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
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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,
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ISBN
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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
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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.
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6
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: E-SN23LI
j
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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
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85
"30
120
^
s=
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|
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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
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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
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1.5
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Structures
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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
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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)
—
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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
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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
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1 0
1 2
3
deformation angle (%)
(a)S6, 17 = 0.50
••"••
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Fig. 4.16. Load-deformation curves.
145
146
Design of Modern Highrise Reinforced Concrete
400
Structures
S9
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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
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'
R
i
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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
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(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
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i
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30-016
Elements
30
60
40
40 100
40
a
60
30
(a) column section
240
*o.«o
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4
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o.f?. 4 9 | *<»
I
I
40 40 40 40 4Q 40
I I I I I
l\
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.(•)•
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10-D13
10-D13
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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
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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
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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£
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A
A
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A
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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
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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
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A
\
A""
l~h
£
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A
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a
A
A
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A
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Fig. 9.4.
~~i
a
A
A
A
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A
A
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A
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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^
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yper- wall
super b
JJffiLi
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(b) middle and lower floors
©
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I
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(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
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boiler bldg.
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turbine bldg.
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Fig. 9.18. Elevations of the building.
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Feasibility Studies and Example Buildings
1Q250 10250
10250 10230
foundation girder
D=3.0m_
foundation girder
D=7.5m
6
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2
CGI
Fig. 9.19. Plan of foundation.
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10000
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Plan of top girders.
©
419
Design of Modern Highrise Reinforced
Concrete
Structures
_S2_
_£Q1_
VFLJ-HOOO
VFL«0
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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
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end
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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
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