Advanced Design Examples of Seismic Retrofit of Structures [Illustrated] 0081025343, 9780081025345

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Advanced Design Examples of Seismic Retrofit of Structures

Advanced Design Examples of Seismic Retrofit of Structures

Mohammad Yekrangnia

Butterworth-Heinemann is an imprint of Elsevier The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States © 2019 Elsevier Ltd. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability 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. Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library ISBN: 978-0-08-102534-5 For information on all Butterworth-Heinemann publications visit our website at https://www.elsevier.com/books-and-journals

Publisher: Matthew Dean Acquisition Editor: Ken McCombs Editorial Project Manager: Leticia Lima Production Project Manager: Anitha Sivaraj Cover Designer: Victoria Pearson Typeset by SPi Global, India

Contributors Numbers in parentheses indicate the pages on which the authors’ contributions begin.

Salar Arian (1), International Institute of Earthquake Engineering and Seismology (IIEES), Tehran, Iran Behnam Azmoudeh (279), APS Designing Energy, Rome, Italy Aida Bejanli (119), Sarzamin Consulting Engineers, Tehran, Iran Morteza Raissi Dehkordi (13, 279), Iran University of Science and Technology, Tehran, Iran Mahdi Eghbali (279), Department of Civil Engineering, Faculty of Engineering, University of Zanjan, Zanjan, Iran Teymour Honarbakhsh (119), Sarzamin Consulting Engineers, Tehran, Iran Kamyar Karbasi (119), Sarzamin Consulting Engineers, Tehran, Iran Arash Mardani (13), Bureau of Technical and Supervision, DRES, Tehran, Iran Abdoreza S. Moghadam (13, 279), International Institute of Earthquake Engineering and Seismology (IIEES), Tehran, Iran Samaneh Mohamadi (119), Sarzamin Consulting Engineers, Tehran, Iran Kamran Rahmati (119), Department of Reinforcement and Maintenance of Bridges and Technical Buildings of Tehran Municipality, Tehran, Iran Hamed Seyri (201), Bureau of Technical and Supervision, DRES, Tehran, Iran Mohammad Yekrangnia (1, 13, 201, 391), Department of Civil Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran

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Preface Earthquake vulnerability of buildings has been acknowledged across the globe with many examples of seismic damage in China, India, Latin America, and Europe as well as the United States. Much attention has been focused on this topic worldwide from both societal and engineering perspectives. As a result, a significant amount of development work has been carried out to evaluate various assessment methodologies and evaluate possible retrofit methods. The main challenges in seismic retrofit are usually attributed to understanding the available codes requirements, modeling assumptions, methods, and retrofitting schemes. Seismic retrofit of structures covers a broad range of structural types and retrofit methods, and hence it is more complex than designing new buildings. It is quite likely that two very different retrofit methods may be proposed for a single project by two different consulting engineers. Even the details of a unique retrofit technique may differ for a single project by different design engineers. Part of this variety originates from the design and implementation ambiguities regarding retrofit projects. Compared to designing new buildings, retrofitting has never been an undergraduate or graduate compulsory course; and there are fewer retrofitting projects than there are new buildings being constructed. As a result, experience in the design and implementation of retrofit projects is very limited compared to ordinary construction projects. Although there are good retrofit codes available to professionals, experiences prove that the engineers’ “interpretations” of these codes may vary a lot. Therefore, there is a need to elaborate the concepts of design and the construction details of retrofit projects. In response to this need, the current book tries to present some real projects that can be regarded as good representatives of different retrofit projects with the emphasis on dealing with ambiguities, questions, and difficulties in design and construction. The idea for this book started some years ago with university students and industry colleagues, with the goal of facilitating the use of design codes related to seismic retrofit of common structures. Beginning with the introduction of concepts and approaches, this book aims at presenting several examples of real retrofitting projects that cover a broad range of structural systems and retrofitting methods. In-depth design calculation procedures are found in each example and the reason behind the selection of a particular method or assumption is elaborated. The book not only provides a valuable source for previously

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implemented retrofit projects in design methods perspective but also supplies several photos and constructional details and problems regarding various retrofit projects. The book at times addresses the challenges in implementation of some retrofit techniques and proposes solutions to each of the design and construction challenges. The content and treatment of the subjects in this book are intended to appeal to graduate-level students, teachers, and professional engineering community members. An aspect of the current book that distinguished it from previous texts on seismic retrofit of structures is that this book provides detailed calculations and step-by-step guidelines for the retrofit of various types of structural systems. In some parts, this book also adopts a practical approach that focuses on providing readers with several photos of structural damages, retrofit details, and construction phases of the retrofit projects. The major features of this book that make it unique are as follows. – The book is example-based and hence further helps readers to identify and understand the problems regarding seismic retrofit of structures. – It deals with real retrofitting projects in all the examples, and is full of images and construction details. – The book covers a broad range of structures from nonengineered houses to frame buildings. – It contains various retrofitting techniques through the examples, and in some cases their performance is compared. It is assumed that readers have good familiarity with the basic design concepts of steel, reinforced concrete, and unreinforced masonry buildings. Moreover, preliminary knowledge of the concepts and approaches in seismic retrofit of structures is required. Because the US design and seismic retrofit codes are among the most widespread design codes and their approach and methodologies are widely adopted by other codes, emphasis has been placed on using the US codes in this book. In addition, the seismic design codes of several countries are more or less similar to the corresponding US codes, which makes the US codes one of the best possible choices in this regard. I must acknowledge that the book does not cover all the common structural systems around the world; nor have all the possible retrofitting methods for the example buildings been evaluated in detail in the chapters. The selection of the best solution for the vulnerable buildings in the form of the implemented retrofit methods is subjective and hence, retrofit methods other than those selected in this book may seem more appropriate to some readers. I would be grateful for any constructive comments or criticisms that readers may have and for notification of any errors that they may detect. Special thanks goes to the Organization for Development, Renovation and Equipping Schools of IR Iran (DRES) for their support and cooperation in my using some of its materials. From 2006 to 2016, vast undertakings were made by DRES in the realm of seismic risk reduction and improvement of school safety.

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For the study and design of seismic vulnerability and also construction of retrofit projects for nearly 130,000 classrooms in Iran, more than 100 privatesector consulting companies, two sets of national project management systems, several elite university professors, and more than 400 contractors were involved. Various common and innovative retrofit methods and procedures were implemented in school buildings on the available structural systems including unreinforced masonry (URM), steel, and reinforced concrete (RC) frame buildings. In total, about $3 billion were dedicated and spent on reconstruction and retrofit projects by DRES. Observations from recent major earthquakes indicate that the seismic performance of the retrofitted school buildings was satisfactory and these buildings maintained the performance level of immediate occupancy (IO), whereas many other buildings sustained major damages or experienced collapse. In recognition of these actions, the United Nations SASAKAWA prize for Disaster Risk Reduction was awarded to DRES in 2017. I have been fortunate to be taught, advised, and mentored by several extraordinary instructors and researchers with expertise in seismic retrofit of structures. Many individuals have extended their help in one way or another in the preparation of this book, and the support of such individuals is gratefully acknowledged. Thanks are due to all the contributors for their careful preparation of the contents of this book. I am grateful to Dr. Ali Bakhshi and Dr. Mohammad Ali Ghannad, my supervisors during my MSc and PhD for their mentorship. I would also like to thank my friend Mr. Alireza Mahdizadeh for his encouragement and support. Mohammad Yekrangnia

Chapter 1

Introduction Mohammad Yekrangnia* and Salar Arian† * †

Department of Civil Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran, International Institute of Earthquake Engineering and Seismology (IIEES), Tehran, Iran

Aims By reading this chapter, you are introduced to: l seismic risk reduction strategies; l performance-based earthquake engineering; l basic terminology in seismic retrofit standards; and l the concept of seismic resilience.

1.1 INTRODUCTION Because of the rich literature of earthquake engineering and decades of international efforts toward seismic risk characterization all around the world, the major categories of possible losses from seismic damage are well classified. The most important type of losses is the extent of casualties which led to introduction of the provision of life safety as the main concern of minimum technical requirements in codes and standards around the world. The second sources of concern are financial losses, either from direct costs of loss of or damage to properties including the structures, infrastructures, and nonstructural components, or due to loss of the function of the buildings and the recovery time for the services provided by them. Identification of all types of potential losses allows different stakeholders such as individual owners of buildings and governments to compare their importance against other demands for the use of limited resources for budget allocation. Performance-based earthquake engineering, whether used for risk assessment and retrofit of existing buildings or design of new ones, provides a standard framework for determination and measurement of losses [1]. In the case of construction of new buildings, the basic design procedures as well as technical details to prevent dangerous failure modes are well known for most engineered structural systems around the world. Although building codes are still constantly being updated, the challenges with new buildings are Advanced Design Examples of Seismic Retrofit of Structures. https://doi.org/10.1016/B978-0-08-102534-5.00001-5 © 2019 Elsevier Ltd. All rights reserved.

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essentially about the economic and political policies to implement and enforce design requirements. However, old buildings constructed with almost no seismic considerations are considered to be the chief source of seismic risk threatening the most communities. These buildings must be identified and evaluated to determine their level of seismic risk, and then appropriate risk management solutions should be selected and implemented for them. This chapter presents the overall steps of procedures for risk assessment and retrofit of individual buildings as risk assessment; readers can find more detailed information describing these methodologies elsewhere [2]. The seismic vulnerability evaluation of the existing buildings covers almost every aspect of earthquake engineering and construction techniques. On the other hand, retrofit of individual buildings is the main part of the evaluation and risk reduction strategies. It is worth noting that there are a variety of research topics that will not be presented in detail here. In the next sections, a brief review on these fields of study is described.

1.2 SEISMIC RISK REDUCTION STRATEGIES Seismic codes and standards traditionally have not been developed on the basis of reliability methods such as load and resistance factor design (LRFD), because of the lack of a variety of unknown parameters that must have been defined in a reliable manner in this design methodology. The need to know the probability of failure of code-compatible buildings has been recognized since the provision of the associated commentary of ATC 3-06 [3]. Efforts through quantifying the mentioned problem has been made by the SAC Steel Project [4]. To propose a performance-based framework for the design of steel moment frames, the first methodology was developed to estimate the probability of collapse of a building under excitation by different ground motions [5]. The proposed approach tried to alleviate the variation in maximum demands of structures under scaled-tosame-level time histories as well as other sources of uncertainties. Although the method focuses on the quantification of the collapse as a target performance level, the framework provided a basis that could be extended to other performance targets. In the 1967 edition of the Blue Book [3], a clear performancerelated set of criteria were defined for buildings designed to its provisions: (1) resist minor earthquakes without damage; (2) resist moderate earthquakes without structural damage, but with some non-structural damage; and (3) resist major earthquakes, of the intensity of severity of the strongest experienced in California, without collapse, but with some structural as well as nonstructural damage. Analysis of responses of the vast majority of buildings for the effect of seismic ground motion requires consideration of nonlinear structural behavior [3]. It is not economically efficient to keep structural systems in the elastic range under strong earthquakes, and it should be borne in mind that an elastic superstructure response would severely increase displacement demands. Therefore,

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characterization of a nonlinear response is mandatory for existing buildings, most of which suffer from limited deformation capacity. Due to the nonlinear behavior and the complex nature of lateral force resisting systems in existing buildings, the retrofit of a building is essentially a different process compared to the design of new buildings, in which a demand is simply estimated and a resisting element is selected so that its capacity may overcome the predefined imposed demand. Generally, a specific verification analysis is required to ensure that all important structural components pass their corresponding acceptable limits after applying a retrofit solution. In the terminology of performancebased earthquake engineering, the evaluation process determines the performance level of the building for the design ground motion. Similarly, after a retrofit, it must be ensured that the structure meets the target performance level for the specified seismic hazard level. A convenient way to discuss the engineering issues of evaluation and retrofit is to break down the process into steps, as shown in Fig. 1.1. For any given building, the sequence of highlighted steps may differ, but generally engineers must deal with all issues listed in each of the steps.

Develop knowledge of as-built conditions

Determine local response characteristics

Create mathematical model

Perform global analysis

Determine acceptability NO

Select retrofit procedures

YES

NO

Classify per evaluation procedure or policy

FIG. 1.1 The engineering process of risk assessment or retrofit [6].

Finished

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1.3 PERFORMANCE-BASED EARTHQUAKE ENGINEERING Typically, seismic evaluations, and consequently building retrofits, are intended to ensure preservation of life or to control the risk of casualties in an earthquake. As was mentioned earlier, reducing economic losses from damage, either due to repair costs or lost functionality of the building, is the other goal of seismic design. The cost of retrofit, often over 25% of the value of the building [3], has also caused interest in costs and benefits analyses of several retrofit options (all satisfying expected performance). This interest in predicting the level of damage expected in a building before and/or after retrofit has motivated the provision of frameworks for performance-based seismic engineering. This development is gradually moving toward procedures already available for performance-based design codes that have been implemented in other disciplines, such as fire protection [1]. Detailed analytical risk assessment and retrofit as discussed in this book are within a framework of performance-based engineering in accordance with up-to-date guidelines such as ASCE 41-13 [7]. The theoretical background of PBEE is on the basis of probabilistic seismic demand analysis. The Pacific Earthquake Engineering Research (PEER) center framework is a popular methodology in order to estimate the mean annual frequency (MAF) of exceedance of a particular limit state (LS), as expressed mathematically in Eq. (1.1): Z Z GðLSjEDPÞ  jdGðEDPjIMÞj:jdλðIMÞj (1.1) MAFðLSÞ ¼ IM EDP

where EDP is the engineering demand parameter, for example, maximum inter story drift ratio; IM is the intensity measure, for example, spectral acceleration (Sa) at the first period of structure and a given damping ratio; G(LS jEDP) denotes the probability of exceeding LS conditioned on the value of EDP; and G(EDP jIM) denotes the probability of exceeding EDP conditioned on the value of IM. It is assumed that the seismic hazard is characterized by an elastic response spectrum at a minimum. Some nonlinear analysis methods may also require inelastic design spectra or time histories representing the site seismic hazard. There are many issues associated with determination of seismic hazard, both concerning the technical methodologies used and the policy decisions regarding the level of risk. The state of the art in these areas is documented elsewhere. An issue that needs improvement in earthquake engineering is the interaction between structural analysts and ground motion specialists to advance the characterization of ground motions to include potentially more useful parameters, such as duration and convenient measurement of near-fault pulses. The current methodology used in retrofit standard and guidelines that is sometimes called the first generation of PBEE satisfies performance objectives by providing sufficient system performance at a given hazard level, as is schematically presented in Fig. 1.2. The next generation would utilize

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FIG. 1.2 The first generation of PBEE: To achieve a desired “System Performance” at a given “Seismic Hazard.” (J.P. Moehle, A framework for performance-based earthquake engineering, in: Proc. ATC-15-9 Workshop on the Improvement of Building Structural Design and Construction Practices, Maui, HI, June, 2003.)

FIG. 1.3 The PBEE concept; the first versus the second generation.

probabilistic damage analysis rather than the current deterministic approach that considers 100% probability of exceedance, when an EDP value exceeds predefined damage measures. Fig. 1.3 depicts the basics of two mentioned methodologies.

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1.4 BASIC TERMINOLOGY IN SEISMIC RETROFIT STANDARDS 1.4.1 Design Basis Provisions of standards for seismic rehabilitation are mostly founded on a performance-based design methodology that differs from seismic design procedures for the design of new buildings currently specified in most building codes. The framework in which these requirements are specified is purposefully broad so that rehabilitation objectives can accommodate buildings of different types that satisfy a variety of performance levels for different seismic levels.

1.4.2 Rehabilitation Objective Building performance can be described qualitatively in terms of: the safety afforded to building occupants during and after the event; the cost and feasibility of restoring the building to its pre-earthquake condition; the length of time for which the building is removed from service for effective repairs; and economic, architectural, or historic impacts on the larger community. These performance characteristics are directly related to the extent of damage that would be sustained by the building. In this scope, the extent of damage to a building is categorized as a building performance level. A broad range of target building performance levels may be selected when determining rehabilitation objectives. Probabilistic earthquake hazard levels are frequently used in standards or their corresponding mean return periods (the average number of years between events of similar severity). The rehabilitation objective selected as a basis for design will determine, to a great extent, the cost and feasibility of any rehabilitation project, as well as the benefit to be obtained in terms of improved safety, reduction in property damage, and interruption of use in the event of future earthquakes. Readers are referred to [8] for more details on the efficient selection of rehabilitation objectives.

1.4.3 Target Building Performance Levels A target building performance level consists of a combination of a structural performance level and a nonstructural performance level. Table 1.1 presents a sample of such performance levels derived from FEMA 356 [6].

1.5 REVIEW OF COMMON RETROFIT OPTIONS There are many specific methods of intervention available to retrofit designers, both to improve the behavior of individual building components and to improve overall behavior [5]. A complete listing of all techniques becomes a treatise on structural engineering because all materials and systems used in new construction can also be used in a retrofit. The selection of the specific type of element or prefabricated hardware depends on local cost, availability, and suitability for

TABLE 1.1 Sample of Structural Performance Levels [6] Target Building Performance Levels (1-A)

Operational Level

Overall Damage

Severe

Moderate

Light

Very light

General

Little residual stiffness and strength, but load-bearing columns and walls function. Large permanent drifts. Some exits blocked. Infills and unbraced parapets failed or at incipient failure. Building is near collapse

Some residual strength and stiffness left in all stories. Gravity-load-bearing elements function. No outof-plane failure of walls or tipping of parapets. Some permanent drift. Damage to partitions. Building may be beyond economical repair

No permanent drift. Structure substantially retains original strength and stiffness. Minor cracking of fac¸ades, partitions, and ceilings as well as structural elements. Elevators can be restarted. Fire protection operable

No permanent drift. Structure substantially retains original strength and stiffness. Minor cracking of fac¸ades, partitions, and ceilings as well as structural elements. All systems important to normal operation are functional

Nonstructural components

Extensive damage

Falling hazards mitigated but many architectural, mechanical, and electrical systems are damaged

Equipment and contents are generally secure, but may not operate due to mechanical failure or lack of utilities

Negligible damage occurs. Power and other utilities are available, possibly from standby sources

Comparison with performance intended for buildings designed under the NEHRP (National Earthquake Hazards Reduction Program) provisions, for the design earthquake

Significantly more damage and greater risk

Somewhat more damage and slightly higher risk

Less damage and lower risk

Much less damage and lower risk

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Immediate Occupancy Level (1-B)

1

Life Safety Level

(3-C)

Introduction Chapter

Collapse Prevention Level

(5-E)

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Advanced Design Examples of Seismic Retrofit of Structures

the structure in question. It is thus an extensive task to develop guidelines for such selection. Conceptual design techniques, on the other hand, can be systematically categorized and design strategies formulated. The primary focus of determining a viable retrofit scheme is on vertically oriented systems because of their significance in providing either lateral stability or gravity load resistance. Deficiencies in vertical elements are caused by excessive inter-story deformations that create either unacceptable force or deformation demands. Given an initial understanding of the importance of the nontechnical issues described in the previous section, alternate retrofit schemes can be developed. Retrofit actions can be classified into three types: l

l l

connectivity, consisting of ensuring that individual elements do not become detached and fall, ensuring a complete load path, and ensuring that the modeled force distributions can occur; modification of global behavior, usually decreasing deformations; and modification of local behavior, usually increasing deformation capacity.

These three types of actions balance one another in that employing more of one will mean less of another is needed. It is obvious that providing added global stiffness will require less local deformation capacity, but it is often less obvious that careful placement of new lateral elements may minimize a connectivity issue such as a diaphragm deficiency.

1.5.1 Connectivity Connectivity deficiencies are within the load path: wall out-of-plane connection to diaphragms; connection of diaphragm to vertical elements; connection of vertical elements to foundation; and connection of foundation to soil. A complete load path of some minimum strength is always required, so connectivity deficiencies are usually a matter of degree. A building with a complete, but relatively weak or brittle load path might be a candidate for seismic isolation design to keep the superstructure in the elastic range. Yielding in connections within the basic load path can create profound complications on the overall building model. An early decision has to be made concerning modeling such behavior or preventing it by reducing demand or strengthening of the local connections. Demand can be reduced by adding vertical load resisting elements (reducing individual collector or foundation loads) or by seismic isolation.

1.5.2 Improvement of Global Behavior Modification to global behavior normally focuses on deformation. Overall seismic deformation demand can be reduced by adding stiffness in the form of shear walls or braced frames. A significant period shift is normally required to protect deformation sensitive elements in this way. New elements may be added, or

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created from a composite of new and old components. Examples of such composites include filling in openings in infill frames and using existing columns for chord members for “new” shear walls or braced frames. If existing lateral force resisting elements are to be used in conjunction with new ones to provide the required stiffness, the potential for degradation due to poor detailing in the existing structure must be considered. If loss of lateral stiffness of the existing elements will reduce the overall strength to levels that could cause P-delta instability, the existing elements should be discounted and additional new elements employed.

1.5.3 Improvement of Local Behavior Rather than providing retrofit actions that affect the entire structure, deficiencies may be eliminated at the local, component level. This can be done by enhancing the existing shear or moment strength of an element, or simply by altering the element in a way that allows addition deformation without compromising vertical load carrying capacity. As previously discussed, certain yielding sequences are almost always benign: beams yielding before columns, bracing members yielding before connections, and bending yielding before shear failure in columns and walls. These relationships can be obtained by local retrofit in a variety of ways. Columns in frames and connections in braces can be strengthened, and the shear capacity of columns and walls can be enhanced to be stronger than the shear that can be delivered. Concrete columns can be wrapped with steel, concrete, or other materials to provide confinement and shear strength. Concrete and masonry walls can be layered with reinforced concrete, plate steel, and other materials. Composites of glass or carbon fibers and epoxy are becoming popular to enhance shear strength and confinement in columns, and to provide shear-only strengthening to walls. However, such materials must be used with caution, because moment capacity can be inadvertently added, the material can be incorrectly designed to be incompatible with the existing element, or the system can be applied incorrectly in the field.

1.6 FUTURE DIRECTIONS; TOWARD SEISMIC RESILIENCE Risk and resilience strategies are not equivalent. Risk-based strategies are most effective when hazard probabilities are known or can be estimated. However, ignorance of emergent hazards does not justify a lack of preparedness. Three recent disasters, the Fukushima nuclear reactors, Deepwater Horizon, and Hurricane Katrina, reinforce the view that some degree of ignorance in complex systems is irreducible. Therefore, an exclusively risk-based management approach is never fully justified, and lack of attention to resilience will exacerbate the consequences of inevitable failures. Risk management begins with hazard identification. This step has some difficulties because hazards are usually unknown, inestimable, or very low-probability. Also, high-consequence events,

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particularly in complex coupled systems, all probabilities of risks are conditional on some background knowledge, including suppositions that camouflage unknown hazards. Given that a full knowledge of unexpected hazards and how the cascading effects emerge in a complex coupled system cannot be gained, risk management can fail when confronted with unexpected shocks. Resilience represents an alternative design and management strategy. Resilience thinking suggests adoption of design and management strategies for responding to unknown and unexpected hazards through adaptation, flexibility, diversity, and experimentation or innovation. Nowadays, designers and engineers approach a structure as if it stands alone, without considering the interaction with the community, which instead should be considered as an integrated part of the design process. There is now a new fundamental way of looking at all problems. The building is not considered alone, but as a group of buildings using the “portfolio approach” which will allow regional loss analysis. This concept is borrowed from the financial industry, where modern portfolio theory (MPT) was developed in the 1950s through the early 1970s and was considered an important advance in the mathematical modeling of finance. MPT is defined as a theory of investment which attempts to minimize risk for a given level of expected return, by carefully choosing the proportions of various assets. In the last decade, earthquake engineers have given more attention to deformations during their analysis, and life safety, while less attention has been given to socio-economic parameters [9]. Nowadays, attention is shifting toward the necessity to develop a damage-free structure using risk assessment tools which should develop more robust structures against uncertainties. Shorter recovery processes are possible at the building level if the structural damage is minimal; otherwise it might take months to recover. One of the options in order to achieve more resilient structures in face of an earthquake is, for example, providing them with advanced technologies such as self-centering capabilities with minimum residual deformations, which will allow a faster recovery.

1.7 THE ORGANIZATION OF THE BOOK CHAPTERS Focusing on the practical application considered for the current guideline, different chapters are designed to cover a variety of issues from design calculations to the construction stages. The seismic upgrade of masonry existing building through shotcrete and reinforcement is provided in Chapter 2. In Chapter 3, seismic retrofit of an reinforced concrete (RC) building by adding shear walls is investigated in detail. A relatively comprehensive discussion is dedicated to the quantification of masonry infill behavior and its effect on the seismic performance of a typical steel building in Chapter 4. The provision of concentric bracing system as an efficient retrofit solution for an under-code steel structure is presented in Chapter 5. Finally, seismic performance improvement techniques for nonengineered buildings are encompassed in Chapter 6. In these chapters, the aim is to provide readers with sufficient knowledge about the most

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important failure modes of any selected resisting system, for them to be able to understand both quantitatively and qualitatively the concept of applied retrofit strategy as well as the mechanism of performance upgrade attained by which.

REFERENCES [1] H. Yilmaz, T. Hachmann, Hands-on-experience on seismic retrofit in four different countries, Int. J. Saf. Secur. Eng. 7 (4) (2017) 557–567. [2] M. Arau´jo, J.M. Castro, A critical review of European and American provisions for the seismic assessment of existing steel moment-resisting frame buildings, J. Earthqu. Eng. (2017) 1–29. [3] W.T. Holmes, Risk assessment and retrofit of existing buildings, Bull. N.Z. Soc. Earthqu. Eng. 33 (3) (2000) 222–248. [4] S.J. Venture, G.D. Committee, Recommended Seismic Design Criteria for New Steel MomentFrame Buildings: Federal Emergency Management Agency, 2000. [5] R. Hamburger, Implementing performance-based seismic design in structural engineering practice, in: Paper Presented at the Proceedings of 11th World Conference on Earthquake Engineering, Acapulco, Mexico, 1996. [6] Federal Emergency Management Agency (FEMA), Prestandard and Commentary for the Seismic Rehabilitation of Buildings, 2000. [7] ASCE, Seismic rehabilitation of existing buildings (ASCE/SEI 41-13), American Society of Civil Engineers, Reston, VA, USA, 2013. [8] Federal Emergency Management Agency (FEMA), NEHRP Commentary on the Guidelines for the Seismic Rehabilitation of Buildings: (FEMA 274), Reston, VA, 1997. [9] G.P. Cimellaro, A.M. Reinhorn, M. Bruneau, Seismic resilience of a hospital system, Struct. Infrastruct. Eng. 6 (1–2) (2010) 127–144.

Chapter 2

Example of a Two-Story Unreinforced Masonry Building Retrofitted by Shotcrete☆ Arash Mardani*, Morteza Raissi Dehkordi†, Abdoreza S. Moghadam‡ and Mohammad Yekrangnia§ *

Bureau of Technical and Supervision, DRES, Tehran, Iran, †Iran University of Science and Technology, Tehran, Iran, ‡International Institute of Earthquake Engineering and Seismology (IIEES), Tehran, Iran, §Department of Civil Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran

Aims By reading this chapter, you are introduced to: l l l l l

URM buildings’ characteristics and failure modes; evaluation of URM buildings by linear static procedure (LSP); the effects of horizontal ties on vulnerability of URM buildings; the effects of diaphragm rigidity on vulnerability of URM buildings; and design procedure of shotcrete.

2.1 INTRODUCTION In this chapter, the building under study is a two-story unreinforced masonry (URM) school building located in Tehran, Iran. The plans and sanctions of the example two-story URM school building are shown in Figs. 2.1 and 2.2, respectively. A view of the example two-story URM school building is presented in Fig. 2.3. The main reason for selecting a school building over a typical residential building is that unsafe existing buildings expose school administrators to the following risks [1]: ☆ This chapter is part of a research project sponsored by the Organization for Development, Renovation and Equipping Schools of IR. Iran (DRES). The majority of the details and photos presented in this chapter belong to DRES. The authors of this chapter appreciate the financial and technical support of DRES. Advanced Design Examples of Seismic Retrofit of Structures. https://doi.org/10.1016/B978-0-08-102534-5.00002-7 © 2019 Elsevier Ltd. All rights reserved.

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A 8a 7a

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(B) FIG. 2.1 Plan of the example two-story URM school building. (A) Floor (story 0). (B) First story (story 1). l l l l

death and injury of students, teachers, and other staff; damage to or collapse of buildings; damage and loss of furnishings, equipment, and building contents; and disruption of educational programs and school operations.

Also, school buildings usually follow one of the available standard modular forms in architecture. As a result, evaluation and proposing a retrofit solution for a typical school building can be easily extended to several buildings of this type.

2.2 ASSUMPTIONS The main assumptions in different parts of this chapter are as follows: l

The evaluation of the considered building is performed according to “Seismic Evaluation and Retrofit of Existing Buildings, ASCE 41” [2].

Example of a Two-Story Unreinforced Masonry Building Chapter 8a

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D

E

F

G

H

I

J

K

L

M

(B) A

B

(C) FIG. 2.2 Sections of the example two-story URM school building. (A) West view. (B) South view. (C) North view.

FIG. 2.3 A view of the example two-story URM school building. (Permission from DRES.) l

l

Evaluation of the nonstructural parts of the building is not within the scope of this chapter. The seismic hazard is the only hazard of the site. As a result, there shall be no liquefaction, slope failure, or surface fault rupture hazard present at the

16

l

l

Advanced Design Examples of Seismic Retrofit of Structures

building site. Alternatively, if such a hazard is present, the hazard has been mitigated by the design of the lateral-force-resisting system, including foundations [2]. The target is to offer a retrofit solution for several buildings of this type under different circumstances. In order to take into account the effects of different structural features on the vulnerability of the considered school buildings, the items below are considered as variables and the vulnerability assessment is performed for each case; accordingly, the retrofit solution for each case is then proposed. - Existence of tie columns: two cases are considered, unconfined unreinforced masonry (UM hereafter), and the corresponding confined unreinforced masonry building (CM henceforth). - Diaphragm rigidity: two cases are considered; one case is the building with a flexible diaphragm, and other is the corresponding building with a rigid diaphragm. - The effects of mortar shear strength, soil condition, and seismicity of the region: all of these factors contribute directly to capacity of the building and seismic demand. Considering that many school buildings of this kind have peripheral walls which isolate the building from its adjacent buildings, it is assumed that the effects of surrounding buildings on seismic performance of the school building are negligible (Fig. 2.4); otherwise, data will be collected to permit

FIG. 2.4 Isolation of the adjacent building from the considered URM school building. (Permission from DRES.)

Example of a Two-Story Unreinforced Masonry Building Chapter

2

17

evaluation of the effects of building pounding, wherever a portion of an adjacent structure is located within 4% of the height above grade at the location of potential impact [2].

2.3 FACTORS INFLUENCING URM SEISMIC DAMAGE The extent of damage to URM buildings depends on the parameters below [3].

2.3.1 Seismic Intensity and Other Strong-Motion Characteristics Seismic structural damage depends mainly on the earthquake record characteristics, e.g., magnitude, focal depth, fault mechanism, duration, number of effective cycles, Arias intensity, cumulative absolute velocity (CAV), peak ground acceleration (PGA), peak ground velocity (PGV), and dominant frequency. However, in some cases, there are researches with contradictory results which have proven each of these parameters to be the most effective one in determination of structural damage. For example, Bommer et al. [4] pointed out that the near-field records which impose considerable energy on the structures in a short period of time tend to bring about more severe damage compared to far-field ground motions; however, Kostov and Koela [5] stated that the opposite is true, as near-field records cause smaller damage compared to farfield earthquakes, which usually have significant CAVs.

2.3.2 Geometrical Characteristics of URM Buildings Geometry of URM buildings including dimensions, walls locations, roof system, opening location, and also foundation is one of the most influential parameters in their seismic performance. IT should be noted that there are strict regulations in different seismic design codes which necessitate regular plan in terms of limiting the length to width ratio or any protrusion in the plan. Based on Iranian National Building Code, Part 8: Design and Construction of Masonry Buildings [6], the most important geometry regulations of URM buildings are categorized as follows: - Geometry of plan l Length must not exceed width by >3 times; l Plan should be symmetric in two axis; l Plan should not have any unusual protrusion or concavity; - Limitations of height and number of stories l Maximum number of stories above the ground level is 2; l Load transfer path to the foundation should be continuous; l Sudden change in mass and stiffness of adjacent stories should not occur;

18

Advanced Design Examples of Seismic Retrofit of Structures

- Limitations of structural walls l Maximum free length of 5 m; l Maximum free height of 4 m; l Height to thickness ratio in regions with high seismic activity 50% of that in the adjacent floors, the diaphragm is deemed to be irregular [10]. All the diaphragms are regular in the studied building in this chapter. Out-of-Plane Based on Code 360, when one of the lateral load-bearing components in a story is misaligned compared to other adjacent components, the building is deemed to be irregular [10]. An example of this type of irregularity is when for some reason, for example, architectural limitation, a masonry wall is placed eccentric with respect to the axis on which other walls are placed. In the present example building, there is no such condition and all the walls are aligned in several axes to complete that particular line of resistance. Nonparallel Sometimes, the lateral load-bearing components of the buildings are aligned in way that none of the building’s main directions is alongside those components. In this case, the building is considered irregular by Code 360 because of the existence of “nonparallel” load-bearing components [10].

2.5.4.2 In Height (Vertical) There are numerous cases in which vertical irregularities of buildings resulted in major problems. While the horizontal irregularities can pose extra seismic demands on some structural components, mainly because of excessive torsions in the stories, the vertical irregularities can cause more severe dangers, for example, collapse that is directly attributed to the building’s gravitational load path. All vertical elements in the seismic-force-resisting system should be continuous with the foundation. Vertical irregularity, that is, a discontinuity of strength, stiffness, geometry, or mass in one story with respect to adjacent stories should be avoided [2].

48

Advanced Design Examples of Seismic Retrofit of Structures

Geometrical Based on Code 360, when dimensions of a story are larger than 130% of its adjacent stories, the building is considered irregular in geometry [10]. The example building satisfies Code 360 regulation in this regard, and hence is regular in geometry. Mass According to Code 360, the total mass of each story should be within 50% difference with that of its adjacent buildings; otherwise, the building is deemed to be irregular in mass [10]. For the example building, the total masses of the first and second stories are 1055 ton and 836 ton, respectively. Consequently, this building is regular in mass. Disconnection of Load-Bearing Elements Sometimes there is discontinuity in the lateral load-bearing system in height of the building. This condition, which is classified by Code 360 as an irregularity, results in an overturning effect on beams, diagrams, columns, and shear walls [10]. For the studied building in this example, there is no discontinuity in corresponding walls of the stories, and hence the building is regular. In Strength (Weak Story) The sum of the shear strengths of the seismic-force-resisting system in any story in each direction shall not be QUD

(2.38)

where: m ¼ component capacity modification factor to account for expected ductility associated with this action at the selected structural performance level. The m-factors for use with corresponding expected strength shall be obtained from Table 2.11;

Unconfined Confined Unconfined Confined

Rocking

Bed-joint sliding

Rocking

Bed-joint sliding

N.A.

Bed-joint sliding

2heff  1:5 L 3heff  1:5 L

1:5heff  1:0 L

3:0heff  3:75 L

1:5heff  1:0 L

2.0

3.0

1:5 

3.0

1:5heff  1:5 L

LS

1.0

1.0

1.0

1:0 

IO

Performance Level

4:0heff  5:0 L

4:5heff  2:0 L

3heff  2:0 L

4.5

3.0

4.0

2:0 

CP

a

m-factors for rocking apply only for walls and wall piers with fa/fm0 less than or equal to 4%, unless it can be demonstrated by analysis using moment curvature or other acceptable means that toe crushing does not occur at the expected pier drift; otherwise, walls and wall piers shall be considered force controlled. Alternatively, nonlinear procedures and acceptance criteria should be used.

Code 360-12

N.A.

Rocking

ASCE 41-13

Confinement

a

Failure Mode

Code

TABLE 2.11 m-Factors in LSP for URM In-Plane Walls and Piers

80 Advanced Design Examples of Seismic Retrofit of Structures

Example of a Two-Story Unreinforced Masonry Building Chapter

2

81

QCE ¼ expected strength of component deformation-controlled action of an element at the deformation level under consideration which is determined according to Section 2.7.5.1; and κ ¼ knowledge factor defined in according to Table 2.12 which is assumed to be 1.0 because usual level of knowledge exists about the example buildings including material properties, as-built sketches, etc. This factor is used to account for uncertainty in the collection of as-built data, a knowledge factor, κ, shall be selected considering the selected performance objective, analysis procedure, and data collection process. It is noteworthy that only Code 360 considers the effects if confining ties in capacity calculation for URM walls, whereas the previous version of this code, that is, Code 360-2006, does not take this effect into account. ASCE 41 is also silent about confined masonry walls.

2.7.6.2 Force-Controlled Actions Acceptance criteria for force-controlled actions in components shall satisfy Eq. (2.39): κQCL > QUF

(2.39)

where QCL ¼ lower-bound strength of a force-controlled action of an element at the deformation level under consideration which is determined according to Section 2.7.5.2. Code 360 allows increasing the lower-bound strength of a force-controlled action for unreinforced confined masonry walls by 20% [10].

2.7.7 Final Results and Conclusions The values of QCE and QCL, together with their vulnerability, failure mode, and their DCR for the walls in the example building, are presented in Appendix Tables A-C-2-11, A-C-2-12, and A-C-2-13, for the example building with a rigid diaphragm, with a flexible diaphragm having horizontal ties, and with a flexible diaphragm without horizontal ties, respectively. As an example, the related calculations of Wall#1 on the first row of these tables are as follows. The vulnerability of the walls of the example building in the two stories under various diaphragm conditions are shown in Figs. 2.40–2.42. In these figures, the vulnerable walls are shown in blue. Also, the failure mode and their DCR are also shown besides each wall, with “B” and “R” indicating bed-joint sliding and rocking failure modes, respectively. As can be seen, the example building is vulnerable in all the considered cases. As an example, calculations of DCR for different failure modes of Wall#1 are presented here.

From default values

0.75

Material properties

Knowledge factor (κ)

LSP, LDP

0.75

Analysis procedures

Knowledge factor (κ)

1.00

0.75

1.00

All

Enhanced or lower

From drawings and tests

Visual

b

a

0.75

All

Special

1.00

From usual tests

Comprehensive

Design drawings or equivalent

Usual testing

From default values

Comprehensive

No drawings

All

LS or lower

Usual

Level of Knowledge

If the building meets the benchmark requirements of standard material, e.g., ASTM, then κ ¼ 1.0. If inspection or testing records are available to substantiate the design drawings, then κ ¼ 1.0.

Enhanced or lower

0.90a,b

From design drawings

Retrofit level

Code 360-12

Visual

Condition assessment

Minimum

Visual

No tests

Design drawings or equivalent

Drawings

LSP, LDP

Analysis procedures

Testing

LS or lower

ASCE 41-13

Performance level

Data

TABLE 2.12 Data Collection Requirements

1.00

All

Special

1.00

From usual tests

Visual

1.00

From comprehensive tests

Comprehensive

Construction documents or equivalent

Comprehensive testing

All

Higher than LS

Comprehensive

82 Advanced Design Examples of Seismic Retrofit of Structures

Example of a Two-Story Unreinforced Masonry Building Chapter

1.29 B

1.86 R 2.15 R

1.19 R

1.22 R

1.22 R

1.24 R

1.22 T

1.77 R

2.46 T

2.46 T

0.85

0.77

1.36 T

2.04 T 0.33 0.29

0.83

0.85

0.85

1.13 R

1.99 R

0.38

3.34 T

1.59 B

0.88

1.59 B

0.44 0.95

0.42 0.39

1.13 R

0.61 1.1 B

1.28 B

1.23 R

83

2

0.79

0.8 1.74 B 1.18 B

1.28 B

2.46 T

1.3 B

2.46 T

6.9 R 2.14 R

1.18 R

1.24 R

1.21 R

1.2 R

4.57 R

6.9 R2.8 R

1.71 R

1.67 R

1.64 R

0.96

1.09 B

0.67

0.89

0.89

2.9 R

2.14 R

1.21 R

(A) 0.98

1.13 R

0.9

0.87

0.9

1.05 B

0.85

0.36 1.28 B

2.36 B

1.43 B

0.81

0.81

2.06 B 0.73 0.55

2.36 B

0.8

0.81

0.81

1.88 B

1.68 B 0.65

1.4 B 1.28 B

0.8

0.79 0.73

0.71

1.03 R

0.85

0.83

0.82 1.42 B

3.87 B 1.06 B

1.43 B

2.36 B

2.36 B

1.2 B 2.34 R

1.11 R

0.97

0.84

0.9

0.92

0.9

2.74 R 2.341 R64 R 1.34 B

1.42 B

1.51 B

1.7 R

1.1 R

(B) FIG. 2.40 Plan of the vulnerable walls of the example building with a flexible diaphragm having horizontal ties. (A) Floor story. (B) First story.

- For a rigid diaphragm: DCRb ¼

fUD mb Vbjs

DCRb ¼

8463 ¼ 0:33 3  8493

DCRr ¼

fUD mr Vr

8463 ¼ 0:95 1:55  5726 fUF DCRd ¼ Vdt

DCRr ¼

DCRd ¼

3005 ¼ 0:31 9549

3.39 R 4.67 R

1.54 R

1.81 R

1.92 R

1.81 R

1.32 B

1.65 B 3.66 B

1.91 B

3.66 B

1.16 B

1.14 B

2.62 R

1.3 B

46.56

1.16 B

2.68 B R37.8 R

2.32 B 7.44 R

1.19 B

4.97 B

4.24 R

2.52 B

2.73 R

1.12 B

7.78 R 9.03 R

8.93 R

1.62 R

1.62 R

2.76 R 13.76 R

1.19 B

1.21 B

1.16 B

1.19 B

2.49 B 1.91 B

3.66 B

2.16 B

3.66 B

1.66 B

11.36 R 21.79 R 11.365R1.14 R 1.93 R 4.59 R

1.44 R

1.89 R

1.68 R

1.68 R

1.6 R

1.72 R

1.55 R

4.96 R

1.25 B

1.25 B

2.07 R

4.39 R

(A) 1.66 R 2.26 R

1.24 B

1.25 B

1.26 B

1.25 B

1.23 B

1.7 R

1.28 B

1.22 B

7.13 R 1.92 B

2.46 B

2.83 B

2.13 B

2.75 B 3.53 B

2.15 B

3.53 B

14.33 R

17.39 R

1.15 B

1.15 B

1.15 B

3.03 R

1.17 B

3.31 R 3.7 R

3.72 R

1.16 B

1.16 B

1.14 B

1.17 B

1.16 B

1.15 B 2.11 B

5.8 B 1.62 B

2.15 B

3.53 B

3.53 B

1.98 B 19.91 R 27.73 R 19.91 2.47 R R

2.28 R

1.23 B

1.25 B

1.24 B

1.24 B

1.24 B

1.26 B

1.25 B

1.25 B

2.38 R

2.18 R

(B) FIG. 2.41 Plan of the vulnerable walls of the example building with a flexible diaphragm without horizontal ties. (A) Floor story. (B) First story.

FIG. 2.42 Plot of damage-progression index versus earthquake severity for unretrofitted structures (ABC) and for stability-based (GHI) and strength-based (DEF) retrofitted structures [16].

Example of a Two-Story Unreinforced Masonry Building Chapter

fUF Vtc 3005 DCRt ¼ ¼ 0:5 5953 DCRt ¼

Therefore, this wall is not vulnerable. - For a flexible diaphragm having horizontal ties: fUD mb Vbjs 9812 ¼ 0:39 DCRb ¼ 3  8493 fUD DCRr ¼ mr Vr 9812 ¼ 1:11 DCRr ¼ 1:55  5726 fUF DCRd ¼ Vdt 3483 ¼ 0:36 DCRd ¼ 9549 fUF DCRt ¼ Vtc 3483 ¼ 0:59 DCRt ¼ 5953 DCRb ¼

Therefore, rocking is the failure mode of this wall. - For a flexible diaphragm without horizontal ties: fUD mb Vbjs 19, 558 DCRb ¼ ¼ 1:15 2  8493 fUD DCRr ¼ mr Vr 19, 558 DCRr ¼ ¼ 2:28 1:50  5726 fUF DCRd ¼ Vdt 6944 DCRd ¼ ¼ 0:87 7958 DCRb ¼

2

85

86

Advanced Design Examples of Seismic Retrofit of Structures

fUF Vtc 6944 DCRt ¼ ¼ 1:40 4961 DCRt ¼

Therefore, rocking is the failure mode of this wall. From these figures, several conclusions can be drawn, as follows: l

l l

l

The inclusion of horizontal ties can significantly reduce the vulnerability of the building; especially for the internal longer walls. The building with the rigid roof has the least vulnerability. Generally speaking, the longer walls are more vulnerable in the building with a rigid roof. This is because the shear force demand is distributed between the walls stiffness-proportionally and longer walls contribute more to load-bearing. Because in the transverse direction, all the walls have the characteristics in terms of the length and gravitational load-bearing contribution, the inclusion of horizontal ties and/or a rigid roof is ineffective in reducing their vulnerability.

