for concrete being used, but inspection lot consists of each placement zone and day. Three tests per lot is required, and in case concrete quantity for one lot exceeds 300 m 3 , at least one test per 100 m 3 is required, but if the concrete quantity for one lot is less than 30 m 3 , one test for the lot is sufficient. 390 Design of Modern Highrise Reinforced Concrete Structures Acceptance criterion for compressive s t r e n g t h is t h a t t h e average of est i m a t e d s t r u c t u r a l concrete s t r e n g t h for one lot exceeds t h e specified design strength. T w o kinds of structural concrete s t r e n g t h control are available. O n e is t o use s t a n d a r d - c u r e d cylinders, a n d t h e other is t o use t e m p e r a t u r e history chasingcured cylinders or simplified adiabatic-cured cylinders. W h e n s t a n d a r d - c u r e d cylinders are used, it can b e replaced by cylinders for t h e concrete being used, a n d the acceptance j u d g m e n t is m a d e by XN ^ Fc + SQ. O n t h e other hand, if t e m p e r a t u r e history chasing-cured cylinders or simplified adiabatic-cured cylinders are used, t h e acceptance j u d g m e n t is m a d e by XN ^ Fc. References 8.1. Aoyama, H., Current state-of-the-art and future problems of highrise reinforced concrete buildings, Concrete J. 24(5), May 1986, pp. 4-13. 8.2. Tomozawa, F., Current state-of-the-art and future problems of high strength concrete for highrise reinforced concrete construction, Architectural Institute of Japan, 1987 Annual Convention Construction Division Report. 8.3. Masuda, Y., Trend in research on high strength concrete in architectural engineering, Concrete J. 28(12), December 1990, pp. 14-24. 8.4. Kemi, T. et al., Experimental study on pump conveying of high strength concrete, Architectural Institute of Japan, 1990 Annual Convention Speech Summary. 8.5. Architectural Institute of Japan, Recommendations for Practice of Placing Concrete by Pumping Methods, January 1994. 8.6. Architectural Institute of Japan, Recommendation for Design and Construction Practice of High Durability Concrete, July 1991. Chapter 9 Feasibility Studies and Example Buildings Hideo Fujitani Performance System Division, Codes and Evaluation Research Center Building Research Institute, Ministry of Land, Infrastructure and Transport, 1 Tachihara Tsukuba, ttaraki 305-0802, Japan E-mail: fuji@kenken.go.jp 9.1. Feasibility Studies In the course of New RC project, feasibility of new structures utilizing high strength materials was studied in several cooperative research projects between the Building Research Institute and private sectors. Three kinds of such studies are introduced in this chapter: highrise flat slab buildings, megastructures, and a large size box column structure for thermal power plant. 9.1.1. Highrise Flat Slab Buildings Flat slab construction has an architectural advantage in providing large window openings or intensive underfloor piping because of no floor beams protruding down from the soffit of floor slabs. It is particularly advantageous for apartment buildings and hence it is widely used in many parts of the world. However it has not been used much in highly seismic countries such as Japan, because it is generally difficult to withstand seismic load solely by columns and floor slabs. This feasibility study was conducted to see whether fiat slab construction can be made acceptable in seismic zones by providing lateral stiffness and resistance with the use of structural walls. 391 392 Design of Modern, High-rise Reinforced Concrete Structures co © @ © © © © @ © •— (Y8) -ej- © © CD T LO ** LO * LO ^, LO tb-- ^r to ^r to • C7 • C4 • C5 • C6 , CO © © fa . |6.4| |5.4| |5.4| |6.4| , 1.8| 6.4 5.4 6.4 |1. 8 41 -8 Uint(m) Fig. 9.1. Highrise flat slab condominium with core walls. 50FL IMS s-1 i e !Wfra SSJt 45FL_ M& *K!32 JOFL^ -mw -taas 35FL» —- - - — 4&5u — ass <s>m tt^i wr -rwr* iSBH _30FL_ sfta 25FL_ •Bf .•ess 10FL_ TO" •ft". k&h w&B. sga. 15FL -pfl* 1-iES •gnus SfjK «™ IOFL SFL H^E 2FL_ IFL_ u lt(m? Y ^m °.tla= CiTIt B"-P Fr Fig. 9.2. Section of the building. Feasibility Studies and Example Buildings 393 Two types of highrise flat slab buildings were adopted as the object of this study. The first was a fifty-story flat slab condominium with structural core walls, and the second was a forty-story flat slab resort condominium with curved structural walls. They were both designed initially by using materials in Zone II—1 of Fig. 2.1, that is, the combination of ultrahigh strength concrete and high strength reinforcing bars. However it was found during the feasibility study that the use of ultrahigh strength re-bars was indispensable. Hence the target of material usage was changed from Zone II—1 to Zone III. 9.1.1.1. Highrise Flat Slab Condominium with Core Walls The first building, a highrise flat slab condominium of fifty stories, is shown in Figs. 9.1 and 9.2. One floor area is 2061 m 2 , and total floor area is 103 058 m 2 . Story height is 3 m except for the first story of 4.5 m. The total building height is 151.5 m. It has no basement. The foundation, assumed to be placed Table 9.1. Structural materials. Concrete Member Story Strength (MPa) 31-50 60 Columns, 21-30 70 Walls 11-20 80 Slabs, Girders 6-10 90 1-5 100 1-roof 60 Re-bars Member Slabs Grade Yield Points (MPa) SD345 345 Columns, Girders USD685 685 Wall (vertical) USD685 685 Wall (horizontal) USD980 980 Lateral Re-bars in Columns, Girders USD1275 1275 394 Design of Modern High-rise Reinforced Concrete Structures on the piles in the intermediate soil, is regarded outside the scope of the study. Table 9.1 shows the materials used for this building. As mentioned earlier, they belong to Zone III in the New RC material combination. The structure consists of flat slabs 250 mm thick, square columns ranging from 950 mm in the lower five stories to 800 mm in the upper 25 stories, core walls with thickness from 950 mm in the lower ten stories to 750 mm in the upper 30 stories, coupling girders which connect .L-shaped core walls with the same width as walls, and girders within the core 600 mm wide. Depth of all girders are uniformly 800 mm. Columns have no capitals, and slabs have Table 9.2. Typical structural member sections. F l a t Slabs Story Thickness Column Strip Middle S t r i p All floors 25 c m SD345-D13Q100 SD345-D13Q100 L - s h a p e d Walls Story Thickness 21-50 11-20 1-10 Vertical R e - b a r s Horizontal R e - b a r s 75 c m USD685-D35 Pg = 3.33% USD980-D13O150 Pw = 0.68% 85 c m USD685-D38 Pg = 3.75% USD980-D13<ai50 P „ = 0.70% 95 cm USD685-D41 Pg = 4.35% USD980-D16Q150 P „ = 1.12% Story Section Axial Bars 36-50 80 cm X 80 cm USD685-12-D35 Pt = 0.50% USD1275-4-D10Q100* P „ = 0.36% 16-35 85 cm x 85 cm USD685-12-D35 Pt = 0.53% USD1275-4-D10@100 Pw = 0.33% 11-15 90 cm x 90 cm USD685-12-D38 Pt = 0.56% USD1275-4-D13O100 P „ = 0.56% 6-10 90 c m x 90 cm USD685-16-D38 Pt = 0.70% USD1275-4-D13@100 Pw = 0.56% 1-5 95 cm x 95 cm USD685-16-D41 Pt = 0.74% USD1275-4-D13@100 P „ = 0.53% Columns Lateral B a r s Girders Lateral Bars Section Axial B a r s 22-R 75 cm X 80 cm USD685-10-D38 P , = 2.17% USD1275-4-D16@100 Pw = 1.06% 12-21 85 c m x 80 cm USD685-12-D38 Pt = 2.30% USD1275-4-D16@100 Pw = 0.94% 2-11 95 cm x 80 cm USD685-14-D38 Pt = 2.40% USD1275-4-D16Q100 Pw = 0.84% w / i n core 60 cm X 80 cm USD685-4-D32 Pt = 0.76% USD1275-4-D13@100 P „ = 0.85% Story "four legs in two ways Feasibility Studies and Example Buildings 395 no drop panels. Table 9.2 summarizes the reinforcement arrangement in the structural members. The structure is reasonably regular and uniform. The design criteria, summarized in Table 9.3, essentially conform with those for general New RC structures, as presented in Chapter 6. These design criteria were commonly applied to this building and the following resort condominium. Additional design criteria were adopted as needed for each building specifically. As related to the structural design of flat slabs, several points should be mentioned. The first is the protection against punching shear failure. The effective critical section was assumed at half depth away from the column surface as shown in Fig. 9.3, and an equation in the AIJ Reinforced Concrete Table 9.3. Design criteria for highrise flat slab buildings. External Force (design condition) Performance of Frame (walls, columns, girders) (1) w/in allowable stress Permanent Load Performance of Flat Slabs Deformation (capacity) (2) w/in allowable stress (3) vibration w/in rank 1 of evaluation standard* (4) w/in elastic limit (5) reusable after earthquake with minor repair, and vibration w/in rank 2 of evaluation standard* (6) story drift w/in 0.5% (8) reusable after earthquake with repair Level 2 Earthquake (7.1) walls: before flex, yield (7.2) columns: before flex, yield (7.3) girders: flex, yield permitted (9) total drift at centroid w/in 0.8% Design limit Deformation (11) walls: before (14) w/in limit deformation (15) horizontal ultimate capacity (aviod shear failure at capacity w/in connections) (12) columns, girders: 0.25 RtZ w/in limit Deformation (13) no hinges formed at unexpected positions Level 1 Earthquake "For explanation of ranks 1 and 2 of evaluation standard, refer to the text. 396 Design of Modern Highiise Reinforced Concrete Structures d/2 Cx d/2 d.effective depth of slab Fig. 9.3. Effective critical section of flat slab around a column. Standard (Ref. 9.1) was used for the safety evaluation against punching shear, where effect of both vertical shears and moments around the critical section was taken into account. The next item is the evaluation of flexural crack width under permanent loading. Crack width was calculated using the equation in the AIJ Structural Design Guideline for Prestressed and Reinforced Concrete (Ref. 9.2) which takes into consideration average steel strain and concrete drying shrinkage. Calculated crack widths were not to exceed the permissible value of 0.2 mm. The third item is the evaluation of deflection under permanent loading. An equation in the AIJ Reinforced Concrete Standard (Ref. 9.1) was used for this purpose, which accounted for cracking, creep, and drying