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Proceedings of the

One-day Symposium

Contemporary Seismic Engineering 2010 Organized by Joint Structural Division, The Hong Kong Institution of Engineers Sponsored by Department of Civil and Structural Engineering, The Hong Kong Polytechnic University The Hong Kong Institute of Steel Construction

Funded by

Professional Development Programme in Seismic Engineering for Structural Engineers

27 August 2010

COMMERCE AND ECONOMIC DEVELOPMENT BUREAU THE GOVERNMENT OF THE HONG KONG

SPECIAL ADMINISTRATIVE REGION

One-day Symposium

Funded by Professional Development Programme in Seismic Engineering for Structural Engineers

Contemporary Seismic Engineering 2010

Organized by Joint Structural Division, The Hong Kong Institution of Engineers

Sponsored by

Department of Civil and Structural Engineering,

The Hong Kong Polytechnic University and

The Hong Kong Institute of Steel Construction

COMMERCE AND ECONOMIC DEVELOPMENT BUREAU THE GOVERNMENT OF

THE HONG KONG SPECIAL ADMINISTRATIVE REGION

Funding Organization:

"Any opinions, findings, conclusions or recommendations expressed in this material / any event organized under this Project do not reflect the views of the Government of the Hong Kong Special Administrative Region or the Vetting Committee for the Professional Services Development Assistance Scheme."

Disclaimer No responsibility is assumed for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. The Institute of Steel Construction, the authors and the reviewers assume no responsibility for any errors in or misinterpretations of such data and/or information or any loss or damage arising from or related to their use. Copyright © 2010 reserved by The Hong Kong Institute of Steel Construction All rights reserved. No part of this publication may be produced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the copyright holder. The authors retain the right to republish their contributions consisting solely of their own work.

Printed in Hong Kong ISBN: 978-988-99140-8-0


www.hkisc.org

Preface

Traditionally and currently, seismic design is not required in building structures in Hong Kong

and inertia loads due to seismic motion are not needed for consideration in local structural

design codes. After various earthquakes in China and other places, the public and

professional in Hong Kong begin to reconsider whether or not there is a need of considering

earthquake scenarios in Hong Kong. The Mainland Chinese seismic design code GB50011‐

2001for seismic design includes Hong Kong in the seismic fortification intensity of 7 degree

which implies a basic ground acceleration equal to 0.15 g. This indicates another justification

for consideration of seismic loads in design of structures in Hong Kong. In addition to the

local possible need of considering seismic loads for construction in Hong Kong, its engineers

regularly work in the Mainland and overseas such as those countries in the Middle East,

Southeast Asia and Macau. Many of these places require a different degree of seismic

consideration in the framing plan and in the member and element design. While the local

practice does not have this consideration, local engineers may not be so familiar with its

design and thus they are at a disadvantageous position when competing with engineers from

other countries in tender or project bidding and in design stages. This seminar is aimed to

remedy the above shortfalls with an aim to improve Hong Kong engineers’ competence in

design of structures in Hong Kong and other places.

The editors would like to take this opportunity to express their sincere thanks to the

sponsoring organisations namely as Commerce and Economic Development Bureau of the

Government of Hong Kong SAR Government, The Hong Kong Polytechnic University and the

Joint Structural Division of the Hong Kong Institution of Engineers for their efforts and

supports in making this seminar a reality. They would also like to thank you the speakers of

this seminar in sharing their expertise with us.

SL Chan ST Chan CK Lau Aldows Tang

27th August 2010, Hong Kong, China

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Time Program Session Chairmen

08:45 am Registration

09:05 am Welcoming Speech Ir C.K. Lau, Immediate Past Chairman of JSD, HKIE Chairman of Structural Discipline Advisory Panel and Head of Structural Section, Sun Hung Kai Properties Limited

Ir Dr. Andy Lee

09:15 am Opening Speech Ir Prof. KK Choy, Vice‐President, The Hong Kong Institution of Engineers

Lecture 1 09:30 am

"Revision of seismic design codes corresponding to building damages in the “ 5.12” Wenchuan Earthquake Prof. Y.Y. Wang, Main editor of the National Code for Seismic Design of Buildings GB50011‐2008, Mainland China

Ir Adam Choy

Lecture 2 10:00 am

Application of Buckling‐Restrained Braces in Steel Frameworks against Earthquakes. Prof. G.Q. Li , Professor, Tongji University, Shanghai

Lecture 3 10:30 am

Scaling the ground motion accelerations for response history analysis of tall buildings Prof. KC Tsai, National Taiwan University, Taiwan

11:00 am Tea Break

Lecture 4 11:30 am

Progress of Seismic Design for Steel Structures in China Mainland Prof. GP Shu and Dr. S Sun, Southeast University, Nanjing

Ir Ken Ng

Lecture 5 12:00 noon

Design of Plate‐reinforced Composite Coupling Beams in Tall Buildings Dr. Ray Su, University of Hong Kong, HK

12:30 pm Lunch

Lecture 6 14:15 pm

Performance Based Seismic Design for Contemporary ArchiStructures Dr. Goman Ho, Ove Arup and Partners Limited

Ir Dr. Y.L. Wong

Lecture 7 14:45 pm

Seismic Risk Analysis Prof. TT Soong, State University of New York at Buffalo, USA

Lecture 8 15:15 pm

Seismic mitigation of mid‐rise buildings by new earthquake resistant system using base isolation and story isolators Ir Dr.S.S. Lam, Hong Kong Polytechnic University, Hong Kong

15:45 pm Tea Break

Lecture 9 16:15 pm

Spectrum and time history analysis of building structures by software NIDA Dr. Y.P. Liu & Prof. S.L. Chan, Hong Kong Polytechnic University, HK

Ir Dr. SW Yuen

Lecture 10 16:45 pm

Closing remarks Ir S.T. Chan, Assistant Director, Housing Department, HK SAR Government

17:00 pm End

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CONTENTS

Page no. Preface i Programme ii Contents iii Revision of seismic design codes corresponding to building damages 1 in the “ 5.12” Wenchuan Earthquake Prof. Y.Y. Wang, Main editor of the National Code for Seismic Design of Buildings GB50011‐2008, Mainland China Application of Buckling‐Restrained Braces in Steel Frameworks 19 against Earthquakes Prof. G.Q. Li , Professor, Tongji University, Shanghai, Mainland China Scaling the ground motion accelerations for response history analysis 35 of tall buildings Prof. K.C. Tsai, National Taiwan University, Taiwan Progress of Seismic Design for Steel Structures in China Mainland 55 Prof. G.P. Shu, Southeast University, Nanjing, Mainland China Design of Plate‐reinforced Composite Coupling Beams in Tall Buildings 63 Dr. Ray Su, University of Hong Kong, Hong Kong Performance Based Seismic Design for Contemporary ArchiStructures 83 Dr. Goman Ho, Ove Arup and Partners Limited, Hong Kong Seismic Risk Analysis 91 Prof. T.T. Soong and I.-S. Ahn, State University of New York at Buffalo, USA Seismic mitigation of mid‐rise buildings by new earthquake resistant system 105 using base isolation and story isolators Ir Dr.S.S. Lam and Z.D. Yang, Hong Kong Polytechnic University, Hong Kong Spectrum and time history analysis of building structures by software NIDA 123 Dr. Y.P. Liu and Prof. S.L. Chan, Hong Kong Polytechnic University, Hong Kong iii

REVISION OF SEISMIC DESIGN CODES CORRESPONDING TO BUILDING DAMAGES IN THE “5.12” WENCHUAN

EARTHQUAKE

Wang Yayong Institute of Earthquake Engineering, China Academy of Building Research

Beijing 100013, China

[email protected] ABSTRACT A large number of buildings were seriously damaged or collapsed in the “5.12” Wenchuan earthquake. Based on field surveys and studies of damage to different types of buildings, seismic design codes have been updated. This paper briefly summarizes some of the major revisions that have been incorporated into the “Standard for classification of seismic protection of building constructions GB50223-2008” and “Code for Seismic Design of Buildings GB50011-2001.” The definition of seismic fortification class for buildings has been revisited, and as a result, the seismic classifications for schools, hospitals and other buildings that hold large populations such as evacuation shelters and information centers have been upgraded in the GB50223-2008 Code. The main aspects of the revised GB50011-2001 code include: (a) modification of the seismic intensity specified for the Provinces of Sichuan, Shanxi and Gansu; (b) basic conceptual design for retaining walls and building foundations in mountainous areas; (c) regularity of building configuration; (d) integration of masonry structures and pre-cast RC floors; (e) requirements for calculating and detailing stair shafts; and (f) limiting the use of single-bay RC frame structures. Some significant examples of damage in the epicenter areas are provided as a reference in the discussion on the consequences of collapse, the importance of duplicate structural systems, and the integration of RC and masonry structures. Keywords: Wenchuan Earthquake; Earthquake Damage to Buildings; Revision of Seismic Design Codes Supported by: National Natural Science Foundation of China Under Grant No. 50439010; NSFC and Korea Science and Engineering Foundation Under Grant No. 50811140341

Contemporary Seismic Engineering 2010, Hong Kong 27 August 2010

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1. INTRODUCTION Many buildings and infrastructure were seriously damaged or collapsed in the “5.12” Wenchuan earthquake of 2008. A much better understanding of the damage mechanism of different types of buildings has been obtained through comprehensive observations in the field. There was a legal requirement to quickly update China’s seismic codes following this event, and experts from throughout the country worked to complete this process. The new versions of the “Standard for Classification of Seismic Protection of Building Constructions GB50223-2008” and “Code for Seismic Design of Buildings GB50011-2001 (2008 version)” were completed within three months after the event and were issued on July 30, 2008 by the national administration. The aim of the newly issued codes is to guarantee the seismic safety of construction and to guide the recovery and reconstruction process in the disaster areas. This paper summarizes the main changes to the codes based on typical damage observed during the event. It is recognized that the buildings that were designed and constructed following the seismic regulations of the 1989 Code or the 2001 Code performed very well. Most of these buildings were severely damaged by the main shock of the event, since an estimated seismic intensity of 3–4 times greater than the specified intensity occurred in the epicenter region, but they still did not collapse. The three seismic performance objectives of “operational at the minor earthquake level,” “life safety at the moderate earthquake level” and “collapse prevention at the major earthquake level” were achieved. The main causes of severe damage were a lack of seismic measures in older buildings and low-cost housing in rural areas, and poor quality of design and construction. In addition, the higher effective seismic intensity beyond the specified intensity, the effects of wave propagation, and topographic and geological conditions contributed to the serious losses in this disaster. It was observed through the field investigation of damage to buildings that different types of buildings suffered varying degrees of damage even at the same site. For example, some RC structures with a higher seismic capacity collapsed and masonry structures with a lower seismic capacity had severe cracks but did not collapse. In the region of high seismic intensity, sudden collapse of the bottom part of some structures was caused by a lack of redundancy and/or a duplicate structural system, while serious failures of other structures occurred because of large open spaces and irregular configurations. Other types of damage observed throughout the disaster region included “strong beam and weak column,” knocking and sequential collapse due to improper arrangement of partitions, destruction of stair shafts in masonry houses, pre-cast RC floor and room slabs as well as nonstructural members, etc. Therefore, the study of the seismic behavior of buildings had to be carried out both for damaged and collapsed buildings, as well as for those that cracked but stood or even remained in good condition, in order to offer successful experiences together with the failure lessons to be included in future code revisions.


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2. REVISION OF “STANDARD FOR CLASSIFICATION OF SEISMIC PROTECTION OF BUILDING CONSTRUCTIONS GB50223-2008” (CITED AS THE 2008 STANDARD)

2.1 Lowest Requirement for Seismic Risk Reduction The 2008 Standard regulates that all engineered buildings, including new, rebuilt and expanded structures, shall identify their seismic class which shall not be ranked below the corresponding class regulated in the Standard. The lowest requirement of seismic risk reduction is based on a combination of factors, including the environment of earthquake risk potential, the ability to predict the occurrence of an earthquake, the occupancy and operation of buildings and infrastructures, as well as the sequence of potential disasters. This means that the seismic category for buildings shall handle both safety and economics. It also sometimes allows the seismic class to be enhanced for a specified building in case the owner wants to do so. 2.2 Seismic Category of Buildings The seismic category of buildings can be expressed as either Class A (special), Class B (important), Class C (regular) or Class D (proper) in the 2008 Standard. The previous 1995 Standard focused on seismic requirements for lifeline systems to ensure continuation of industrial and economic activities. Instead, the updated 2008 Standard gives more attention to life safety and the impact to society, and also to emergency response and rescue work. The field survey has shown that the 512 earthquake occurred during school hours, at 2:28 pm, and thousands of pupils were killed or injured by collapsed school buildings. This indicated that the seismic capacity of school buildings had to be upgraded. The 2008 Standard has therefore stressed that the seismic category all buildings holding pupils in kindergartens, primary and secondary schools be at least Class B (important), which had already been required for kindergartens and primary schools by the 2004 Standard. In addition, the seismic category of large scale hospital buildings has to be Class A (special) or Class B (important) to accommodate emergency rescue needs. It is also necessary to upgrade the seismic category of local hospitals and clinics with the capability to perform surgical operations from Class C to Class B, to enable first aid to be available immediately after an event. The 2008 Standard has regulated that buildings functioning as a rescue center be of Class A or B, and that infrastructure such as gas and water supply systems and drainage engineering, and facilities for public service such as supermarkets, sports, entertainment, etc., be categorized as Class B. 3. REVISION OF “CODE FOR SEISMIC DESIGN OF BUILDINGS GB50011-

2008” (CITED AS THE 2008 CODE) 3.1 Modification to the National Standard “The Map of Earthquake Zoning in

China GB18306-2001” for Western China Earthquake zoning parameters such as seismic intensity, basic peak ground acceleration (PGA) and seismic design categories have been modified following the “5.12” Wenchuan earthquake for over 70 cities and counties in Sichuan, Gansu and Shaanxi provinces.


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3.2 Geological Disaster and Seismic Design for Buildings in Mountainous Areas Many buildings were severely damaged in mountainous areas in the earthquake. A strict limit for siting construction has been given in the revised 2008 Code, so that Class A and B buildings are prohibited from being located in areas with a high potential for geological hazards, such as landslides, rock falls, ground subsidence, cracking, debris flow and earthquake rupture slipping, etc. Some buildings with damage induced by geological disasters are shown in Fig. 1 to Fig. 4. Figure 1 shows totally collapsed buildings in a range of 27 m wide along the rupture line, and an area of about 220 m wide, where moderate to severe damage occurred. This indicates that the location of buildings should meet a requirement of a minimum distance of 200 to 300 m from the earthquake rupture issued by the code. Not long after the event, a heavy rain fell for two days on September 23–24, 2008, which induced a turbulent debris flow from the mountain area, sweeping Beichuan County and burying many streets and buildings. The debris cover was 6 m at shallow sites to over 40 m at its deepest. Figure 4 shows a four-story apartment building buried by the mud flow. Retaining walls are required by the 2008 Code for construction in mountainous areas. Space between the building foundation from the foot of a hill is also specified in the 2008 Code. It is very dangerous and forbidden to locate a building on a retaining wall.

Figure 1. Collapses induced by Rupture Slipping on the Ground (Photo from Yuan Yifan)

Figure 2. Maoba High School buried by a Rock Slide in Qushan Town, Beichuan County


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Figure 3. Apartment Building Partially buried by Landslide in Wenchuan County Figure 5 shows a failure of the bottom frame structure of a complex building used for commerce and residential purposes in Beichuan County, where severe damage was caused by pressure from the retaining wall.

Figure 4. Apartment Building mostly buried by Debris Flow Late Sept. in Beichuan County

Figure 5. Bottom Frame Structure Severely Damaged due to Failure of Slope Wall


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3.3 Essential Requirements for Seismic Design 3.3.1 Regularity of configuration The 2008 Code has stressed that both architects and engineers should follow seismic design concepts. Special measures should be taken for irregular configurations of a building. It is prohibited to design an irregular building to be located in seismic regions. Much damage was caused by irregular designs in this event. For example, two complex buildings with a bottom frame of RC and a masonry structure above were severely damaged and even partially collapsed due to their irregular plan and elevation (see Figs. 6 and 7). Figure 8 shows a damaged complex building with a two-story RC bottom frame and an upper masonry structure. It is known that this type of complex structure performs poorly in earthquake regions and should be carefully designed or not used. 3.3.2 Structural integrity and conceptual design Structural integrity primarily depends on the detailing of the joints among structural members in addition to their own strength. The 2008 Code has regulated that conceptual designs with “strong column and weak beam,” “capacity of strong shear and weak moment” and “strong joint and weak element” should be used for RC structures. The RC boundary beam and tie column, and RC core column or reinforced wall should be used for masonry structures. Finally, partial or complete buckling and yielding of elements should be avoided for steel structures. Reliable measures should be taken to guarantee the integrity of the joints among precast RC slabs of the roof and floor system.

Figure 6. Damaged RC Bottom Frame Structure (0.1g/0.4g). Note: (0.1g/0.4g) = (specified PGA/estimated PGA)


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Figure 7. Damaged Upper Walls of Masonry Building with RC Bottom Frame Structure (0.1g/0.4g)

Figure 8. Damaged Masonry Building with Two-Story RC Bottom Frame Structure (0.1g/1.0g)

Figure 9. Plastic Hinges on Top of a Column (0.1g/0.3g) (Photo from Yao Qiulia)


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3.3.2.1 “Strong column and weak beam” design for RC frame structures The definition of strong column and weak beam indicates that the moment capacities of the beam and column at the joint should be defined as

aby

acy MM

The 2001 Code simply adopts a factor ηc to enlarge the moment capacity of the column by

bcc MM

where ηc = 1.1, 1.2, 1.4, respectively, for different grades of RC columns. However, in practice, the goal of strong column and weak beam cannot be achieved because the flexural stiffness of the beam is multiplied simply by a factor of 1.5–2.0 to consider the area where the floor slab joins with the beam while calculating the moment at the ends of the beam. In the “5.12” Wenchuan earthquake, the failure of many RC frame structures was due to problems associated with a “strong beam and weak column. Figure 9 shows the failure mechanism of a six-story RC frame structure in Dujiangyan City. Plastic hinges can be seen at the top of the column of the ground floor, but beams and slabs remained undamaged. Figure 10 shows a collapsed RC frame structure in Beichuan County, the epicenter area, where it can be seen that the reinforcement ratio of the beams was much larger than the columns. 3.3.2.2 Cast-in-situ RC floor and roof slabs The floor and roof systems integrated with cast-in-situ RC slabs performed well in cases of large deflection, which have been commonly used in multi-story and tall buildings. In the 2008 Code, the use of cast-in-situ RC floor slabs was encouraged for large masonry schools and hospitals. Figure 11 shows the collapsed ground floor and internal walls of a five-story student hostel building made of masonry. Note that the cast-in-situ RC floor slab remains with large deflection. 3.3.2.3 Pre-cast RC floor and roof slabs The field survey revealed that pre-cast floor and roof slabs might collapse if the support wall or beam was broken or large horizontal displacement occurred due to poor detailing of the joints and structural integration. Figure 12 shows a completely collapsed three-story primary school masonry building. There was no connecting detail between either the slab & beam or the slab & slab. Figure 13 shows a partially collapsed five-story masonry school building that lacked the required RC tie- column and boundary-beam.


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Figure 10. Less Reinforcements to Column than Beam (0.1g/1.0g)

Figure 11. Large Deflection of Floor formed with Cast-in-Situ RC Beams and Slabs (0.1g/1.0g)

Figure 12. Collapsed Pre-cast RC Floor Slabs (0.1g/0.2g)


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Figure 13. Partially Collapsed Masonry Structure due to Lack of Required Tie-Column and Boundary-Beam (0.1g/0.3g)

The goal of collapse prevention can be achieved even for pre-cast RC structures if the connection details between slabs, slab & wall, and slab & support beam are properly designed and constructed. Figures 14–16 show a three-story masonry school building which was subjected to earthquake forces scaled at an estimated seismic intensity of four times the specified intensity. The building was severely damaged but remained standing due to the excellent connection between the RC slabs and tie-beams surrounding each floor and the roof. Therefore, the 2008 Code has regulated that reliable measures to ensure the integrity of the connection joint among pre-cast RC slabs of the floor and roof system be mandated.

Figure 14. Severely Damaged Three-Story Masonry School Building (0.05g/0.20g)


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Figure 15. Collapse of Transverse Wall (0.05g/0.20g)

Figure 16. Stable Floor of Pre-cast Slabs with Excellent Joints and Tie-beams (0.05g/0.20g)

Figure 17. Two Bottom Stories Collapsed and Five Upper Stories Remained Standing, Beichuan County (0.1g/1.0g)


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3.3.2.4 Duplicate earthquake resistance system The concept of a duplicate earthquake resistance system was addressed in the 2001 Code, which was significant in preventing the collapse of some structures. It is known that the secondary members of a structure, such as the bracing of a frame structure or the coupling beam of a shear wall structure, may be damaged before major members such as a column and/or shear wall are affected, to reduce the earthquake forces. The RC tie column and boundary-beam are required to enhance the ductility of masonry walls and could act as secondary members to prevent masonry structures from collapse in major earthquakes. (1) Features of structural damage in epicenter regions The ground motion in the epicenter area was so strong that the bottom floor of many structures suddenly collapsed at the moment of the initial arrival of the earthquake wave, and therefore the ground motion could be isolated by the collapsed layer to save the upper stories from severe failures. Figure 17 shows a confined masonry apartment building located in Beichuan County, in the epicenter area. The two bottom-stories were destroyed and suddenly collapsed by the first shock at the initial arrival of earthquake wave, but the five upper stories remained intact. (2) Structural redundancy The 2008 Code required structural systems to avoid a loss of loading capacity and seismic capacity due to the failure of a part of the structure or its elements. Adoption of a duplicate system and increasing the structural redundancy by means of a multi-bay frame, additional braces or shear wall is encouraged. The seismic capacity of key parts of a structure and its members should be enforced to prevent the entire structure from sequential collapse. It was learned from building damage in the 1995 Kobe earthquake, 1999 Chi-Chi earthquake and again in the 2008 Wenchuan earthquake that use of a single-bay RC frame structure for tall buildings should be restricted due to its lack of structural redundancy. Figure 18 shows the Xuankou High School before the event in Yingxiu Town, Wenchuan County. The five-story teaching building and laboratory were constructed of two-bay RC frame structures with some redundancy. Fortunately, more than 1,200 students escaped from these two buildings, which survived the main shock with an intensity of over 11 degrees (PGA≈1.0g) in the epicenter area. The teaching building partially collapsed and the laboratory totally collapsed in the aftershock (see Figures 19–21). (3) Ductility of masonry structures For masonry structures, the limits of height, number of stories and floor heights are specified in the 2008 Code. The limits for Class B buildings should be taken based on a seismic intensity of one degree higher than the specified intensity. For Class B school and hospital buildings, the limits should be defined based on a seismic intensity of two degrees higher than the specified one. Some questions were proposed after the “5.12” Wenchuan earthquake. Could masonry structures be used again in earthquake-prone areas? Should school buildings be made of RC? Should pre-cast RC slabs be prohibited for use as the floor system for masonry structures? The careful study of the performance of masonry structures in regions


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severely impacted by a disaster indicates that if the special technique of using a confined RC boundary-beam and tie-column has been taken, the seismic performance objectives of “operational at the minor earthquake level,” “life safety at the moderate earthquake level” and “collapse prevention at the major earthquake level” can be achieved for masonry structures. For example, there was a four-story RC single-bay frame hospital structure and a masonry residential structure located side by side at the site of an effective seismic intensity of 9 degrees (PGA = 0.40g) in Nanba Town, Pingwu County. The seismic design was based on the specified intensity of 7 degrees (PGA = 0.10g), which was much lower than the estimated actual intensity at the site. The hospital building was severely damaged and nearly collapsed, while the residential building survived due to the excellent confinement of the masonry structure (see Figs. 22–24). (4) Collision and sequential collapse A seismic partition for a building with an irregular plan is required by the design code. The position and the width of the separation joint should be set depending upon the specified seismic intensity, type of structure and building height. The upper structures at both sides of the partition should be completely separated to avoid knocking. However, it is not necessary to set partitions for any irregular building. The 2008 code requires that the width of a partition be large enough to avoid collision of the upper structures during earthquakes that may result in a sequential collapse. Figures 25–26 show an example of a sequential collapse of buildings in Beichuan County, the epicenter area. The commercial buildings on the left side of the street sequentially collapsed due to knocking from the office building on the right side of the street. (5) Seismic design of stair shaft The stair shaft, at the entrance and exit of buildings, provides the only way for people to evacuate and should therefore guarantee safety in the case of any disaster, including earthquake. Clause 7.3.1 of the 2008 Code stresses that RC tie-columns should be set up at the corners of stair shaft and exterior walls, ends of step beam, the joints of interior and exterior walls, etc. in masonry structures. Clause 7.3.8 again requires that the pre-cast step beam be appropriately connected with the platform beam, and the RC tie-columns should expand up to the top of the stair shaft above the roof. Figure 27 shows a severely damaged three-story masonry teaching building. The stair shaft collapsed due to a lack of tie columns at its corners. In contrast, Fig. 28 presents an example of a successful design. Although the brick walls and step beams of the six-story masonry residential building were severely damaged, the stair shaft remained stable because the tie-columns were appropriately set at the ends of the platform beam.


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Figure 18. Xuankou High School Constructed in 2006

Figure 19. Damaged Xuankou High School (0.1g/1.0g)

Figure 20. Partially Collapsed Teaching Building (0.1g/1.0g)


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Figure 21. Totally Collapsed Laboratory Building (0.1g/1.0g)

Figure 22. Damage to Two Nearby Buildings (0.1g/0.4g)

Figure 23. Severely Damaged Four-story RC Single-bay Frame Single Span

Hospital Building (0.1g/0.4g)


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Figure 24. Good Performance of Four-Story Confined Masonry Apartment Building (0.1g/0.4g)

Figure 25. Collision between an Office Building and Apartment Buildings in Beichuan County (0.1g/1.0g)

Figure 26. Sequential Collapse of Commercial Buildings in Beichuan County (0.1g/1.0g)


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Figure 27. Collapsed Stair Shaft of a Three-Story School Building in Mianzhu County (0.1g/0.3g)

Figure 28. Six-Story Masonry Residence Building Remained Stable with a Severely Damaged Stair Shaft (0.1g/0.3g)

4. CONCLUSIONS Some members of the Code Editorial Group have taken part in field investigations in the disaster areas after the “5.12” Wenchuan earthquake. A large amount of damage data from buildings and infrastructure was collected. The study of building damage on structures of different ages in accordance with the corresponding design codes was carried out after the earthquake. A revision of the “Standard for Classification of Seismic Protection of Building Constructions GB50223-2008” and “Code for Seismic Design of Buildings GB50011-2001(2008 version)” was completed within three months and published on 30 July, 2008. In general, the seismic capacity of many structures has been upgraded. The seismic class for schools, hospitals and buildings with a high occupancy rate, low-cost houses in rural areas, and infrastructure has been raised to a higher level by the 2008 Standard.


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A study that compared code regulations with observed damage has shown that the seismic conceptual design, i.e., the essential requirements issued by the code, is sometimes more significant and difficult for engineers to deal with than the structural calculation. The 2008 Code stresses that (a) the integration and duplicate seismic structural systems are very important and necessary for some structures, (b) the configurations of buildings should be regular and symmetric to the extent possible, and (c) structural redundancy is a key factor in ensuring that collapse is avoided when an individual member fails. There is no doubt that the Code should be further improved gradually. There are still many issues that need to be addressed. For example, how can the “strong column and weak beam” for a frame structure be realized? How can the partition of a building be set correctly? How can buildings avoid sequential collapse? How is the stair shaft involved in modeling of structure analyses? How are the joints of pre-cast RC slabs detailed properly? How can nonstructural members and their joints, such as infill walls, ceilings, curtain walls, etc., be designed? Can a complex structure with a bottom frame and upper masonry walls be used in seismic regions? These questions are expected to be resolved in the next revision of the code. REFERENCES 1. Standard for Classification of Seismic Protection of Building Constructions GB50223-

2008 (2008), Beijing: China Architecture & Building Press. (in Chinese) 2. Code for Seismic Design of Buildings GB50011-2001 (2008 version), Beijing: China

Architecture & Building Press. (in Chinese) 3. Wang, Yayong, “Lessons Learned from the 5.12 Wenchuan Earthquake: Evaluation of

Earthquake Performance Objectives and the Importance of Seismic Conceptual Design Principles,” Earthquake Engineering and Engineering Vibration, 2008, Vol. 7, No. 3, pp. 255–262.