2.8 RETROFIT MEASURES 2.8.1 Strength Versus Stability-Based Design Approach According to the concept introduced by Tolles et al. [16], two fundamental design approaches can be taken to improve the earthquake performance of masonry buildings: strength-based design and stability-based design. The former, which is the general traditional design approach, assumes the elastic behavior of the building. The latter is concerned with the overall performance of the building and with assuring structural stability during the postelastic, postyielding phase. Stability-based design features can reduce the potential for severe structural damage and collapse after yielding has occurred. Implementation of strength-based design usually indicates that masonry buildings would not perform well during even moderate seismic ground motions, during which the masonry material will fail. Because masonry buildings have massive walls and the masonry itself is a low-strength material, the dynamic or equivalent static forces are large and the tensile properties of the material are easily exceeded. While a strength-based analysis can accurately predict when cracks will occur, it cannot provide insight into the postelastic performance of masonry buildings. On the other hand, a stability-based design analysis can take advantage of the unique characteristics of the postelastic performance of adobe and the effects of a proposed retrofit system. The extent of retrofit intervention required to stabilize different parts of a typical masonry building is often relatively small and relies on many of the inherent properties of these buildings. Nevertheless, the current trend in engineering design, that is, performancebased design (PBD) is to design for multiple, specifically defined levels of performance at different earthquake levels. The fundamental goal of

Example of a Two-Story Unreinforced Masonry Building Chapter

2

87

performance-based design is to predict a building’s response accurately during increasing levels of seismic excitation. With the state-of-the-art capabilities of numerical simulation and the large experimental data and earthquake field observations, it is now possible to predict accurately many response characteristics of masonry buildings. In some cases, for example, adobe buildings and historic structures, for which the current design codes approaches are strength-based if not silent, the performance levels are usually judged by available test data, numerical analysis and simple hand calculations (refer to Chapter 6). These two design strategies are not mutually exclusive: the strength-based approach addresses the elastic behavior of the structure, while the stabilitybased approach addresses the postelastic performance. In fact, the two approaches can be complementary. The sole use of the strength-based approach can be justified only when there is a known relationship between the level at which yielding first occurs and the level at which the structure collapses. In the case of masonry buildings, there is no clear relationship between these two events. Some measures that are designed to improve the elastic behavior of a building may have little or no effect on structural stability during major seismic events. Yet stability-based retrofitting measures, which may have little effect on the initiation or prevention of minor cracks, may have a significant impact on the development of severe damage and on preventing collapse. The conceptual representation of different retrofit approaches is shown in Fig. 2.43 in which a dimensionless damage index indicating the overall quantitative structural damage is plotted against the earthquake intensity, for

100%

Safety benefits

Incremental seismic rehabilitation Optimal risk reduction with minimal cost and disruption

Single-stage seismic rehab maximum cost and disruption

Delayed single-stage rehab maximum cost and disruption

Delayed single-stage rehab maximum cost and disruption

0% 0 Years

Today

10 Years

20 Years

30 Years

Building life

FIG. 2.43 Life-cycle benefit analysis of ISR method versus SSR method [1].

40 Years

88

Advanced Design Examples of Seismic Retrofit of Structures

example, PGA. The path ABC indicates a typical unretrofitted structure in which point “B” is the threshold of the irreparable damage. As can be seen, a small increase in earthquake intensity from point “B” leads to a large increase in damage index up to the point “C.” If retrofitted according to the strengthbased approach, the performance of the building follows path DEF. A significantly higher earthquake intensity is required to cause low to intermediate levels of damage index. However, the performance improvement in larger earthquake intensities are small compared to the corresponding unretrofitted building. In other words, in severe earthquakes, the vulnerability of the building retrofitted according to the strength-based approach decreases marginally. Nonetheless, considerable reduction in the vulnerability of the building is achieved thanks to the retrofitting method based on the stability-based approach. However, marginal improvement compared to the corresponding unretrofitted building results in the lower earthquake intensities. During earthquakes, tensile, shear and even compressive stresses in masonry parts exceeds their strength and these results in cracking and crushing of URM buildings. However, the main weakness of many URM buildings is not lack of strength, but lack of ductility. The extent of damage in ductile structures depends on the earthquake’s magnitude. In other words, in an earthquake with the magnitude of 7.0, severe damage can be expected in the central parts of the affected areas and by receding from the epicenter, the severity of damage decreases. However, this does not follow for URM buildings which collapse in central parts, and suddenly we encounter some areas with almost unaffected URM buildings. The reason behind this is the behavioral parameters of URM buildings and also records’ characteristics. Seismic performance of a URM building can be summarized as follows [3]: (A) Earthquake is not strong enough to demolish URM building and URM building maintains its strength capacity. (B) Earthquake can cause some damage in URM building in the last seconds of excitation. However, since these changes occur in the last seconds of the earthquake, they cannot cause major damage in the building. (C) Earthquake intensity is high and, in the initial seconds, causes structural damage. Severe strength and stiffness degradation occurs, which results in the collapse of the building. These three stages depend on earthquake magnitude and usually stage C happens in earthquakes with large magnitude for the masonry buildings located in areas close to the epicenter. Since the dissipation of the seismic waves with distance, URM buildings can act according to stages A or B according to Fig. 2.43. As a result, borders in which performance of URM buildings changes from stage C to stage B can be considered. The area inside this border is named the “cracking threshold area.” For instance, in the Manjil earthquake, the cracking threshold area was found to be 48 km from Manjil, with the local PGA of 0.36 g.

Example of a Two-Story Unreinforced Masonry Building Chapter

2

89

2.8.2 Incremental Seismic Rehabilitation As mentioned in the first part of this chapter, the present example deals with retrofitting of a typical two-story unreinforced masonry building. Speaking of school buildings, some challenges arise for their retrofit in addition to those in ordinary residential buildings. Although vulnerable school buildings need to be replaced with safe new construction or rehabilitated to correct deficiencies, for many school districts new construction is limited (at times severely) by budgetary constraints, and seismic rehabilitation is expensive and disruptive. However, an innovative approach that phases a series of discrete rehabilitation actions implemented over a period of several years, incremental seismic rehabilitation, is an effective, affordable, and nondisruptive strategy for responsible mitigation action. It can be integrated efficiently into ongoing facility maintenance and capital improvement operations to minimize cost and disruption. The strategy of incremental seismic rehabilitation (ISR) makes it possible to start now on improving earthquake safety in a school district [1]. The benefits of seismic rehabilitation of a building are [1]: l l l l

reduced reduced reduced reduced

risk of death and injury of students, teachers, and staff; building damage; damage of school contents and equipment; and disruption of the delivery of school services.

Incremental rehabilitation phases seismic rehabilitation into an ordered series of discrete actions implemented over a period of several years, and whenever feasible, these actions are timed to coincide with regularly scheduled repairs, maintenance, or capital improvements. Such an approach, if carefully planned, engineered, and implemented, will ultimately achieve the full damage reduction benefits of a more costly and disruptive single-stage seismic rehabilitation (SSR) [1]. An initial prioritization of seismic rehabilitation increments should be established primarily in terms of their respective impact on the overall earthquake resistance of the structure. Facility managers will begin with these priorities when determining the order of seismic rehabilitation increments to be undertaken. However, the final order of increments may deviate from this priority order depending on other planning parameters [1]. When following the ISR concept, a “worst first” approach should be used. For example, in case of the URM buildings, the walls usually pose a great danger to the overall stability of the building; as a result, retrofitting of walls should be placed as a high priority. In the next phases, the roofs and foundation may be considered for retrofit. A generalized life-cycle benefit analysis shows that incremental approaches can return a substantial portion of the expected benefits of single-stage seismic rehabilitation carried out now. The schematic diagram shown in Fig. 2.44 illustrates such a life-cycle benefit analysis. The three wide arrows represent the benefits of SSR occurring at three points in time: now, in 20 years, and in

90

Advanced Design Examples of Seismic Retrofit of Structures

(A)

(B)

FIG. 2.44 Examples of retrofit of masonry walls by shotcrete. (A) Internal walls. (B) External walls. (Permission from DRES.)

40 years. Clearly, the largest benefit derives from a single-stage rehabilitation done now, and it is designated as 100%. The benefits of single-stage rehabilitation done in the future must be discounted and expressed as some percentage lower than 100%, as represented by the decreased arrows. The stepped portion of the diagram represents incremental rehabilitation starting soon, and completed in four increments over 20 years. The benefits of the future increments must also be discounted, and the benefit of the completed incremental rehabilitation is therefore expressed as a percentage lower than 100%, but higher than the single-stage rehabilitation in year 20. Reducing the overall duration of the incremental rehabilitation will increase its benefit, and extending the duration will decrease it [1].

2.8.3 Common Methods 2.8.3.1 Shotcrete In the retrofit of masonry buildings, shotcrete refers to the method in which reinforcing mesh (usually steel) is installed on one side or both side of existing masonry walls; then, under a specified pressure, fine-aggregate concrete or mortar is poured to the surfaces of the walls. In order to improve the bonding between the added layer of concrete to the walls, it is usually necessary to remove the walls’ finishing before installation of the reinforcing mesh. Fig. 2.45 shows examples of retrofit of masonry walls by shotcrete. Shotcreting one or both sides of masonry walls have proved to be a very effective method in reducing seismic vulnerability of masonry buildings. Shotcreted masonry walls not only have larger strength capacities, but also show larger ductility capacity. ElGawady et al. [17] performed static cyclic testing on unretrofitted and shotcreted specimens. The ultimate lateral load resistance of the walls was increased by a factor of approximately 3.6. An increase in the maximum force capacity of about 3 was reported by Abrams and Lynch [18].

Example of a Two-Story Unreinforced Masonry Building Chapter

2

91

FIG. 2.45 An example of grout injection. (Permission from Desoi.)

A larger increase in this parameters of 6–25 was observed by Kahn when using thicker shotcrete layers [19]. In order to transfer the shear stress across shotcrete-masonry interface, shear dowels (6–13 mm diameter @ 25–120 mm) are fixed using epoxy or cement grout into holes drilled into the masonry wall [18–20]. Nonetheless, the results of a study by Kahn reveled that a bonding agent like epoxy is required to be painted or sprayed on the brick so that adequate brick-shotcrete bond is developed [19]. However, there is no agreement on brick-to-shotcrete bonding and the need for dowels. Diagonal tension tests of single and double wythe URM panels retrofitted with shotcrete showed that dowels did not improve the composite panels response or the brick-shotcrete bonding, and header bricks satisfactorily joined the wythe of existing masonry panels. Furthermore, Kahn recommended wetting the masonry surface prior to applying shotcrete. He shows that such brick surface treatment does not significantly affect the cracking or ultimate load, and extends the inelastic deformations in a limited fashion. The negative points regarding the use lie in the facts that use of shotcrete is timeconsuming, creates disturbance in occupancy, and affects the esthetics [21].

2.8.3.2 Ferrocement Covering of the Walls Ferrocement consists of closely spaced multiple layers of hardware mesh of fine rods with reinforcement ratio of 3%–8% completely embedded in a high strength (15–30 MPa) cement mortar layer (10–50 mm thickness) [22]. As mentioned by Abrams et al. [23], “ferrocement overlay” refers to coating of concrete reinforced with steel hardware cloth. The steel hardware cloth was 19 gauge wire 1 mm diameter with 13 mm grid spacing. The cement plaster coating was made of a 1:3 volume ratio of Portland cement and sand with water added until a workable consistency was achieved. The compressive strength of the cement was approximately 6.9 MPa.

92

Advanced Design Examples of Seismic Retrofit of Structures

Ferrocement is ideal for low-cost housing since it is cheap and can be used by unskilled workers. It improves both in-plane and out-of-plane behavior. The mesh helps to confine the masonry units after cracking and thus improves in-plane inelastic deformation capacity. In a static cyclic test [18], this retrofitting technique increased the in-plane lateral resistance by a factor of 1.5 [23].

2.8.3.3 Repointing In many cases, the surfaces of masonry walls are exposed; over the long term, this results in weathering and erosion of masonry by freeze and thaw, sunlight, wind, rain, and snow [24]. In cases where bricks are of good quality but the mortar is poor, the mortar can be replaced to some extent with a higher-strength bonding material. The advantages of this technique include minimal cost and convenience of implementation. However, this method is not sustainable and the success of this technique lies in the compatibility of the new mortar with that of existing bricks [21]. 2.8.3.4 Tying Paralleled Walls One of the main causes of collapse of an arched roof is the unbalanced motions of the support walls. If the walls move monolithically during seismic actions, arched roofs can probably withstand earthquakes without experiencing serious damage because they are among the most stable geometrical roof systems. In order to enforce in-phase response of the support walls, they can be tied together. This is usually done by steel rods passing through the parallel walls. For more information, see Chapter 6, “Shaking Table Tests” section. 2.8.3.5 Adding Tie Columns The confinement prevents disintegration and improves ductility and energy dissipation of URM buildings, but has a limited effect on the ultimate load resistance [25, 26]. For new constructions, according to EC 8, no contribution of vertical confinement to lateral resistance should be taken into account in the design [27]. However, the real confinement effect mainly depends on the relative rigidity between the masonry wall and the surrounding frame, and to a lesser extent on material characteristics. Before cracking, the confinement effect can be neglected [20, 26, 27]. At ultimate load, the confinement increased the lateral resistance by a factor of 1.2 [25, 26]. However, for walls with a higher aspect ratio, the confinement increased the lateral resistance by a factor of 1.5 [27]. In addition, the confinement improved the lateral deformations and energy dissipation by >50% [25, 27, 28]. 2.8.3.6 Grout and Epoxy Injection Grout injection is a popular strengthening method especially for historic buildings, as it does not alter the esthetic and architectural features of the existing buildings. The main purpose of injections is to restore the original integrity

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(A)

2

93

(B)

FIG. 2.46 Examples of using external reinforcement. (A) Using horizontal and vertical steel bamboos [34]. (B) Using diagonal steel strips [35]. ((A) Permission from Taylor and Francis. (B) Permission from ASCE.)

of the retrofitted wall and to fill the voids and cracks, which are present in the masonry due to physical and chemical deterioration and/or mechanical actions. For multiwythe masonry walls, injecting grout into empty collar joint enhances composite action between adjacent wythe. The success of a retrofit by injection depends on the injectability of the mix used, and on the injection technique adopted [22]. The technique is effective at restoring the initial stiffness and strength of masonry. A cement-based grout injection is capable of restoring up to about 0.8 of the unretrofitted masonry compressive strength [29], 0.8–1.1 of the unretrofitted wall in-plane stiffness, and 0.8–1.4 of the wall unretrofitted in-plane lateral resistance [30–32]. In addition, a cement-based grout injection can increase the interface shear bond of multiwythe stonewalls by a factor of 25–40 [33]. Walls retrofitted with epoxy injection tend to be stiffer than the unretrofitted, but the increase in stiffness (10%–20%) is much less dramatic than the increase in strength. The increment in lateral resistance ranged from 2 to 4 times the unretrofitted resistance. An example of grout injection of masonry walls is shown in Fig. 2.46.

2.8.3.7 External Reinforcement External reinforcement on masonry walls are usually performed by adding horizontal, vertical, and/or diagonal elements in the form of steel strips and bamboo canes. In designing the retrofitting elements, the relative rigidities of the unretrofitted structure and the new steel bracing are an important factor that should be taken into consideration. In an earthquake, cracking in the original masonry structure is expected and after sufficient cracking has occurred, the new steel system will have comparable stiffness and be effective [36, 37].

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Advanced Design Examples of Seismic Retrofit of Structures

FIG. 2.47 An example of poststressing of masonry walls. (Permission from Cintec.)

The vertical and diagonal bracing improves the lateral in-plane resistance of the retrofitted wall by a factor of 4.5 [35]. As the results of Somi’s tests shows [38], the improvement in the lateral resistance was limited by crushing of the masonry at ends (toes) followed by vertical strips’ global buckling. Examples of using external reinforcement are shown in Fig. 2.47.

2.8.3.8 Using Center-Core Rods The center-core system consists of a reinforced, grouted core placed in the center of an existing URM wall. A continuous vertical hole is drilled from the top of the wall into its basement wall. The core achieved by this oil-well drilling technique may be 50–125 mm in diameter, depending on the thickness of the URM wall and the retrofitting required. With existing technology, this core can be drilled precisely through the entire height of a two- or three-story masonry wall. The drilling is a dry process, with the debris removal handled by a vacuum and filter system that keeps the dust to a minimum. After placing the reinforcement in the center of the hole, a filler material is pumped from the top of the wall to the bottom so that the core is filled from the bottom under pressure controlled by the height of the grout. Shear tests by Plecnik et al. [39] show that specimens made with cement grout were generally 30% weaker than specimens made with sand/epoxy or sand/polyester grouts. This technique is successfully used to double the resistance of URM wall in a static cyclic test. Although a high lateral displacement was achieved during the test, the energy dissipated was limited. The tensile yield of the bar did not occur due to the bar anchorage problem. However, the system has several advantages: it will not alter the appearance of the wall’s surface, and the function of the building will not be impaired since the drilling and reinforcing operation can be done externally from the roof. The main disadvantage to this technique is that it tends to create zones with widely varying stiffness and strength properties.

Example of a Two-Story Unreinforced Masonry Building Chapter

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2.8.3.9 Posttensioning There has been little application of this technique; posttensioning is mainly used to retrofit structures characterized as monuments. Tendons are placed inside steel tubes (ducts) either within holes drilled along the mid-plane of the wall or along groves symmetrically cut on both surfaces of the wall. Holes are cement grouted and external grooves are filled with shotcrete [40, 41]. In this case, the tendons are fully restrained (i.e., not free to move in the holes). This is true even if the tendon is unbonded, that is, no grout is injected between the duct and the tendons [42]. One of the major drawbacks for using steel bars is corrosion. However, fiber-reinforced plastic presents a promising solution for this problem [43]; in addition, this method as a retrofit solution may result in a negative response of masonry walls with significant vertical loads, such as walls in the lower stories of multistory building and also walls with low-quality material. Vertical posttensioning results in substantial improvement in wall ultimate behavior for both in-plane and out-of-plane; in addition, it improves both cracking load and redistribution of internal forces. Rosenboom and Kowalsky [40] show that for cavity walls, the posttension grouted specimen has lateral resistance much higher (40%) than the ungrouted one. For grouted specimens, although to bonding the bars have insignificant effect on lateral resistance; the specimen which has unbonded bars has higher lateral drift (70%) over the bonded specimen. The unbonded grouted specimen has a drift up to 6.5%. However, unbonded posttension tendons may show low energy dissipation due to the lack of yielding of reinforcement [44]. An example of grout injection of masonry walls is shown in Fig. 2.48. 2.8.3.10 Safe Room The main aim of a “safe room” is to mitigate human casualties during earthquakes. In other words, the performance improvement of the building retrofitting with a “safe room” cannot be considered more than “life safety.” The “safe room” is a 3D steel, concrete-filled frame which is installed in some rooms which are considered vulnerable against earthquakes. This room will prevent

(A)

(B)

FIG. 2.48 Schematic view of the safe room [45]. (A) Safe rooms extracted from the building. (B) Safe room elements.

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FIG. 2.49 Schematic representation of the retrofitted walls (shown with inclined stripes).

the roof from collapsing on the residents during an earthquake. The weight of each frame is about 500 kg. In other words, with an affordable budget for the people, each house or school will be equipped with a “safe room” [45]. A schematic view of the safe room is presented in Fig. 2.49.

2.8.3.11 Placement of Steel, Polymer, or Plastic Grids Two types of polymer mesh that have been used to retrofit URM structures are an industrial geo-grid and a weaker mesh that is usually used as a “soft” fence on construction sites. The mesh is wrapped around the wall and then coated with a mud plaster finish. Three variations of the geo-grid (100%, 75%, and 50% area coverage) and one soft mesh system (80% area coverage) were tested by Blondet et al. [46]. The results proved satisfactory responses of retrofitted specimens compared to those in the control specimens. Another method of reinforcement uses PP packaging strips that can be found in many packaged items. Testing under static loading had been carried out by Macabuag [47], in which two scaled wall sections were constructed and tested under diagonal compression. It was found that the horizontal strips prevent separation of bricks on the same row. Vertical bands increase the frictional resistance between rows and consequently prevent sliding. In conclusion, this method effectively improves the shear resistance of test specimens under static loading, but there was a recurring problem of the mesh snapping at points of stress concentration such as the wall corners. A similar test was carried out at Tokyo University by Meguro et al. [48] under dynamic loading conditions. The testing showed how the retrofit improved the specimen seismic performance significantly, displaying increased load resistance and ductility before failure. Macabuag et al. [49] studied the effect of retrofitting of URM buildings in Nepal using PP meshing, being subjected to artificially generated strong shocks. The study concluded that use of PP mesh prevents spoiling out the masonry blocks, and thus enables the system to accommodate more deformation without collapse.

Example of a Two-Story Unreinforced Masonry Building Chapter

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This steel mesh was applied externally at critical locations of adobe walls such as at corners and free ends. This was then covered with a layer of mortar. A large earthquake (Mw 8.0) occurred in Pisco, Peru on August 15, 2007 resulting in 519 deaths, the collapse of over 70,000 houses, and the serious damage of >33,000 houses. However, five houses in Ica that had been reinforced in 1998 survived the earthquake without suffering any damage. A comparison of various retrofit methods for URM buildings is presented in Table 2.13.

2.8.4 Shotcrete In this part, performance improvement of the considered building by shotcreting method is evaluated. In the absence of the available design codes for determination of the capacity and acceptance criteria of shotcreted masonry walls, the

TABLE 2.13 Comparison of Various Retrofit Methods for URM Buildings [22] Retrofit Method

Pros

Ferrocement

l l l

Low cost Low technology Limited added mass

Cons l l l

l l

Reinforced plaster

l l

Low technology Limited added mass

l l l

Shotcrete

l

l

High improvement in ultimate strength Very significant improvement in energy dissipation

l l l

l l l

Injection

l l

l l

No added mass No effect on building function No space reduction No architectural impact

l

l l l

Space reduction Architectural impact Requires architectural finishing Limited efficiency Limited improvement in energy dissipation Space reduction Architectural impact Required architectural finishing Space reduction Heavy mass Violation of performance level Disturbance occupancy Architectural impact Requires architectural finishing Epoxy create zones with varying stiffness and strength High cost of epoxy No significant increment in ultimate strength using cement-based grout Continued

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Advanced Design Examples of Seismic Retrofit of Structures

TABLE 2.13 Comparison of Various Retrofit Methods for URM Buildings—cont’d Retrofit Method External reinforcement

Pros l l l

High increment in Fur Prevent disintegration Improves ductility and energy dissipation

Cons l l l

l

l

Confinement

l l

Prevent disintegration Improve ductility and energy dissipation

l l

l

l

Posttension

l l

Center Core

l l l

No added mass No effect on building function No space reduction No architectural impact No effect on building function

l l l l

Corrosion Heavy mass Violation of performance level Requires architectural finishing Disturbance occupancy Not easy to introduce Limited effect on ultimate strength Requires architectural finishing Disturbance occupancy High losses Anchorage system Corrosion potential Creation of zones with varying stiffness and strength

results of the studies by Ghiassi et al. [50] are used here. They considered three failure modes for shotcreted masonry walls: sliding, shear-tensile, and flexural. They proposed relations for determination of the capacity for each failure mode. The acceptance criteria similar to the corresponding reinforced masonry walls in ASCE 41-06 [15] were assumed for the shotcreted masonry walls. The details of their proposed relations are presented in the next parts of this chapter.

2.8.4.1 Selection of the Walls for Shotcreting Generally, the vulnerable walls which were determined in the previous sections of this chapter are considered for retrofit. This approach works well for URM buildings without any ties which have flexible diaphragms. In these buildings, each wall reacts independently to the seismic demands and its vulnerability is independent of the vulnerabilities of other walls. However, this is not the case for URM buildings having confined ties and/or with rigid diaphragms. In these buildings, a group of parallel walls reacts to the seismic demand forces and each wall in this group interacts with other walls. In this example, instead of

Example of a Two-Story Unreinforced Masonry Building Chapter

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retrofitting the vulnerable walls, all walls of half of the classrooms on each story are retrofitted in the three considered cases and the results are compared. The schematic representation of the retrofitted walls is shown in Fig. 2.50. The shotcrete layer is assumed to be 6 cm in thickness and the compressive strength of the concrete is 18 MPa. The reinforcement of the shotcrete layer is assumed to be a grid made of φ8@200 mm with the yield strength of 400 MPa for the bars. Some important steps for shotcreting of URM walls are shown in Fig. 2.51 in the form of example photos of some retrofit projects. Moreover, there are some important points to consider for construction of shotcreting of URM walls which are shown in Fig. 2.51. There are, however, some cases in which implementation of shotcrete faced with some problems. The common construction problems of shotcreting of URM walls are listed in Fig. 2.52. These problems can be easily avoided by proper supervision on different phases of the retrofit projects. For more information about the requirements for implementation of shotcrete, the reader is referred to the Practical Instruction for Shotcrete in Seismic Rehabilitation of Schools [51]. Besides shotcreting of walls, many retrofitting projects consist of several steps on other structural parts of URM buildings. The most important steps of these projects related to structural parts other than walls are shown in Fig. 2.53. Progression of the retrofit project on the example building is shown in Fig. 2.54. In this figure, the constructed retrofit details consisted of shotcreting of all the peripheral walls which is different from the assumed retrofitting scheme in this example.

2.8.4.2 Determination of Shotcreted Walls Stiffness Based on the studies by Ghiassi et al. [50], the relation for stiffness determination of shotcreted masonry walls is similar to that of the unretrofitted masonry wall, except for the equivalent modulus of elasticity and shear modulus, which are replaced by their corresponding modulus for masonry material. As an example, consider ASCE 41-13 [2] relation for determination of masonry wall’s stiffness as Eq. (2.44): Ke ¼

1 H3 H + λEm Im Av Gm

where: H ¼ wall’s height; Em ¼ equivalent modulus of elasticity of masonry material; Gm ¼ equivalent shear modulus of masonry material; Av ¼ wall’s cross-sectional area; and λ ¼ 3 and 12 for cantilever and fixed-fixed walls, respectively.

(2.40)

(A)

(B)

(C)

(D)

(E)

(F)

(G) FIG. 2.50 The necessary steps in shotcreting of walls. (A) Removing the walls finishing. (B) Cleaning the walls surface by water jet. (C) Drilling the walls for insertion of shotcrete connection bars. (D) Installation of reinforcement grid. (E) Spraying concrete. (F) Concrete curing. (G) Applying walls finishing and painting. (Permission from DRES.)

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(A)

(B)

(C)

(D)

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101

FIG. 2.51 Some important points for construction of shotcreting of URM walls. (A) Overlapping of reinforcing bars. (B) Overlapping of the reinforcement grids at top and bottom of the wall (connection to the rigid diaphragm and the foundation). (C) Welding of the reinforcement grids at top of the wall to the steel angles in flexible diaphragm. (D) Using proper facility for spraying concrete with targeted pressure. (Permission from DRES.)

Accordingly, the relation for stiffness determination of shotcreted masonry walls is based on Eq. (2.41), in which the equivalent modulus of elasticity and shear modulus are based on regression analysis of several tests data by Ghiassi et al. [50] according to Eqs. (2.42) and (2.43), respectively. The relations for determination of the stiffness of masonry walls in multistory buildings follows the same procedure as per the proposed modifications to the ASCE 41-13 relation based on Eqs. (2.12)–(2.16). Ke ¼

1 3

H H + λEeq Im Av Geq

(2.41)

(A)

(B)

(C)

(D)

(E)

(F)

(G) FIG. 2.52 Common construction problems of shotcreting of URM walls. (A) Damage to the walls surfaces due to excessive removing of walls finishing and also insufficient cleaning of the walls surface. (B) Using improper reinforcement in terms of size and simple rebar; improper overlapping; not using grout in injection of connection bars. (C) Improper dowel bar. (D) Spraying concrete from top to bottom and holding the nozzle not perpendicular to the walls surface. (E) Improper concrete; improper spraying device. (F) Insufficient bars cover. (G) “Hand polishing” the concrete instead of spraying it with a device; also using mortar instead of concrete. (Permission from DRES.)

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(A)

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103

(B)

(C)

(D)

(E) FIG. 2.53 Other necessary undertakings besides shotcreting of walls. (A) Providing the roof with integrity. (B) Providing the roof with integrity. (C) Providing the roof with rigidity (reinforcement). (D) Providing the roof with rigidity (casting concrete). (E) Connection of reinforcement grids to proper foundation. (Permission from DRES.)

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Advanced Design Examples of Seismic Retrofit of Structures

(A)

(B)

(C)

(D)

(E) FIG. 2.54 Progression of the retrofit project on the example building. (A) The building before retrofit. (B) Finalized reinforcement installation. (C) Spraying concrete. (D) Finalized concrete spray. (E) Implementation of the walls finishing. (Permission from DRES.)


 tm Eeq ¼ 0:623 0:070 + 1:10 Ec tc
 tm Geq ¼ 0:190 0:062 + 1:06 Ec tc

(2.42) (2.43)

2.8.4.3 Acceptance Criteria Typically, the shotcrete overlay is assumed to resist all the lateral force applied to a retrofitted wall with the brick masonry being neglected altogether [18].

Example of a Two-Story Unreinforced Masonry Building Chapter

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This is a reasonable assumption for strength design since the flexural and shear strength of the reinforced shotcrete overlay can be many times more than that of the URM wall. This assumption may result in some cracking of the masonry as the reinforcement in the shotcrete strains past yield. This may violate a performance objective for immediate occupancy or continued operation [22]. The Iranian Instruction for Seismic Rehabilitation of Schools [52] considers shear failure for the shotcreted masonry walls only, and neglects the contribution of URM to the strength of these walls. The expected capacity of the shotcreted masonry walls according to this instruction is determined based on Eq. (2.44):


pffiffiffiffi   L (2.44) ; fc0 inMPa QCE ¼ 0:17 fc0 tc L + As fy S where: fc0 ¼ compressive strength of concrete which should be at least 20 MPa during construction; however, this parameter is conservatively assumed to be 15 MPa in design calculations; L ¼ wall’s length; tc ¼ thickness of shotcrete layer; As ¼ area of the each reinforcement bar in steel grid; fy ¼ yield strength of the steel grid; and S ¼ distance of the of each reinforcement bar in steel grid. It is assumed that shear failure in shotcreted masonry wall is a deformationcontrolled action. According to Eq. (2.38), the m-factor and the knowledge factor are conservatively assumed to be 2.0 and 1.0, respectively. However, in this chapter, the capacity of the shotcreted masonry walls is determined using the relations proposed by Ghiassi et al. [50]. Failure Modes Flexural According to Ghiassi et al. [50], the behavior of shotcreted masonry walls can be similar to that of the corresponding reinforced masonry walls. Consequently, the concepts for capacity determination of the latter for different failure modes can be adopted for the former. This is also the case for considering acceptance criteria and m-factors in linear analysis. By assuming plane sections remain plane after deformation, elastic-perfectly plastic behavior of steel bars, neglecting tensile strength of concrete, and assuming the “a” and “α” factors as 0.85 and 0.85, respectively, as shown in Fig. 2.55, the moment capacity of the shotcreted wall is determined based on Eq. (2.45) after some manipulations and simplifications. It is worth noting that in determination of the flexural capacity of the wall, it is assumed that compressive failure of masonry is unlikely. This assumption is justified by the low reinforcement ratio commonly used for reinforcement of shotcrete. Moreover, the majority of masonry buildings are lowrise, which means there are low-to-moderate vertical forces acting on the walls. As a result, the flexural failure of these walls occurs when all the vertical reinforcements yield in tension and compression.

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Advanced Design Examples of Seismic Retrofit of Structures

Lw

A11

X

A12

A13

A14

A15

A16

i

(A) ε1

ε2

c ε3 ε4

(B) fy1

εu

ε5 ε6

fy2

fy3

fy4

afmeq a

(C)

FIG. 2.55 Stress and strain distribution in wall’s section. (A) Cross-section of the retrofitted wall. (B) Strain pattern in walls section by assuming ultimate strain at the far compressive end of the wall. (C) Stress pattern with respect to the assumed strain pattern.


 Pe  ω+α 1 Me ¼ 0:5nAs fye Lw 1 + + Asb fyeb d nAs fye 2ω + 0:722

(2.45)

ω¼

nAs fye Lw tw fmeq

(2.46)

α¼

Pe Lw tw fmeq

(2.47)

where: Me ¼ expected flexural moment of the composite section of the shotcreted wall; fye ¼ expected yield strength of steel bars; Lw ¼ wall’s length; tw ¼ wall’s thickness; n ¼ total number of vertical reinforcement elements in steel grid; As ¼ area of the each reinforcement bar in steel grid; Pe ¼ axial force acting on the wall from gravitational and seismic actions; Asb ¼ total reinforcement area; fyeb ¼ expected yield strength of steel bars in the wall’s boundary elements; d ¼ center-to-center distance of the reinforcement at the two boundary elements of the wall; and

Example of a Two-Story Unreinforced Masonry Building Chapter

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fmeq ¼ equivalent compressive strength of the composite section of the shotcreted wall. The equivalent compressive strength of the composite section fmeq can be determined by assuming compatible strains at shotcreted layer and masonry wall based on Eq. (2.48): fmeq ¼

fm0 tm + fc0 tc tm + tc

(2.48)

where: fm0 ¼ compressive strength of masonry prism; fc0 ¼ compressive strength of concrete in the shotcrete layer; tm ¼ thickness of masonry wall; and tc ¼ thickness of the shotcrete layer. Shear (Diagonal Tension) The proposed relation for determination of the capacity of shotcreted masonry walls with shear failure mode is according to Eq. (2.49) [50]. All terms of this equation except for Vc are included in the relation for determination of reinforced masonry capacity in ASCE 41-13 [2]. Also: Vd ¼ V m + V c + V s + V p
 pffiffiffiffiffi M Vm ¼ 0:083α 4  1:75 Ag fm0 Vde pffiffiffiffi Vc ¼ 0:2 fc0 tc de Vs ¼ 0:5fy Av

H S

Vp ¼ 0:25Pu

(2.49) (2.50) (2.51) (2.52) (2.53)

where: Vd ¼ expected shear capacity of shotcreted masonry wall; Vm ¼ contribution of masonry wall in the shear strength of the wall; Vc ¼ contribution of shotcrete layer in the shear strength of the wall; Vs ¼ contribution of shear reinforcement in the shear strength of the wall; Vp ¼ contribution of vertical loads in the shear strength of the wall; M ¼ flexural moment in the section; V ¼ shear force in the section; de ¼ effective length of the wall equal to 0.8 of the total wall’s length; Ag ¼ wall’s cross-sectional area; fm0 ¼ compressive strength of masonry prism; fc0 ¼ compressive strength of concrete in shotcrete layer; tc ¼ the thickness of shotcrete layer;

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Advanced Design Examples of Seismic Retrofit of Structures

fy and Av ¼ yield strength of reinforcement steel and area of each shear reinforcement element in steel grid, respectively; H ¼ wall’s height; S ¼ distance of the horizontal reinforcement; Pu ¼ vertical loads on the wall according to a proper load combination; and α ¼ coefficient which takes into account the effects of reinforcement on the shear strength of masonry as Eq. (2.54): α ¼ Φ 1 Φ2

(2.54)

Φ1 ¼

15ndb 1 Lw

(2.55)

Φ2 ¼

7:5qdb 1 tm

(2.56)

where: n ¼ total number of shear reinforcement bars in the section; db ¼ diameter of the reinforcement elements in steel grid; q ¼ factor which is 1.0 for one-sided shotcrete and 2.0 for two-sided shotcrete; and tm ¼ thickness of masonry. Sliding Based on Ghiassi et al. [50], the relation for determination of sliding failure of shotcreted masonry walls which is an adaptation of FEMA306 [53] relation for determination of sliding failure capacity of reinforced masonry walls is based on Eq. (2.57). This equation includes the terms related to masonry friction and concrete friction; the assumed values of the frictional coefficient for masonry and concrete are 0.7 and 0.9, respectively. Vsliding ¼ 0:7Pu + 0:9Av fy

(2.57)

m-Factors for Linear Static Analysis As previously stated, design codes are silent about the shotcreted URM walls in terms of introducing their failure modes, providing relations for determination of their strength, and their deformation capacity and acceptance criteria. By studying the results of several previously performed test data, Ghiassi et al. [50] proposed m-factors for linear static analysis. In this example, these proposed factors shown in Table 2.14 for various failure modes and performance levels are taken into account.

2.8.4.4 Results The vulnerability of the walls (unretrofitted and shotcreted) of the example building in the two stories under various diaphragm conditions are shown in Figs. 2.56–2.58. In these figures, the vulnerable walls are shown in blue.

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109

TABLE 2.14 m-Factors in LSP for Shotcreted URM In-Plane Walls and Piers Performance Level

Reference

Failure Mode

fae fme

ρf y fme

IO

LS

CP

Ghiassi et al. [50]

Flexural

0.04

0.07

4

7

8

>0.07

1.5

2.0

2.5

0.07

2.0

3.5

4.5

>0.07

1.0

2.0

2.5

Shear

2

2

3

Sliding

1

3

4

>0.04

0.58 0.8

0.96

0.92

0.37

0.92

1.01

0.91

1.11 0.96

1.14 0.92

0.84 0.22 0.19

0.9

0.96

0.79

0.41

1.12

0.95

0.94

0.81

0.25

0.84

0.93

0.58

1.36

0.31 0.33

0.27

0.94

0.83

0.22

0.89

0.75

0.71

0.76

1.01 0.81

1.14

0.96

1.2

0.6 1.66

0.8

0.99

0.89

0.37

0.37

0.37

0.92

0.92

0.36

0.92

0.91

1.7

1.660.58

0.35

0.92

0.93

0.73

0.44

0.49

0.91

0.92

0.92

0.87

0.66

(A)

0.84

0.96

0.16 0.87

1.06

1.21 0.89

0.94 0.35 0.27

1

0.56

0.92

0.87

0.31

0.91

0.54

1

0.39

1.05

0.52 0.45

0.47

0.94

0.53

0.84

0.89 1.04

1.17 0.55

1.21

1.06

1.03

0.81 0.61

0.84

0.92

0.92

0.4

0.93

0.95

0.72

0.61 0.44

0.35

0.9

0.89

0.77

0.89

(B) FIG. 2.56 Plan of the vulnerable walls of the example partially shotcreted building with rigid diaphragm. (A) Floor story. (B) First story.

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Advanced Design Examples of Seismic Retrofit of Structures

1.24 1.53

1.76

1.85

0.71

1.76

1.94

1.29 0.91

0.47 0.52

1.1 0.14 0.12

1.29

0.45

0.54

0.88

2.03

1.8

1.67

0.71

0.57

1.75

0.16

1.23

0.57

0.38

0.88

0.17 0.61

0.27 0.2

2.03

0.42

1.75

0.73

0.53 0.63 1.21

0.47

0.91

1.72

0.78 5.57

2

2.48

2.24

0.94

0.93

0.94

1.01

1.02

0.4

1.02

1.01

5.71

5.571.95

1.18

3.07

3.14

2.46

0.53

0.59

1.1

1.11

1.11

1.06

1.65

(A)

0.92

1.06

0.18 1.29

0.86

1.69

0.65

0.92 1.06

0.67

1.05

0.42

0.67

0.34 0.26

0.3

0.38

0.39

0.7

0.45 0.36

0.7

0.42

1.02

0.84

0.53

0.69 0.68

1.35 1.07

0.67

1.06

1.08

0.79 1.2

0.88

0.97

0.96

0.42

0.98

1

1.41

1.20.88

0.69

1.78

1.75

1.51

0.93

(B) FIG. 2.57 Plan of the vulnerable walls of the example partially shotcreted building with flexible diaphragm having horizontal ties. (A) Floor story. (B) First story.

The failure mode and their DCR are also shown besides each wall. As can be seen, the majority of the walls in the example building are not vulnerable in all the considered cases thanks to adding a shotcrete layer on half of the walls. As mentioned, the approach of not retrofitting all the vulnerable walls works best for buildings with rigid diaphragms.

2.8.4.5 Construction Details Some example details of shotcreting of URM walls are presented in Fig. 2.59. For more information about the various possible details of shotcreting of URM walls, the reader is referred to the Practical Instruction for Shotcrete Connection in Seismic Rehabilitation of Schools [54]. (a) Connection of perpendicular walls from the external face. (b) Connection of perpendicular walls from the internal face.

Example of a Two-Story Unreinforced Masonry Building Chapter

3.84 3.04

1.46

1.61

2.24

1.61

1.33

1.8

1.32

2.04

2

1.5

1.5

111 2.64

19.42 1.68

2.36

1.23

0.61

0.67 0.91

0.47 0.4

0.91

1.18

47.37 38.45

0.4

7.57

2.78

0.4

2.37 1.24

9.18 2.85

0.41

0.47

1.18

1.21

0.6 1.69

0.47

0.91

3.73

2.2 15.39

2.9

1.37

1.57

1.97

1.86

1.97

0.79

0.87

1.26

0.87

0.73

45.68

15.39 6

2.24

1.59

1.48

3.23

1.23

1.08

0.81

0.81

1.46

5.13

(A) 1.72 1.66

7.71

1.28

1.93

0.86

2.47

0.66

0.84 1.06

0.67 0.51

1.06

1.16

17.5 14.42

0.54

3.05

1.18

1.31 3.72

1.53

0.55

1.17

0.55

0.53

1.18

0.51 0.67

1.35 1.63

0.67

1.06

1.06

0.86 20.03

1.62

0.76

0.87

1.25

0.77

0.81

27.9

20.03 2.56

1.27

0.85

0.8

1.76

1.52

(B) FIG. 2.58 Plan of the vulnerable walls of the example partially shotcreted building with flexible diaphragm without horizontal ties. (A) Floor story. (B) First story.

(c) Connection of internal shotcrete to the foundation. (d) Connection of external shotcrete to the gravels in the absence of proper foundation. (e) Shotcrete around openings. (f ) Shotcrete on internal walls in multistory buildings with filler-joist diaphragm. (g) Shotcrete on external walls in single-story buildings with jack-arch roof made rigid by casting concrete layer. (h) Shotcrete on external walls in single-story buildings with jack-arch roof left as flexible diaphragm.

Detail a

50 cm

Pos.3

Ø12@30cm

Pos.3

(B)

FIG. 2.59 Example details of shotcreting of URM walls. (Permission from DRES.)

Hole d = 4 cm

Ø12@30cm Pos.3

Detail a

Ø--@--cm 5-20

5-20

A

SECTION

Ø10@30cm Hole d=3cm

Pos.1

Ø--@--cm

Detail a

Ø12@30cm Pos.3

Ø10@30cm Hole d=3cm

Pos.1

5-20 Ø--@--cm

Pos.3

A -

Ø10@30cm Hole d=3cm

Ø12@30cm

Pos.1

30°

(A)

A -

Pos.3

Ø--@--cm

Ø12@30cm

A

Ø--@--cm

Ø12@30cm Pos.3

5-20

30°

SECTION

A

5-20

50 cm

30°

A Ø--@--cm

5-20 Ø12@30cm

Pos.3

Detail a

Ø10@30cm Hole d=3cm

Pos.1

20

cm 50 cm

Pos.1 Pos.3

112 Advanced Design Examples of Seismic Retrofit of Structures

30°

50 cm

10 cm

FIG. 2.59, CONT’D

(C)

20

20

20 cm Pos.1

10 cm

Ø10@60cm

(D)

Pos.7

Ø10@60cm Hole d = 3cm

Shotcrete layer (thickness= Var.) Concrete compressive strength 300kg/m3

Hole d = 3cm

Pos.1

30 °

30 ° 30 °

20C m

50

(Continued)

Cm

Pos.1 Pos.7

Max Height 150 cm

Ø10@30cm Pos.1 Hole d = 3cm

Example of a Two-Story Unreinforced Masonry Building Chapter 2

113

10 cm 10 cm

FIG. 2.59, CONT’D

(E)

Pos.1

Ø12@20cm

Pos.4

Ø10@60cm Hole d = 3cm

Ø--@--cm

Grout

Hole d = 3cm , L = 20cm Angle = 30° , 60*60cm

10 cm

cm

10 cm

Shotcrete layer (thickness=Var.) Concrete compressive strength 300kg/m3

100 cm

20

(F)

Shotcrete layer (thickness= Var.) Concrete compressive strength 300kg/m3

30 °

SECTION

Ø10@60cm Hole d= 3cm

Pos.1

°

30

30 °

1 -

Grouting

Ø[email protected] Embedding with epoxy

20

cm

Pos.1 Pos.14

50 cm 2 10 cm 0 cm

Pos.4 Pos.1

114 Advanced Design Examples of Seismic Retrofit of Structures

5

20C m

FIG. 2.59, CONT’D

Grouting

SECTION

° 30

1 -

Shotcrete layer (thickness = Var.) Concrete compressive strength 300kg/m3

Ø10@60cm Pos.1 Hole d= 3cm

Ø--@--cm

Ø12@50cm Pos.11 Hole d = 1.2cm

PL100×8 Continous

cm

10 cm

(H)

50 cm

20

Beam

Grouting

SECTION

Ø12@30cm

1 -

30°

(G)

Width Wall

5

10 cm

PL 120× 60×8

Pos.1

30°

Pos.11

30°

Pos.1 Pos.2

L60× 60×6 Continous

Concrete 300kg/m³

Shotcrete layer (thickness= Var.) Concrete compressive strength 300kg/m3

Ø10@60cm Pos.1 Hole d= 3cm

Ø--@--cm

Horizontal tie

Pos.2

Ø12@50cm

Example of a Two-Story Unreinforced Masonry Building Chapter 2

115

90 cm

6

116

Advanced Design Examples of Seismic Retrofit of Structures

REFERENCES [1] FEMA-395, Incremental Seismic Rehabilitation of School Buildings (K-12) Prepared for the Federal Emergency Management Agency, Washington, DC, USA, (2002). [2] ASCE, Seismic rehabilitation of existing buildings (ASCE/SEI 41-13), American Society of Civil Engineers, Reston, VA, USA, 2013. [3] M. Yekrangnia, A. Mahdizadeh, URM Buildings and Earthquake: In-depth Evaluation of Earthquake Damages to URM Buildings, State Organization of Schools Renovation Development and Mobilization, Tehran, Iran, 2009. [4] J.J. Bommer, G. Magenes, J. Hancock, P. Penazzo, The influence of strong-motion duration on the seismic response of masonry structures, Bull. Earthq. Eng. 2 (1) (2004) 1–26. [5] M. Kostov, N. Koleva, Damage potential of the seismic strong motion, 8th Pacific Conference on Earthquake Engineering, Singapore, 2007. [6] Iranian National Building Code, Part 8: Design and Construction of Masonry Buildings, Tehran, Iran, (2014). [7] Standard 2800. Iranian code of practice for seismic resistant design of buildings. Third Revision, Building and Housing Research Center, Iran (in Persian). [8] Uniform Building Code (UBC), International Conference of Building Officials, vol. 2, (1997). [9] Iranian National Building Code (2014), P.L.o.B., Tehran, Iran. [10] Instruction for Seismic Rehabilitation of Existing Buildings (No. 360), Management and Planning Organization Office of Deputy for Technical Affairs, (2014). [11] Yekrangnia M., Bakhshi A., Ghannad M.A., “Force-Displacement Model for Solid Confined Masonry Walls with Shear-dominated Failure Mode”, Earthq. Eng. Struct. Dyn., https://doi. org/10.1002/eqe.2902. [12] M. Yekrangnia, Risk Assessment of Confined Masonry Buildings, (PhD thesis)Sharif University of Technology, Tehran, Iran, 2016. [13] Abaqus, User’s Manual Version 6.9, Hibbett, Karlsson and Sorensen Inc., Pawtucket, RI, USA, 2005 [14] ASCE 7-10. American Society of Civil Engineers. (2010). Minimum Design Loads for Buildings and Other Structures. [15] ASCE, Seismic Rehabilitation of Existing Buildings (ASCE/SEI 41-06), American Society of Civil Engineers, Reston, VA, USA, 2006. [16] E.L. Tolles, E.E. Kimbro, W.S. Ginell, Planning and Engineering Guidelines for the Seismic Retrofitting of Historic Adobe Structures, Getty Publications, 2003. [17] M.A. ElGawady, P. Lestuzzi, M. Badoux, Retrofitting of masonry walls using shotcrete, in: NZSEE Conference, Paper 45, 2006. [18] D.P. Abrams, J.M. Lynch, Flexural behavior of retrofitted masonry piers, KEERC-MAE Joint Seminar on Risk Mitigation for Regions of Moderate Seismicity, Illinois, USA, 2001. [19] L. Kahn, Shotcrete retrofit for unreinforced brick masonry, 8th WCEE, USA, 1984, pp. 583–590. [20] F. Karantoni, M. Fardis, Effectiveness of seismic strengthening techniques for masonry buildings, ASCE 118 (7) (1992) 1884–1902. [21] S. Bhattacharya, S. Nayak, S.C. Dutta, A critical review of retrofitting methods for unreinforced masonry structures, Int. J. Disaster Risk Reduct. 7 (2014) 51–67. [22] M. ElGawady, P. Lestuzzi, M. Badoux, A review of conventional seismic retrofitting techniques for URM, In 13th International Brick and Block Masonry Conference, 2004, pp. 1–10. [23] D. Abrams, T. Smith, J. Lynch, S. Franklin, Effectiveness of rehabilitation on seismic behavior of masonry piers, J. Struct. Eng. 133 (1) (2007) 32–43.