shrinkage of concrete. Calculated values were not to exceed 20 mm nor 1/350 of span length. The fourth item for the flat slab design is the habitability, or serviceability in ambient vibration. According to the AIJ Guidelines for the Evaluation of Habitability (Ref. 9.3) the response of floor vibration due to human walk was analyzed by elastic finite element time-history analysis, assuming damping coefficient of 0.02 for floors. For the "new" structure prior to level 1 earthquake the result remained within the desired range of rank 1 response, and for the post-level 1 earthquake state it also remained within the range of rank 1 although the design criteria of Table 9.3 allowed rank 2 response in this case. Ranks 1 and 2 here refer to recommended (or more desirable) level and standard level of habitability, respectively. The guidelines (Ref. 9.3) indicate following examples of human senses for a stationary vibration of rank 1 Feasibility Studies and Example Buildings 397 of a floor: (1) in a living room or bedroom, nobody senses the floor vibration, (2) in a conference room, few people sense the floor vibration, (3) in an office, some people sense the floor vibration. For rank 2, the guidelines give following examples: (1) in a living room or bedroom, few people sense the floor vibration, (2) in a conference room, some people sense the floor vibration, (3) in an office, most people sense the floor vibration. The final item was the determination of effective width of flat slabs in the idealized frame in each direction. A three-dimensional finite element analysis was carried out and the result was compared with an equivalent planar frame analysis considering flexural and shear deformation and rigid zones around joints. It was found that effective width to span ratio varied with span length and location of flat slab within the building, that is, whether it is located within exterior frame, interior frame, or frames near the core walls, but did not vary much with the column size. The ratio was approximately from 0.45 to 0.60, most typically 0.50. Earthquake response analysis was conducted for levels 1 and 2 earthquake ground motions, using condensed model and more elaborate frame model shown in Fig. 9.4, both considering nonlinear restoring force characteristics condense 1 wall boundary beams condense frame A" 1 >f A \ A"" l~h £ & A a a"~ & a A A A A A — A A a •• a & A" A" A A A A 1 Fig. 9.4. ~~i a A A A A A " : A A A A - A ""A A A A A A' a A A A A"" «~~ A ' A Condensation from frame model to condensed model. 398 Design of Modern Highrise Reinforced Concrete Structures of members which were determined as follows. For the flat slab with the aforementioned effective width, Takeda model with the unloading stiffness index 7 of 0.9 was used. The L-shaped walls in the core were first analyzed by fiber models under static incremental loading, and Takeda model with 7 = 0.5 was determined by the best fit. For the columns and connecting girders, Takeda model with 7 = 0.4 was used. Table 9.4 summarizes natural periods in the elastic range for frame model and condensed model. For five kinds of input earthquake motions of levels 1 and 2 intensity, response of condensed model showed the same trend of larger response values for two kinds of New RC motions (synthetic ground motions developed in New RC project). Frame model was analyzed for these two waveforms only, and all the response values stayed within the prescribed design criteria. The maximum response structural drift at the centroid of lateral forces under level Table 9.4. Natural periods. Mode 1st 2nd 3rd 4th 5th Frame Model (second) 3.89 1.10 0.54 0.33 0.23 Condensed Model (second) 3.98 1.14 0.55 0.34 0.23 0.1 based on upper bound strength based on dependable strength \ 0.08 -—~~~ \ C„=0.25Rf ^ 0.06 0.04 response drift limit 0.8% 0.02 design drift limit / 50 1.3% 1 100 V . 150 200 250 centroidal deflection 8 (cm) Fig. 9.5. Static push-over analysis with response drift limit and design drift limit. Feasibility Studies and Example Buildings 399 2 earthquake motion was 0.73 percent for New RC 01 waveform. The response drift limit was determined to be 0.83 percent to cover this maximum response. Static push-over analysis was carried out as shown in Fig. 9.5, and the design drift limit of 1.30 percent was determined from the double-energy criteria as explained in Chapter 6. At this design drift limit, the base shear coefficient based on the dependable material strength was 0.0727 which exceeded the design criterion of 0.25i?t' which was 0.0650. Maximum ductility in the coupling beams and flat slabs are 3.6 and 2.0, respectively. The building was also analyzed for earthquake input in the 45 degrees direction. Under static push-over analysis, the base shear at the design drift limit under diagonal loading exceeded that under parallel loading by 27 percent. Dynamic response values in the diagonal direction are generally similar to, or in some cases smaller than, those in the parallel direction. Thus it was shown that a 50 story flat slab building with core walls was a feasible structure using New RC material. However several problems were pointed out during the course of this feasibility study. The first was that the restoring force characteristics of flat slabs were determined by empirical equations from experimental data for ordinary strength materials which might be different from high strength materials. The second was that there was a need for more experimental data for the behavior of L-shaped walls. The third point was that the condensed model developed for this building did not quite successfully simulate the response of frame model which could be regarded too complicated for practical purposes, hence development of practically accurate and simple model was desired. 9.1.1.2. Highrise Flat Slab Condominium with Curved Walls The second building for the feasibility study, shown in Figs. 9.6 and 9.7, is a highrise flat slab resort condominium of forty stories. One floor area is 1440 m 2 , and total floor area is 57600 m 2 . Story height is 3 m with the exception of the first story of 6 m, and the total building height is 123 m above ground. It has no basement. The structure consists basically of flat slabs 250 mm thick and structural walls 400 mm thick except for the first story where walls are 600 mm thick. In addition the exterior wall of service core is made into a curved shape with flanges, called "hyper-wall", and is connected to the main structure at three levels with so-called "superbeams", having the depth of 3 m, that is, one story 400 Design of Modern Highrise Reinforced Concrete OIL) : | » | " | 7-oon I Structures \ (c) upper floors typicol floors/ floors above super beams ±^r j (A) X^ h yper- wall super b JJffiLi k't 61»6 (b) middle and lower floors © I » I r3s.QQp I " I '-"nil I I ©<*)<£> I © (a) ground floor Fig. 9.6. Highrise flat slab building — a resort condominium. Feasibility Studies and Example Buildings 401 look—out restaurant -(-123m 40F ' ' mesonette j unit units skj£jounge_ 27F mesonette unit super beam hyper—wall units sky lounge 14F mesonette unit super beam units entrance hall AD_j P) Fig. 9.7. ® IAD 1J i_i2.0 (A) Section of the building — a resort condominium. high. This structural planning provided a variety of architectural possibilities in addition to flat slab, such as wide frontage of condominium rooms to enjoy open view, sky lounge or sky discotique above the superbeams, mesonette (two-storied) units at stories of superbeams (which block the hallway) to 402 Design of Modern Highrise Reinforced Concrete Structures increase the variety of dwelling units, exterior surface of hyper-wall used as sign board or large screen for outdoor events. At the same time the structural planning gave rise to several structural design problems. Walls arranged into various directions and curved hyper-wall were intended to prevent torsional vibration, but they required three-dimensional analysis against seismic ground motion in any directions. A megastructure composed by superbeams connecting the main building and hyper-wall required development of a suitably simplified model for earthquake response analysis, and a more complicated model for static structural analysis. Walls in the first story had to have large openings to provide open spaces for entrance reception, lounge and restaurant, and the structural effect of large openings had to be investigated in full detail. Table 9.5 summarizes the material to be used for this building. Like the previous example of a flat slab structure, this building also utilizes material in Zone III of Fig. 2.1, concrete up to 100 MPa compressive strength and main bars in walls, columns and superbeams of 980 MPa yield point. The structural design criteria were essentially same as those in Table 9.3 for general New RC buildings, with several additions specifically for this building. The design for gravity loading follows the same principle of allowable stress Table 9.5. Structural materials. Concrete Member Walls, Columns, Superbeams Flat Slabs Story Strength (MPa) 28-40 60 22-27 70 15-21 80 8-14 90 1-7 100 1-roof 60 Re-bars Member Size Grade Walls, Columns, Superbeams D28, D32, D35, D38 USD980 Shear Reinforcement D16 USD1275 Flat Slabs D19 SD490 Beams D22 SD345 Feasibility Studies and Example Buildings 403 design as for general RC buildings. In other words the high strength of materials used for this building has no particular advantage. The check for allowable shear stress was substituted by the check for shear cracking. In addition to the conventional design for gravity loading, the floor slab vibration was required to remain within the severest criterion of rank 1 of the Evaluation Guidelines for Habitability by AIJ (Ref. 9.3). The design for level 1 earthquake motion is basically same as Chapter 6. Walls and columns must remain essentially within the elastic limit. Elastic limit is defined by maximum concrete strain on the compression fiber or steel yield strain in the outermost re-bar in tension. Superbeams which couple two shear walls and other coupling beams subjected to stress concentration may yield, up to