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APPLICATION OF BUCKLING-RESTRAINED BRACES IN STEEL FRAMEWORKS AGAINST EARTHQUAKES

GUO-QIANG LI 1,*, FEI-FEI SUN 1, SU-WEN CHEN 1 and XIAO-KANG GUO 2 1 State Key Laboratory for Disaster Reduction in Civil Engineering

2 China College of Civil Engineering, Tongji University, China

[email protected]* , [email protected], [email protected] and [email protected]

ABSTRACT Due to the excellent seismic performance, buckling restrained brace (BRB) has been rapidly accepted as a promising seismic device world widely. Through more than thirty full scale specimen tests, two types of BRBs were developed at Tongji University in the past three years. TJI-type is an all-steel BRB designed for small tonnage application, while TJII-type consists of concrete-filled steel tube applied for larger ones. Cyclic test results demonstrated that both of the two types of BRBs have stable hysteretic behavior, substantial energy dissipation capacity and good ductility. Then, the advantages of buckling restrained braced steel frames (BRBFs) than concentrically braced steel frames (CBFs) against design and severe earthquakes were investigated by contrast on a typical 8-story building through nonlinear time history analysis. As an alternative application of BRBs, the structural system of simple-connected steel frame with buckling restrained braces (SSBFs) was proposed for multi-story buildings. Seismic performance of this system was investigated by static and time-history analysis. Analysis results indicated that the proposed structural system can perform well as steel moment frame does. The elasto-plastic behavior of the system was also verified by shaking table test. Keywords: Buckling Restrained Braces, Buckling Restrained Braced Frames, Concentrically Braced Frames, Simple-Connected Steel Frame with Buckling Restrained Braces, Seismic Behavior, Shaking Table Test


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1. INTRODUCTION A buckling restrained brace (BRB) is generally composed of a ductile steel core element that carries the axial load and a constraining element that prevents the core element buckling in compression. The steel core is designed to yield in both tension and compression that can dissipate a significant amount of energy in earthquakes. After the Northridge (1994) and Kobe (1995) earthquakes, BRBs have been quickly accepted as an alternative choice for concentrically braces (Reina et al. [1], Clark et al. [2]) and the buckling restrained braced frames (BRBFs) also have emerged as a very promising structural system to resist seismic excitation throughout the world. However, the earliest research of BRB was reported by Kimura et al. [3] in 1976. From then, numerous studies of BRBs and BRBFs have been done by Koetaka et al. [4], Tremblay et al. [5], Blacks et al. [6], Sabelli et al. [7], Fahnestock et al. [8], Uang et al. [9], and Tsai et al. [10], etc, at component, sub-assemblage, and frame levels. A lot of BRBs with different configuration were developed in Japan, United States and Taiwan (Xie [11], Uang [12]), most of which are patent and proprietary. However, there is no performance standard of BRB available in Japan, because BRB is treated as hysteretic damper in structural design, the performance requirement of which is based on structural design target. But in the U.S., performance requirements and standard loading protocols of BRBs with a design guideline of BRBFs have been compiled in the 2005 AISC Seismic Provisions (AISC [13]). In mainland of China, no domestic BRB was developed in the past and the BRBs adopted by very a few of buildings were all imported from overseas. Related research of BRBs has just been launched during the recent five years. After the Wenchuan earthquake (2008), benefits of BRBs against earthquakes are paid even more attention. Therefore, there is a great need to determine the performance standard and the design requirements of BRBs according to Chinese building seismic design code [14] and to develop BRBs using domestic technologies and materials in mainland of China. BRB’s performance standard that meets the requirements of Chinese building seismic design code will be proposed in this paper, firstly. Then, two types of buckling restrained braces were developed by using different kinds of domestic steels, including low yield strength steels. Properties of the BRBs were also investigated by series of cyclic loading tests. Owing to the limited ductility and energy dissipation capacity of conventional concentrically braced frame (CBF) systems, significant research efforts (Sabelli et al. [7], Iwata et al. [15]) have gone towards developing new CBF systems with stable hysteretic behavior, good ductility and large energy dissipation capacity. Buckling-restrained braced frame (BRBF) is one of new systems with improved seismic behavior, which is composed of a CBF with buckling-restrained braces (BRBs). A design example was compared between a CBF and a BRBF to illuminate the advantages of BRBs for earthquake resistance in details. The conventional philosophy of seismic design depends on inelastic deformation of structural members for dissipation of energy (Kim et al. [16]). This design concept may provide safety and economy, but may not prevent damages in structures by earthquakes. The damage in main structural members can be prevented or minimized by employing simple-connected frames to support vertical loads (Kim et al. [17]), and buckling-restrained brace to withstand lateral seismic or wind loads, which is called simple-connected steel frame with buckling restrained braces (SSBFs). By static and time-history analysis, the seismic behavior of simple-connected steel frame with buckling restrained braces was investigated. The static analysis results showed that this proposed structural system has a good energy-dissipation behavior as well as the rigid steel frame. The time-history analysis results showed that the


20

maximum inter-story drifts are relatively uniform under severe seismic excitation and the braces in each story may yield to dissipate earthquake-input energy though relatively weak story in this structural system exists. The feature of the elasto-plastic behavior of SSBFs was also verified by the shaking table tests. 2. DEVELOPMENT OF TJ-TYPE BRBS 2.1 Loading Scheme When considering BRB’s performance, two key issues should be taken into account, i.e., ultimate ductility and cumulative plastic ductility (CPD). Relationship between axial average deformation ratio of BRB and inter-story drift ratio of structure can be approximately expressed as Equation 1 (see Figure 1).

/ 0.5 sin 2L L (1)

where is the angle between BRB and beam, L and L are the axial deformation and the length of BRB, respectively. As required by Chinese building seismic design code, should not exceed 1/50 under severe earthquakes. Accordingly, will be less than 1/100. By referring to the 2005 AISC Provisions, the cumulative plastic deformation of BRB is also recommended to reach no less than 200 times of its initial yield deformation. However, to avoid the bother of finding the accurate initial yield deformation of BRB in testing process, the loading history to test the performance of BRBs is recommended as follows. Using deformation controlled loading method, four levels of axial deformation are selected as the amplitudes of the loading cycles, i.e., 1/300, 1/200, 1/150, 1/100 of the BRB’s total length, and each level of the deformation repeats 3 cycles, as shown in Figure 2. During the test, BRBs should have stable hysteretic behavior without significant deterioration of performance.

-0.010

-0.005

0.000

0.005

0.010

Level-4 L/100Level-3 L/150Level-2 L/200Level-1 L/300

L= BRB's total length

Axi

al a

vera

ge d

efor

mat

ion

ratio

Load steps

Figure 1. Relationship of and Figure 2. Proposed loading scheme 2.2 Test Arrangement Two types of BRBs were developed by cyclic loading tests conducted on more than thirty full scale specimens in Tongji University from year 2007 to 2009. They are entitled as TJI-type and TJII-type BRB. The former is made of all steel, using steel stiffeners to constrain the steel core. While, the latter consists of both steel and concrete with the crisscross section steel core restrained by concrete-filled steel tube. In this paper, the tests on eight representative specimens were selected to present. The BRB specimens are different in length, core steel type, core plate thickness, yield force Fy and connection type as shown in Table 1. The test arrangements were shown in Figure 3 and Figure 4 for TJI-BRB and TJII-BRB, respectively.


21

In Table 1, Le, Ly, L, Ct, Cw, Tt, W1 and W2 represent length of elastic segment, length of yielding segment, length of BRB specimen, thickness and wideness of core plate, thickness of tube and the external dimensions of the BRB, respectively.

Table 1. Design Details of the BRB Specimens

Specimen No.

Core steel type

Le (mm)

Ly (mm)

L (mm)

Ct (mm)

Cw (mm)

Tt (mm)

W1 (mm)

W2 (mm)

Fy (kN)

Connection

TJI-1 LY160 965 1252 3182 40 214 10 238 238 1200 Bolt TJI-2 LY225 923 1205 3051 26 230 10 254 254 1200 Bolt TJI-3 Q195 923 1205 3051 26 260 10 284 284 1300 Bolt TJI-4 Q235 918 1215 3051 26 260 10 230 284 1600 Bolt TJI1-1 LY225 830 6340 8000 55 296 10 550 550 6050 Welded TJII-2 LY225 830 6340 8000 55 296 10 550 550 6050 Welded TJII-3 Q235 345 3180 3870 30 116 10 220 220 1400 Welded TJII-4 LY225 300 3100 3700 30 160 10 236 236 1800 Welded

Figure 3. Test Arrangement for TJI-BRB

Figure 4. Test Arrangement for TJII-BRB

2.3 Test Results The eight BRB specimens’ hysteretic curves measured from tests were shown in Figure 5. It can be seen that all the specimens have stable and plump hysteretic loops without deterioration of stiffness and strength during the test processes. For all the specimens, different additional loading histories were conducted after the proposed loading scheme.

-60 -40 -20 0 20 40 60

-3000

-2000

-1000

0

1000

2000

3000

TJI-1

Axi

al l

oad

(kN

)

Axial deformation (mm) -40 -20 0 20 40

-2000

-1000

0

1000

2000

TJI-2

Axi

al lo

ad (

kN)

Axial deformation (mm)


22

-60 -40 -20 0 20 40 60-3000

-2000

-1000

0

1000

2000

3000 TJI-3

Axi

al lo

ad (

kN)

Axial deformation (mm) -40 -20 0 20 40

-3000

-2000

-1000

0

1000

2000

3000 TJI-4

Axi

al lo

ad (

kN)


-120 -80 -40 0 40 80 120-12000

-8000

-4000

0

4000

8000

12000

TJII-1

Axi

al lo

ad (

kN)

Axial deformation (mm) -200 -100 0 100 200 300 400 500

-12000

-8000

-4000

0

4000

8000

12000TJII-2

Axi

al lo

ad (

kN)


-50 -25 0 25 50-3000

-2000

-1000

0

1000

2000

3000

Axi

al lo

ad (

kN)


TJII-3

-50 -40 -30 -20 -10 0 10 20 30 40 50

-3000

-2000

-1000

0

1000

2000

3000

TJII-4

Axi

al f

orce

(kN

)

Axial deformation(mm)

Figure 5. Hysteretic Curves of the BRB Specimens The main parameters’ values measured from the hysteretic curves of the specimens were

listed in Table 3, in which max and max represent the maximum average strain rate of the BRB

and the BRB’s yielding segment, respectively; CPD1 means the cumulative plastic ductility during the standard loading history proposed and CPD2 represents the cumulative plastic ductility during the additional loading cycles; CPDt is the total cumulative plastic ductility of the BRB specimen when the test was stopped or the specimens failed.

Table 3. Parameters of the Test Specimens

Specimen No.

yF

(kN)

'yF

(kN) maxuF

(kN)

maxuF

(kN)

yu

(mm) max max

(%)

CPD1 CPD2 CPDt

TJI-1 1200 1216 2750 3075 2.14 2.53 1.01 1.12 1/60 4.24 398 401 799 TJI-2 1200 1293 1996 2228 2.44 1.72 1.08 1.12 1/60 4.22 327 414 741 TJI-3 1300 1658 2616 2677 3.25 1.61 1.28 1.02 1/60 4.22 234 187 421 TJI-4 1600 1718 2572 2714 3.04 1.58 1.07 1.06 1/80 4.98 217 175 392 TJII-1 6050 7059 9239 10884 9.21 1.54 1.17 1.18 1/80 1.58 213 237 450 TJII-2 6050 7006 10655 11068 9.38 1.58 1.16 1.04 1/16 7.89 204 155 359 TJII-3 1400 1636 2406 2618 4.16 1.60 1.17 1.09 1/80 1.52 217 255 472 TJII-4 1800 2133 2854 2976 3.71 1.40 1.19 1.04 1/80 1.49 399 1077 1476


23

2.4 Conclusions From the test results, some instructive conclusions can be drawn as follows: (1) The eight BRB specimens have stable hysteretic property; large ultimate ductility and their cumulative plastic ductility capacity are much higher than 200, which all satisfy the requirements of BRB’s performance for application proposed in this paper. (2) The strain hardening factor ω of LY160 is much higher than the other three types. (3) The compression and tension capacity of the BRBs are very similar, considering the β index of the eight specimens all less than 1.2. (4) The proposed loading scheme for testing BRB’s performance in this paper is harder than that presented in the AISC Provisions (2005), notice that the cumulative plastic ductility of the specimens all exceeded 200 at the end of the proposed standard loading history. 3. APPLICATION IN MOMENT STEEL FRAME BRBs can provide an alternative and efficient solution to overcome the problems that may exist in concentrically braced steel frames (CBFs) to resist earthquake excitation. The benefits of BRBs in design and severe earthquakes will be investigated by comparison of a BRBF and a CBF with the same structural layout and vertical loads through non-linear time history analysis as bellow. 3.1 Analysis model Software MTS programmed by Tongji University was adopted to do the non-linear time history analysis. The 3D architectural layout of the structure was shown in Figure 6. To simplify the analysis, the side span was chose to establish a 2D model as shown in Figure 7. To consider the influence of adjacent spans, 100kN concentrated force was added on each beam-column joints. The dead load was 50kN/m and the live load was 20kN/m for each floor. Sectional and material properties of beams, columns and braces were listed in Table 4. Features of ground motion adopted were shown in Table 5. The peak ground motion accelerations were scaled to 400gal and 620gal for design and severe earthquakes respectively in the design earthquake level-9 according to Chinese building seismic design code.

3600

3600

3600

3600

3600

3600

3600

3600

2880

0

9000 9000250020500

Figure 6. 3D Layout Figure 7. 2D Layout


24

Table 4. Properties of Members

Floor Beam (Q345)

Column (Q345)

CB (Q345)

BRB (Q235)

1~4 HN500×200 □400×15 HM340×250 Fy=1500kN 5~8 HN500×200 □400×12 HM294×200 Fy=1000kN

Table 5. Properties of Ground Motion

Ground motion Seismic design level Site typeDesign earthquake PGA

Severe earthquake PGA

El-centro 9 Ⅱ 400gal 620gal 3.2 Analysis Results The main results including inter-story shear force and displacement, hysteretic properties of the braces and structure and plastic hinge distribution were shown in Table 6.

Table 6. Main Results of Time History Analysis Design earthquake Severe earthquake BRBF CBF BRBF CBF

0 5 10 15 20 25 300

1

2

3

4

5

6

7

8Design earthquake BRBF

max

=1/121

Story

Inter story displacement(mm)

Dmax

=29.51mm

0 5 10 15 20 25 30

0

1

2

3

4

5

6

7

8Design earthquake CBF

max

=1/120

Story


Dmax

=29.77mm

0 5 10 15 20 25 30 35 40

0

1

2

3

4

5

6

7

8Severe earthquake BRBF

max

=1/93

Story


Dmax

=38.75mm

0 10 20 30 40 50

0

1

2

3

4

5

6

7

8Severe earthquake CBF

max

=1/69

Story


Dmax

=51.91mm

0 1000 2000 3000 40000

1

2

3

4

5

6

7

8

Vmax

=3536.83kN

Design earthquake BRBF

Story

Shear force(kN) 0 1000 2000 3000 4000

0

1

2

3

4

5

6

7

8

Vmax

=3761.64kN

Design earthquake CBF

Stor

y

Shear force(kN) 0 1000 2000 3000 4000

0

1

2

3

4

5

6

7

8

Vmax

=3872.85kN

Severe earthquake BRBF

Story

Shear force(kN)0 1000 2000 3000 4000

0

1

2

3

4

5

6

7

8

Vmax

=4194.58kN

Severe earthquake CBF

Sto

ry

Shear force(kN)

-15 -10 -5 0 5 10 15 20-2000

-1500

-1000

-500

0

500

1000

1500

2000

Hysteretic curve of BRB in design earthquake

Axia

l fo

rce(

kN)


-30 -25 -20 -15 -10 -5 0 5 10-2500

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

Hysteretic curve of CB in design earthquake

Axial force(kN)

Axial deforamtion(mm) -20 -15 -10 -5 0 5 10 15 20 25 30

-2000

-1500

-1000

-500

0

500

1000

1500

2000

Hysteretic curve of BRB in severe earthquake

Axial force(kN)

Axial deformation(mm) -80 -70 -60 -50 -40 -30 -20 -10 0 10

-2500

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

Hysteretic curve of CB in severe earthquake

Axial force(kN)



25

-30 -20 -10 0 10 20-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

Hysteretic curve of BRBF in design earthquake(2nd floor)

St

ory

shea

r(kN

)

Story displacement(mm) -25 -20 -15 -10 -5 0 5 10 15

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

Hysteretic curve of CBF in design earthquake(2nd floor)

Story shear(kN)

Story displacement(mm) -40 -30 -20 -10 0 10 20 30

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

Hysteretic curve of BRBF in severe earthquake(2nd floor)

Shear forc

e(kN)

Story displacement(mm) -30 -20 -10 0 10 20 30 40 50

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

Hysteretic curve of CBF in severe earthquake(2nd floor)

Shear force(kN)

Story displacement(mm)

Plastic hinge distribution Plastic hinge distribution Plastic hinge distribution Plastic hinge distribution

3.3 Conclusions From the analysis results, some main conclusions can be drawn as follows: (1)In design earthquakes, the CBF and BRBF generally had a similar performance, because the story shear and displacement distributions of the two were much the same and only one plastic hinge formed in each of the two structures. However, most of the BRBs dissipated the earthquake energy by axial yielding of the steel core almost evenly along the structural height, while the concentrically braces buckled only in some stories, which may cause weak part of the structure system, and the out of plane deformation of the braces would also make decorative layer damaged. (2)In severe earthquakes, the BRBF definitely performed much better than the CBF did. A lot of plastic hinges formed in the main frame of CBF led to unsafely and difficulty of repairment after earthquakes. The maximum story drift of the CBF is 1/69, which is much bigger than 1/93 of the BRBF. From the typical hysteretic properties of the two structures, it is easy to find that BRBs can absorb most of the earthquake energy to make the main frame maintain elastic. 4. Application in Simple-Connected Steel Frame Although BRBFs perform much better than CBFs in severe earthquakes, it may not prevent the damage formed in the main structural members totally, which may bring much cost for repairment after the earthquakes. The damage in main structure can be prevented or minimized by employing simple-connected frames to support vertical loads and buckling-restrained brace to withstand lateral seismic or wind loads, which is proposed as simple-connected steel frame with buckling restrained braces (SSBFs). SSBF is a new-style structural system. The structural behavior was investigated by static analysis, dynamic analysis and shaking table test as bellow. 4.1 Analysis Model For the structure shown in Figure 8, plane truss method with continuous chord can be employed to calculate deformation and stress under lateral loads in elastic analysis. For elasto-plastic analysis, the beam and column can be elastic element, and the brace should be elasto-plastic element.


26

Figure 8. Schematic of SSBF Figure 10. Elevation Schematic of Brace 4.2 Lateral Stiffness of the SSBFs The lateral stiffness is provided by frame and braces. Because the frame is simple-connected, its lateral stiffness is very small compared with brace, which can be neglected. For the stiffness provided by brace, the values are different before and after its yielding.

Figure 9. Steel Core in BRB

The steel core in a typical BRB was shown in Figure 9. It is composed of three parts, connecting sections, transition sections and buckling restrained section. The lengths of three parts are 3l , 2l and 1l . And cross section areas of the three parts are 3A , 2A and 1A . Then the

axial stiffness of the brace can be obtained by Equation 2.

1 2 3

2 3 1 2 1 32 2e

k k kk

k k k k k k

(2)

where 11

1

EAk

l , 1 3

22 1 3

( )

(ln ln )

E A Ak

l A A

, 3

33

EAk

l .

For the buckling restrained brace, only the buckling restrained section will yield. The axial stiffness of the brace after yield can be obtained by Equation 3.

1 2 3

2 3 1 2 1 32 2p

pp p

k k kk

k k k k k k

(3)

where 11

1p

qEAk

l , q is hardening coefficient.

Since the lateral stiffness of simple-connected frame is too small to be neglected, the overall structural lateral stiffness can be obtained from all the BRB’s lateral stiffness. For a single BRB, the lateral stiffness can be given by


27

2cosbiK k (4)

where k is the axial stiffness of the BRB, is the angle between brace and floor (see Figure 10). The overall floor lateral stiffness is sum of the lateral stiffness of all BRB in the floor.

biK K (5)

4.3 Behavior of the SSBFs Because the beam hinge-connected to the column, will only bear vertical loads, it will remain elastic under earthquake action. Thus elastic elements are used for the beams. For the columns in the first floor, they may yield when the bases are rigid, otherwise it will remain elastic. Thus for the columns with rigid base in the first floor, elasto-plastic element should be employed. For the columns in other floors and the columns with hinge base in the bottom floor, elastic elements will be applied. The refined fiber plastic hinge models are applied in modeling the elasto-plastic columns. 4.4 Monotonic Loading The behavior of rigid frame and SSBF were compared. The models were shown in Figure 10. The height and the span are 3m and 4m respectively for both structures. The steel for beams and columns were Q235, and the steel for the core of BRB was Q195.

H20

0×20

0×12

×12

H20

0 ×20

0×12

×12

H200×100×8×10

Core Steel：100×

10

H15

0×15

0×10

×10

H15

0 ×15

0×10

×10

H200×100×8×10

0

50

100

150

200

250

300

0 0.05 0.1 0.15 0.2 0.25 0.3Drift(m)

Lat

eral

Loa

d(kN

)

rigid frame SSFBRB

Figure 10. Two Different Structure Type Figure 11. Lateral Load-drift Curve

Lateral load was applied on the top of the frame, until 10% story drift angle was reached. For the SSBF, the brace was in compression under the lateral load. The relationship between drift and lateral load was presented in Figure 11. Though the floor yield strengths are similar; the lateral stiffness of SSBF is larger than rigid frame. Moreover, in SSBF only the BRB has plastic deformation, beam and columns still remain elastic. 4.5 Cyclic Loading To analyze the energy dissipating capacity, the structures were conducted on cyclic load according to the loading scheme as shown in Figure 12. The hysteretic curves of rigid frame and SSBF were shown in Figure 13 and Figure 14, respectively.


28

h/200

h/80h/50h/30

h/30h/50h/80

h/200

displacement

-200

-100

0

100

200

-0.12 -0.06 0 0.06 0.12

Drift(m)

Sto

ry S

hear

(kN

)

-200

-100

0

100

200

-0.12 -0.06 0 0.06 0.12

Drift(m)

Sto

ry S

hear

(kN

)

Figure 12. Loading Scheme Figure 13. Hysteretic Curve of Rigid Frame

Figure 14. Hysteretic Curve of SSBF

Based on the comparing results, it can be seen that the hysteretic behaviors of rigid frame and SSBF are similar. The energy dissipating capacity of the SSFBRB is as good as rigid steel frame. 4.6 Dynamic Analysis Besides the behavior under static loads, the dynamic behaviors need to be analyzed. As shown in Figure 15, a six stories plane SSBF was designed, and the seismic behavior was studied by time-history analysis. The section area of the core steel in BRB is 2100mm2 in floor 1 to floor 3, and 1050mm2 in floor 4 to floor 6, the sectional properties were listed in Table 7. The El-centro earthquake record was used as ground motion input. The acceleration peak was increased from 220gal to 400gal and then to 620gal, a damping ratio of 0.05 was adopted.

Figure 15. Model for Time-history Analysis Table 7. Sectional Properties The deformation and drift of the model were shown in Figure 16 and Figure 17. The maximum drift angles for case 400 gal and 620gal are 1/58 and 1/55 respectively, which were smaller than 1/50. From Figure 17, it can be found that the drift angles of other floors for these two cases are quite different though the maximum drift angels are similar. This result shows that, in SSBF, when the BRB in one floor yielded, the drift of the floor did not increase rapidly, because the BRBs in other floors would yield and participate in energy dissipations. Thus, in SSBF the phenomenon of weak floor exists but the performance would be better compared to rigid frames.


29

0

1

2

3

4

5

6

0 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.24

Floor defromation(m)

Flo

or

220gal

400gal

620gal

0

1

2

3

4

5

6

0 0.005 0.01 0.015 0.02

Drift angle(rad)

Flo

or 220gal

400gal

620gal

Figure 16. Maximum Story Deformations Figure 17. Maximum Inter-story Drifts The maximum story shear reactions of the model were shown in Figure 18 to Figure 20. In these figures, the maximum story shear, maximum shear carried by BRB, and maximum shear carried by columns were listed. Because the shear forces of story, columns and BRB did not reach simultaneously, the shear carried by BRB in some stories was larger than the story shear. Inter-story seismic shear was mainly carried by the buckling restrained braces except in the first story, where a portion of the shear was carried by columns. With the development of the plastic deformation, the shear carrying ratio between BRB and columns decreases. The reason is that the load carrying capacity of BRB will not increase after it yields, so the increasing portion of story shear will be carried by columns.

0

1

2

3

4

5

6

0 100 200 300 400Story shear(kN)

Flo

or

Shear carried byBRBShear carried bycolumnsStory shear

0

1

2

3

4

5

6

0 200 400 600 800Story shear(kN)

Flo

or


0

1

2

3

4

5

6

0 200 400 600 800 1000

Story shear(kN)

Floo

r


Figure 18. Maximum Story Shear in Case 220gal

Figure 19. Maximum Story Shear in Case 400gal

Figure 20. Maximum Story Shear in Case 620ga

The design target of a simple-connected steel frame with buckling restrained braces is to let the beams and columns remain elastic even when the structure is subjected to severe earthquake, so that the structure will not collapse. The beam is simple-connected to the column, so the stress will not increase much when earthquake attacks. For the columns, the Equation 6 is used to evaluate the stress. The stress ratio at the base of the column is defined by

eqy y

N M

Af Wf (6)


30

where N and M are the axial force and bending moment at the base of the column, A and W are area and elastic modulus of the column section, yf is the yield stress of the column steel. If

the stress ratio eq is smaller than 1, the column will remain elastic. The maximum stress ratio

at the column base under severe earthquake was presented in Table 8. Based on the results in Table 8, the column remains elastic under severe earthquake. The design target was achieved.

Table 8. The Maximum Stress Ratios at the Column base under Severe Earthquake Peak acceleration

220gal 400gal 620gal

eq 0.285 0.394 0.673

4.7 Shaking Table Test of SSBF In order to study the seismic behavior of the SSBF, a full-scale model of simple-connected steel frame with buckling restrained braces was tested on the shaking table. 4.8 Test Model The dimension of the test model was shown in Figure 21. The column section is H150×150×8×8 and the beam section is H180×100×6×8. The steel core of the TJI type BRB is 60×6mm, and outline dimension is 92×92mm. The column is rigid connected to the base. The total weight of the test model, as shown in Figure 22, is about 13.2 ton. The El-centro S90W earthquake record and Shanghai wave, an artificial earthquake wave, were used as ground motion input. The time scaling factor is 1:2 and acceleration scaling factor is 1:1.

Figure 21. Dimension of the Test Frame Figure 22. Test Arrangement

4.9 Test Results The relationship between dynamic magnification factor and input acceleration peak value was shown in Figure 23. The maximum factor is 2.8. And the factor in floor1 is larger than that of floor2.


31

0

0.5

1

1.5

2

2.5

3

0 0.2 0.4 0.6 0.8 1 1.2

0

1

2

0 1/200 1/100Drift angle

Flo

or

0.05g

0.10g

0.20g

0.30g

0.50g

0.70g

1.00g

0

1

2

1/200 1/100

shw-1.2g

Drift angle

Floo

r

Figure 23. Acceleration Ratio Figure 24. Drifts under El-centro S90W

Figure 25. Drifts under Shanghai Wave

Drift is an important parameter in seismic analysis. For the test model, when the BRB yield, the drift angle is 1/356. The drift angle under El-centro earthquake record action was shown in Figure 24. When the peak acceleration reaches 0.5g, BRB begin to yield. The maximum drift angle under Shanghai wave is 1/104, as shown in Figure 25. The BRB has obvious plastic deformation, but there is no buckling phenomenon appeared. And the beams and columns remain elastic during the tests. Based on the results of the shaking table tests of SSBF, the structural system has good seismic behavior. The conclusions based on static and dynamic analysis are verified. 4.10 Conclusion Based on static and dynamic analysis, it can be found that the simple-connected steel frame with buckling restrained braces has good hysteretic behavior as a steel rigid frame. The shaking table test results showed that the beam and column may remain elastic even under severe earthquake (peak acceleration as higher as 1.2g). The BRB has obvious plastic deformation, but there is no buckling phenomenon appeared. The theoretic and test results approved that the simple-connected steel frame with buckling restrained braces can be used in seismic region. 5. SUMMARY AND CONCLUSION In this paper, the uniform performance standard for BRBs was proposed according to the requirements of Chinese building seismic design code firstly. Then, two types of BRBs with different configuration were developed by adopting Chinese materials and technologies. The BRBs’ performance of very stable hysteretic behavior, large ultimate ductility and excellent low-cycle fatigue life were also verified by series of cyclic loading tests. Then, advantages of buckling restrained braced steel frames (BRBFs) than concentrically braced steel frames (CBFs) against design and severe earthquakes were investigated in details by a contrast design example though nonlinear time history analysis. A new structural system, simple-connected steel frame with buckling restrained braces (SSBFs), was proposed. The structural behavior was investigated by static analysis, dynamic analysis and shaking table test, which demonstrated that SSBFs can be used in seismic region. 6. ACKNOWLEDGMENTS This study was financially supported by the National Key Technology R&D Program of China (Grant No. 2006BAJ01B02), the financial supports are highly appreciated.


32

REFERENCES 1. Reina, P. and Normile, D., “Fully Braced for Seismic Survival”, Engineering News

Record, July 21, 1997, pp. 34-36. 2. Clark, P. Aiken, I., Kasai, K., Ko, E., and Kimura, I., “Design Procedures for Buildings

Incorporating Hysteretic Damping Devices.” Proceedings, 69th Annual Convention, SEAOC, Sacramento, CA, 1999.

3. Kimura, K., Yoshioka. K., Takeda. T., Fukuya. Z. and Takemoto. K., “Tests on Braces Encased by Mortar in-filled Steel Tubes”, Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan, 1976, pp. 1041-2 [in Japanese].

4. Koetaka, Y., Narihara, H. and Tsujita, O., “Experimental Study on Buckling Restrained Braces”, In: Proceedings of the sixth pacific structural steel conference, 2001, Vol. I, pp. 208-13.

5. Tremblay, R., Bolduc, P., Neville, R. and Devall, R., “Seismic Testing and Performance of Buckling-Restrained Bracing Systems”, Canadian Journal of Civil Engineering, 2006, Vol. 33, No. 2, pp.183-98.

6. Black, C.J., Makris, N. and Aiken, I.D., “Component Testing, Seismic Evaluation and Characterization of Buckling-Restrained Braces”, Journal of Structural Engineering, 2004, Vol. 130, No. 6, pp. 880-94.

7. Sabelli, R., Mahin, S. and Chang, C., “Seismic Demands on Steel Braced Frame Buildings with Buckling-Restrained Braces”, Engineering Structures, 2003, Vol. 25, pp. 655-66.

8. Fahnestock, L.A., Ricles, J.M. and Sause, R., “Experimental Evaluation of a Large-Scale Buckling-Restrained Braced Frame”, Journal of Structural Engineering, 2007, Vol. 133, No. 9, pp. 1205-14.