Example of a Two-Story Unreinforced Masonry Building Chapter

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[24] M. Ebrahimiyan, M. Golabchi, M. Yekrangnia, Field observation and vulnerability assessment of Gonbad-e Qabus, J. Architect. Eng. 23 (4) (2017) 05017008. [25] N. Zezhen, D. Qi, C. Jianyou, Y. Runtao, A study of aseismic strengthening for multi-story brick building by additional R/C columns, 8th WCEE, USA, 1984, pp. 591–598. [26] S. Chuxian, L. Guiqiu, W. Wenchao, The design of Brick masonry structure with concrete column, 11th IB2 MaC, Shanghai, China, Vols. 626–633, 1997. [27] M. Tomazˇevicˇ, I. Klemenc, Seismic behaviour of confined masonry walls, Earthq. Eng. Struct. Dyn. 26 (10) (1997) 1059–1071. [28] M. Yekrangnia, A. Bakhshi, M.A. Ghannad, A. Aghababai, M. Khanmohammadi, and S.R. Mirghaderi, In-situ cyclic testing on a typical URM school building: Part II: the confined masonry building, 10th International Masonry Conference 2018, July 9–11, 2018, Milan (Italy). [29] A. Schultz, J. Bean, H. Stolarski, Resistance of slender post-tensioned masonry walls with unbonded tendons to transversal loading, 9th NAMC, South Carolina, USA, 2003, pp. 463–473. [30] P. Sheppard, S. Tercelj, The effect of repair and strengthening methods for masonry walls, 7th WCEE, Istanbul 6 (1980) 255–262. [31] G. Calvi, G. Magenes, Experimental results on unreinforced masonry shear walls damaged and repaired, 10th IB2 MaC, Calgary, Canada, Vols. 509–518, 1994. [32] T. Manzouri, M. Schuller, P. Shing, B. Amadei, Repair and retrofit of unreinforced masonry structures, Earthq. Spec. 12 (4) (1996). [33] A. Hamid, T. El-Sayed, A. Salama, Seismic retrofit of historic multiwythe stone masonry walls, 8th NAMC, Austin, Texas, USA, 1999. [34] B. Samali, D.M. Dowling, J. Li, Static and dynamic testing of adobe-mudbrick structures, Aust. J. Struct. Eng. 8 (2) (2008) 159–170. [35] M. Taghdi, M. Bruneau, M. Saatcioglu, Seismic retrofitting of low-rise masonry and concrete walls using steel strips, J. Struct. Eng. ©ASCE 126 (9) (2000) 1017–1025. [36] A. Hamid, A. Mahmoud, S. Abo El Maged, Strengthening and repair of unreinforced masonry structures: state-of-the-art, 10th IB2 MaC, Calgary, Canada, 1994, pp. 485–497. [37] D. Rai, S. Goel, Seismic strengthening of unreinforced masonry piers with steel elements, Earth. Spec. 12 (1996) 845–862. [38] F. Somi, M. Yekrangnia, A. Bakhshi, M.A. Gannad, S.E. Hashemi-Rafsanjani, Study of in-plane behavior of adobe walls with cyclic tests, in: The 6th International Conference on Seismology and Earthquake Engineering (SEE-6), May 16–18, Tehran, Iran, 2011. [39] J. Plecnik, T. Cousins, E. Oı´conner, Strengthening of unreinforced masonry buildings, J. Struct. Eng. ASCE 112 (1986) 1070–1087. [40] O. Rosenboom, M. Kowalsky, Investigation of alternative details for seismic design of posttensioned clay masonry walls, 9th NAMC, South Carolina, USA, 2003, pp. 475–485. [41] A. Al-Manaseer, V. Neis, Load tests on post-tensioned masonry wall panels, ACI Struct. J. 84 (6) (1987) 467–472. [42] N. Mojsilovic, P. Marti, Load Tests on Post-Tensioned Masonry Walls, IBK Nr. 0011, Swiss Federal Institute of Technology, Zurich, Switzerland, 1996. [43] S. Lissel, N. Shrive, Construction of diaphragm walls post-tensioned with carbon fiber reinforced polymer tendons, 9th NAMC, Clemson, South Carolina, USA, 2003, pp. 192–203. [44] VSL, Post-Tensioned Masonry Structures, VSL Report Series # 2, VSL Int. Ltd., Switzerland, 1990 [45] M. Yekrangnia, A. Mahdizadeh, Performance of safe-room under jack-arch roof gravity loads, in: The 6th International Conference on Seismology and Earthquake Engineering (SEE-6), May 16–18, Tehran, Iran, 2011.

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[46] M. Blondet, G. Garcia, S. Brzev, Earthquake-resistant construction of adobe buildings: tutorial, in: Published as a Contribution to the EERI/IAEE World Housing Encyclopedia, Proc., 2003. www.world-housing.net. [47] J. Macabuag, An introduction to modelling and retrofitting of non-engineered masonry buildings under seismic loading, in: MEng Research Report, Oxford University, 2007. [48] K. Meguro, P. Mayorca, N. Sathiparan, R. Guragain, K. Nasrollahzadeh Nesheli, PP-Band Retrofitting Technique: Affordable, Acceptable and Feasible Method for Developing Countries, Institute of Industrial Science, University of Tokyo, 2005. [49] J. Macabuag, R. Guragain, S. Bhattacharya, Seismic retriofitting of non-engineered masonry in rural Nepal. Proc. ICE – Struct. Build. (2012). https://doi.org/10.1680/stbu.10.00015. [50] B. Ghiassi, M. Soltani, A.A. Tasnimi, Seismic evaluation of masonry structures strengthened with reinforced concrete layers, J. Struct. Eng. 138 (6) (2011) 729–743. [51] Practical Instruction for Shotcrete in Seismic Rehabilitation of Schools, No. 10289/2-3016, Organization for Development, Renovation and Equipping Schools, Tehran, Iran, (2010). [52] Regulations for Seismic Retrofit of Masonry School Buildings, Organization for Development, Renovation and Equipping Schools, Tehran, Iran, (2011). [53] Applied Technology Council (ATC), FEMA 306: evaluation of earthquake damaged concrete and masonry wall buildings, in: Basic Procedures Manual, 1998. [54] Practical Instruction for Shotcrete Connection in Seismic Rehabilitation of Schools, No. 10289/2-13613, Organization for Development, Renovation and Equipping Schools, Tehran, Iran, (2011).

Chapter 3

Example of an RC Building Retrofitted by RC Shear Walls☆ Teymour Honarbakhsh*, Kamyar Karbasi*, Samaneh Mohamadi*, Aida Bejanli* and Kamran Rahmati† *

Sarzamin Consulting Engineers, Tehran, Iran, †Department of Reinforcement and Maintenance of Bridges and Technical Buildings of Tehran Municipality, Tehran, Iran

Aims By reading this chapter, you are introduced to: l l l l

introduction to several retrofitting techniques suitable for RC buildings; comparison of three different retrofitting strategies; introduction to linear dynamic spectral analysis; and introduction to converting dominant behavior of RC shear walls.

3.1 INTRODUCTION The presented RC building, designed as an office building and printing house, is divided into two northern and southern parts which are connected to each other by jack-arch roofs at each story. Expansion joints of 3–5 cm in width close to the elevator and staircase divide these two parts of the building. The building has two basement levels, a pilot, and 8 stories and 9 stories in the southern and northern part, respectively. The overall area of the building is nearly 22,000 m2 with the diaphragm-column which was constructed in 1969. The building was vacant for a period of time and no as-built drawings were available. Different views of the example building are shown in Fig. 3.1. Preliminary evaluation of the building indicated the building was in good condition under the service loads. Based on the special features of the building as an icon building in newspapers publication industry, sustainable development considerations and ☆ This chapter is mainly a part of a project sponsored financially and technically by the Technical Bureau of the Municipality of Tehran. The authors of this chapter thank the support of this organization. Appreciation is also extended to Dr. Pirouz Hanachi, Mr. Behnam Atabaki, Mr. Ehsan Noushabadi Zerangi. Advanced Design Examples of Seismic Retrofit of Structures. https://doi.org/10.1016/B978-0-08-102534-5.00003-9 © 2019 Elsevier Ltd. All rights reserved.

119

120

Advanced Design Examples of Seismic Retrofit of Structures

(A)

(B)

(C)

(D)

(E)

(F)

FIG. 3.1 Different views of the example building. (A) Location. (B) Eastern view. (C) Southern view. (D) North-east view. (E) West-south view. (F) West-north view. (Photos taken by T. Honarbakhsh.)

environmental concerns, it was decided to study the possibility of retrofit of the building instead of demolition/reconstruction. The project consists of two phases: vulnerability assessment of the building and designing the retrofit system. The vulnerability assessment phase involves the qualitative and quantitative evaluation of the building and the second phase includes studying the possible retrofit methods and finally selection and design of the best method. In order to perform qualitative evaluation of the building,

Example of an RC Building Retrofitted by RC Shear Walls Chapter

3

121

the architectural drawings, as-built sketches, different details, and material properties should be available. The accuracy and completeness of the data depends on the “target” of seismic retrofit strategy and the method of structural analysis. The “performance objective” in the seismic retrofit strategy is decided during the qualitative evaluation of the building in coordination with the owner of the building. The decision depends on factors including the quality of the building and its importance. Because it was planned to use the retrofitted building as headquarter of four deputies of the municipality of Tehran, the importance of the building is high and the target of the retrofit strategy is “enhanced.” As a result, and in the absence of any information regarding the present conditions of the building, data collection and field testing were performed in order to provide the conditions based on which the knowledge factors of 1.0 can be used for the “enhanced” performance objective. It is noteworthy that there were 1200 m2 openings in the roof of the stories
1, pilot, and +1, which made room for the printing house facilities. These openings, shown in Fig. 3.2, are later filled by reinforced concrete. In the 3rd to the 8th stories, a URM building with jack-arch roof had been added to the main building in the area between axis E and F in the northern part of the building (see Fig. 3.3). This building is dismantled completely and a new steel frame building with composite diaphragm is replaced in these stories with the area of 600 m2. A steel frame building in the southern part of the building with area of 600 m2 is also added with the same structural system. In the northern part of the building, the roof of the pilot was located at +7.94 m between axis A and F and 4th to 6th. In this area, a new 230 m2 frame is added at the +4.00 m. Also, stories are added in the northern part of the building including 55 m2 building between axis A1 and B and 1st to 4th as a restaurant, the 65 m2 airconditioning room at the 9th story, the 85 m2 south-west elevator duct, and the other spaces with an area of 100 m2. This chapter presents a brief review of the main stages of the retrofit design of the considered building. Example of calculations, available documents, and test results together with the details and construction photos are also presented. For brevity, the report does not include the design of nonstructural parts of the

(A)

(B)

FIG. 3.2 The opening in the diaphragms. (A) Story + 1. (B) Story
1. (Photos taken by T. Honarbakhsh.)

122

Advanced Design Examples of Seismic Retrofit of Structures

Northern part

Southern part

FIG. 3.3 Overall plan of the building.

building. Examples of these parts in this project are supports of the dry stack brick masonry veneer, partition walls, lintels, dropped ceiling, parapet walls, and supports for electrical and mechanical equipment.

3.2 QUALITATIVE EVALUATION The important works in this phase include: l l l

l l

preparation of the architectural drawings; preparation of the structural sketches; field sampling and data collection of structural members in order to determine the quality of concrete and the type of reinforcing bars in the general scale; performing a general structural analysis; and determination of the performance objective; based on Table 3.1, the building is categorized as “important” and consequently, the “enhanced” performance objective is selected for retrofit. Based on this performance objective, the Life Safety (LS) performance level in Earthquake-1 (10% probability of

Example of an RC Building Retrofitted by RC Shear Walls Chapter

3

123

TABLE 3.1 Determination of the Performance Objectives for Buildings [1] Performance Level

Retrofit Target

Earthquake-1

Earthquake-2

Building Type

Functionality

Strategic

Armed forces and police headquarters, ministry buildings, TV and radio central buildings, communication centers; airport and ports guidance centers

Special

A-1

A-2

Political

Central buildings of the parliament, judiciary, provincial government, central bank, treasury, governor’s office

Special

B-1

C-3

Emergency

Hospitals and large clinics

Special

B-1

C-2

Central buildings of emergency, firefighting, Red Cross, police

Special

B-1

C-3

Organizational

Counties offices, provincial buildings of armed forces and police

Special

B-2

C-4

Lifeline

Main buildings for water supply, electric supply, gas supply, TV and radio, airports control rooms

Special

B-1

C-2

Cultural heritage

Museums, historic buildings, special libraries (national, parliament,

Special

B-2

C-3

Continued

124

Advanced Design Examples of Seismic Retrofit of Structures

TABLE 3.1 Determination of the Performance Objectives for Buildings—cont’d

Building Type

Functionality

Performance Level

Retrofit Target

Earthquake-1

Earthquake-2

center of national documents) Infrastructure

Main buildings of refinery, power plants, petrochemical centers, chemical factories

Special

B-1

C-3

Important

Universities, schools, institutes

Enhanced

C-3

E-5

Provincial offices of ministries and central offices of organizations

Enhanced

B-2

E-5

Municipality saloons, religious-related buildings, cinemas and theatres, stadiums, libraries, terminals, malls and rooms with capacity of more than 300 persons

Enhanced

C-3

E-5

Residential, officecommercial buildings, hotels, parking buildings, industrial buildings

Basic

C-3

–

Agricultural stores, aviculture buildings and temporary buildings

Basic or limited

D-4

–

Public

Example of an RC Building Retrofitted by RC Shear Walls Chapter

3

125

TABLE 3.2 Results of the Qualitative Evaluations Phase Parameters affecting vulnerability

l

l

l

l l

l l l

l

Causes of vulnerability of structural members Causes of vulnerability of non-structural members

Serious changes in design codes since the 1960s and significant increase in the design-level earthquakes Necessity of using ribbed bars in structural members and modifications in the reinforcing bars details Selected structural system considering the plan dimensions and the number of stories Improper arrangement of structural members Arrangement of the RC shear walls in the plan of the building and torsional forces Irregularities in plan and elevation Large openings in diaphragms Small distance between the two parts of the building and the possibility of pounding during earthquakes It was found that the DCR under gravitational loads of a majority of the columns in the first story in the southern building part is 0.7. This ratio is even higher for the corresponding columns in the northern building part

l

Low strength columns Low strength RC shear walls Reinforcing bars details

l

Improper detailing of the large window

l l

exceedance in 50 years or 475 years of returning period) and the Collapse Prevention (CP) performance level in Earthquake-2 (2% probability of exceedance in 50 years or 2475 years of returning period) should be provided. The summary of the evaluations in this phase is presented in Table 3.2. Based on the results above, the building is vulnerable to Earthquake-1 and Earthquake-2. A more accurate determination of the vulnerability of the building is calculated after carrying out the field evaluation, material testing and quantitative study. Details of material testing based on Instruction for Seismic Rehabilitation of Existing Buildings (Code 360) [1] are presented in Table 3.3.

3.2.1 Field Testing A complete set of standard testing of materials, structural details, soil condition, and groundwater level were performed and the results are presented briefly here.

126

Advanced Design Examples of Seismic Retrofit of Structures

TABLE 3.3 Details of Material Testing Based on Code 360 [1] Item

Tests

Required Number

1

Determination of the size and type of bars in columns

70

2

Determination of the size and type of bars in RC shear walls and their thickness

20

3

Determination of the size and type of bars in diaphragms and their thickness

6

4

Determination of the size and type of bars in beams

2

5

Determination of the size and type of bars in stairs and the diaphragm thickness

2

6

Determination of the size and type of bars in columns ends

4

7

Determination of the size of foundation

15

8

Coring of column (66), shear walls (20), diaphragms (6), stairs (2), foundation (8), and characteristic compressive strength of concrete

66

9

Schmitt hammer test on columns, shear walls and diaphragm

116

10

Geotechnical bore hole and the related studies. This hole with 15 m in depth is to determine the soil characteristics and the groundwater level. Also, soil layers, physical, chemical and mechanical properties of soils can be determined. The allowable stress, settlements properties, Chloride and Sulfate, lateral pressure coefficient can also be determined

1

11

Tensile testing of bars and determination of tensile strength

4

3.2.1.1 Characteristic Compressive Strength of Concrete Based on the results of coring from 19 samples of columns, 9 samples from shear walls, 5 samples from diaphragms, and 53 and 20 Schmitt hammer tests on columns and shear walls, respectively, the characteristic compressive strength of concrete is determined based the method in Chapter 2 of Code 360 (see Table 3.4). 3.2.1.2 Characteristics of Bars Based on the tensile tests on two unribbed φ14mm and φ20mm bars, these bars are made of AI (yield strength of 240 MPa) and AII (yield strength of 300 MPa). Conservatively, all the unribbed bars are assumed to be AI. Also, based on the

Example of an RC Building Retrofitted by RC Shear Walls Chapter

3

127

TABLE 3.4 Compressive Strength of Concrete Member

Characteristic Compressive Strength (fCE) (MPa)

Lower-bound compressive Strength (fCL) (MPa)

Column

20

16.5

Shear wall

20

16.5

Diaphragm

21

18.0

tensile tests on two ribbed φ14mm and φ18mm bars, these bars are made of AII and AIII (yield strength of 400 MPa). Conservatively, all the ribbed bars are assumed to be AII.

3.2.1.3 Characteristics of the Foundation and the Structural Members By performing sondage for determination of dimensions of the foundation and the structural members including columns, shear walls, and diaphragms, and by carrying out nondestructive ultrasonic tests, the arrangements, size, and type of bars were determined. Examples of the results in this part are shown in Figs. 3.4–3.7. The characteristics of columns based on the mentioned tests are presented in Table 3.5. 3.2.1.4 Columns, Shear Walls, and Diaphragms Typology and as-Built Sketches The final stage in this part is to prepare the as-built sketches based on the results of tests and sondages. Examples of these sketches are shown in Figs. 3.8–3.14.

3.3 QUANTITATIVE EVALUATION (PHASE-2, STAGE-1) After preparation of the as-built sketches of the building, determination of the physical and mechanical properties of concrete and bars, and determination of the structural service loads in different parts, the numerical modeling, analysis, and quantitative vulnerability evaluation of the building can be achieved. The quantitative evaluation is performed under two assumed conditions: first, the northern and the southern parts of the building are modeled separately, i.e., the two parts are assumed to respond independently against the loads. In the other scenario, the two parts are assumed to be connected properly and, consequently, act monolithically. The results of these analyses lead to a better understanding of the response of the building and also pave the way to the proper selection of the retrofit strategy. The structural members are classified in Table 3.6 according to their dominant response in terms of force-controlled

FIG. 3.4 Foundation plan and observations at level
2. (Photos taken by T. Honarbakhsh.)

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3

FIG. 3.5 Columns, shear walls and diaphragm plan and observations at level
2. (Photos taken by T. Honarbakhsh.)

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FIG. 3.6 The results and observations from sondage of columns at level
2. (Photos taken by T. Honarbakhsh.)

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FIG. 3.7 The results and observations from sondage of columns at level +7. (Photos taken by T. Honarbakhsh.)

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Diameter, cm

90

90

90

80

80

70

70

70

70

70

70


1

0

1

2

3

4

5

6

7

8

9

110

110

100


2


1

0

Southern part

100


2

Northern part

Story No.

5.5

5.5

5.5

5.0

5.0

5.0

5.0

5.0

5.0

5.0

5.0

5.0

5.0

5.0

5.0

Concrete Cover, cm

TABLE 3.5 Characteristics of Columns

95

125

150

70

70

70

70

70

70

70

85

85

85

125

125

Bars Overlap, cm

2.5

2.8

3.2

2.0

2.0

2.0

2.0

2.0

2.0

2.0

2.2

2.2

2.2

2.5

2.8

Longitudinal Bars Diameter, cm

1.2

1.6

1.6

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

Transverse Bars Diameter, cm

9

9

9

7

7

7

7

7

7

7

7

7

7

7

7

Transverse Bars Spacing, cm

30

30

30

20

20

20

20

20

22

22

22

24

24

28

28

No. of Longitudinal Bars

132 Advanced Design Examples of Seismic Retrofit of Structures

100

100

90

90

70

70

70

70

70

1

2

3

4

5

6

7

8

9

5.5

5.5

5.5

5.5

5.5

5.5

5.5

5.5

5.5

85

85

85

95

95

95

95

95

95

1.8

1.8

1.8

2.2

2.2

2.2

2.5

2.5

2.5

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.2

1.2

9

9

9

9

9

9

9

9

9

40

30

30

30

30

30

30

30

30

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FIG. 3.8 Foundation plan.

(FC) or deformation-controlled (DC). It is noteworthy that the expected material strength (mean value) is used for determination of the members’ capacity with DC action, and the lower-bound material strength (mean value minus one standard deviation) is used for the members’ capacity with FC action. With regards to the above considerations, the model of the building is prepared, and linear dynamic analysis by consideration of 40 natural modes of the building is performed.

3.3.1 Modeling and Analysis of the Building The three-dimensional modeling of the building is performed by using SHELL elements for RC shear walls and FRAME elements for columns and beams.

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FIG. 3.9 Columns plan.

The P-D and P-d effects are taken into account. The diaphragms of the building are modeled as rigid. All the columns, shear walls, and beams are considered as primary elements and they contribute in lateral stiffness of the building and loads distribution between the structural members. The torsion is automatically computed in the model and the accidental torsion is considered in the calculations of the seismic demands on the structural members. The soil-structure interaction is not considered in this project. The effects of simultaneous application of earthquake components—100% of the most critical direction of ground motion and 30% of the ground motion in the orthogonal axis—were applied to the model.

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FIG. 3.10 Column C-S-1.

3.3.2 Quantitative Evaluation of the Overall Performance of the Building 3.3.2.1 Lateral Displacements The lateral displacements of stories of two loading directions under a critical loading combination (presented in Section 3.5.1.3) are shown in Fig. 3.15 for the northern and southern parts of the building. As can be seen in this figure, for the North-South loading direction, the lateral displacement of the 7th story in the southern and the northern parts of the building is 24 cm and 37 cm,

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FIG. 3.11 Column C-S-5.

respectively. This means the collision of the two parts of the building and hence the pounding is inevitable.

3.3.2.2 Center of Mass and Center of Rigidity Coordinates The distance of center of mass (CoM) and center of rigidity (CoR) in each story in two directions are shown in Fig. 3.16. From this figure, the CoM-CoR

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FIG. 3.12 Column C-N-3.

eccentricities in the northern and the southern parts of the building, as independent buildings, are 28% and 38%, respectively. However, this eccentricity in the monolithic building is reduced to 18%.

3.3.2.3 Conclusions Based on the results in this part, the main causes of vulnerability of the building under two scenarios of two independent, isolated buildings parts and a

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FIG. 3.13 Details of column ends.

monolithic building are listed in Table 3.7. According to the aforementioned results, it can be concluded that the vulnerability of the building is more critical in the first scenario than that in the second one. Considering the performance superiority of the monolithic building compared that of the building with two independent, isolated parts, the general recommendations are as follows: – reduction of the CoM-CoR eccentricity of all the stories in both directions to up to 20% of the external dimension of the building plan; – elimination of the pounding of the two building parts; and – minimum reduction of 10% in mean values of the structural members’ DCR.

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FIG. 3.14 Shear walls plan.

TABLE 3.6 Structural Members Actions Action Type Member

FC

DC

Beams

Shear

Flexural

Columns

Shear and axial

Flexural

Shear walls

Shear and axial

Flexural and shear

Diaphragms

Shear

Flexural

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0.45

Building diaphragm displacements, m

0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 INT-X S-X N-X

STORY9 STORY8 STORY7 STORY6 STORY5 STORY4 STORY3 STORY2 STORY1 STORY0 STORY-1 STORY-2 0.17 0.16 0.13 0.11 0.11 0.09 0.07 0.05 0.03 0.02 0.01 0.00 0.14 0.13 0.14 0.12 0.13 0.10 0.08 0.05 0.03 0.02 0.01 0.00 0.41 0.26 0.21 0.18 0.14 0.11 0.08 0.06 0.04 0.02 0.01 0.00

(A) 0.45

Building diaphragm displacements, m

0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 INT-Y S-Y N-Y

STORY9 STORY8 STORY7 STORY6 STORY5 STORY4 STORY3 STORY2 STORY1 STORY0 STORY-1 STORY-2 0.34 0.31 0.27 0.23 0.19 0.15 0.11 0.07 0.04 0.02 0.00 0.00 0.29 0.28 0.24 0.20 0.17 0.13 0.10 0.07 0.04 0.02 0.01 0.00 0.45 0.42 0.37 0.32 0.26 0.21 0.16 0.11 0.06 0.03 0.00 0.00

(B) FIG. 3.15 Lateral displacements of stories of two loading directions under critical loading combination. (A) X-direction. (B) Y-direction.

3.3.2.4 Retrofit solutions Based on the results in previous parts, the main approach in the design of the retrofit method is towards: – proper connection of the two northern and southern parts of the building; – reduction of the stiffness of the northern RC shear walls in both of the building parts; and

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Distance of building center of rigidity and center of mass, %

0.40

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0.00 Integrated-DX South-DX North-DX

STORY9 0.15 0.15 0.09

STORY8 0.16 0.22 0.17

STORY7 0.17 0.17 0.18

STORY6 0.17 0.16 0.18

STORY5 0.18 0.16 0.18

STORY4 0.18 0.15 0.18

STORY3 0.16 0.13 0.17

STORY2 0.13 0.11 0.13

STORY1 0.07 0.03 0.09

STORY6 0.07 0.24 0.13

STORY5 0.16 0.37 0.18

STORY4 0.19 0.38 0.22

STORY3 0.18 0.37 0.24

STORY2 0.18 0.35 0.23

STORY1 0.18 0.32 0.28

STORY0 0.08 0.14 0.21

STORY-1 STORY-2 0.13 0.08 0.19 0.13 0.36 0.17

(A) Distance of building center of rigidity and center of mass, %

0.40

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0.00 Integrated-DY South-DY North-DY

STORY9 0.07 0.05 0.20

STORY8 0.06 0.08 0.05

STORY7 0.05 0.24 0.08

STORY0 STORY-1 STORY-2 0.14 0.09 0.09 0.16 0.05 0.02 0.28 0.13 0.15

(B) FIG. 3.16 Distance of center of mass and center of rigidity in each story. (A) X-direction. (B) Y-direction.

– development of “resisting cores” in the most favorable locations of the building in accordance with the architectural concerns in order to minimize the CoM-CoR eccentricity and irregularity, increasing the stability, ensuring proper stiffness distribution, and increasing the resistance of the building. In the next stage, the possible retrofit solutions are studied and the best method is selected based on technical, economical, and feasibility considerations.

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TABLE 3.7 The Main Causes of Vulnerability Building with two independent, isolated building parts Causes l

l

l l l

Improper arrangements structural system to withstand the seismic demands of a region with very high seismicity Considerable irregularity in the plan of the building because of improper arrangements of structural members, especially the RC shear walls Low ductility of the RC shear walls because of their details and using unribbed bars Low capacity of RC shear walls Pounding of the two northern and southern parts of the building during earthquakes

Conclusions l

The building is very vulnerable under Earthquake-1

Monolithic building Causes l

l l l l

Improper arrangements structural system to withstand the seismic demands of a region with very high seismicity Irregularity in the plan Irregularity in the height of the building Low ductility of the RC shear walls because of their details and using unribbed bars Low capacity of RC shear walls

Conclusions l

The building is very vulnerable under Earthquake-1

3.4 PRELIMINARY DESIGN AND STUDY OF THE POSSIBLE RETROFIT METHODS (PHASE-1, STAGE-2) Based on the main causes of vulnerability of the building and the recommendations in the previous parts of this chapter, three candidates for seismic retrofit of the building are proposed and studied. These retrofit solutions are as follows.

3.4.1 Proper Connection of the Two Building Parts l

The main strategies are as follows: – The method should be designed to make the best out of the building potentials. – The method should be feasible, preferably straightforward, and economical. – The method should improve the stiffness distribution in the plan of the building.

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– By increasing stiffness, the demands in the existing RC shear walls and columns are reduced. This can be done by adding extra shear walls to the building in proper locations. – The retrofitted elements or the added structural members are better located on the corners of the building in order to minimize the conflict with the operation related to architectural, electrical, and mechanical equipment during the retrofit project. – The demolition tasks should be limited to local scale with the aim of connecting the added members to the existing ones. Environmental considerations also pose limits to the extent of demolition. – The method should preferably minimize the required costs additional to the cost related to the “basic” performance objective. The results of the study are as follows: – No modification to the load-bearing system for the gravitational loads is necessary. – The extent of demolition is minimal. – The columns do not need to be retrofitted (this is very important considering the huge number of columns and the geometry of the columns’ ends). – The existing RC shear walls do not need to be retrofitted for flexural actions. – Some of the RC shear walls need to be retrofitted for shear actions. – The southern building part requires retrofitting by adding RC shear walls at the South-East and South-West corners. However, by properly connecting the two building parts together, there is no need for adding RC shear walls at the South-East corner of the northern building. – The total cost of retrofitting according to this strategy is estimated to be $300,000. The general schematic view of the first retrofit strategy is shown in Fig. 3.17.

3.4.2 Isolation the Two Building Parts From Each Other and Increasing Stiffness of Each Part l

l

The main strategies are as follows: – Providing the freedom for each building part to experience the necessary displacements. – Increasing stiffness of each building part to ensure a more optimum distribution of stiffness and to reduce the seismic demands in the existing shear walls and columns. The results of the study are as follows: – The columns do not need to be retrofitted. – The existing RC shear walls do not need to be retrofitted for flexural actions. – Some of the RC shear walls need to be retrofitted for shear actions.

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FIG. 3.17 General schematic view of the first retrofit strategy (Pilot). l

The drawbacks are as follows: – Considerable demolition. – Requirement for adding a system of columns and beams to tolerate the gravitational loads. In order to activate the added beams in load bearing, application of vertical loads by hydraulic jacks may be required which adds to the complexity of the retrofit process.

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– An elevator is missed. – Requirement of adding a passage bridge between the two building parts which results in the necessity of stairs due to difference between the elevations of the stories in the two building parts. – Missing an area enclosed between axis F in the southern part and the elevator wall of the northern part. – Requirement of demolishing the walls in the South-East corner of the northern building part and reconstruction by proper materials. – The details of the floor between the two buildings is rather complex. – The required time for this strategy is longer than that of the strategy in Section 3.4.1. – The required budget for this strategy is larger than that of the strategy in Section 3.4.1. – The total cost of retrofitting according to this strategy is estimated to be $385,000. A general schematic view of the first retrofit strategy is shown in Fig. 3.18.

3.4.3 Isolation the Two Building Parts From Each Other and Decreasing Stiffness of Each Part l

l

The main strategies are as follows: – Providing the freedom for each building part to experience the necessary displacements. – Decreasing stiffness of each building part to ensure a more optimum distribution of stiffness and to reduce the seismic demands in the existing shear walls and columns. The drawbacks are as follows: – Considerable demolition. – Requirement for adding a system of columns and beams to tolerate the gravitational loads. – An elevator is missed. – The majority of columns need to be retrofitted because the increase in their seismic demands. – The existing RC shear walls need to be retrofitted for flexural and shear actions. – Requirement of adding a passage bridge between the two building parts, which results in the necessity of stairs due to the difference between the elevations of the stories in the two building parts. – Requirement of demolishing the walls in the South-East corner of the northern building part and reconstruction by proper materials. – The details of the floor between the two buildings are rather complex.

In this method, the columns ends should be retrofitted. As a result, the costs for the “enhanced” performance objective are considerably higher than those in the

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FIG. 3.18 General schematic view of the second retrofit strategy.

“basic” one. This is because the seismic demands are 1.5 times larger in the latter performance objective, while the m-factor of the RC columns is 1.25 times larger in the IO performance level compared to that for the LS. For other structural members, the increase in the seismic demands and the capacity are both 1.5 times. In this strategy, the shear wall in the South-East corner should be

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extended to the highest story. In stories where there is a setback in the diaphragm, the 80 60 cm RC beams should be used in order to keep the DCR of the northern shear wall as 3.5 (compared to that of 2.5 in the first retrofit strategy). If the shear wall does not extend to the upper stories, the DCR of the northern shear wall increases to 5.5. Consequently, this strategy is unacceptable. The general schematic view of the third retrofit strategy is shown in Fig. 3.19.

3.4.4 Scoring the First and the Second Retrofit Strategies In order to compare the first and the second retrofit strategies, the analytic hierarchy process (AHP) [2] scoring table is presented in Table 3.8. The first strategy has a higher score and hence is selected as the retrofit strategy for this project.

3.5 DETAILED DESIGN OF THE SELECTED RETROFIT METHOD (PHASE-2, STAGE-2) As previously mentioned, the used analysis method is the linear dynamic one, which is performed for two earthquake levels: Earthquake-1 and Earthquake-2, for which the target performance levels are LS and CP, respectively. In the models, all columns and shear wall P2 are considered as secondary members. Other walls (P1, P1L, P3, P3T, P4, P5, P6, P8) and other structural members are considered as primary members. There are a total of 40 modes which are considered to take at least 90% of the dynamic mass of the building into account [3]. Two main tasks are considered in the selected retrofit strategies: proper connection of the northern and southern building parts; and modification of the shear walls aspect ratio, arrangements, retrofit, and adding new shear walls in both directions. It is noteworthy that selection of the location of the shear walls is based on minimizing the torsion and more balanced distribution of the seismic demands between the structural members. In addition, architectural, feasibility, and economical considerations play a role in this selection. One idea in the retrofit design is to divide the existing shear walls P1 and P4 with the dominant shear behavior (due to their geometrical characteristics) in order to alter it to flexural behavior. To do this, the shear wall P4 is demolished in the length of 2.5 m from the West in all stories. The remaining part of this wall is divided into two separate parts by cutting through the wall with a 20-cm width vertical groove. This creates the two new walls P4 and P8 in the plan of the retrofitted building. Moreover, the shear wall P1 is divided into two P1L and P1, and two flanges are also added to each new wall as shown in Fig. 3.20. Some views of the process of demolition and dividing these shear walls are shown in Figs. 3.21 and 3.22.

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(A) FIG. 3.19 General schematic view of the third retrofit strategy. (A) Overall view. (Continued)

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FIG. 3.19, CONT’D (B) Zoomed view.

TABLE 3.8 AHP Scoring Table of the Retrofit Strategies 1st Strategy

2nd Strategy

20

20

14

Construction time

15

15

12

3

Parallel progress in architectural, mechanical and electrical equipment

17

6

5

4

Flexibility for possible changes in architecture

6

5

4

5

Feasibility and straightforwardness

6

5

3

6

Unnecessary full-time supervision

6

5

4

7

Possibility of further retrofitting of members (if necessary)

7

5

4

8

Unnecessary added foundation

10

7

6

9

Environmentally-friendly

8

6

4

10

Unnecessary maintenance costs

8

8

4

11

No conflict with the access routes, pathway, etc.

7

6

3

100

88

63

No.

Item

1

Construction costs

2

Overall score

Score

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FIG. 3.20 Overall scheme of the RC shear walls. (A) Initial condition. (B) After retrofit.

3.5.1 Assumptions Based on the results of field testing on the materials in Section 3.2.1, the assumptions presented in Table 3.9 are made in the modeling of the building. – Based on the geotechnical studies of the soil adjacent to the building, the soil type II according to Iranian Code of Practice for Seismic Resistant Design of Buildings (Standard 2800) [4] which is moderate to loose rock to very dense soil with the average shear wave speed of 375–750 m/s is confirmed. – The concrete cover in foundation is 8 cm. – The Poisson’s ratio of concrete and steel is assumed to be 0.15 and 0.30, respectively. pffiffiffiffi – The modulus of elasticity of concrete is based on Ec ¼ 4700 fc0 (MPa) [5]. The modulus of elasticity of steel is Es ¼ 2.1  105 MPa. – The contributions of dead loads and live loads on all stories including the roof in calculation of the weight of the building are 100% and 20%, respectively [4]. – The analyses are spectral linear dynamic, and hence the behavior of all materials is assumed linear elastic. – The design codes used are Code 360 [1] and ASCE 7-10 [6]. – The effects of simultaneous earthquake components are considered by application 100% of the most critical direction of ground motion, and 30% of the ground motion in the orthogonal axis [4]. – Based on the data collection in Section 3.2.1, the knowledge factor of the building is 1.0 [1].

FIG. 3.21 Partial demolition of shear wall P4. (Photos taken by T. Honarbakhsh.)

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FIG. 3.22 Dividing shear walls P1 and P4. (Photos taken by T. Honarbakhsh.)

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TABLE 3.9 Assumed Material Properties Value, MPa Parameter

fex

fcL

Compressive strength of concrete in the shear wall of the northern building part

22.5

14.5

Compressive strength of concrete in the shear wall of the southern building part

24.5

17.5

Compressive strength of concrete in the columns

19.7

13.5

Compressive strength of concrete in the diaphragms

21.0

18.0

Tensile strength of unribbed bars

300

Tensile strength of ribbed bars

370

3.5.1.1 Loads The considered load cases are dead, live, and seismic, which are based on the Iranian National Building Code; Part 6: Loading [7]. Dead and Live Loads The dead loads of the peripheral walls are defined in the model based on the details from the field studies. The assumed dead and live loads are presented in Table 3.10. TABLE 3.10 Dead and Live Loads Dead Loads Peripheral walls with 20 cm thickness

660 kg/m

Parapet walls

123 kg/m

Stories and roof

240 kg/m2

Live loads Offices

250 kg/m2

Partition walls

100 kg/m2

Roof

150 kg/m2

Stairs

500 kg/m2

Equipment rooms

400 kg/m2

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Seismic Loads According to Code 360, the seismic loads in the linear static procedure are considered based on Eq. (3.1); QE
LSP ¼ C1 C2 Cm Sa W

(3.1)

where: QE
LSP ¼ pseudo lateral force in linear static procedure; Sa ¼response spectrum acceleration, at the fundamental period and damping ratio of the building in the direction under consideration; C1 ¼modification factor to relate expected maximum inelastic displacements to displacements calculated for linear elastic response which is based on Eq. (3.2), which is 1.0 for the example building: 1  C1 ¼ 1 +

Ts
T 2Ts
0:2

(3.2)

C2 ¼modification factor to represent the effect of pinched hysteresis shape, cyclic stiffness degradation, and strength deterioration on maximum displacement response. In the absence of precise calculations, C2 can be taken as 1.0; and Cm ¼effective mass factor to account for higher modal mass participation effects obtained from Table 3.4 of Code 360 [1]. Cm is 0.8 for RC buildings with at least three stories in this table. As a result, the equivalent static load is: QE
LSP ¼ 0:8Sa W The seismic loads in the linear dynamic procedure are considered based on Eq. (3.3): QE
LDP ¼ C1 C2 Sa W

(3.3)

and hence: QE
LDP ¼ Sa W ¼ ABW According to Code 360, the natural period of the first mode of vibration for the example building is according to: T ¼ 0:05H0:75

(3.4)

where: T ¼ natural period of the first mode; and H ¼ total height of the building. For both the northern and southern buildings, the reflection factor (B) is 1.94 and the design acceleration (A) for the region with very high seismicity is 0.35.

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TABLE 3.11 Seismic Forces Coefficients Natural Period of the Building

Tx, y 5 0.05 × 41.250.75 5 0.8 s

C1


T C1 ¼ 1 + 2TTss
0:2 ¼1

C2

C2 ¼ 1.0

Sa (Earthquake-1)

Sa ¼ (A  g) B ¼ 0.35  9.81  B ¼ 3.43B

Seismic forces coefficient in X and Y directions (Earthquake-1)

C1C2Sa ¼ 1  1  3.43B ¼ 3.43B

Sa (Earthquake-1)

Sa ¼ 1.5(A  g)B ¼ 1.5 (0.35  9.81  B) ¼ 5.14B

Seismic forces coefficient in X and Y directions (Earthquake-2)

C1C2Sa ¼ 1  1  5.14B ¼ 5.14B

We have: QE
LDP ¼ ABW ¼ 0:35  1:94W ¼ 0:68W In the linear dynamic procedure, all the demand forces and deformations are multiplied by coefficients C1 and C2. The seismic forces coefficients are presented in Table 3.11.