the ductility factor of 2.0. As for flat slabs, residual crack width after the level 1 earthquake is to be controlled in order that the structure is serviceable after a light amount of repair works. For this purpose the response deformation at the slab-wall connection was limited so that the residual crack width remains within certain permissible value. Experimental works carried out for this feasibility study were referred to in establishing relationship between the deformation angle and residual crack width. The yield deformation of flat slab-wall connection is very large, to be about 2 to 3 percent in terms of drift angle, so the crack width control is more critical. The effective width of floor slab is to be determined by static elastic analysis. In addition the floor slab vibration after the level 1 earthquake was required to remain within rank 2 of the Evaluation Guidelines (Ref. 9.3) after the light repair work such as epoxy injection. The design for level 2 earthquake motion is more conservative than Chapter 6. Considering that walls carry essentially all the lateral load due to earthquake, no yield hinges are allowed at the wall base. Also no yield hinges are allowed in the columns considering high level of axial load. Wall coupling beams, on the other hand, may yield under level 2 earthquake motion, but its deformation should remain within the ultimate deformation limit. The overall deformation of building is limited as shown in Table 9.3, which is same as Chapter 6. This will automatically protect flat slab-wall connection from yielding. The criteria associated with the ultimate limit under static push-over analysis are same as in Chapter 6. In carrying out structural analysis as well as response analysis, the direction of loading must be carefully considered because of uneven arrangement of walls. Four directions shown in Fig. 9.8, including two principal axes of X and Y, were chosen as representative directions. It turned out that principal axes were the most fundamental in representing the stress and deformation in any direction. 404 Design of Modern Highrise Reinforced Concrete Structures Fig. 9.8. Direction of loading. Fig. 9.9. Space model of linear elements. Figure 9.9 illustrates the three-dimensional frame model composed of linear vertical elements for each wall and linear horizontal elements for fiat slabs. Effective width of flat slab was determined from the finite element (FEM) analysis. Table 9.6 shows natural periods of vibration for first four modes in the direction of two principal axes. Numbers in parentheses indicate natural periods determined from the FEM analysis. The first mode periods are in reasonable agreement. Feasibility Studies and Example Buildings 405 Table 9.6. Natural periods of linear model [FEM Model in ( )]• Longitudinal (X) Transversal (Y) Ti = 2.077 s e c o n d (2.173 s e c o n d ) T 2 = 0.592 (1.454) T 3 = 0.296 (0.834) T 4 = 0.177 (0.575) rp f-\ -I q y o s e c o n d '^•r'ysecond's T 2 = 0.483 (0.431) T3 = 0.220 (0.207) T4 = 0.126 (0.200) Earthquake response analysis was carried out using mass-and-spring models consisting of equivalent shear springs and equivalent torsional springs. Two floors above and below superbeams, connecting the main building with the hyper-wall at three levels, were concentrated into a single mass, hence the 40story building was idealized into 37 masses. The restoring force characteristics of each spring was assumed to be bilinear, connecting the flat slab cracking point and the deformation associated with base shear coefficient of Co = 0.25. Damping of 3 percent for first mode and 4 percent for second mode was assumed to define a Rayleigh-type damping. Two synthetic waves, introduced in Chapter 6, were chosen and assumed in four direction in Fig. 9.8. Both level 1 and 2 responses were found to satisfy all the design criteria depicted in Table 9.3. Flat slabs with 25 cm thickness were found to be satisfactory for both serviceability and seismic safety. D19 bars at 200 mm on centers are to be provided in two directions, top and bottom. The natural frequency in elastic range was about 10 Hz, and that after level 1 earthquake was about 6 Hz, both of which happened to be within rank 1 of the Evaluation Guidelines. Among walls, the most intensively stressed portions were found to be in the first story, notwithstanding the wall thickness increased to 600 mm from 400 mm in upper stories. Figure 9.10 illustrates bar arrangement in some part of the first story walls. Thus, it was shown that a 40-story flat slab building with shear walls was a feasible New RC building in seismic zones. By conducting structural as well as response analyses in four directions, major structural members could be 406 Design of Modern Highrise Reinforced Concrete Structures key plan (1 st story) wall in line C, 1st story wall with opening, 1st story 600 15-D38 hoop:D16D-@100 vertical : 48-D38 ( Pg = 2.1% ) hoop:D16D-@100 (Pw = 0.66% ) vertical : D19-@200 double horizontal : D16-O200 double horizontal : D16-9200 double (Pw = 0.33% ) 3,000 J Fig. 9.10. Sections of 1st story walls. shown to be proportioned in the practically reasonable dimensions. Under two levels of earthquake motions, major structural members with the exception of superbeams remained within the elastic limit, and flat slabs maintained their serviceability. It should be mentioned that the experimental works carried out in conjunction with this study gave helpful evidence of satisfactory performance of flat slab-vertical member connections within the deformation range assumed in the design. The use of high strength materials enhances the strength of the structure, and increases the possibility of remaining within the elastic limit even under the severest earthquake motion for design. Feasibility Studies and Example Buildings 9.1.2. 407 Megastructures Megastructure usually means a structure composed of members much larger than usual, both in length as well as in sectional dimensions. Combined with secondary members of much smaller size, a megastructure gives dynamic appearance to the architecture. In the past, this concept had been applied only to steel structures. Reinforced concrete megastructures had never been attempted probably because of excessive weight. In the course of feasibility studies possibility of reinforced concrete megastructure was explored, with the new idea that a megastructure might be utilized as the artificial ground — that is, a megastructure is to offer the base for lowrise buildings to be constructed atop each floor of the megastructure. Much longer lifetime is expected to such a megastructure, possibly of centuries long, hence reinforced concrete becomes the most desirable construction material. Six buildings were proposed and studied. They are shown in Figs. 9.11 to 9.16. 9.1.2.1. OP200 Straight Type The megastructure in Fig. 9.11 is called OP200 Straight Type. It consists of straight single span open frames in two directions with five stories. Total height is 200 m. Hence the height of one megastory is 40 m, more than enough to accommodate 8 story substructure on each mega-floor. Floor plan is 40 m square. At four corners L-shaped mega-columns are located, whose size is 6 m x 6 m with 2 m thickness. Mega-girders are rectangular 2 m x 6 m section. The service core at the center of the mega-floor has wall thickness of 800 mm, and is supposed to carry vertical load, but no horizontal load. Substructures are to be made of steel frames. Average normal stress of gravity loading at the bottom section of the first story column was estimated to be 10.1 MPa. Concrete with compressive strength of 100 MPa and steel with yield srength of 1200 MPa are used. The base shear coefficient for seismic design is 0.05, and the maximum response shear for level 2 earthquake motion is 0.090 with drift angle of 0.88 percent. Fundamental natural period is 3.4 second. At the design seismic deformation limit, the maximum normal stress in the column is 22.3 MPa and the base shear coefficient is 0.101. This base shear coefficient at the design deformation limit is larger than the following OP300 Straight Type, due to the 408 Design of Modern Highrise Reinforced Concrete Structures r-" \ * — l JJ 1W IP ll 1—. *± :_::~ 3 40000 plan <0.000 elevation Fig. 9.11. OP200 Straight Type. fact that larger safety margin was assumed for OP200 Straight Type considering it was supported by only four columns at the corners of mega-floors. 9.1.2.2. OP300 Straight Type The megastructure in Fig. 9.12 is called OP300 Straight Type. It has 8 columns along the periphery of 56 m square mega-floors, forming two span open frames in two directions. It consists of five megastories, each 60 m high, and the total building is 300 m. Each mega-floor accomodates up to 13 story substructure of steel construction. The first megastory has K-braces on each face to eliminate central columns. Feasibility Studies and Example Buildings 409 28a | 28m 56m elevation Fig. 9.12. OP300 Straight Type. Mega-columns are 5.5 m square, with solid cross section for central columns and with 1.5 m thick box section (2.5 m square hollow space) for corner columns. Mega-girders are also box section of 5.5 m x 9.0 m with 1.5 m thickness, if-braces in the first megastory is 5 m solid square section. Average normal stress of gravity loading at the bottom section of the first story column is 17.5 MPa. Concrete with compressive strength of 120 MPa and steel with yield point of 1200 MPa are to be used. The design shear coefficients for seismic design of upper stories correspond to base shear coefficient of 0.05, but the first story is designed for shear coefficient of 0.17 considering high stiffness of braced structure. Fundamental 410 Design of Modern Highrise Reinforced Concrete Structures natural period is 5.0 second, and at the design seismic deformation limit the maximum normal stress in the column is 46.9 MPa and the upper story shear coefficients correspond to base shear coefficient of 0.078. 