9. Kiggins, S. and Uang, C.M., “Reducing Residual Drift of Buckling-Restrained Braced Frames as a Dual System”, Engineering Structures, 2006, Vol. 28, pp. 1525-32.

10. Tsai, K.C., Hwang, Y.C., Weng, C.S., Shirai, T., and Nakamura, H., “Experimental Tests of Large Scale Buckling Restrained Braces and Frames”, Proceedings, Passive Control Symposium, December, Tokyo Institute of Technology, Tokyo, Japan, 2002.

11. Xie, Qiang, “State of the Art of Buckling-Restrained Braces in Asia”, Journal of Constructional Steel Research, 2005, Vol. 61, pp. 727-748.

12. Uang, C.M., Nakashima, M. and Tsai, K.C., “Research and Applications of Buckling-Restrained Braced Frames”, International Journal of Steel Structures, Korean Society of Steel Construction, 2004, Vol.4, No. 4, pp. 301-313.

13. American Institute of Steel Construction (AISC), “Seismic Provisions of Structural Steel Buildings”, Chicago: AISC, 2005.

14. Chinese Building Seismic Design Code, GB50011-2001, 2001. 15. Mamoru, Iwata and Massatishi, Murai, “Buckling-Restrained Brace using Steel Mortar

Planks; Performance Evaluation as a Hysteretic Damper”, Earthquake Engineering and Structural Dynamics, 2006, Vol. 35, pp. 1807-1826.

16. Kim, Jinkoo and Choi, Hyunhoon, “Behavior and Design of Structures with Buckling-Restrained Braces”, Engineering Structures, 2004, Vol. 26, pp. 639-706.

17. Kim, Jinkoo and Seo, Youngil, “Seismic Design of Low-Rise Steel Frames with Buckling-Restrained Braces”, Engineering Structures, Vol. 16, No. 5, pp. 543-551.


33


34

SCALING THE EARTHQUAEK GROUND ACCELERATIONS FOR RESPONSE HISTORY ANALYSIS

OF TALL BUILDINGS

Keh-Chyuan Tsai*, Yuan-Tao Weng**, Pei-Ching Chen** and Sheng-Jhih Jhuang** *National Taiwan University, Taipei, Taiwan

**National Center for Research on Earthquake Engineering, Taipei, Taiwan

[email protected], [email protected], [email protected], [email protected] ABSTRACT This paper proposes a ground motion scaling method considering multi-mode effects for nonlinear response history analysis (NLRHA) of tall buildings using a case study. The original structural design of this case study consisted of five basement floors and a 34-story hotel tower in Kaohsiung, Taiwan. The construction started in 1993 and the erection of the entire steel frame and the pouring of concrete slabs up to the 26th floor were completed before 1996. However, construction was suspended for 10 years. Recently, this building has been retrofitted. Buckling restrained braces and eccentrically braced frames were incorporated into the seismic design of the new building. This paper presents the seismic resisting structural system, seismic design criteria and the detailed analytical models. Results of NLRHA indicate that the inelastic deformational demands of the original and the redesigned structures induced by the maximum considered earthquakes are less than those found in the seismic building codes or laboratory tests. It is demonstrated by using several ground motion scaling methods that the proposed scaling method worked well in reducing the scatter in estimated peak seismic demands. Keywords: Response history analysis, ground motion scaling method, seismic retrofit, BRB, EBF, welded moment connection


35

1. INTRODUCTION When non-linear dynamic time-history analyses are conducted as part of a performance-based seismic design approach, the analyses often require the ground motion records be scaled to a specified level of seismic intensity. The elastic dynamic analysis procedures in the current Taiwan seismic design provisions [1] prescribe that a series of time-history analyses are required with ground motion records selected from no less than three events. After scaling the dynamic base shear with respect to the static design base shear, the maximum values of all the response parameters, such as inter-story drift or member forces, were adopted in the design. However, research shows that some scaling methods could introduce a very large scatter in the analysis results [2–5]. If the design response spectrum represents the design target that the structural engineer aims to achieve, then the large scatter resulted from a specific scaling method suggests that the seismic demand estimates may be biased. It could lead to designs with significant uncertainties and unknown safety margins, unless the average of a relatively large number of records is used [2]. In addition, for high-rise buildings, multi-mode effects are not adequately considered in some common ground motion scaling methods. This paper proposes a multi-mode ground motion scaling (MMS) method and applied it herein to the 34-story steel building. Especially, this method takes into account the modal characteristics and minimizes the difference between the spectral responses of a given ground motion and the smoothed design response spectrum at the first few modes. The original structural design of the example building was for a hotel tower in Kaohsiung, Taiwan. It is a steel frame building, which consists of five basement floors and a 34-story tower. Construction of the tower started in 1993 and the erection of the entire steel structure and the pouring of concrete slabs up to the 26th floor were completed before 1996. Due to financial difficulties faced by the developer, the construction of the original hotel was suspended for 10 years. Recently, this building has been retrofitted and remodeled for residential purposes. The building height remains almost the same, but the floor area in some of the lower floors is reduced while vice versa for the higher floors. The original structural system was no longer able to meet the new seismic force requirements mandated in 2005. In order to meet the more stringent seismic performance requirements, buckling restrained brace (BRB) members and new eccentrically braced frame (EBF) configurations were incorporated into the seismic design of the new residential tower. To verify the rotational capacity of the existing welded moment connections, two as-built welded beam-column moment connections were removed from the construction site. A novel stiffening scheme was developed and applied in strengthening one of the connections before tests were carried out to compare the performance of the existing and the stiffened connection details. In this paper, the change of seismic force requirements is presented and the new seismic performance requirements for this building are discussed. In addition, test results are presented and analytical models for simulating the experimental responses of the BRB and the stiffened welded moment connection were examined. Finally, the seismic performance of the structural system and response modification elements were evaluated by conducting 3-dimensional nonlinear response history analyses of the original and redesigned structures subjected to design base earthquakes in two principal axes.


36

2. THE EXAMPLE BUILDING STRUCTURE 2.1 Original Structural System The original hotel tower was designed and built as a dual system consisting of steel EBFs and special moment resisting frames (SMRFs) using the Taiwan 1989 Code provisions for seismic force requirements (Code’89) [6]. The 1989 and 2005 versions of design force requirements are shown in Figure 1 in terms of the weight of the structure. The structural framing plan of the original hotel tower is similar to those shown in Figure 2. The floor construction consists of 15 cm thick concrete slab with metal deck over steel framing. The design live load for the hotel room was 2.0 kN/m2. The total height of the original hotel building was 124.7 m. The occupancy importance factor I was 1.25. All columns are of built-up box shape using A572 Grade 50 steel, while the rolled wide flange beams are mostly A36. The hotel building fundamental periods computed using the analytical model were 4.27 seconds and 3.74 seconds in the longitudinal and transverse directions respectively. The design seismic base shears based on the Code ’89 were 0.033W (based on I=1.25) for both directions as the vibration period was governed by the empirical formula, Tmax=1.4(0.07h3/4)=3.66 seconds. 2.2 Redesigned Structural System The building has then been retrofitted and remodeled since 2006. The building height remains almost the same, but the floor area in some of the lower floors is reduced while vice versa for the higher floors. Although the total height has been increased slightly from 124.7 m to 128 m, substantial weight of the building has been shifted from the lower floors to the higher floors due to the new architectural configuration. The average floor dead load (DL) including all the walls is about 7.0 kN/m2, and the design live load (LL) for the residential unit is 2.0 kN/m2. Compared to Code’89, the 2005 version of seismic force requirements (Code’05) for buildings has changed rather significantly (refer to Figure 1). However, before retrofitting, this building has already gotten the building permit. Therefore, the Kaohsiung City Building Department treated this project as an unfinished case. The Kaohsiung City Building Department and the structural design review committee agreed with the structural engineers to maintain the use of the same response spectrum suggested in Code ’89 for the building seismic retrofit and reconstruction for residential purposes. Nevertheless, the occupancy importance factor I was allowed to change from 1.25 for a major hotel to 1.0 for a residential building. Using the LRFD approach, design load combinations include: (1) 1.4DL, (2) 1.2DL+1.6LL, (3) 1.2DL+0.5LL+1.6WL, (4) 1.2DL+0.5LL+1.0EQ, (5) 0.9DL-1.0EQ, and (6) 0.9DL-1.6WL. The redesigned building fundamental periods computed using the analytical model are 3.75 seconds and 3.59 seconds in the longitudinal and transverse directions respectively. Thus, the design base shear was reduced from 0.033W for the original hotel building to 0.031W (14276 kN) computed based on the empirical vibration period of 3.75 seconds for the two principal building axes. The design base shear would have to be increased by 26% from 0.033W (for the original hotel building) to 0.039W if the Code’05 was to be followed (Figure 1). Thus, the design engineers agreed to conduct detailed nonlinear response history analyses (NLRHA) using synthetic ground acceleration compatible with the elastic response spectrum prescribed in Code’05 [1]. The NLRHA and the performance of the redesigned super-structure will be presented in detail later in this paper.


37

2.3 Upgrading of Seismic Force Resisting System Considering some structural members had deteriorated much due to weathering after construction was suspended for many years, it was decided that all steel framing above the 26th floor be removed. New EBFs were chosen for strengthening the 12th to 25th stories whenever the structural and architectural designs allow the installation of the new brace but

Figure 1. Design Force Structural Weight Spectra

(a)

(b) Figure 2. Typical Floor Framing Plan of the Building: (a) 1st to 11th Stories; (b) 26th to 34th Stories

0 1 2 3 4 5Period (sec)

0

0.04

0.08

0.12

0.16

VD/W

Code '89DE-Code '05

T1=3.75 sec

0.031W

0.039W


38

(a) (b)

(c) (d) Figure 3. Elevations of the Building: (a) Frame A; (b) Frame D; (c) Frame 3; (d) Frame 4


39

require accommodating a door opening. In order to enhance the seismic performance of this building, A572 Grade 50 steel BRB elements were added into 1st to 11th stories whenever there was no requirements of providing door opening. All the new or existing link beams in the EBFs are shear links with a length smaller that 1.1Mp/Vp, where Mp and Vp are beam plastic moment and shear capacities respectively. Since the pouring of concrete slabs up to the 26th floor was completed before the re-construction, all the existing frame girders using the pre-Northridge type of welded moment connections could not be conveniently removed below the 26th floor. Thus, a new beam-to-column connection stiffening scheme using two steel web side plates were proposed. The side plates can be conveniently installed in the welded moment connections without removing the concrete slab above the beam flange. It was tested before implementing it into strengthening all the existing welded moment connections. Figures 2 and 3 display the typical floor framing plans and the elevations of this redesigned building. The specimen design and the test results can be found in the reference. 3. ANALYTICAL MODEL The Platform of Inelastic Structural Analysis for 3D Systems (PISA3D), developed in NTU and NCREE [8], is an object-oriented general-purpose computational platform for nonlinear structural analysis. It provides more than 35 different characteristics of structural elements for simulation of structural responses. In particular, its beam-column element can conveniently simulate the shear yielding or flexural yielding responses of steel wide flange sections. Thus, PISA3D has been applied to carefully model the welded moment connections, BRBs and EBFs in order to investigate the seismic performance of the 34-story steel structure under severe earthquakes. 4. SIMPLIFIED ANALYTICAL APPROACH 4.1 Welded Beam-to-Column Moment Connections Without using the rigid end offset feature, the beam-column element flexural stiffness was computed from the node-to-node dimensions. The output of the force responses was also located at the nodal point. To simplify the analytical models and avoid the use of rigid end zones, the yield strength of the beam was modified so that yielding of the beam at the column face can be well represented. As shown in Figure 4a, the beam plastic moment capacity was modified using the following equation:

fcpp LLMM (1)

where Mp is the plastic moment capacity of the bare steel beam, pM is the modified beam

moment capacity, Lc is the distance from the beam mid-span to the center of the column, and Lf is the distance from the beam mid-span to the column face. Figure 4b shows the use of the plastic hardening material model and the proposed modification of the beam flexural capacity (modified beam, or MB Model) in simulating the experimental response of Specimen 1. The plastic hardening material model considers both the kinematic and isotropic hardening commonly found in structural steel material. Figure 4b displays the simulation results derived from using the same material properties without modifying beam flexural capacity but adopting the rigid end zone and a panel zone element (PZ Model). It was found that both


40

inflection point

moment diagram

MpMp+

CLCL

Lc

Lf

inflection point

moment diagram

MpMp++

CLCL

Lc

Lsf

models simulated the test results quite well. However, the PZ Model increases one degree of freedom at every beam-to-column moment connection. The same technique was found to be equally effective in modeling the stiffened welded moment connection for Specimen 2.

(a) (b) Figure 4. (a) Illustration of the Moment Gradient for Flexural Capacity Modification; (b) Hysteretic Responses of the Specimen 1 obtained from Experimental and Analytical Results using MB Model and PZ Model

(a)

(b) (c) Figure 5. (a) Simplified Moment Capacity for MB Model after Strengthening; (b, c) Hysteretic Responses of the Specimen 2 obtained from Experimental and Analytical Results using the MB Model

-4 -2 0 2 4Beam End Rotation (% radian)

-800

-400

0

400

800

Fo

rce

(kN

)

MB ModelSpecimen 2

-1.2 -0.8 -0.4 0 0.4 0.8 1.2Beam End Rotation (% radian)

-600

-400

-200

0

200

400

600

Fo

rce

(kN

)

MB ModelSpecimen 2


-800

-400

0

400

800

Fo

rce

(k

N)

PZ ModelSpecimen 1


-800

-400

0

400

800

Fo

rce

(k

N)

MB Model


41

-100 0 100-50 50Axial Displacement (mm)

-8000

-4000

0

4000

8000

-6000

-2000

2000

6000

Axi

al F

orc

e (k

N)

-400

0

400

-600

-200

200

600

Co

re S

tres

s (M

Pa)

-0.02 0 0.02-0.01 0.01Core Strain (Core Length = 3500 mm)

K.T. BRB (VB68)

Py

- Py

1.3 Py

-1.3 PyPy= 3737 kN

19 cycles @1.5Dbm

(a) (b)

(c) (d) Figure 6. (a) BRB Loading Protocol; (b) Hysteretic Responses of the BRB Specimen; (c) Low Cycle Fatigue Test; (d) a Photo of BRB Members at the Construction site

Table 1. 1st to 6th Modal Periods of the Original Structure and the Redesigned Structure Original (unit: second) Redesigned (unit: second) 1st Mode T1,O = 4.27 T1,R = 3.75 2nd Mode 3.88 3.59 3rd Mode 3.74 3.21 4th Mode 1.80 1.21 5th Mode 1.57 1.18 6th Mode 1.44 1.08

The stiffened beam section was not built in the model. However, the plastic hinge was to be formed outside of the stiffeners. As shown in Figure 5a, the beam plastic moment capacity was thus modified accordingly: sfcpp LLMM (2)

where pM is the modified plastic moment and Lsf is the distance from the beam mid-span to

the edge of the stiffeners. Figure 5b suggests that the proposed MB model can satisfactorily simulate the experimental response at low-level deformations; while Figure 5c shows that the same MB model can accurately simulate the responses of Specimen 2 at large deformations. Thus, the MB model was adopted for all the welded moment connections in the 3D structural model for the 34-story steel superstructure.

-100 -80 -60 -40 -20 0 20 40 60 80 100Axial Displacement (mm)

-8000

-4000

0

4000

8000

Axi

al F

orc

e (k

N)

-0.02 -0.01 0 0.01 0.02Core Strain (Core length = 3500 mm)

TestPISA3D

-600

-400

-200

0

200

400

600

Co

re S

tres

s (M

Pa

)

-Py

Py

1.3Py

-1.3Py


42

0 10 20 30 40 50 60 70Time (sec)

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

Accele

rati

on

(g

) 2006/12/26, M=6.4KAU station, E-W

PGA=0.119 g

0 10 20 30 40 50 60 70Time (sec)

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

Accele

rati

on

(g

) 2006/12/26, M=6.4KAU station, N-S

PGA=0.123 g

0 10 20 30 40 50 60 70Time (sec)

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-0.08

-0.04

0

0.04

0.08

0.12

Accele

rati

on

(g

) 2006/12/26, M=6.4KAUP station, N-S

PGA=0.107 g

0 10 20 30 40 50 60 70Time (sec)

-0.4

-0.2

0

0.2

0.4

Acc

ele

rati

on

(g

) 2006/12/26, M=6.4KAUP station, N-S

Artificial, PGA=0.40 g

0 10 20 30 40 50 60 70Time (sec)

-0.4

-0.2

0

0.2

0.4

Ac

cele

rati

on

(g

) 2006/12/26, M=6.4KAU station, N-S


0 10 20 30 40 50 60 70Time (sec)

-0.4

-0.2

0

0.2

0.4

Acc

ele

rati

on

(g

) 2006/12/26, M=6.4KAU station, E-W


4.2 EBF Shear-link Beams The beam element in PISA3D is able to simulate the shear and/or flexural yielding of the steel wide flange sections. Using the rigid end offset feature for link beam in EBF, the determination of shear yielding or flexural yielding is based on the clear length of the link beam. Therefore, the rigid end offset option was applied so that the shear and flexural strength of the link beam can be correctly incorporated into the determination of shear or flexural yielding. To simplify the analytical model, the panel zone element was not considered at the link beam-to-column joint. 4.3 Buckling Restrained Braces The proposed double-core BRB consists of the energy dissipation core yielding segment, the transition region and the core projection [9, 10]. The equivalent axial stiffness, Ke was computed for constructing the PISA3D model using the following equation:

2 2j t c

et c j j c t j t c

E A A AK

A A L A A L A A L

(3)

where Ac, At, Aj and Lc, Lt, Lj are the cross-sectional area and the length of the energy dissipation core yielding segment, the transition region and the core projection respectively. To examine the quality of the BRBs made by the fabricator, a BRB was arbitrary chosen and tested before the installation of all BRBs. The loading protocol and force versus deformation relationships for this A572 Gr.50 steel BRB specimens are shown with the actual yield capacity (Py=AcFy,actual) in Figure 6. The BRB sustained the standard loading protocol [7] before the 19 cycles of constant-strain (1.5 times the maximum considered earthquake induced strain, or 1.50MCE strain) cyclic loading were applied. It was evident that the inelastic axial strain of the BRB specimen reached 0.022 (2 times of that associated with the design story drift). From Figures 6b and 6c, it can be found that the BRB specimen achieved a cumulative plastic deformation (CPD) of 555, greater than the requirement (200 times the yield deformation) before fracture. Figure 6d shows the added BRB members installed at the construction site.

(a) Original (b) Synthetic


43

(c) Figure 7. (a) Original Historical Ground Motion Records; (b) Synthetic Ground Accelerations; (c) the Design Compatible Elastic Spectra

Table 2. Earthquake Records used in this Study Records, Component Epicenter distance (km) PGA (g) KAU, EW 26.7 0.119 KAU, NS 26.7 0.123 KAUP, NS 27.3 0.107 SPT, EW 29.6 0.088 SPT, NS 29.6 0.093 SGL, EW 35.1 0.073 SGL, NS 35.1 0.083

Longitudinal Dir. (X-Dir.)

(a) (b)

(c) (d) Figure 8. Comparison of Longitudinal Peak Seismic Responses between the Original and Redesigned Structures induced by Synthetic Ground Motion Records: (a) Peak Story Displacement; (b) Peak Inter-Story Drift; (c) Peak Story Shear; (d) the Capacity Curves of the Redesigned Structure obtained from IDA

0 2 4 6Period (sec)

0

0.2

0.4

0.6

0.8

1

Sa(

g)

5% damping ratioPGA=0.32 g

AkauewAkaunsAkaupns'05_MCE

T1,R=3.75 secT1,O=4.27 sec

-8 -4 0 4 8

Story Shear (kN)

02468

10121416182022242628303234

Sto

ry

0 1 2 3Roof Drift Ratio (% radian)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

V/W

OriginalEQ1EQ2EQ3

RedesignedEQ1EQ2EQ3

-2 -1 0 1 2Peak Story Drift (%, radian)

02468

10121416182022242628303234

Sto

ry

-1200 -800 -400 0 400 800 1200Peak Story Disp (mm)

02468

10121416182022242628303234

Sto

ry


44

All BRB members were modeled using plastic hardening truss elements. In Figure 6b, it is demonstrated that the PISA3D analytical model can accurately simulate the cyclic response of the BRB specimen. The vibration periods of the 1st to 6th mode of the original and the redesigned structures computed by PISA3D are listed in Table 1, respectively. 5. SEISMIC RESPONSE ANALYSIS USING SYNTHETIC GROUND MOTIONS The phase angles of three historical ground motion records: KAUEW, KAUNS, and KAUPNS, were selected for the construction of the synthetic ground accelerations (Figure 7a). These three records (Table 2) were recorded in Kaohsiung during a recent earthquake that struck at the southern coast of Taiwan on December 26th in 2006 [11]. Figure 7b shows the three synthetic ground accelerations, denoted as AKAUEW (EQ1), AKAUNS (EQ2) and AKAUPNS (EQ3). Figure 7c confirms that the response spectra of the three synthetic ground motions are compatible with the elastic design spectrum suggested by Code ’05 for a MCE-level (PGA=0.32g) earthquake.

6. SEISMIC PERFORMANCE EVALUATION 6.1 Nonlinear Response History Analysis (NLRHA) and Incremental Dynamic

Analysis (IDA) The NLRHA was conducted for both the DE-level (PGA=0.29g) and the MCE-level (PGA=0.32g) earthquakes. However, it was found that the responses of the superstructure were similar under the excitation of these two levels of earthquake. Only the key responses of the original and the redesigned structures under the MCE-level earthquakes are presented. The peak story displacements, peak inter-story drifts, and the peak story shears under the application of these three synthetic earthquakes of MCE-level are shown in Figures 8a, 8b, and 8c respectively. Figure 11a shows peak roof displacement reached 1.12 m and 1.03 m for the original and redesigned structures, respectively. Figure 8b shows peak inter-story drifts are reduced from the 1st to 11th floors but increased from the 26th to 34th floors after retrofitting. This could be because the floor weight in some lower floors was reduced while that of the higher floors was increased. Peak inter-story drifts of the original and the redesigned structures reached 0.012 and 0.014 radians, respectively. Nevertheless, the peak inter-story drift demand (0.014 radian) under the MCE-level excitation was still small enough to meet the Life-Safety performance criterion (0.015 radian) for new steel braced frames suggested in FEMA-450 [12]. Figure 8c shows that almost all the peak story shears were increased slightly after the structure was retrofitted. Incremental dynamic analysis (IDA [13]) was conducted using the same three earthquakes to compare the capacities between the original and the redesigned structures. The resulting roof drift versus the base shear to building weight ratio relationships are shown in Figure 8d. It can be found that the lateral stiffness and the strength of the original structure are smaller than those of the redesigned. Although the dynamic responses of the original structure were not significantly reduced after retrofitting, the owner and the design engineer of the building decided to add response modification elements into the re-construction. It is because that the pre-Northridge type of welded moment connection adopted in the original structure may not be able to reliably provide sufficient deformational capacities, especially when the original structural frame was exposed to weathering for more than 10 years.


45

Under the MCE-level EQ3 earthquake applied in the longitudinal direction, Figure 9a illustrates the plastic hinge distributions in Frame Line D of the redesigned structure. Figure 9b indicates that the ratios between the brace shear Vbraces and story shear VT along the building height range from 0.1 to 0.9. Figures 9c, 9d and 9e show the corresponding hysteretic responses of some specific structural members where nonlinear responses are more pronounced than elsewhere: BRB member at 8th floor, shear-link beam at 21st floor and welded moment connection at 8th floor respectively. The stated BRB peak axial core strain demand was about 0.077 (Figure 9c), and the peak total beam end flexural rotation demand reached 0.01 radian (Figure 9d). Figure 9e shows that the link beam total shear rotation demands of the original and redesigned buildings reached 0.065 and 0.033 radians respectively. Both are smaller than the 0.08 radian recommended for the shear link [7]. Clearly, some of the EBF link beam rotational demand in the original structure has been significantly reduced. The analyses also suggest that the rotational demand imposed on the welded moment connection is only about 0.01 radian, much smaller than the rotational capacity (0.04 radian) found in the test results of the retrofitted connection. 7. SCALING OF HISTORICAL GROUND MOTIONS As shown above, synthetic ground motions have been applied in the response analyses of the example building. Generally speaking, spectrum compatible method may be more appropriate where fewer ground motions are used. However, effects of spectrum matching on nonlinear response are not well understood at this time. Some engineers are concerned with skewing the energy content of ground motions through spectrum matching, which may have an unknown effect on the nonlinear response. To gain insights into the nonlinear responses of the example structure under the excitation of historical ground accelerations, further NLRHA were conducted. The techniques of ground motion scaling methods [2, 14 and 15] have also been studied in this research. Two of the most common ground motion scaling methods used in Taiwan are as follow: 1. Code method: the ground motion scaling procedure prescribed in Code’05 [1]. Given a

suite of ground motion records, a scale factor is applied to each record to either increase or decrease its intensity. If T1 is the fundamental vibration period of the building in the considered direction, each scale factor is selected such that the corresponding spectral accelerations between the period range from 0.2 T1 to 1.5 T1 satisfy the following two requirements: (1) Any spectral acceleration of the given ground motion shall be greater than 0.9 times that of the design response spectrum; and (2) The average of response spectrum from the scaled motion does not fall below the target design response spectrum.

2. Sa(T1) method [2]: each ground motion is scaled so that its spectral acceleration value, Sa(T1), at the linear-elastic fundamental period of the structure being analyzed, matches the design spectrum.

Both the Code and Sa(T1) methods depend on the structural dynamic characteristic (T1) as well as the frequency contents of the ground motion. Currently there is no consensus on the preferable approach (scaling or spectrum compatible) for nonlinear dynamic analysis. The advantage of scaling method is that individual ground motion record retains its original characteristics including peaks and valleys in the response spectrum. However, to avoid the response being uncharacteristically dominated by the peaks and valleys of any one ground motion, it is recommended that no less than seven ground motion records are to be used[14].


46

In addition, when the scaling approach is adopted, the upper limit of the scale factor should be 4 and 6 for 10%/50 yr and 2%/50 yr hazard levels respectively [16]. Nevertheless, for high-rise buildings, high-mode effects can be rather pronounced. If a ground acceleration record is scaled without properly incorporating the design spectral acceleration values at the significant periods of a building, it can seriously overestimate or underestimate the seismic demands. This argument will be verified later in this paper. To properly incorporate the high-mode effects in the estimation of the seismic demand, the multi-mode scaling (MMS) methods were investigated and presented in this paper. 8. MULTI-MODE GROUND MOTION SCALING PROCEDURE The general idea of MMS is to minimize the modal participating difference between the spectral accelerations or displacements of a scaled ground motion and that of the smoothed design response spectra for the first few modes. According to the response spectra analysis (RSA) procedure [17], the peak modal responses can be estimated by adopting the square-root-of-sum-of-squares (SRSS) or the complete quadratic combination (CQC) rules. For discussion purposes, the SRSS rule is used to illustrate the computation of the scaling factor for the MMS method. If rno is the peak value of the nth mode contribution rn(t) to the total response r(t), then the peak total response ro is:

2/1

1

200

N

nnrr (5)

The base shears (Vd and VEQ) and roof displacements (uroof,d and uroof,EQ) can be expressed as:

N

ndesaiiid SLV

1

2, ,

N

nEQaiiiEQ SLV

1

2, (6)

and

N

nidesaiidroof Su

1

22,, ,

N

niEQaiiEQroof Su

1

22,, (7)

where Vd (or uroof,d) and VEQ (or uroof,EQ) are calculated from the smoothed design spectrum and the spectrum obtained from the natural earthquake accelerations respectively. On the other hand, i is the ith vibration frequency of the MDF system; i and Li are the modal participation factor and modal excitation factor of the ith mode respectively; finally Sai,des and Sai,EQ are the spectral accelerations in the smoothed design spectrum and the spectrum obtained from the natural earthquake accelerations respectively. 9. COMPUTING THE SCALING FACTORS FROM THE MMS METHOD The least square error fitting method was used to reduce the modal participating difference between the first few modal spectral accelerations or displacements of a scaled ground motion and that of the smoothed design response spectra. For example, the desired number of the first few modes N is three. The corresponding smoothed spectral accelerations are Sa1,des,


47

Sa2,des, and Sa3,des, and those of the original un-scaled spectral accelerations are Sa1,EQ, Sa2,EQ, and Sa3,EQ. Therefore, the square error of these two sets of accelerations can be expressed as:

2,3,232

,2,222

,1,112

EQadesaEQadesaEQadesa SSFSWSSFSWSSFSWerror (8)

where SF is the scaling factor whereas W1, W2 and W3 are the weighting factors associated with the first three modes respectively. The minimum error can then be achieved when the partial derivative of error2 with respect to the SF becomes zero:

0

2

SF

error (9)

So the SF can be expressed as:

2,332

,222

,11

,2,23,2,22,1,11

EQaEQaEQa

EQadesaEQadesaEQadesa

SWSWSW

SSWSSWSSWSF

(10)

Since the elastic peak base shear, Vi and roof displacement, uroof,i of ith mode are expressed as iLiSai and iiSai/i

2 respectively (refer to Equations 6 and 7), it is proposed that the weighting factors, Wi for each mode be expressed as shown below for the computation of scaling factors. For computation of base shear:

N

ili

iii

L

LW

1

22

22

(i = 1~N) (11a)

whereas for computation of roof displacement:

N

iii

iiiW

1

22

22

(i = 1~N) (11b)

Thus, weighting factors given in Equation 11a can be applied in Equation 10 for the computation of scaling factors when base shear is considered as the key design parameter, while Equation 11b can be applied when the roof displacement is the key parameter of interest. These two weighting factors (Equations 11a and 11b) and the corresponding ground motion scaling factors will be applied in order to examine their effectiveness in the seismic performance evaluations of the retrofitted 34-story example building. Since the proposed method incorporates multiple modes into the scaling (MMS) procedures, for the purpose of discussion, the method is identified as MMS-V (V for shear) or MMS-D (D for displacement) when Equation 11a or Equation 11b is applied respectively. It is important to consider the recommendation that the number of modes to be determined includes at least 90% of the total building mass when the RSA method is applied [14]. Lopez and Cruz [18] have also proposed some empirical formulas to determine the minimum number of modes N for the response computations. For the purpose of illustrating the effectiveness of the MMS method, only three modes (constitute 84% of the total building mass) were incorporated into the


48

computation of the scaling factors and the response spectra shown in Figure 10a. The modal participation factors i, modal excitation factors Li, spectral accelerations Sai,des computed from the smoothed MCE spectrum and each scaled historical earthquake for the first three modes in the x-direction can be found in the reference [19]. In that paper, the first three modal spectral accelerations in the response spectra computed from the aforementioned seven un-scaled historical earthquakes are also provided.