3.5.1.2 Action Calculation Deformation-Controlled Based on Code 360, deformation-controlled actions for LDP denoted by QUD shall be calculated in accordance with Eq. (3.5): QUD ¼ QG + QE

(3.5)

where: QE ¼ action caused by the response to the selected seismic hazard level calculated using Section “Seismic Loads” of this example; and QG ¼ action caused by gravity loads as determined according to either of these methods: 1) Where the effects or actions of gravity loads and seismic forces are additive, the action caused by gravity loads, QG, shall be obtained in accordance with Eq. (3.6): QG ¼ 1:1ðQD + QL + Qs Þ

(3.6)

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Where: QD ¼ action caused by dead loads; QL ¼ action caused by live load, equal to 25% of the unreduced live load obtained in accordance with ASCE 7 [6] but not less than the actual live load; and Qs ¼ action caused by effective snow load, which is assumed to be zero in this example; and QUD ¼ deformation-controlled action caused by gravity loads and earthquake forces. 2) Where the effects or actions of gravity loads and seismic forces counteract each other, the action caused by gravity loads, QG, shall be obtained in accordance with Eq. (3.7): QG ¼ 0:9QD

(3.7)

Force-Controlled According to Code 360, force-controlled actions for LSP denoted as QUF shall be calculated using one of the following methods: 1) QUF shall be taken as the maximum action that can be developed in a component based on a limit-state analysis, considering the expected strength of the components delivering force to the component under examination, or the maximum action developed in the component as limited by the nonlinear response of the building. 2) Alternatively, QUF shall be calculated in accordance with Eq. (3.8): QUF ¼ QG 

QE C1 C2 J

(3.8)

where: QUF ¼force-controlled action caused by gravity loads in combination with earthquake forces; and J ¼force-delivery reduction factor, greater than or equal to 1.0, taken as the smallest DCR of the components in the load path delivering force to the component in question. Alternatively, values of J equal to 3.5 for CP performance level, 2.5 for LS performance level, and 1.0 for IO performance level shall be permitted where not based on calculated DCRs. In this example, this factor is assumed to be 2.5 and 3.5 for Earthquake-1 and Earthquake-2 seismic demands, respectively. As a result, we have: QUF ¼ QG  0:4QE for LS QUF ¼ QG  0:286QE for CP

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Advanced Design Examples of Seismic Retrofit of Structures

3.5.1.3 Loads Combinations The loads combinations for the LDP for force-controlled and deformationcontrolled structural elements are presented in Tables 3.12 and 3.13 for under gravitational and two Earthquake-1 and Earthquake-2 seismic demands, respectively. TABLE 3.12 Loads Combinations Under Gravitational Loads Combo Name

Type

Case

Factor

Case Type

QG1

ADD

DEAD

1.1

Static

LIVE

1.1

Static

DEAD

0.9

Static

QG1 QG2

ADD

TABLE 3.13 Loads Combinations Under in Earthquake-1 and Earthquake-2 for Deformation-Controlled and Force-Controlled Actions Combo Name

Loads Combinations

Earthquake-1; deformation-controlled QUD1L1

QG1

1SPECX-1

QUD2L1

QG1

QUD3L1

QG1

1SPECX-1

0.3SPECY-1

QUD4L1

QG1

0.3SPECX-1

1SPECY-1

QUD5L1

QG2

1SPECX-1

QUD6L1

QG2

QUD7L1

QG2

1SPECX-1

0.3SPECY-1

QUD8L1

QG2

0.3SPECX-1

1SPECY-1

1SPECY-1

1SPECY-1

Earthquake-1; force-controlled QUF1L1

QG1

0.4SPECX-1

QUF2L1

QG1

QUF3L1

QG1

0.4SPECX-1

0.12SPECY-1

QUF4L1

QG1

0.12SPECX-1

0.4SPECY-1

QUF5L1

QG2

0.4SPECX-1

QUF6L1

QG2

QUF7L1

QG2

0.4SPECX-1

0.12SPECY-1

QUF8L1

QG2

0.12SPECX-1

0.4SPECY-1

0.4SPECY-1

0.4SPECY-1

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TABLE 3.13 Loads Combinations Under in Earthquake-1 and Earthquake-2 for Deformation-Controlled and Force-Controlled Actions—cont’d Combo Name

Loads Combinations

Earthquake-2; deformation-controlled QUD1L2

QG1

1SPECX-2

QUD2L2

QG1

QUD3L2

QG1

1SPECX-2

0.3SPECY-2

QUD4L2

QG1

0.3SPECX-2

1SPECY-2

QUD5L2

QG2

1SPECX-2

QUD6L2

QG2

QUD7L2

QG2

1SPECX-2

0.3SPECY-2

QUD8L2

QG2

0.3SPECX-2

1SPECY-2

1SPECY-2

1SPECY-2

Earthquake-2; force-controlled QUF1L2

QG1

0.286SPECX-1

QUF2L2

QG1

QUF3L2

QG1

0.286SPECX-1

0.086SPECY-1

QUF4L2

QG1

0.086SPECX-1

0.286SPECY-1

QUF5L2

QG2

0.286SPECX-1

QUF6L2

QG2

QUF7L2

QG2

0.286SPECX-1

0.086SPECY-1

QUF8L2

QG2

0.086SPECX-1

0.286SPECY-1

0.286SPECY-1

0.286SPECY-1

3.5.2 Design Controls The monolithic performance of the diaphragms and the new shear walls necessitates the adequacy of both structural elements and the connection system between the two building parts. For this purpose, the controls as follows should be considered: l

l

RC shear walls – Flexural design – Shear design Diaphragms – In-plane shear in diaphragms – Connection of diaphragms

160 l

l

Advanced Design Examples of Seismic Retrofit of Structures

Connections – Diaphragms-to-shear walls – New shear walls-to-existing shear walls Foundation

3.5.2.1 RC Shear Walls Flexural Design The flexural design of the RC shear walls is according to Eq. (3.9) [8]. This equation should be used for the eight aforementioned loads combinations under 100% of the most critical direction of ground motion, and 30% of the ground motion in the orthogonal axis. Also, these controls should be made for the Earthquake-1 and Earthquake-2 levels for satisfying LS and CP performance levels, respectively. As a result, there are a total of 64 controls for each RC shear wall.     MUDy 2 MUDx 2 + 1 (3.9) mx κMCEx my κMCEy where: MUDx ¼design bending moment about the x-axis for axial load PUF; MUDy ¼design bending moment about the x-axis for axial load PUF; MCEx ¼ expected bending strength of a member about the x-axis; MCEy ¼expected bending strength of a member about the y-axis; κ ¼a knowledge factor used to reduce component strength based on the level of knowledge obtained for individual components during data collection; mx ¼value of m for bending about the x-axis of a member; and my ¼value of m for bending about the y-axis of a member. The significant scale of computations in this part led to development of a MATLAB code, which automatically perform the tasks as follows: (A) Receiving forces and moments in the shear walls from the numerical model based on the expected values of concrete and steel as input data. (B) Receiving forces and moments in the shear walls from the numerical model based on the lower bound values of concrete and steel as input data. (C) Development of the axial force-flexural moment interaction curves, i.e., (P-M)x and (P-M)y for the expected values of concrete and steel in four main angles of 0 degree, 90 degree, 180 degree, and 270 degree (MUDx is computed based on angles 0 degree and 180 degree; MUDy is computed based on angles 90 degree and 270 degree). (D) Determination of the expected value of flexural capacity of the applied axial forces from force-controlled loads combinations about the x- and y-axes under four main angles of 0 degree, 90 degree, 180 degree, and 270 degree. It is noteworthy that according to Section 10.7.2.3 of ASCE

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161

41-13 [8], the upper-bound value of the effective length equal to the total height of the shear wall was taken into account for walls P5 and P6. (E) In order to determine the mx and my for each story, the procedure below was followed: – Determination of the shear force per length (q) assuming the cantilever action of the shear wall based on the flexural capacity of the wall in story
2 from Step D. – Determination of the shear force at each story based on multiplication of q into the total height of the story. – Determination of the m-factors based on Table 3.14. (F) Checking satisfaction of Eq. (3.9). If not satisfied, steel plates are attached to the walls in order to improve their flexural capacity. As an example, the calculations in this part are presented for shear wall P1 at story
2. (A) Forces and moments based on the expected values of concrete and steel characteristics for deformation-controlled actions. PUD (ton)

VUDx (ton)

VUDy (ton)

T (ton. m)

MUDx (ton. m)

MUDy (ton. m)

1703


529


368

1300


23,395


2093

TABLE 3.14 m-Factors for Linear Procedures for RC Shear Walls [8] Performance Level Component Type

Conditions 

 As
A0s fy + P tw lw fc0

Primary

Secondary

V pffiffiffiffi tw lw fc0

Confined Boundary

IO

LS

CP

LS

CP

0.1

4

Yes

2

4

6

6

8

0.1

6

Yes

2

3

4

4

6

0.25

4

Yes

1.5

3

4

4

6

0.25

6

Yes

1.25

2

2.5

2.5

4

0.1

4

No

2

2.5

4

4

6

0.1

6

No

1.5

2

2.5

2.5

4

0.25

4

No

1.25

1.5

2

2

3

0.25

6

No

1.25

1.5

1.75

1.75

2

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Advanced Design Examples of Seismic Retrofit of Structures

10,000

0 Degree 90 Degree 180 Degree 270 Degree

Axial force, kN

5000 0 –5000 –10,000 –15,000

–20,000 –40,000 –30,000 –20,000 –10,000 0 10,000 20,000 30,000 40,000 Flexural moment, kN.m FIG. 3.23 P-M interaction curves for shear wall P1 at story
2.

(B) Forces and moments based on the lower-bound values of concrete and steel for force-controlled actions. PUF (ton)

VUFx (ton)

VUFy (ton)

T (ton. m)

MUFx (ton. m)

MUFy (ton. m)


319


164


92

373


6938


664

(C) Development of the axial force-flexural moment interaction curves (see Fig. 3.23). (D) Determination of the expected value of flexural capacity. MCEx 0 degree (kN m)

MCEy 90 degree (kN m)

MCEx 180 degree (kN m)

MCEy 270 degree (kN m)


15758


8213


9358


9358

(E) Determination of the shear force per length, shear for each story, and the m-factors. q(kN) 0 degree 6 VUFx(kN) 0 degree 250 m-factor 0 degree 2.5

180 degree
7 180 degree
316

90 degree 44 VUFy(kN) 90 degree 145

270 degree 578 270 degree 6

180 degree 2.5

90 degree 4.0

270 degree 4.0

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(F) Checking satisfaction of Eq. (3.9). This equation shall be checked for four possible cases: MCEx+, MCEx
, MCEy+, and MCEy
. The eight load combinations lead to 32 possible cases for each section in each shear wall for each seismic hazard (Earthquake-1 and Earthquake-2). Finally, the most critical load case is considered for the design of each section. For the walls that cannot satisfy Eq. (3.9), steel plates are used to increase their flexural capacity. These plates are connected to the foundation and embedded in an RC section with a thickness of 70 cm. Examples of construction stages of the shear walls P5 and P6 are shown in Figs. 3.24–3.26. Some retrofitting stages of the vulnerable shear walls P3 and P4 are presented in Figs. 3.27–3.31.

Shear Design The algorithm for design of the shear walls under shear demands is as follows; (A) Classification of the shear walls including their added legs (if any) into segments in North-South and West-East directions. (B) Determination of the length, thickness, concrete compressive strength, and steel yield strength, number and size of the shear reinforcements in each shear wall segment. (C) Determination of the shear capacity of each segment under two conditions of the expected and the lower-bound capacity. (D) Control of smaller shear strength of reinforcement than four times of that of the concrete. In segments for which this control does not satisfy, the shear strength of reinforcement is assumed to be four times of that of the concrete. (E) Determination of the ratio of the shear force resulted from the flexural capacity of the shear wall to the lower-bound shear strength of the segment. Also, determination of the ratio of the shear force in deformationcontrolled action to the expected shear capacity of the segment. (F) Comparison of the values of the ratios in the previous step and determination of the most critical ratio. (G) In segments in which the shear capacity is smaller than the shear force in the segment, horizontal steel strips (with 1 cm or 2 cm in thickness and 10 cm or 15 cm in width) are used to compensate the shear capacity inadequacy. (H) The connection of the added steel plates to the RC shear walls are made by M25 and M20 bolts made of AIII steel which are drilled into the wall at 40 cm distance. The number of required bolts is determined based on the shear capacity of each steel strip and the shear capacity of each bolt. The shear capacity of each bolt is based on Eq. (3.10). Fv ¼ 0:45Fu Ag

(3.10)

FIG. 3.24 Cutting through the foundation for installation of the starter bars of the shear walls P5 and P6. (Photos taken by T. Honarbakhsh.)

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FIG. 3.25 Flush butt welding of bars due to excessive bars density in construction of shear walls P5 and P6. (Photos taken by T. Honarbakhsh.)

FIG. 3.26 Form working, concrete casting, and quality control in construction of shear walls P5 and P6. (Photos taken by T. Honarbakhsh.)

FIG. 3.27 Retrofitting shear walls P3 and P4 by steel plates (drilling, bolts insertion, and bond tests). (Photos taken by T. Honarbakhsh.)

166 Advanced Design Examples of Seismic Retrofit of Structures

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167

FIG. 3.28 Making template of the inserted bolts, drilling and installation of the steel plates, and quality control of welds. (Photos taken by T. Honarbakhsh.)

FIG. 3.29 Quality control of welds in the steel plates and the supports heel. (Photos taken by T. Honarbakhsh.)

FIG. 3.30 Installation of the supports heel and connection to the foundation, installation of the connection bars of the new foundation to the existing one, bars placement, and casting concrete into the support foundation of the added steel plates. (Photos taken by T. Honarbakhsh.)

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Advanced Design Examples of Seismic Retrofit of Structures

FIG. 3.31 Grouting behind the steel plates, pre-stressing of the bolts, and quality control by the torque meter. (Photos taken by T. Honarbakhsh.)

where Fv ¼ expected shear capacity of each bolt, Fu ¼ ultimate strength of material of the bolt assumed as 520 MPa, and Ag ¼ cross sectional area of the bolt. As an example, the calculations in this part are presented for three shear walls. (A) Classification of the shear walls. Three walls are selected; one wall in West-East and two walls in North-South directions. (B) Determination of each wall’s characteristics. L (cm)

t (cm)

West-East 700 40 North-South 378 40 317 40

φv (mm)

S (cm)

Fy (MPa)

fCL (MPa)

fCE (MPa)

16

20

300

14.5

22.5

16 16

20 20

400 400

35.0 35.0

43.8 43.8

(C) Determination of the shear capacity of each segment. (D) Control of upper bound shear strength of reinforcement. VCL (ton)

VCE (ton)

West-East 170 212 North-South 143 159 120 134

VSL (ton)

VSE (ton)

VL (ton)

VE (ton)

VS < 4VC

338

388

508

600

OK

243 204

280 234

386 323

439 368

OK OK

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169

(E) Determination of the ratio of the shear force to the shear capacity of the segment. (F) Comparison of the values of the ratios in the previous step and determination of the most critical ratio. Some retrofitting stages of the vulnerable shear wall P1L are presented in Figs. 3.32–3.34.

3.5.2.2 Diaphragms All the diaphragms are assumed to be force-controlled members, and hence the force-controlled loads combinations are used for their evaluation. The controls for the diaphragms include the following. In-Plane Shear For evaluation the shear adequacy of the diaphragms, the shear forces in the diaphragms under various loads combinations are calculated and compared to the shear capacity of the section which is as follows. pffiffiffiffi vc ¼ 0:53 fc0 (3.11) pffiffiffiffiffiffiffiffi ¼ 0:53 170 ¼ 7 kg=cm2 vs ¼

Ash fy bd

  20  102 ð300Þ    ¼ 3:0 MPa, Ash ¼ 2ðφ18@25 cmÞ ¼ 20 cm2 ¼ 100  102 20  102 vn ¼ vc + vs ¼ 0:7 + 3:0 ¼ 3:7 MPa;use vn ¼ 3:0 MPa

(3.12)

As an example, the shear stresses at the roof of story
2 are compared with the assumed value of 3.0 MPa (see Fig. 3.35). The areas where these stresses exceed 3.0 MPa are concentrated at the vicinity of the columns’ ends. Because of the wedge shape of the column ends with the average thickness of two time of the diaphragm’s thickness (50 cm), the shear capacity of the section is larger than the shear demands. Connection of Diaphragms The connection of the new shear walls to the diaphragms and also the connection of the diaphragms at the connection line between the two building parts are assumed to be made by two layers of crossed φ16 @ 20 cm. As ¼ 2000 mm2 =m, fy ¼ 400 MPa The shear capacity of the connection line is: As fy ¼ 2000  400 ¼ 800 kN=m which is considerably larger than the shear forces in the diaphragms (determined from the results of the model) in all the stories.

FIG. 3.32 Drilling the shear wall, bolts insertion, and preparation of template in shear wall P1L. (Photos taken by T. Honarbakhsh.)

170 Advanced Design Examples of Seismic Retrofit of Structures

FIG. 3.33 Drilling the steel plates and their installation in shear wall P1L. (Photos taken by T. Honarbakhsh.)

FIG. 3.34 Grouting behind the steel plates, pre-stressing of the bolts, and quality control by the torque meter in shear wall P1L. (Photos taken by T. Honarbakhsh.)

FIG. 3.35 Shear stresses in the roof of story
2 (kg/cm2).

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3.5.2.3 Connections Diaphragms-to-Shear Walls To control the diaphragm’s shear capacity at the connection to the shear walls, the force-controlled shear demand (from the model) at CP performance level at the most critical loads combination for each wall is considered. These forces are compared with the friction shear capacity of the diaphragms by assuming the yield strength of the reinforcement of 300 MPa. The controls are made in Tables 3.15 and 3.16 for the existing and the new shear walls, respectively, which indicate the adequacy of shear capacity in all the shear walls. The friction shear capacities of the diaphragms are based on Eq. (3.13). Vs ¼ 0:9As fy =S

(3.13)

It is noteworthy that extra shear reinforcements are needed at the connection of the diaphragms to some of the new shear walls. These extra shear reinforcements are shown in bold in Table 3.16. New Shear Walls-to-Existing Shear Walls Similar to the previous section, the shear forces demand at the connection of the new shear walls to the old ones are compared with the friction shear capacity of the shear walls. For the connections in which the shear capacity is not adequate, additional shear reinforcements (stitching) are used. For example, for the shear wall W2 with φ16 @ 20 cm, we have: 0:9As fy Vn ¼  2 S π 16 300 ¼ 541 kN=m ¼ 2  0:9   200 4 Vn  0:2fc0 Ac ¼ 0:2  14:5  350  1000 ¼ 1015 kN=m OK The shear forces in the shear wall under most critical loads combination are shown in Fig. 3.36. As can be seen, the forces are smaller than the calculated capacity.

3.5.2.4 Foundation Control and Design The results of the evaluations indicate there is no concern for the soil pressure and settlement; however, at the vicinity of the RC shear walls, the foundation requires retrofitting. The related actions are as follows. Control of the Structural Adequacy of the Foundation Under Gravitational Loads In this part, the controls of soil pressure, settlement, and flexural and shear adequacy of the foundation under the factored gravitational loads are made. The

20

20

25

25

25

18

16

14

16

14

P1L

P3T

P3

P6

P4

STop (mm)

φTop (mm)

Wall

–

14

14

–

–

φTop2Auxiliary (mm)

–

5

25

–

–

STop2Auxiliary (mm)

14

16

14

16

18

φBot (mm)

TABLE 3.15 The Friction Shear Capacity of the Existing Shear Walls

25

25

25

20

20

SBot (mm)

–

–

–

–

–

φBot2Auxiliary (mm)

–

–

–

–

–

SBot2Auxiliary (mm)

332.3

600.2

498.5

542.6

686.7

Vs (kN/m)

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173

25

25

25

14

14

16

P4

P5

P6

STop (mm)

φTop (mm)

Wall

14

16

16

φTop2Auxiliary (mm)

25

25

25

STop2Auxiliary (mm)

TABLE 3.16 The Friction Shear Capacity of the New Shear Walls

16

14

14

φBot (mm)

25

25

25

SBot (mm)

16

16

16

φBot2Auxiliary (mm)

25

25

25

SBot2Auxiliary (mm)

817.0

766.4

766.4

Vs (kN/m)

174 Advanced Design Examples of Seismic Retrofit of Structures

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175

FIG. 3.36 Shear forces in the shear wall W2 (10
1 kN/m).

aim of these controls is determination of the capacity adequacy of the soil and foundation. Loads Combinations For controlling the soil pressure and settlement, the load combination D +L is used. The load combination 1.2D + 1.6L is utilized for controlling the foundation capacity. ACI 318 [5] is used in this part. Controlling the Soil Pressure Under Foundation Based on the geotechnical consultant recommendation, the modulus of soil reaction in vertical direction (Ks) is assumed as 2.2  107 N/m3. The results of Fig. 3.37 indicate the soil pressure in the majority of locations is smaller than the allowable soil stress qa ¼ 0.35 MPa. It is noteworthy that the equipment load is assumed to be 4 kPa. Controlling the Soil Settlement The results of Fig. 3.38 show the soil settlement in the southern and the northern parts are 1.5 cm and 1.0 cm, respectively, which are smaller than the allowable settlement of 5.0 cm.

6.00 5.00 4.00 3.00 2.00 1.00 0.00 –1.00 –2.00 –3.00 –4.00 –5.00 –6.00 –7.00

FIG. 3.37 Soil pressure (10
1 MPa).

0.45 0.30 0.15 0.00 –0.15 –0.30 –0.45 –0.60 –0.75 –0.90 –1.05 –1.20 –1.35 –1.50

FIG. 3.38 Soil pressure (10
2 m).

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177

Controlling the Foundation In the field sampling and data collection of structural members, the thickness of the foundation of the northern and the southern building parts were determined to be 120 cm and 100 cm, respectively. The upper and the lower reinforcements were φ20 @ 150 cm. The flexural behavior of this section is shown in Fig. 3.39. The flexural strength of the foundation under the columns is approximately 2.6  106 N m/m, because of the wedge shape of the foundation in these areas as well as the auxiliary reinforcements (Fig. 3.40). The shear strength pffiffiffiffiffiffiffiisffi determined based on pffiffiffiffi of the foundation vc ¼ 0:53∅s fc0 ¼ 0:53  0:75  250 ¼ 0:6 MPa, which leads to 600 kN/m and 1000 kN/m of capacity for locations other than under columns and the locations under columns, respectively.

Foundation Retrofit Design The controls of the soil pressure and foundation are carried out for the CP performance level under Earthquake-2. It is noted that there are no acceptance criteria for the soil settlement for the CP performance level. Controlling the Soil Pressure Under Foundation Because, in the modeling of the building, the supports were assumed to be rigid, the behavior of the soil under the foundation is deformation-controlled and its adequacy is controlled according to Eq. (3.14) [1].

FIG. 3.39 Flexural behavior of the foundation section (101 kN m/m).

90 70 50 30 10 –10

90 70 50 30 10 –10

FIG. 3.40 Flexural demands in the foundation (101 kN m/m). (A) West-East direction. (B) North-South direction.

–130

–110

–90

–70

–50

–130

–110

–90

–70

–50

–30

110

110

–30

130

130

178 Advanced Design Examples of Seismic Retrofit of Structures

Example of an RC Building Retrofitted by RC Shear Walls Chapter

QUD 1 2κmQc

179

3

(3.14)

where Qc ¼ ultimate capacity of soil. The expected capacity of the foundation is calculated according to Eq. (3.15): qc ¼ 3qa

(3.15)

Based on the geotechnical consultant recommendation, the allowable capacity of the soil is qa ¼ 0.35 MPa. We have: qc ¼ 3qa ¼ 3  0:35 ¼ 1:05 MPa Because the m-factor of 4.0 in the CP performance level has been included in the demand forces, we have: QUD  1 ! QUD  2Qc ¼ 2  1:05 ¼ 2:1 MPa 2  1  Qc The maximum stresses from the envelop of the results of the deformationcontrolled loads combinations shown in Fig. 3.41 is 1.83 MPa, which is smaller than the calculated capacity.

0.0 –1.5 –3.0 –4.5 –6.0 –7.5 –9.0 –10.5 –12.0 –13.5 –15.0 –16.5 –18.0 –19.5

FIG. 3.41 The stresses in the soil (10
1 MPa).

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Advanced Design Examples of Seismic Retrofit of Structures

Design of the New Foundation Based on Code 360 [1], the behavior of foundations is assumed to be force-controlled. As a result, the forces of the linear analysis are reduced to the corresponding forces related to force-controlled actions. QUF ¼

QUD QUD ¼ m 4

The process of designing the foundation includes the following steps: (A) Spectral linear dynamic analysis considering simultaneous application of earthquake components, 100% of the most critical direction of ground motion, and 30% of the ground motion in the orthogonal axis under Earthquake-2 and CP performance level. The coefficients of 1.5/4 ¼ 0.375 in one direction and 0.3  0.375 ¼ 0.1125 in the orthogonal axis are applied. (B) The shear story is calculated and applied at the CoM of that story. (C) The supports reactions are calculated by linear static analysis. (D) Modeling is done. (E) To control the foundation adequacy, the out-of-plane shear and flexure of the section are checked in each direction against the corresponding capacity. (F) The vulnerability of the foundation is observed in the strips with the width of 6–9 m all around the foundation of the southern building part, and also, at the in the strips with a width of 6 m at the northern part of the foundation of the northern building part. (G) For providing the vulnerable parts with adequate capacity, a layer of concrete with the thickness of 70 cm having a reinforcement layer at the top is added to the foundation in those parts. (H) The capacity of the new section for MTop and MBot is calculated (see Fig. 3.42) and is compared with the flexural demands from the envelop of the loads combinations (see Figs. 3.43 and 3.44). The details related to retrofit of the foundation are presented in Figs. 3.45 and 3.46. The main steps in the retrofit process of the foundation are illustrated in Figs. 3.47–3.50.

3.5.2.5 Design of the Added Parts for Filling Diaphragms Openings As previously noted, there is more than 1200 m2 of opening area in stories
1, pilot and +1 which have to be filled. In order to keep the loads from filling these openings to minimum, composite deck system is selected. The 30 cm edges of the existing RC diaphragm are partially demolished by light jackhammers, and the steel plates acting as the supports to the steel beams in the new deck are inserted into these edges. The beams of the composite deck are

FIG. 3.42 Flexural capacity of the retrofitted section (101 kN m). (A) MTop ¼ 3480 kN m. (B) MBot ¼ 3290 kN m.

Example of an RC Building Retrofitted by RC Shear Walls Chapter 3

181

–294 –348

–348

FIG. 3.43 The negative moments (101 kN m). (A) West-East direction. (B) North-South direction.

–241

–294

–27

–187

27 –27

27

–241

80

80

–187

134

134

–80

187

187

–134

241

241

–80

294

294

–134

348

348

182 Advanced Design Examples of Seismic Retrofit of Structures

(A)

(B)

FIG. 3.44 The positive moments (101 kN m). (A) West-East direction. (B) North-South direction.

–329

–278

–228

–177

–127

–76

–25

25

76

127

177

228

278

329

–329

–278

–228

–177

–127

–76

–25

25

76

127

177

228

278

329

Example of an RC Building Retrofitted by RC Shear Walls Chapter 3

183

184

Advanced Design Examples of Seismic Retrofit of Structures

FIG. 3.45 Reinforcement details of the new foundation.

installed, and the casting of concrete is performed after form working and reinforcements. Examples of the results of the diaphragms analysis are shown in Figs. 3.51 and 3.52. Details of filling the diaphragm openings are presented in Figs. 3.53 and 3.54. The construction stages of filling the diaphragms openings are illustrated in Fig. 3.55.

Example of an RC Building Retrofitted by RC Shear Walls Chapter

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FIG. 3.46 Details of the connection bars between the existing and the new foundation.

3.5.2.6 Design of the Added Building Between Axes D–F and 4–6 at the Third to the Eighth Stories As previously stated, the masonry buildings between axes D–F and 4–6 at the third to the eighth stories were demolished and a new building part with RC diaphragms, steel columns, and column ends similar to those in the existing building were designed and constructed. The details and construction stages of the added building between the two building parts are shown in Figs. 3.56–3.59.

186

Advanced Design Examples of Seismic Retrofit of Structures

FIG. 3.47 Removing the 140 cm flooring on the foundation.

FIG. 3.48 Insertion of the connection bars. (Photos taken by T. Honarbakhsh.)

FIG. 3.49 Reinforcement of the new foundation. (Photos taken by T. Honarbakhsh.)

FIG. 3.50 Casting concrete and quality control. (Photos taken by T. Honarbakhsh.)

–9.5

–7.6

–5.7

–3.8

–1.9

0.0

1.9

3.8

5.7

7.6

9.5

11.4

(B)

–10.0

–8.5

–6.9

–5.4

–3.8

–2.3

–0.8

0.8

2.3

3.8

5.4

6.9

FIG. 3.51 Flexural moments about x-axis in the diaphragm at story
1 (ton m). (A) Before filling the openings. (B) After filling the openings.

(A)

–13.3 –11.4

8.5

10.0

Example of an RC Building Retrofitted by RC Shear Walls Chapter 3

187

–8.5

–6.9

–5.4

–3.8

–2.3

–0.8

0.8

2.3

3.8

5.4

6.9

8.5

10.0

(B)

–10.0

–8.5

–6.9

–5.4

FIG. 3.52 Flexural moments about y-axis after filling the openings (ton m). (A) Story
1. (B) Story 0.

(A)

–10.0

–3.8

–2.3

–0.8

0.8

2.3

3.8

5.4

6.9

8.5

10.0

188 Advanced Design Examples of Seismic Retrofit of Structures

Example of an RC Building Retrofitted by RC Shear Walls Chapter

FIG. 3.53 Details of filling the diaphragm openings at story
1.

3

189

190

Advanced Design Examples of Seismic Retrofit of Structures

FIG. 3.54 Connection details of the new diaphragm to the existing one.

3.5.2.7 Design of the Added Building at the Eighth Story in the Southern Building Part In order to provide extra spaces, a new building part with RC diaphragms, steel columns, and column ends similar to those in the existing building were designed and constructed at the eighth story in the Southern building part. The details and construction stages of the added building between the two building parts are shown in Figs. 3.60–3.63.

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191

FIG. 3.55 Construction stages of filling the diaphragms openings. (Photos taken by T. Honarbakhsh.)

192

Advanced Design Examples of Seismic Retrofit of Structures

FIG. 3.56 Development of the northern building part in connection with the southern part at the third to the eight stories.

Example of an RC Building Retrofitted by RC Shear Walls Chapter

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FIG. 3.57 Corridor between the Northern and the Southern building parts. (Photos taken by T. Honarbakhsh.)

FIG. 3.58 The office area at the first and the second stories. (Photos taken by T. Honarbakhsh.)

FIG. 3.59 Erection of the steel columns, form works, reinforcement, and casting concrete in the new diaphragms at the connection area between the two building parts. (Photos taken by T. Honarbakhsh.)

194 Advanced Design Examples of Seismic Retrofit of Structures

Example of an RC Building Retrofitted by RC Shear Walls Chapter

FIG. 3.60 Partial demolition of the roof.

3

195

196

Advanced Design Examples of Seismic Retrofit of Structures

FIG. 3.61 Beams arrangement in the added roof.

Example of an RC Building Retrofitted by RC Shear Walls Chapter

FIG. 3.62 Beams and columns details of the new roof.

3

197

198

Advanced Design Examples of Seismic Retrofit of Structures

FIG. 3.63 Construction stages of the added story. (Photos taken by T. Honarbakhsh.)

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REFERENCES [1] Instruction for Seismic Rehabilitation of Existing Buildings (No. 360) (2014). Management and Planning Organization Office of Deputy for Technical Affairs, Iran (in Persian). [2] T.L. Saaty, Decision making with the analytic hierarchy process, Int. J. Serv. Sci. 1 (1) (2008) 83–98. [3] A.K. Chopra, Dynamics of Structures-Theory and Applications to Earthquake Engineering, third ed., Prentice Hall, New Jersey, 2007. [4] Building and Housing Research Center. Iranian Code of Practice for Seismic Resistant Design of Buildings (Standard 2800). Fourth Revision, Building and Housing Research Center, Iran (in Persian). [5] ACI Committee 318, Building Code Requirements for Structural Concrete (ACI 318-14) and Commentary (ACI 318R-14), American Concrete Institute, Farmington Hills, 2014. [6] ASCE. 2010. Minimum Design Loads for Buildings and Other Structures. ASCE/SEI Standard 7-10. [7] MHUD. Iranian National Building Code, Part 6: Loading, Iran, 2014. [8] ASCE, Seismic Evaluation and Retrofit of Existing Buildings, ASCE/SEI 41-13, American Society of Civil Engineers, Reston, VA, 2014.

Chapter 4

Example of a Steel Frame Building With Masonry Infill Walls☆ Mohammad Yekrangnia* and Hamed Seyri† * †

Department of Civil Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran, Bureau of Technical and Supervision, DRES, Tehran, Iran

Aims By reading this chapter, you are introduced to: l l l l

Damage classification of infilled frames; Evaluation procedure for infill walls; Evaluation procedure for the effects of infill walls on beams and columns; Retrofitting of infill walls by shotcrete;

4.1 INTRODUCTION In this chapter, a typical three-story steel simple frame with brick masonry infill walls is evaluated making use of ASCE 41 [1] and the Iranian Code for Evaluation and Rehabilitation of Infilled Frame Buildings (ICERIFB) [2]. The building has a total area of 1450 m2 including the ground, first, and second stories. The first and second stories are used for office and educational activities, respectively. The structural system in both directions is a simple frame without any lateral load-bearing elements. The roof system is filler-joist (see Fig. 2.26, Chapter 2) in all stories. The foundation of the building is spread footing.

☆ This chapter partially consists of the results of research projects sponsored by Organization for Development, Renovation and Equipping Schools of IR. Iran (DRES). Also, the majority of the details and photos presented in this chapter belong to DRES. The authors of this chapter appreciate the financial and technical support of DRES. Advanced Design Examples of Seismic Retrofit of Structures. https://doi.org/10.1016/B978-0-08-102534-5.00004-0 © 2019 Elsevier Ltd. All rights reserved.

201

202 Advanced Design Examples of Seismic Retrofit of Structures

Kitchen

Computer lab

Computer lab

Office

Office

Office WC

Office

Classroom

Praying room

Library

Classroom

Classroom

Classroom

Office

Office

Teachers’ room

(A)

Classroom

Office

Office

Classroom

Classroom

Classroom

Classroom

Classroom

Classroom

Laborator

(B)

Classroom

Classroom

Classroom

Exam room

Classroom

Office

Classroom

Classroom

Classroom

Classroom

Classroom

(C) FIG. 4.1 The plan and section of the example building (dimensions in cm). (A) Floor story. (B) First story. (C) Second story.

The plan and section of the example building is shown in Fig. 4.1. As can be seen, the building has no lateral load-bearing element in both directions; however, under certain circumstances, the infill walls can be regarded as the loadbearing system. Otherwise, the concentric braces are considered for retrofit of the building (Fig. 4.2).

Example of a Steel Frame Building With Masonry Infill Walls Chapter

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203

(A)

(B)

(C) FIG. 4.2 Sections of the steel frame building. (A) North view. (B) South view. (C) East view.

4.2 ASSUMPTIONS The main assumptions in different part of this chapter are as follows: l

l

l

The evaluation of the considered building is performed according to “Seismic Evaluation and Retrofit of Existing Buildings, ASCE 41” [1]. Evaluation of the nonstructural parts of the building is not within the scope of this chapter. The seismic hazard is the only hazard of the site. As a result, there shall be no liquefaction, slope failure, or surface fault rupture hazard present at the building site. Alternatively, if such a hazard is present, the hazard has been mitigated by the design of the lateral-force-resisting system, including foundations [1].

204 Advanced Design Examples of Seismic Retrofit of Structures

4.3 DAMAGE CLASSIFICATION The behavior of infill walls in infilled frames depends on several factors which include but not limited to inclusion of openings in the wall, rigidity of the beamcolumn connections, material properties of infill wall and frame, flexural stiffness of the frame members compared to stiffness of the infill wall, ratio of height to length of the frame, and connection between the infill and the frame. Generally speaking, infill walls increase the stiffness and strength of frame buildings (Fig. 4.3). The results of the tests by Moghaddam and Dowling [5] indicate that the stiffness and strength of the infilled frame is 2.0 and 2.7 times larger than those of the corresponding bare frame. Neglecting the added mass of the infills, a higher stiffness usually leads to lesser drift ratios. However, infill walls place considerable forces on the frame members and, if not designed for these forces, the columns and beams may fail in shear or flexure. Moreover, the beam-column connections may not be able to transfer the increased forces from the infill walls. As an acceptable approximation, the effects of infill walls can be replaced by a compression-only diagonal strut, schematically shown in Fig. 4.4. Another negative effect from adding infill walls to the frame building is a possible increase in the ductility demand. As infill walls tend to decrease the natural vibration period of structures, they may also decrease the normalized yield strength f y of the structure, defined as Eq. (4.1) [6]. fy ¼

fy f0

(4.1)

where fy ¼ yield strength of the elasto-plastic system and f0 ¼peak value of the earthquake-induced resisting force in the corresponding linear system. As an example, the ductility demand for elasto-plastic system due to El Centro ground motion is shown in Fig. 4.5. In this figure, the possible effects of

(A)

(B)

FIG. 4.3 Damage in frame members caused by infill walls. (A) Shear failure (Permission from Springer) [3]. (B) Flexural failure due to shot column effect (Copyright holder: Elsevier) [4].

Example of a Steel Frame Building With Masonry Infill Walls Chapter

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205

Linf

Fxi

rin

f

a

hinf

hco

FIG. 4.4 Equivalent strut model [1].

adding infill walls are shown by two arrows. As can be seen, the infill walls can result in a considerable ductility demand in the frame buildings. On the other hand, experimental investigations show divergent results in terms of ductility capacity of infilled frames with respect to the corresponding bare frames; some results indicate a slight to moderate increase in ductility thanks to the inclusion of infill walls [7], while others indicate a considerable reduction in the ductility in the frame buildings after adding infill walls [8]. Brittleness of masonry in masonry infill walls especially tends to reduce the ultimate displacement capacity of infilled frames compared to the corresponding bare frames. Other effects of infill walls on the overall performance of buildings can be soft/weak stories because of discontinued infill walls at the lower stories (see Fig. 4.6). There are still important factors influencing the behavior of the infill walls, e.g., their interaction with the braces, and the effects of voids, which have been addressed very rarely in the available literature (see Fig. 4.7). The failure mode of infill walls usually starts from cracks the interface between the frame and the infill wall. Due to deformation incompatibility between the frame and the infill wall, the hairline to moderate cracks start at the perimeter of the infill walls in early stages of loads and small drift ratios (Fig. 4.8A). Following that, shear-sliding cracks form in the infill wall; this is usually related to the expected shear strength of infill walls (Fig. 4.8B).

206 Advanced Design Examples of Seismic Retrofit of Structures

FIG. 4.5 Ductility demand for elasto-plastic system due to El Centro ground motion (critical damping ratio¼5%) [6]; the possible effects of adding infill walls are shown by arrows.

(A)

(B)

FIG. 4.6 Soft story. (A) After Bam earthquake, 2003. (B) After Avaj earthquake, 2002. (Permission from DRES.)

Finally, the corners of the infill wall experience crushing due to concentration of compressive stress at the wall’s corners (Fig. 4.8C). Corner crushing of the infill may not always occur because of either small drift demands or strong infill/ weak frame.

Example of a Steel Frame Building With Masonry Infill Walls Chapter

(A)

4

207

(B)

FIG. 4.7 Some lesser studied effects on the behavior of infill walls. (A) Interaction with concentric braces; after Bam earthquake, 2003 (Permission from DRES). (B) Weak line from the duct of the heater; after Ahar earthquake, 2012. (Photo taken by Mohammad Yekrangnia.)

(A)

(B)

(C)

FIG. 4.8 Failure modes of infill walls. (A) Separation of infill and frame; after Ahar earthquake, 2012. (B) Shear-sliding failure; after Ezgeleh earthquake, 2017. (C) Corner-crushing failure; after Ezgeleh earthquake, 2017. (Photos taken by Mohammad Yekrangnia.)

The infill walls can also experience failure in out-of-plane direction. Performance of the infill walls in out-of-plane direction significantly depends on the extent of arching action activated in the infill wall. This action is related to the infill wall’s area, the ratio of height to thickness of infill, rigidity of the frame members, and openings. Examples of out-of-plane failure of infill walls are shown in Fig. 4.9. In conclusion, the effects of infill walls on the seismic performance of frame buildings are prominent and should be taken into account in design and evaluation.

208 Advanced Design Examples of Seismic Retrofit of Structures

(A)

(B)

FIG. 4.9 Out-of-plane failure of infill walls. (A) Infill walls with three-sided boundary conditions; look at the crack pattern because of free upper side under lightweight roof; after Avaj earthquake, 2002 (Permission from DRES). (B) Collapse of infill walls due to lack of wall post or other measures preventing from outward movement; after Ezgeleh earthquake, 2017. (Photo taken by Mohammad Yekrangnia.)

4.4 EVALUATION OF THE BUILDING In this part, the example building is evaluated for possible retrofit using criteria according to ASCE 41 [1] and Iranian Code for Evaluation and Rehabilitation of Infilled Frame Buildings (ICERIFB) [2]. The main target is to evaluate sufficiency of the existing infill walls in the load-bearing mechanism of the building.

4.4.1 Applicability of the Used Codes 4.4.1.1 Frame The buildings which can be evaluated according to ICERIFB [2] should have up to three stories and the frame alone should be adequate for tolerating the load combinations due to gravity loads, QG, according to the following actions: (1) Where the effects or actions of gravity loads and seismic forces are additive, the action caused by gravity loads, QG, shall be obtained in accordance with Eq. (4.2): QG ¼ 1:1ðQD + QL + Qs Þ

(4.2)

where: QD ¼ action caused by dead loads; QL ¼ action caused by live load, equal to 25% of the unreduced live load obtained in accordance with ASCE 7 [9] but not less than the actual live load; and

Example of a Steel Frame Building With Masonry Infill Walls Chapter

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209

Qs ¼ action caused by effective snow load, which is assumed to be zero in this example. (2) Where the effects or actions of gravity loads and seismic forces counteract each other, the action caused by gravity loads, QG, shall be obtained in accordance with Eq. (4.3): QG ¼ 0:9QD

(4.3)

The demands should be compared with the lower-bound capacity of the frame members. Acceptance criteria for force-controlled actions in components shall satisfy Eq. (4.4): κQCL > QUF

(4.4)

where: QCL ¼ lower-bound strength of a force-controlled action of an element at the deformation level under consideration; QUF ¼ force-controlled action caused by gravity loads in combination with earthquake forces; and κ ¼ knowledge factor which is assumed to be 1.0 because the usual level of knowledge exists about the example buildings including material properties, as-built sketches, etc. According to the Instruction for Seismic Rehabilitation of Existing Buildings (Code 360) [10], the target performance level of the building is considered to be “Life Safety” (LS) and the level of knowledge is “Preferred.” As a result, the knowledge factor of the building is 1.00. The results of the analysis show that the frame alone is adequate for tolerating the load combinations due to gravity loads.

4.4.1.2 Walls All the walls in the building are made of solid bricks with sand-cement mortar; they are hence classified as infill walls according to ICERIFB [2] (Fig. 4.10). 4.4.1.3 Mechanical Properties of Brickwork According to ASCE 41 [1], the condition of masonry can be classified into three groups: l

l

l

Good condition: masonry found during condition assessment to have mortar and units intact, with no visible cracking. Fair condition: masonry found during condition assessment to have mortar and units intact, but with minor cracking. Poor condition: masonry found during condition assessment to have degraded mortar, degraded masonry units, or significant cracking.

210 Advanced Design Examples of Seismic Retrofit of Structures

FIG. 4.10 An example of the infill wall with sold bricks and sand-cement mortar. (Permission from DRES.)

Field observations of the infill walls indicate that the quality of brick work in the example building is fair to good; hence, according to ICERIFB [2], the expected compressive strength of the masonry prism (fme) and the expected shear strength of mortar (vme) are 5.000 MPa and 0.165 MPa, respectively. The modulus of elasticity of the masonry prism is: Eme ¼ 550fme ¼ 550  5 ¼ 2750MPa

(4.5)

4.4.1.4 Conditions for Activation of Infill Wall Behavior At this stage, it is assumed that all the frame members can acceptably tolerate the forces from the infill walls. The acceptance criteria for each frame member are checked in Section “The Results” and, if vulnerable, proper retrofit solution is proposed to upgrade these members. According to ICERIFB [2], each wall should have all of these conditions in order to be considered as an infill wall: l

The wall shall have adequate strength to when subjected to out-of-plane force. By assuming the arching action in the walls, the lower-bound outof-plane strength of the infill panel is determined using Eq. (4.6). QCL ¼

0:7fmL λ1 λ2  144 hinf tinf

where: fmL ¼ lower bound of masonry compressive strength; λ1 ¼ slenderness parameter as defined in Table 4.1;

(4.6)

Example of a Steel Frame Building With Masonry Infill Walls Chapter

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211

TABLE 4.1 Values of λ1 for Use in Eq. (4.6) hinf tinf

5

10

15

25

λ1

0.129

0.060

0.034

0.013

Note: Linear interpolation is used.

λ2 ¼ 0.6; hinf ¼ infill wall’s height; and tinf ¼ infill wall’s thickness. The lower-bound transverse strength of URM infill panels shall exceed normal pressures, as prescribed in Eq. (4.7): 0:4ap Ss Wp
z 1+2 Fp ¼ (4.7) Rp h where: Fp ¼out-of-plane force per unit area for design of a wall spanning between two out-of-plane supports; ap ¼amplification factor according to Table 4.2; Rp ¼response modification factor according to Table 4.2; Wp ¼wall’s weight per unit area; Ss ¼spectral response acceleration at short periods for the selected hazard level and damping, adjusted for site class; z ¼the height of the center of mass of the wall with respect to the building’s base; and h ¼the height of the building. It is noteworthy that the arching action in the wall can be considered when: – the panel is in full contact with the surrounding frame components; – the product of the elastic modulus, Efe, multiplied by the moment of inertia, If, of the most flexible frame component exceeds a value of 1  107 N. m2. – the frame components have sufficient strength to resist thrusts from arching of an infill panel; and hinf ratio is less than or equal to 25. – the tinf l The mortar should be sand cement based on the properties prescribed in Seismic Rehabilitation of Existing Unreinforced Masonry Buildings (Code 376) [11]. Other types of mortar, e.g., sand-clay, cannot meet this requirement. l The panel is in full contact with the surrounding frame components. If there are gaps between the infill panel and the surrounding frame, they

212 Advanced Design Examples of Seismic Retrofit of Structures

TABLE 4.2 ap and Rp Factors Wall Type

ap

Rp

Connected to the frame at all sides

1.0

1.5

Cantilever and parapet

2.5

2.5

Brick

(A)

Concrete

(B)

FIG. 4.11 Common details for filling the upper wythe of infill panels. (A) An example of unacceptable details (look at the weak line cause by inclined placement of bricks without using mortar; after 2012 Ahar-Varzahgan earthquake of Azerbaijan, Iran; Photo taken by Mohammad Yekrangnia). (B) Acceptable details.

l

l l

should be filled with expandable mortar. The details shown in Fig. 4.11B, which are usually practiced in some countries for filling the upper wythe of infill panels, are not acceptable unless all the voids are filled with concrete or other proper materials with a compressive strength equal or larger to that of the masonry brickwork. All the head joints should be filled with mortar; otherwise, these joints should be cleaned and proper mortar should then be injected into them. If the gaps between the adjacent bricks are very narrow which prevent injection of the mortar, a proper grout should be poured on the wall surface to fill these gaps. In this condition, a reduction factor of 40% should be considered for the stiffness and strength of the infill panel. However, evaluation of the frame members should be based on the 100% of the infill capacity, and the abovementioned reduction factor shall not be considered in this process. If the head joints of the wall are left unfilled, the wall cannot meet the requirements of infill panels. The wall shall not have any cracks with a width of more than 3 mm. The walls should be constructed with running bond layup in which each brick overlaps with at least 25% of the length of the brick above.