9.1.2.3. OP300 Tapered Type The megastructure in Fig. 9.13 is called OP300 Tapered Type. It is again single span open frames in two directions, but the floor plan varies from 48 m square at the roof to 60.8 m x 73.6 m rectangle at the base, forming a tapered (trapezoidal) elevation. The total height is 300 m with five megastories, each of which accomodates 12 or 13 story steel substructures. Height to base width ratios are 4.69 in the short direction, and 3.75 in the long direction. G L. +600m elevation Fig. 9.13. OP300 Tapered Type. Feasibility Studies and Example Buildings 411 L-shaped mega-columns are located at four corners, whose size is 10.35 m x 10.35 m with 1.5 m thickness. In proportion they are almost L-shaped walls. Mega-girders in the lower two stories are 1.5 m wide and 12 m deep, and those in the upper three stories are 1.5 m wide and 8 m deep. The service core at the center of floor plan has vertical members to carry vertical loads only. Average normal stress of gravity loading at the bottom section of the first story column is 28.2 MPa. Concrete with compressive strength of 120 MPa and steel with yield point of 1200 MPa are assumed. The tapered shape was shown to be effective in resisting earthquake. The design base shear coefficient is 0.04. The level 2 response drift remains under two-thirds of a percent. Fundamental natural period is 6.1 second in the short direction, and 5.6 second in the long direction. At the design seismic deformation limit, the maximum normal stress in the column is 45.2 MPa, and the base shear coefficient is 0.062. RFL 20.0 46H 20.0 m 41FI ^ 36fl ^ 31fl ^ 20.0 20.0 20.0 26FI 20.0 21FL ^ 16fL ^ Uft ^ 6FI ^ 20.0 <5.0 20.0 10.5 20.0 LL.LUr 10.51 24 . 0 45.0 |10. 5 20.0 1FI plan elevation Fig. 9.14. BR200 K-brace Type. 412 Design of Modern Highri.se Reinforced Concrete Structures 9.1.2.4. BR200 K-brace Type The megastructure in Fig. 9.14 is called BR200 if-brace Type. It has eight mega-columns, forming two single span frames of 45 m long and 24 m apart, independently in two directions. It consists of ten megastories, each 20 m high for five story steel substructures, with the total height of 200 m. Frames in two directions have AT-braces in each story, placed inside the building space. They transmit major portion of gravity load to the column, thereby easing the stress in the mega-girders due to gravity loading. Braces also carry major portion of seismic loading. By the independent arrangement of frames in two directions, each mega-column is subjected to forces from unidirectional seismic loading only. Size of mega-columns vary from 1.8 m x 2.8 m in the first story to 1.2 m x 2.0 m in the top story. Mega-girders are 1.0 m x 2.5 m, and braces vary from 0.9 m x 1.0 m in the first story to 0.6 m x 1.0 m in the top story. Average normal stress due to gravity loading at the bottom section of the first story column is 25.2 MPa. Concrete with compressive strength of 100 to 120 MPa and steel with yield strength of 1200 MPa are to be used. The design base shear coefficient was selected to be 0.179 referring to the level 2 seismic response analysis. Because it is a braced structure and has relatively high lateral stiffness, the selected value is the highest among six megastructures. The level 2 response drift was less than 0.7 percent, causing no yielding of steel. The fundamental natural period is 3.6 second. At the design seismic deformation limit, the maximum normal stress in the column is 80.4 MPa, and the base shear coefficient is 0.189. 9.1.2.5. BR200 D-brace Type The megastructure in Fig. 9.15 is called BR200 Z?-brace Type (D stands for diagonal). It has eight mega-columns around 45 m square mega-floors, and ten mega-girders along the height of 200 m, forming ten story two span frames in two directions. One brace is placed in each story of a frame as shown in Fig. 9.15, and another one in the opposite direction in each story of the parallel frame. This arrangement guarantees symmetric force-displacement relationships under positive and negative lateral loading. Braces in the orthogonal direction are arranged so that symmetric force-displacement relationship is maintained under rotational loading. In other words, braces in two adjacent faces come to the corner column at the same height. Feasibility Studies and Example Buildings 1 413 T T T T ' TTTTTT j 22.5 f m 22.5 45 0 plan, typical floor 8 22.5 22.5 — • « | + 1 r\& mm w :_ - _j^ — 22.5 22.5 H 45.0 plan, mega-floor 22.5 22.5 45.0 elevation Fig. 9.15. BR200 D-brace Type. Mega-columns at corners are 2.6 m square and those at the midspan are 2.2 m x 3.0 m rectangle. Mega-girders are 1.75 m x 4.4 m rectangle. Braces are made of composite steel and RC, having 1.05 m square cross section. The building has core walls around the central service core to carry the vertical loads only. Substructures of three to four story on each mega-floor are constructed by steel structure, and supported by steel trusses under mega-floors. Average normal stress of gravity loading at the bottom section of the first story column is 22.0 MPa. Concrete with compressive strength of 100 MPa, reinforcement with yield point of 800 MPa, and structural steel of SM490A (JIS G 3101) are to be used. 414 Design of Modern Highrise Reinforced Concrete Structures The design base shear coefficient was determined to be 0.0854 from level 1 response analysis. The response under level 2 earthquake reached the base shear coefficient of 0.135, with the maximum story drift of about 0.4 percent. Similar to other megastructures, no yielding was initiated under level 2 earthquake. The fundamental natural period is 2.8 second. The maximum normal stress in the column at the design seismic deformation limit is 56.0 MPa, and the base shear coefficient at the same limit is 0.184. 9.1.2.6. BRZ00 X-brace Type The megastructure in Fig. 9.16 is called BR300 X-brace Type. It consists of six megastories of 50 m high for steel substructure of 10 to 12 stories, with the total building height of 300 m. It has two mega-columns on each face of 60 m square mega-floor, 38 m apart. Mega-girders connecting these mega-columns have thus 1 1 m cantilevers at both ends, which help reduce the gravity moment at the midspan. X-type braces are located between the two mega-columns on each face. Braces carry major portion of lateral loads, and floor girders connecting opposite mega-columns, made of structural steel, are pin-connected to megacolumns not to carry lateral loads. Other floor girders connecting opposite mega-girders are also pin-connected to avoid torsional effect on the megagirders. Mega-columns on the adjacent sides of a floor corner are connected by diagonal girders to produce three-dimensional stiffness and strength. Size of mega-columns is 3.0 m square except for upper two stories where the size is reduced to 2.8 m square and 2.5 m square. Mega-girders are all 2.0 m x 8.0 m. X-type braces are made of concrete-filled steel pipes of 2.0 m diameter except for upper two stories, where the diameter is reduced to 1.8 m and 1.5 m. Average normal stress due to gravity loading at the bottom section of the first story column is 29.9 MPa. Concrete with compressive strength of 120 MPa, main bars with yield strength of 1200 MPa, and lateral reinforcement with yield strength of 800 MPa are to be used. The design base shear coefficient was determined to be 0.08. The preliminary response analysis for level 1 earthquake motion showed that the design base shear could be taken as 0.04, but it was increased to twice as much by engineering judgment. The maximum response for level 2 earthquake motion was 0.118 in terms of base shear coefficient, and about 0.4 percent in terms of maximum story drift. No yielding occurred. The fundamental natural period is 5.8 sec, which is the longest among six megastructures. The maximum Feasibility Studies and Example Buildings 415 1-rN t— 1 —1 t--I. !1 1— u 1 1 plan, typical floor a j^ plan, mega-floor elevation Fig. 9.16. BR300 X-brace Type. normal stress in the column at the design seismic deformation limit is 76.9 MPa, and the base shear coefficient at the same limit is 0.119. 9.1.2.7. Concluding Remarks By comparing six megastructure buildings and their seismic design, following concluding remarks could be made. 416 Design of Modern Highrise Reinforced Concrete Structures The aspect ratio, or height-to-width ratio, of buildings ranges mostly from 4.5 to 5.0, which is about the same as commonly constructed highrise buildings in Japan. The largest number of aspect ratio is 6.0. On the other hand the height-to-width ratio of one megastory is about 1.0 in one group, and about 0.5 in another group, the latter being BR200 if-brace and BR200 D-brace types. Reinforced concrete is used to most parts of megastructures, except in some cases steel trusses are used for floor girders of megastory. Braces in three braced buildings are designed by using different materials, namely reinforced concrete, composite steel and reinforced concrete, and concrete-filled steel pipes. Steel structure is adopted to most substructures, chiefly in order to reduce dead weight. Various methods are applied for the load transfer from substructures to megastructures. However, it should be noted that the detailing of structural member joints was not fully studied in general. High strength materials are required to most buildings up to the highest limit of material range prescribed for the New RC project, namely up to 120 MPa for concrete and up to 1200 MPa for steel. Design for gravity loading presented a common problem to all megastructures. Due to large column spacing which was required for a versatile architectural use of megastories, span length of mega-floor girders become very long. Reinforced concrete is used for girders connecting mega-columns, but high strength of materials cannot be fully utilized in the design for gravity loading. It will be easily understood when one thinks of cracking or deflection limit state. Thus the design of long span reinforced concrete girders for gravity loading became a common problem to be further studied in future. Each megastructure building was designed with some kind of devices for gravity loading in structural planning. They include the use of subcolumns that carry vertical load only, the use of central