(a) (b) Standard volume per 0.005 unit: : plastic average axial strain, : plastic flexural hinge, : plastic shear hinge

(c) (d) (e)_ Figure 9. Nonlinear seismic responses: (a) plastic hinge distribution in Frame D of the redesigned building; (b) peak Vbrace/VT ratio of the redesigned building; (c) BRB member; (d) welded moment connection and (e) shear-link beam induced by the EQ3 acceleration record for the MCE-Level (PGA=0.32g)

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7Total shear rotation (% radian)

-2000

-1000

0

1000

2000

Sh

ear

forc

e (k

N)

OriginalRedesigned

21FL, Frame D

Vy

-Vy

-1.5 -1 -0.5 0 0.5 1 1.5Beam end rotation (% radian)

-3000

-2000

-1000

0

1000

2000

3000

Mo

men

t (k

N-m

)

OriginalResigned

8FL, Frame A

My

-My

-1 -0.5 0 0.5 1Axial core strain (% radian)

-2000

-1000

0

1000

2000

Ax

ial fo

rce

(k

N)

Py=1191.8 kN

8FL, Frame D

Py=1191.8 kN

0 0.2 0.4 0.6 0.8 1Vbrace/VT

5

10

15

20

25

Sto

ry


49

-0.8 -0.4 0 0.4 0.8COV of Story Shear

02468

10121416182022242628303234

Sto

ry

-2 -1 0 1 2COV of Overturning Moment

2468

10121416182022242628303234

Sto

ry

-1 -0.5 0 0.5 1COV of Story Drift

02468

10121416182022242628303234

Sto

ry

-1.2 -0.8 -0.4 0 0.4 0.8 1.2COV of Story Displacement

2468

10121416182022242628303234

Sto

ry

MMS-VMMS-DSa(T1)

Code

(c) (d)

(e) (f)

(a) (b)

Figure 10. (a) The mean elastic 5%-damped spectral acceleration; (b) the corresponding COV spectrum and scatter in MDOF seismic demands after seven ground motion records scaled by four scaling methods; the COVs of the peak seismic demands along the building height: (c) story shear; (d) overturning moment; (e) story drift; (f) story displacement

0 1 2 3 4 5Period (sec)

0

1

2

3

4

Sa (

g)

MMS-VMMS-DSa(T1)

Code2%/50-MCE

T1X

T2X

T3X

0 1 2 3 4 5Period (sec)

0

1

2

3

4

5

CO

V o

f S

a

MMS-VMMS-DSa(T1)

Code

T1X

T2X

T3X


50

10. COMPARING THE MMS WITH THE CODE AND SA(T1) METHODS Seven natural ground motion records listed in Table 2 were used to investigate the variability of seismic demands computed using different ground motion scaling methods. For the 34-story steel building, the first three vibration periods are 3.75 sec (T1x), 1.21 sec (T2x) and 0.68 sec (T3x) in the longitudinal direction. Figure 10a shows the smoothed 5% damped elastic acceleration response spectrum of the MCE. In the same figure, four other response spectra (constructed from the averaged responses of the seven historical earthquakes scaled according to four different rules) are also compared. They include the Code, Sa(T1), MMS-V and MMS-D methods described previously. Figure 10b shows the COVs, with respect to the smoothed MCE response spectrum, computed from the four scaling methods. It is evident in Figure 10a that the average of seven spectra computed using MMS-V method is closer to the smoothed design spectrum in the range from T3x to T1x. Figure 10b on the other hand shows a significant reduction in the scatter of the spectral acceleration computed using MMS-V method for vibration periods less than about 3.0 seconds. This study therefore is able to compare the effectiveness of the MMS-V and MMS-D to the Code or Sa(T1) methods in reducing the scatter of the peak seismic demands computed from both the RSA and NLRHA. 10.1 Response Spectral Analysis (RSA) Assuming the structural system remains elastic under the effects of all magnitude of earthquakes, Vd= 91958 kN and uroof,d,= 991.7 mm can be computed from Equations 6 and 7 respectively. The weighting factors, Wi computed using Equations 11a and 11b has been documented [19]. The scaling factors, SF and the corresponding PGA values, base shears, VEQ and Vd, roof displacements, uroof,EQ computed from Equations 6 and 7 are also provided. In addition, the VEQ/Vd and uroof,EQ/uroof,d ratios were calculated. When the ratio is closer to 1.0, this implies that the estimate of the peak seismic shear or roof displacement demand is closer to that computed from the smoothed response spectrum. Clearly, with the exception of the MMS-V method, the scaling factors determined from the MMS-D, Sa(T1) and Code methods have all exceeded the suggested limit of 6.0. For each earthquake, the MMS-V method evidently provides the best agreement between VEQ and Vd. In addition, the MMS-D method provides the best estimate of the peak roof displacement compared to the other three methods. 10.2 Nonlinear Response History Analysis (NLRHA) NLRHA was conducted by applying the scaling factors for the seven ground motions. In addition, arithmetic mean of the peak values obtained via NLRHA using the three MCE-level synthetic ground motions were first computed, subsequently the COV of the specific peak responses computed for the seven ground motions can be ascertained. The COVs are presented for four key responses along the height of the superstructure: 10.3 Variability of Peak Story Shear Figure 10c shows the COVs of the peak story shear profiles along the building height in the longitudinal direction using the four described methods. The results suggest that the MMS-V method significantly reduces the variation of the peak story shear demand estimate from the ground floor to the 6th floor and from the 25th floor to the 34th floor compared to other scaling methods.


51

10.4 Variability of Peak Overturning Moment On the other hand, Figure 10d shows the COVs of the peak overturning moment profiles in the longitudinal direction. The results indicate that the MMS-V method provides an effective reduction of the scatter in the peak overturning moment along the full building height compared to the other three scaling methods. 10.5 Variability of Peak Inter-story Drift Next, Figure 10e shows similar trends for the COVs of the peak inter-story drift profiles. The COVs computed for the MMS-D, Sa(T1), and Code methods vary noticeably along the building height but its magnitude and variation are significantly reduced when using the MMS-V method. 10.6 Variability of Peak Story Displacement Lastly, Figure 10f shows the COV values of the peak story displacement profiles along the building height. It can be deduced that the MMS-D and Sa(T1) methods fare better in reducing the scatter of the peak story displacement for upper floors compared to other scaling methods. The effectiveness of the MMS-D method in reducing the scatter of the peak story displacement along the building height is hence demonstrated. 11. CONCLUSIONS From the experimental and analytical studies, the following conclusions can be drawn: (a) The proposed beam-to-column connection stiffening scheme using two steel web side

plates can be conveniently installed in the welded moment connections without removing the existing concrete slab above the beam flange;

(b) Test confirms that the proposed side-plate stiffening scheme is effective in preventing the fracture occurred in the beam flange. The stiffened welded moment connection possesses a larger rotational capacity than that in the original pre-Northridge type connection;

(c) The proposed analytical models are found to be accurate in simulating the experimental responses of BRB member, and welded moment connections before and after stiffening;

(d) Nonlinear dynamic analyses confirmed that the rotational demand on the EBF link beams has been significantly reduced by adopting the response modification elements in the redesigned structure;

(e) Nonlinear response history analyses show that almost all the story shear demands were increased slightly after the structure was retrofitted. Analytical results indicate that the ratios between the brace shear and story shear along the building height range from 0.1 to 0.9;

(f) With the exception of the MMS-V method, the scaling factors determined from the MMS-D, Sa(T1) and Code methods exceeded the suggested limit. Furthermore, it appears that the other three methods often lead to overestimation of the seismic force responses for the building. The proposed MMS-D method provides the best estimate of the peak roof displacements among all the methods adopted; and

(g) The MMS-V method provides an effective reduction in the scatter of the estimates of the peak story shear, overturning moment and peak inter-story drift. Due to its simplicity and inclusion of multi-mode effects, the MMS-V method is deemed to be more applicable for the example building than the other scaling methods considered in this study.


52

REFERENCES 1. ABRI, “Recommended Provisions for Building Seismic Regulations”, Taipei, 2005.

(in Chinese) 2. Shome, N,, Cornell, C., “Normalization and Scaling Accelerograms for Nonlinear

Structural Analysis”, Sixth U.S. National Conference on Earthquake Engineering, Seattle, WA, 1998. (CD-ROM)

3. Vidic, T., Fajfar, P. and Fischinger, M., “Consistent Inelastic Design Spectra: Strength and Displacement”, Earthquake Engineering and Structural Dynamics, 1994, Vol. 23, pp. 507– 521.

4. Miranda, E., “Site-dependent Strength-reduction Factors”, Journal of Structural Engineering (ASCE), 1993, Vol. 119, pp. 3503–3519.

5. Nau, J. and Hall, W., “Scaling Methods for Earthquake Response Spectra”, Journal of Structural Engineering (ASCE), 1984, Vol. 110, pp. 91–109.

6. ABRI, “Recommended Provisions for Building Seismic Regulations, Taipei, 1989. (in Chinese)

7. AISC, “Seismic Provisions for Structural Steel Buildings”, Chicago, IL, 2005. 8. Lin, B.Z., Chuang, M.C. and Tsai, K.C., “Object-oriented Development and

Application of a Nonlinear Structural Analysis Framewor”, Advances in Engineering Software, 2008. (accepted)

9. Tsai, K.C., Hsiao, P.C., Weng, Y.T., Lin, M.L., Lin, K.C., Chen, C.H., Lai, J.W. and Lin, S.L., “Pseudo-dynamic Tests of a Full-scale CFT/BRB Frame. Part 1: Specimen Design, Experiment and Analysis”, Earthquake Engineering and Structural Dynamic 2008a, Vol. 37, pp. 1081–1098.

10. Tsai, K.C. and Hsiao, P.C., “Pseudo-dynamic Tests of a Full-scale CFT/BRB Frame”, Part 2: Seismic Performance of Buckling Restrained Braces and Connections, Earthquake Engineering and Structural Dynamic, 2008b, Vol. 37, pp. 1099–1115.

11. NCDR and NCREE, The Preliminary Reconnaissance Report of 2006 Hengtsun Earthquake, December 2006. (in Chinese)

12. BSSC, “NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures”, FEMA 450, Federal Emergency Management Agency: Washington, DC, 2003.

13. Vamvatsikos, D. and Cornell, C.A., “Incremental Dynamic Analysis”, Earthquake Engineering and Structural Dynamics, 2002, Vol. 31, No. 3, pp. 491-514.

14. International Council of Building Officials (ICBO), Uniform Building Code. Whittier, CA, 2006.

15. Kurama, Y.C. and Farrow, K.T., “Ground Motion Scaling Methods for Different Site Conditions and Structure Characteristics”, Earthquake Engineering and Structural Dynamics, 2003, Vol. 32, pp. 2425-2450.

16. Malhotra, P.K., “Strong-Motion Records for Site-Specific Analysis”, Earthquake Spectra, 2003, Vol. 19, No. 3, pp. 557-578.

17. Chopra, A.K., “Dynamic of Structures: Theory and Applications to Earthquake Engineering”, Prentice Hall, 2nd ed., Englewood, Cliffs, N J, 2003.

18. Lopez, O.A. and Cruz, M., “Number of Modes for the Seismic Design of Buildings”, Earthquake Engineering and Structural Dynamics, 1996, Vol. 25, pp. 837-855.

19. Weng, Y.T., Tsai, K.C., Chen, P.C., Chou, C.C., Chan, Y.R., Jhuang, S.J. and Wang, Y.Y., “Seismic Performance Evaluation of a 34-Story Steel Building Retrofitted with Response Modification Elements”, Earthquake Engng Struct. Dyn., 2009, Vol. 38, pp. 759–781.


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54

PROGRESS OF SEISMIC DESIGN FOR STEEL STRUCTURES IN CHINA MAINLAND

G.P.Shu College of Civil Engineering, Southeast University, Nanjing, China

[email protected]

ABSTRACT The progress of seismic design of steel structures in China Mainland is closely connected with the building and revising of seismic code in China mainland. From directly using the seismic code in USA and Europe to gradually building the seismic design method of China mainland, this progress of the seismic design of steel structure in China mainland is continous and innovative, and reflects the development of seismic technology and project in China mainland.


55

1. THE DEVELOPMENT OF SEISMIC DESIGN CODE IN CHINA MAINLAND The seismic codes in different countries have relation to their economic status, research of seismic design, and comprehension of all previous earthquake over the world. After the Xingtai earthquake in 1966, the first seismic code, seismic design code of industrial and civil structure (TJ11-74), only with 38 pages was published in China mainland. After Tangshan earthquake in 1976, the new seismic code, seismic design code of industrial and civil structure (TJ11-78) (78 code for short), was published. Then, after the reform and opening-up policy, the Code for seismic design of buildings (GBJ11-89) (89 code for short) was published, and the three seismic fortification target, “intact under small earthquake, rehabilitative under middle earthquake, and non-collapsing under great earthquake”, was first presented. After that, the Code for seismic design of buildings (GB50011-2001) (2001 code for short) was published with 327 pages, was published. After the Wenchuan earthquake, according to certain departments’ requirements, the revised 2008 version of the Code for seismic design of buildings (GB50011-2001) was published. This version with 343 pages is the current seismic design code in China mainland. The development of seismic design code in China mainland undergoes three major phases. The first phase is represented by the 78 code. In this phase, by learning the seismic design methods in USA and Union of Soviet Socialist Republics and summarizing the lessons of Tangshan earthquake in 1976, the 78 code was published. In this code, the structure inner force analysis is based on the fortification earthquake, the damping ratio is 0.05, and by discounting the elastic earthquake action with the structure influnce coefficient C, the design earthquake actions of different structure system and structure materials are considered. The second phase is represented by the 89 code. By deeply researching the structure breakage of Tangshan earthquake, with the great development of seismic design project and seismic research in China mainland, and with much more international intercourses, the 89 code was published. This version of seismic design code is approaching the international advaced level. In the 89 code, the seismic design concept varied greatly comparing with the 78 code. The structure elastic inner force is obtained based on the small earthquake. The third phase is represented by the 2001 code. The 2001 code is consistent with the 89 code in basic concept and code frame. In this code, the damping ratio and elastic reponse curve are modified, the new structue system and new seismic techneque are added, the specifications are more detailed. Now the new version of seismic code is under revising, it will take the lessens of Wenchuan earthquake, revise some inconsequent specifications, and admit some new structure systems.


56

2. THE BASIC REQUIREMENTS OF SESIMIC DESIGN IN CHINA MAINLAND In order to accomplish the seismic fortification target, “the three levels and two-stage design” are used in current seismic code in China mainland. Firstly, the seismic fortification intensity, the basic seismic acceleration, and the design seismic group should be carefully chosen. Then, the structure’s horizontal and vertical earthquake actions should be calculated by the specified method of seismic code. After that, the structure’s inner forecs and deformations under earthquake should be checked according to the two-stage design of seismic code. In addition, the structure engineers should pay much attention to the seismic concept design of structure. They should not only depend on the calculating results, but also reinforce the structure by choosing the right system and seimic measurements to provide multi-ortification under earthquake. 2.1 The Seismic Fortification Intensity Code for seismic design of buildings (GB50011-2001) provides the seismic fortification intensity of 10% exceedance probability of 50 years in every region of China, corresponding design basic acceleration of ground motion, and seismic design group.

Table 1. Seismic Fortification Intensity and Design Basic Acceleration of Ground Motion seismic fortification intensity 6 degree 7 degree 8 degree 9 degree design basic acceleration of ground motion

0.05g 0.10(0.15)g

0.20(0.30)g

0.40g

Generally speaking, the seismic fortification intensity should be used according to the region of the building. For the special important or unimportant buildings, the seismic fortification intensity can be improved or reduced. 2.2 Seismic Fortification Target (1) Intact under small earthquake: under the action of frequently occurred earthquake (numerous intensity earthquake of 63% exceedance probability in 50 years) lower than the region’s fortification intensity, the buildings are commonly not damaged. (2) Rehabilitative under middle earthquake: under the action of occasionally occurred earthquake (basic intensity earthquake of 10% exceedance probability in 50 years) of the region’s fortification intensity, the buildings can be damaged, but can be reused after repairing. (3) Non-collapsing under great earthquake: under the action of seldom occurred earthquake (seldom occurred intensity earthquake of 2%~3% exceedance probability in 50 years, about 1 degree higher than the region’s fortification intensity) higher than the region’s fortification intensity, the buildings do not collapse and lead to severe damage dangerous to human’s life. (4) For the tall buildings exceeding the limitations, the buildings with special functions, or the buildings of special requirements of owners, the predicting target can be decided according to real circumstance, and the seismic design can be done with the design methods based on the performance.


57

2.3 Two-Stage Seismic Design Method The two-stage seismic design method can achieve the seismic fortification requirement of each intensity criterion. The first stage: the elastic analysis of structure is done under frequently occurred earthquake, and the inner forces and deformation of structure by the earthquake action are obtained. Then, those results are combined with other load cases to check the structure members’ capacity, stability and story drift. Both the structure capacity reliability under frequently occurred earthquake and the fortification of rehabilitation under middle earthquake are satisfied. Through the conception design and necessary detail measures, the design requirements under seldom occurred earthquake are satisfied. For most structures, the first stage design is enough. The second stage: under the seldom occurred earthquake action, the elastic-plastic story drift of weak story are checked, and the corresponding details measures are taken to keep the structure from collapsing under great earthquake. 2.4 Lateral Earthquake Action and Vertical Earthquake Action (1) For the structure less than 40 meter, mostly with shear deformations, with evenly distributed mass and stiffness along its height, and equal to single mass point, the equivalent base shear method can be used. (2) Except the structures adapted to the first entry, the modal analysis method should be used to calculate the lateral earthquake action. (3) For the tall buildings exceeding the limitations, the buildings of the first category, and the tall buildings whose height is among the extent of table 2, the time history method should be used to calculate the action of frequently occurred earthquake, and the maximum value of the average of several time history results and the modal analysis methods results should be used.

Table 2. The Height Extent of Buildings for Time History Analysis Fortification intensity, site classification Height extent of building 8 degree inⅠ, Ⅱ site and 7 degree >100 8 degree inⅢ, Ⅳ site >80 9 degree >60

Structures whose vertical earthquake action should be calculated: (1) The tall buildings of 9 degree seismic fortification intensity. (2) The great span and long cantilever structure of 8 or 9 degree seismic fortification intensity. (3) The high position connective structure, the high position great span transition structure and high position cantilever transition structure of 8 degree seismic fortification intensity.


58

3. THE SEISMIC DESIGN METHOD OF STEEL STRUCTURE IN CHINA MAINLAND The seismic design specifications of steel structure are concentrated in multi-story and tall buildings. Except the above requirements of general seismic design of building, the steel structure should satisfy some special rules including the following three parts. Firstly, the basic seismic requirements of different steel structure systems are provided, including frame structure, centric-braced frame structure, eccentric-braced frame structure, frame and tube structure, and mega-structure. It also specified that the steel structure buildings should apply different adjusting coefficients of earthquake action and use different seismic fortification measurements based on the seismic intensity, structure type, and building height. Secondly, the deciding points of steel structure’s seismic design are specified including the following five parts: (1) the inner force and deformation analysis of steel structure under earthquake actions, (2) the seismic capacity checking methods of steel frame structure’s members and joints, (3) the seismic capacity checking methods of centric-braced frame structure’s members, (4) the seismic capacity checking methods of eccentric-braced frame structure’s members, (5) the connections of steel structure’s members under earthquake action should be designed elastically, and their limit capacity should be checked including: connections between beam and column, connections between brace and frame or between brace and brace, and connections between column and column or beam and beam. Thirdly, the seismic fortification measurements of steel frame structure, centric-braced frame structure, and eccentric-braced frame structure are specified including the following eight parts: (1) the slenderness ratio of frame column, (2) the ratio between width and thickness of frame beam or column’s plates, (3) the lateral brace of beam and column, (4) the details of connections between beam and column, (5) the slenderness ratio and the plate’s ratio between width and thickness of centric brace member, (6) the details of connections of centric brace, (7) the slenderness ratio of brace members of eccentric-braced frame structure, (8) the details of energy dissipating beam segment. 4. THE DISCUSSION AND SUGGESTION OF THE SEISMIC DESIGN METHODS OF STEEL STRUCTURE IN CHINA MAINLAND With the research of seismic design of steel structure by scholars in China mainland, the seismic design methods of steel structure will have further developments. At present, several parts in the current design code need to be further revised.


59

4.1 “Rehabilitative under Middle Earthquake” of “Three Levels” is not Checked “The three levels” of seismic fortification target are “Intact under small earthquake, Rehabilitative under middle earthquake, and Non-collapsing under great earthquake”. The current seismic code uses two-stage design method to accomplish “the three levels” of seismic fortification target. The small earthquake is also named “frequently occurred earthquake”, its fortification intensity is 1.55 degree lower than the middle earthquake’s fortification intensity, and its exceedance probability in 50 years is 63%. The middle earthquake is also named “fortification earthquake”, its intensity is also named “fortification intensity”, and its exceedance probability in 50 years is 10%. The great earthquake is also named “seldom occurred earthquake”, its fortification intensity is 1.0 degree higher than the middle earthquake’s fortification intensity, and its exceedance probability in 50 years is 2%~3%. Some researches show that the intensity with exceedance probability of 63% is 0.5~2.8 degree lower than the fortification intensity, and the intensity with exceedance probability of 2%~3% is not 1.0 degree higher than the fortification intensity. So, the frequently occurred earthquake and the seldom occurred earthquake do not have the uniform exceedance probability in the whole country. The “Intact under small earthquake” is achieved by the first stage of two-stage design, in this stage, the elastic analysis of structure is performed and the members’ capacities are checked. The “Non-collapsing under great earthquake” is achieved by the second stage of two-stage design, in this stage, the elastic and plastic analysis of structure is performed and the structue’s deformations are checked. The “Rehabilitative under middle earthquake” is achieved by deciding the seismic intensity and taking certain seismic fortification measurements. Because the frequently occurred earthquake and seldom occurred earthquake do not have the uniform exceedance probability, and the middle earthquake with uniform exceedance probability is not checked, the three seismic fortification targets of seismic design do not have the uniform reliability. The structure under the middle earthquake is checked in the seismic code of other countries. In seismic code of USA, the structure is checked under the middle earthquake, and its fortification target is that the structures have the same probability of resisting collapse under great earthquake. It has the advantage of easier seismic design method, but it does not have the same probability. In seismic code of Europe, the two-stage method are used to check the elastic deformation under small earthquake and the inner force under the middle earthquake. It does not check the capability of resisting collapse of structure under great earthquake. In seismic code of Japan, the same two-stage method as Eurocode is used. Professor Shen Zuyan of Tongji University pointed out that the three-stage method based on the middle earthquake is the more reasonable method at present. Namely, the method of checking the elastic deformation under small earthquake, checking the inner force under middle earthquake, and checking elastic and plastic deformation under great earthquake is corresponding to three levels. Hence, the seismic design method in China mainland should keep the current frame and be consistent with international codes. A lot of work should be done to accomplish the above target.


60

4.2 The Current Seismic Code does not Consider Different Ductility of Structure in Seismic Design

The investigation of earthquake show that the deficiency of strength of structure is not the major effect to the structure’s collapsing. As long as the structure’s strength can be maintained during earthquake and the structure has certain elasto-plastic deformation capability, the structure can be survived in the earthquake. Hence, the seismic code in other countries all use the “performace-based method”. In this method, the structure systems with different ductility are differentiated, the earthquake action of structure with better ductility can be discounted more greatly. In seismic code of USA, the steel frames are differentiated into four categories. These are SMF, IMF, OMF, and MF, representing special moment frame, intermediate moment frame, ordinary moment frame, and moment frame without seismic details requirements. In seismic code of Europe, the steel frames are differentiated into four categories. These are DCH, DCM, DCM-DCL, and DCL, representing high ductility frame, intermediate ductility frame, low ductility frame, and frame without seismic details requirements. In seismic code of Japen, the steel frames are differentiated into four categories. These are FA, FB, FC, and FD, representing highest ductility frame, high ductility frame, intermediate ductility frame, and low frame. And the different discounting coefficients are used according to frame structure with different ductility. The frame structure with higher ductility uses the greater discounting coefficients, and the frame structure with lower ductility uses the smaller discounting coefficients. The concept of discounting the earthquake action by differentiating the structure’s ductility is used in the above seismic design codes. The current seismic code in China mainland does not use the “performace-based method”. The current method can be named “frequently occured earthquake-seismic fortification measurement” design method. It does not differentiate the structure with different ductility, and does not have the quantity indication of structure’s ductility. The ductility requirements of structure are used as the safety measurements to resist earthquake action. And the method of using one discounting coefficient for all steel structures will lead to unreasonable larger earthquake action to high ductility frame. So, the steel structure can not fullfil its advantages under earthquake action by using the current method and this method need to be revised according to further reseaches. 5. CONCLUSION This paper briefly review the development of seismic design code in China mainland, and introduce the current seismic design method of steel structure. At the end, two parts in current seismic design code, which need to be further complemented and revised, are pointed out for the future researches.


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62

DESIGN OF PLATE-REINFORCED COMPOSITE COUPLING BEAMS FOR TALL BUILDINGS

R.K.L. Su Department of Civil Engineering, The University of Hong Kong, China

[email protected]

ABSTRACT Plate-reinforced composite (PRC) coupling beams are fabricated by embedding a vertical steel plate into conventional reinforced concrete coupling beams to enhance their strength and deformability. Shear studs are weld on the surfaces of the steel plate to transfer forces between the concrete and steel plate. Based on extensive experimental studies and numerical simulation of PRC coupling beams, a design procedure based on Hong Kong design codes of practice is proposed to aid engineers in designing this new type of beams. The proposed design guidelines consist of four main parts, which are (1) estimation of ultimate shear capacity of beam, (2) design of RC component and steel plate, (3) shear stud arrangement in beam span, and (4) design of plate anchorage in wall piers. An example is given to illustrate the use of the guidelines for the design of PRC coupling beams. Keywords: Coupling Beams, Embedded Steel Plate, Shear Studs, Design Guidelines, Steel and Concrete Composite


63

1. INTRODUCTION Coupling beams in coupled shear walls are often the most critical members in tall buildings subject to earthquake or wind loads. To ensure the survival of shear walls under high-intensity cyclic loading, these beams, which normally have limited dimensions, should possess high deformability and good energy absorption while being able to resist large shear forces. In view of that, the author and his co-workers developed plate reinforced composite (PRC) coupling beams which are fabricated by embedding a steel plate in a conventional RC beam and using shear studs to couple the steel plate and the concrete. PRC coupling beams are flexible in design and easy to construct. The insertion of steel plate has the least disturbance to reinforcement details, so that reinforcement from walls, slabs and coupling beams respectively can be harmoniously integrated together. The vertical arrangement of steel plate allows concrete to be placed and compacted easily, so honeycomb type of defects can be avoided. Furthermore, the cast-in steel plate can naturally be protected by the surrounding concrete against fire and lateral buckling. This new approach is a simple and economic design solution for high strength coupling beams. Extensive experimental and numerical studies [1-6] have been conducted to investigate the load-deformation behaviour and load-carrying capacity of PRC coupling beams. Based on the results and findings from these studies, design guidelines for this new type of beams according to British Standards were established [7]. To facilitate local engineers to conduct the design, the guidelines presented in this paper are revised based on the local construction practice [8, 9]. An example is given to illustrate the use of the guidelines for design of PRC coupling beams.