Example of a Steel Frame Building With Masonry Infill Walls Chapter

l l

4

213

The wall shall not have any inclination or sagging. The maximum length and height of the wall shall not exceed 6.0 m and 4.0 m, respectively.

Based on the conditions above, the walls in the longitudinal direction of the building do not meet the requirements for infill panels because their length exceeds 6.0 m. Consequently, other retrofit solutions should be considered to provide the building with an acceptable lateral-load bearing system. Moreover, according to ICERIFB [2], the wall in I-1-3 does not meet the infill panels requirements because the distance from the edge of opening in this wall to either of the columns in the surrounding frame is located closer to 20% of its length, or the distance from the edge of opening to either of the beams is less than 20% of its height.

4.4.1.5 Summary From the conditions of the building, it can be concluded that the example building does not have any lateral load-bearing system in the longitudinal direction because the walls do not meet the infill panels’ requirements; hence, a proper solution should be considered to provide lateral-resisting system for the structure. In the transverse direction, the walls, except for a single wall, pass the requirements for becoming infill panels. As a result, the building may benefit from these several infill panels in the transverse direction in terms of providing the building with stiffness and strength if these panels sufficiently tolerate the actions from their surrounding frame members; these are discussed in detail in Section “The Results” of this chapter.

4.4.2 Retrofit Solution Once the need to retrofit a building is determined as noted in the previous section, evaluation of the sufficiency of the structural members of the building is carried out. In addition, retrofit solutions are proposed here for the vulnerable members.

4.4.2.1 Material Properties In order to determine the mechanical properties of structural members and connections, it is necessary to determine the yield strength of steel. According to ICERIFB [2], when the expected strength of the material is required, it can be determined based on the lower-bound material properties multiplied by a factor of 1.1. In the example, the lower-bound yield strength of steel is 240 MPa, hence the expected yield strength of steel (Fye) is 264 MPa.

214 Advanced Design Examples of Seismic Retrofit of Structures

TABLE 4.3 Flexural Strength of All Beam Sections in the Example Building QCE 5 MCE 5 ZFye (ton cm)

No.

Section Profile

Ix (cm4)

Sx (cm3)

Zx (cm3)

1

IPE200

1940

194

221

583

2

IPE220

2770

252

285

752

3

IPE270

5790

429

484

1278

4

INP180

1450

161

187

494

5

INP240

4250

354

411

1085

6

INP260

5740

442

513

1354

4.4.2.2 Capacity Determination of the Structural Members Expected-Values of Strength Flexural Strength of Beams As can be seen in Table 4.3, there are six types of beams used in the building. According to ASCE 41 [1], for bare beams bent about their major axes and symmetric about both axes, satisfying the requirements of compact sections, and Lb < Lp, QCE shall be computed in accordance with Eq. (4.8). QCE ¼ MCE ¼ MPCE ¼ ZFye

(4.8)

where: Lb ¼ distance between points braced against lateral displacement of the compression flange, or between points braced to prevent twist of the cross section, per the Load and Resistance Factor Design Specification for Structural Steel Buildings (LRFD) (AISC 360) [12]; Lp ¼ limiting lateral unbraced length for full plastic bending capacity for uniform bending from Load and Resistance Factor Design Specification for Structural Steel Buildings (LRFD) (AISC 360) [12]; MPCE ¼ expected plastic moment capacity; and Fye ¼ expected yield strength of the material. Otherwise, QCE shall be computed in accordance with Eq. (4.9). 5 QCE ¼ MCE ¼ Fb S 3

(4.9)

where Fb ¼ allowable flexural stress according to the American Institute of Steel Construction (AISC) [12] and S¼ elastic section modulus. In the following, an example of INP240 beam is presented for checking the compactness and flexural strength of the section. The flexural strength of all beam sections in the example building is presented in Table 4.3.

Example of a Steel Frame Building With Masonry Infill Walls Chapter

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b 10:6 545 545 ¼ 8:09  pffiffiffiffiffi ¼ pffiffiffiffiffiffiffiffiffiffi ¼ 10:6 INP240 ! B ¼ 10:6cm,t ¼ 1:31cm ! ¼ t 1:31 Fy 2640 QCE ¼ ZFye ¼ 410:27  2640 ¼ 10:8 ton m Flexural and Shear Strength of Columns As can be seen in Table 4.4, six types of columns are used in the building. The method of determination of the flexural strength of column sections is similar to that for the beam sections which was presented in Section “Flexural Strength of Beams.” According to ASCE 41 [1], the shear strength of columns, QCE, shall be computed in accordance with Eq. (4.10). QCE ¼ VCE ¼ 0:55Fye dc tp

(4.10)

where dc ¼column depth and tp ¼thickness of column web. Since the column sections are made of double profiles with discontinuous welding, none of the column sections satisfies the compactness requirements, hence their flexural strength is determined in accordance with Eq. (4.9). In the following, an example of a 2UNP180 +2PL160 10 column is presented for checking the flexural and shear strength of the section. The expected flexural and shear strengths of all the column sections in the example building are presented in Table 4.4. 2UNP180 + 2PL160  10 ! A ¼ 87:92cm2 ,Sx ¼ 559:7cm3 , Sy ¼ 598:2cm3 , Aw ¼ 31:94cm2 5 5 QCEx ¼ Sx Fb ¼  559:7  0:6  2640 ¼ 1478 ton cm 3 3 5 5 QCEy ¼ Sy Fb ¼  598:2  0:6  2640 ¼ 1579 ton cm 3 3 QCE ¼ VCE ¼ 0:55Fye dc tp ¼ 0:55  2640  31:94 ¼ 46 ton

Lower-Bound Values of Strength Axial and Flexural Strength of Columns The axial strength of columns, QCL, shall be computed in accordance with Eq. (4.11). QCL ¼ PCL ¼ 1:7Fa A   1  0:5β2 Fy KL  Cc ! Fa ¼ if F:S: r

(4.11)

Section Profile

2UNP180+2PL160 10

2UNP180+2PL220 10

2UNP180+2PL240 10

2UNP220+2PL240 10

2UNP240+2PL220 10

2UNP240+2PL240 10

No.

1

2

3

4

5

6

132.58

128.58

122.88

103.92

99.92

87.92

A (cm2)

1130.6

1082.5

977.8

704.2

668.1

559.7

Sx (cm3)

1020.5

982

916.1

722.9

682.2

598.2

Sy (cm3)

49.51

49.28

43.57

32.77

32.59

31.94

Aw (cm2)

2985

2858

2581

1859

1764

1478

QCE 5 MCEx (ton cm)

2694

2592

2419

1908

1801

1579

QCE 5 MCEy (ton cm)

TABLE 4.4 Flexural and Shear Strengths of all the Column Sections in the Example Building [12a]

72

72

63

48

47

46

QCE 5 VCE (ton)

216 Advanced Design Examples of Seismic Retrofit of Structures

Example of a Steel Frame Building With Masonry Infill Walls Chapter

4

217

sffiffiffiffiffiffiffiffiffiffi KL 2π 2 E 6440 ¼ pffiffiffiffiffi β ¼ r ,F:S: ¼ 1:67 + 0:375β  0:125β2 , Cc ¼ Cc Fy Fy if

KL 12π 2 E 105  105 > Cc ! Fa ¼  2 ¼  2 r KL KL 23 r r

where: PCL ¼lower-bound compression strength of the column; A ¼column cross-sectional area; K ¼effective length factor determined in accordance with AISC [12]; L ¼ laterally unbraced length of the member; and r ¼governing radius of gyration. The lower-bound axial strength of all the column sections in the example building is presented in Table 4.5. The lower-bound flexural strength of all the column sections in the example building which is presented in Table 4.6 is determined based on the method in Section “Flexural and Shear Strength of Columns,” except for replacing FyL as the lower-bound yield strength of the material with FyE.

4.4.2.3 The Retrofit Solution As previously stated, because of the high length of the walls in longitudinal direction, these walls cannot be regarded as infill walls; therefore, the building is seismically vulnerable. However, the walls in transverse direction can provide stiffness and strength to the building because they meet the requirement for infill panels. Based on these results, the following retrofit solution for the building is proposed: l l

Longitudinal direction: inclusion of concentric steel braces to the building. Transverse direction: considering the existing infill panels as the lateral load-bearing system; if not adequate, retrofitting these panels with shotcreting is considered.

In this example, only the retrofit of the building in a transverse direction which is related to the retrofit of infill walls is presented. The retrofit design process of adding concentric steel braces to the building, which is recommended for this example building in the longitudinal direction, is presented in a separate example in Chapter 5.

4.4.2.4 Modeling of the Building For modeling of the building, ETABS is used. It is assumed that the example building is located in an area with very high seismicity with the design PGA of 0.35 g according to Iranian Code of Practice for Seismic Resistant Design of Buildings (Standard 2800) [13]. The soil condition is III according to

Section Profile

2UNP18PL22X1

2UNP22PL24X1

2UNP24PL22X1

2UNP24PL24X1

2UNP18PL24X1

2UNP18PL16X1

2UNP22PL24X1

2UNP24PL22X1

2UNP24PL24X1

2UNP18PL22X1

No.

1

2

3

4

5

6

7

8

9

10

99.92

132.58

128.58

122.88

87.92

103.92

132.58

128.58

122.88

99.92

A (cm2)

320

320

320

320

320

340

340

340

340

340

L (cm)

9.42

10.29

10.25

10.03

9.40

9.51

10.29

10.25

10.03

9.42

r2 (cm)

8.18

10.53

10.46

9.77

7.98

8.23

10.53

10.46

9.77

8.18

r3 (cm)

39.12

31.1

31.22

32.75

40.1

41.31

33.04

33.17

34.8

41.56

rmax

KL

0.30

0.24

0.24

0.25

0.31

0.31

0.25

0.25

0.26

0.32

β

1.78

1.76

1.76

1.76

1.78

1.78

1.76

1.76

1.77

1.78

F. S.

TABLE 4.5 Lower-Bound Axial Strength of All the Column Sections in the Example Building [12a] kg cm2



1289.84

1327.70

1327.15

1320.18

1284.97

1278.88

1318.86

1318.26

1310.67

1277.6

Fa



219.10

299.24

290.10

275.78

192.06

225.93

297.25

288.15

273.79

217.02

QCL 5 PCL (ton)

218 Advanced Design Examples of Seismic Retrofit of Structures

Section Profile

2UNP180+ 2PL16010

2UNP180+ 2PL22010

2UNP180+ 2PL24010

2UNP220+ 2PL24010

2UNP240+ 2PL22010

2UNP240+ 2PL24010

No.

1

2

3

4

5

6

132.58

128.58

122.88

103.92

99.92

87.92

A (cm2)

1130.6

1082.5

977.8

704.2

668.1

559.7

Sx (cm3)

1020.5

982

916.1

722.9

682.2

598.2

Sy (cm3)

49.51

49.28

43.57

32.77

32.59

31.94

Aw (cm2)

2713

2598

2347

1690

1603

1343

QCE 5 MCEx (ton cm)

TABLE 4.6 Lower-Bound Flexural Strength of All the Column Sections in the Example Building [12a]

2449

2357

2199

1735

1637

1436

QCE 5 MCEy (ton cm)

Example of a Steel Frame Building With Masonry Infill Walls Chapter 4

219

220 Advanced Design Examples of Seismic Retrofit of Structures

FIG. 4.12 The 3D model building.

TABLE 4.7 Dead Loads  Item

Load

Floors

530

Roof

535

Exposed peripheral walls

1476

Unexposed peripheral walls

2374

Internal walls

1282

Parapet walls

474

Stairs (ramp)

666

Stairs (staircase)

408

kg m2



Standard 2800, which is moderate to dense soil with the average shear wave speed of 175–375 m/s. It is noted that the model should be 3D in order to take the effect of torsions into account. The model building is shown in Fig. 4.12. Based on the Iranian National Building Code; Part 6: Loading [14], the dead loads and live loads of the different parts of the example building are presented in Tables 4.7 and 4.8, respectively.

Example of a Steel Frame Building With Masonry Infill Walls Chapter

4

221

TABLE 4.8 Live Loads  Load

Item Classrooms

(A)

kg m2



3500

Corridors

500

Office rooms

250

Public rooms without fixed chairs

500

Roof

150

(B)

FIG. 4.13 Cradle-type connection. (A) An example (Permission from DRES). (B) Details.

Connections The beam-to-column connections in example building are cradle-type as shown in Fig. 4.13, which is considered as a simple connection. In order to determine the stiffness of the connection, the method according to Karami [15] is used. Based on the recommendation of Moghaddam [16], the torsional stiffness of the cradle-type connections is approximately 900 ton m/rad. For modeling the connections, an arbitrary 10 cm beam element with circular section is used. The diameter of these elements is determined based on the aforementioned assumed torsional stiffness. rffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 5 4 32  900  10  10 GJ πd4 4 32kθ L ffi 10:5cm !d¼ ¼ kθ ¼ ,J ¼ 32 L πG π  0:4  2  106 Infill Panels In-Plane Direction In the model of the example building, the effects of infill walls are considered as compressive-only diagonal strut as per ASCE 41 [1].

222 Advanced Design Examples of Seismic Retrofit of Structures

The thickness of the strut and the modulus of elasticity of the material assigned to struts are the same as those in the real infill panels in the example building. The effective width of these struts is determined based on the method presented in this section, which is based on ASCE 41. It is noteworthy that the proposed relations in ASCE 41 are based on solid infill panels inside frames with rigid connections. As a result, these relations should be modified to be used in this example building, as some of the infill panels have openings and all the frame connections are simple. Also, in order to capture better the demands from the infill walls on the frame members, several multi-strut models have been proposed which can be alternatively used for simulation of the effects of infill walls [17, 18]. Effective Width. According to ASCE 41 [1], the effective width of the infill (a) is determined based on Eq. (4.12). a ¼ 0:254ðλl hcol Þ0:4 rinf R1 R2 where:

(4.12)



10Eme tinf Sin ð2θÞ 0:25 Efe Icol hinf hcol ¼ column height between centerlines of beams; hinf ¼ height of infill panel; Efe ¼ expected modulus of elasticity of frame material; Eme ¼ expected modulus of elasticity of infill material; Icol ¼moment of inertia of column; rinf ¼ diagonal length of infill panel; tinf ¼thickness of infill panel and equivalent strut; θ ¼angle whose tangent is the infill height-to-length aspect ratio (radians); λl ¼ coefficient used to determine equivalent width of infill strut; and R1 ¼the reduction coefficient for frame connections according to ICERIFB [2]; if the connection is rigid or pin, the coefficient is unity and 0.5, respectively. For other cases, this coefficient is determined according to Eq. (4.13). λl ¼

R1 ¼ 0:5ð1 + CRÞ

(4.13)

where CR ¼ the rigidity of the connection, with CR ¼ 1 as the rigid connection and CR ¼ 0 as the pin connection, and R2 ¼the reduction coefficient for infill panels having opening according to ICERIFB [2] which is determined according to Eq. (4.14): R2 ¼ 0:6

    AOpening 2 AOpening +1  1:6 APanel APanel

(4.14)

where AOpening ¼the area of the opening and APanel ¼the area of the panel. According to Karami [15], the cradle-type connections are semi rigid; however, due to lack of sufficient data about the rigidity of this type of connection,

Example of a Steel Frame Building With Masonry Infill Walls Chapter

4

223

it is conservatively assumed that the frame connections in the example building is pin, hence R1 ¼ 0.5. It is worth mentioning that the wall in the axis B-1-3 cannot be regarded as the infill panel, because it does not meet the requirements of the position of the opening according to ICERIFB; however, by reducing the size of the opening in this wall, it is possible to consider this wall as an infill panel. The infill panels and the effective width of their equivalent struts are presented in Table 4.9. Thickness. Because the infill panels in the example building are completely located inside the frames, their whole thickness is considered in calculations. However, it is necessary to install steel plates at the corners of the infill in order to improve the connection between the infill panels and the surrounding frame. The details of this plate are presented in Section “Evaluation of the Frame Connections.” Expected Shear Strength. According to ASCE 41 [1], the shear behavior in infill panels is considered a deformation-controlled action. The expected shear strength of infill panels shall be computed in accordance with Eq. (4.15). QCE ¼

a  tinf  fme  cos θ 2:5

(4.15)

where: a ¼effective width of infill panels which is computed in accordance with Eq. (4.9); tinf ¼ thickness of infill panel and equivalent strut; fme ¼expected compressive strength of infill material which is assumed to be 5.0 MPa in this example; and θ ¼angle whose tangent is the infill height-to-length aspect ratio (radians). The expected shear strengths of infill panels in the transverse direction are presented in Table 4.10.

4.4.2.5 Analysis of the Building In the presented example, the linear static procedure (LP) is utilized to analyze the building under seismic demands.

Natural Period of the Building According to ICERIFB [2], the natural period of the building can be determined according to Eq. (4.16). 3

T ¼ 1:25  0:05  H 4

(4.16)

where H is the total height of the building. 3

H ¼ 9:8 m ! T ¼ 1:25  0:05  9:84 ¼ 0:346 s

Axis

A1-3

A4-5

B1-3

B4-5

C1-3

C4-5

F-13

F-45

G1-3

G4-5

H1-3

H4-5

Story

Floor

Floor

Floor

Floor

Floor

Floor

Floor

Floor

Floor

Floor

Floor

Floor

None

None

None

None

None

None

None

None

None

Door

None

None

Opening

280

280

280

280

280

280

280

280

280

280

280

280

hinf (cm)

540

540

540

540

540

540

540

540

540

540

540

540

Linf (cm)

340

340

340

340

340

340

340

340

340

340

340

340

hcol (cm)

2UNP18PL22X1

2UNP24PL22X1

2UNP18PL22X1

2UNP24PL22X1

2UNP18PL22X1

2UNP24PL24X1

2UNP18PL22X1

2UNP24PL24X1

2UNP18PL22X1

2UNP24PL22X1

2UNP18PL22X1

2UNP22PL24X1

Col Sec (left)

2UNP24PL22X1

2UNP18PL24X1

2UNP24PL22X1

2UNP18PL24X1

2UNP24PL24X1

2UNP22PL24X1

2UNP24PL24X1

2UNP22PL24X1

2UNP24PL22X1

2UNP18PL24X1

2UNP22PL24X1

2UNP18PL24X1

Col Sec (right)

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Col Direction

8868

13,503

8868

13,503

8868

14,032

8868

14,032

8868

13,503

8868

12,367

Icol2left (cm4)

TABLE 4.9 Infill Panels and the Effective Width of Their Equivalent Struts [12a]

13,503

9398

13,503

9398

14,032

12,367

14,032

12,367

13,503

9398

12,367

9398

Icol2left (cm4)

8868

9398

8868

9398

8868

12,367

8868

12,367

8868

9398

8868

9398

Icol2min (cm4)

608.28

608.28

608.28

608.28

608.28

608.28

608.28

608.28

608.28

608.28

608.28

608.28

rinf (cm)

20

20

20

20

20

20

20

20

20

20

20

20

tinf (cm)

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

θ (degree)

0.0308

0.0304

0.0308

0.0304

0.0308

0.0284

0.0308

0.0284

0.0308

0.0304

0.0308

0.0304

λl

1

1

1

1

1

1

1

1

1

0.857

1

1

R2

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

R1

30.17

30.35

30.17

30.35

30.17

31.19

30.17

31.19

30.17

26.01

30.17

30.35

a (cm)

I-13

I-45

A1-3

A4-5

B1-3

B4-5

C1-3

C4-5

F-13

F-45

G1-3

G4-5

H1-3

H4-5

Floor

Floor

1st

1st

1st

1st

1st

1st

1st

1st

1st

1st

1st

1st

None

None

None

None

None

None

None

None

None

None

None

None

None

None

280

280

280

280

280

280

280

280

280

280

280

280

280

280

540

540

540

540

540

540

540

540

540

540

540

540

540

540

320

320

320

320

320

320

320

320

320

320

320

320

340

340

2UNP18PL16X1

2UNP24PL22X1

2UNP18PL16X1

2UNP24PL22X1

2UNP18PL16X1

2UNP24PL24X1

2UNP18PL16X1

2UNP24PL24X1

2UNP18PL16X1

2UNP24PL22X1

2UNP18PL16X1

2UNP22PL24X1

2UNP18PL22X1

2UNP22PL24X1

2UNP24PL22X1

2UNP18PL22X1

2UNP24PL22X1

2UNP18PL22X1

2UNP24PL24X1

2UNP22PL24X1

2UNP24PL24X1

2UNP22PL24X1

2UNP24PL22X1

2UNP18PL22X1

2UNP22PL24X1

2UNP18PL22X1

2UNP22PL24X1

2UNP18PL24X1

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

7776

13,503

7776

13,503

7776

14,032

7776

14,032

7776

13,503

7776

12,367

8868

12,367

13,503

8868

13,503

8868

14,032

12,367

14,032

12,367

13,503

8868

12,367

8868

12,367

9398

7776

8868

7776

8868

7776

12,367

7776

12,367

7776

8868

7776

8868

8868

9398

608.28

608.28

608.28

608.28

608.28

608.28

608.28

608.28

608.28

608.28

608.28

608.28

608.28

608.28

20

20

20

20

20

20

20

20

20

20

20

20

20

20

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

0.0319

0.0308

0.0319

0.0308

0.0319

0.0284

0.0319

0.0284

0.0319

0.0308

0.0319

0.0308

0.0308

0.0304

1

1

1

1

1

1

1

1

1

1

1

1

1

1

30.51

30.92

30.51

30.92

30.51

31.96

30.51

31.96

30.51

30.92

30.51

30.92

30.17

30.35

Continued

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

Axis

A1-3

A4-5

B1-3

B4-5

C1-3

C4-5

F-13

F-45

G1-3

G4-5

H1-3

H4-5

Story

2nd

2nd

2nd

2nd

2nd

2nd

2nd

2nd

2nd

2nd

2nd

2nd

None

None

None

None

None

None

None

None

None

None

None

None

Opening

280

280

280

280

280

280

280

280

280

280

280

280

hinf (cm)

540

540

540

540

540

540

540

540

540

540

540

540

Linf (cm)

320

320

320

320

320

320

320

320

320

320

320

320

hcol (cm)

2UNP18PL16X1

2UNP24PL22X1

2UNP18PL16X1

2UNP24PL22X1

2UNP18PL16X1

2UNP24PL24X1

2UNP18PL16X1

2UNP24PL24X1

2UNP18PL16X1

2UNP24PL22X1

2UNP18PL16X1

2UNP22PL24X1

Col Sec (left)

2UNP24PL22X1

2UNP18PL22X1

2UNP24PL22X1

2UNP18PL22X1

2UNP24PL24X1

2UNP22PL24X1

2UNP24PL24X1

2UNP22PL24X1

2UNP24PL22X1

2UNP18PL22X1

2UNP22PL24X1

2UNP18PL22X1

Col Sec (right)

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Col Direction

7776

13,503

7776

13,503

7776

14,032

7776

14,032

7776

13,503

7776

12,367

Icol2left (cm4)

TABLE 4.9 Infill Panels and the Effective Width of Their Equivalent Struts—cont’d

13,503

8868

13,503

8868

14,032

12,367

14,032

12,367

13,503

8868

12,367

8868

Icol2left (cm4)

7776

8868

7776

8868

7776

12,367

7776

12,367

7776

8868

7776

8868

Icol2min (cm4)

608.28

608.28

608.28

608.28

608.28

608.28

608.28

608.28

608.28

608.28

608.28

608.28

rinf (cm)

20

20

20

20

20

20

20

20

20

20

20

20

tinf (cm)

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

θ (degree)

0.0319

0.0308

0.0319

0.0308

0.0319

0.0284

0.0319

0.0284

0.0319

0.0308

0.0319

0.0308

λl

1

1

1

1

1

1

1

1

1

1

1

1

R2

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

R1

30.51

30.92

30.51

30.92

30.51

31.96

30.51

31.96

30.51

30.92

30.51

30.92

a (cm)

Example of a Steel Frame Building With Masonry Infill Walls Chapter

4

227

TABLE 4.10 Expected Shear Strengths of Infill Panels [12a] Story

Axis

hinf (cm)

Linf (cm)

tinf (cm)

θ (degree)

QCE (kg)

Floor

A-1-3

280

540

20

27.41

11,008

Floor

A-4-5

280

540

20

27.41

11,008

Floor

B-1-3

280

540

20

27.41

9233

Floor

B-4-5

280

540

20

27.41

11,008

Floor

C-1-3

280

540

20

27.41

11,008

Floor

C-4-5

280

540

20

27.41

11,008

Floor

F-1-3

280

540

20

27.41

11,008

Floor

F-4-5

280

540

20

27.41

11,008

Floor

G-1-3

280

540

20

27.41

11,008

Floor

G-4-5

280

540

20

27.41

11,008

Floor

H-1-3

280

540

20

27.41

11,008

Floor

H-4-5

280

540

20

27.41

11,008

Floor

I-1-3

280

540

20

27.41

11,008

Floor

I-4-5

280

540

20

27.41

11,008

1st

A-1-3

280

540

20

27.41

11,008

1st

A-4-5

280

540

20

27.41

11,008

1st

B-1-3

280

540

20

27.41

11,008

1st

B-4-5

280

540

20

27.41

11,008

1st

C-1-3

280

540

20

27.41

11,008

1st

C-4-5

280

540

20

27.41

11,008

1st

F-1-3

280

540

20

27.41

11,008

1st

F-4-5

280

540

20

27.41

11,008

1st

G-1-3

280

540

20

27.41

11,008

1st

G-4-5

280

540

20

27.41

11,008

1st

H-1-3

280

540

20

27.41

11,008

1st

H-4-5

280

540

20

27.41

11,008

2nd

A-1-3

280

540

20

27.41

11,008

2nd

A-4-5

280

540

20

27.41

11,008

2nd

B-1-3

280

540

20

27.41

11,008

2nd

B-4-5

280

540

20

27.41

11,008 Continued

228 Advanced Design Examples of Seismic Retrofit of Structures

TABLE 4.10 Expected Shear Strengths of Infill Panels—cont’d Story

Axis

hinf (cm)

Linf (cm)

tinf (cm)

θ (degree)

QCE (kg)

2nd

C-1-3

280

540

20

27.41

11,008

2nd

C-4-5

280

540

20

27.41

11,008

2nd

F-1-3

280

540

20

27.41

11,008

2nd

F-4-5

280

540

20

27.41

11,008

2nd

G-1-3

280

540

20

27.41

11,008

2nd

G-4-5

280

540

20

27.41

11,008

2nd

H-1-3

280

540

20

27.41

11,008

2nd

H-4-5

280

540

20

27.41

11,008

Building’s Base Shear Based on the LSP, the seismic demand force is calculated based on Section 3-33-2 of the Iranian Code of Retrofitting of Existing Structures (Code 360) [10] as follows: V ¼ C1 C 2 C m S a W

(4.17)

where: V ¼pseudo lateral force; and Sa ¼ response spectrum acceleration, at the fundamental period and damping ratio of the building in the direction under consideration which is determined based on Section 1-7 of Code 360 [10]. The example building is located on soil type III in a region with very high seismicity. As a result, and based on the natural period of the building determined in Section “Natural Period of the Building,” Sa is the maximum spectral acceleration 2.75 0.35 g¼ 0.9625 g (see Fig. 4.14); W ¼ effective seismic weight of the building, including the total dead load and applicable codified portions of other gravity loads. According to Code 360, the dead loads also include the weight of partition walls and the total operating weight of permanent equipment, and the live loads are 20% of the codified live loads including snow [10]; and C1 ¼ modification factor to relate expected maximum inelastic displacements to displacements calculated for linear elastic response. This factor is determined based on either of these methods.

Example of a Steel Frame Building With Masonry Infill Walls Chapter

4

229

1.2

Spectral acceleration, g

1 0.8 0.6 0.4 0.2 0 0

0.5

1

1.5

2

2.5

Natural period, s FIG. 4.14 Design spectral acceleration on soil type III with very high seismicity.

(1) Based on Eq. (4.18). 25ðRu  1Þ a Ru  1 0:2 < T  1 ! C1 ¼ 1 + aT 2 T > 1 ! C1 ¼ 1

T  0:2 ! C1 ¼ 1 +

(4.18)

where: a ¼ site class factor: ¼130 site Class A or B according to ASCE 41 [1]; ¼90 site Class C according to ASCE 41; ¼60 site Class D, E, or F according to ASCE 41; T ¼ fundamental period of the building in the direction under consideration, calculated in Section “Natural Period of the Building”; and Ru ¼ ratio of elastic strength demand to yield strength coefficient calculated in accordance with (4.19). If the elastic base shear capacity substituted Ve is available, Eq. (4.20) can be used interchangeably. DCRmax Cm  1 1:5 Sa Ru ¼ Cm Ve =W

Ru ¼

(4.19) (4.20)

where DCRmax is the largest demand to capacity ratio (DCR) computed for any primary component of a building in the direction of response under consideration, taking C1 ¼ C2 ¼ Cm ¼ 1.0.

230 Advanced Design Examples of Seismic Retrofit of Structures

(2) Based on Eq. (4.21) when Ru cannot be determined: 1  C1 ¼ 1 +

Ts  T 2Ts  0:2

(4.21)

where Ts is the natural period at the intersection of the acceleration-sensitive and velocity-sensitive regions, which for soil type III is 0.7 according to Standard 2800 [13]. C1 ¼ 1 +

0:7  0:346 ¼ 1:295 2  0:7  0:2

where C2 ¼ modification factor to represent the effect of pinched hysteresis shape, cyclic stiffness degradation, and strength deterioration on maximum displacement response. Based on Code 360 [10], this parameter is can be determined based on either of these methods. (1) Based on Eq. (4.22): 25ðRu  1Þ  a  1 Ru  1 2 T  0:7 ! C2 ¼ 1 + 800 T T  0:7 ! C2 ¼ 1 +

(4.22)

(2) In the absence of precise calculations, C2 can be taken as 1.0. For the example building, it was assumed that C2 ¼ 1. Cm ¼ effective mass factor to account for higher modal mass participation effects obtained from Table 3.4 of Code 360 [10]. Cm is 1.0 for the example building in the transverse direction which is a steel unbraced frame, categorized as “Other” structural systems in this table. This coefficient is 0.9 for the building in the longitudinal direction as a three-story braced building. The design base shear of the example building in the two longitudinal (X) and transverse (Y) directions are as follows: Vx ¼ 1:295  1:0  1:0  0:9  0:35  2:75  W ¼ 1:12W Vy ¼ 1:295  1:0  1:0  1:0  0:35  2:75  W ¼ 1:25W The seismic force Fx applied at any floor level x shall be determined in accordance with Eqs. (4.23) and (4.24) [10]: Fx ¼ Cvx V

(4.23)

wx hkx Cvx ¼ X n wi hki

(4.24)

i¼1

Example of a Steel Frame Building With Masonry Infill Walls Chapter

4

231

where: V ¼ pseudo-lateral force based on Eq. (4.18); and Cvx ¼ vertical distribution factor; k ¼ 2.0 for T 2.5s, 1.0 for T  0.5s, and 0.5 T + 0.75 for 0.5< T< 2.5s; wi ¼ portion of the effective seismic weight W located on or assigned to level i; wx ¼ portion of the effective seismic weight W located on or assigned to level x; hi ¼ height from the base to level i; and hx ¼ height from the base to level x.

Applicability of Linear Static Procedure According to ASCE 41 [1], linear procedures are appropriate where the expected level of nonlinearity is low. This is measured by component demand capacity ratios (DCRs) of less than 2.0. As is shown in Section “The Results,” most of the components’ DCRs in the example buildings are larger than 2.0. However, in a case in which the DCR of even a single component is larger than 2.0, the LSP can still be utilized if at least two of the conditions below are met. Irregularity In-Plane Discontinuity. An in-plane discontinuity irregularity shall be considered to exist in any primary element of the lateral-force-resisting system wherever a lateral-force-resisting element is present in one story, but does not continue or is offset within the plane of the element in the story immediately below. Out-of-Plane Discontinuity. An out-of-plane discontinuity irregularity shall be considered to exist in any primary element of the lateral-force-resisting system where an element in one story is offset out-of-plane relative to that element in an adjacent story. Weak Story. A weak story irregularity shall be considered to exist in any direction of the building if the ratio of the average shear DCRs of any story to that of an adjacent story in the same direction exceeds 125%. The average DCR of a story shall be calculated by Eq. (4.25): n X

DCR ¼

1

DCRi Vi

n X

(4.25) Vi

1

where: DCR ¼average DCR for the story; DCRi ¼critical action DCR for element i of the story; Vi ¼ total calculated lateral shear force in an element i due to earthquake response, assuming that the structure remains elastic; and n ¼total number of elements in the story.

232 Advanced Design Examples of Seismic Retrofit of Structures

For buildings with flexible diaphragms, each line of framing shall be independently evaluated. Torsional Strength. A torsional strength irregularity shall be considered to exist in any story if the diaphragm above the story under consideration is not flexible and, for a given direction, the ratio of the critical element DCRs for primary elements on one side of the center of resistance of a story, to those on the other side of the center of resistance of the story, exceeds 1.5. In the example building, there is no in-plane or out-of-plane discontinuity. Because of the similar number of components in the stories and their similar section profiles, the difference of the ratio of the average shear DCR of any story and that of an adjacent story in the same direction is less than 25%. In addition, the building has no torsional strength irregularities. The Fundamental Period of the Building, T, Is Greater Than or Equal to 3.5 Times Ts; The natural period of the example building is 0.346 sec according to Section “Natural Period of the Building,” which does not exceed 3.5  0.7 ¼ 2.45 s. The Ratio of the horizontal dimension at any story to the corresponding dimension at an adjacent story exceeds 1.4 (excluding penthouses); There is no major difference in the horizontal dimensions of the stories in the example building. The building has a torsional stiffness irregularity in any story. A torsional stiffness irregularity exists in a story if the diaphragm above the story under consideration is not flexible and the results of the analysis indicate that the drift along any side of the structure is more than 150% of the average story drift; As Table 4.11 shows, the example building has no torsional stiffness irregularity in any story. The building has a vertical stiffness irregularity. A vertical stiffness irregularity exists where the average drift in any story (except penthouses) is more than 150% of that of the story above or below; According to the results presented in Table 4.11, the example building has no vertical stiffness irregularity. The building has a non-orthogonal lateral-force-resisting system; As the lateral-force-resisting system, the example building has concentric braces in the longitudinal direction (which is assumed to have already been added to the building) and the infill panels in the transverse direction. In conclusion, the example building can be analyzed by the linear static procedure.

4.4.2.6 Evaluation of the Building Actions Calculations Deformation-Controlled Based on Code 360 [10], deformation-controlled actions for the LSP denoted by QUD shall be calculated in accordance with Eq. (4.26): QUD ¼ QG + QE

(4.26)

Example of a Steel Frame Building With Masonry Infill Walls Chapter

4

233

TABLE 4.11 Comparison of the Maximum and Average Drifts in Both Directions [12a] Story

Δmax2X (mm)

Δmax2Y (mm)

Δave2X (mm)

Δave2X (mm)

Δmax X ΔaveX

Δmax Y ΔaveY

3

7.84

28.96

7.49

23.66

1.05

1.22

2

5.62

21.95

5.35

18.53

1.05

1.18

1

2.77

10.97

2.63

10.03

1.05

1.09

where: QUD ¼ deformation-controlled action caused by gravity loads and earthquake forces; QE ¼ action caused by the response to the selected Seismic Hazard Level calculated using Section “Building’s Base Shear” of this example; and QG ¼ action caused by gravity loads as determined according to either of these methods. In this example, the load combinations based on Eq. (4.27) are used for deformation-controlled actions: QUD ¼ 1:1QD + 0:44QL  QEX ðaÞ QUD ¼ 1:1QD + 0:44QL  QEXP ðbÞ QUD ¼ 1:1QD + 0:44QL  QEXN ðcÞ QUD ¼ 1:1QD + 0:44QL  QEY ðdÞ QUD ¼ 1:1QD + 0:44QL  QEYP ðeÞ QUD ¼ 1:1QD + 0:44QL  QEYN ð f Þ QUD ¼ 0:9QD  QEX ðgÞ QUD ¼ 0:9QD  QEXP ðhÞ QUD ¼ 0:9QD  QEXN ðiÞ QUD ¼ 0:9QD  QEY ð jÞ QUD ¼ 0:9QD  QEYP ðkÞ QUD ¼ 0:9QD  QEYN ðlÞ

(4.27)

where: QD ¼ action caused by dead loads; QL ¼ action caused by live load, equal to 25% of the unreduced live load obtained in accordance with ASCE 7 [9] but not less than the actual live load; and QEX, QEY, QEXP, QEYP, QEXN and QEYN ¼ actions caused by seismic loads. Force-Controlled Based on Code 360 [10], force-controlled actions for the LSP denoted by QUF shall be calculated in accordance with Eq. (4.28): QUF ¼ QG 

QE C1 C2 J

(4.28)

234 Advanced Design Examples of Seismic Retrofit of Structures

where: QUF ¼ force-controlled action caused by gravity loads in combination with earthquake forces; and J¼ force-delivery reduction factor, greater than or equal to 1.0, taken as the smallest DCR of the components in the load path delivering force to the component in question. Alternatively, values of J equal to 2.0 for a high level of seismicity, 1.5 for a moderate level of seismicity, and 1.0 for a low level of seismicity shall be permitted where not based on calculated DCRs. In any case where the forces contributing to QUF are delivered by components of the seismic-forceresisting system that remain elastic, J shall be taken as 1.0. In this example, this factor is conservatively assumed to be 2.0; this is based on the fact the considered building is located in Tehran, which has a high level of seismicity. In this example, the load combinations based on Eq. (4.29) are used for forcecontrolled actions: QUF ¼ 1:1QD + 0:44QL  0:41QEX ðaÞ QUF ¼ 1:1QD + 0:44QL  0:41QEXP ðbÞ QUF ¼ 1:1QD + 0:44QL  0:41QEXN ðcÞ QUF ¼ 1:1QD + 0:44QL  0:50QEY ðdÞ QUF ¼ 1:1QD + 0:44QL  0:50QEYP ðeÞ QUF ¼ 1:1QD + 0:44QL  0:50QEYN ð f Þ QUF ¼ 0:9QD  0:41QEX ðgÞ QUF ¼ 0:9QD  0:41QEXP ðhÞ QUF ¼ 0:9QD  0:41QEXN ðiÞ QUF ¼ 0:9QD  0:50QEY ð jÞ QUF ¼ 0:9QD  0:50QEYP ðkÞ QUF ¼ 0:9QD  0:50QEYN ðlÞ

(4.29)

For the columns at the corners of the building where the two orthogonal lateral-force-resisting systems coincide, the concurrent multidirectional seismic effects must be considered. These components of the building shall be designed for combinations of forces and deformations from separate LSP analyses performed for ground motions in X and Y directions as follows: (a) forces and deformations associated with 100% of the design forces in the X direction plus the forces and deformations associated with 30% of the design forces in the Y direction; and for (b) forces and deformations associated with 100% of the design forces in the Y direction plus the forces and deformations associated with 30% of the design forces in the X direction. Other combination rules shall be permitted where verified by experiment or analysis. Acceptance Criteria Deformation-Controlled Acceptance criteria for deformation-controlled actions in components shall satisfy Eq. (4.30): mκQCE > QUD

(4.30)

Example of a Steel Frame Building With Masonry Infill Walls Chapter

4

235

TABLE 4.12 m-Factors for Masonry Infill Panels β¼

Vfre Vinf

β < 0.7

β  0.7 < 1.3

β 1.3

m-Factors

Linf Hinf

IO

LS

CP

0.5

1.0

4.0

N.A.

1.0

1.0

3.5

N.A.

2.0

1.0

3.0

N.A.

0.5

1.5

6.0

N.A.

1.0

1.2

5.2

N.A.

2.0

1.0

4.5

N.A.

0.5

1.5

8.0

N.A.

1.0

1.2

7.0

N.A.

2.0

1.0

6.0

N.A.

where: m ¼component capacity modification factor to account for expected ductility associated with this action at the selected structural performance level. The m-factors for use with corresponding expected strength shall be obtained from Table 4.12. When using this table, Vfre, the expected capacity of the bare frame, should be determined; QCE ¼ expected strength of component deformation-controlled action of an element at the deformation level under consideration which is determined according to Section “Expected Shear Strength.” The actions in infill panels are considered deformation-controlled. It is noted that this strength is equal to the horizontal component of the axial force in the equivalent strut; and κ ¼knowledge factor is assumed 1.0 because usual level of knowledge exists about the example buildings including material properties, as-built sketches, etc. Force-Controlled Acceptance criteria for force-controlled actions in components shall satisfy Eq. (4.31): κQCL > QUF

(4.31)

where QCL ¼ lower-bound strength of a force-controlled action of an element at the deformation level under consideration.

236 Advanced Design Examples of Seismic Retrofit of Structures

The Results The results of evaluation of infill panels under the deformation-controlled actions according to Section “Deformation-Controlled” are shown in Table 4.13. As can be seen, none of the infill panels meets the acceptance criteria as set out in Section “Deformation-Controlled,” and hence all of them should be considered for retrofit. As an example, calculations for infill panel A-1-3 in the floor story are presented. It is noted that in calculation of the expected capacity of the bare frame (Vfre), only the sum of the shear capacity of the columns in this frame is considered. hinf ¼ 280 cm, Linf ¼ 540 cm, tinf ¼ 20 cm, a ¼ 31 cm     1 hinf 1 280 ¼ tan ¼ 27:41 degrees θ ¼ tan Linf 540 9 Left column : 2UNP22PL24  1 ! As ¼ 41:57 cm2 = ! Asmin Right column : 2UNP18PL24  1 ! As ¼ 32:77 cm2 ; ¼ 32:77 cm2 and Cv ¼ 1:0 fm ¼ 5 MPa, Fy ¼ 240 MPa Vinf ¼ QCE ¼

a  tinf  fme  cos θ 31  20  50  cos ð27:41Þ ¼ ¼ 11; 008 kg 2:5 2:5

Vfre ¼ 0:6Fy As Cv ¼ 0:6  2400  32:77  1:0 ¼ 47; 189 kg 8 Vfre 47,189 > > < β ¼ V ¼ 11,008 ¼ 4:287 inf ! based on Table 4:12 : m ¼ 6:07 Linf 540 > > : ¼ 1:93 ¼ hinf 280 Table 4.14 shows the checking of the compact section of the columns of the example building. In addition, the results of evaluation of the columns under displacement-controlled and force-controlled actions are presented in Table 4.15. According to ASCE 41 [1], the acceptance criteria of steel columns under combined axial compression and bending stress, where the axial column load is less than 50% of the lower-bound axial column strength, PCL, the column shall be considered deformation-controlled for flexural behavior and forcecontrolled for compressive behavior and the combined strength shall be evaluated by Eq. (4.32) or (4.33).