core to resist dead load only, relocation of mega-columns from corners to the inside of span with exterior cantilevers, or increased number of mega-columns. Average normal stress of gravity loading at the bottom section of first story columns is described for each building, which ranges from 10.1 to 29.9 MPa, all satisfying the common criterion of one quarter of concrete strength. Seismic safety of all six buildings was checked by the same process. First, static incremental load analysis was conducted. Mass-and-spring dynamic analysis model was constructed based on the static analysis, and it was subjected to several earthquake motions of levels 1 and 2 intensity. For some examples frame analysis was conducted to earthquake response. All megastructures Feasibility Studies and Example Buildings 417 remained in the pre-yield stage in level 2 response. Thus the megastructures sustained the elastic state, implying very narrow crack width remaining after a level 2 earthquake. Response deformation limit was defined at a deformation level covering all level 2 response, and twice the potential energy of load-deflection curve as that for this limit was used to define the design deformation limit. Structures were checked at the design deformation limit if there were any defect or excessive local strain at any part of the structure. This process, as described in Chapter 6, was created for New RC structures of Zone I material combination, but it was shown here to be applicable to structures of Zone III material combination. Natural periods for the fundamental mode, as described before, were shown to be from 2.8 to 5.8 second, the maximum compressive stress in the column at the design deformation limit ranged from 22.3 to 80.4 MPa, and the base shear coefficient at this limit ranged from 0.062 to 0.189. This implies that these design parameters vary considerably according to the structural planning of megastructures. Fig. 9.17. Box column thermal power plant. 418 Design of Modern Highrise Reinforced Concrete 9.1.3. A Box Column Structure Structures for Thermal Power Plant A recent trend in the design of thermal power plant is to arrange boiler, turbine, desulfuring and denitric equipments and so on, into a vertical array, and to make an effective use of the land. An example of such power plant is shown in Fig. 9.17. For the feasibility study of using New RC materials to this type of structure, a power plant building, which elevations are shown in Fig. 9.18, was designed. The building is 100 m high, consists of four box reinforced concrete columns of 10 m square, supporting steel top girder grill. At the center of this top girders is the boiler hanging. Figure 9.19 shows the plan of the foundation and four box columns, and Fig. 9.20 shows the plan of the top girder grill. It has cantilevers on one side of the square plan, and Fig. 9.21 illustrates the section of the building including this cantilever. Unlike feasibility studies in the preceding two sections, this study aimed at the more practical feasibility. Hence the material selected for this study was 60 MPa concrete and SD 685 steel. In other words, they were selected from the Zone I material range. For the top girders, structural steel of grade SM570 was used. electric precipitator |\ /t\ /l\ / I electric precipitator boiler bldg. lj turbine bldg. ® ® ® HBiaioooa irao ® © ® Fig. 9.18. Elevations of the building. ® msn lonool aa © © © Feasibility Studies and Example Buildings 1Q250 10250 10250 10230 foundation girder D=3.0m_ foundation girder D=7.5m 6 5 3 2 CGI Fig. 9.19. Plan of foundation. " O 1 ® 1 =3, m Gl m 1 °, ! O 0 Ui 8 O 1 Gl 8 8 O Ui I 1" 0 =§. 1 : i 8 8 "8 G1A © G1A © 10000 © 35500 © Fig. 9.20. 10000 © Plan of top girders. © 419 Design of Modern Highrise Reinforced Concrete Structures _S2_ _£Q1_ VFLJ-HOOO VFL«0 T¥ Fig. 9.21. A-A section of the building. vertical horizontal /~~ bars y ^ b a r s level FL(m) III 420 vertical horizontal 50 2-D35O200 2-D25O200 60 2-D32@200 2-D25@200 70 2-D32@2O0 2-D29O200 70 2-D35@200 2-D29O200 reinforcement 99.4 83.9 thickness 83.9 41.0 41.0 29.0 10000 29.0 0.0 grade: vertical SD685 horizontal SD390 Pig. 9.22. Plan and reinforcement schedule of box columns. Feasibility Studies and Example Buildings 421 CndeSM570 mark GO position end G1A Cl cent. end cent eti4 cent. 03 through G3 CGI CG2 through fixed end fixed end g 8 ~ "= g | I | 1 | I I section "^ U Heel In»l UsJ """ bad [ml U u bad "*" "*" boJ Lml BH.3500XKU BH- 5000X100 BH-3J0OXMO BK-60OOX9O0 BH-35O0X9O0 BH-MO0X900 BH-1KOXKOX50XJ25 •HOJOOXWOX » X | O 0 BH-3500XIOOXJOX1M BH-JKUXIMXWXIOO XSOX100 X40*M x N X 123 XWX1O0 X 5OX10O Fig. 9.23. Schedule of top girders. Figure 9.22 summarizes the section of box columns. Its outside measurement is 10 m square, and the wall thickness varies from 700 mm at the base to 500 mm at the top. These box columns have many openings in the wall, and the reinforcement shown in Fig. 9.22 was determined by the proportioning of a column with the largest openings. Figure 9.23 illustrates the schedule of top girders. Girders are made of builtup I sections with the depth of 3.5 m. GO girders suspending the boiler and Gl(GlA) girders holding GO girders have midspan depth of 6 m. The portions of top girder grill that rest on the box columns are called crown elements, which have to be rigidly connected to the top of box columns. For this purpose the wall thickness at the top of box columns is increased from 500 mm to 1200 mm, and anchor bolts of SD685 with D51 size, 200 mm on centers, are embedded in the wall. Crown element itself is 3.5 m deep, consists of flanges 950 mm wide and 125 mm thick and web plates 80 mm thick with stiffners and rib plates. For the anchorage of high strength steel anchor bolts, use of anchor plates or splicing to wall bars are temporarily considered, however its detail is yet to be developed. Also it is desirable to increase the stiffness of crown elements to avoid stress concentration at the corners and to evenly distribute the reaction forces. This is another points to be explored in future. Foundation of the structure is to be supported by cast-in-place concrete piles. The plan shown in Fig. 9.19 illustrates arrangement of 1.5 m diameter piles, which was determined by assuming an imaginary site with relatively deep bed rock. Footings measure 20.5 m square or 17.5 m square, both 7.5 m deep, and foundation beams have 12 m x 7.5 m section. It is considered necessary in future to investigate means to reduce amount of material for the foundation, to investigate the evaluation method of pile group effect including proper pile 422 Design of Modern Highrise Reinforced Concrete Structures arrangement, alternate use of continuous underground walls in place of castin-place concrete piles. Design seismic forces were determined independently to four box columns from the preliminary response analysis. Design shears and design moments were independent as they do not necessarily act on the box columns simultaneously. Design stress distribution for top girders and box columns were analyzed using linear elements for members and plate elements for joints. In addition to gravity loading and seismic loading, stress distribution for gravity loading considering the erection progress was also analyzed. Rigidity of connection between top girder crown elements and anchor bolts to box columns was a concern from the early stage of the feasibility study. An additional analysis using a model with spring elements between crown elements and box columns showed that the flexibility of connection did not affect very much on the stress distribution in the top girders, crown elements and box columns. Top girders hanging the boiler will be subjected to considerable effect of vertical earthquake motion. Dynamic response analysis was conducted for Hachinohe UD waveform corresponding to level 2 intensity. It was shown that the top girder end moment increases due to vertical response by 10 to 20 percent from the values due to horizontal response. Top girders were designed to remain elastic even under the combined effect of vertical motion. Another consideration was the effect of temperature change of box columns and top girders. It was shown that the temperature effect was negligible as it increases the member forces not more than 2 percent from the design values. Earthquake response analysis was conducted against four waveforms using base-fixed model and sway-rocking model considering deformation of piles. Input waves were assumed to act in x- and y-directions, as well as in the 45 degrees direction. Design criteria to evaluate the response analysis results were set to be similar to those in Chapter 6. This was determined after the following consideration. On one hand this structure is composed of only four columns and is basically a single story structure, hence the degree of statical indeterminateness is low, which may lead to more conservative design criteria. On the other hand the structure is used as power plant, supporting boiler and other equipments, and no heavy human or furniture occupancy is expected. Considering these two contradicting factors to influence on the decision of design criteria, it was concluded to adopt similar criteria as for general highrise residential or office buildings, or those in Chapter 6. Feasibility Studies and Example Buildings 423 Response drift under level 1 earthquake motions in x- and y-directions fell well below the design criterion, being 0.15 to 0.27 percent. Box columns and top girders did not show any yielding under level 1 input. It is anticipated from the box column deformation that columns would not even crack at this stage. Response drift under level 2 earthquake motions, being 0.40 to 0.72 percent, also satisfied the criterion. Box column reinforcement did not yield, but yield hinges were formed at the ends of top girders. The rotation angle of column bottom of 0.38 percent corresponds, according to the experiments mentioned later, to fiexural cracking with steel strain about half-way to yielding. Response under level 1 and 2 earthquake motions in the diagonal direction was essentially similar to that in