Figure 1. Typical Arrangement of PRC Coupling Beams 2. FEATURES OF PRC COUPLING BEAMS Fig. 1 shows a typical arrangement and geometry of a PRC coupling beam. In this design, a steel plate is vertically embedded into the conventional RC beam section across the whole span. Throughout the span, shear studs are welded on both vertical faces of the plate along the top and the bottom longitudinal reinforcement to enhance the plate/ RC composite action. The plate is anchored in the wall piers and shear studs are provided in these regions to increase the plate bearing strength. With the embedded steel plate of a PRC coupling beam framing into the wall piers, a continuous shear transfer medium far less affected by concrete cracking at the beam-wall interfaces during inelastic stage is provided, thus preventing brittle failure and increasing the rotational deformability of the beam. The experimental study [5]

Beam Elevation

Wall Panel Wall Panel

Steel Plate

Coupling Beam

Shear Studs

Main bars

Shear Links

l La

Steel Plate

Shear Studs

Beam Section

hp h

b


64

further indicated that the steel plate is effective in taking both shear and bending forces for deep coupling beams. PRC coupling beams are flexible in design and easy to construct. By using different amounts of longitudinal reinforcement and steel plate, the flexural capacity of the beam can be easily adjusted to suit different magnitudes of design moment. Unlike other approaches, such as embedding steel sections in coupling beams, the insertion of steel plate has the least disturbance to reinforcement details, so that vertical, lateral and longitudinal reinforcement from walls, slabs and coupling beams respectively can be harmoniously integrated together. The vertical arrangement of steel plate allows concrete to be placed and compacted easily, so honeycomb type of defects can be avoided. Furthermore, the cast-in steel plate can naturally be protected by the surrounding concrete against fire and lateral buckling. Small holes through the plate to accommodate pipes and conduits are also possible. As shear studs are welded on the plate to couple the concrete element and the steel plate, it is much simpler, faster and economical than fabricating compound steel sections. 3. PROPOSED DESIGN PROCEDURES The design procedure of PRC coupling beams described in this section is applicable to normal practical ranges of span/depth ratios (1≤l/h≤4) and plate depth/ beam depth ratios (0.95>hp/h>0.8) 3.1 Ultimate Shear Capacity of PRC Coupling Beams PRC coupling beams were recommended to be designed for shear stresses not exceeding 12MPa for grade 60 concrete. For other concrete grades lower than grade 60 concrete, the following ultimate shear stress capacity of PRC coupling beam should be adopted,

MPa125.1)/( cuuu fbdVv (1)

where Vu is the ultimate shear force resisted by the beam, b is the beam width, d is the effective depth measured from top fiber to centre of longitudinal tensile steel and fcu is the characteristic concrete cube strength. It should be noted that the material partial safety factor (1.25) of shear has been incorporated in Equation (1). 3.2 Shear Resistance Design of Steel Plate In the design of PRC coupling beams, a steel plate is cast in a conventional RC coupling beam to supplement the RC component for resisting shear. The steel plate is required to take up the additional shear when the design ultimate shear Vu exceeds the maximum allowable shear in the RC component VRC,allow, which varies depending on the concrete grade. Numerical investigation [6] revealed that the load shared by the steel plate should not be more than 0.45Vu even for beams with a small span/depth ratio and embedded with a thick plate. Thus the plate shear demand Vp,req is expressed as

uallowRCureqp VVVV 45.0,, (2)


65

According to the Code of Practice for the Structural Use of Steel 2005 [9], there are two possible cases for the design shear in a steel plate, low shear load and high shear load. Low shear load is defined as

ppyppyreqp htphtpV 312.03/9.06.0, (3)

where py is the design strength of the steel plate and tp is the thickness of the steel plate. This load case usually corresponds to medium-length and long coupling beams with span-to-depth ratios, l/h ≥1.5. Alternatively, high shear load is defined as

ppyreqp htpV 312.0, (4)

This loading case is more often associated with short coupling beams (l/h<1.5). As the embedded steel plate is restrained from buckling, plastic hinge can be developed with sufficient rotation capacity, thus Class 1 plastic section is assumed in the design. In this case, bending strength of the steel plate have to be reduced by a factor 1-ρ1, where ρ1 has been given in the Code of Practice for the Structural Use of Steel 2005 [9] and is expressed as,

2

,1 1

281.0

p

reqp

V

V

(5) It is noted that in the cases of low shear load, ρ1=0. Based on Structural Use of Steel 2005 [9], the shear capacity Vp of steel plates can be obtained as: for low shear load condition

reqpppyp VhtpV ,312.0 (6a)

for high shear load condition

reqpppyp VhtpV ,519.0 (6b)

At the beam-wall joints, the plate is subject to combined bending, axial and shear forces. In order to reserve sufficient load-carrying capacity for the steel plate to resist the bending and axial forces, for the cases of high shear load, the design shear load is advised to be

preqp VV 8.0, (7)

such that the stress reduction factor ρ1 is less than 0.3.


66

For sizing of plate, the depth of plate hp can be determined geometrically. Based on Equations (2), (6) and (7), a suitable plate thickness tp can be selected for short coupling beams (l/h ≤ 1.5), of which the design is controlled by shear force only. For the cases of long coupling beams where the design is controlled by bending, sizing of steel plate and reinforcement will be described in the next section. 3.3 Bending Resistance Design of Steel Plate and RC Section In typical RC coupling beam designs, the same amount of top and bottom reinforcements is often provided as both reinforcements are required for taking tension under reversing cyclic loads. Also, because of the plate/RC interaction in a PRC coupling beam, the RC component will be under an axial compression and the standard design procedure for RC beams in Code of Practice for Structural Use of Concrete 2004 [8] cannot be applied to determine the required longitudinal reinforcement. A new design procedure for design PRC coupling beams under bending is proposed herein.

Figure 2. Strain and Simplified Stress Diagrams of Beam Section under Ultimate Sagging Moment

Under partial plate/RC composite action, the flexural strains of the concrete and the steel plate will not be the same. Horizontal forces Fx would be exerted on the RC part and the steel plate respectively in equal magnitudes but at opposite directions. The previous numerical and experimental investigations found that beam-wall joints are the most critical location for the plate design and yielding often occurs at the ultimate loading stage. The simplified stress blocks of member forces at beam-wall joints are shown in Fig. 2. The force of longitudinal compression steel can be expressed as

ms

syscsscs

AfEA

x

dhxEAC

(8)

where sc is the strain of longitudinal compression steel, c is the ultimate compressive strain of concrete, E is the Young’s modulus of steel bars, x is the neutral axis depth, fy is the yield strength of reinforcement, As is the area of longitudinal tensile or compressive reinforcement and ms is the partial safety factor of reinforcement. Using the simplified rectangular stress block, the compression of concrete can be obtained and expressed in Equation (9).

mc

pcu

mc

pcuc

xtbfxtbfC

)(603.0)(9.067.0

(9)

0.67fcu/mc

scE fy/ms

fy/ms

Neutral Axis of RC Section

Stress in RC

sc

c =0.0035

st (> y)

Strain in RC

x

As

As

h hp

yp

yp

fyp(1-ρ1)/mp

Stress in Plate

Compression

Tension

xp

Strain in Plate

Neutral Axis of Steel Plate

fyp(1-ρ1)/mp


67

where mc is the partial safety factor of concrete. When the concrete compressive strain has reached its ultimate value (εc= 0.0035 for fcu≤60MPa), the deformation of the longitudinal tensile steel has usually exceeded the yield limit and the tensile force of the reinforcement can be calculated by Equation (10).

msyss fAT (10)

Due to the horizontal force interaction between the RC part and the steel plate, a net compressive force Fx is exerted on the RC section at the beam-wall joints. In the parametric study [6], the tensile force Fx was found to be dependent on the steel ratio of the longitudinal bars, the plate thickness to beam width ratio, and the span/depth ratio of the beam. The plots of Fx /Vu against l/h with various steel ratios ρs are reproduced in Fig. 3 for reference.

Figure 3. Axial Force of Steel Plate at Beam-Wall Joint When εsc< εy, where εy is the yield strain of reinforcement, the neutral axis depth of RC section is derived as,

pmc

cu

scpmc

cusc

ms

yxsc

ms

yx

tbf

EAdhtbf

AEf

FAEf

F

x

206.1

412.2

2

(11a)

Alternatively, when εsc ≥ εy, the neutral axis depth can be simplified to

pcu

xmc

tbf

Fx

603.0

(11b)

From the force equilibrium, the neutral axis depth of the steel plate can be expressed as

0.0

0.5

1.0

1.5

2.0

2.5

0 1 2 3 4 5l/h

0.05

0.08

0.15

t p /b

s = 0.5%

Fx/

Vu

0.0

0.5

1.0

1.5

2.0

2.5

0 1 2 3 4 5 l/h

0.05

0.08

0.15

t p / b

s = 1%

Fx/

Vu

0.0

0.5

1.0

1.5

2.0

2.5

0 1 2 3 4 5l/h

0.050.08

0.15

t p /b

s = 2%

Fx/

Vu

0.0

0.5

1.0

1.5

2.0

2.5

0 1 2 3 4 5 l/h

0.050.080.15

t p / b

s = 4%

Fx/

Vu


68

1122

py

xp tp

Fhx (12)

The compression of steel plate is equal to

22

1 1 xppyp

FthpC

(13)

And the tension of steel plate is

22

1 1 xppyp

FthpT

(14)

Taking moment at the neutral axis of the RC section, the bending moment capacities of RC section and steel plate are expressed, respectively, as

xCdhxCxdTM cssRC 55.0)()( (15)

11 144144 yp

xppp

yp

xpppp pt

FhxxC

pt

FhxxTM (16)

By choosing a suitable steel ratio of longitudinal reinforcement As and plate thickness tp, the total bending capacity of the section can be designed to be greater than the ultimate design moment Mu, i.e.

upRC MMM (17)

3.4 Shear Resistance Design of RC Section After determining the steel area of reinforcement As, the shear reinforcement can be provided to resist the shear force Vu– Vp,req and the corresponding shear stress, i.e.

dtb

VVv

p

reqpureqRC

,

, (18)

where vRC,req is the required shear stress in RC part. The design concrete shear strength according to Structural Use of Concrete 2004 [8] is

3

14

131

25

40010079.0

cu

p

s

mvc

f

ddtb

Av

(19)

where 3100

dtb

A

p

s and 1400

d

.


69

For span/depth ratio l/h≤4, shear enhancement described in the clause 6.1.2.5, Structural Use of Concrete 2004 [8] may be used. The design shear stress may be increased by 2d/av, where av is the distance measured from the concentrated load to the support and it may be taken as half of the span length of the coupling beam. In any case, the design shear stress should not be higher than 0.8√fcu or 7MPa [8].

mvyv

creqRCp

v

sv

f

vvtb

s

A

/,

(20)

where Asv, sv and fyv are the area, the spacing and the yield strength of transverse reinforcement respectively. It should be noted that Equation (20) has only considered the shear area from the shear links. The shear area contributed from the vertical steel plate is ignored conservatively. 3.5 Shear Stud Arrangement in Beam Span Shear studs are required in the beam span to serve four functions as illustrated in Fig. 4. Based on the observations from the parametric study [6], design equations for estimating the required shear connection strengths, and the numbers of shear studs required in turn, for these functions are listed below.

Figure 4. Functions of Shear Studs in Beam Span 3.6 Function 1: Vertical Stud Forces for Inducing Shear on Steel Plate Shear studs should be provided within a width of 0.3 hp away from the beam-wall joint at each beam end for transferring the plate shear force. The required transverse shear connection force for inducing shear on the steel plate Pt1,req is

1.0

75.0

,1 065.0s

upreqt

VP

(21)

where )/(100 hbth ppp [%] is the ratio of plate sectional area to the beam sectional area

and )/(100 hbAss [%] is the steel ratio.

3.7 Function 2: Vertical Stud Forces for Maintaining Tension Tie Effect of Steel Plate Such forces are provided within the central (l-0.6hp) region near the top and the bottom plate fibres, and the required transverse shear connection strength for providing tension tie effect Pt2,req was found to be

Beam-wall Joint

Shear Stud Force

Function (1) Function (2) Function (3) Function (4)

Steel Plate


70

usreqt VhlP 1.065.0,2 /3.0 (22)

3.8 Function 3: Horizontal Stud Forces for Inducing Moment on Steel Plate It was proposed that the required longitudinal shear connection force within the beam span for transferring moment Pl1,req would be

upsreql Vh

lP 4.045.0

3.0

,1 165.0

(23)

3.9 Function 4: Horizontal Stud Forces for Inducing Axial Force on Steel Plate The required longitudinal shear connection forces within the beam span for inducing axial force on steel plate Pl2,req was expressed as

0.20.07

4.0

15.075.0

2.2

,2

0.106

0217.0

max

ps

u

pps

u

reql

ρρ

V

l

h

h

M

h

l

P

(24)

It should be noted that the contribution of natural plate/RC bonding to transfer shear forces is ignored in the design. The numerical results [6] showed that shear studs provided in the central beam region could not be effectively mobilized. By arranging all shear studs near the beam-wall joints and near the top and the bottom fibres of the steel plate, where shear studs could be effectively mobilized, a high degree of shear stud mobilization could be assumed. According to Structural Use of Steel 2005 [9], the shear stud force Q is taken as 0.8Qk and 0.6Qk under positive and negative moments respectively when designing conventional composite beams with RC slabs and structural steel beams interconnected by shear studs. As the plate/RC interface slips in a PRC coupling beam are unlikely to be as large as in the case of conventional composite beams under positive moments, Q = 0.6Qk is considered when calculating the numbers of shear studs required in different regions in the beam span.

Figure 5. Regions of Steel Plate in Beam Span for Shear Stud Arrangement The steel plate of a PRC coupling beam can be divided into five regions in the beam span

0.3hp 0.3hp

Region V (no shear stud)

Region III

Region IV

Region II

Region I


71

according to the different shear stud arrangements (Fig. 5). Based on the above proposals, and assuming the width of Regions I and II to be 0.3hp, the required numbers of shear studs (nreq) in different regions are expressed as follows: Region I or Region II:

k

reqlreqlpreqt

req Q

PPlhPn

6.0

/3.05.0 2,2,1

2,1

(25)

Region III or Region IV:

k

reqlreqlpreqt

req Q

PPlhPn

6.0

/3.05.05.0 2,2,1

2,2

(26)

3.10 Design of Plate Anchorage in Wall Piers The simplified plate anchorage design model adopted in this paper is depicted in Fig. 6. Design plate anchorage loads near the beam-wall joints The plate anchors of a PRC coupling beam are designed to take up the ultimate plate moment

pM and part of the ultimate plate shear yF (as part of the shear transfer will take place in the

beam span). They also need to resist an axial force xF jointly induced by the plate/RC

interaction under bending and the beam elongation upon cracking of concrete. The load-carrying capacity of PRC coupling beams and the plate anchorage design loads near the beam-wall joints are controlled by the shear and flexural capacities of the steel plate. The shear and flexural capacities of PRC coupling beams are expressed, respectively, in Equations (27) and (28). Shear capacity upRCPRC VVVV (27)

Flexural capacity upRCPRC MMMM (28)

where VRC, Vp, MRC and Mp can be calculated from Equations (6), (15), (16) and (18) to (20).

Figure 6. Simplified Plate Anchorage Design Model The PRC coupling beam is flexural-controlled when lMV PRCPRC /2 or shear-controlled

Beam-wall Joint

Fy

M2

M1

Fx

Centerline of Plate Anchor

Resisting Force from Plate Anchor

Load Applied on Plate Anchor

yF

hp

La

pM

xF


72

when lMV PRCPRC /2 . When the beam is flexural-controlled, the plate has reserved shear

but not flexural capacity. In such cases, the capacities of the steel plate, the plate anchorage and the PRC coupling beam are all governed by the yield moment of the steel plate. The design applied moment of the plate anchorage (equal to the yield moment) can be obtained by taking moment about the centroid of the plate, and is expressed in Equation (29).

p

ppp x

hhCM

2 (29)

Assuming the plate has fully yielded with the stress distribution as shown in Fig. 2, the compression of steel plate can be determined and Equation (29) becomes

1

22

122

pyp

pp tpx

hhM (30)

The shear load taken by the steel plate near the beam-wall joint, which is less than or equal to the shear capacity of the steel plate, is estimated by Equation (31).

pPRC

pPRCp V

M

MVV

(31)

Conversely, when the beam is shear-controlled, the shear load taken by the steel plate near the beam-wall joint may be obtained from Equation (6), such that, pp VV . The design plate

anchorage moment of the steel plate may then be estimated as,

pPRC

pPRCp M

V

VMM

(32)

It was observed in the parametric study [6] that the plate anchor of a PRC coupling beam would take up about 50 to 75% of the design plate shear pV . As the shear studs in beam span

near each beam-wall joint have been designed (in Equation 21) to transfer 0.5Pt1,req to the plate, the remaining vertical force required to be taken by the plate anchor is

reqtpy PVF ,15.0 (33)

The axial force xF induced on a plate anchor is equal to Fx acting on the plate and can be

determined from Fig. 3. The design plate anchorage loads obtained ( pM , xF and xF ) will be

used for calculating the bearing stress distribution and designing the shear stud arrangement in plate anchors.


73

3.11 Bearing Stress Distributions and Shear Stud Arrangements in Plate Anchors Taking moment about the centroid of beam section at the beam-wall joint, the required resisting moments of the plate anchor can be expressed as:

pay MLFMM 5.021 (34)

Figure 7. Recommended Minimum Plate Anchorage Length

Figure 8. Distributions of Resisting Moments in Plate Anchor The required moment resistance has to be determined in conjunction with the plate anchorage length La of which the minimum length is given in Figure 7. Note that slightly longer plate anchorage length than the recommended minimum value may be assumed first, as the recommendation is based on the arrangement of shear studs at minimum allowable spacing throughout the whole anchor, which is not necessarily the case in the design. The distributions of resisting moments, which depend on the geometry of the plate anchor, were investigated in the parametric study [3] and are plotted in Fig. 8. Assuming high degrees of shear stud mobilizations (i.e. Q = 0.6Qk), the required numbers of shear studs nreq in different regions are calculated from Equations (35) and (36). The design envelopes for the bearing stress distributions in the vertical and the horizontal directions are

/h

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8l

Rec

omm

ende

d M

inim

um L

a/l

/h

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

L a p

i = 1

i = 2

Mi/(

M1+

M2)


74

shown in Fig. 9 for arranging shear studs in Regions I and II in the plate anchors. Region I (width LI = 2

2 6MLF ay ):

k

Iypx

a

I

req Q

Lwhw

L

L

n6.0

22

1

22

(35)

Region II (width LII = aay LMLF 261 ):

k

IIya

pxII

req Q

LwL

hwL

n6.0

22

2

(36)

where

2

1 26

p

pxx

h

hFMw

(37)

2

21

6

a

yay

L

FLMw

(38)

2

22

6

a

yay

L

FLMw

(39)

Note that although the effects of shear studs in the shaded area in Fig.9 are ignored, evenly distributed shear studs are provided in Region II for simplicity. Furthermore, the code [9] states that the minimum allowable shear stud spacing is five times and four times the nominal shank diameter in the directions along and perpendicular to the major shear stud action respectively. As the major shear stud actions can either be in the horizontal or in the vertical directions, it is recommended that a minimum shear stud spacing of five times the nominal shank diameter be provided in all cases. By setting the material partial safety factors equal to unity and using the aforementioned design procedure, the theoretical design capacity can be calculated. By comparing the predicted design capacity with the numerical and experimental results, the reliability and accuracy of the proposed design procedure following the British Standards have been verified [7]. Consistent results form the proposed design procedure and finite element analysis were observed over a wide range of span/ depth ratios, plate thicknesses and steel ratios of PRC coupling beams. In general, the predicted capacity underestimated that from the numerical analysis by around 10%.


75

Figure 9 Regions of plate anchor with different shear stud arrangements and simplified design bearing stress blocks 4. A DESIGN EXAMPLE The design information of the long PRC coupling beam is listed as follows: Dimensions: l = 2m, b = 250mm, h = 500mm, cover = 30mm Material strengths: fcu = 40MPa, fy = fyv = 460MPa, py=345MPa E=205000MPa Design ultimate loading: Vu = 800kN, Mu = 800kNm Partial safety factors: 5.1mc , 25.1mv , 15.1ms

Main longitudinal steel = T40 and steel plate thickness = 25mm 4.1 Ultimate Shear Resistance Assume using T40 longitudinal reinforcement and T12 stirrups, d ≈ 500 – 30 –12 – 20 = 438mm Ultimate shear resistance of the PRC coupling is

2223

N/mm12N/mm48.9405.1N/mm3.7438250

10800

uv

4.2 Shear Resistance Design of Steel Plate d/h = 438/500 = 0.88 ≈ 0.9 hp ≈ 500 – 30 – 30 – 12 – 12 – 15 = 401mm Adopt hp = 400mm hp /h = 400/500 = 0.8 Use Grade S355 steel plate, assuming 16mm < tp ≤ 40mm, py = 345N/mm2

VRC,allow ≈ 5 × (250 – 25) × 438/1000 = 492kN Vp,req = Vu – 492 = 308kN ≤ 0.45Vu=360kN Hence, for low shear load

kN308kN10761000/25400345312.0 pV

wy1

Region I

wx

wx

Region II

Beam-wall Joint

Effects of shear studs ignored in central area wy2 wy2

0.5hp

0.5LII

LII

LI = 2

2

3

4

6M

LFL

w

w aya

LI


76

4.3 Bending Resistance Design of Steel Plate and RC Section

%01.2)250500/(10012562 s , 1.0250/25/ bt p

From Fig. 3, kN9608002.12.1 ux VF

According to Equation (11a)

N440,162212562050000035.015.1

460960000

sc

ms

yx AE

fF

Assume εsc< εy, then

mm6.199

252505.1

40206.1

25122050000035.0438500252505.1

40412.2162440162440 2

x

From Equation (8),

kN1005100015.1

251246012421000/25122050000035.0

6.199

4385006.199

sC

Hence the compressive reinforcement has been yielded and from Equation (11b)

mm2652525040603.0

9600005.1

x

kN1005100015.1

2512460

ss TC

kN96010005.1

265)25250(40603.0

cC

Hence the moment resistance of RC part according to Equation (15) is

By Equations (12) to (14)

mm19401253452

960000

2

500

px

kN1245

2

960

2

25400

1000

01345

pC

kN2205

2

960

2

25400

1000

01345

pT

From Equation (16), the moment resistance of the steel plate is

kNm3041000/01345254

960000

4

4001942651245

01345254

960000

4

4002651942205

pM

Total moment resistance of the composite beam is kNm800kNm822304518 pRC MM

kNm5181000/26596055.0)438500(2651005)265438(1005 RCM


77

4.4 Shear Resistance Design of RC Section As the span-to-depth ratio of the PRC coupling beam is 4 >>1.5, the beam is flexural- controlled. The design moment of the steel plate, according to Equation (29), is

kNm318194.0

2

5.04.01245

pM

The design shear load in the steel plate near the beam-wall joint may be estimated by Equation (31)

kN318800

318800

pV

23

, N/mm89.443825250

10318800

reqRCv

2

31

31

N/mm01.125

40

43825250

2512100

25.1

79.0

cv

/mmmm65.1

15.1/460

01.189.425250 2

v

sv

s

A

Provide T12-125-S.S., v

sv

s

A (provided) = 1.81mm2/mm

4.5 Shear Stud Arrangement in Beam Span Use shear studs of 16mm shank diameter, Qk = 66.5kN, minimum spacing = 80mm, as-welded height = 70mm, ρp = 8%, ρs = 2.01%,

kN23080001.2

8065.0

1.0

75.0

,1 reqtP

kN63380001.243.0 1.065.0,2 reqtP

kN629800801.24165.0 4.045.03.0,1 reqlP

kN31

801.2

80025.00.106

kN39710801.24.0

1080040217.0

max

2.007.04.0

315.075.0

32.2

,2 reqlP =397kN

For Region I or Region II,

2.3

5.666.0

3976292000/4003.02305.0 22

reqn

For Region III or Region IV,

8.13

5.666.0

3976292000/4003.05.06335.0 22

reqn

Provide 2 shear studs in one column in Region I or Region II, and 7 shear studs in one row in Region III or Region IV on each side of plate.


78

4.6 Plate Anchorage Design From Fig. 3, uxx VFF 2.1 = 960kN.

From Equation (33), kN2032305.0318 yF

Referring to Fig. 7, assume La = 0.45l = 900mm

25.2400

900

p

a

h

L

From Fig. 8,

14.021

1 MM

M and 86.0

21

2 MM

M

From Equation (34), 3189.02035.05.021 pay MLFMM = 409kNm

M1 = 57kNm and M2 = 352kNm

mm773526

10009.0203 2

IL and mm82377900 IIL

Figure 10. Steel Plate and Shear Stud Arrangements of the PRC Coupling Beam Furthermore, use shear studs of 16mm shank diameter, Qk = 66.5kN, minimum spacing = 80mm

kN/m69374.0

4.096025762622

1

p

pxx

h

hFMw

kN/m28339.0

2039.03526622

21

a

yay

L

FLMw

kN/m23829.0

2039.03526622

22

a

yay

L

FLMw

@80

c/c

400

60 269

2000

T12-125 S.S. @80c/c

40

80

T40

T40

@557c/c900

COUPLING BEAM WALL PIER WALL PIER A

A

25mm thk GRADE S355 PLATE

LEGEND 16mm dia SHEAR STUDS

T40 16mm SHEAR

25mm thk x 400mm

SECTION A-A


79

For Region I (width = LI = 77mm),

2.6

5.666.0

077.028332

4.06937

9.0

077.0 222

reqn

For Region II (width = LII = 823mm),

3.80

5.666.0

823.023829.0

4.06937823.0 22

reqn

Provide 4 shear studs in one column in Region I, and 40 shear studs in 10 columns in Region II on each side of plate. Figure 10 shows the detailing of the PRC coupling beam in this example. 5. CONCLUSIONS With the aim of providing the construction industry with a practical, effective and economical coupling beam to resist high shear force and large rotational demand from large wind or seismic loading, plate-reinforced composite (PRC) coupling beam was developed. The effectiveness and efficiency of this new form of beams were demonstrated by extensive experimental studies and numerical simulations. The practicality of PRC coupling beams in terms of integration of steel plate together with neighbouring reinforcement, easy of concreting and no special requirement for protecting steel plate against fire and lateral buckling was highlighted. Furthermore, original design guidelines compiled with local construction practice are proposed to ensure proper beam detailing for desirable performances of PRC coupling beams. The guidelines consist of four main parts, which are (1) estimation of ultimate shear capacity of beam, (2) design of RC component and steel plate, (3) shear stud arrangement in beam span, and (4) design of plate anchorage in wall piers. An example is given to illustrate the use of the guidelines for designing a PRC coupling beam. ACKNOWLEDGEMENTS The research described here was supported by the Sichuan Earthquake Roundtable Fund of The University of Hong Kong. REFERENCES 1. Lam, W.Y., Su, R.K.L. and Pam, H.J., “Strength and Ductility of Embedded Steel

Composite Coupling Beams”, Advances in Structural Engineering, 2003, Vol. 6, pp. 23-35.

2. Lam, W.Y., Su, R.K.L. and Pam, H.J., “Experimental Study on Embedded Steel Plate Composite Coupling Beams”, Journal of Structural Engineering, ASCE, 2005, Vol. 131, pp. 1294-1302.


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3. Lam, W.Y., Su, R.K.L. and Pam, H.J., “Behavior of Plate Anchorage in Plate-Reinforced Composite Beams”, Steel and Composite Structures (accepted).

4. Su, R.K.L., Pam, H.J. and Lam, W.Y., “Effects of Shear Connectors on Plate-Reinforced Composite Coupling Beams of Short and Medium-Length Spans”, Journal of Constructional Steel Research, 2006, Vol. 62, pp. 178-188.

5. Su, R.K.L., Lam, W.Y. and Pam, H.J., “Experimental Study of Plate-Reinforced Composite Deep Coupling Beams”, The Structural Design of Tall and Special Buildings, 2009, Vol. 18, pp. 235-257.

6. Su, R.K.L., Lam, W.Y. and Pam, H.J., “Behaviour of Embedded Steel Plate in Composite Coupling Beams”, Journal of Constructional Steel Research, 2008, Vol. 64, pp. 1112-1128.

7. Su, R.K.L. and Lam, W.Y., “A Unified Design Approach for Plate-Reinforced Composite Coupling Beams”, Journal of Constructional Steel Research, 2009, Vol. 65, pp. 675-686.

8. Buildings Department, "Code of Practice for Structural Use of Concrete 2004" (Second Edition), The Government of the Hong Kong Special Administrative Region, pp.180, 2008.

9. Buildings Department, "Code of Practice for the Structural Use of Steel 2005", The Government of the Hong Kong Special Administrative Region, pp.357, 2005.


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82

PERFORMANCE BASED SEISMIC DESIGN FOR CONTEMPORARY ARCHISTRUCTURES

Goman Ho Arup Group

[email protected]

ABSTRACT With the 2008 Beijing Olympics; development of “Informal” engineering approach1 and contemporary architectural design as catalyst, Performance Based Seismic Design (PBSD) approach is becoming an essential tool in designing structures in seismic region. Couple of complete projects will be presented in this paper to further demonstrate the importance and merits of adoptability performance based approach in seismic design over the traditional code base approach. Keywords: Performance Base, Seismic, Nonlinear Analysis, Severe Earthquake


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1. INTRODUCTION Design Codes and Practice are typically prescribe design and construction rules developed largely based on past performance and experience. They were believed by most engineers and approval authorities that structures designed according to the codes are capable of attaining desired safety level and performance. This is usually correct for regular structures. Nevertheless, if the structures are somehow fall outside the coverage of the codes, e.g. new structural system, the rules set based on past experience is not longer valid or applicable to the new structural system. In most of these cases, authorities will instruct the designers or engineers themselves to increase the design forces in the structures. It is believed that such “increase” will therefore increase member stiffness and strength and hence the safety level and performance of the overall structures. This assumption is not always true. Cheng-Meng Lin2 et al had pointed out that such increases could have significant impacts on the design and also decrease the performance of the structures. We understand that if codes are prepared based on past experience or research experiments, there are definitely area which is not covered by the codes. Furthermore, most codes are developed to satisfy One objective – the safety, this single objective approach is now unable to satisfy the current development on the society demand. Therefore, a systematic methodology was developed from end 90’s to overcome the lead of code guidance design. This is the Performance Based Seismic Design (PBSD) approach which this paper is focused on. The following sections will briefly explained the background of PBSD approach; the theory. The use of PBSD in BJ Olympics projects will also be presented to demonstrate the success of this approach in solving engineering problems which are outside the coverage of any Chinese and National Codes. 2. BACKGROUND Performance Based Seismic Design (PBSD) concept was developed by late 90’s. Unlike most of the current single level target codes of practices, PBSD will design the structures that satisfy multi-level performance objectives at say minor, medium and severe level of earthquake. PBSD allows the design team (client, engineer, architect, insurance company etc.) to work together to determine the appropriate level of performance objectives against various levels of ground motion shaking. Therefore, PBSD is not just to provide the ultimate safety requirement but also the control in downtime and damage. The following describes the different between current building design codes and PBSD approach. 2.1 Current Building Code Requirement • Only one objective – life safety for the design earthquake intensity level; • By means of seismic detailing to increase enhance the structural performance but the

resulting level of performance is not explicitly defined;


84

• In Chinese Code, the design seismic load is a function of the material/damping and structural system while UBC codes is a function of which related to the ductility of the system factor, “R”

• Chinese code allows different seismic detailing for different structural members which creates unpredictable structural behavior in severe earthquake;

• UBC code use R-factor which the reduction of seismic load applies to the whole building.