PUF PCL

PUF  0:5 For 0:2  PCL

My 8 Mx  1:0 + + 9 mx MCEx my MCEy

(4.32)

Axis

A-1-3

A-4-5

B-1-3

B-4-5

C-1-3

C-4-5

F-1-3

F-4-5

G-1-3

G-4-5

H-1-3

H-4-5

I-1-3

Story

Floor

Floor

Floor

Floor

Floor

Floor

Floor

Floor

Floor

Floor

Floor

Floor

Floor

280

280

280

280

280

280

280

280

280

280

280

280

280

hinf (cm)

540

540

540

540

540

540

540

540

540

540

540

540

540

Linf (cm)

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

θ (degree)

20

20

20

20

20

20

20

20

20

20

20

20

20

tinf (cm)

31

31

31

31

31

31

31

31

31

31

26

31

31

a (cm)

47,189

46,930

47,189

46,930

47,189

46,930

62,741

46,930

62,741

46,930

47,189

46,930

47,189

Vfre (kg)

TABLE 4.13 The Results of Evaluation of Infill Panels [12a]

11,008

11,008

11,008

11,008

11,008

11,008

11,008

11,008

11,008

11,008

9233

11,008

11,008

Vinf 5 QCE (kg)

1.93

1.93

1.93

1.93

1.93

1.93

1.93

1.93

1.93

1.93

1.93

1.93

1.93

Linf hinf

4.287

4.263

4.287

4.263

4.287

4.263

5.699

4.263

5.699

4.263

5.111

4.263

4.287

β

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

m

1

1

1

1

1

1

1

1

1

1

1

1

1

κ

11.01

11.01

11.01

11.01

11.01

11.01

11.01

11.01

11.01

11.01

9.23

11.01

11.01

QCE (ton)

66.8

66.8

66.8

66.8

66.8

66.8

66.8

66.8

66.8

66.8

56

66.8

66.8

mκQCE (ton)

241

229

232

226

226

218

219

227

229

236

200

245

246

QUD (ton)

214

203

206

201

201

193

195

201

203

209

177

218

219

3.20

3.04

3.08

3.01

3.01

2.89

2.92

3.01

3.04

3.13

3.16

3.26

3.28

DCR

Continued

QUD cos θ (ton)

Axis

I-4-5

A-1-3

A-4-5

B-1-3

B-4-5

C-1-3

C-4-5

F-1-3

F-4-5

G-1-3

G-4-5

H-1-3

H-4-5

Story

Floor

1st

1st

1st

1st

1st

1st

1st

1st

1st

1st

1st

1st

280

280

280

280

280

280

280

280

280

280

280

280

280

hinf (cm)

540

540

540

540

540

540

540

540

540

540

540

540

540

Linf (cm)

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

θ (degree)

20

20

20

20

20

20

20

20

20

20

20

20

20

tinf (cm)

31

31

31

31

31

31

31

31

31

31

31

31

31

a (cm)

45,994

46,930

45,994

46,930

45,994

62,741

45,994

62,741

45,994

46,930

45,994

46,930

46,930

Vfre (kg)

TABLE 4.13 The Results of Evaluation of Infill Panels—cont’d

11,008

11,008

11,008

11,008

11,008

11,008

11,008

11,008

11,008

11,008

11,008

11,008

11,008

Vinf 5 QCE (kg)

1.93

1.93

1.93

1.93

1.93

1.93

1.93

1.93

1.93

1.93

1.93

1.93

1.93

Linf hinf

4.178

4.263

4.178

4.263

4.178

5.699

4.178

5.699

4.178

4.263

4.178

4.263

4.263

β

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

m

1

1

1

1

1

1

1

1

1

1

1

1

1

κ

11.01

11.01

11.01

11.01

11.01

11.01

11.01

11.01

11.01

11.01

11.01

11.01

11.01

QCE (ton)

66.8

66.8

66.8

66.8

66.8

66.8

66.8

66.8

66.8

66.8

66.8

66.8

66.8

mκQCE (ton)

217

220

204

206

181

185

176

179

174

177

172

175

242

QUD (ton)

192

196

181

183

161

165

156

159

155

157

153

155

215

QUD cos θ (ton)

2.87

2.93

2.71

2.74

2.41

2.47

2.34

2.38

2.32

2.35

2.29

2.32

3.22

DCR

A-1-3

A-4-5

B-1-3

B-4-5

C-1-3

C-4-5

F-1-3

F-4-5

G-1-3

G-4-5

H-1-3

H-4-5

2nd

2nd

2nd

2nd

2nd

2nd

2nd

2nd

2nd

2nd

2nd

2nd

280

280

280

280

280

280

280

280

280

280

280

280

540

540

540

540

540

540

540

540

540

540

540

540

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

27.41

20

20

20

20

20

20

20

20

20

20

20

20

31

31

31

31

31

31

31

31

31

31

31

31

45,994

46,930

45,994

46,930

45,994

62,741

45,994

62,741

45,994

46,930

45,994

46,930

11,008

11,008

11,008

11,008

11,008

11,008

11,008

11,008

11,008

11,008

11,008

11,008

1.93

1.93

1.93

1.93

1.93

1.93

1.93

1.93

1.93

1.93

1.93

1.93

4.178

4.263

4.178

4.263

4.178

5.699

4.178

5.699

4.178

4.263

4.178

4.263

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

1

1

1

1

1

1

1

1

1

1

1

1

11.01

11.01

11.01

11.01

11.01

11.01

11.01

11.01

11.01

11.01

11.01

11.01

66.8

66.8

66.8

66.8

66.8

66.8

66.8

66.8

66.8

66.8

66.8

66.8

128

131

120

123

101

106

97

101

95

98

93

95

113

116

107

109

90

94

86

89

85

87

82

85

1.69

1.74

1.60

1.63

1.35

1.41

1.29

1.33

1.27

1.30

1.23

1.27

Column

C1

C1

C1

C2

C2

C2

C3

C3

C3

C4

C4

C4

C5

C5

C5

C6

C6

C6

Story

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

2UNP18PL22X1

2UNP18PL16X1

2UNP18PL16X1

2UNP18PL22X1

2UNP18PL16X1

2UNP18PL16X1

2UNP18PL22X1

2UNP18PL16X1

2UNP18PL16X1

2UNP18PL22X1

2UNP18PL16X1

2UNP18PL16X1

2UNP18PL22X1

2UNP18PL16X1

2UNP18PL16X1

2UNP18PL22X1

2UNP18PL16X1

2UNP18PL16X1

Section

340

320

320

340

320

320

340

320

320

340

320

320

340

320

320

340

320

320

L (cm)

26

26

26

26

26

26

26

26

26

26

26

26

26

26

26

26

26

26

bf (cm)

2.1

2.1

2.1

2.1

2.1

2.1

2.1

2.1

2.1

2.1

2.1

2.1

2.1

2.1

2.1

2.1

2.1

2.1

tf (cm)

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

h (cm)

1.6

1.6

1.6

1.6

1.6

1.6

1.6

1.6

1.6

1.6

1.6

1.6

1.6

1.6

1.6

1.6

1.6

1.6

tw (cm)

8.18

7.98

7.98

8.18

7.98

7.98

8.18

7.98

7.98

8.18

7.98

7.98

8.18

7.98

7.98

8.18

7.98

7.98

r3 (cm)

TABLE 4.14 Checking the Compact Section of the Columns [12a]

9.42

9.4

9.4

9.42

9.4

9.4

9.42

9.4

9.4

9.42

9.4

9.4

9.42

9.4

9.4

9.42

9.4

9.4

r2 (cm)

99.92

87.92

87.92

99.92

87.92

87.92

99.92

87.92

87.92

99.92

87.92

87.92

99.92

87.92

87.92

99.92

87.92

87.92

A (cm2)

668.1

559.7

559.7

668.1

559.7

559.7

668.1

559.7

559.7

668.1

559.7

559.7

668.1

559.7

559.7

668.1

559.7

559.7

SX (cm3)

682.2

598.2

598.2

682.2

598.2

598.2

682.2

598.2

598.2

682.2

598.2

598.2

682.2

598.2

598.2

682.2

598.2

598.2

SY (cm3)

778.1

664.1

664.1

778.1

664.1

664.1

778.1

664.1

664.1

778.1

664.1

664.1

778.1

664.1

664.1

778.1

664.1

664.1

ZX (cm3)

853.1

739.1

739.1

853.1

739.1

739.1

853.1

739.1

739.1

853.1

739.1

739.1

853.1

739.1

739.1

853.1

739.1

739.1

ZY (cm3)

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

K3

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

K2

41.6

40.1

40.1

41.6

40.1

40.1

41.6

40.1

40.1

41.6

40.1

40.1

41.6

40.1

40.1

41.6

40.1

40.1

(KL/ r)3

36.1

34

34

36.1

34

34

36.1

34

34

36.1

34

34

36.1

34

34

36.1

34

34

(KL/ r)2

41.6

40.1

40.1

41.6

40.1

40.1

41.6

40.1

40.1

41.6

40.1

40.1

41.6

40.1

40.1

41.6

40.1

40.1

(KL/ r)max

C7

C7

C7

C8

C8

C8

C9

C9

C9

C10

C10

C10

C11

C11

C11

C12

C12

C12

C13

C13

C13

C14

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

2UNP22PL24X1

2UNP24PL22X1

2UNP24PL22X1

2UNP24PL22X1

2UNP24PL22X1

2UNP24PL22X1

2UNP24PL22X1

2UNP24PL24X1

2UNP24PL24X1

2UNP24PL24X1

2UNP24PL24X1

2UNP24PL24X1

2UNP24PL24X1

2UNP24PL22X1

2UNP24PL22X1

2UNP24PL22X1

2UNP22PL24X1

2UNP22PL24X1

2UNP22PL24X1

2UNP18PL22X1

2UNP18PL16X1

2UNP18PL16X1

320

340

320

320

340

320

320

340

320

320

340

320

320

340

320

320

340

320

320

340

320

320

27

27.5

27.5

27.5

27.5

27.5

27.5

27.5

27.5

27.5

27.5

27.5

27.5

27.5

27.5

27.5

27

27

27

26

26

26

2.25

2.3

2.3

2.3

2.3

2.3

2.3

2.3

2.3

2.3

2.3

2.3

2.3

2.3

2.3

2.3

2.25

2.25

2.25

2.1

2.1

2.1

24

26

26

26

26

26

26

26

26

26

26

26

26

26

26

26

24

24

24

20

20

20

1.8

1.9

1.9

1.9

1.9

1.9

1.9

1.9

1.9

1.9

1.9

1.9

1.9

1.9

1.9

1.9

1.8

1.8

1.8

1.6

1.6

1.6

9.77

10.46

10.46

10.46

10.46

10.46

10.46

10.53

10.53

10.53

10.53

10.53

10.53

10.46

10.46

10.46

9.77

9.77

9.77

8.18

7.98

7.98

10.03

10.25

10.25

10.25

10.25

10.25

10.25

10.29

10.29

10.29

10.29

10.29

10.29

10.25

10.25

10.25

10.03

10.03

10.03

9.42

9.4

9.4

122.88

128.58

128.58

128.58

128.58

128.58

128.58

132.58

132.58

132.58

132.58

132.58

132.58

128.58

128.58

128.58

122.88

122.88

122.88

99.92

87.92

87.92

977.8

1082.5

1082.5

1082.5

1082.5

1082.5

1082.5

1130.6

1130.6

1130.6

1130.6

1130.6

1130.6

1082.5

1082.5

1082.5

977.8

977.8

977.8

668.1

559.7

559.7

916.1

982

982

982

982

982

982

1020.5

1020.5

1020.5

1020.5

1020.5

1020.5

982

982

982

916.1

916.1

916.1

682.2

598.2

598.2

1138.1

1269.2

1269.2

1269.2

1269.2

1269.2

1269.2

1319.2

1319.2

1319.2

1319.2

1319.2

1319.2

1269.2

1269.2

1269.2

1138.1

1138.1

1138.1

778.1

664.1

664.1

1126.1

1201.7

1201.7

1201.7

1201.7

1201.7

1201.7

1247.7

1247.7

1247.7

1247.7

1247.7

1247.7

1201.7

1201.7

1201.7

1126.1

1126.1

1126.1

853.1

739.1

739.1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

32.8

32.5

30.6

30.6

32.5

30.6

30.6

32.3

30.4

30.4

32.3

30.4

30.4

32.5

30.6

30.6

34.8

32.8

32.8

41.6

40.1

40.1

32.8

33.2

31.2

31.2

33.2

31.2

31.2

33

31.1

31.1

33

31.1

31.1

33.2

31.2

31.2

34.8

32.8

32.8

41.6

40.1

40.1

Continued

31.9

33.2

31.2

31.2

33.2

31.2

31.2

33

31.1

31.1

33

31.1

31.1

33.2

31.2

31.2

33.9

31.9

31.9

36.1

34

34

Column

C14

C14

C15

C15

C15

C16

C16

C16

C17

C17

C17

C18

C18

C18

C19

C19

C19

C20

Story

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

2UNP24PL22X1

2UNP24PL22X1

2UNP24PL22X1

2UNP24PL22X1

2UNP24PL24X1

2UNP24PL24X1

2UNP24PL24X1

2UNP24PL24X1

2UNP24PL24X1

2UNP24PL24X1

2UNP24PL22X1

2UNP24PL22X1

2UNP24PL22X1

2UNP22PL24X1

2UNP22PL24X1

2UNP22PL24X1

2UNP22PL24X1

2UNP22PL24X1

Section

320

340

320

320

340

320

320

340

320

320

340

320

320

340

320

320

340

320

L (cm)

27.5

27.5

27.5

27.5

27.5

27.5

27.5

27.5

27.5

27.5

27.5

27.5

27.5

27

27

27

27

27

bf (cm)

2.3

2.3

2.3

2.3

2.3

2.3

2.3

2.3

2.3

2.3

2.3

2.3

2.3

2.25

2.25

2.25

2.25

2.25

tf (cm)

26

26

26

26

26

26

26

26

26

26

26

26

26

24

24

24

24

24

h (cm)

1.9

1.9

1.9

1.9

1.9

1.9

1.9

1.9

1.9

1.9

1.9

1.9

1.9

1.8

1.8

1.8

1.8

1.8

tw (cm)

10.46

10.46

10.46

10.46

10.53

10.53

10.53

10.53

10.53

10.53

10.46

10.46

10.46

9.77

9.77

9.77

9.77

9.77

r3 (cm)

TABLE 4.14 Checking the Compact Section of the Columns—cont’d

10.25

10.25

10.25

10.25

10.29

10.29

10.29

10.29

10.29

10.29

10.25

10.25

10.25

10.03

10.03

10.03

10.03

10.03

r2 (cm)

128.58

128.58

128.58

128.58

132.58

132.58

132.58

132.58

132.58

132.58

128.58

128.58

128.58

122.88

122.88

122.88

122.88

122.88

A (cm2)

1082.5

1082.5

1082.5

1082.5

1130.6

1130.6

1130.6

1130.6

1130.6

1130.6

1082.5

1082.5

1082.5

977.8

977.8

977.8

977.8

977.8

SX (cm3)

982

982

982

982

1020.5

1020.5

1020.5

1020.5

1020.5

1020.5

982

982

982

916.1

916.1

916.1

916.1

916.1

SY (cm3)

1269.2

1269.2

1269.2

1269.2

1319.2

1319.2

1319.2

1319.2

1319.2

1319.2

1269.2

1269.2

1269.2

1138.1

1138.1

1138.1

1138.1

1138.1

ZX (cm3)

1201.7

1201.7

1201.7

1201.7

1247.7

1247.7

1247.7

1247.7

1247.7

1247.7

1201.7

1201.7

1201.7

1126.1

1126.1

1126.1

1126.1

1126.1

ZY (cm3)

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

K3

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

K2

30.6

32.5

30.6

30.6

32.3

30.4

30.4

32.3

30.4

30.4

32.5

30.6

30.6

34.8

32.8

32.8

34.8

32.8

(KL/ r)3

31.2

33.2

31.2

31.2

33

31.1

31.1

33

31.1

31.1

33.2

31.2

31.2

33.9

31.9

31.9

33.9

31.9

(KL/ r)2

31.2

33.2

31.2

31.2

33

31.1

31.1

33

31.1

31.1

33.2

31.2

31.2

34.8

32.8

32.8

34.8

32.8

(KL/ r)max

C20

C20

C21

C21

C21

C22

C22

C22

C23

C23

C23

C24

C24

C24

C25

C25

C25

C26

C26

C26

C27

C27

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

2UNP18PL22X1

2UNP18PL22X1

2UNP18PL24X1

2UNP18PL22X1

2UNP18PL22X1

2UNP22PL24X1

2UNP22PL24X1

2UNP22PL24X1

2UNP22PL24X1

2UNP22PL24X1

2UNP22PL24X1

2UNP18PL24X1

2UNP18PL22X1

2UNP18PL22X1

2UNP18PL24X1

2UNP18PL22X1

2UNP18PL22X1

2UNP22PL24X1

2UNP22PL24X1

2UNP22PL24X1

2UNP24PL22X1

2UNP24PL22X1

320

320

340

320

320

340

320

320

340

320

320

340

320

320

340

320

320

340

320

320

340

320

26

26

26

26

26

27

27

27

27

27

27

26

26

26

26

26

26

27

27

27

27.5

27.5

2.1

2.1

2.1

2.1

2.1

2.25

2.25

2.25

2.25

2.25

2.25

2.1

2.1

2.1

2.1

2.1

2.1

2.25

2.25

2.25

2.3

2.3

20

20

20

20

20

24

24

24

24

24

24

20

20

20

20

20

20

24

24

24

26

26

1.6

1.6

1.6

1.6

1.6

1.8

1.8

1.8

1.8

1.8

1.8

1.6

1.6

1.6

1.6

1.6

1.6

1.8

1.8

1.8

1.9

1.9

8.18

8.18

8.23

8.18

8.18

9.77

9.77

9.77

9.77

9.77

9.77

8.23

8.18

8.18

8.23

8.18

8.18

9.77

9.77

9.77

10.46

10.46

9.42

9.42

9.51

9.42

9.42

10.03

10.03

10.03

10.03

10.03

10.03

9.51

9.42

9.42

9.51

9.42

9.42

10.03

10.03

10.03

10.25

10.25

99.92

99.92

103.92

99.92

99.92

122.88

122.88

122.88

122.88

122.88

122.88

103.92

99.92

99.92

103.92

99.92

99.92

122.88

122.88

122.88

128.58

128.58

668.1

668.1

704.2

668.1

668.1

977.8

977.8

977.8

977.8

977.8

977.8

704.2

668.1

668.1

704.2

668.1

668.1

977.8

977.8

977.8

1082.5

1082.5

682.2

682.2

722.9

682.2

682.2

916.1

916.1

916.1

916.1

916.1

916.1

722.9

682.2

682.2

722.9

682.2

682.2

916.1

916.1

916.1

982

982

778.1

778.1

816.1

778.1

778.1

1138.1

1138.1

1138.1

1138.1

1138.1

1138.1

816.1

778.1

778.1

816.1

778.1

778.1

1138.1

1138.1

1138.1

1269.2

1269.2

853.1

853.1

899.1

853.1

853.1

1126.1

1126.1

1126.1

1126.1

1126.1

1126.1

899.1

853.1

853.1

899.1

853.1

853.1

1126.1

1126.1

1126.1

1201.7

1201.7

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

39.1

39.1

41.3

39.1

39.1

34.8

32.8

32.8

34.8

32.8

32.8

41.3

39.1

39.1

41.3

39.1

39.1

34.8

32.8

32.8

32.5

30.6

34

34

39.1

39.1

41.3

39.1

39.1

34.8

32.8

32.8

34.8

32.8

32.8

41.3

39.1

39.1

41.3

39.1

39.1

34.8

32.8

32.8

33.2

31.2

Continued

35.8

34

34

33.9

31.9

31.9

33.9

31.9

31.9

35.8

34

34

35.8

34

34

33.9

31.9

31.9

33.2

31.2

Column

C27

C28

C28

C28

Story

STORY1

STORY3

STORY2

STORY1

2UNP18PL24X1

2UNP18PL22X1

2UNP18PL22X1

2UNP18PL24X1

Section

340

320

320

340

L (cm)

26

26

26

26

bf (cm)

2.1

2.1

2.1

2.1

tf (cm)

20

20

20

20

h (cm)

1.6

1.6

1.6

1.6

tw (cm)

8.23

8.18

8.18

8.23

r3 (cm)

TABLE 4.14 Checking the Compact Section of the Columns—cont’d

9.51

9.42

9.42

9.51

r2 (cm)

103.92

99.92

99.92

103.92

A (cm2)

704.2

668.1

668.1

704.2

SX (cm3)

722.9

682.2

682.2

722.9

SY (cm3)

816.1

778.1

778.1

816.1

ZX (cm3)

899.1

853.1

853.1

899.1

ZY (cm3)

1

1

1

1

K3

1

1

1

1

K2

41.3

39.1

39.1

41.3

(KL/ r)3

35.8

34

34

35.8

(KL/ r)2

41.3

39.1

39.1

41.3

(KL/ r)max

Col.

C1

C1

C1

C2

C2

C2

C3

C3

C3

C4

C4

C4

C5

C5

C5

C6

C6

C6

C7

Story

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3



1285

1277.6

1285

1285

1277.6

1285

1285

1277.6

1285

1285

1277.6

1285

1285

1277.6

1285

1285

1277.6

1285

1285

kg cm2

F a

8.2

193.4

116.2

43.8

153.9

80

34.9

188.3

111.2

41.4

158.6

91.3

35.9

154.6

83.1

33

156.4

83.2

29.6

PUF

(ton)

192.1

217

192.1

192.1

217

192.1

192.1

217

192.1

192.1

217

192.1

192.1

217

192.1

192.1

217

192.1

192.1

PCL

0.9

0.6

0.7

0.4

0.5

0.6

0.3

0.6

0.6

0.3

0.5

0.5

0.1

0.5

0.5

0.1

0.2

1.1

0.4

MUFx

3.3

5

9

4

5.1

8.3

4.1

5.3

7.4

3.8

5.9

6.9

3.8

6.3

6.7

3.8

6.3

6.7

3.1

MUDx

1.4

1.5

1.7

0.9

1.2

1.6

0.9

1.6

1.6

0.9

1.2

1.3

0.2

1.2

1.3

0.2

1.2

1.8

0.3

(ton m)

MUFy

4.7

8.9

17.5

4.6

9.5

15.8

4.7

10

13.8

4

11.4

12.4

4

12.4

11.7

4

11.1

10

3.5

MUDy

0.04

0.89

0.6

0.23

0.71

0.42

0.18

0.87

0.58

0.22

0.73

0.48

0.19

0.71

0.43

0.17

0.72

0.43

0.15

PUF PCL

TABLE 4.15 The Results of Evaluation of the Columns [12a] Action

DC

FC

FC

DC

FC

DC

DC

FC

FC

DC

FC

DC

DC

FC

DC

DC

FC

DC

DC

mx

10

—

—

8.2

—

3.9

9.2

—

—

8.5

—

2.6

9.1

—

3.5

9.4

—

3.5

9.8

my

10

—

—

8.2

—

3.9

9.2

—

—

8.5

—

2.6

9.1

—

3.5

9.4

—

3.5

9.8

1100.3

1164

1100.3

1100.3

1164

1100.3

1100.3

1164

1100.3

1100.3

1164

1100.3

1100.3

1164

1100.3

1100.3

1164

1100.3

1100.3

Pex (ton)

1526.8

1543.6

1526.8

1526.8

1543.6

1526.8

1526.8

1543.6

1526.8

1526.8

1543.6

1526.8

1526.8

1543.6

1526.8

1526.8

1543.6

1526.8

1526.8

Pey

13.4

16

13.4

13.4

16

13.4

13.4

16

13.4

13.4

16

13.4

13.4

16

13.4

13.4

16

13.4

13.4

MCLx

14.4

16.4

14.4

14.4

16.4

14.4

14.4

16.4

14.4

14.4

16.4

14.4

14.4

16.4

14.4

14.4

16.4

14.4

14.4

MCLy

15.9

18.7

15.9

15.9

18.7

15.9

15.9

18.7

15.9

15.9

18.7

15.9

15.9

18.7

15.9

15.9

18.7

15.9

15.9

MPCLx

17.7

20.5

17.7

17.7

20.5

17.7

17.7

20.5

17.7

17.7

20.5

17.7

17.7

20.5

17.7

17.7

20.5

17.7

17.7

MCEx

14.8

17.6

14.8

14.8

17.6

14.8

14.8

17.6

14.8

14.8

17.6

14.8

14.8

17.6

14.8

14.8

17.6

14.8

14.8

(ton m)

MPCLy

15.8

18

15.8

15.8

18

15.8

15.8

18

15.8

15.8

18

15.8

15.8

18

15.8

15.8

18

15.8

15.8

MCEy

17.5

20.5

17.5

17.5

20.5

17.5

17.5

20.5

17.5

17.5

20.5

17.5

17.5

20.5

17.5

17.5

20.5

17.5

17.5

MPCEx

DCR

0.08

1.22

1.23

0.5

1.04

0.98

0.45

1.22

1.1

0.47

1.1

0.94

0.42

1.1

0.89

0.41

1.1

0.93

0.37

Continued

19.5

22.5

19.5

19.5

22.5

19.5

19.5

22.5

19.5

19.5

22.5

19.5

19.5

22.5

19.5

19.5

22.5

19.5

19.5

MPCEy

C11

C12

C12

C12

C13

C13

C13

C14

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

C10

STORY3

STORY1

C9

STORY1

C11

C9

STORY2

STORY2

C9

STORY3

C11

C8

STORY1

STORY3

C8

STORY2

C10

C8

STORY3

C10

C7

STORY1

STORY1

C7

STORY2

TORY2

Col.

Story



1320.2

1318.3

1327.2

1327.2

1318.3

1327.2

1327.2

1318.9

1327.7

1327.7

1318.9

1327.7

1327.7

1318.3

1327.2

1327.2

1310.7

1320.2

1320.2

1277.6

1285

kg cm2

F a

18.2

159.1

83.3

26.9

157.2

84

27.9

151.3

81.4

27.8

150.4

81.6

28.5

144.7

78.2

28

129.5

65.7

17.1

124.3

12.8

PUF

(ton)

275.8

288.2

290.1

290.1

288.2

290.1

290.1

297.3

299.2

299.2

297.3

299.2

299.2

288.2

290.1

290.1

273.8

275.8

275.8

217

192.1

PCL

0.7

0.3

0.3

0.1

0.3

0.3

0.2

0.2

0.4

0.2

0.3

0.2

0.1

0.3

0.2

0.1

0.8

0.7

0.9

0.2

0

MUFx

0.3

3.8

10.5

0.4

4.3

8.9

0.4

5.2

7.1

0.8

6

5.8

0.8

6.9

5.7

0.3

6.4

4.6

0.5

1.6

8.9

MUDx

0.5

0.9

0.9

0.4

0.9

0.9

0.5

0.7

1

0.5

0.7

0.7

0.1

0.7

0.6

0.2

1.2

0.3

0.9

0

0.8

(ton m)

MUFy

0.1

8.8

25.4

2.4

10.3

21.7

2.2

13

17.7

3.2

15.1

14.3

3

17.1

13.2

2.2

15.5

10

0

1.5

16.8

MUDy

0.07

0.55

0.29

0.09

0.55

0.29

0.1

0.51

0.27

0.09

0.51

0.27

0.1

0.5

0.27

0.1

0.47

0.24

0.06

0.57

0.07

PUF PCL

TABLE 4.15 The Results of Evaluation of the Columns—cont’d

DC

FC

DC

DC

FC

DC

DC

FC

DC

DC

FC

DC

DC

FC

DC

DC

DC

DC

DC

FC

DC

Action

10

—

6.8

10

—

6.8

10

—

7.2

10

—

7.2

10

—

7.2

10

2.6

7.9

10

—

10

mx

10

—

6.8

10

—

6.8

10

—

7.2

10

—

7.2

10

—

7.2

10

2.6

7.9

10

—

10

my

2305.2

2449.1

2764.9

2764.9

2449.1

2764.9

2764.9

2559.3

2889.2

2889.2

2559.3

2889.2

2889.2

2449.1

2764.9

2764.9

2042

2305.2

2305.2

1164

1100.3

Pex (ton)

2429.5

2351.8

2655

2655

2351.8

2655

2655

2443.9

2759

2759

2443.9

2759

2759

2351.8

2655

2655

2152.1

2429.5

2429.5

1543.6

1526.8

Pey

23.5

26

26

26

26

26

26

27.1

27.1

27.1

27.1

27.1

27.1

26

26

26

23.5

23.5

23.5

16

13.4

MCLx

22

23.6

23.6

23.6

23.6

23.6

23.6

24.5

24.5

24.5

24.5

24.5

24.5

23.6

23.6

23.6

22

22

22

16.4

14.4

MCLy

27.3

30.5

30.5

30.5

30.5

30.5

30.5

31.7

31.7

31.7

31.7

31.7

31.7

30.5

30.5

30.5

27.3

27.3

27.3

18.7

15.9

MPCLx

27

28.8

28.8

28.8

28.8

28.8

28.8

29.9

29.9

29.9

29.9

29.9

29.9

28.8

28.8

28.8

27

27

27

20.5

17.7

MCEx

25.8

28.6

28.6

28.6

28.6

28.6

28.6

29.8

29.8

29.8

29.8

29.8

29.8

28.6

28.6

28.6

25.8

25.8

25.8

17.6

14.8

(ton m)

MPCLy

24.2

25.9

25.9

25.9

25.9

25.9

25.9

26.9

26.9

26.9

26.9

26.9

26.9

25.9

25.9

25.9

24.2

24.2

24.2

18

15.8

MCEy

30

33.5

33.5

33.5

33.5

33.5

33.5

34.8

34.8

34.8

34.8

34.8

34.8

33.5

33.5

33.5

30

30

30

20.5

17.5

MPCEx

29.7

31.7

31.7

31.7

31.7

31.7

31.7

32.9

32.9

32.9

32.9

32.9

32.9

31.7

31.7

31.7

29.7

29.7

29.7

22.5

19.5

MPCEy DCR

0.07

0.71

0.69

0.1

0.72

0.63

0.11

0.71

0.54

0.11

0.74

0.49

0.11

0.78

0.49

0.11

0.77

0.44

0.07

0.68

0.18

C14

C14

C15

C15

C15

C16

C16

C16

C17

C17

C17

C18

C18

C18

C19

C19

C19

C20

C20

C20

C21

C21

C21

C22

C22

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

1289.8

1289.8

1310.7

1320.2

1320.2

1318.3

1327.2

1327.2

1318.3

1327.2

1327.2

1318.9

1327.7

1327.7

1318.9

1327.7

1327.7

1318.3

1327.2

1327.2

1310.7

1320.2

1320.2

1310.7

1320.2

49.9

11.2

115.4

42.4

18.2

206.9

125.5

51.5

202.5

123.4

51.1

188

112.8

47.9

190.7

113

47.6

185.3

112.2

46.5

179.5

99.4

35.2

67

42.1

219.1

219.1

273.8

275.8

275.8

288.2

290.1

290.1

288.2

290.1

290.1

297.3

299.2

299.2

297.3

299.2

299.2

288.2

290.1

290.1

273.8

275.8

275.8

273.8

275.8

1.1

0.4

0.3

1.3

0.7

0.3

0.4

0.2

0.3

0.3

0.2

0.5

0.2

0.5

0

0.8

0.2

0.3

0.2

0.1

0.8

0.7

0.9

0.3

1.3

7.1

2.8

3.3

11.1

0.4

3.9

10.5

0.3

4.5

9

0.3

4.7

5.8

1.6

5.5

4.4

1.6

7.2

5.7

0.3

6.6

4.6

0.5

3.2

11.1

2

0.2

0.1

1.7

0.4

0.8

0.9

0.5

0.8

0.8

0.5

0.9

0.3

0.8

0.4

1.3

0.2

0.7

0.6

0.2

1.1

0.3

1

0.2

1.8

10.4

2.8

7.8

27.3

0

8.9

25.4

2.3

10.6

21.8

2.1

12.6

16.5

3.8

14.7

13.1

3.7

17.4

13.3

2.1

15.7

10.1

0.1

7.6

27.3

0.23

0.05

0.42

0.15

0.07

0.72

0.43

0.18

0.7

0.43

0.18

0.63

0.38

0.16

0.64

0.38

0.16

0.64

0.39

0.16

0.66

0.36

0.13

0.24

0.15

DC

DC

DC

DC

DC

FC

DC

DC

FC

DC

DC

FC

DC

DC

FC

DC

DC

FC

DC

DC

FC

DC

DC

DC

DC

8.2

10

3.8

9.8

10

—

3.5

9.3

—

3.7

9.3

—

4.8

9.7

—

4.8

9.7

—

4.6

9.7

—

5.2

10

7.8

9.9

8.2

10

3.8

9.8

10

—

3.5

9.3

—

3.7

9.3

—

4.8

9.7

—

4.8

9.7

—

4.6

9.7

—

5.2

10

7.8

9.9

1314

1314

2042

2305.2

2305.2

2449.1

2764.9

2764.9

2449.1

2764.9

2764.9

2559.3

2889.2

2889.2

2559.3

2889.2

2889.2

2449.1

2764.9

2764.9

2042

2305.2

2305.2

2042

2305.2

1742.6

1742.6

2152.1

2429.5

2429.5

2351.8

2655

2655

2351.8

2655

2655

2443.9

2759

2759

2443.9

2759

2759

2351.8

2655

2655

2152.1

2429.5

2429.5

2152.1

2429.5

16

16

23.5

23.5

23.5

26

26

26

26

26

26

27.1

27.1

27.1

27.1

27.1

27.1

26

26

26

23.5

23.5

23.5

23.5

23.5

16.4

16.4

22

22

22

23.6

23.6

23.6

23.6

23.6

23.6

24.5

24.5

24.5

24.5

24.5

24.5

23.6

23.6

23.6

22

22

22

22

22

18.7

18.7

27.3

27.3

27.3

30.5

30.5

30.5

30.5

30.5

30.5

31.7

31.7

31.7

31.7

31.7

31.7

30.5

30.5

30.5

27.3

27.3

27.3

27.3

27.3

20.5

20.5

27

27

27

28.8

28.8

28.8

28.8

28.8

28.8

29.9

29.9

29.9

29.9

29.9

29.9

28.8

28.8

28.8

27

27

27

27

27

17.6

17.6

25.8

25.8

25.8

28.6

28.6

28.6

28.6

28.6

28.6

29.8

29.8

29.8

29.8

29.8

29.8

28.6

28.6

28.6

25.8

25.8

25.8

25.8

25.8

18

18

24.2

24.2

24.2

25.9

25.9

25.9

25.9

25.9

25.9

26.9

26.9

26.9

26.9

26.9

26.9

25.9

25.9

25.9

24.2

24.2

24.2

24.2

24.2

20.5

20.5

30

30

30

33.5

33.5

33.5

33.5

33.5

33.5

34.8

34.8

34.8

34.8

34.8

34.8

33.5

33.5

33.5

30

30

30

30

30

0.67

0.07

0.57

0.64

0.07

0.88

0.84

0.2

0.89

0.78

0.19

0.83

0.59

0.23

0.85

0.57

0.22

0.93

0.61

0.17

0.96

0.57

0.13

0.38

0.64

Continued

22.5

22.5

29.7

29.7

29.7

31.7

31.7

31.7

31.7

31.7

31.7

32.9

32.9

32.9

32.9

32.9

32.9

31.7

31.7

31.7

29.7

29.7

29.7

29.7

29.7

Col.

C22

C23

C23

C23

C24

C24

C24

C25

C25

C25

C26

C26

C26

C27

C27

C27

C28

C28

C28

Story

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1



1278.9

1289.8

1289.8

1278.9

1289.8

1289.8

1278.9

1289.8

1289.8

1310.7

1320.2

1320.2

1310.7

1320.2

1320.2

1278.9

1289.8

1289.8

1278.9

kg cm2

F a

127.7

11.9

7.9

151

76.8

19.8

113.7

53.7

11.6

148

78.2

22.4

112.6

57.2

17.1

111

51.7

15

117.3

PUF

(ton)

225.9

219.1

219.1

225.9

219.1

219.1

225.9

219.1

219.1

273.8

275.8

275.8

273.8

275.8

275.8

225.9

219.1

219.1

225.9

PCL

0.2

0.1

0.9

0.6

0.7

0.4

0.5

0.5

0.4

0.6

1.4

0.3

0.9

0.2

0.4

0.5

0.6

0.1

0.3

MUFx

1.3

9.3

2.9

4.5

9.5

3.7

4.8

7.9

3.8

4.2

6.1

0.8

5.3

5.1

0.9

6

7

3.5

6.1

MUDx

0

2.1

1.6

1.7

1.7

1

1.3

1.4

1

2

2.8

1.2

2

1.4

0.6

1.3

1.4

0.3

1.3

(ton m)

MUFy

1

16

3.6

8.1

18.6

3.6

9.1

14.7

3.8

9.2

13.5

2.2

11.9

10.9

1.9

12.2

12.4

3.3

11

MUDy

0.56

0.05

0.04

0.67

0.35

0.09

0.5

0.25

0.05

0.54

0.28

0.08

0.41

0.21

0.06

0.49

0.24

0.07

0.52

PUF PCL

TABLE 4.15 The Results of Evaluation of the Columns—cont’d

FC

DC

DC

FC

DC

DC

FC

DC

DC

FC

DC

DC

DC

DC

DC

DC

DC

DC

FC

Action

—

10

10

—

5.4

10

—

7.8

10

—

6.9

10

4

8.6

10

2.2

8

10

—

mx

—

10

10

—

5.4

10

—

7.8

10

—

6.9

10

4

8.6

10

2.2

8

10

—

my

1225.4

1314

1314

1225.4

1314

1314

1225.4

1314

1314

2042

2305.2

2305.2

2042

2305.2

2305.2

1225.4

1314

1314

1225.4

Pex (ton)

1636.2

1742.6

1742.6

1636.2

1742.6

1742.6

1636.2

1742.6

1742.6

2152.1

2429.5

2429.5

2152.1

2429.5

2429.5

1636.2

1742.6

1742.6

1636.2

Pey

16.9

16

16

16.9

16

16

16.9

16

16

23.5

23.5

23.5

23.5

23.5

23.5

16.9

16

16

16.9

MCLx

17.3

16.4

16.4

17.3

16.4

16.4

17.3

16.4

16.4

22

22

22

22

22

22

17.3

16.4

16.4

17.3

MCLy

19.6

18.7

18.7

19.6

18.7

18.7

19.6

18.7

18.7

27.3

27.3

27.3

27.3

27.3

27.3

19.6

18.7

18.7

19.6

MPCLx

21.6

20.5

20.5

21.6

20.5

20.5

21.6

20.5

20.5

27

27

27

27

27

27

21.6

20.5

20.5

21.6

MCEx

18.6

17.6

17.6

18.6

17.6

17.6

18.6

17.6

17.6

25.8

25.8

25.8

25.8

25.8

25.8

18.6

17.6

17.6

18.6

(ton m)

MPCLy

19.1

18

18

19.1

18

18

19.1

18

18

24.2

24.2

24.2

24.2

24.2

24.2

19.1

18

18

19.1

MCEy

21.5

20.5

20.5

21.5

20.5

20.5

21.5

20.5

20.5

30

30

30

30

30

30

21.5

20.5

20.5

21.5

MPCEx

23.7

22.5

22.5

23.7

22.5

22.5

23.7

22.5

22.5

29.7

29.7

29.7

29.7

29.7

29.7

23.7

22.5

22.5

23.7

MPCEy

0.64

0.16

0.06

0.95

0.9

0.12

0.79

0.7

0.08

0.74

0.58

0.09

0.66

0.42

0.07

0.84

0.64

0.09

0.86

DCR

Example of a Steel Frame Building With Masonry Infill Walls Chapter

PUF < 0:2 PCL My Mx + +  1:0 mx MCEx my MCEy

4

249

For

PUF 2PCL

(4.33)

where: PUF ¼ axial force in the member; PCL ¼ lower-bound compression strength of the column; Mx ¼ bending moment in the member for the x-axis; My ¼ bending moment in the member for the y-axis; MCEx ¼expected bending strength of the column for the x-axis; MCEy ¼ expected bending strength of the column for the y-axis; mx ¼ value of m for the column bending about the x-axis in accordance with Table 4.16; and my ¼ value of m for the column bending about the y-axis in accordance with Table 4.16. Steel columns with axial compressive forces exceeding 50% of the lower-bound axial compressive strength, PCL, shall be considered force-controlled for both axial loads and flexure and shall be evaluated using Eq. (4.34): PUF MUFx MUFy + +  1:0 PCL MCLx MCLy

(4.34)

where: MUFx ¼ bending moment in the member for the x-axis; MUFy ¼ bending moment in the member for the y-axis; MCLx ¼lower-bound bending strength of the column for the x-axis; and MCLy ¼ lower-bound bending strength of the column for the y-axis.

TABLE 4.16 m-Factors for LSP for Steel Columns

For

PUF PCL

IO

LS

CP

< 0:2

bf 2tf

300 ffiffiffiffiffi  p52ffiffiffiffiffi and thw  p

2

6

8

bf 2tf

460 ffiffiffiffiffi  p65ffiffiffiffiffi and thw  p

1.25

1.25

2

Fye

Fye

Fye

Fye

For 0:2  PPUF  0:5 CL bf 2tf

300 ffiffiffiffiffi  p52ffiffiffiffiffi and thw  p

1.25


 9 1  53 PPCL


 12 1  53 PPCL

bf 2tf

400 ffiffiffiffiffi  p65ffiffiffiffiffi and thw  p

1.25

1.25

1.5

Fye

Fye

Fye

Fye

250 Advanced Design Examples of Seismic Retrofit of Structures

(A)

(B)

(C)

(D)

FIG. 4.15 Retrofit details of the vulnerable columns. (A) Existing 2UNP18PL22x1. (B) Retrofitted 2UNP18PL22x1. (C) Existing 2UNP18PL16x1. (D) Retrofitted 2UNP18PL16x1 [12a].

Steel columns under combined axial tension and bending stress shall be considered deformation-controlled and shall be evaluated using Eq. (4.35): My T Mx + +  1:0 mt TCE mx MCEx my MCEy

(4.35)

where: mt ¼ value of m for the column in tension based on Table 5.11 (in Chapter 5 of this book); T¼ tensile load in column; and TCE ¼expected tensile strength of column computed in accordance with Eq. (4.36). QCE ¼ TCE ¼ Fye Ac where: Ac ¼ area of column; and Fye ¼ expected yield strength of the material.

(4.36)

As can be seen, except for three columns, all columns meet the acceptance criteria. In order to retrofit the vulnerable columns, welded steel plates are used in accordance with the details shown in Fig. 4.15. Shotcreting of the Infill Panels in Transverse Direction There are different methods to improve the seismic performance of infill walls in order to improve the in-plane and out-of-plane performance; these methods include installation of FRP strips on the infill wall and using cementitious

Example of a Steel Frame Building With Masonry Infill Walls Chapter

(A)

4

251

(B)

FIG. 4.16 Some steps in implementation of shotcrete. (A) Water-jetting the walls. (B) Using standardized pumps. (Permission from DRES.)

composites [19]. Because the infill walls in this example are made of masonry, several retrofitting methods for URM buildings can also be applied to masonry infill walls, albeit with some modifications. Among these methods, shotcreting of the vulnerable infill walls is considered. Based on ICERIFB [2], if the surface of the walls that are to be shotcreted is smooth, the surface should be made rough by water-jet or sandblast (see Fig. 4.16A). Before shotcrete, all the walls’ finishing should be removed and the surface of the walls should be slightly wet to facilitate the bonding of concrete to the masonry. In addition, the cement grout should be poured on the walls’ surface in order to fill the surface voids on the masonry walls. Shotcreting should be carried out using standardized equipment (see Fig. 4.16B); shotcreting by hand is not acceptable due to the low pressure of concrete on the walls. The reinforcement should be at least 0.3% in each direction and should be according to the related code requirements. Curing concrete which is based on the related codes’ requirements should be particularly monitored, considering the high surface-to-volume ratio of concrete. If the shotcrete is applied on one side of the wall only, the dowel bars (shown in Fig. 4.17) should be able to transfer total force acting on the wall in the out-ofplane direction, which is determined in Section “Evaluation of the Walls in Outof-Plane Direction.” The minimum dowel bars ratio is 0.03% and the maximum allowable distance in each direction is 50 cm (see Fig. 4.17). The dowel bars should be bent over the most external reinforcement layer to at least 10 cm. The shotcrete should be uniformly applied on the walls, and the thickness related to a triangular area with the chord 1.5 times of the width of the equivalent strut based on Eq. (4.12) should not be less than the thickness of the rest. In the design procedure, the shotcrete with the least thickness should be considered. The thickness of shotcrete usually ranges from 2.5 cm to 5.0 cm.

252 Advanced Design Examples of Seismic Retrofit of Structures

Shotcrete layer

URM wall

Reinforcing grid

Reinforcing grid

Shotcrete layer Shotcrete layer

Reinforcing grid

URM wall

(A)

(B)

FIG. 4.17 Details of the dowel bars in shotcreted masonry infill walls. (A) One-sided shotcrete. (B) Two-sided shotcrete. (Permission from DRES.)

If the implemented shotcrete is thicker than the designed shotcrete, the adequacy of the columns and beams against the increased forces from shotcrete should be taken into account [2]. When determining the equivalent strut width of the shotcreted masonry infill walls, the homogenized modulus of elasticity of the infill can be considered according to Eq. (4.37) [2]: n X

Ei ti

i¼1

Einf ¼ X n

(4.37) ti

i¼1

In order to connect the infill wall fully to the frame members considering the gap between the double beam members (see Fig. 4.18), steel plates with the length of 1.5a should be added to the beams and columns at the corners. The expected strength of the shotcreted masonry infill walls can be determined based on Eq. (4.38) [2]: QCE ¼

atinf Fme cos θ 2:5

(4.38)

Upper gusset plate Upper gusset plate

Fillet weld

Fillet weld

Weld

Seat plate

Lower gusset plate Complete penetration grove weld

FIG. 4.18 Simple cradle-type connection [10].

Angle

Example of a Steel Frame Building With Masonry Infill Walls Chapter

4

253

where: a ¼effective width of the infill based on Eq. (4.12); tinf ¼total thickness of infill wall including the masonry and shotcrete; θ ¼angle of the diagonal of infill with respect to the horizontal; and Fme ¼average compressive strength of infill layers based on Eq. (4.39): n X

Fme ¼

Fmei ti

i¼1

n X

(4.39) ti

i¼1

where Fmei is the average (expected value) of the compressive strength of the ith layer of the infill wall. The acceptance criteria and m-factors of shotcreted infill walls is the same as those related to unretrofitted infill walls which were presented in Section “Acceptance Criteria” and Table 4.12, respectively. For more information about the various details of shotcrete and the considerations during implementation of shotcrete, the reader may refer to Practical Instruction for Shotcrete in Seismic Rehabilitation of Schools [20], Practical Instruction for Shotcrete Connection in Seismic Rehabilitation of Schools [21], and the Code of Practice for Design Specification Manufacturing and Construction of 3D Panel Structures (Code 385) [22]. The results of evaluation of infill panels after shotcrete are presented in Table 4.17. Based on the results in Table 4.13, all the infill walls are vulnerable. These walls are shotcreted on both surfaces of the walls. The total shotcrete layer thicknesses of the infill walls are 15 cm and 10 cm in the floor story and other stories, respectively. All the retrofitted infill walls adequately meet the requirements presented in Section “Acceptance Criteria” and are not vulnerable. None of the thickness of the layers in the shotcreted infill walls exceeds the flange width of the frame member; hence, no reduction of the effective thickness of the infill is required in the design procedure. Example details of shotcreting masonry infill walls are shown in Figs. 4.19 and 4.20.