the x- and y-directions. Strain in the re-bars of box columns was higher, but it was still in the elastic range. Top girders produced yield hinges, but the stress was lower than the previous case. Analysis of sway-rocking model showed slightly larger response drift, but still conforming to design criteria. Elastic behavior of box columns and formation of yield hinges at top girder ends were also similar to those of base-fixed model. Finite element static analysis of box columns was conducted to investigate effect of openings to the overall stress distribution and also the local stress concentration around openings. The overall stress distribution significantly changes due to openings, and it could not be corrected by providing additional reinforcement around openings. Hence it is necessary to evaluate overall stress distribution considering the size, shape, and distribution of openings. Openings are to be provided with additional periphery reinforcement, and it is generally understood that the periphery reinforcement improves the structural behavior after cracking, but it does not prevent cracking itself. From the FEM analysis, concentrated arrangement around the periphery is found to be more effective for stiffness as well as strength than the diffusive arrangement. Also it was found that cracking at the opening corners did happen at the early stage of loading, but it did not lead to the re-bar yielding, and overall stiffness and strength were not affected very much. Experimental works were also conducted of two box column specimens in 1/7 scale, that is 1.4 m square and 4.2 m long, and they were subjected to bidirectional reversal of loading, one in 0 degrees-90 degrees directions, and another in 45 degrees-135 degrees directions. They behaved elastically up to deformation drift of 0.12 percent, and bar yielding was initiated at drift of 424 Design of Modern Highrise Reinforced Concrete Structures 0.5 to 0.75 percent. The specimen in 0 degrees-90 degrees directions failed by a sudden crushing in the compression flange at the side of opening at the box column base. The failure occurred after the maximum load of 942 kN was reached, at the deformation drift of 1.39 percent, without being accompanied with the strength reduction. The specimen in 45 degrees-135 degrees directions showed concrete crushing at the box corners, then shear compression failure progressed gradually, maximum load of 939 kN being observed at drift of 1.05 percent. Both of them showed 5-type load-deflection curves under load reversal, with relatively small hysteresis loop area, or in other words small energy absorbing capacity. Observed damage and failure at various deformation stages were directly useful in evaluating the structure's behavior under levels 1 and 2 earthquake input. Finally, method of construction should be mentioned. Two most important construction stages are the construction of box columns and the erection of top girders including crown elements. Several construction methods for these two stages were selected and compared. As to box column construction, both slip forms and jump forms were found to be applicable, with slight advantage of slip forms in the reduction of construction period. The erection of top girders are to be as follows. Top girders together with cantilever portions and divided crown elements are up-lifted first, then slided laterally at the column top, jacked down to the position, connected together and to the anchor bolts, and then central portion of top girder grill is lifted up. Such construction process is judged to be the most superior in terms of quality control, cost, construction period, and construction safety. Thus it was concluded that a thermal power plant boiler building utilizing reinforced concrete box columns, 10 m square and 100 m high, was a feasible structure with the use of material combination of Zone I of New RC project. 9.2. Example Buildings This section of Chapter 9 summarizes construction examples to March, 1997, of buildings utilizing high strength concrete and high strength steel that were explored in the New RC project. As early as 1992-1993, the last fiscal year for the five-year New RC project, a building with concrete strength of 60 MPa and USD685 steel for column axial core bars was designed, and subjected to review of the Technical Appraisal Committee for Highrise Buildings of the Building Center of Japan. Table 9.7 summarizes all buildings using either high strength concrete in excess of 48 MPa or high strength reinforcement in Feasibility Studies and Example Buildings 425 Table 9.7(1). Buildings that passed the technical appraisal. No. Name of Building Structural Design Date of T.A. No. of Story Height Max Strength of Materials 1 Viraton Shima Hotel Taisei Construction Co. Feb. 1992 38 story 133.85 m 60 MPa SD390 2 Ebina Prime Tower Shimizu Construction Co. Mar. 1992 25 story 107.80 m 60 MPa SD490 3 The Garden Towers Taisei Construction Co. July 1992 39 story 125.30 m 60 MPa USD390 4 The Scene Johoku Kajima Construction Co. Sept. 1992 45 story 160.00 m 60 MPa USD685 5 Gran Corina Seishin-Minami Takenaka Construction Co. Dec. 1992 22 story 68.25 m 60 MPa SD490 6 Hankyu Hills Court Takatsuki Obayashi Construction Co. Feb. 1993 20 story 63.90 m 60 MPa SD490 7 Ship Residence N T T Design, Nissoken Design, Kajima Construction Co. Mar. 1993 28 story 88.35 m 42 MPa USD685 8 Seiyo Hasune Project Obayashi Construction Co. May 1994 41 story 126.00 m 60 MPa SD490 9 Ikeshita Redevelopment Building B Konoike-KokedoPudo JV June 1994 26 story 88.30 m 60 MPa SD490 10 Hon-Komagome 2-Chome Building B Toda Construction Co. Sept. 1994 22 story 67.65 m 60 MPa SD490 11 Tsuchiura Redevelopment Project Building RIA Kumagai Construction Co. Nov. 1994 31 story 100.30 m 60 MPa SD490 excess of 390 MPa yield point, and passed the review of the Technical Appraisal Committee by the end of March, 1997. The table contains 28 examples, and the highest strength used for concrete and reinforcement in each building is tabulated. Starting from the Building No. 9, Ikeshita Redevelopment Building B, seismic design method developed in the New RC project and described in Chapter 6 has been applied in the practice, and approved in the review process as an effective method of seismic design. 426 Design of Modern Highrise Reinforced Concrete Structures Table 9.7(2). Buildings that passed the technical appraisal. No. Name of Building Structural Design Date of T.A. No. of Story Height Max Strength of Materials Fujima Building Sato Construction Co. Jan. 1995 22 story 71.45 m 60 MPa SD490 13 King Mansion Doujimagawa Taisei Construction Co. Apr. 1995 43 story 131.10 m 60 MPa SD490 14 King Mansion Tenjin-Bashi II Obayashi Construction Co. Sept. 1995 30 story 89.30 m 60 MPa SD490 15 I'm Fujimino Shimizu Construction Co. Sept. 1995 31 story 108.00 m 60 MPa SD490 16 Yamagata Kaminoyama Mansion Kumagai Construction Co. Dec. 1995 41 story 128.00 m 100 MPa USD685B 17 Furukawa Station West Project Kuma Design, Toda Construction Co. Jan. 1996 28 story 91.75 m 60 MPa SD490 18 Sakai Station Redevelopment Project Section B ObayashiOkumuraDainippondoboku JV Feb. 1996 43 story 142.88 m 70 MPa USD685 19 Sakai Station Redevelopment Project Section A TakenakaTaiseiTokai Kogyo JV Mar. 1996 43 story 138.58 m 70 MPa USD685 20 Matsubara Station Residence Toda Construction Co. July 1996 30 story 96.90 m 60 MPa SD490 21 River Sangyo Kyobashi Maeda Construction Co. July 1996 40 story 128.05 m 60 MPa SD390 12 Table 9.7 does not show the construction site. All buildings are constructed in Japan, mostly in Tokyo or in Osaka areas. The seismicity in these areas are more or less same, and design criteria as in Chapter 6 are generally applicable. Building No. 2, Ebina Prime Tower, is a 25-story building for office and hotel use shown in Fig. 9.24. It is a mixed structure, consisting of reinforced concrete box-shaped core walls and steel peripheral frames. Core walls take up most of lateral seismic load. Steel hat trusses are provided at the top of core walls to reduce flexural deflection of core walls. Short coupling girders at the Feasibility Studies and Example Buildings 427 Table 9.7(3). Buildings that passed the technical appraisal. No. Name of Building | Structural Design Max Strength of Materials Date of No. of Story T.A. ! Height 22 8-Canal Town West Kajima Construction Co. Nov. 1996 37 story 111.65 m 60 M P a SD490 23 Moto-Yawata D-l Redevelopment Project Souzousha Design, Mitsui Construction Co. Dec. 1996 24 story 78.15 m 60 M P a SD490 24 Ritto Station Commercial Area Residence Fujita Construction Co. Dec. 1996 31 story 95.10 m 60 M P a SD490 25 Rinkai Fuku-Toshin Daiba Section I TaiseiKumagaiTobishimaKokudo J V Dec. 1996 32 story 99.90 m 100 M P a SD685 26 Tokorozawa East Project Shimizu Construction Co. Jan. 1997 27 story 84.00 m 100 M P a USD685 27 River City 21 North Block Building N TaiseiMitsuiHaseko J V Feb. 1997 43 story 134.55 m 28 Moji Port Retro Heimat Takenaka Construction Co. Feb. I 1997 31 story 126.55 m Fig. 9.24. Ebina Prime Tower (Building No. 2). ! 