2.2 PBSD Approach • Allows the owner, architect, engineer, insurance company, operator to select the

appropriate level of protection at various level of ground motion; • Multi-level of ground motion can be evaluated against various level of performance

objectives; • With the understanding of the behavior of the structures at various earthquake

intensities, we can determine the actual seismic load that should be applied to the structures and members instead of single damping value or single R-factor.

3. PBSD DESIGN PROCEDURE Generally speaking, three levels of performance are defined as follow: Serviceability Level Negligible structural and nonstructural damage; nearly no

downtime for the use of the building; and re-pair costs are minimal to nil.

Immediate Occupancy Level

Negligible structural damage and minor non-structural damage; structure may not function but with limited interruption of operations; building requires repairing but cost is limited.

Collapse Prevention Level

Extensive structural and non-structural damage; building is unable to be re-use; repair cost might be too high and re-build is recommended.

Because of the above, we sometime may also call PBSD as “3D” design. “3D” in PBSD refers to Downtime, Damage and Deaths which are all a factor in risk analysis.

RISK = PDeaths (safety)

Dollars (damage)

Downtime (loss of use)RISK = PP

Deaths (safety)

Dollars (damage)

Downtime (loss of use)

PBSD is a series of design and evaluation process on a structural system to enforce certain behavior of structural as well as nonstructural system and/or components under application of simultaneous ground motions at various probabilities of exceedance.


85

The design process of PBSD has 4 steps namely 1 Setup Performance Objectives in various Hazard Level; 2 Conceptual Design; 3 Design Evaluation and 4 Modification (if required) 3.1 Setup Performance Objectives in Various Hazard Level Performance Objectives should be selected based on the hazard level and the building’s occupancy; the importance of functions occurring within the buildings; economic consideration including costs related to building damage repair and business interruption. Hazard levels are based on the probability of exceedance of earthquake. In Chinese code, it refers to 63%, 10% and 2% in 50 years as minor (Level 1), moderate (Level 2, or design intensity) and severe (Level 3) earthquake respectively. The following is an example extracted from FEMA 356 on setting-up the Performance Objectives:

3.2 Conceptual Design Once the performance objectives were established with the design team, the engineer should then develop the concept on how to achieve the performance objectives. It could be achieved by means of strength, stiffness, ductility, damping device (base isolators, unbonded braces) and control on the locations of structural fuses etc.


86

3.3 Design Evaluation As PBSD involves the design of structure at various earthquake hazard levels, various tools are generally require to carry out the design evaluation work. For example, in level 1 earthquake, the structure is supposed to be no damage and therefore it should be basically remain elastic. Therefore, elastic static and elastic dynamic (time-history) should be able to handle this evaluation process.

Moreover, if the designer wants to capture the behavior of the structures in level 2 and 3 earthquakes where minor or major plasticity had been occurs in the structures, nonlinear analysis software will be an essential tool at this stage of work. With the current development on computer software, push-over and nonlinear time-history analysis is becoming more popular.

3.4 Modification Because PBSD requires the structure to satisfy the performance objectives at multiple hazel levels, convergence and cost to achieve the performance objectives may sometime requires the design team to review and modify either the structures or the original performance objectives.

4. PBSD Approach for Contemporary Architectural Projects Because the increase of living standard and growth of economic, starting from millennium, there are many projects especially in China which are very challenge to engineers. However, at the same time, the limitation of Chinese code had created barriers for these projects. To go through the hurdle, PBSD is used to demonstrate to the Chinese approval authorities on not just the safety but also the performance of the structures at multiple hazel levels. 5. Examples 5.1 Example 1: CCTV CCTV (photo 1) new headquarters is located the new Central Business District (CBD) of Beijing City. The main “twins” tower is named as CCTV consists of 450,000m2 GFA which GFA is equivalent to 2.5 IFC2 in Hong Kong. Both towers are tilted by 6 degrees in both directions. The maximum height of the tower is 234m and both towers are connected by means of a 9 to 13 storey overhang cantilevers of 67 to 70m. By flipping the links vertically, the tower becomes two 300m tall towers. At the base of the towers, there are 3 levels of basement and a 9 storey podium. The engineering challenge for CCTV is how to design the building such that it can satisfy the basic performance objective set in Chinese Code – no damage in Minor EQ; repairable damage in Design Intensity EQ Level and finally no collapse in Severe EQ. Because the building geometry, general core plus frame lateral system would not work. Therefore, external mega frame system was selected. Each structural member had to meet the Chinese Code as the basic requirement.


87

Furthermore, specific performance objectives for CCTV and for various structural elements at various zones were established with the client and the approval authority based on FEMA3563 are listed as follow:

Service Level Earthquake (SLE) (50 year)

Design Bases Earthquake (DBE) (475 year)

Maximum Credited Earthquake (MCE) (2500 year)

Performance Objective No Damage (Structure remains in Elastic)

Repairable Damage Collapse Prevention

Allowable Drift Ratio h/300 h/100 h/50

Inter-storey Ductility Requirement

< 1(Elastic) < 2 < 4

Steel Beam Performance Objective

Elastic < 0.01 radians < 0.04 radians

Steel Bracing Performance Objective

Elastic Majority Remain Elastic

Comp. Strain 7Dc Tensile Strain 9Dt

Columns Performance Objective

Elastic Elastic

SRC Comp. Strain 0.02 Steel Comp. Strain 7Dc Tensile Strain 5Dt

Transfer Structure Performance Objective

Elastic Elastic Elastic


88

Nonlinear time-history analysis was adopted to justify the performance had meet the objective. The approval of the seismic expert panel review was obtained in 9 months after the project was started. Such period of design and approval time is similar to those building structures which exceeds the code limit. 5.2 Example 2: National Stadium National Stadium is one of the most importance stadiums for 2008 Beijing Olympics. The National Stadium is 260m (wide) x360m (long)x 60m (high) which houses 96,00 audiences in Olympics period. The structures were divided into two parts namely the bowl and the roof. The bowl was made of reinforced concrete. The roof is made of structural steel with the majority of the sections being 1.2m square boxes. For area which does not affect the appearance, 800mm square box sections were used.

Figure 1a. Primary Structures

Figure 1b. Primary and Secondary Structures

Similar to CCTV, the performance objectives were first determined and agreed with the authorities. Because of the nature (geometry and function) of National Stadium is different from “buildings” only secondary members are designed as structural fused in level 3 EQ in order to protect the preliminary structures to behave elastically in all levels of EQ.


89

6. CONCLUSIONS The concept of performance was briefly described. With the success of the applications in projects like BJ CCTV, National Stadium and others such Water Cube, China World Trade Centre phase 3A, Beijing T3 airport etc. This new design tool is becoming more and more popular for engineers in designing structures. REFERENCES 1. Balmond, Cecil, “Informal”, 2007, Prestel. 2. Lin, Cheng-Ming, Ho, Lawrence Y. and Sabol, Thomas A., “Impact of Increased

Code Design base Shear on Seismic Behaviour of Reinforced Concrete Moment Frame Buildings with Long Periods”, The Structural Design of tall and Special Buildings, 2004, Vol. 13, pp. 391-408, Wiley Interscience.

3. FEMA 356, “Prestandard and Commentary for the Seismic Rehabilitation of Buildings”, Fedral Emergency Management Agency, November 2000.


90

SEISMIC RISK ANALYSIS

T.T. Soong and I.-S. Ahn Department of Civil, Structural and Environmental Engineering

State University of New York at Buffalo Buffalo, New York 14260, USA

[email protected] and [email protected]

ABSTRACT In earthquake engineering, seismic risk analysis is a topic of critical importance to engineers and planners in assessing seismic vulnerability of existing structures, and in designing and constructing new structures, so that they perform successfully in an earthquake. Since seismic activities are random events, probabilistic tools are called upon to carry out necessary steps involved. In this paper, the fundamental concepts of seismic risk analysis are introduced and demonstrated through examples. Keywords: Earthquake Engineering, Seismic Risk, Structural Vulnerability, Structural Design


91

1. INTRODUCTION AND METHODOLOGY The ultimate goal of seismic risk analysis is to develop a rational procedure that can be used to make decisions on seismic safety of existing and new structures. This decision process requires a logical and consistent approach, which can be viewed as consisting of four steps as shown in Figure 1 (McGuire [1]). As seen in this figure, results obtained from seismic risk analysis are not ends in themselves, but are used to make important decisions regarding cost and benefits, risk aversion, and options for risk mitigation associated with existing structural vulnerability and new structural design and construction.

Figure 1. Seismic Risk Analysis and Decision (McGuire [1])

Probabilistic Seismic Hazard Analysis (PSHA) A probabilistic seismic hazard analysis (PSHA) for a specific site consists of determining the probability associated with an earthquake characteristic, such as peak acceleration of the ground motion, taking on a certain range of values during a fixed time interval in the future, such as 50 years. For example, let the earthquake characteristic be denoted by a random variable C and the specified range of values of C be larger than 0.5g. The probability of interest is 0.5 1 0.5 (1) where is the probability distribution function (PDF) of C at c (Soong [2]). Instead of probability, the frequency, that is, the number of earthquakes of which peak accelerations are greater than 0.5g per unit time, denoted by 0.5 , can sometimes be a more convenient way to define the earthquake hazard. This is done in PSHA. The procedure for carrying out a PSHA is shown schematically in Figure 2. Concerning the specific threat of ground motion, Step A divides the earthquake threat into sources that produce the specific earthquake characteristic. With estimated or postulated size distribution and rate of occurrence (Step B), and ground motion estimation (Step C), the seismic hazard at the site for earthquake characteristic C is defined as the frequency with which c is exceeded. It is calculated at Step D from

Probabilistic SeismicHazard Analysis

Damage andLoss Functions

Seismic Risk Analysis

Decision Analysis


92

∬ | ̅ ̅ ̅ (2) where j is the frequency with which c is exceeded from earthquakes at source j; ̅ is a vector of source properties; is the rate of occurrence of earthquakes of interest at source j;

| ̅ is the conditional probability that c is exceeded at the site, given that an earthquake at source j, with properties ̅ at location l, has occurred; and ̅ is the probability that an earthquake with source properties ̅ occurs at location l.

(A) Seismic source j, earthquake locations in

space lead to a distribution of location: | ̅

(B) Size distribution (magnitude m) and rate of occurrence for source j: ̅ ,

(C) Ground motion estimation: | ̅

(D) Probability analysis:

∬ | ̅ ̅ ̅

Figure 2. Steps for Performing a PSHA (McGuire [1])

The total seismic hazard at the site is given by ∑ (3)

Location l

Rupture

Site

Fault j

Location l

P[

l | s

]=

f( l

| m)

Magnitude mm m0 max

P[

s ]=

f (

m)

M

c

m=7

m=6

l

GroundMotionLevel(log scale)

P[ C > c | s at l ]

Location (distance on log scale)Ground Motion Level c (log scale)

[ C

> c

] (

log

scal

e)


93

Damage and Loss Functions Damage functions provide a relationship between levels of damage and the corresponding levels of shaking, where damage usually refers to physical damage of a structure. Damage functions can be derived either empirically or analytically. On the other hand, loss functions define relationships between monetary or human loss and earthquake damage or levels of ground shaking. Thus, loss can be estimated directly from earthquake shaking or by estimating the levels of damage first. The derivation of loss functions can be difficult and is usually carried out empirically or based on experience data. It is worth pointing out that methods of calculating damage and loss functions based on geographic information system (GIS) have become popular. With these methods, large databases of building inventories, soil conditions, and earthquake faults over a region can be combined to estimate earthquake damage and loss in the region. Seismic Risk Analysis As Figure 1 shows, the combination of the results obtained under PSHA and the knowledge of damage and loss functions leads to the determination, or estimation, of seismic risk. In the context of structural design and structural vulnerability studies, seismic risk is calculated as a probability of failure of a structure (or a nonstructural component) when its capacity is exceeded under a selected performance objective. The capacity of a structure under earthquake loading depends on design and construction details, which can be described by a random variable D. As random variable C has been used to represent the characteristic of the seismic hazard, random variable D also represents the characteristic of the capacity. For instance, D may be story drift ratio, lateral displacement, damage, damage indices, or cost to repair damages. For given probability distribution functions of C and D, the probability of failure can be defined by the shaded area in Figure 3. In this figure, it is assumed that c represents the spectral acceleration and the probability density function is ⁄ . The random variable D is expressed in terms of the spectral acceleration, and its probability density function is ⁄ .

Figure 3. Definition of the Probability of Failure

c

fD

fC

Spectral Acceleration

Probability Density Functions


94

Thus, the probability of failure, , is defined as ∑ ∩ ∑ | 1 (4) or ∑ ∩ ∑ | (5) Eqs. (4) and (5) and their variations provide the basis of the seismic risk analysis. It is noted that, unlike seismic hazard, seismic risk is quantified by a probability, not a frequency. Seismic risk analysis can also be performed for a set of multiple sites. As an example, suppose three sites are considered and the failure for these three sites occurs if earthquake damage at site 1 and at site 2 occurs, or damage at site 3 occurs, or both. For total damage or loss estimation for this set of three sites, failure can be defined as D d ∩ ∪ (6) and 1 1 ∩ 2 2 ∪ 3 3 (7) which can be calculated based on probability theory (Soong [2]). In Eqs. (6) and (7), the symbols ∩ and ∪ represent, respectively, intersection and union of sets in set theory. It has been mentioned that structural failure must be defined carefully in terms of a selected performance objective. For example, Figure 4 shows the performance objectives for buildings recommended in Vision 2000 (SEAOC [3]). Three different performance objectives, basic, essential/hazardous, and safety critical, are specified on top of the combination of four different earthquake performance levels and four earthquake design levels. Important buildings, such as hospitals and emergency response centers may require the safety critical performance objective. Conventional office buildings may experience significant damages under very rare earthquake, which is an acceptable situation under the basic performance objective. For each performance level, Vision 2000 describes damages that various structural components and systems, architectural elements, mechanical/electrical/plumbing (MEP) system components, and contents of a building may have. These descriptions are mostly qualitative; so it is challenging for structural engineers to select engineering demand parameters to satisfy the performance objective (Krawinkler and Miranda [4]). ASCE 41-Seismic Rehabilitation of Existing Buildings (ASCE [5]), also takes the performance-based design approach, which has been evolved from FEMA 273 (FEMA [6]), FEMA 274 (FEMA [7]), and FEMA 356 (FEMA [8]). In this standard, provisions for evaluating engineering demand parameters are specified along with numerical criteria with respect to the performance levels (Immediate Occupancy, Life Safety, and Collapse Prevention). These provisions make it possible to implement the performance evaluation in the practical assessment and design process.


95

Figure 4. Performance objectives for buildings (SEAOC [3])

In current performance-based seismic design formats, the performance levels and seismic hazard levels are discrete. This provides a simpler way to represent the performance objective as given in Figure 4; however, many valuable information can be lost in the process of converting continuous engineering demand parameters into discrete performance levels. Figure 5 shows a relationship between seismic hazard intensity and structural performance. The discrete performance levels are indicated by IO (Immediate Occupancy), LS (Life Safety), and CP (Collapse Prevention) as the structural performance (e.g. lateral displacement or story drift ratio) changes. This figure indicates that the LS region encompasses 20~50% of the replacement cost, 0.0001~0.001% of the casualty rate, and 1~30 days of the downtime. These ranges are so broad that one cannot assess the consequence of the design precisely. Therefore, introducing continuous variables–usually, they are called decision variables–for determining the performance objective is required. In addition, continuous variables can be worked with reliability-based methods and conventional risk estimation techniques easily.

Figure 5. Conceptual relationship between seismic hazard intensity and structural

performance (Moehle [9])


96

For new buildings, the urgency for adopting the performance-based design may be less. For example, the recently developed 2009 NEHRP Recommended Seismic Provisions for New Buildings and Other Structures (BSSC [10]), which constitute a seismic model code, maintain the conventional approach where seismic risk or seismic hazard is implicitly given in the definition of design earthquake. It needs to be noted that 2009 NEHRP Provisions make progress in the definition of design earthquake. In the previous provisions, including 1997, 2000, and 2003 provisions, design earthquakes were defined to have a 2% probability of being exceeded in 50 years. These so-called uniform-hazard ground motions have been changed into uniform-collapse motions, 1% probability of collapse in 50 years. By defining design earthquake to have the same consequences (uniform-collapse) instead of having the same causes (uniform-hazard), the 2009 NEHRP provisions resolve issues of “not providing for a uniform probability of failure for structures designed for ground motions in the previous provisions (Luco, Ellingwood et al. [11]).” 2. SEISMIC FRAGILITY Among many possible representations of seismic risk, a simple and effective one is seismic fragility, which is defined as the probability of failure as a function of an earthquake characteristic. It is thus a conditional probability represented by | (8) where Y is a demand random variable representing the earthquake characteristic, for example, ground motion intensity or peak floor acceleration. It is seen from Eq. (8) that is a function of y and a plot of as a function of y is called a seismic fragility curve. Fragility curves can be generated empirically, analytically, or through laboratory experiments. Empirical fragility curves can be developed based on damage data recorded in previous earthquakes or, when laboratory tests are feasible, with the use of experimental data. Analytical fragility curves can be developed with the use of statistical data obtained with the use of accurate mathematical models that represent the underlying physical phenomena (Shinozuka, Feng et al. [12]). Fragility curves can be conveniently used to present vulnerability data for both structural and nonstructural components. They can also be used to compare different seismic rehabilitation techniques and to optimize seismic design of structures. In the following, examples are given to demonstrate the utility of the fragility techniques. Example 1. Fragility of Structural Members (Singhal and Kiremidjian [13]) The evaluation of fragility for a given site or a region requires the following tasks:

Characterization of the potential ground motions Characterization of the structures Quantification of the structural response Estimation of damage or damage indices


97

Among various parameters to characterize the intensity of ground motions, the spectral acceleration has been adopted, which corresponds to the random variable Y in Eq. (8). When

takes a specific value, for example 0.2 , the corresponding potential ground motions can be obtained from recorded data or by using artificial ground motion generation methods. Usually, the number of recorded ground motions is not large enough to generate a consistent ensemble. The ground motions in this study, therefore, are generated from nonstationary ARMA methods, and they show reasonable consistence with recorded data in respect of intensity and strong motion duration. As sample structures, three RC frame structures are used as shown in Figure 6. They are referred to as low-rise, mid-rise, and high-rise buildings and designed according to the 1990 SEAOC Recommendations (SEAOC [14]) for special moment resisting frames. In the evaluation of the structural behavior of these buildings, various parameters including the compressive strength of concrete, the yield strength of reinforcing steel, hysteretic behavior, damping ratio, member size, and the amount of reinforcing steel influence the response and the capacity of members. Among them, it is assumed that the compressive strength of concrete follows a normal distribution (mean=1.14×nominal strength, =0.14) and the yield strength of reinforcing steel follows a lognormal distribution (mean=1.05×nominal strength, =0.11).

Figure 6. Sample Structures (Singhal and Kiremidjian [13]) Monte-Carlo simulation is a numerical method to determine probability distribution functions when it is not possible or impractical to apply analytical methods to drive them. In the present example, the values of random variables are assigned by the Latin hypercube sampling method, and nonlinear time history analysis of example buildings are performed by computer

Plan View

Elevation View

Low-Rise

Mid-Rise

High-Rise

5 @ 7.62m = 38.1m

7.62

m

7.62m 7.62m 7.62m

3.05

mT

YP.

3.05

mT

YP.

3.05

mT

YP.


98

programs IDARC2D and DRAIN-2DX under artificial ground motions. For a given building and given spectral acceleration, 100 random samples are used with 100 ground motions. A bilinear model without strength and stiffness degradation is employed as hysteretic damping model. Once the response of a structure is evaluated at each run, it is more convenient to use a damage index in order to determine the severity of expected damage. For reinforced concrete structures, the Park and Ang model (Park and Ang [15, 16]) has been widely used, which can be expressed as in Eq. (9) for a structural component.

(9)

where is the maximum positive or negative plastic hinge rotation; is the plastic hinge rotation capacity under monotonic loading; is the model parameter (0.15 is used); My is the calculated yield strength; and dE is the incremental dissipated hysteretic energy. The first term of Eq. (9) represents the damage due to maximum deformation, and the second term represents the damage due to cumulative hysteretic energy dissipation. The damage index could be 0 if there is no damage, and it would be 1 if that member fails. After obtaining damage indices of all structural members, one can estimate the global damage index, DT, in Eq. (10), which represents the performance of the whole structure. ∑ (10) where ∑⁄ and is the energy dissipated at location i. In general, damages in a structure are expressed in a qualitative way such as minor, moderate, severe, or collapse, and the damage index can be bounded as shown in Table 1. Eventually, it can be thought that random variable D in Eq. (8) takes a value within the damage state vector

d , d ,⋯ , d where d =none, d =minor, … , d =collapse.

Damage State ( ) Range of the Park and Ang Index

Minor Moderate Severe Collapse

0.1 – 0.2 0.2 – 0.5 0.5 – 1.0

> 1.0 Table 1. Ranges of Park and Ang’s Damage Index for Discrete Damage State

(Singhal and Kiremidjian [13])

After completing Monte-Carlo simulation for a given structure (e.g., low-rise building) and given spectral acceleration (e.g., 4.0 ), one can estimate the probability distribution of the damage as shown in Figure 7. The lognormal distribution function fits well to represent the simulation results. By applying the ranges in Table 1 for each damage state, the boundary values of the cumulative distribution function can be identified and those values are marked in the fragility curves in Figure 8 when 4.0 . Repeating this procedure for varying spectral acceleration values, one can acquire the complete fragility curves for a structure. Then, lognormal distribution functions are used to generate smooth fragility curves by curve fitting. Fragility curves of mid-rise and high-rise buildings can be obtained through the same procedures.


99

Figure 7. Probability Distribution for Low-Rise Building when 4.0

(Singhal and Kiremidjian [13])

Figure 8. Fragility Curves for Sample Low-Rise Building (Singhal and Kiremidjian [13])

As one sees, fragility curves provide a convenient way of understanding seismic risk of a structure with respect to the seismic hazard. For example, the probability of collapse of a low-rise building can be estimated as about 0.2 when the spectral acceleration 3.0 . The damage estimates may be used for cost-benefit analysis to assess the appropriate repair and retrofit strategy or risk analysis.

0.0 0.5 1.0 1.5 2.0 2.5 3.0

1.0

0.8

0.6

0.4

0.2

0.0

Park-Ang Damage Index

Cu

mu

lativ

e D

istr

ibu

tion

Fu

nct

ion

0.0 1.0 2.0 3.0 4.0

1.00

0.75

0.50

0.25

0.00

Minor

Moderate

Severe

Collapse

Simulation ResultsFitted Curves

Spectral Acceleration (g)

P[D

d |

S

]>

ii


100

Example 2. Fragility of Suspended Ceiling Systems (Badillo-Almaraz, Whittaker et al. [17]) From past experiences, damages occurred in nonstructural components and contents of a building are substantial even though the structure did not experience severe damage. Damages to nonstructural components not only influence the functionality of a building but also threat human lives inside and outside a building. The present example focuses on the seismic risk analysis of suspended ceiling systems in terms of fragility. Failure of the suspended ceiling in the past earthquakes has been observed in office buildings, hospitals, and critical facilities, which resulted in serious injuries and disruption of functionality. Compared with structural members in the previous example, it is difficult to employ mathematics or mechanics based dynamic analysis for this suspended ceiling system since the behavior is too complicated to be solved by conventional numerical analysis methods. Consequently, experimental investigation is a better way to quantify useful and reliable seismic risk. The procedure of performing seismic risk assessment is similar to that used in the previous example except that full-scale shake table tests are used instead of Monte-Carlo simulations. The ground motions used in the shake table tests are generated by a spectrum-matching method, and the overall process satisfies procedures in the ICBO-AC 156 “Acceptance Criteria for Seismic Qualification Testing of Nonstructural Components” (ICBO [18]). The spectral acceleration is used to characterize the intensity of ground motions. During the tests, the spectral accelerations are changed from 0.25g to 2.5g with 0.25g increments, and the ground motions are scaled to acquire a close match with values in the specified spectrum for each spectral acceleration intensity. The contribution of vertical ground motion is substantial in the present investigation; so the vertical ground motions are also generated and their values in the target spectrum take 2/3 of horizontal spectral values.

(a) Shake Table Test Set-up (b) Example of Damaged Ceiling

Figure 9. Full-Scale Shake Table Test of Suspended Ceiling System (Badillo-Almaraz, Whittaker et al. [17])

In the tests, a 4.88m×4.88m square frame is utilized in the installation of commercial suspended ceiling systems, and six different installation set-ups have been tested. Figure 9(a) shows the full-scale shake table test set-up, and Figure 9(b) shows a damaged ceiling system after shaking. Damages occurred in the ceiling system are described by five damage states such as none, minor, moderate, major, and grid failure.


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The fragility curves are generated, firstly, by identifying the probability of reaching or exceeding damage states and the corresponding spectral accelerations from the tests. Secondly, a probability function is used to match those data points, and lognormal distribution functions are used in the present example. Then the fragility curves consist of these probability functions. Even though the input ground motions are adjusted to make the mean value within a fixed period range be the same as in the target spectra, the spectral values show substantial variations. Therefore, the fragility curves are developed for different period values of 0.0, 0.2, 0.5, 1.0, 1.5, and 2.0 sec. Figure 10 shows two sets of fragility curves for different periods: T=0sec and T=0.2sec. Notice that the probabilities of exceedance in y-axis are the same at two data points, one from Figure 10(a) and the other from Figure 10(b) at the corresponding position. The differences between two points are the spectral accelerations due to the period change.

(a) T=0 sec (b) T=0.2 sec

Figure 10. Fragility Curves of Suspended Ceiling System (Badillo-Almaraz, Whittaker et al. [17])

The full-scale shake table tests indicate that the combined actions of horizontal and vertical ground motions result in more significant damages. Also, the connections of main support beams are so flexible that ceilings close to the connection experience severe damage. 3. CONCLUSIONS This paper summarizes the basic principles involved in formulating and conducting a seismic risk analysis. It is shown that seismic risk analysis is of vital importance to engineers and planners in formulating rational procedures for evaluating vulnerability of existing structures and for designing/constructing new structures under the expected or design seismic load. Both areas are particularly important to regions such as Hong Kong where incorporation of a seismic code is being considered. The discussion presented herein includes recent thinking in the U.S. regarding seismic risks, structural performance levels, and performance-based structural design. Examples are presented to demonstrate the working details of performing a seismic risk analysis and what the results imply in terms of structural reliability and safety.

Experiment Results

Fitted Curves

0.0 0.5 1.0 1.5 2.0 2.5Spectral Acceleration (g)

1.0

0.8

0.6

0.4

0.2

0.0

P[D

d |

S

]>

ii

Minor

Major

GridFailure

Moderate Experiment Results

Fitted Curves

0.0 1.0 2.0 3.0 4.0 5.0

1.0

0.8

0.6

0.4

0.2

0.0

Spectral Acceleration (g)

P[D

d

| S

]>

ii

Moderate

Minor

GridFailure

Major


102

REFERENCES 1. McGuire, R.K., “Seismic Hazard and Risk Analysis”, Monograph No. 10, Earthquake

Engineering Research Institute: Oakland, CA, 2004. 2. Soong, T.T., “Fundamentals of Probability and Statistics for Engineers”, Wiley:

Chichester, U.K. and New York, USA, 2004. 3. SEAOC, “Vision 2000: Performance Based Seismic Engineering of Buildings”,

Structural Engineers Association of California: Sacramento, CA, 1995. 4. Krawinkler, H. and Miranda, E., "Performance-Based Earthquake Engineering”,

Earthquake Engineering (Y. Bozorgnia and V. V. Bertero eds.), CRC Press: Boca Raton, London, New York, and Washington, D.C., 2004.

5. ASCE, “Seismic Rehabilitation of Existing Buildings (41-06)”, American Society of Civil Engineers: Reston, VA, 2007.

6. FEMA, “NEHRP Guidelines for the Seismic Rehabilitation of Buildings (FEMA 273)”, U.S. Federal Emergency Management Agency: Washington, D.C., 1996.

7. FEMA, “NEHRP Commentary on the Guidelines for the Seismic Rehabilitation of Buildings (FEMA 274)”, U.S. Federal Emergency Management Agency: Washington, D.C., 1996.

8. FEMA, “Prestandard and Commentary for the Seismic Rehabilitation of Buildings (FEMA 356)”, U.S. Federal Emergency Management Agency: Washington, D.C., 2000.

9. Moehle, J.P. "A Framework for Performance-Based Earthquake Engineering," ATC-15-9, Workshop on the Improvement of Building Structural Design and Construction Practices, Maui, HI, 2003.

10. BSSC, “NEHRP Recommended Seismic Provisions for New Buildings and Other Structures (FEMA P-750)”, Building Seismic Safety Council: Washington, D.C., 2009.

11. Luco, L., Ellingwood, B.R., et al., "Rick-Targeted versus Current Seismic Design Maps for the Conterminous United States", SEAOC 2007 Convention, Lake Tahoe, CA., 2007.

12. Shinozuka, M., Feng, M.Q., et al., "Statistical Analysis of Fragility Curves." Journal of Engineering Mechanics-ASCE, Vol. 126, No. 12, pp. 1224-1231, 2000.

13. Singhal, A. and Kiremidjian, A.S., "Method for Probabilistic Evaluation of Seismic Structural Damage", Journal of Structural Engineering-ASCE, Vol. 122, No. 12, pp. 1459-1467, 1996..

14. SEAOC, “Recommended Lateral Force Requirements and Commentary”, Structural Engineers Association of California: Sacramento, CA, 1990.

15. Park, Y.-J. and Ang, A.H.-S., "Mechanistic Seismic Damage Model for Reinforced Concrete”," Journal of Structural Engineering-ASCE, Vol. 111, No. 4, pp. 722-739, 1985.