Evaluation of the Beam and Columns The adequacy of beams and column with retrofitted infill walls is similar to the procedure in Sections “Expected-Values of Strength” and “Lower-Bound Values of Strength.” The internal forces and moments from the activation of the ultimate strength of the infill wall against which the adequacy of frame moments is checked is based on Eq. (4.40), which is 2.5 times of the expected strength of the shotcreted masonry infill wall based on Eq. (4.38) [2]: FU ¼ atinf Fme cos θ

(4.40)

Axis

A-1-3

A-4-5

B-1-3

B-4-5

C-1-3

C-4-5

F-1-3

F-4-5

G-1-3

G-4-5

H-1-3

H-4-5

I-1-3

I-4-5

A-1-3

A-4-5

B-1-3

B-4-5

Story

Floor

Floor

Floor

Floor

Floor

Floor

Floor

Floor

Floor

Floor

Floor

Floor

Floor

Floor

1st

1st

1st

1st

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

tinf (cm)

31

31

31

31

31

31

31

31

31

31

31

31

31

31

31

26

31

31

a (cm)

15

15

15

15

20

20

20

20

20

20

20

20

20

20

20

20

20

20

fc (MPa)

0

10

10

10

10

15

15

15

15

15

15

15

15

15

15

15

15

15

15

tshot (cm)

10,723

10,723

10,723

10,723

10,723

10,723

10,723

10,723

10,723

10,723

10,723

10,723

10,723

10,723

10,723

10,723

10,723

10,723

Eme (MPa)

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

λ1

TABLE 4.17 The Results of Evaluation of Infill Panels After Shotcrete [12a]

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

R1

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

0.9

1.0

1.0

R2

25.2

25.5

25.2

25.5

24.9

25.0

24.9

25.0

24.9

25.0

24.9

25.7

24.9

25.7

24.9

21.5

24.9

25.0

ashot (cm)

92.9

92.9

92.9

92.9

114.3

114.3

114.3

114.3

114.3

114.3

114.3

114.3

114.3

114.3

114.3

114.3

114.3

114.3

Fme (MPa)

29.1

29.4

29.1

29.4

35.4

35.6

35.4

35.6

35.4

35.6

35.4

36.6

35.4

36.6

35.4

30.5

35.4

35.6

QCE (ton)

176

179

176

179

215

216

215

216

215

216

215

222

215

222

215

185

215

216

mκQCE (ton)

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

Result

C-1-3

C-4-5

F-1-3

F-4-5

G-1-3

G-4-5

H-1-3

H-4-5

A-1-3

A-4-5

B-1-3

B-4-5

C-1-3

C-4-5

F-1-3

F-4-5

G-1-3

G-4-5

H-1-3

H-4-5

1st

1st

1st

1st

1st

1st

1st

1st

2nd

2nd

2nd

2nd

2nd

2nd

2nd

2nd

2nd

2nd

2nd

2nd

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

31

31

31

31

31

31

31

31

31

31

31

31

31

31

31

31

31

31

31

31

15

15

15

15

15

15

15

15

15

15

15

15

20

20

15

15

15

15

15

15

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10,723

10,723

10,723

10,723

10,723

10,723

10,723

10,723

10,723

10,723

10,723

10,723

10,723

10,723

10,723

10,723

10,723

10,723

10,723

10,723

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

0.0491

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

25.6

25.9

25.6

25.9

25.6

26.8

25.6

26.8

25.6

25.9

25.6

25.9

25.2

25.5

25.2

25.5

25.2

26.4

25.2

26.4

83.3

83.3

83.3

83.3

83.3

83.3

83.3

83.3

83.3

83.3

83.3

83.3

114.3

114.3

92.9

92.9

92.9

92.9

92.9

92.9

22.7

23

22.7

23

22.7

23.8

22.7

23.8

22.7

23

22.7

23

35.8

36.2

29.1

29.4

29.1

30.4

29.1

30.4

138

140

138

140

138

144

138

144

138

140

138

140

217

220

176

179

176

185

176

185

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

Hole d = 3 cm

Ø10@60 cm

Pos.1

1

Ø--@--cm

Grouting

(B)

Pos.1

Ø12@20 cm

Pos.4

Ø10@60 cm Hole d = 3 cm

Ø--@--cm

Grout

Hole d = 3 cm, L= 20 cm Angle =30 degree, 60*60 cm 10 cm

10 cm

20 c

m 100 cm

Shotcrete layer (thickness = Var.) Concrete compressive strength 300 kg/m3

FIG. 4.19 Details of shotcrete on masonry infill walls [21]. (A) Wall without opening. (B) Wall with opening. (Permission from DRES.)

(A)

Hole d = 3 cm, L= 20 cm Angle = 30 degree, 60*60 cm

1

256 Advanced Design Examples of Seismic Retrofit of Structures

Pos.4 Pos.1

(A)

(B)

FIG. 4.20 Details of overlapping reinforcing bars [21]. (A) Overall view. (B) Welding the overlapped bars.

Example of a Steel Frame Building With Masonry Infill Walls Chapter 4

257

258 Advanced Design Examples of Seismic Retrofit of Structures

(A)

(B)

FIG. 4.21 Beams and columns as two-end pin members under infill action. (A) Beams. (B) Columns.

Because the beam-column connections in this example are simple, as an alternative, the beams and columns of the building are checked as two-end pin isolated beams with the infill action applied in lceff and lbeff from one end for the columns and beams, respectively (see Fig. 4.21). The more precise method to evaluate the adequacy of frame members involves modeling the beams and columns and connection details. Based on considering the frame members as two-end pin beams, the extreme flexural moments and shear forces and the flexural and shear strengths of each member are calculated as:   Pleff l  leff (4.41) M¼ l   P l  leff V¼ (4.42) l MCE ¼ ZFye

(4.43)

VCE ¼ 1:5  0:4  As Fye

(4.44)

Because the shotcrete layers are applied on both sides of the infill wall, there is no eccentricity from the frame in-plane symmetric axis, and hence no torsion is activated on the frame sections. Evaluation of the Walls in Out-of-Plane Direction The infill walls should be able to tolerate the inertial forces acting in the out-ofplane direction. The out-of-plane stiffness of the infill walls should be neglected in modeling. The relations and acceptance criteria in this section are applicable to

Example of a Steel Frame Building With Masonry Infill Walls Chapter

(A)

4

259

(B)

FIG. 4.22 Examples of masonry walls with different head joints details. (A) Filled head joints. (B) Unfilled head joints with clear distance between bricks. (Photos taken by Mohammad Yekrangnia.)

infill walls with their head joints filled with mortar (see Fig. 4.22A). If the heads joints are not filled with mortar, cement grout should be poured on the walls. Also, in calculating the stiffness and strength of these infill walls in the out-of-plane direction, 75% of the thickness of the infill should be replaced with tinf. If there is a clear distance between the bricks, 50% of the thickness of the infill should be considered in relations (see Fig. 4.22B) (Tables 4.18 and 4.19). The infill walls with hinf/tinf smaller than those found in Table 4.20 can fully benefit from the arching action and hence may not be checked under out-ofplane direction. In the example building, the height of all the infill walls is 2.8 m and their thicknesses are 0.2 m and 0.3 m. The building is located in Tehran, which has very high seismicity, and the target performance level is Life Safety (LS); as a result, all the infill walls of the building are vulnerable in the out-of-plane direction. The out-of-plane force and strength of masonry infill walls are determined based on Section “Conditions for Activation of Infill Wall Behavior.” According to ICERIFB [2], if the reinforcement of shotcrete can resist the out-of-plane forces acting on the infill wall, no other enhancement is required except to connect the bars properly to the frame members. Because all the infill walls in this example have been retrofitted by shotcrete, they are no longer vulnerable against out-of-plane forces, as the results in Table 4.21 show. Consequently, there is no need to connect the bars in shotcrete layers to the frame members. In addition, evaluation of the infill walls in out-of-plane direction with respect to the design of bars to frame connection is carried out here. Based on the Iranian National Building Code; Part 10: Steel Buildings [23], the required weld length (L) to transfer force Fp is determined based on Eq. (4.45): L¼

Fp Ainf 0:3ϕFue ae

(4.45)

Axis

A-1-3

A-4-5

B-1-3

B-4-5

C-1-3

C-4-5

F-1-3

F-4-5

G-1-3

G-4-5

H-1-3

H-4-5

I-1-3

I-4-5

A-1-3

A-4-5

B-1-3

B-4-5

C-1-3

C-4-5

Story

STORY1

STORY1

STORY1

STORY1

STORY1

STORY1

STORY1

STORY1

STORY1

STORY1

STORY1

STORY1

STORY1

STORY1

STORY2

STORY2

STORY2

STORY2

STORY2

STORY2

280

280

280

280

280

280

280

280

280

280

280

280

280

280

280

280

280

280

280

280

hinf (cm)

540

540

540

540

540

540

540

540

540

540

540

540

540

540

540

540

540

540

540

540

Linf (cm)

31

31

31

31

31

31

31

31

31

31

31

31

31

31

31

31

31

26

31

31

a (cm)

2UNP18PL16X1

2UNP24PL24X1

2UNP18PL16X1

2UNP24PL22X1

2UNP18PL16X1

2UNP22PL24X1

2UNP18PL22X1

2UNP22PL24X1

2UNP18PL22X1

2UNP24PL22X1

2UNP18PL22X1

2UNP24PL22X1

2UNP18PL22X1

2UNP24PL24X1

2UNP18PL22X1

2UNP24PL24X1

2UNP18PL22X1

2UNP24PL22X1

2UNP18PL22X1

2UNP22PL24X1

Column Section (Left)

2UNP24PL24X1

2UNP22PL24X1

2UNP24PL22X1

2UNP18PL22X1

2UNP22PL24X1

2UNP18PL22X1

2UNP22PL24X1

2UNP18PL24X1

2UNP24PL22X1

2UNP18PL24X1

2UNP24PL22X1

2UNP18PL24X1

2UNP24PL24X1

2UNP22PL24X1

2UNP24PL24X1

2UNP22PL24X1

2UNP24PL22X1

2UNP18PL24X1

2UNP22PL24X1

2UNP18PL24X1

Column Section (Right)

TABLE 4.18 Results of Evaluation of the Columns [12a]

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Direc tion

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

θ (Rad)

0.43

0.43

0.43

0.43

0.43

0.43

0.43

0.43

0.43

0.43

0.43

0.43

0.43

0.43

0.43

0.43

0.43

0.44

0.43

0.43

θc (Rad)

34.06

34.06

34.06

34.06

34.06

34.06

34.06

34.06

34.06

34.06

34.06

34.06

34.06

34.06

34.06

34.06

34.06

28.68

34.06

34.06

lceff (cm)

72.65

76.1

72.65

73.61

72.65

73.61

88.43

88.94

88.43

88.94

88.43

88.94

88.43

91.42

88.43

91.42

88.43

76.22

88.43

88.94

Fu (ton)

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

m

3.18

3.33

3.18

3.22

3.18

3.22

3.87

3.89

3.87

3.89

3.87

3.89

3.87

4

3.87

4

3.87

2.87

3.87

3.89

M (ton m)

9.33

9.78

9.33

9.46

9.33

9.46

11.36

11.43

11.36

11.43

11.36

11.43

11.36

11.74

11.36

11.74

11.36

10.01

11.36

11.43

V (ton)

993.5

1187

970.5

1027.5

932.5

989.5

989.5

1012.5

1027.5

1050.5

1027.5

1050.5

1050.5

1187

1050.5

1187

1027.5

1050.5

989.5

1012.5

Z (cm3)

40.725

46.54

40.61

40.935

37.755

38.08

38.08

38.17

40.935

41.025

40.935

41.025

41.05

46.54

41.05

46.54

40.935

41.025

38.08

38.17

As (cm2)

26.23

31.34

25.62

27.13

24.62

26.12

26.12

26.73

27.13

27.73

27.13

27.73

27.73

31.34

27.73

31.34

27.13

27.73

26.12

26.73

MCE (ton m)

64.51

73.72

64.33

64.84

59.8

60.32

60.32

60.46

64.84

64.98

64.84

64.98

65.02

73.72

65.02

73.72

64.84

64.98

60.32

60.46

VCE (ton)

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

Result

F-1-3

F-4-5

G-1-3

G-4-5

H-1-3

H-4-5

A-1-3

A-4-5

B-1-3

B-4-5

C-1-3

C-4-5

F-1-3

F-4-5

G-1-3

G-4-5

H-1-3

H-4-5

STORY2

STORY2

STORY2

STORY2

STORY2

STORY2

STORY3

STORY3

STORY3

STORY3

STORY3

STORY3

STORY3

STORY3

STORY3

STORY3

STORY3

STORY3

280

280

280

280

280

280

280

280

280

280

280

280

280

280

280

280

280

280

540

540

540

540

540

540

540

540

540

540

540

540

540

540

540

540

540

540

31

31

31

31

31

31

31

31

31

31

31

31

31

31

31

31

31

31

2UNP18PL16X1

2UNP24PL22X1

2UNP18PL16X1

2UNP24PL22X1

2UNP18PL16X1

2UNP24PL24X1

2UNP18PL16X1

2UNP24PL24X1

2UNP18PL16X1

2UNP24PL22X1

2UNP18PL16X1

2UNP22PL24X1

2UNP18PL16X1

2UNP24PL22X1

2UNP18PL16X1

2UNP24PL22X1

2UNP18PL16X1

2UNP24PL24X1

2UNP24PL22X1

2UNP18PL22X1

2UNP24PL22X1

2UNP18PL22X1

2UNP24PL24X1

2UNP22PL24X1

2UNP24PL24X1

2UNP22PL24X1

2UNP24PL22X1

2UNP18PL22X1

2UNP22PL24X1

2UNP18PL22X1

2UNP24PL22X1

2UNP18PL22X1

2UNP24PL22X1

2UNP18PL22X1

2UNP24PL24X1

2UNP22PL24X1

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.43

0.43

0.43

0.43

0.43

0.43

0.43

0.43

0.43

0.43

0.43

0.43

0.43

0.43

0.43

0.43

0.43

0.43

34.06

34.06

34.06

34.06

34.06

34.06

34.06

34.06

34.06

34.06

34.06

34.06

34.06

34.06

34.06

34.06

34.06

34.06

56.75

57.5

56.75

57.5

56.75

59.45

56.75

59.45

56.75

57.5

56.75

57.5

89.42

90.6

72.65

73.61

72.65

76.1

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

2.48

2.52

2.48

2.52

2.48

2.6

2.48

2.6

2.48

2.52

2.48

2.52

3.91

3.96

3.18

3.22

3.18

3.33

7.29

7.39

7.29

7.39

7.29

7.64

7.29

7.64

7.29

7.39

7.29

7.39

11.49

11.64

9.33

9.46

9.33

9.78

970.5

1027.5

970.5

1027.5

993.5

1187

993.5

1187

970.5

1027.5

932.5

989.5

970.5

1027.5

970.5

1027.5

993.5

1187

40.61

40.935

40.61

40.935

40.725

46.54

40.725

46.54

40.61

40.935

37.755

38.08

40.61

40.935

40.61

40.935

40.725

46.54

25.62

27.13

25.62

27.13

26.23

31.34

26.23

31.34

25.62

27.13

24.62

26.12

25.62

27.13

25.62

27.13

26.23

31.34

64.33

64.84

64.33

64.84

64.51

73.72

64.51

73.72

64.33

64.84

59.8

60.32

64.33

64.84

64.33

64.84

64.51

73.72

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

Axis

A-1-3

A-4-5

B-1-3

B-4-5

C-1-3

C-4-5

F-1-3

F-4-5

G-1-3

G-4-5

H-1-3

H-4-5

I-1-3

I-4-5

A-1-3

A-4-5

B-1-3

B-4-5

C-1-3

Story

STORY1

STORY1

STORY1

STORY1

STORY1

STORY1

STORY1

STORY1

STORY1

STORY1

STORY1

STORY1

STORY1

STORY1

STORY2

STORY2

STORY2

STORY2

STORY2

280

280

280

280

280

280

280

280

280

280

280

280

280

280

280

280

280

280

280

hinf (cm)

540

540

540

540

540

540

540

540

540

540

540

540

540

540

540

540

540

540

540

Linf (cm)

31

31

31

31

31

31

31

31

31

31

31

31

31

31

31

31

26

31

31

a (cm)

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

θ (Rad)

0.53

0.53

0.53

0.53

0.53

0.53

0.53

0.53

0.53

0.53

0.53

0.53

0.53

0.53

0.53

0.53

0.52

0.53

0.53

θb (Rad)

TABLE 4.19 Results of Evaluation of the Beams [12a]

61.39

61.39

61.39

61.39

61.39

61.39

61.39

61.39

61.39

61.39

61.39

61.39

61.39

61.39

61.39

61.39

52.23

61.39

61.39

lbeff (cm)

76.1

72.65

73.61

72.65

73.61

88.43

88.94

88.43

88.94

88.43

88.94

88.43

91.42

88.43

91.42

88.43

76.22

88.43

88.94

Fu (ton)

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

m

3.14

3

3.04

3

3.04

3.65

3.67

3.65

3.67

3.65

3.67

3.65

3.77

3.65

3.77

3.65

2.73

3.65

3.67

M (ton m)

5.11

4.88

4.95

4.88

4.95

5.94

5.98

5.94

5.98

5.94

5.98

5.94

6.14

5.94

6.14

5.94

5.22

5.94

5.98

V (ton)

570

570

570

570

570

570

570

570

570

570

570

570

570

570

570

570

570

570

570

Z (cm3)

25.96

25.96

25.96

25.96

25.96

25.96

25.96

25.96

25.96

25.96

25.96

25.96

25.96

25.96

25.96

25.96

25.96

25.96

25.96

As (cm2)

15.05

15.05

15.05

15.05

15.05

15.05

15.05

15.05

15.05

15.05

15.05

15.05

15.05

15.05

15.05

15.05

15.05

15.05

15.05

MCE (ton m)

41.12

41.12

41.12

41.12

41.12

41.12

41.12

41.12

41.12

41.12

41.12

41.12

41.12

41.12

41.12

41.12

41.12

41.12

41.12

VCE (ton)

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

Result

C-4-5

F-1-3

F-4-5

G-1-3

G-4-5

H-1-3

H-4-5

A-1-3

A-4-5

B-1-3

B-4-5

C-1-3

C-4-5

F-1-3

F-4-5

G-1-3

G-4-5

H-1-3

H-4-5

STORY2

STORY2

STORY2

STORY2

STORY2

STORY2

STORY2

STORY3

STORY3

STORY3

STORY3

STORY3

STORY3

STORY3

STORY3

STORY3

STORY3

STORY3

STORY3

280

280

280

280

280

280

280

280

280

280

280

280

280

280

280

280

280

280

280

540

540

540

540

540

540

540

540

540

540

540

540

540

540

540

540

540

540

540

31

31

31

31

31

31

31

31

31

31

31

31

31

31

31

31

31

31

31

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.48

0.53

0.53

0.53

0.53

0.53

0.53

0.53

0.53

0.53

0.53

0.53

0.53

0.53

0.53

0.53

0.53

0.53

0.53

0.53

61.39

61.39

61.39

61.39

61.39

61.39

61.39

61.39

61.39

61.39

61.39

61.39

61.39

61.39

61.39

61.39

61.39

61.39

61.39

56.75

57.5

56.75

57.5

56.75

59.45

56.75

59.45

56.75

57.5

56.75

57.5

89.42

90.6

72.65

73.61

72.65

76.1

72.65

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

6.07

2.34

2.37

2.34

2.37

2.34

2.45

2.34

2.45

2.34

2.37

2.34

2.37

3.69

3.74

3

3.04

3

3.14

3

4.88

3.81

3.87

3.81

3.87

3.81

4

3.81

4

3.81

3.87

3.81

3.87

6.01

6.09

4.88

4.95

4.88

5.11

570

570

570

570

570

570

570

570

570

570

570

570

570

570

570

570

570

570

570

25.96

25.96

25.96

25.96

25.96

25.96

25.96

25.96

25.96

25.96

25.96

25.96

25.96

25.96

25.96

25.96

25.96

25.96

25.96

15.05

15.05

15.05

15.05

15.05

15.05

15.05

15.05

15.05

15.05

15.05

15.05

15.05

15.05

15.05

15.05

15.05

15.05

15.05

41.12

41.12

41.12

41.12

41.12

41.12

41.12

41.12

41.12

41.12

41.12

41.12

41.12

41.12

41.12

41.12

41.12

41.12

41.12

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

OK

264 Advanced Design Examples of Seismic Retrofit of Structures hinf TABLE 4.20 Maximum Allowable tinf [2] Performance Level

Low Seismicity

Moderate Seismicity

High and Very High Seismicity

IO

14

13

8

LS

15

14

9

CP

16

15

10

where: Fp ¼ compressive stress in the out-of-plane direction acting on the infill; as an example, Fp ¼0.0686 kg/cm2 for the longitudinal-internal and transverseinternal infill walls in the upper story (see Table 4.21); Ainf ¼ area of infill walls equals Linf  hinf; ϕ ¼inspection factor; it is assumed that the inspection by a licensed inspector is made on the fabrication site; hence ϕ ¼ 0.75; ae ¼effective weld throat equal to 30% of the weld size (the weld size is assumed to be 4 mm); and Fue ¼ ultimate tensile strength of the weld material; it is assumed that E60 electrode is used, and hence Fue ¼420 MPa. L¼

0:0686  540  280 ¼ 91:5 cm 0:3  0:75  4200ð0:3  0:4Þ

There is a total 9.5 cm of weld with aforementioned specifications to transfer to total out-of-plane force from the infill to the frame members. If 10 bars are welded to the frame, the required weld length for each bar is 5 cm. These bars can be bent over the flange of the columns and welded. The details of connection of shotcrete bars to the frame members are shown in Fig. 4.23.

Evaluation of the Beams Against Gravitational Loads Because of the simple connections between beams and columns, the infill walls and the added concentric braces are the only later load-bearing elements in transverse and longitudinal directions, respectively, the beams in the frame are only evaluated against gravitational loads. Also, the beams should be checked against the actions from the infill walls. The beams were previously evaluated for the actions from the infill walls in Section “Evaluation of the Beam and Columns.” The results of evaluation of the beams against gravitational loads with the load combination 1.1DL +0.44LL are presented in Table 4.22. As can be seen, seven beams are vulnerable and hence should be retrofitted to resist the gravitational loads adequately. The retrofit of these

Transverseinternal

Transverseexternal

Longitudinalinternal

Infill Wall Location

1.5

1.5

1.5

1

1

1.5

1

1

1.5

1

1.5

1

1.5

1.5

1

1

1.5

Rp

1

ap

280

280

280

280

280

280

280

280

280

hinf (cm)

540

540

540

540

540

540

715

715

715

Linf (cm)

20

20

20

20

20

20

20

20

20

tinf (cm)

820

500

180

820

500

180

820

500

180

Z (cm)

980

980

980

980

980

980

980

980

980

H (cm)

TABLE 4.21 Results of Evaluation of the Infill Walls in Out-of-Plane Direction [12a]

458

458

458

848

848

848

458

458

458

Wp (kg/m2)

0.0686

0.0518

0.0351

0.1270

0.0959

0.0649

0.0686

0.0518

0.0351

Fp (kg/cm2)

OK

OK

OK

OK

OK

OK

OK

OK

OK

Result

Example of a Steel Frame Building With Masonry Infill Walls Chapter 4

265

266 Advanced Design Examples of Seismic Retrofit of Structures

FIG. 4.23 Details of connection of shotcrete bars to the frame members [12a].

beams may be done by adding steel plates on the flanges in order to increase their flexural capacity.

Evaluation of the Frame Connections All the beam-column connections in the example building are simple cradletype. Because of the age of the building, as-built sketches of connections were not available. These connections should be able to transfer the shear forces and flexural moments from the beams to the columns. As indicated in Section “Shotcreting of the Infill Panels in Transverse Direction,” steel plates with the length of 1.5a and width of double flange width of beams plus the width of the column section should be added to the columns and beams at the corners in order to provide full contact between the infill walls and the frame members. Based on Section “Evaluation of the Beam and Columns,” the beams experience a concentrated force P from the infill walls at the distance of lbeff. Accordingly, the fillet welds in the connection are under shear force P and flexural moment P. lbeff. These added plates should be stiffened by triangular stiffeners. As an example for determination of the size of these stiffeners, the beam A-1-3 on STORY1 is considered. In this bay, the shear force of 6.74 ton is applied at the distance of 61.4 cm. Assuming that four stiffeners with the length of 30 cm are added with the weld size of 8 mm, we have: P A Mc fb ¼ I fv ¼

Example of a Steel Frame Building With Masonry Infill Walls Chapter

4

267

A ¼ 4  2  30  0:8 ¼ 192 cm2 0:8  303 ¼ 14; 400 cm4 12 6740 kg fv ¼ ¼ 35 2 192 cm

I ¼42

6740  61:4  15 kg ¼ 431 2 14,400 cm qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi kg fr ¼ fv 2 + fb 2 ¼ 352 + 4312 ¼ 433 2 cm fb ¼

where: A ¼weld area; I ¼moment of inertia of the weld line about the axis of flexure; fv ¼shear stress; fb ¼ bending stress; and fr ¼resultant stress. Based on the Iranian National Building Code; Part 10: Steel Buildings [23], the allowable stress of the weld is 0.3 ϕFue. The inspection is made by a licensed inspector on the fabrication site and hence ϕ ¼0.75. It is assumed that E60 electrode is used, and hence Fue ¼420 MPa. Fvw ¼ 0:3ϕFue ¼ 0:3  0:75  4200 ¼ 945 ae ¼

kg cm2

fr 433 ae 0:46 ¼ ¼ 0:46 ! aw ¼ ¼ 0:65 cm ¼ Fvw 945 0:707 0:707

where ae ¼effective weld throat and aw ¼weld throat. Consequently, four triangular plates with the length of 30 cm and thickness of 1 cm on each side of the connections can be considered as stiffeners to the corner plates. The retrofit details of the cradle-type connections are shown in Fig. 4.24. More information about the retrofitting of cradle-type connections can be found in Moghaddam [16] and Code 360 [10].

4.5 ISOLATION OF INFILL WALLS NOT MEETING INFILL PANEL REQUIREMENTS FROM THE FRAME In some case where the walls cannot meet the minimum requirements of infill walls, or it is intended to exclude the infill wall from contributing to the loadbearing mechanism because of excessive demands on the frame members or the imposed irregularity on the building, isolation of the infill from the surrounding frame can be considered as an option. The design procedure of the isolation system should lead to guaranteeing isolation of the wall from the frame in the

BayID

B3

B3

B3

B6

B6

B6

B9

B9

B9

B12

B12

B12

B15

B15

B15

B18

B18

B18

B21

Story

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

INP240

INP180

INP240

IPE200

IPE200

INP240

INP240

IPE200

INP240

INP240

IPE200

INP240

IPE200

IPE200

INP240

IPE200

IPE200

INP240

IPE200

SecID

0.114

1.242

0.632

0.676

1.036

0.632

0.417

1.036

0.632

0.417

1.036

0.632

0.676

1.036

0.632

0.676

0.96

0.591

0.627

PMMRatio

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

Story

B68

B67

B67

B67

B66

B66

B66

B65

B65

B65

B64

B64

B64

B63

B63

B63

B62

B62

B62

BayID

INP240

INP260

IPE270

INP240

IPE270

INP260

INP240

IPE270

INP260

INP240

IPE270

INP260

INP240

IPE270

INP260

INP240

IPE270

INP260

INP240

SecID

0.108

0.831

0.734

0.844

0.673

0.698

0.771

0.683

0.734

0.771

0.681

0.734

0.771

0.681

0.734

0.771

0.684

0.736

0.771

PMMRatio

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

Story

B43

B43

B43

B40

B40

B40

B37

B37

B37

B34

B34

B34

B33

B33

B33

B32

B32

B32

B31

BayID

TABLE 4.22 The Results of Evaluation of the Beams Against Gravitational Loads [12a]

IPE200

INP240

IPE200

IPE200

INP240

IPE200

IPE200

INP240

IPE200

INP260

IPE270

INP240

INP260

IPE270

INP240

IPE270

INP260

INP240

IPE270

SecID

0.03

0.03

0.03

0.03

0.03

0.03

0.028

0.028

0.028

0.13

0.115

0.116

0.932

0.808

0.939

0.757

0.769

0.86

0.728

PMMRatio

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

Story

B98

B98

B98

B97

B97

B97

B96

B96

B96

B95

B95

B95

B94

B94

B94

B93

B93

B93

B92

BayID

IPE270

INP260

INP240

IPE270

INP260

INP240

IPE270

INP260

INP240

IPE270

INP260

INP240

IPE270

INP260

INP240

IPE270

INP260

INP240

IPE270

SecID

0.733

0.789

0.858

0.733

0.789

0.858

0.727

0.785

0.844

0.214

0.227

0.844

0.214

0.227

0.844

0.727

0.785

0.844

0.732

PMMRatio

B21

B21

B22

B22

B22

B23

B23

B23

B24

B24

B24

B25

B25

B25

B26

B26

B26

B27

B27

B27

B28

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

INP240

IPE270

INP260

INP240

IPE270

INP260

INP240

IPE270

INP260

INP240

IPE270

INP260

INP240

IPE270

INP260

INP240

IPE220

INP260

INP240

IPE220

INP260

0.861

0.773

0.836

0.861

0.773

0.836

0.861

0.732

0.79

0.861

0.727

0.786

0.86

0.687

0.739

0.832

1.691

1.103

0.908

0.589

0.381

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

B89

B86

B86

B86

B83

B83

B83

B80

B80

B80

B77

B77

B77

B74

B74

B74

B71

B71

B71

B68

B68

INP240

INP180

INP240

IPE200

IPE200

INP240

INP240

IPE200

INP240

INP240

IPE200

INP240

IPE200

IPE200

INP240

IPE200

IPE200

INP240

IPE200

INP260

IPE270

0.113

0.042

0.03

0.03

0.03

0.03

0.03

0.03

0.03

0.03

0.03

0.03

0.03

0.03

0.03

0.03

0.028

0.028

0.028

0.126

0.108

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

B58

B58

B58

B57

B57

B57

B56

B56

B56

B55

B55

B55

B52

B52

B52

B49

B49

B49

B46

B46

B46

IPE270

INP260

INP240

IPE270

INP260

INP240

IPE220

INP260

INP240

IPE220

INP260

INP240

INP180

INP240

IPE200

IPE200

INP240

INP240

IPE200

INP240

INP240

0.681

0.734

0.77

0.626

0.667

0.744

1.52

0.997

0.816

0.525

0.347

0.105

0.042

0.03

0.03

0.03

0.03

0.03

0.03

0.03

0.03

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

B111

B111

B111

B108

B108

B108

B105

B105

B105

B102

B102

B102

B101

B101

B101

B100

B100

B100

B99

B99

B99

IPE200

INP240

IPE200

IPE200

INP240

IPE200

IPE200

INP240

IPE200

INP260

IPE270

INP240

INP260

IPE270

INP240

IPE270

INP260

INP240

IPE270

INP260

INP240

Continued

1.036

0.632

0.676

1.036

0.632

0.676

0.96

0.591

0.627

0.136

0.119

0.116

0.884

0.811

0.939

0.712

0.771

0.858

0.732

0.788

0.858

BayID

B28

B28

B29

B29

B29

B30

B30

B30

B31

B31

Story

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

STORY1

STORY3

STORY2

INP260

INP240

IPE270

INP260

INP240

IPE270

INP260

INP240

IPE270

INP260

SecID

0.786

0.86

0.728

0.787

0.86

0.728

0.787

0.86

0.732

0.79

PMMRatio

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

Story

B92

B92

B91

B91

B91

B90

B90

B90

B89

B89

BayID

INP260

INP240

IPE270

INP260

INP240

IPE220

INP260

INP240

IPE220

INP260

SecID

0.788

0.857

0.692

0.741

0.829

1.696

1.104

0.907

0.593

0.381

PMMRatio

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

Story

B61

B61

B61

B60

B60

B60

B59

B59

B59

BayID

TABLE 4.22 The Results of Evaluation of the Beams Against Gravitational Loads—cont’d

IPE270

INP260

INP240

IPE270

INP260

INP240

IPE270

INP260

INP240

SecID

0.77

0.83

0.771

0.77

0.83

0.771

0.684

0.735

0.771

PMMRatio

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

STORY1

STORY2

STORY3

Story

B120

B120

B120

B117

B117

B117

B114

B114

B114

BayID

INP180

INP240

IPE200

IPE200

INP240

INP240

IPE200

INP240

INP240

SecID

1.242

0.632

0.676

1.036

0.632

0.417

1.036

0.632

0.417

PMMRatio

Example of a Steel Frame Building With Masonry Infill Walls Chapter

4

271

FIG. 4.24 The retrofit details of the cradle-type connections [12a].

in-plane direction (even at experienced lateral drifts equal to the drift acceptable by the design performance level of the building), while preventing the wall from out-of-plane overturning. According to ASCE 41, anchorage of walls to diaphragms shall be evaluated or retrofitted for forces calculated using Eq. (4.46), which shall be developed into the diaphragm. Fp ¼ 0:4SXS ka kh χWp

(4.46)

Fp,min ¼ 0:2ka χWp

(4.47)

Lf 30:48   1 2za kh ¼ 1+ hh 3 ka ¼ 1:0 +

(4.48) (4.49)

where: Fp ¼seismic force for anchorage of walls to diaphragms; ka ¼factor to account for diaphragm flexibility, equal to 1.0 for rigid diaphragms and need not exceed 2.0 for flexible diaphragms; Lf ¼ span, in feet, of a flexible diaphragm that provides the lateral support for the wall between vertical primary seismic-force-resisting elements that provide lateral support to the diaphragm in the direction considered; kh ¼factor to account for variation in force over the height of the building when all diaphragms are rigid—for flexible diaphragms, use 1.0; za ¼height of the wall anchor above the base of the structure; hh ¼height, in feet, above the base to the roof level; χ ¼ factor for calculation of out-of-plane wall forces, equal to 1.3 for LS performance level; SXS ¼spectral response acceleration parameter at short periods for the selected hazard level and damping, adjusted for site class, without any adjustment for soil–structure interaction; and Wp ¼weight of the wall tributary to the wall anchor.

150 x 40 x 3 mm L = 200 mm

PL.50 x 2mm

Ø8 PL.250 x 150 x 6 mm

PL.250 x 150 x 6 mm

2L40 x 40 x 4 mm

60 x 60 x 6 L = 100 mm

2L40 x 40 x 4 mm

Gypsum (5 mm)

Wire lath

FIG. 4.25 Details of the anchoring the infill walls against out-of-plane actions. (A) Solid infill wall. (Permission from DRES.)

(A)

2L40 x 40 x 4 mm

Polypropylene (40 mm)

PL.250 x 100 x 8 mm

P L.50 x 2 mm

DETAIL-2 PL.250 x 150 x 6 mm

PL.50 x 2 mm

DETAIL-1 PL.250 x 150 x 6 mm

272 Advanced Design Examples of Seismic Retrofit of Structures

FIG. 4.25, CONT’D (B) Infill walls with opening.

[Continued]

Example of a Steel Frame Building With Masonry Infill Walls Chapter

4

273

FIG. 4.25, CONT’D (C) Connection to columns.

274 Advanced Design Examples of Seismic Retrofit of Structures

4

275

FIG. 4.25, CONT’D (D) Connection to beams. (Permission from DRES.)

Example of a Steel Frame Building With Masonry Infill Walls Chapter

276 Advanced Design Examples of Seismic Retrofit of Structures

(A) (B)

(C)

(D)

FIG. 4.26 Examples of isolation of walls from the frame. (A) In a steel frame. (B) Using compressed foam between the wall panels and the frame and brace members. (C) In an RC frame building during construction. (D) In an RC frame building after construction. (Permission from DRES.)

Also, all components shall have adequate strength to span between locations of out-of-plane support when subjected to out-of-plane forces calculated using Eq. (4.50), but not less than forces calculated using Eq. (4.51): Fp ¼ 0:4SXS χWp

(4.50)

Fp,min ¼ 0:1χWp

(4.51)

where Fp ¼ out-of-plane force per unit area for the analysis of a wall spanning between two out-of-plane supports. Fig. 4.25 shows the details of the anchoring the infill walls against out-ofplane actions. Examples of isolation of walls from the frame are shown in Fig. 4.26.

REFERENCES [1] ASCE/SEI Seismic Rehabilitation Standards Committee, Seismic Rehabilitation of Existing Buildings (ASCE/SEI 41-06), American Society of Civil Engineers, Reston, VA, 2007.

Example of a Steel Frame Building With Masonry Infill Walls Chapter

4

277

[2] Building and Housing Research Center. Iranian Code for Evaluation and Rehabilitation of Infilled Frame Buildings (ICERIFB) (Code 398), Tehran, Iran, 2016. ´ lvarez, Performance of buildings with masonry infill [3] L. Hermanns, A. Fraile, E. Alarco´n, R. A walls during the 2011 Lorca earthquake, Bull. Earthq. Eng. 12 (5) (2014) 1977–1997. [4] ˙I.H. C ¸ agˇatay, Failure of an industrial building during a recent earthquake in Turkey, Eng. Fail. Anal. 12 (4) (2005) 497–507. [5] H.A. Moghaddam, P.J. Dowling, The State of the Art in Infilled Frames, Imperial College of Science and Technology, Civil Engineering Department, London, 1987. [6] A.K. Chopra, Dynamics of Structures-Theory and Applications to Earthquake Engineering, third ed., Prentice Hall, New Jersey, 2007. [7] A.A. Tasnimi, A. Mohebkhah, Investigation on the behavior of brick-infilled steel frames with openings, experimental and analytical approaches, Eng. Struct. 33 (3) (2011) 968–980. [8] E. Yuksel, H. Ozkaynak, O. Buyukozturk, C. Yalcin, A.A. Dindar, M. Surmeli, D. Tastan, Performance of alternative CFRP retrofitting schemes used in infilled RC frames, Constr. Build. Mater. 24 (4) (2010) 596–609. [9] ASCE. 2010. Minimum Design Loads for Buildings and Other Structures. [10] Management and Planning Organization Office of Deputy for Technical Affairs. Instruction for Seismic Rehabilitation of Existing Buildings (No. 360), Iran (in Persian), 2014. [11] Management and Planning Organization Office of Deputy for Technical Affairs. Seismic Rehabilitation of Existing Unreinforced Masonry Buildings, No. 376, 2007. [12] AISC Committee, Specification for Structural Steel Buildings (ANSI/AISC 360-10), American Institute of Steel Construction, Chicago-Illinois, 2010. [12a] M. Mohammadi, M. Shavandi, Seismic retrofit plan of a typical high school building, The report to Organization for Development, Renovation and Equipping Schools of IR, DRES, Iran, 2012 (in Persian). [13] Building and Housing Research Center. Iranian Code of Practice for Seismic Resistant Design of Buildings (Standard 2800). Fourth Revision, Iran (in Persian). [14] MHUD. Iranian National Building Code, Part 6: Loading, Iran, 2014. [15] Karami R (1991), The Mechanical Properties of Cradle-Type Connections, M.Sc. Thesis, Sharif University of Technology, Tehran, Iran. [16] H. Moghaddam, Earthquake Engineering; Theory and Application, third ed., Mahdi Publications, Tehran, Iran, 2006. [17] M. Yekrangnia, M. Mohammadi, A new strut model for solid masonry infills in steel frames, Eng. Struct. 135 (2017) 222–235. [18] W.W. El-Dakhakhni, M. Elgaaly, A.A. Hamid, Three-strut model for concrete masonryinfilled steel frames, J. Struct. Eng. 129 (2) (2003) 177–185. [19] A. Dehghani, G. Fischer, F.N. Alahi, Strengthening masonry infill panels using engineered cementitious composites, Mater. Struct. 48 (1–2) (2015) 185–204. [20] Technical & Supervising Deputy Seismic Rehabilitation Office, Organization for Development, Renovation and Equipping Schools of Iran. Practical Instruction for Shotcrete in Seismic Rehabilitation of Schools (No. 10289/2-3016), 2010. [21] Technical & Supervising Deputy, Bureau of Schools Seismic Rehabilitation, Organization for Development, Renovation and Equipping Schools of Iran. Practical Instruction for Shotcrete Connection in Seismic Rehabilitation of Schools (NO. 10289/2-13613), 2011. [22] Office of Deputy for Strategic Supervision Department of Technical Affairs. The Code of Practice for Design Specification Manufacturing and Construction of 3D Panel Structures (Code 385) (First Revision), Tehran, Iran, 2013. [23] MHUD. Iranian National Building Code; Part 10: Steel Buildings, 2014.

Chapter 5

Example of a Steel Frame Building Retrofitted with Concentric Braces☆ Abdoreza S. Moghadam*, Behnam Azmoudeh†, Morteza Raissi Dehkordi‡ and Mahdi Eghbali§ *

International Institute of Earthquake Engineering and Seismology (IIEES), Tehran, Iran, †APS Designing Energy, Rome, Italy, ‡Iran University of Science and Technology, Tehran, Iran, § Department of Civil Engineering, Faculty of Engineering, University of Zanjan, Zanjan, Iran

Aims By reading this chapter, you are introduced to: l l l l

the evaluation procedure for steel frame buildings with braces; the evaluation procedure for cradle-type connections; the evaluation procedure for foundations; and comparison of three different brace systems as the retrofitting methods with regards to performance improvement, construction costs, and construction time.

5.1 INTRODUCTION In this chapter, a typical two-story steel simple frame is evaluated making use of ASCE 41 [1], Iranian Code of Practice for Seismic Resistant Design of Buildings (Standard 2800) [2], and Instruction for Seismic Rehabilitation of Existing Buildings (Code 360) [1]. The building is located in Kermanshah, Iran, which has high seismicity (design acceleration of 0.3 g). The building has a total area of 1095 m2 across the floor and first stories, and was constructed in 1996. On the floor, the building has cradle-type (2INP240) beam-column connections (see Fig. 4.13, Chapter 4) in the North-South direction and simple connection (2IPE140) in the West-East direction. The connection of the first story in both directions is similar to the latter one. In addition to the main building, there is a ☆ This chapter is mainly a part of a retrofit project ordered by Organization for Development, Renovation and Equipping Schools of IR. Iran (DRES). The authors of this chapter appreciate the financial and technical support of DRES. Advanced Design Examples of Seismic Retrofit of Structures. https://doi.org/10.1016/B978-0-08-102534-5.00005-2 © 2019 Elsevier Ltd. All rights reserved.

279

280

Advanced Design Examples of Seismic Retrofit of Structures

sports salon with an area of 180 m2. This building has simple beam-column connections in the West-East direction with L80
80 braces but has no lateral loadbearing member in the North-South direction which has truss beams due to its large span. These buildings are separated from each other except at the roof level (Fig. 5.1). The structural system in both directions is simple frame with masonry infill walls without any lateral load-bearing elements. The diaphragm system of floor story of both buildings is jack-arch (see Fig. 2.27, Chapter 2) in all stories. The roof of the first story of both buildings is a light roof. The foundation of the building is singular. The soil type is III according to Standard 2800 [2], which is moderate to dense soil with an average shear wave speed of 175–375 m/s. Based on the field observations and the results of boreholes, soil and site characteristics are presented in Table 5.1. The plans and sections of the example building are shown in Figs. 5.2 and 5.3, respectively. The thickness of the external and internal infill walls in the main building is from 25 to 45, and 20 cm, respectively. The height-to-thickness ratios of the internal and the external infill walls are 15.0 and 9.7, respectively, which are higher than the maximum allowable ratio in Table 4.20 in Chapter 4 for activating of the arching action. The thickness of the external and internal infill walls in the sports building is 20 cm, which leads to a height-to-thickness ratio of 25.75.

FIG. 5.1 Interface between two building parts. (Photo taken by A.S. Moghadam.)

TABLE 5.1 Soil and Site Characteristics

Cohesion

Young’s Modulus (MPa)

Poisson’s ratio

Underground Water Level (m)

Liquefaction

Landslide

17

0.21

9

0.4

> > < Δ f ð xÞ ¼

5

291

5
1026:27
ð2160Þ4 ¼ 0:34 ðcmÞ 384
30030
28108938916:67

2 > > > : ΔsðxÞ ¼ 1:5
1026:27
ð2160Þ ¼ 2:08 ðcmÞ 8
34430
12512:5   ΔDiaphragm ) ΔStory ¼ 2:42 ðcmÞ7! 2 ΔStory 8 > 5
391:31
ð900Þ4 > > ¼ 0:16 ðcmÞ ¼ Δ < f ð yÞ 384
30030
668250000 2 > > > : ΔsðyÞ ¼ 1:5
391:31
ð900Þ ¼ 0:47 ðcmÞ 8
9900
12512:5   ΔDiaphragm ) ΔStory ¼ 0:63 ðcmÞ7! 2 ΔStory

As a result, the diaphragm in the floor story of the main building in two directions is flexible. The diaphragm of the first story in the main building is lightweight and, as such, it is flexible. The same procedure for the diaphragm of the sports building leads to a flexible diaphragm.

5.4.3 Torsion Based on ASCE 41 [1], the torsion in rigid and semi-rigid diaphragms including the accidental torsion should be included. The torsion may not be included in the flexible diaphragms.

5.4.4 Soil-Structure Interaction Based on ASCE 41 [1], the effects of soil-structure interaction (SSI) shall be evaluated for those buildings in which an increase in fundamental period caused by SSI effects results in an increase in spectral accelerations. For other buildings, the effects of SSI need not be evaluated.

5.5 ANALYSIS PROCEDURE In this example, the linear static procedure (LSP) and nonlinear static procedure (NSP) are utilized for determination of the demands and capacity of each structural member.