100 M P a USD685 60 M P a SD490 1 428 Design of Modern Highrise Reinforced Concrete Structures core wall openings were provided with X-type bar arrangement. High strength concrete of 60 MPa is used in core walls, and high strength bars of SD490 grade is used for X-bars in the coupling girders. Building No. 3, The Garden Towers, is a 39-story building for residence, with partial use for stores shown in Fig. 9.25. It consists of space frames of reinforced concrete, using precast concrete elements for columns and partially precast units for girders. High strength concrete of 60 MPa is used for columns. Building No. 4, the Scene Johoku, shown in Fig. 9.26, is a 45-story residential building with the height of 160 m, the tallest among 28 buildings tabulated Fig. 9.25. The Garden Towers (Building No. 3). Feasibility Studies and Example Buildings 429 Fig. 9.26. The Scene Johoku (Building No. 4). in Table 9.7. This is the building utilizing 60 MPa concrete and 685 MPa steel, before the completion of the New RC project in 1993. It consists of reinforced concrete space frame, with increased number of stories and longer spans than preceding reinforced concrete highrise buildings and yet composed by approximately same size members as before, which was realized owing to the use of high strength material. An architectural improvement was achieved by the adoption of stepped girders that made it possible to eliminate steps on the loor finishing in a dwelling unit. Also the use of shallow depth girders around the building periphery provided better view and feeling of openness to the residents. Building No. 5, Gran Corina Seishin-Minami, is a 22-story residential building as in Fig. 9.27. Its structure consists of frames in the longitudinal direction, 430 Design of Modern Highrise Reinforced Concrete Structures Fig. 9.27. Gran Corina Seishin-Minami (Building No. 5). and frames with two single-span shear walls in the transverse direction. High strength concrete of 60 MPa and SD490 steel are used in columns and shear walls up to the 5th story. Building No. 6, Hankyu Hills Court Takatsuki, is a 20-story residential building shown in Fig. 9.28. It is a reinforced concrete frame building with the full use of precast construction technique. Anchorage of beam bars in the beam-column joints is a special feature of the structural design. Building No. 7, Ship Residence, is a 28-story residential building as shown in Fig. 9.29. It is a reinforced concrete building with special features of structural design. The peripheral frames consist of columns with reversed beams, that is, spandrel beams with floor slabs connected to the lower face of beam sections, Feasibility Studies and Example Buildings Fig. 9.28. Hankyu Hills Court Takatsuki (Building No. 6). ^§li' ^ Fig. 9.29. Ship Residence (Building No. 7). 431 432 Design of Modern Highrwe Reinforced Concrete Structures consisting a tube structure which is connected to interior frames only by floor slabs. In other words the first interior span around the building has no beams, allowing free arrangement of architectural partitions. At the central portion of interior frames are located what the structural engineers call "honeycomb dampers" made of mild steel plate with hexagonal openings, which are expected to yield at relatively small story drift and to dissipate seismic energy. Concrete up to 42 MPa is combined with high strength steel of USD685. Building No. 9, Ikeshita Redevelopment Building, is a 26-story building for residence and partial use for stores, shown in Fig. 9.30. Its structural feature is reinforced concrete space frame with span length 8.5 m in both directions, which is much longer than other highrise buildings up to date. Girders are made of half-precast construction, and floor subbeams are constructed by PRC (prestressed and reinforced concrete) where SD490 steel is used for pretensioning. High strength concrete of 60 MPa is used in lower part of the structure. Fig. 9.30. Ikeshita Redevelopment Building B (Building No. 9). Feasibility Studies and Example Buildings Fig. 9.31. Hon~Komagome 2-chome Building B (Building No. 10). Fig. 9.32. Tsuchiura Redevelopment Project Building (Building No. 11). 433 434 Design of Modem Highrise Reinforced Concrete Structures Building No. 10, Hon-Komagome 2-chome Building, is a 22-story residential building as shown in Fig. 9.31. It consists of reinforced concrete space frame using concrete up to 60 MPa and steel of grade SD490. Columns are precast, and girders and floor slabs are partially precast, to speed up the construction. Building No. 11, Tsuchiura Eedevelopment Project Building, is a 31-story residential building, shown in Fig. 9.32. It is a reinforced concrete space frame building whose material and construction method are similar to Building No. 10 above. Building No. 12, Fujima Building, is a 22-story residential building, shown in Fig. 9.33. It is a reinforced concrete space frame building whose material is similar to three preceding examples, but precast units are used for girders and floor slabs only. Columns are cast in place. Building No. 13, King Mansion Doujimagawa, is a 43-story residential building, shown in Fig. 9.34. It is also a reinforced concrete space frame, utilizing precast technique in all structural members. Fig. 9.33. Fujima Building (Building No.K 12). Feasibility Studies and Example Buildings 435 Fig. 9.34. King Mansion Doujimagawa (Building No. 13). Other buildings in Table 9.7 are more or less similar to these buildings. They are mostly residential buildings, ranging from 24 to 43 stories. Use of concrete in excess of 60 MPa in compressive strength is seen in Building Nos. 18 and 19, where 70 MPa concrete is adopted, and in Building Nos. 16, 25 and 27, where 100 MPa concrete is used in the limited part of the structure. High strength steel higher than 490 MPa yield point is used in five cases, that is, grade USD685 is used for Building Nos. 16, 18, 19, 25 and 27. Thus, USD685 steel is always combined with concrete stronger than 60 MPa. The recent trend as extracted from the analysis of these example buildings of New RC is summarized below. First, the scope of reinforced concrete construction is being extended to taller buildings than before, but high strength material is also widely used for medium-high buildings. Secondly, span length of reinforced concrete is now getting longer than before, and is comparable to the span length that had been regarded as being suitable for composite 436 Design of Modern Highrise Reinforced Concrete Structures steel and reinforced concrete construction. Thirdly, it appears that the use of SD490 steel for girders and that of USD685 steel for columns will become the favorite choice of structural engineers in future. Lastly, it seems that the precast construction will increase, and at the same time more attempts of hybrid structural system as in Building No. 2 will be made in future. References 9.1. Architectural Institute of Japan, Standard for Structural Calculation of Reinforced Concrete Structures. 9.2. Architectural Institute of Japan, Recommendation for Design and Construction of Partially Prestresed Concrete (Class III Prestressed Concrete) Structures, 1986. 9.3. Architectural Institute of Japan, Guidelines for the Evaluation of Habitability to Building Vibration, 1992. Index accelerated neutralization test, 382 acceptance criteria, 389 aggregate, 64 aggregate interlock, 229 air-entraining and high-range water-reducing agents, 66 air tubes, 363 alkali-aggregate reaction, 381 alternate reversal of loading, 96 amino-sulfonate acid chain, 350 analytical models, 231 anchorage, 104 anchorage of girder bars, 20 anchorage strength, 107 andesite, 66 arc welding, 100 ascending and descending waves, 282 beams, 128, 236 bearing failure, 106 bend direction, 107 bend position, 107 bend radius, 107 bendability, 93 biaxial effect, 239 biaxial loading test, 123 bidirectional earthquake motion, 289 bidirectional flexure, 147 bidirectional horizontal motions, 272 bidirectional loading, 178, 196 bond, 104, 229 bond index, 135 bond link element, 235 bond splitting, 216 bond-splitting failure, 129 box column structure for thermal power plant, 418 buckling, 121 buckling of axial re-bars, 121 Building Standard Law, 369 bar diameter, 108 bar diameter column depth ratio, 110 bars with screw-type deformation, 354 base shear coefficient, 26 basement, 12 beam bar bond index, 192 beam bar slip, 109 beam-column joints, 30, 105, 189, 255 beam-hinge mechanism, 22 beam model, 28 capacity-demand diagram method, 337 cement, 62 chemical admixture, 66, 348, 384 chemical component, 93 chloride content, 381 circular section, 116 cold work, 94 column section, 13 columns, 128, 251 compatibility matrix, 326 90 degree bend, 105 180 degree bend, 105 3-D joints, 196 60-story apartment building, 291 L-type flow test, 350 437 438 Design of Modern Highrise Reinforced Concrete Structures compressive deterioration of cracked concrete, 229 compressive strength, 76, 118, 377 compressive strength reduction coefficient, 238 concrete, 229 Concrete Committee, 61 concrete confinement models, 248 concrete core, 377 concrete cover, 383 concrete mix, 349 concrete placement, 21 concrete pump truck, 357 concrete strength, 15 concrete temperature, 366 confined concrete, 77, 113 confinement effect, 238 confinement, 13 consolidation, 387 constitutive equations, 125 Construction and Manufacturing Committee, 345 construction joints, 363, 388 construction management, 21 Construction Standard for New RC, 375 core bars, 14 core-in-tube structure, 305 core strength, 368 correction factor for temperature, 379 corrosion resistance, 99 cracking, 229 cracking strength, 140, 240 cracking stress, 125 cracks, 234 creep, 80 critical section, 102 cured in water on site, 347 curing, 388 cylinder strength cured in seal on site, 368 damping, 34 damping proportional to incremental stiffness, 35 deformation capacity after yielding, 141 deformation capacity of columns, 215 deformation capacity of walls, 178 degrees-of-freedom, 320 dependable material strength, 277 dependable strength, 274, 283 design criteria, 23 design drift limit, 275, 278 design drift limitations, 275 design earthquake intensity, 275 design earthquake motion, 279 design seismic deformation limit, 271, 272 direction of seismic design, 286 discrete crack model, 234 dissemination of results, 59 double tube structure, 299 double-tube system, 10, 11 dowel action, 229 drilled cores, 347 drying shrinkage, 80, 382 ductility of girders, 28 dumbbell type section walls, 170, 184 durability, 82, 97, 381 durability index, 382 earthquake response analysis, 32, 315 effective width, 140 elongation, 93 end-tail portion, 108 entrained air, 386 epoxy grout splices, 100 equation of motion, 336 equivalent linearization, 316, 337 equivalent SDF system, 337 equivalent viscous damping, 214 equivalent viscous damping factor, 194, 286 etringite type special admixture, 70, 384 example buildings, 424 explosion, 382 exposed engineering bedrock, 279 exterior beam-column joint, 198 Feasibility Studies and Example Buildings exterior joints, 105, 203 factor to multiply standard deviation, 379 failure criterion, 123 feasibility of new structures, 391 FEM analysis, 