16. Park, Y.-J. and Ang, A.H.-S., "Seismic Damage Analysis of Reinforced Concrete Buildings", Journal of Structural Engineering-ASCE, Vol. 111, No. 4, pp. 740-757, 1985.

17. Badillo-Almaraz, H., Whittaker, A.S., et al., “Seismic Fragility of Suspended Ceiling Systems (MCEER-06-0001)”, University at Buffalo: Buffalo, NY, 2006.

18. ICBO, “ICBO-AC 156 Acceptance Criteria for the Seismic Qualification of Nonstructural Components”, International Conference of Building Officials: Whittier, CA, 2000.


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104

SEISMIC MITIGATION OF MID-RISE BUILDINGS BY A NEW EARTHQUAKE RESISTANT SYSTEM USING

BASE ISOLATION AND STORY ISOLATORS

Z.D. Yang 1 and Eddie S.S. Lam 2 1PhD student, Department of Civil & Structural Engineering

The Hong Kong Polytechnic University, Hong Kong 2Associate Professor, Department of Civil & Structural Engineering

The Hong Kong Polytechnic University, Hong Kong

[email protected] ABSTRACT In this study, a new earthquake resistant system is proposed and is demonstrated through a frame-core structure. It is consisted of base isolators and story isolators. The former “isolate” the frame from the foundation and the latter “separate” the frame from the center core. Equations of motion are formulated to study response of the building to strong earthquake motion. Parametric studies are performed to assess the impact of varying both stiffness and damping ratio of story isolators to the building. In the present case, optimum stiffness and damping ratio of story isolator are 1×105 N/m and 0.03 respectively. As compared with the base isolated building, the new system shows substantial reduction on structural response to earthquake motion. Keywords: Seismic Mitigation, Base Isolator, Story Isolator, Numerical Simulations


105

1. INTRODUCTION Conventional earthquake resistant systems are based on strengthening key structural members to resist the horizontal force due to earthquake and to avoid collapse (e.g. capacity design). In the last few decades, other structural systems have been introduced to absorb the earthquake energy and/or to counteract the damaging earthquake motion to reduce the structural response and possible damage. These systems include energy dissipation system, seismic isolation system, etc.

Figure 1. Dampers installed at Beijie Primary School

Figure 2. Lead Rubber Bearings installed at the Foundation Level

Energy dissipation system “add damping” to a structure (Symans et al. [1]) and is designed to limit or eliminate possible damage to the gravity-load resisting system (Whittaker and Constantinou [2]). Figure 1 shows an example of retrofit at Beijie Primary School, Dujiangyan town, after Wenchuan earthquake. Here, earthquake-induced energy is dissipated through dampers. Another example is the installation of tuned mass damper at upper stories of a high-rise building. It is specially designed to reduce the amplitude of vibration (Villaverde [3]). Seismic isolation system includes base isolation system, mid-story isolation system, smart frame story isolation system, etc. Objective of seismic isolation system is to “isolate” the structure above the seismic isolation system from ground motion, thus reducing the inertia force acting on the structure above. Seismic isolation system can be designed to provide (a) large horizontal displacement with ability to restore to initial position; (b) energy dissipation; and (c) sufficient rigidity to counteract other types of loading, e.g. wind load. Base isolation system is perhaps the most commonly used seismic isolation system in low-rise buildings. By incorporating base isolators between foundation and superstructure (see Figure 2), the latter is isolated from earthquake motion (Kelly [4]). Figure 3 shows two commonly used isolators, namely lead rubber bearings (Naeim and Kelly [5]) and friction pendulum bearing (Kravchuk et al. [6]).


106

Figure 3. Cross-section of a Lead Rubber Bearing [5]

Figure 4. Cross-section of a Friction Pendulum Bearing [6]

Mid-story isolation system has isolators at the mid-story. It mitigates the earthquake effect by separating the upper structure from the lower structure (Kobayashi et al. [7]) and has application on seismic retrofit. This technology has also been used in buildings over or beside a railway track to alleviate the vibration so induced by the railway track (Takei et al. [8]). Mar et al. [9] proposed a smart frame story isolation system. As shown in Figure 5, the system is consisted of gravity frames and lateral load resisting reaction frames. The two are connected via an assembly of springs and passive dampers. By tuning the characteristics of the system (i.e. stiffness and damping), fundamental periods of the structure can be effectively controlled. The above-mentioned energy dissipation devices can be invasive and may adversely affect the useable floor area. Although base isolators have many successful applications in low-rise buildings, they are less effective for long period structures and offer limited resistance to overturning that one would expect to occur in mid- to high-rise buildings. Considering merits and limitations of the above, a new earthquake resistant system with performance compatible to the above-mentioned systems is developed.

Figure .5 Smart Frame Story Isolation System (Mar et al. [9])

Reaction frame Low-friction sliders

Gravity frame

Dampers

Gravity frame

Slide

Base steel plate

Top steel plate Top steel plate connected to column

Base steel plate connected to foundation

Lead

core Natural rubber Steel shims


107

2. DESIGN PROVISIONS ON SEISMIC ISOLATION SYSTEM In the USA, provisions on seismic isolation have been included in the building codes since 1991 [10]. In 2001, design of seismic isolation and energy dissipation system has been included in the Chinese seismic code [11]. In 2003, the Italian seismic code has allowed the used of seismic isolators (Higashino et al. [12]). Japan has also introduced guideline for design of seismically isolated buildings in 2005 summarizing basic concepts for performing time-history analysis on seismically isolated buildings [13]. In what follows, the Chinese seismic code is briefly discussed to illustrate the design principle. Some of the main provisions in accordance with the Chinese seismic code GB50011-2001 are as follows:- 1. Seismic isolation system is deemed to be suitable if the building is not located on soil

type IV and the foundation is sufficiently rigid. Here, soil type IV presents a very soft soil site that may produce a predominance of long period ground motion.

2. Horizontal seismic reduction coefficient (defined as maximum shear force of base

isolated structure to the corresponding fixed base structure) shall not be less than 0.25, i.e. the superstructure must sustain not less than 25% of the maximum horizontal force of the corresponding fixed-base structure.

3. Tensile stress is not allowed to occur in any isolator. Characteristics of a base isolated building under earthquake motion are related to response of the building and displacement of the base isolators. These can be estimated by carrying out time-history analysis using commercial analysis software, e.g. ETABS, SAP2000, etc. Figure 6 outline the design process (using time-history analysis or spectral analysis).

Figure 6. Design of a Base Isolated Building

If larger than allowable

Preliminary design of superstructure

Select/design base isolators

If larger than allowable

Check maximum horizontal displacement

Check story drift and member forces

Setup analysis model and estimate response of base isolated building


108

3. BASE ISOLATED BUILDING AND THE NEW EARTHQUAKE RESISTANT BUILDING

3.1 Earthquake Record The buildings are assumed to be located in an area with seismic intensity at the VIII degree and type III site category (characteristic period at 0.45 s). Figure 7 shows the earthquake record used in this study. It is the I-ELC180 component of Imperial Valley 1940 earthquake recorded at El-Centro. Peak ground acceleration is 4 m2/s and represents a seldom occurred earthquake.

Figure 7. El-Centro Earthquake Record 3.2 Base Isolated Building Figure 8 shows a 20-storey, 60 m high base isolated building. Structural system comprises a reinforced concrete center core and frames at 6 m grids. Floor system is based on traditional beam-slab construction with 200 mm thick two-way slabs. Grade C30 concrete is assumed and the Modulus of Elasticity is 30.0 kN/mm2. It has a total mass of 24,400 ton and total weight of 239,000 kN. Base isolators (lead rubber bearings of 800 mm diameter) are installed to support each and every column and the center core. Properties of the base isolators are shown in Table 1.

Table 1. Properties of Base Isolators Vertical stiffness 5389 KN/mm

Horizontal stiffness after yield 1.88 KN/mm Equivalent horizontal stiffness 2.66 KN/mm

Damping ratio 18.1%

Acc

eler

atio

n (m

/s2 )

time(s)


109

Figure 8. Base Isolated Building

○1 ○2 ○3 ○4 ○5 ○6

3m

3m

3m

3m

3m

3m

3m

3m

3m

3m

3m

3m

3m

3m

3m

3m

3m

3m

3m

3m

20×

3=60

m

Colum

Shear wall

Floor

Isolators

Elevation

○1 ○2 ○3 ○4 ○5 ○6

6m

6m

6m

6m

6m

○F

○E

○D

○C

○B

○A

6m 6m 6 m 6m 6m

Typical floor plan

Analysis model

mbase

……

m1

C2 K2

C1 K1 ξequivalent

Kbase

m20

C20 K20

m2

C19 K19

m19


110

3.3 New Earthquake Resistant System

Analysis model

Figure 9. Arrangement of the New Earthquake Resistant System

Figure 9 shows elevation of the building with the new earthquake resistant system. Typical floor plan of the building is the same as that considered in the base isolated building except the following. Base isolators are installed at the foundation at locations with concentrated vertical forces to support the columns. Characteristics of the base isolators are given in Table 1. Story isolators are installed between the frames and center core. The load transferring mechanism is as follows: 1. When subjected to gravity load, center core and frames will both contribute to the load

transferring mechanism. 2. Under wind loading, center core will provide the necessary lateral stiffness to limit the

lateral deflection and to prevent possible wind induced oscillation.

Elevation

○1 ○2 ○3 ○4 ○5 ○6

3m3m 3m 3m 3m3m

3m 3m 3m 3m 3m

3m

3m

3m

3m 3m 3m 3m 3m 3m

20×

3=60

m

Story isolator connected to core wall

○4

Core-tube

Story isolator

Story isolator

Corbel

Core-wall

Floor

Beam


111

3. Under earthquake motion, frames will be protected by base isolators and center core. The building is subjected to a wind force of about 4,000 kN. To satisfy the deflection limit of the building at H/500 or 0.12 m, total base isolator stiffness is 2.442×107 N/m (after yield). To limit the displacement at the ground floor, damping ratio of base isolators is chosen to be at 0.15. 3.4 Equations of Motion Equations of motion of a base isolated building (Figure 8) are developed based on a two-dimensional formulation [14] in the form of:-

}}{}{{}}{{}}{{}}{{ groundXIMXKXCXM (1)

{M}, {C} and {K} are the respective and mass, stiffness, and damping matrices of the system. {X}, {Ẋ} and {Ẍ} are the respective system’s displacement vector, velocity vector and acceleration vector relative to the ground. {Ẍground} is the ground acceleration vector. {I} is a unit vector. In the new earthquake resistant system (Figure 9), floor isolators are modeled by linear springs (i.e. force in proportional to relative displacement) and linear dashpots (i.e. damping in proportional to relative velocity). Equations of motion, i.e. equation (1), are now decomposed into two components to incorporate characteristics of story isolators in the form of:-

}}{}{}{}0{

}0{}{{}}{

}{}{}{

}{}{}{{

}}{}{}{}{

}{}{}{{}}{

}{}0{

}0{}{{

groundfr

core

sifsi

sisicore

sifrsi

sisicore

fr

core

XIM

MX

KKK

KKK

XCCC

CCCX

M

M

(2)

Contributions by center core, frame and story isolators are represents by the subscripts core, fr and si respectively. In respect of center core, Rayleigh damping is assumed with the first and second modal damping ratios at 0.02.

}{}{}{ corecorecore KMC (3)

Detail of the matrices and vectors are given in the Appendix for easy reference.

4. NUMERICAL STUDIES 4.1 Method of Analysis

Response (e.g. acceleration, velocity and displacement) at any time t is obtained by solving the equations of motion numerically using the Newmark method. It is essentially a step-by-step integration method assuming linear variation of acceleration over time interval t. In consideration of the high initial stiffness of base isolation system, very small time interval is


112

used at 200 steps per increment of ground acceleration (at 100 readings per second). Hence, t = 0.01/200 = 0.00005 s. In the analysis, center core and frames are assumed to behave linearly elastic throughout the loading history. Masses are assumed to be lumped at each floor level. 4.2 Base Isolated Building Table 2 compares the 1st fundamental periods and maximum accelerations of the based isolated building to the corresponding fixed based building. Based isolated building shows improvement on seismic responses. Maximum displacement at ground floor is 0.1589 m which is within the allowable limit of 0.55 x diameter of base isolator.

Table 2. Comparison between Fixed Based Building and Based Isolated Building

Description Fixed based building Based isolated

building = 0.02 = 0.05 1st fundamental period (s) 1.682 1.682 2.758 Maximum acceleration (m/s2) 12.37 10.08 Max. 3.5

Figures 10 and 11 are the respective variation of maximum acceleration and maximum overturning moment against total base isolator stiffness for different base isolator damping ratios (base). Note that stiffness of commercially available base isolators ranges from 0.5×106

N/m to 5×106 N/m. The following are observed:- 1. Maximum acceleration and maximum overturning moment decrease with decreasing

total base isolation stiffness. This is partly due to an increase in the fundamental periods of the building leading to reduction in the acceleration.

2. When total base isolator stiffness is less than 2×108 N/m, increasing the damping ratio

increases the maximum acceleration. 3. When total base isolator stiffness is less than 1×107 N/m, decrease in total base isolation

stiffness has less significant effect on the maximum acceleration.

Figure 10. Plots of Maximum Acceleration Against Total Base Isolator Stiffness

Max

imum

acc

eler

atio

n (m

/s2 )

Total base isolator stiffness (N/m)

4

3

2

1

0 1×10

8.5 1×10

8 1×10

7.5 1×10

7

05.0base

1.0base

15.0base

181.0base

2.0base

25.0base


113

Figure 12 shows variation of maximum ground floor displacement against total base isolator stiffness for different base isolator damping ratios (base). The following are observed:- 1. When total base isolator stiffness is between 1.2×107 N/m and 1.0×108 N/m, increasing

the total base isolator stiffness generally reduces the maximum displacement. 2. Further increase in total base isolator stiffness may increase the maximum displacement. 3. Increasing base isolator damping ratio may reduce the maximum displacement. It is important to ensure sufficient total base isolator stiffness to preserve lateral stiffness and fundamental period of the base isolated building. The following have to be taken into account:-

Figure 11. Plots of Maximum Overturning Moment Against Total Base Isolator Stiffness

Total base isolator stiffness (N/m)

05.0base

1.0base

15.0base

181.0base

2.0base

25.0base

Maxim

um overturning moment (M

N∙m

)

1×108.5 1×10

8 1×10

7.5 1×10

7

Figure 12. Variation of Maximum Ground Floor Displacements Against Total Base Isolator Stiffness

Total base isolator stiffness (N/m) 1×10

8.5 1×10

8 1×10

7.51×10

7

0.1

0.15

0.2

0.25

0.3

0.35 05.0base

1.0base

15.0base

181.0base

2.0base

25.0base

Maxim

um ground floor displacemen

t (m

)


114

1. Deflection limit due to wind load has to be satisfied. 2. In the cases of small total base isolator stiffness, the building has low lateral stiffness

and could be vulnerable to wind induced vibrations. 3. Base isolators have to provide sufficient restoring force. Otherwise, the structure may

not be able to return to the original position after an earthquake. In the present case, the optimal total base isolator stiffness does not provide sufficient stiffness to satisfy the deflection limit (i.e. less than H/500, where H is the height of building). To circumvent such problem, a new structural system is proposed using base isolators and story isolators to reduce the response caused by earthquake; to allow an increase in base isolator stiffness to resist the wind load; and to provide sufficient restoring force. 4.3 The New Earthquake Resistant System With the wind load at about 4,000 kN, total base isolator stiffness is assumed to be 2.442×107 N/m (after yield) with equivalent damping ratio at 0.15. To optimize characteristics of story isolators, parametric studies are conducted. Figure 13 shows variation of maximum acceleration against stiffness of story isolator at different damping ratios. The following are noted:- 1. Interaction between story isolators and center core commences when stiffness of story

isolators approaches the threshold values (e.g. 2.75×105 N/m in the case of damping ratio is 0.00).

2. Increase in damping ratio of story isolators is effective only when stiffness of story

isolators is above the threshold values.

Figure 13. Maximum Acceleration Versus Characteristics of Story Isolator

Figures 14 and 15 show response of the new earthquake resistant system in respect of maximum overturning moment and maximum base shear respectively. In general, increase in stiffness of story isolator increases maximum overturning moment and maximum base shear.

1×106 1×105 1×104 1×103

Maxim

um acceleration (m/s

2 )

Stiffness of story isolator (N/m)

05.0isolator

story

1.0isolator

story

15.0isolator

story

181.0isolator

story

2.0isolator

story

25.0isolator

story


115

Figure 14. Maximum Overturning Moment Versus Characteristics of Story Isolator

Figure 15. Maximum Base Shear Versus Characteristics of Story Isolator

Figure 16 shows variation of maximum floor displacement against stiffness of story isolator. The following are observed:- 1. With increasing stiffness of story isolator, maximum floor displacement increases. 2. Stiffness of story isolator has insignificant effect to the maximum floor displacement if

it is less than 3.25×105 N/m. 3. Damping ratio of story isolators has insignificant effect to the maximum floor

displacement, especially when stiffness of story isolator is less than 2 ×105 N/m.

05.0

isolator

story

1.0isolator

story

15.0isolator

story

181.0isolator

story

2.0isolator

story

25.0isolator

story

1×106 1×105 1×104 1×103 Stiffness of story isolator (N/m)

Maxim

um overturning moment (M

N∙m

)

05.0

isolator

story

1.0isolator

story

15.0isolator

story

181.0isolator

story

2.0isolator

story

25.0isolator

story

1×106 1×105 1×104 1×103 Stiffness of story isolator (N/m)

Maxim

um base shear (MN)


116

Figure 16. Maximum Floor Displacements Versus Characteristics of Story Isolator All in all, if stiffness of story isolator is lesser than a threshold value, story isolator has limited effect to the building. In order to provide sufficient lateral stiffness to the “base isolated” frame and without significantly affecting overall performance of the building, stiffness and damping ratio of story isolator are chosen to be at 1×105 N/m and 0.03 respectively. 4.4 Comparison between the Two Buildings Table 3 compares responses of the based isolated building with that obtained from the earthquake resistant system. Maximum acceleration, maximum overturning moment, maximum base shear and maximum ground floor displacement are reduced by about 51%, 69%, 67% and 18% respectively. As compared with the base isolated building, the new structural system shows substantial reduction on structural response to earthquake motion.

Table 3. Base Isolated Building Versus the New Earthquake Resistant System

Maximum values (a) Base isolated

building (b) New system (b)/(a)

Acceleration (m/s2) 1.756 0.858 48.87% Overturning moment (MNm) 9.51×105 2.93×105 30.81%

Base shear (kN) 2,680 887 33.08% Ground floor displacement (m) 0.1589 0.1303 82.02%

Figures 17 and 18 show the acceleration against time at ground floor and at 20th floor respectively. It is worth notice that the incorporation of story isolators have led to reduction on acceleration as well as altering the dynamic characteristics of the building.

1×106 1×105 1×104 1×103

Stiffness of story isolator (N/m)

050.0isolator

story

100.0isolator

story

150.0isolator

story

181.0isolator

story

200.0isolator

story

250.0isolator

story

Max

imum

flo

or d

ispl

acem

ent (

m)


117

5. CONCLUSIONS In this study, effects of total base isolator stiffness and its damping ratio on the response of a based isolated building to earthquake motion is studied. Dynamic response of the building is reduced with reducing total base isolator stiffness and its damping ratio. By optimizing total base isolator stiffness, the building may have difficulty to effectively resist the anticipated wind force. To circumvent the above, a new earthquake resistant system is proposed. Equations of motion are formulated to study responses of the new system to strong earthquake motion. Parametric studies are performed to assess the impact of varying both stiffness and damping ratio of story isolator to the building. In the present case, optimum stiffness and optimal damping ratio of story isolator are 1×105 N/m and 0.03 respectively. As compared with the base isolated building, the new earthquake resistant system shows substantial reduction on structural response to earthquake motion. ACKNOWLEDGEMENT The authors are grateful to the financial support from The Hong Kong Polytechnic University.

0 2 4 6 8 10 12 14 16 18 20-2

-1.5

-1

-0.5

0

0.5

1

1.5

Figure 17. Ground Floor

New system

Base isolated building

Time (s)

Acc

eler

atio

n (m

/s2 )

0 2 4 6 8 10 12 14 16 18 20-2

-1.5

-1

-0.5

0

0.5

1

1.5

Time (s)

Acc

eler

atio

n (m

/s2 )

Base isolated building

New system

Figure 18. 20th Floor


118

Appendix (A) Based isolated building:-

20

2

1

base

0000

0

000

000

000m

}{

m

m

m

M

(4)

Here, mbase, m1, … m20 are the masses of the respective floors.

20

322

2211

11base

0000

0

00

0

00K

}{

K

KKK

KKKK

KK

K

(5)

Kbase is the total base isolation stiffness. K1, K2 … K20 are stiffness of the respective floor and are related to the lateral stiffness of vertical elements in the form of [15]:

columnshearwallkkKKK 322

2021 (6)

Kshearwall is lateral stiffness of shear walls and can be estimated by the following equation [16]:

)

31(

3

2

3

HGA

EIH

EIk

wall

wall

wallshearwall

(7)

Where, EIwall, G, Awall, H and are the respective rigidity of shear wall; shear modulus of elasticity; cross-sectional area of shear wall; story height and Poisson’s ratio. Kcolumn is lateral stiffness of a column and can be estimated by the D-value method [16]. Damping matrix is defined by assuming stiffness-proportional damping [17] and is expressed in the following form:

20

322

2211

111

1

1

1

0000

0

00

0

00

2}{

K

KKK

KKKK

KKK

C

basebase

base

(8)


119

Where, 1 is damping ratio of the building with fixed base, 1 is 1st modal frequency of the building with fixed base, base is effective damping ratio of the building and base is 1st modal frequency of the frame. (B) The new earthquake resistant system:- Mass matrix and stiffness matrices of the new earthquake resistant system are similar to that of equations (4) and (5) respectively. For the center core, Rayleigh damping is adopted and the coefficients and are defined as follows:-

21

212

, 21

2

(9)

Where, 1 and 2 are the 1st and 2nd modal frequencies of the center core respectively. Damping matrix of frames is similar to that of equation (8). REFERENCES 1. Symans, M.D., Charney, F.A., Whittaker, A.S., Constantinou, M.C., Kircher, C.A.,

Johnson, M.W. and McNamara, R.J., “Energy Dissipation Systems for Seismic Applications: Current Practice and Recent Developments”, Journal of Structural Engineering, 2008, Vol. 134, No. 1, January 1.

2. Whittaker, A. and Constantinou, M., “Seismic Energy Dissipation Systems for Buildings”, Earthquake Engineering From Engineering Seismology to Performance-Based Engineering, 2006, pp. 716-744.

3. Villaverde, R., “Roof Isolation System to Reduce the Seismic Response of Buildings: A Preliminary Assessment”, Earthquake Spectra, 1998, Vol. 14, No. 3, pp. 521-532.

4. Kelly, J.M., “Aseismic Base Isolation: Review and Bibliography”, Soil Dynamics and Earthquake Engineering, 1986, Vol. 5, Issue 4, pp. 202-216.

5. Naeim, F. and Kelly, J.M., “Design of Seismic Isolated Structures”, John Wiley & Sons, New York, 1999.

6. Kravchuk, N., Colquhoun, R. and Porbaha, A., “Development of a Friction Pendulum Bearing Base Isolation System for Earthquake Engineering education”, Proceedings of the 2008 American Society for Engineering Education Pacific Southwest Annual Conference.

7. Kobayashi, M., Wa, I.Y. and Koh, T., “The Prediction Method of Earthquake Responses on Mid-Story Isolated System Considering Modal Coupling Effect”, J. Struct. Constr. Eng., AIJ, No. 572, Oct. 2003, pp. 73-80.

8. Takei, Y., Yamada, S., Izumi, Y. and Fujii, K., “Application of Seismic and Vibration Isolation Structure System to Design of Over-Track Buildings”, Quarterly Report of Railway Technical Research Institute, Feb. 2007, Vol. 48, No. 1, pp. 51-57.

9. Mar, D. and Tipping, S., "Story Isolation: A New High-Performance Seismic Technology", 9th U.S.-Japan Workshop on the Improvement of Structural Design and Construction Practices, Victoria, British Columbia, Canada, 2000.

10. AASHTO, “Guide Specifications for Seismic Isolation Design”, American Association of State Highway and Transportation Officials, Washington, D.C., 1999.


120

11. Ministry of Construction, PRC, “Code for Seismic Design of Buildings”, GB50011–2001, Beijing: Chinese Architecture & Building Press, 2001.

12. Higashino, M. and Okamoto, S., “Response Control and Seismic Isolation of Buildings”, Taylor & Francis, London and New York, 2006.

13. MLIT, BRI, BCJ, JAGM and JSSI, “The Notification and Commentary on the Structural Calculation Procedure for Building with Seismic Isolation-2000”, 2000.

14. Clough, R.W. and Penzien, J., “Dynamics of Structures”, 2nd edition, Singapore, McGraw-Hill, 1993.

15. Cheng, W.R., Yan, D.H., Kang, G.Y. and Jiang, J.J., “Concrete Structure: Structural Design”, Beijing: Chinese Architecture & Building Press, 2003.

16. Smith, S.B. and Coull, A., “Tall Building Structures: Analysis and Design”, New York: John Wiley & Sons, 1991.

17. Ye, L.P., “Introduction to Seismic Isolation”, Beijing: Science Press, 1998.


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122

RESPONCE SPECTRUM AND TIME HISTORY ANALYSIS OF BUILDING STRUCTURES BY SOFTWARE NIDA

Y.P. Liu and S.L. Chan Department of Civil and Structural Engineering, The Hong Kong Polytechnic University,

Hung Hom, Kowloon, Hong Kong, China

[email protected] ABSTRACT In last two decades many strong earthquakes occurred in the world which led to severe damage of numerous buildings and loss of thousands of lives. Also, earthquakes are responsible for hundreds of millions of dollars in property loss either in direct or indirect way annually. Unfortunately, the hazards mentioned above were almost entirely associated with man-made structures. Although the prediction techniques for occurrence of earthquakes are not fully reliable till now, the contemporary seismic design concepts and structural analysis methods are gradually mature. It is the responsibilities of structural engineers to utilize these techniques to mitigate earthquake hazards. Response spectrum and time history analysis as two widely accepted methods in seismic design codes can be applied to design new buildings or seismic evaluation of existing buildings. In this paper, the theoretical background of the two methods is briefly described. Further, two examples will be given by software NIDA [1] to illustrate the application of this two methods. It should be noted that time history (nonlinear dynamic) analysis is an advanced method compulsively used for high-rise or important buildings and long-span bridges. This is noted that simulation-based nonlinear analysis software has an advantage of consistency in designing conventional structures under static and dynamic seismic cases. Keywords: Response Spectrum Analysis, Time History Analysis, Seismic Engineering, Dynamics, NIDA


123

1. INTRODUCTION In last two decades many strong earthquakes occurred, for example, 1994 USA Northridge earthquake, 1995 Japan Kobe earthquake, 1999 Taiwan Chi-Chi earthquake, 2008 China Wenchuan earthquake, 2010 Haiti earthquake, 2010 Chile earthquake and 2010 China Yushu earthquake. The magnitude of 2010 Chile earthquake is 8.8 and the corresponding released energy is 80 times of 2010 Haiti earthquake and 16 times of 2008 China Wenchuan earthquake. Numerous buildings collapsed and many people died from these earthquakes. The property loss included billions of dollars. It is unfortunate to find that the earthquake hazards were almost entirely associated with man-made structures. This undoubtedly pushes researchers and structural engineers to develop and utilize new seismic design concepts, methods and technologies to minimize seismic hazards. Generally speaking, the reasons for structural damage suffered from an earthquake include: (1) failure of supporting ground which may be due to insufficient foundation or soil liquefaction; (2) poor structural arrangement such as in-plane or out-of-plane discontinuity or irregularity, “weak” or “soft” story, severe torsional strength irregularity and so on; (3) inadequacy of structural elements or components, for example, buckling of columns and bracings, plastic hinges formed at the ends of beams and columns, “top down” failure of floor slabs due to lack of steel ties, failure of connections, etc.; (4) damage of nonstructural elements, for example, fall of surface finishes, fracture of curtain wall, cracking of infilled wall and (5) external influence, for example, landslide, rockfall, insufficient space between adjacent buildings leading to pounding between buildings. Development of modern seismic design codes is extended to consider loss of structural functionality and repair but not simply on safety. The traditional seismic design is significantly upgraded to performance-based seismic design (PBSD) which is believed to be a general design philosophy in future. The design criteria will be expressed in terms of performance objectives (such as operational, immediate occupancy, life safety, collapse prevention) associated with seismic hazard levels (such as frequent, occasional, rear, very rear) under the framework of performance-based design. A performance objective is essentially associated with an acceptable risk meeting the owner’s expectations. It should be pointed out that the performance objectives are varied in different seismic codes. This may be due to the different development levels either in research, economy or both. Eurocode 8 [2] explicitly specifies two performance objectives (i.e. no-(local-)collapse and damage limitation) while GB50011 [3] states three performance levels (no damage, repairable, collapse prevention). The USA document FEMA356 [4] gives more performance levels and provides guidelines to implement performance based design. It is a future trend that the seismic design should permit multiple performance and hazard levels according to owner’s expectations. The performance levels are related to displacement and drift in codes. That is, the seismic codes are transforming to displacement-based design but not conventional force-based design which focused mainly on stress. There are four well-known analysis methods specified in seismic codes for seismic performance evaluation, i.e. the linear static analysis (also named equivalent static analysis or base shear method in GB50011 [3]), modal response spectrum analysis, nonlinear static (pushover) analysis and nonlinear dynamic (time history) analysis. The first method is very simple and convenient for engineers who are familiar with static equilibrium analysis under the actions rather than earthquake. However, this method is limited to regular and low-rise


124

structures in which the high-mode effects can be ignored. Similarly, the nonlinear static analysis is also limited to some simple cases like linear static method though this method can provide valuable information for performance evaluation. Thus, this paper will mainly focus on modal response spectrum analysis (MRSA) and time history analysis (THA) because the former has the statistical element to consider uncertainty of earthquake while the latter is deemed to be an “exact” method which can provide response with high accuracy. Interestingly, Eurocode 8 [2] does not explicitly mentioned the linear static analysis and consider the response spectrum analysis as the reference method while the US codes such as UBC97 [5] and IBC2006 [6] still take the linear static method as the reference one. In GB50011 [3], a two-stage design procedure is specified for seismic design. The first step is based on the elastic analysis under the hazard level of frequent earthquake with 63.2% exceedance probability in 50 years in which both linear static analysis and MRSA can be used. The second step is allowed the inelastic analysis corresponding to the hazard level of rear earthquake with 2% exceedance probability in 2000 years and the time history analysis is preferred unless the conditions for pushover analysis can be met. In this paper, both the theoretical background and considerations of response spectrum and time history analysis will be summarised. Further, two examples will be demonstrated by software NIDA [1] to illustrate the application of these two methods. It should be noted that as an advanced method the time history analysis is compulsory for high-rise and important buildings and long-span bridges. Nonlinear-based software NIDA [1] has an inherent advantage for both conventional second-order nonlinear design and nonlinear dynamic seismic design. The beam-column element [7] used in NIDA [1] is based on the stability function theory which not only provides exact solutions but also leads to quick convergence in nonlinear incremental-iterative procedure with the use of one element per member allowing for initial member imperfection. Specially, the semi-rigid connections can be taken into account by NIDA [1] and as a result the structural behaviour can be precisely traced. The study of joint behaviour is particularly important as many joint failures observed under earthquake. However, this paper does not detail semi-rigid connection for simplicity. The plastic hinge model for considering inelastic behaviour of structural members as well as the detailed procedure for pushover analysis by NIDA [1] can be referred to Liu [8]. 2. MODAL RESPONSE SPECTRUM ANALYSIS 2.1 Response Spectra of SDOF Systems Although a real structure may be very complicated and possess many degrees of freedom, the design spectra are essentially obtained from a single-degree-of-freedom (SDOF) system as shown in Figure 1. For this typical SDOF system, the equation of motion can be formulated by expressing the equilibrium of all forces acting on the system as, ( ) ( ) ( ) ( ) 0I D SF t F t F t F t (1)

in which, ( )F t is time-varying force, ( )IF t is inertial force, ( )DF t is damping force, ( )SF t is

elastic restoring force. The governing equation of motion can be rewritten as


125

( ) ( ) ( ) ( )gmu t cu t ku t mu t (2)

where m is mass of the SDOF system produced inertial force, c is damping constant presented energy dissipation mechanism, k is linear stiffness of the spring provided elastic resistance.

Figure 1. SDOF System under Horizontal Force By defining the natural frequency and damping ratio as

k

m (3)

2

c

km (4)

The governing equation of a SDOF system subjected to ground acceleration ( )gu t becomes

2( ) 2 ( ) ( ) ( )gu t u t u t u t (5)

Eq. (5) clearly shows that for a given ( )gu t the displacement response ( )u t of the system

depends only on its natural frequency (or period T ) and damping ratio . That is, the same response ( )u t will be produced for any two systems having the same values T and under a specified earthquake. Thus, the response spectrum determined from a SDOF system can be applied to any structures though their stiffness and mass may be very different. The evaluation of the dynamic response such as displacement, velocity, acceleration, internal force and stress at every time instant during an earthquake is usually conducted by numerical integration (e.g. Newmark’s method [9], central difference method). For engineering application purpose, only the maximum absolute values of displacement, velocity and acceleration responses experienced by a structure are of interest as below:

max

max

max

( ) ( , )

( ) ( , )

( ) ( , )

d d

v v

a a

S u t S T

S u t S T

S u t S T

(6,7,8)

in which dS is spectral displacement, vS is spectral velocity, aS is spectral acceleration.

DF cu

SF ku

IF mu ( )F t( )F t

c

m

SF ku

/ 2k

u

(a (b


126

In engineering practice, the following approximations are generally employed:

2

pv d v

pa d a

S S S

S S S

(9,10)

in which pvS is pseudo-spectral velocity, paS is pseudo-spectral acceleration. The prefix

‘pseudo’ indicates that the values do not correspond to the actual peak spectral velocity and acceleration. The above spectral relationships significantly expedite the construction of earthquake response spectra because only the spectral displacement dS needs to be

determined by numerical integration. A plot of the peak value of a spectral ordinate (i.e. dS , vS or pvS , aS or paS ) against the

natural period T is called the response spectrum for that spectral ordinate. Each of these plots is for SDOF systems having a fixed damping ratio and therefore a family of plots will be produced to cover the range of damping values encountered in real structures. 2.2 Design Spectra The response spectrum mentioned above is obtained from a specified past earthquake record. The shape of the response spectrum is normally very irregular for a given earthquake. However, certain similarities exist among the earthquake ground motions recorded under similar conditions. Thus, the design spectra can be derived from statistical analyses based on the response spectra obtained from earthquakes with common characteristics. The design spectra in seismic codes are usually presented as smooth curves and/or straight lines. Acceleration response spectra are commonly implemented in seismic design codes such as GB50011 [3], Eurocode 8 [2] and UBC97 [5] because they are related directly to the base shear used in the seismic design. For structures with long period, the displacement response spectra become more important for seismic design. It is convenient that the pseudo-spectral acceleration paS is normalized by gravity

acceleration g (GB50011 [3], UBC97 [5]) or design acceleration ga (Eurocode 8 [2]) to a

dimensionless quantity. In GB50011 [3], this dimensionless quantity is called seismic influence coefficient defined as /paS g (11)

2.3 Modal Response Spectrum Analysis Modal response spectrum analysis (MRSA) is used to find the maximum responses rather than the full responses during a likely earthquake. This method is performed using mode superposition. For a multi-degree-of-freedom structure, the governing equation of motion of the structure undergone an earthquake is given as [ ]{ ( )} [ ]{ ( )} [ ]{ ( )} [ ]{ ( )}gM u t C u t K u t M u t (12)


127

where M is mass matrix, C is damping matrix, K is stiffness matrix, and { ( )}gu t is

ground acceleration vector. Making use of the modal decomposition method,

1

{ ( )} [ ]{ } { } ( )n

j jj

u t q q t

(13)

the following modal equation can be obtained 2( ) 2 ( ) ( ) ( )j j j j j j j gq t q t q t u t (14)

in which j is natural frequency, j is damping ratio, and

1

2

1

{ } [ ]{1} { } [ ]{1}

{ } [ ]{ }

n

T T i jij j i

j nTj j j

i jii

mm m

M m m

(15)

in which { } j is the modal shape for jth mode which can be determined by modal analysis,

and j is the earthquake participation factor for jth mode.

The modal response ( )jq t for jth mode can be obtained by the Duhamel integral expression

( )

0( ) ( )sin ( ) ( )j j

t tjj g j j j

j

q t e u t d t

(16)

where

( )

0

1( ) ( )sin ( )j j

t t

j g jj

t e u t d

(17)

Once the modal response ( )jq t is obtained, the displacement and acceleration responses for

ith DOF in physical coordinates can be determined by

1 1

1 1

( ) ( ) ( )

( ) ( ) ( )

n n

i j ji j j jij j

n n

i j ji j j jij j

u t q t t

u t q t t

(18,19)

The inertia force on ith DOF is expressed as ( ) [ ( ) ( )]i i i gF t m u t u t (20)


128

Using the relationship 1

1n

j jij

, we have

1

( ) ( )n

g j ji gj

u t u t

(21)

Substituting Eqs. (19) and (21) into Eq. (20), the inertia force on ith DOF for jth mode can be written as ( ) [ ( ) ( )]ji i j ji j gF t m t u t (22)

For engineering applications, we only need to know the maximum inertia force. ji j j ji iF G (23)

where max| ( ) ( ) |j j gt u t (24)

i iG m g (25)

The displacement response of ith DOF for jth mode can be calculated as

2

1ji j j ji

j

u

(26)

Thus, the other responses such as internal force and stress can be further determined from displacement response. Although there are many seismic design codes in the world, the difference between them when using MRSA mainly lies in the difference of determination of the coefficient j . Eq.

(11) shows the definition of the coefficient j . Figure 2 shows the curve for determination

of j specified in GB50011 [3].

Figure 2. Seismic Influence Coefficient (GB50011)

( )T s

0 0.1 gT 5 gT 6.0

2 max

max0.45

2 max( )gT

T

2 1 max[ 0.2 ( 5 )]gT T


129

2.4 Participating Mass Ratio From above, it can be seen that the response spectrum analysis is based on the modal analysis which is used to find the natural frequencies and the vibration modes of the structures. When performing a modal analysis for a structure with large degrees of freedom, it only need to consider a relatively small number of modes p in the response calculations, such that p << n ( n is the number of all modes). Otherwise, it needs huge computer time to calculate

all vibration modes. Thus, the displacement response in Eq. (18) can be approximated as

)np()t()t(q)t(up

1j

p

1jjijjjiji

(27)

in which ( )iu t

represents the truncated response for p < n .

However, the number p cannot be too small though small value of p means time saving. Otherwise, some important higher-mode effects will be ignored and, consequently the output may be not accurate enough. For this, the effective mass concept is widely used to determine the number of modes p to be input in the modal analysis. The effective mass for jth mode,

ejM , is defined as

2

1

2

1

{ } [ ]{ }

n

i jiiT

ej j j n

i jii

m

M m Im

(28)

The sum of the effective masses for all modes is equal to the total mass M of the structure,

i.e. 1

n

ejj

M M

(29)

This leads to a means for determining the number of truncated modes necessary to accurately represent the structure response. If the structural response is calculated from the truncated modes, the ratio calculated by the sum of the effective masses from these modes over the total mass M should be not less than a predefined percentage. This ratio is called participating mass ratio which is given by

1

/p

M ejj

P M M

(30)

Many seismic design codes specify that at least 90% of the participating mass of the structure must be included in the response spectrum analysis. 2.5 Combination of Modal Responses Noted that the maximum responses for different modes do not occur simultaneously and therefore the maximum structural response cannot be obtained by taking the sum of the maximum modal responses. Two methods have been widely used for modal combination, i.e. the square-root-of-the-sum-of-the-squares (SRSS) method, and the complete-quadratic-combination (CQC) method.


130

(1) SRSS method The SRSS method is usually applied for calculating the maximum response for two-dimensional systems exhibiting well-separated modes. In this method,

2

1

p

EK jj

S S

(31)

in which, EKS is the structural response such as internal force and displacement considering

all selected modes, and jS is the structural response for jth mode.

(2) CQC method The CQC method is usually applied for calculating the maximum response for three-dimensional systems and/or systems with closely spaced modes. In this method,

1 1

p p

EK jk j kj k

S S S

(32)

in which, jk is the correlation coefficient for jth mode and kth mode. When using constant

damping ratio , this coefficient is calculated as

2 3/ 2

2 2 2 2

8 (1 )

(1 ) 4 (1 )jk

r r

r r r

(33)

where /j kr and must be not greater than 1.0.

2.6 Combination of the Effects of the Components of the Seismic Action In real world, an earthquake may come from any directions such that a designed structure should be capable of resisting earthquake shaking from all possible directions. Generally, two horizontal components and one vertical component of seismic action should be considered to act simultaneously on a spatial structure. There are denoted here as EXS and EYS for the

structural responses of the two horizontal components and EZS for the vertical. Since the

peak value of the seismic action effects do not occur simultaneously, a combination rule is required to produce reasonable results. Two approaches have been widely used for directional combination, i.e. the square-root-of-the-sum-of-the-squares (SRSS) method, and the absolute-sum (ABS) method. (1) SRSS method The SRSS method for directional combination assumes the components are independent of each other. In this method,

2 2 2EK EX EY EZS S S S (34)


131

(2) ABS method The ABS method assumes that when the maximum response from one component occurs, the responses from the other two components are taken part of their maximum. In this method, 1 2 3max( , , )EKS S S S (35)

where

1

2

3

( )

( )

( )

EX EY EZ

EY EZ EX

EZ EX EY

S S S S

S S S S

S S S S

(36)

The value in Eq. (36) is usually taken as 0.3 in seismic design codes. 3. TIME HISTORY ANALYSIS Many seismic design codes compulsively require a time history analysis (THA) to evaluate the structural performance. For example, GB50011 [3] specifies that the buildings in extremely irregular configuration, buildings assigned Seismic Design Category A, and tall buildings in the height range shown in Table 1, a time history analysis should be performed.

Table 1. Buildings Required Time History Analysis Seismic Intensity & Site Class Range of Building Height Intensity 7, Intensity 8 with Site Class I & II > 100 m Intensity 8 with Site Class III & IV > 80 m Intensity 9 > 60 m

Unlike MRSA which only gives best estimates of the peak response and generally ignores the degradation of strength and stiffness during an earthquake, THA can provide exact response quantities within the framework of the reliability and representativeness of the nonlinear modeling of the structure. 3.1 Direct Integration for Equation of Motion The incremental form of the equation of motion Eq. (12) can be written as. [ ]{ } [ ]{ } [ ]{ } { }M u C u K u F (37) in which { }F is equal to [ ]{ }gM u . For simplicity, the “(t)” in acceleration ( )u t , velocity

( )u t and displacement ( )u t will be omitted hereafter. Noted that the damping matrix [ ]C is usually employed the Rayleigh damping model which is given as [ ] [ ] [ ]C a M b K (38) in which a is mass proportional coefficient, and b is stiffness proportional coefficient. The two coefficients can be calculated by


132

1 1 2 22 2

1 2

1 2 2 1 1 22 2

1 2

4 ( )

( )

( )

( )

T Ta

T T

TT T Tb

T T

(39)

in which 1T and 2T are the first and second natural periods of the structure respectively, and

1 and 2 are the damping ratios corresponding to 1T and 2T respectively.

MRSA solves the dynamic equilibrium equation by mode superposition approach while THA widely adopts numerical integration method. In NIDA [1], the famous Newmark [9] method is utilized for step-by-step solution of Eq. (37). Newmark [9] truncated the Taylor’s series for displacement { }u and velocity { }u and finally expressed them as, { } { } (1 ) { } { }t t t t t tu u t u t u (40) 2 2{ } { } { } (0.5 )( ) { } ( ) { }t t t t t t tu u t u t u t u (41) where { }t u , { }t u and { }t u are the total displacement, velocity and acceleration vectors at time t , and t is time increment. The parameters and define the variation of acceleration over a time step and determine the stability and accuracy characteristics of the method. Typically, 0.5 and 1/ 6 1/ 4 can provide stable results. By using Eqs. (40) and (41), the equation of motion Eq. (37) can be finally written as, [ ]{ } [ ]t

eff effK u F (42)

in which 1 4[ ] [ ] [ ] [ ]effK c M c C K (43)

2 5 3 6[ ] { } ( [ ] [ ]){ } ( [ ] [ ]){ }t t t

effF F c M c C u c M c C u (44)

with

1 2 32

4 5 6

1 1 1; ;

( ) 2

; ; ( 1)2

c c ct t

c c c tt

(45)

After obtaining { }t u from Eq. (42), the incremental velocity { }t u and acceleration { }t u can be calculated by 4 5 6{ } { } { } { }t t t tu c u c u c u (46)

1 2 3{ } { } { } { }t t t tu c u c u c u (47)


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Further, the total vectors for next time step are updated as

{ } { } { }

{ } { } { }

{ } { } { }

{ } { } { }

t t t t

t t t t

t t t t

t t t t

u u u

u u u

u u u

F F F

(48)

For nonlinear dynamic analysis, iterations for solving Eq. (42) are needed for correction of equilibrium error. To check the equilibrium, both the displacement and force norms are recommended, i.e.

TOLERANCE{ } { }

{ } { }

t T ti i

t t T t ti i

u u

u u

(49)

* *

TOLERANCE{ } { }

{ } { }

t T ti i

t t T t ti i

F F

F F

(50)

in which the subscript “ i ” is the number of iterations within a time step, and *{ }t F is the unbalanced residual force increment vector determined by *{ } { } ([ ]{ } [ ]{ } { })t t t t t t t t tF F M u C u R (51) where { }t t R is the resisting force of the complete structure. Once the conditions given in Eqs. (49) and (50) are satisfied, the procedure presented in Eqs. (42-50) is repeated for next time step until the target time steps reach or the structure is collapsed. 3.2 Selection of Earthquake Wave It should be pointed out that the artificial/recorded/simulated waves of ground motion selected for a time history analysis may significantly affect the outcome. Therefore, seismic design codes explicitly or implicitly specify some requirements for selecting earthquake waves when performing a nonlinear dynamic analysis. The theoretical background for selection of earthquake wave is generally based on the three characteristics of ground motion, i.e. peak ground motion, time duration and frequency content. Peak ground motion, primarily peak ground acceleration (PGA), influences the vibration amplitude and has been commonly employed to scale earthquake design spectra and acceleration time histories. Time duration of ground motion affects the severity of ground shaking. For example, an earthquake with a high PGA poses a high hazard potential, but if it is sustained for only a short period of time it is unlikely to inflict significant damage to many types of structures. On the contrary, an earthquake with a moderate PGA and a long duration can build up damaging motions in certain types of structures. When the frequency content of the ground motion is close to the natural frequencies of the structure, the resonant phenomenon, in which the vibration amplitude of the structure grows indefinitely in theory, will occur.


134

From above, the general rules for selection of earthquake waves in GB50011 [3] are listed as below. (1) Minimum Time Duration The duration of the input wave should be long enough, which is generally taken as not less than 5 to 10 times of the fundamental period of the structure. (2) Minimum Number of Waves GB50011 [3] specifies that at least 2 sets of recorded strong earthquake waves and 1 set of artificial wave, based on the seismic intensity, design seismic group and site classification, should be employed. (3) Minimum Base Shear The seismic action represented by the input waves should conform, on average, to the 5% damping elastic response spectrum so that the waves used may have the statistical meaning to some extent. GB50011 [3] states that when performing an elastic time history analysis, the base shear obtained from each wave shall not be less than 65% of that from the response spectrum method, and the average value from all waves shall not be less than 80% of that from the response spectrum method. 4. PLASTIC HINGE METHOD IN NIDA In GB50011 [3], a two-stage design procedure is recommended for seismic design. The first step is based on the elastic analysis subjected to frequent earthquake and the second step is allowed for inelastic analysis under rear earthquake. In the process of time history analysis by NIDA [1], a simple, accurate and efficient method for determining the plastic hinge(s) is used to capture the progressive strength and stiffness degradation of the structure under an earthquake attack. The basis of the plastic hinge method is cross-section plastification. Material yielding is accounted for by zero-length plastic hinges at one or both ends of each element. Plasticity is assumed to be lumped only at the ends of an element, while the portion within the element is assumed to remain elastic throughout the analysis. In this paper, two predefined section springs (see Figure 3), which are used to simulate plastic hinge, will be set at the two ends of each beam-column element. The end section springs will be finally formulated into the element stiffness matrix of the curved stability function beam-column element (Chan and Gu [7]) which has been widely used for second-order P-- analysis. More details about the plastic hinge method can be referred to Chan and Chui [10].


135

Figure 3. Internal Forces of the Curved Element with End Springs The hysteresis model for steel material used in NIDA [1] is shown in Figure 4. As illustrated in Figure 4, initial yielding occurs at point A when the first yield moment capacity Mei is attained. On the curve AB, the gradual yielding occurs and the plastic moment capacity Mp is reached point B. When unloading takes place at point B, gradual yielding characteristics disappears and the path follows the line BDC in which the moment at point C is less than the initial yield moment Mei at point D. On reloading, the path moves along the line CD under the perfectly elastic state and then follows the curve DE under the partial yielding state. Similarly, under unloading conditions at point E, the path moves along EFG’H.

Figure 4. Elastic-Perfectly Plastic & Refined-Plastic Models Employed in NIDA 5. EXAMPLES 5.1 A Six-Story Space Steel Frame A six-story rigid steel space frame (see Figure 5) originally studied by Orbison et al. [11] is adopted here for demonstration of the modal response spectrum analysis by NIDA [1]. The details of the space frame are given as below:

(a) Geometrical dimensions and section sizes: shown in Figure 5; (b) The material properties for all members: Young’s modulus E=206850 MPa, shear

modulus G=79293 MPa, yield strength py=250 MPa;


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(c) Applied loads: uniform floor pressure=9.6 kN/m2, wind loads simulated by point loads of 53.376 kN in Y-direction at every beam-column joints;

(d) Boundary conditions: all columns are fixed to foundation.

Figure 5. Six-story Space Steel Frame The procedure for performing modal response spectrum analysis in NIDA [1] is detailed as below. Step 1: Build the structural model. For example, nodal coordinates, material properties, section properties, applied loads, boundary conditions and so on; Step 2: Define a response spectrum function. According to GB50011 [3], the design seismic intensity of Hong Kong is 7 (0.15g), and the seismic design group is 1, seen Figure 6. Step 3: Define a modal analysis with appropriate consideration of masses to get the natural periods and vibration modes. Besides structural self-weight, the other dead loads and part of live loads should be taken as structural masses, seen Figure 7. Noted that the structural self-weight is automatically included and therefore user need not add them as additional masses once more.

Figure 6. Define a Response Spectrum Function in NIDA

Node=21

Member=13


137

Figure 7. Define a Modal Analysis in NIDA

After performing the modal analysis, the modal participating mass ratios will be shown in the trace window (see Figure 8). In this example, the use of 15 modes can meet the requirement of “at least 90% of the participating mass” in codes. Step 4: Create “single direction” MRSA cases. In this step, user should specify which modal analysis case is used for mode superposition. Also, user should specify the response spectrum function to be used. For example, one x-direction and one y-direction MRSA cases are defined in Figure 9.

Figure 8. Participating Mass Ratios


138

(a) X-Direction (b) Y-Direction

Figure 9. Modal Response Spectrum Analysis Cases

Step 5: Create “directional combination” MRSA cases if needed. If the two horizontal components (vertical component may be also needed) of the seismic action need to be considered simultaneously, user need to conduct directional combination of several MRSA cases. Step 6: Create “load combination” considering both earthquake action and other actions. According to GB50011 [3], the following load combinations are recommended in Hong Kong. (a) 1.2DL+0.28WL+1.3EQX (b) 1.2DL+0.28WL+1.3EQY (c) 1.2DL+0.28WL+1.3(EQX+EQY)+0.5EQZ In this example, the nodal displacement and the member force (indicated in Figure 5) determined by NIDA are listed in Table 2.

Table 2. MRSA Results by NIDA Output Item NIDA Result MRSA Case Disp. Ux (Node 21) 63.5 mm RS-U1-CQC Disp. Uy (Node 21) 39.1 mm RS-U2-CQC Moment My (Member 13) 60.0 kNm RS-U1-CQC Moment Mz (Member 13) 93.2 kNm RS-U2-CQC Axial P (Member 13) 25.9 kN RS-U1-CQC Axial P (Member 13) 70.9 kN RS-U2-CQC

5.2 A 2D Seven-Story Steel Frame A 2D seven-story steel frame as shown in Figure 10 is used here for demonstration of time history analysis by NIDA [1]. The details of the 2D frame are given as below:


139

(a) Geometrical dimensions and section sizes: shown in Figure 10; (b) The material properties for all members: Young’s modulus E=2.034x105 MPa,

Poisson’s ratio v=0.3, yield strength py=250 MPa; (c) Applied static loads: shown in Figure 10; (d) Boundary conditions: all columns are fixed to foundation; (e) Mass: 85 812.16 kg at each story (node 5, 8, 11, 14, 17, 20 and 23); (f) Earthquake wave: the N-S component of the 1940 El Centro earthquake.

The procedure for performing time history analysis in NIDA [1] is detailed as below. Step 1: Build the structural model. For example, nodal coordinates, material properties, section properties, applied loads, boundary conditions and so on; Step 2: Define one or more than one time history functions. User can import a previous earthquake record as shown in Figure 11. Step 3: Define the time history analysis case. Generally, user only needs to give a case name, specify time steps and input the parameters for calculation of damping, seen Figure 12. The default values for Newmark method can be used for many structures. Noted that the Newton-Raphson method is used for the nonlinear incremental-iterative solution when performing a time history analysis in NIDA [1]. In some cases the structural behaviour may be highly nonlinear and therefore several cycles in each time step are needed. In this case, user needs to modify the number of cycles for each time step (see Figure 13).

Figure 10. 2D Seven-Story Steel Frame

88.96 kN

3.96

24m

3.

9624

m

3.96

24m

3.

9624

m

3.96

24m

4.

1148

m

4.11

48m

66.72 kN

55.60 kN

44.48 kN

33.36 kN

22.24 kN

11.12 kN 11.12 kN

9.144m 9.144m


140

Figure 11. Define a Time History Function in NIDA

Figure 12. Define a Time History Analysis Case in NIDA

Figure 13. Parameters for Nonlinear Incremental-Iterative Solution

Active Plastic Analysis


141

Step 4: Define the initial static loads. Besides the earthquake action, other actions such as dead loads and live loads should be taken into account, seen Figure 14. Specially, NIDA [1] allows for initial member and frame imperfection before applying static loads. Step 5: View the results and check the structural adequacy after finishing the analysis. The member capacity has been checked at each time step in NIDA [1]. User needs to check the maximum story and building drift as well as other output indicated the structural behaviour during the time series.

Figure 14. Initial Static Loads of Time History Analysis In this example, the base shear Fx, the displacement Ux of Node 24 calculated from NIDA [1] are shown in Figure 15 and Figure 16 respectively against those results from ANSYS [12]. For easy comparison, the plastic behaviour does not taken into account in the two sets of results. From Figure 15 and Figure 16, it can be seen that the results from NIDA [1] agree well with those from ANSYS [12].

Figure 15. Comparison of Base Shear (Elastic THA) Further, inelastic time history analysis is performed by NIDA [1] for this example. To allow for plastic hinges in beam-column elements, user only needs to active the function “Enable Plastic Advanced Analysis” as shown in Figure 13. After this, the default plastic hinge model as presented in Section 4 will be used in NIDA [1] to capture the plastic behaviour of beam-column elements.


142

Before doing the inelastic time history analysis for this example, the PGA of El Centro earthquake is scaled to 1.4 times for easy observation of plastic hinges. Figure 17 shows the plastic hinges (marked in write point) formed in the frame during the earthquake.

Figure 16. Comparison of Building Drift (Elastic THA)

Figure 17. Plastic Hinges Formed in the Frame (Inelastic THA) 6. CONCLUSIONS In this paper, the theoretical background as well as the common considerations of two widely used seismic analysis methods, i.e. the modal response spectrum analysis (MRSA) and time history analysis (THA), is briefly introduced. The MRSA method is suitable for elastic analysis while the THA is an “exact” method which considers both the geometric and material nonlinearities. The design spectra in codes are based on the statistical theory and therefore the results from MRSA can consider the uncertainties of earthquake to some extent. The earthquake waves used in a time history analysis should be carefully selected so that these waves can reflect the future possible earthquake event. The two methods have been


143

implemented in the software NIDA [1] with careful verification. Further, two examples using software NIDA [1] are given to demonstrate the general procedures of performing the two methods. It should be noted that time history (nonlinear dynamic) analysis as an advanced method is compulsively used for high-rise or important buildings and long-span bridges. Nonlinear-based software NIDA [1] has an inherent advantage either for conventional second-order nonlinear design or nonlinear dynamic seismic design. ACKNOWLEDGEMENTS The authors acknowledges the support of the Research Grant Council of the Hong Kong Government on the project “Advanced Analysis Allowing for Load and Construction Sequences” funded jointly by Construction Industry Institute-Hong Kong (CII-HK) and The Hong Kong Polytechnic University and “Advanced Analysis for Progressive Collapse and Robustness Design of Steel Structures (PolyU 5115/07E)”. REFERENCES 1. NIDA, User's Manual, Nonlinear Integrated Design and Analysis. NIDA 8.0 HTML

Online Documentation. (http://www.nida-naf.com), 2009. 2. Eurocode 8, EN 1998-1: Design of Structures for Earthquake Resistance - Part1:

General Rules, Seismic Actions and Rules for Buildings. European Committee for Standardization, 2004.

3. GB50011, Code for Seismic Design of Buildings, Zhong Hua Ren Min Gong He Guo Jian She Bu, 2008.

4. FEMA356, Prestandard and Commentary for the Seismic Rehabilitation of Buildings. 2000.

5. Uniform Building Code (UBC), Structural Engineering Design and Provisions, Vol. 2. International Conference of Building Officials (ICBO), Whittier, CA., 1997.

6. International Building Code (IBC). International Code Council, INC., USA, 2006. 7. Chan, S.L. and Gu, J.X., “Exact Tangent Stiffness for Imperfect Beam-Column

Members”, Journal of Structural Engineering-ASCE, 2000, Vol. 126, No. 9, pp. 1094-1102.

8. Liu, S.W., Liu, Y.P. and Chan, S.L., “Pushover Analysis by One Element Per Member for Performance-Based Seismic Design”, International Journal of Structural Stability and Dynamics, 2010. Vol. 10, No. 1, pp. 111-126.

9. Newmark, N.M., “A Method of Computation for Structural Dynamics”, ASCE Journal of the Engineering Mechanics Division, 1959. Vol. 85, pp. 67-94.

10. Chan, S.L. and Chui, P.P.T., “Nonlinear Static and Cyclic Analysis of Steel Frames with Semi-rigid Connections”, Elsevier Science, 2000.

11. Orbison, J.G., Mcguire, W. and Abel, J.F., “Yield Surface Application in Nonlinear Steel Frame Analysis”, Comput. Methods Appl. Mech. Engrg, 1982. Vol. 33, No. 1, pp. 557-573.

12. ANSYS, ANSYS User's Manual, ANSYS Release 10.0 Documentation. ANSYS 10.0 HTML Online Documentation, USA: SAS IP, Inc., 2005.


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