231 FEM, 122, 227 fine aggregate ratio, 386 finite element method, 122, 227 fire resistance, 84, 97, 382 first phase design, 24, 26 fixed base model, 281 flexibility matrix, 327 flexural bond, 105 flexural bond resistance, 111 flexural compression failure, 215 flexural cracking, 210 flexural shear model, 32 flexural strength, 187, 214 flexural strength of walls, 219 floor plan, 7 flush butt welding, 354 fly ash fume, 70 form vibrator, 360 formwork, 376 foundation, 13 foundation structure, 289 frame model, 319 freezing-thawing test, 82 fresh concrete, 356 full scale construction test, 345 gas butt welding, 19, 100 ground granulated blast furnace slag, 70, 384 heat treatment, 94 high range AE water reducing agent, 348, 384 high strength concrete, 61, 345 high strength materials, 235 high strength re-bars, 90 high strength reinforcing bars, 86 439 high strength steel, 345 high temperature, 97 High Strength Concrete Committee, 345 high-stress fatigue test, 96 higher mode effect, 29 highrise flat slab buildings, 391 highrise flat slab condominium with core walls, 393 highrise flat slab condominium with curved walls, 399 hot rolling, 94 hydration heat, 382 Hyogoken-Nanbu earthquake, 337 hysteresis, 286 hysteresis model, 28, 319 hysteretic energy dissipation, 286 in-plane shear, 124 index J, 222 initial stiffness, 210 inorganic grout splices, 100 instantaneous stiffness matrix, 342 interior beam-column joint, 191, 198 interior joint, 109 internal viscous damping, 34, 35 JASS (Japan Architectural Standard Specification), 375 JIS G 3109, 87 JIS G 3112, 87 JIS G 3117, 87 joint failure index, 195, 197 laboratory tests, 353 lap splice, 100 lapped splices, 19 large size box column structure, 391 lateral confinement, 113 lateral pressure, 117 lateral pressure index, 118 lateral reinforcement, 113 lath mesh, 363 440 Design of Modern Highrise Reinforced Concrete Structures levels 1 and 2, 273 level 1, 273 level 2, 273 level 2, 277 limestone, 66 limiting deflection, 214 mechanical properties, 104 mechanical splices, 100 mediumrise office buildings, 310 megastructures, 391, 407 member models, 319 metal trowel finishing, 365 method of manufacture, 93 mineral admixture, 66, 347, 384 minimum lead length of 90 degree bent anchorage, 108 mix, 384 mix design, 71 modal analysis, 316 modeling, 232 modeling of structures, 281 moist curing, 388 moment redistribution, 27 monolithic casting, 348 mortar strength, 62 MS model, 328 multi-degree-of-freedom (MDF) system, 335 multiaxial spring model, 328 multimass model, 323 neutralization, 382 New RC buildings, 271, 272 New RC construction standard, 345 New RC earthquake motion, 279 New RC project, 1, 40, 235 New RC structures, 272, 274 Newmark's /3-method, 342 nonlinear earthquake response analysis, 276 nonlinear frame analysis, 33 oblique direction, 287 on-line heat treatment, 94 on-site water-cured cylinder strength 367 one-component model, 325 one-way reversal of loading, 96 ordinary portland cement, 350 organization for the project, 44 outline of results, 53 panels, 236, 265 parametric analysis, 256 P C steel, 94 penthouse, 12 placing, 387 plain concrete plate, 123 plane stress condition, 122 plant tests, 353 polycarbonate acid chain, 350 possible strongest intensity earthquake, 275 post-level 2, 273, 277 preassemblage of reinforcement cage, 18 precast members, 17 pressed collar, 19 probability of nonexceedance, 284 projected embedment length, 108 projected horizontal length of embedment, 107 proportioning strength, 384 push-over analysis, 27, 317, 337 range of material strength, 41 RC, 229 RC members, 235 RC structures, 231 ready-mixed concrete plant, 386 rectangular section, 116 reinforced concrete, 229 reinforced concrete plate, 124 reinforcement, 16, 229 reinforcement cages, 356 Reinforcement Committee, 104 response drift limit, 275 response spectrum, 279, 338 restoring force characteristics, 283 Feasibility Studies and Example Buildings restoring force characteristics of beams, 209 restoring force model, 28 Richart equation, 117 rigid slab, 321 rod-type vibrator, 360 safety performance criteria, 276 sandstone, 66 Sa-Sd response spectrum, 340 screw coupler splices, 100 screw-deformed bars, 20 screw-type coupler joints, 356 SD245, 87 SD295A, 87 SD295B, 87 SD345, 87 SD390, 87 SD490, 87 seal-cured on site, 347 second phase design, 24, 27 segregation resistance, 377 seismic dampers, 11 seismic design, 22 serviceability, 275 serviceability drift limit, 275 serviceability performance criteria, 276 settlement, 360 shear-compression failure, 170 shear failure in the hinge zone, 217 shear model, 32 shear reinforcement ratio, 247 shear stiffness, 239 shear strength, 188, 230 shear strength equation, 166, 174 shear strength of beam-column joints, 221 shear strength of beams and columns, 219 shear strength of beams, 162 shear strength of columns, 156 shear strength of slender walls, 183 shear walls, 11, 169, 236 side concrete cover, 107 441 silica fume, 70, 350, 384 simple mass and spring model, 281 simplified adiabatic curing, 379 single-degree-of-freedom(SDF) system, 335 slab effect, 136 sleeve splices, 20 slump, 377 slump flow, 377 slump flow loss, 363 slump flow test, 350 slump loss, 363 slump test, 350 smeared crack model, 234 soil-foundation-structure interaction, 282 soil structure interaction, 35 soil-structure model, 325 space frame system, 10 space frame with seismic elements, 10 specified design strength, 377 specified yield strength, 91 splice, 100 splitting failure, 106 square sections, 118 SRC, 2 standard-cured, 347 standard curing, 379 standard deviation, 379 static incremental (push-over) analysis, 281 steel grade, 108 stiffness matrix, 331 story drift, 275 strain at yield plateau, 91 strain concentration, 102 stress-strain relationship, 77, 113 strong column-weak beam mechanism, 22 structural concrete, 377 Structural Design Committee, 271 structural drift, 275, 277 Structural Element Committee, 104, 127 442 Design of Modern Highrise Reinforced Concrete Structures structural performance evaluation, 209 structural planning, 7 structural systems, 10 structural walls, 169 surface bubbles, 359 surface cracks, 371 surface finishing, 365, 388 sway-rocking model, 282 Takeda hysteresis model, 326 tamping, 365 tangent stiffness, 342 target of the project, 41 temperature history chasing curing, 379 tensile strength, 77 tension stiffening, 125, 239 three-dimensional analysis, 232 time-history response analysis, 316 top bars, 112 transportation time, 387 two-dimensional analysis, 232 U-bend girder bars, 355 U-type bent anchorage, 354 ultimate load carrying capacity, 26 uniaxial compressive stress-strain curves, 237 unit bulk volume of coarse aggregate, 386 unit water content, 385 upper bound material strength, 277 upper bound strengths, 274, 283 USD1275, 86, 375 USD685A, 86, 375 USD685B, 86, 375 USD785, 86, 375 USD980, 86, 375 vertical ground motion, 289 vertical splitting, 152 vertical splitting crack, 152 VH separate casting, 15, 348 wall girders, 14 wall model, 331 walls, 169, 260 water-binder ratio, 384 weak-beam strong-column type collapse mechanism, 271 web reinforcement ratio, 112 welding, 19 workability, 75 yield yield yield yield deflection, 211 hinge regions, 275 ratio, 92, 102 stiffness reduction factor, 139, 211 Young's modulus, 77, 381 zone zone zone zone I, 42 II-1, 42 II-2, 42 III, 42 This book presents the results of a Japanese national research project carried out in 1988-1993, usually referred to as the New RC Project. Developing advanced reinforced concrete building structures with high strength and high quality materials under its auspices, the project aimed at promoting construction of highrise reinforced concrete buildings in highly seismic areas such as Japan. The project covered all the aspects of reinforced concrete structures, namely materials, structural elements, structural design, construction, and feasibility studies. In addition to presenting these results, the book includes two chapters giving an elementary explanation of modern analytical techniques, i.e. finite element analysis and earthquake response analysis. Hiroyuki Aoyama is Research Professor of Nihon University,Tokyo, and is President of the Aoyama Laboratory, a consultancy for structural engineers. He is also Professor Emeritus at the University of Tokyo. After graduating from the University of Tokyo, Department of Architecture in 1955, he received a doctorate in Engineering in I960 from the same university. He served as a lecturer in 1960-64, an associate professor in 1964-78, and a professor of structural engineering in 197-93, in the Department of Architecture of the University of Tokyo. He was a visiting research scientist in 1961-63, and a visiting professor in 1971-72, at the University of Illinois (Department of Civil Engineering) at Urbana, Illinois, and also a visiting professor in 1980-81 at the University of Canterbury (Department of Civil Engineering), in Christchurch, New Zealand. His honors include the Alfred E. Lindau Award of the American Concrete Institute in 1995, the Minister of Science and Technology Agency Award in 1992, and awards from the Architectural Institute of Japan and the Japan Concrete Institute in 1977 and 1975 respectively. He is currently a vice-president of the International Association of Earthquake Engineering, a foreign associate of the National Academy of Engineering, U.S.A., an honorary member of the American Concrete Institute, a fellow of the New Zealand Society for Earthquake Engineering, and a member of several engineering societies in the U.S.A. and Japan. Professor Aoyama's research interests include seismic behavior and design of structures, particularly of reinforced concrete structures. He has tested and formulated restoring force characteristics of reinforced concrete members and structures, conducted nonlinear earthquake response analysis, pioneered the use of high strength concrete and reinforcement in seismic regions, and developed seismic design methods for highrise concrete structures in seismic countries such as Japan. P204 he ISBN-13 978-1-86094-239-6 ISBN-10 1-86094-239-3 Imperial College Press www.icpress.co.uk 9 "781860"942396"