5.5.1 Demand Forced Calculations The seismic demand force is calculated based on of Code 360 [1] as follows: QE ¼ C1 C2 Cm Sa W where: QE ¼ pseudo-lateral force;

(5.5)

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Advanced Design Examples of Seismic Retrofit of Structures

Sa ¼ response spectrum acceleration, at the fundamental period and damping ratio of the building in the direction under consideration which is determined based Code 360 [1]; W ¼ effective seismic weight of the building, including the total dead load and applicable codified portions of other gravity loads. According to Code 360, the dead loads also include the weight of partition walls and the total operating weight of permanent equipment, and the live loads are 20% of the codified live loads including snow [5]; and C1 ¼ modification factor to relate expected maximum inelastic displacements to displacements calculated for linear elastic response. This factor is determined based on either of these methods. (1) Based on Eq. (5.6) 25ðRu  1Þ a Ru  1 0:2 < T  1 ! C1 ¼ 1 + aT 2

T  0:2 ! C1 ¼ 1 +

(5.6)

T > 1 ! C1 ¼ 1 where: a ¼ site class factor; ¼130 site Class A or B according to ASCE 41-13 [1]; ¼90 site Class C; ¼60 site Class D, E, or F; T ¼ fundamental period of the building in the direction under consideration, calculated in accordance with Section 1.7 of Code 360, including modification for Soil-Structural Interaction (SSI) effects of Section 3.2.6 of this document; and Ru ¼ ratio of elastic strength demand to yield strength coefficient calculated in accordance with Eq. (5.7). If the elastic base shear capacity substituted Ve is available, Eq. (5.8) can be used interchangeably. DCRmax Cm  1 1:5 Sa Cm Ru ¼ Ve =W

Ru ¼

(5.7) (5.8)

where DCRmax is the largest demand to capacity ratio (DCR) computed for any primary component of a building in the direction of response under consideration, taking C1 ¼ C2 ¼ Cm ¼ 1.0. (2) Based on Eq. (5.9) when Ru cannot be determined.

Example of a Steel Frame Building Retrofitted Chapter

1  C1 ¼ 1 +

5

Ts  T 2Ts  0:2

293

(5.9)

C2 ¼ Modification factor to represent the effect of pinched hysteresis shape, cyclic stiffness degradation, and strength deterioration on maximum displacement response. Based on Code 360 [5], this parameter is can be determined based on either of these methods. (1) Based on Eq. (5.10) 25ðRu  1Þ a   1 Ru  1 2 T  0:7 ! C2 ¼ 1 + 800 T T  0:7 ! C2 ¼ 1 +

(5.10)

(2) In the absence of precise calculations, C2 can be taken as 1.0. For the example building, it was assumed that C2 ¼ 1. Cm ¼ Effective mass factor to account for higher modal mass participation effects obtained from Table 3.4 of Code 360. Cm is 1.0 for the steel frames with concentric braces and also the main buildings (simple frame with masonry infill) which is categorized as “Other” structural systems in this table. For determination of the buildings natural period, the recommended relation in Eq. (5.11) in Standard 2800 is used which is categorized as “Other” structural systems.  3 (5.11) T ¼ 0:05ðH Þ 4 where H is the total height of the building.  3 T ¼ 0:05ðH Þ 4 ¼ 0:05ð7:1Þ0:75 ¼ 0:21ðsÞ For the main building  3 T ¼ 0:05ðH Þ 4 ¼ 0:05ð5:55Þ0:75 ¼ 0:18ðsÞ For the sports building Based on the derived natural periods from the model, we have: - For the main building 0:7  0:49 0:7  0:42 C1ðxÞ ¼ 1 + ¼ 1:17, C1ðyÞ ¼ 1 + ¼ 1:23 1:4  0:2 1:4  0:2 C2 ¼ 1:0 Cm ¼ 1:0 SaðxÞ¼ SaðyÞ ¼ 0:3
2:75 ¼ 0:825 VðXÞ ¼ 0:965  W ) VðY Þ ¼ 1:02  W

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Advanced Design Examples of Seismic Retrofit of Structures

- For the sports building 0:7  2:31 0:7  0:3 ¼ 0:341 ! C1ðxÞ ¼ 1:0, C1ðyÞ ¼ 1 + ¼ 1:33 C1ðxÞ ¼ 1 + 1:4  0:2 1:4  0:2 C2 ¼ 1:0 Cm ¼ 1:0 SaðxÞ ¼ 0:3
1:23 ¼ 0:369 SaðyÞ¼ 0:3
2:75 ¼ 0:825 VðXÞ ¼ 0:369  W ) VðY Þ ¼ 1:097  W

5.5.2 Distribution of Demand Forces in Height of the Building The seismic force applied at any floor level i, FUDi, is determined based on Eq. (5.12): W i hk FUDi ¼ Xn i
QE W hk j¼1 j j

(5.12)

where: QE ¼ pseudo-lateral force based on Eq. (5.5); k ¼ vertical distribution factor; k ¼ 2.0 for T 2.5 s; ¼1.0 for T  0.5 s; ¼0.5T + 0.75 for 0.5 < T < 2.5 s; Wj ¼ portion of the effective seismic weight W located on or assigned to level j; Wi ¼ portion of the effective seismic weight W located on or assigned to level i; hj ¼ height from the base to level j; and hi ¼ height from the base to level i.   k ¼ 1:0 TX ¼ 0:49ð sec Þ ) For the main building TY ¼ 0:42sec Þ k ¼ 1:0   k ¼ 0:5T + 0:75 ¼ 0:5
2:3 + 0:75 ¼ 1:9 TX ¼ 2:31ð sec Þ ) k ¼ 1:0 TY ¼ 0:3ð sec Þ For the sports building

5.5.3 Target Displacement The target displacement, δt, at each floor level shall be calculated in accordance with Eq. (5.13):

Example of a Steel Frame Building Retrofitted Chapter

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295

TABLE 5.6 Values for Modification Factors C0 [1] Shear Buildingsa

Other Buildings

Number of Stories

Triangular Load Pattern

Triangular Load Pattern

Any Load Pattern

1

1.0

1.0

1.0

2

1.2

1.15

1.2

3

1.2

1.2

1.3

5

1.3

1.2

1.4

10+

1.3

1.2

1.5

a

Buildings in which, for all stories, story drift decreases with increasing height.

δt ¼ C0 C1 C2 Sa

Te 2 g 4π 2

(5.13)

where C0 ¼ modification factor to relate spectral displacement of an equivalent single-degree-of-freedom (SDOF) system to the roof displacement of the building multi-degree-of-freedom (MDOF) system calculated using one of the following procedures: (1) the first mode mass participation factor multiplied by the ordinate of the first mode shape at the control node; (2) the mass participation factor calculated using a shape vector corresponding to the deflected shape of the building at the target displacement multiplied by ordinate of the shape vector at the control node; or (3) the appropriate value from Table 5.6. In nonlinear static analysis, it is recommended to push the model to lateral displacement larger than the target displacement; the applied displacement can be 1.5 times of the target displacement. Sa ¼ according to the definition in Section 5.5.1; g ¼ acceleration of gravity; C0 ¼ according to the definition in Section 5.5.1; C1 ¼ according to the definition in Section 5.5.1; C2 ¼ according to the definition in Section 5.5.1 Te ¼ according to the definition in Section 5.5.1; ð0:49Þ2
9:81 ¼ 9:93ðcmÞ
1:5 ¼ 14:9ðcmÞ 39:43 2 ð0:42Þ
9:81 ¼ 7:3ðcmÞ
1:5 ¼ 10:94ðcmÞ δtðxÞ ¼ 1:2
1:4
1:2
0:825
39:43

δtðxÞ ¼ 1:2
1:4
1:2
0:825


For the main building

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Advanced Design Examples of Seismic Retrofit of Structures

ð2:31Þ2
9:81 ¼ 84ðcmÞ
1:5 ¼ 126ðcmÞ 39:43 2 ð0:31Þ
9:81 ¼ 3:38ðcmÞ
1:5 ¼ 5:07ðcmÞ δtðyÞ ¼ 1:0
1:43
1:2
0:825
39:43 For the sports building

δtðxÞ ¼ 1:0
1:43
1:2
0:369


5.5.4 Concurrent Seismic Effects Based on ASCE 41, where concurrent multi-directional seismic effects must be considered, horizontally oriented, orthogonal X- and Y-axes shall be established. Components of the building shall be evaluated or retrofitted for combinations of forces and deformations from separate analyses performed for ground motions in X and Y directions as follows. For the example buildings, there is no codified lateral load-bearing system for the main building. Also, no column is subjected to concurrent seismic effects because the braces are along one direction of the building only. As a result, the buildings in this example are not subjected to considering concurrent seismic effects.

5.5.5 Actions Calculations According to ASCE 41, action is referred to an internal moment, shear, torque, axial force, deformation, displacement, or rotation corresponding to a displacement caused by a structural degree of freedom; designated as force- or deformation-controlled [1]. Generally speaking, there are two types of seismic actions; (1) deformation-controlled action: which is an action that has an associated deformation that is allowed to exceed the yield value of the element being evaluated. The extent of permissible deformation beyond yield is based on component modification factors (m-factors); (2) force-controlled action: which corresponds to an action that is not allowed to exceed the nominal strength of the element being evaluated. Based on these definitions, a typical structural component can be deformation-sensitive which is sensitive to deformation imposed by the drift or deformation of the structure, including deflection or deformation of diaphragms. Similarly, force-sensitive structural components are defined.

5.5.5.1 Deformation-Controlled Based on Code 360, deformation-controlled actions for LSP denoted by QUD shall be calculated in accordance with Eq. (5.14): QUD ¼ QG + QE

(5.14)

where: QE ¼ action caused by the response to the selected seismic hazard level calculated using Section 5.6.1 of this example; and QG ¼ action caused by gravity loads as determined according to either of these methods:

Example of a Steel Frame Building Retrofitted Chapter

5

297

(1) Where the effects or actions of gravity loads and seismic forces are additive, the action caused by gravity loads, QG, shall be obtained in accordance with Eq. (5.15): QG ¼ 1:1ðQD + QL + Qs Þ

(5.15)

where: QD ¼ action caused by dead loads; QL ¼ action caused by live load, equal to 25% of the unreduced live load obtained in accordance with ASCE 7 [6] but not less than the actual live load; and Qs ¼ action caused by effective snow load which is assumed to be zero in this example; and QUD ¼ deformation-controlled action caused by gravity loads and earthquake forces. (2) Where the effects or actions of gravity loads and seismic forces are counteracting, the action caused by gravity loads, QG, shall be obtained in accordance with Eq. (5.16): QG ¼ 0:9QD

(5.16)

5.5.5.2 Force-Controlled According to Code 360, force-controlled actions for the LSP denoted as QUF shall be calculated using one of the following methods: (1) QUF shall be taken as the maximum action that can be developed in a component based on a limit-state analysis considering the expected strength of the components delivering force to the component under consideration, or the maximum action developed in the component as limited by the nonlinear response of the building. (2) Alternatively, QUF shall be calculated in accordance with Eq. (5.17). QUF ¼ QG 

QE C1 C2 J

(5.17)

where: QUF ¼ force-controlled action caused by gravity loads in combination with earthquake forces; and J ¼ force-delivery reduction factor, greater than or equal to 1.0, taken as the smallest DCR of the components in the load path delivering force to the component in question. Alternatively, values of J equal to 2.0 for a high level of seismicity, 1.5 for a moderate level of seismicity, and 1.0 for a low level of seismicity shall be permitted where not based on calculated DCRs. In any case where the forces contributing to QUF are delivered by components of the seismic-force-resisting system that remain elastic, J shall be taken as 1.0.

298

Advanced Design Examples of Seismic Retrofit of Structures

TABLE 5.7 Load Combinations Deformation-Controlled

Force-Controlled

Combo1 : DL + LL + EPX

Combo17 : DL + LL + 0.29EPX

Combo2 : DL + LL  EPX

Combo18 : DL + LL  0.29EPX

Combo3 : DL + LL + EPY

Combo19 : DL + LL + 0.29EPY

Combo4 : DL + LL  EPY

Combo20 : DL + LL  0.29EPY

Combo5 : DL + LL + ENX

Combo21 : DL + LL + 0.29ENX

Combo6 : DL + LL  ENX

Combo22 : DL + LL  0.29ENX

Combo7 : DL + LL + ENY

Combo23 : DL + LL + 0.29ENY

Combo8 : DL + LL  ENY

Combo24 : DL + LL  0.29ENY

Combo9 : 0.9DL + EPX

Combo25 : 0.9DL + 0.29EPX

Combo10 : 0.9DL  EPX

Combo26 : 0.9DL  0.29EPX

Combo11 : 0.9DL + EPY

Combo27 : 0.9DL + 0.29EPY

Combo12 : 0.9DL  EPY

Combo28 : 0.9DL  0.29EPY

Combo13 : 0.9DL + ENX

Combo29 : 0.9DL + 0.29ENX

Combo14 : 0.9DL  ENX

Combo30 : 0.9DL  0.29ENX

Combo15 : 0.9DL + ENY

Combo31 : 0.9DL + 0.29ENY

Combo16 : 0.9DL  ENY

Combo32 : 0.9DL  0.29ENY

5.5.5.3 Load Combinations The load combinations for deformation-controlled and force-controlled actions are listed in Table 5.7.

5.5.6 Overturning Effects The overturning effects shall be resisted through the stabilizing effect of dead loads acting alone or in combination with positive connections of structural components to components below the level under consideration. Where dead loads alone are used to resist the effects of overturning, Eq. (5.18) shall be satisfied: MST >

MOT C1 C2 J

(5.18)

Example of a Steel Frame Building Retrofitted Chapter

5

299

where: MOT ¼ total overturning moment induced on the element by seismic forces applied at and above the level under consideration; MST ¼ stabilizing moment produced by dead loads acting on the element; C1 and C2 ¼ coefficients defined in Section 5.6.1; and J ¼ a coefficient defined in Section 5.5.5.2. Alternatively, the load combination represented by Eq. (5.19) shall be permitted for evaluating the adequacy of dead load alone to resist the effects of overturning. 0:9MST >

MOT C1 C2 μOT

(5.19)

where: μOT ¼ 10.0 for collapse prevention (CP); ¼8.0 for life safety (LS); and ¼4.0 for immediate occupancy (IO). For the main building:   V2y ¼ 313:74ðTonÞ V2X ¼ 342:55ðTonÞ , V1y ¼ 1224:82ðTonÞ V1X ¼ 1549:68ðTonÞ MSTX ¼ ð131:97
15:65Þ + ð660:13
19:275Þ ¼ 14789:33ðT  mÞ MSTY ¼ ð131:97
7:55Þ + ð660:13
7:55Þ ¼ 5980:35ðT  mÞ MOTX ¼ ð342:55
7:1Þ + ð1549:68
3:75Þ ¼ 8243:4ðT  mÞ MOTY ¼ ð313:74
7:1Þ + ð1224:82
3:75Þ ¼ 6820:62ðT  mÞ MSTX >

MOTX 8243:4 ) 14789:33 > ¼ 2453:4ðT  mÞ C1 C2 J 1:4
1:2
2

MSTY >

MOTY 6820:62 ) 5980:35 > ¼ 2029:94ðT  mÞ C1 C2 J 1:4
1:2
2

MOTX 8243:4 ) 0:9
14789:33 ¼ 13310:4 > C1 C2 ROT 1:4
1:2
8 ¼ 613:34ðT  mÞ

0:9MSTX >

MOTY 6820:62 ) 0:9
5980:35 ¼ 5382:31 > C1 C2 ROT 1:4
1:2
8 ¼ 507:48ðT  mÞ

0:9MSTY >

For the sports building: Vx ¼ Vy ¼ 251:31ðTonÞ MSTX ¼ 177:6
5 ¼ 888ðT  mÞ MSTY ¼ 177:6
8 ¼ 1420:8ðT  mÞ MOTX ¼ MOTY ¼ 251:31
5:55 ¼ 1394:77ðT  mÞ

300

Advanced Design Examples of Seismic Retrofit of Structures

MSTX > MSTY > 0:9MSTX >

MOTX 1394:77 ) 888 > ¼ 406:4ðT  mÞ C1 C2 J 1:43
1:2
2

MOTY 1394:77 ) 1420:8 > ¼ 406:4ðT  mÞ C1 C2 J 1:43
1:2
2

MOTX 1394:77 ) 0:9
888 ¼ 799:2 > ¼ 101:65ðT  mÞ C1 C2 ROT 1:43
1:2
8 MOTY 1394:77 ) 0:9
1420:8 ¼ 1278:72 > C1 C2 ROT 1:43
1:2
8 ¼ 101:65ðT  mÞ

0:9MSTY >

As can be seen, dead loads can adequately resist the effects of overturning in both buildings.

5.5.7 Modeling Assumptions In this example, the analysis method is the linear and nonlinear static procedure. The nonlinear behavior of structural members is concentrated in plastic hinges at most suitable locations. The characteristics of the plastic hinges follow the dominant behavior of each structural member. In the main building, because the only structural members to carry the lateral loads are infill walls, the axial force plastic hinges (P) are defined in these members. No plastic hinges are defined in columns and beams. The columns are modeled as force-controlled members. The beams are checked against gravity loads. The plastic hinge characteristic of a typical infill wall in the main building is illustrated in Fig. 5.4. For the sports building, the axial force plastic hinges (P) are assigned to the braces and the truss members of the girders at the mid-length of these members. The axial force-flexural moment interaction plastic hinge (PMM) is considered for the columns with (PUF/PCL)  0.5 and for the upper and lower ridge in the truss girders. These hinges are defined at 15% and 85% of the length of columns and at both ends of the upper and lower ridges in the truss girders in the sports building. The column hinges in the main building are defined at 10% and 90% of the length of columns. Plastic hinge characteristics of the braces, columns, and girders ridge are shown in Figs. 5.5–5.8. A view of the numerical models of the main and sports buildings is shown in Fig. 5.9.

5.6 CAPACITY FORCES CALCULATIONS Where evaluating the behavior of deformation-controlled actions, the expected strength, QCE, shall be used. QCE is the expected strength of a deformation controlled action of an element at the deformation level under consideration and is defined as the mean value of resistance of a component at the deformation level anticipated for a population of similar components, including consideration of the variability in material strength and strain hardening and plastic section development [7].

Example of a Steel Frame Building Retrofitted Chapter

FIG. 5.4 Plastic hinge characteristic of a typical infill wall in the main building.

FIG. 5.5 Plastic hinge characteristic of columns in the sports building.

5

301

302

Advanced Design Examples of Seismic Retrofit of Structures

FIG. 5.6 Plastic hinge characteristic of braces in the sports building.

FIG. 5.7 Plastic hinge characteristic of girders ridge in the sports building (0:15 



PUF PCL



 0:5).

Example of a Steel Frame Building Retrofitted Chapter

FIG. 5.8 Plastic hinge characteristic of girders ridge in the sports building (



PUF PCL



5

303

 0:15).

Where evaluating the behavior of force-controlled actions, a lower-bound estimate of the component strength, QCL, shall be used. QCL is the lower-bound estimate of the strength of a force-controlled action of an element at the deformation level under consideration and is defined as the mean minus one standard deviation of the yield strengths, Qy, for a population of similar components [2].

5.6.1 Linear Static Procedure 5.6.1.1 Beams The strength of structural steel elements under flexural actions shall be calculated in accordance with this section if the calculated axial load does not exceed 10% of the axial strength. For bare beams bent about their major axes and symmetric about both axes, satisfying the requirements of compact sections, Lb < Lp, QCE shall be computed in accordance with Eq. (5.20): QCE ¼ MCE ¼ MPCE ¼ Z:Fye

(5.20)

304

Advanced Design Examples of Seismic Retrofit of Structures

FIG. 5.9 A view of the models. (A) Main building. (B) Sports building.

where: Lb ¼ distance between points braced against lateral displacement of the compression flange, or between points braced to prevent twist of the cross section, per AISC 360 [8]; Lp ¼ limiting lateral unbraced length for full plastic bending capacity for uniform bending from AISC 360; MpCE ¼ expected plastic moment capacity; and Fye ¼ expected yield strength of the material. Based on the Iranian National Building Code; Part 10: Steel Building [6], the flexural members are considered braced if the free distance of the compression flange is smaller than the minimum of the results of Eqs. (5.21) and (5.22).

Example of a Steel Frame Building Retrofitted Chapter

5

305

635  bf LC ¼ pffiffiffiffiffi Fy

(5.21)

14
105  LC ¼  d=Af  Fy

(5.22)

where: bf ¼ width of the compression flange; Af ¼ area of the compression flange; and d ¼ height of the flexural member; As an example and for IPE 140 we have: 635:bf 635
7:3 LC ¼ pffiffiffiffiffi ¼ pffiffiffiffiffiffiffiffiffiffi ¼ 95:43ðcmÞ Fy 2360 14
105 14
105  LC ¼  ¼ 347:45ðcmÞ ¼ d=Af  Fy ð14=8:2Þ
2360 ) LC ¼ min ð95:43, 347:45Þ ¼ 95:43ðcmÞ All the beams that carry gravity loads are braced, because the distance of the joists in the diaphragms is smaller than Lc. For the beams that do not carry gravity loads, and where the conditions of braced section are not satisfied, the expected flexural capacity of the section, QCE, shall be computed in accordance with Eq. (5.23): QCE ¼ MCE ¼ 1:1Fye S

(5.23)

where S ¼ the elastic section modulus of a member. The expected flexural capacity of the beams is presented in Table 5.8. If the beam strength is governed by the shear strength of the unstiffened web 418 ffiffiffiffi, then VCE shall be calculated in accordance with Eq. (5.24): and thw  p Fy

TABLE 5.8 Expected Flexural Capacity of Beams MCE (ton m) 3

3

2

Profile

Z (cm )

S (cm )

Fye (kg/cm )

Braced

Unbraced

2INP240

829

708

2360

19.56

18.38

INP240

411

354

2360

9.70

9.19

2IPE140

172

154.6

2360

4.04

4.01

IPE140

88

77.3

2360

2.07

2.01

IPE180

166

146

2360

3.91

3.79

IPE240

366

324

2360

8.63

8.41

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Advanced Design Examples of Seismic Retrofit of Structures

TABLE 5.9 Expected Shear Capacity of Beams Profile

Fye (kg/cm2)

Aw (cm2)

VCE (ton)

2INP240

2360

33.4

47.3

INP240

2360

16.7

23.64

2IPE140

2360

10.52

14.9

IPE140

2360

5.26

7.44

IPE180

2360

7.73

10.94

IPE240

2360

11.78

16.68

QCE ¼ VCE ¼ 0:6:FyE :Aw

(5.24)

where: Aw ¼ nominal area of the web; tw ¼ web thickness; and h ¼ distance from inside of compression flange to inside of tension flange. The expected shear capacity of beams is presented in Table 5.9.

5.6.1.2 Columns The lower-bound strength, QCL, of steel columns under axial compression shall be the lowest value obtained for the limit states of column buckling, local flange buckling, or local web buckling. This lower-bound strength is determined based on Eq. (5.25). QCL ¼ PCL ¼ 1:7
Fa
A

(5.25)

where Fa ¼ allowable axial compressive stress which is based on Eq. (5.26), in which FyLB is replaced by Fy. "   # 1 1 λ 2 1 Fa ¼  Fy F:S 2 CC    3 λ λ  0:125 F  S ¼ 1:67 + 0:375 C C C C (5.26) sffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2π 2  E 2
π 2
2:1
106 ¼ 131:94 CC ¼ ¼ 2275 Fy KL λ¼ r

Example of a Steel Frame Building Retrofitted Chapter

5

307

TABLE 5.10 Lower-Bound Axial Capacity of Columns Profile

r (cm)

A (cm2)

λ

F.S.

Fa (kg/cm2)

QCL (ton)

2IPE140 (Story-1)

5.74

32.8

65.33

1.84

1093.82

61.0

2IPE140 (Story-2)

5.74

32.8

58.36

1.82

1133.04

63.2

2IPE160 (Story-1)

6.57

40.2

57.07

1.81

1144.44

78.2

2IPE160 (Story-2)

6.57

40.2

50.98

1.80

1173.65

80.2

2IPE160 +2PL (Story-1)

6.57

100.2

57.07

1.81

1144.44

194.9

Q Qy

b a

1.0

B

A

C D

E

c q or D

FIG. 5.10 Generalized force-deformation relation for steel elements or components [3].

where: L ¼ laterally unbraced length of the member; r ¼ governing radius of gyration; and K ¼ effective length factor. The lower-bound axial capacity of columns is presented in Table 5.10.

5.6.2 Nonlinear Static Procedure The complete load-deformation relationship of each component as depicted in Fig. 5.10 shall be determined based on plastification by nonlinear momentcurvature and interaction relationships for beams and beam-columns derived from experiment or analysis. The values for expected strength, QCE, shall be the same as those used for linear procedures as specified in Section 5.7.1.

308

Advanced Design Examples of Seismic Retrofit of Structures

5.7 ACCEPTANCE CRITERIA Based on ASCE41-13 [3], for the linear and nonlinear procedure which has been implemented in this example, component actions shall be compared with capacities.

5.7.1 Linear Static Procedure 5.7.1.1 Deformation-Controlled Actions Acceptance criteria for deformation-controlled actions in components shall satisfy Eq. (5.27). mκQCE > QUD

(5.27)

where: m ¼ component capacity modification factor to account for expected ductility associated with this action at the selected structural performance level. The m-factors for use with corresponding expected strength shall be obtained from Table 5.11; QCE ¼ expected strength of component deformation-controlled action of an element at the deformation level under consideration which is determined according to Section 5.7; and κ ¼ knowledge factor defined in according to Table 2.12 which is assumed to be 1.0 because the usual level of knowledge exists about the example buildings, including material properties, as-built sketches, etc. Beams The acceptance criteria of this section shall apply to flexural actions of structural steel elements that have a calculated axial load that does not exceed 10% of the axial strength. Beam flexure and shear shall be considered deformation controlled. Values for the m-factor used in Eq. (5.27) shall be as specified in Table 5.11. Columns Based on ASCE 41 [3], for steel columns under combined axial compression and bending stress, where the axial column load is less than 50% of the lower-bound axial column strength, PCL, the column shall be considered deformation controlled for flexural behavior and force controlled for compressive behavior, and the combined strength shall be evaluated by Eq. (5.28) or Eq. (5.29).  0:5 For 0:2  PPUF CL  My PUF 8 Mx  1:0 (5.28) + + PCL 9 mx MCEx my MCEy

Example of a Steel Frame Building Retrofitted Chapter

5

309

TABLE 5.11 Acceptance Criteria for Linear Procedures-Structural Steel Components [3] m-Factors for Linear ProceduresW Primary

Component/Action

Secondary

IO

LS

CP

LS

CP

2

6

8

10

12

1.25

2

3

3

4

Beams—flexure a:

bf 2tf

 p52ffiffiffiffiffi and

h tw

Fye

b: 2tbff  p65ffiffiffiffiffi or Fye

h tw

418 ffiffiffiffiffi p Fye

640 ffiffiffiffiffi p Fye

c: Other

Linear interpolation between the values on lines a and b for both flange slenderness (first term) and web slenderness (second term) shall be performed, and the lowest resulting value shall be used.

Columns—flexurea,b For P/PCL < 0.2 a:

bf 2tf

 p52ffiffiffiffiffi and

h tw

300 ffiffiffiffiffi p

2

6

8

10

12

 p65ffiffiffiffiffi or

h tw

460 ffiffiffiffiffi p

1.25

1.25

2

2

3

Fye

bf 2tf

b.

Fye

Fye

Fye

c: Other

Linear interpolation between the values on lines a and b for both flange slenderness (first term) and web slenderness (second term) shall be performed, and the lowest resulting value shall be used.

For 0.2  P/PCL  0.5 a:

bf 2tf

 p52ffiffiffiffiffi and

h tw

Fye

b: 2tbff  p65ffiffiffiffiffi or Fye

h tw

c: Other

260 ffiffiffiffiffi p Fye

400 ffiffiffiffiffi p Fye

1.25

–c

–d

–e

–f

1.25

1.25

1.5

2

2

Linear interpolation between the values on lines a and b for both flange slenderness (first term) and web slenderness (second term) shall be performed, and the lowest resulting value shall be used.

a Columns in moment or braced frames shall be permitted to be designed for the maximum force delivered by connecting members. For rectangular or square columns, replace bt/2tf with b/t, replace 52 with 110, and replace 65 with 190. b Columns with P/PCL > 0.5 shall be considered force controlled. c m ¼ 9(1  5/3 P/PCL) in the plane of bending. d m ¼ 12(1  5/3 P/PCL) in the plane of bending. e m ¼ 15(1  5/3 P/PCL) in the plane of bending. f m ¼ 18(1  5/3 P/PCL) in the plane of bending.

For PPUF < 0:2 CL My PUF Mx + +  1:0 2PCL mx MCEx my MCEy

(5.29)

310

Advanced Design Examples of Seismic Retrofit of Structures

where: PUF ¼ axial force in the member computed in accordance with Section 5.5.5.2; PCL ¼ lower-bound compression strength of the column; Mx ¼ bending moment in the member for the x-axis computed in accordance with Section 5.5.5.2; My ¼ bending moment in the member for the y-axis computed in accordance with Section 5.5.5.2; MCEx ¼ expected bending strength of the column for the x-axis; MCEy ¼ expected bending strength of the column for the y-axis; mx ¼ value of m for the column bending about the x-axis in accordance with Table 5.11; and my ¼ value of m for the column bending about the y-axis in accordance with Table 5.11.

5.7.1.2 Force-Controlled Actions Acceptance criteria for force-controlled actions in components shall satisfy Eq. (5.30): κQCL > QUF

(5.30)

where QCL ¼ lower-bound strength of a force-controlled action of an element at the deformation level under consideration, which is determined according to Section 5.7. Columns Steel columns with axial compressive forces exceeding 50% of the lower-bound axial compressive strength, PCL, shall be considered force controlled for both axial loads and flexure, and shall be evaluated using Eq. (5.31). PUF MUFx MUFy + +  1:0 PCL MCLx MCLy

(5.31)

where: MUFx ¼ bending moment in the member about the x-axis, calculated in accordance with Section 5.5.5.2; MUFy ¼ bending moment in the member about the y-axis, calculated in accordance with Section 5.5.5.2; MCLx ¼ lower-bound flexural strength of the member about the x-axis; and MCLy ¼ lower-bound flexural strength of the member about the y-axis.

5.7.2 Nonlinear Static Procedure 5.7.2.1 Deformation-Controlled Actions Primary and secondary components shall have expected deformation capacities not less than maximum deformation demands calculated at target

Example of a Steel Frame Building Retrofitted Chapter

5

311

displacements. Primary and secondary component demands shall be within the acceptance criteria for nonlinear components at the selected structural performance level. Modeling parameters and acceptance criteria for nonlinear procedures—structural steel components are illustrated in Table 5.12.

Beams Flexural actions of beams shall be considered deformation controlled. Permissible plastic rotation deformation shall be as indicated in Table 5.12. Columns Flexural loading of columns, with axial loads at the target displacement less than 50% of PCL shall be considered deformation controlled, and maximum permissible plastic rotation demands on columns, in radians, shall be as indicated in Table 5.12, dependent on the axial load present and the compactness of the section. As an example, the plastic hinge characteristics of the columns and braces of the sports building are presented in Tables 5.13 and 5.14, respectively.

5.7.2.2 Force-Controlled Actions Primary and secondary components shall have lower-bound strengths not less than the maximum analysis forces. Lower-bound strengths shall be determined considering all coexisting forces and deformations. Columns Axial compressive loading of columns shall be considered force controlled. Flexural loading of columns, with axial loads at the target displacement greater than or equal to 50% of PCL, shall be considered force controlled and shall conform to Eq. (5.31).

5.8 RESULTS 5.8.1 Beams With Cradle-Type Connections The results of a typical beam with cradle-type connection are shown in Fig. 5.11. Based on these results for all the beams with cradle-type connection presented in Table 5.15, the vulnerability of the beams is determined. The loading and hand calculations of the beams in cradle-type connections is as follows.

TABLE 5.12 Modeling Parameters and Acceptance Criteria for Nonlinear Procedures-Structural Steel Components [3]

Acceptance Criteria

Plastic Rotation Angle, Radians

Residual Strength Ratio

a

b

c

IO

LS

CP

9θy

11θy

0.6

1θy

9θy

11θy

4θy

6θy

0.2

0.25θy

3θy

4θy

Plastic Rotation Angle, Radians

Beams—flexure a:

bf 2tf

 p52ffiffiffiffiffi and

b:

bf 2tf

 p65ffiffiffiffiffi or

h tw

Fye

Fye

h tw

418 ffiffiffiffiffi p Fye

640 ffiffiffiffiffi p Fye

c: Other

Linear interpolation between the values on lines a and b for both flange slenderness (first term) and web slenderness (second term) shall be performed, and the lower resulting value shall be used.

Columns—flexurea,b For P/PCL < 0.2 a:

bf 2tf

 p52ffiffiffiffiffi and

b:

bf 2tf

 p65ffiffiffiffiffi or

h tw

Fye

Fye

h tw

300 ffiffiffiffiffi p Fye

460 ffiffiffiffiffi p Fye

c: Other

9θy

11θy

0.6

1θy

9θy

11θy

4θy

6θy

0.2

0.25θy

3θy

4θy

Linear interpolation between the values on lines a and b for both flange slenderness (first term) and web slenderness (second term) shall be performed, and the lower resulting value shall be used.

For 0.2  P/PCL  0.5 a:

bf 2tf

 p52ffiffiffiffiffi and

b:

bf 2tf

 p65ffiffiffiffiffi or

h tw

Fye

c: Other

Fye

h tw

260 ffiffiffiffiffi p Fye

400 ffiffiffiffiffi p Fye

–c

–d

0.2

0.25θy

–e

–d

1θy

1.5θy

0.2

0.25θy

1.2θy

1.2θy

Linear interpolation between the values on lines a and b for both flange slenderness (first term) and web slenderness (second term) shall be performed, and the lowest resulting value shall be used.

a Columns in moment or braced frames shall be permitted to be designed for the maximum force delivered by connecting members. For rectangular or square columns, replace bt/2tf with b/t, replace 52 with 110, and replace 65 with 190. b Columns with P/PCL > 0.5 shall be considered force controlled. c Plastic rotation ¼ 11(1  5/3 P/PCL)θy in the plane of bending. d Plastic rotation ¼ 17(1  5/3 P/PCL)θy in the plane of bending. e Plastic rotation ¼ 14(1  5/3 P/PCL)θy in the plane of bending.

Advanced Design Examples of Seismic Retrofit of Structures

Component or Action

312

Modeling Parameters

Column

PUF (ton)

PCL (ton)

a

b

c

IO

LS

CP

C3

0.408

68

9.90

14.85

0.2

0.25

6.93

9.90

C4

0.358

68

9.91

14.87

0.2

0.25

6.94

9.91

C6

0.389

68

9.90

14.85

0.2

0.25

6.93

9.90

C7

0.435

68

9.89

14.84

0.2

0.25

6.92

9.89

C8

0.349

68

9.91

14.87

0.2

0.25

6.94

9.91

C9

0.361

68

9.91

14.86

0.2

0.25

6.94

9.91

C11

0.358

68

9.91

14.87

0.2

0.25

6.94

9.91

C13

0.277

68

9.93

14.90

0.2

0.25

6.95

9.93

Example of a Steel Frame Building Retrofitted Chapter

TABLE 5.13 Plastic Hinges in the Columns of the Sports Building 0.2 ≤ (PUF/PCL) ≤ 0.5 (Refer to Fig. 5.10)

5

313

314

Advanced Design Examples of Seismic Retrofit of Structures

TABLE 5.14 Plastic Hinges in the Braces of the Sports Building (Refer to Fig. 5.10) Brace

a

b

c

IO

LS

CP

Compressive brace

0.5

8

0.2

0.25

3

4

Tensile brace

11

14

0.8

0.25

7

9

DL= 3944 (kg) LL= 1277.5 (kg)

DL= 2139 (kg) LL= 1825 (kg)

DL= 3967 (kg) LL= 1277.5 (kg)

6.0 (m)

3.0 (m)

6.10 (m)

MCE ¼ Z:Fye ¼ 8:3
104
23600 ¼ 19:58ton  m  Mdemand ¼ 13:24ton  m VCE ¼ 1:5Fv AW ¼ 1:5
0:4
23600
ð2
0:87
19:2Þ
104 ¼ 47:3ton  Vdemand ¼ 14:47ton It is concluded that all the beams having cradle-type connections satisfy the requirements of acceptance criteria and are not vulnerable.

5.8.2 Columns The results of the controls of the columns in the main and sports buildings are presented in Tables 5.16 and 5.17, respectively. As can be seen, there are few columns that do not pass the acceptance criteria for the columns and are hence classified as vulnerable.

5.8.3 Infill Walls Control of the infill walls in the main building is made in Table 5.18. Based on this table, there are several vulnerable infill walls. Examples of the plastic hinges formation in the main building are shown in Figs. 5.12 and 5.13. The results of the nonlinear static analysis are presented in Table 5.19.

5.8.4 Upper and Lower Truss Ridges Control of the upper and lower truss ridges in the sports building is shown in Table 5.20.

B

A

C

D

E

F

G

H

K

2IPE140

2IPE140

2IPE140

2IPE140

2IPE140

2IPE140

(A) FIG. 5.11 The results of a typical beam with cradle-type connection. (A) Location in plan.

INP240

INP240

IPE160 IPE160 IPE160

INP240

X

INP240

586.

INP240

2IPE140

586.

IPE140

2INP240

586. INP240

586.

2INP240

INP240 INP240

2INP240

2INP240

2INP240

INP240

680.

586.

IPE140

2INP240

586.

2INP240

2IPE140

586.

INP240

586.

2INP240

2IPE140

586.

IPE140

2IPE140

2INP240

586.

2INP240

2IPE140

586.

680.

2IPE140

2IPE140

2INP240

586.

586.

680.

2IPE140

2IPE140

2INP240

2IPE140

2INP240

586.

680.

2IPE140

2IPE140

2INP240

INP240

586. Y

2INP240

2IPE140

2

2IPE140

2INP240

INP240

586.

2INP240

2INP240

INP240

2IPE140

586.

2IPE140

586.

IPE160

Example of a Steel Frame Building Retrofitted Chapter

586.

3

1

2IPE140

2IPE140

5

7

J

IPE160

6

4

I

5

315

316 Advanced Design Examples of Seismic Retrofit of Structures

FIG. 5.11—CONT’D (B) Shear forces and bending moments.

TABLE 5.15 Control of the Cradle-Type Connections e (cm)

M 5 Ve (kg cm)

S (cm )

B1

8215.98

6.8

55,868.66

67.8

824.02

1770

OK

B2

54.1

6.8

367.88

67.8

5.43

1770

OK

B3

8081.07

6.8

54,951.28

67.8

810.49

1770

OK

B19

221.69

6.8

1507.492

67.8

22.23

1770

OK

B20

108.84

6.8

740.112

67.8

10.92

1770

OK

B33

218.05

6.8

1482.74

67.8

21.87

1770

OK

B34

5692.91

6.8

38,711.79

67.8

570.97

1770

OK

B35

108.84

6.8

740.112

67.8

10.92

1770

OK

B36

5787.95

6.8

39,358.06

67.8

580.50

1770

OK

B37

4596.74

6.8

31,257.83

67.8

461.03

1770

OK

B38

108.84

6.8

740.112

67.8

10.92

1770

OK

B39

221.69

6.8

1507.492

67.8

22.23

1770

OK

B40

5787.95

6.8

39,358.06

67.8

580.50

1770

OK

B41

108.84

6.8

740.112

67.8

10.92

1770

OK

B42

4596.74

6.8

31,257.83

67.8

461.03

1770

OK

B43

218.05

6.8

1482.74

67.8

21.87

1770

OK Continued

317

V2 (kg)

5

Result

Beam

Example of a Steel Frame Building Retrofitted Chapter

Fb (kg/cm2) 50.75Fy

Fa 5 (M/S) (kg/cm2)

3

318

Fb (kg/cm2) 50.75Fy

Result

Beam

V2 (kg)

e (cm)

M 5 Ve (kg cm)

S (cm )

Fa 5 (M/S) (kg/cm2)

B44

108.84

6.8

740.112

67.8

10.92

1770

OK

B45

221.69

6.8

1507.492

67.8

22.23

1770

OK

B48

93.24

6.8

634.032

67.8

9.35

1770

OK

B49

4487.07

6.8

30,512.08

67.8

450.03

1770

OK

B50

4045.3

6.8

27,508.04

67.8

405.72

1770

OK

B52

5983.84

6.8

40,690.11

67.8

600.15

1770

OK

B53

212.52

6.8

1445.136

67.8

21.31

1770

OK

B54

7911.8

6.8

53,800.24

67.8

793.51

1770

OK

3

Advanced Design Examples of Seismic Retrofit of Structures

TABLE 5.15 Control of the Cradle-Type Connections—cont’d

TABLE 5.16 Control of the Cradle-Type Connections in the Main Building

PUF (ton)

PCL (ton)

DCR

Column

PUF (ton)

PCL (ton)

DCR

C1-1

51.4

61

0.843

C43(ST.1)

12.31

78.21

0.157

C3-1

17.04

61

0.279

C43(ST.2)

0.21

80.2

0.003

C4(ST.1)

22.11

78.21

0.283

C45(ST.1)

34.72

78.21

0.444

C4(ST.2)

4.53

80.2

0.056

C45(ST.2)

4.88

80.2

0.061

C5-1

67.2

61

1.102

C47(ST.1)

17.11

78.21

0.219

C7-1

10.27

61

0.168

C47(ST.2)

0.21

80.2

0.003

C8(ST.1)

124.5

78.21

1.592

C49(ST.1)

37.12

78.21

0.475

C8(ST.2)

10

80.2

0.125

C49(ST.2)

4.14

80.2

0.052

C11

5.25

78.21

0.067

C51(ST.1)

11.76

78.21

0.150

C12

6.35

78.21

0.081

C51(ST.2)

0.21

80.2

0.003

C14(ST.1)

18.6

78.21

0.238

C53(ST.1)

33.5

61

0.549

C14(ST.2)

1.48

80.2

0.018

C53(ST.2)

7.86

63.17

0.124

C17(ST.1)

53.6

78.21

0.685

C55(ST.1)

333.88

78.21

4.269

C17(ST.2)

8.61

80.2

0.107

C55(ST.2)

22.36

80.2

0.279

C18(ST.1)

25.32

78.21

0.324

C57(ST.1)

48.85

78.21

0.625

C18(ST.2)

10.45

80.2

0.130

C57(ST.2)

5.53

80.2

0.069

Example of a Steel Frame Building Retrofitted Chapter

C21(ST.1)

82.35

78.21

1.053

C59(ST.1)

333.76

78.21

4.267

5

C21(ST.2)

9.08

80.2

0.113

C59(ST.2)

20.15

80.2

0.251

C23(ST.1)

113.51

78.21

1.451

C61(ST.1)

62.61

78.21

0.801 Continued

319

Column

TABLE 5.16 Control of the Cradle-Type Connections in the Main Building—cont’d 320

PUF (ton)

PCL (ton)

DCR

Column

PUF (ton)

PCL (ton)

DCR

C23(ST.2)

7.31

194.94

0.037

C61(ST.2)

5.51

80.2

0.069

C24(ST.1)

53.6

78.21

0.685

C63(ST.1)

66.06

78.21

0.845

C24(ST.2)

8.61

80.2

0.107

C63(ST.2)

43.17

80.2

0.538

C26(ST.1)

148.28

78.21

1.896

C65(ST.1)

297.71

61

4.880

C26(ST.2)

28.14

194.94

0.144

C65(ST.2)

4.93

63.17

0.078

C28(ST.1)

21.16

78.21

0.271

C67(ST.1)

43.3

78.21

0.554

C28(ST.2)

3.8

80.2

0.047

C67(ST.2)

1.8

80.2

0.022

C30(ST.1)

16.78

78.21

0.215

C69(ST.1)

335.55

78.21

4.290

C30(ST.2)

1.91

80.2

0.024

C69(ST.2)

22.88

80.2

0.285

C31

1.44

36.43

0.040

C71(ST.1)

44.86

78.21

0.574

C35(ST.1)

17.4

78.21

0.222

C71(ST.2)

2.9

80.2

0.036

C35(ST.2)

1.95

80.2

0.024

C73(ST.1)

331

78.21

4.232

C37(ST.1)

124.51

78.21

1.592

C73(ST.2)

26.12

80.2

0.326

C37(ST.2)

26.11

80.2

0.326

C75(ST.1)

57.25

78.21

0.732

C39(ST.1)

17.53

78.21

0.224

C75(ST.2)

2.9

80.2

0.036

C39(ST.2)

1.95

80.2

0.024

C77(ST.1)

173

61

2.836

C41(ST.1)

173.4

61

2.843

C77(ST.2)

36.1

63.17

0.571

C41(ST.2)

23.97

63.17

0.379

Advanced Design Examples of Seismic Retrofit of Structures

Column

Example of a Steel Frame Building Retrofitted Chapter

5

321

TABLE 5.17 Control of the Cradle-Type Connections in the Sports Building Column

PUF (ton)

PCL (ton)

DCR

Column

PUF (ton)

PCL (ton)

DCR

C2

41.51

68

0.610

C8

23.7

68

0.349

C3

27.73

68

0.408

C9

24.57

68

0.361

C4

24.34

68

0.358

C10

42.48

68

0.625

C5

95.05

68

1.398

C11

24.34

68

0.358

C6

26.44

68

0.389

C12

104.87

68

1.542

C7

29.58

68

0.435

C13

18.83

68

0.277

TABLE 5.18 Control of the Infill Walls in the Main Building Infill Wall

QUD (ton)

m

QCE (ton)

mκQCE (ton)

mκQCE ≥QUD

D9

398.94

7.321

11.9

87.12

Not OK

D14

23.5

7.321

11.9

87.12

OK

D20

28.04

6.988

14.35

100.27

OK

D23

406.06

7.321

11.9

87.12

Not OK

D24

404.86

7.321

11.9

87.12

Not OK

D25

81.06

4.54

33.6

152.54

OK

D26

267

4.863

33.6

163.4

Not OK

D27

161.61

6.52

21

136.92

Not OK

D28

133.33

6.52

21

136.92

OK

D29

161.67

6.48

33.6

217.72

OK

D30

134.03

7.543

16.52

124.61

Not OK

D33

84.71

7.57

11.9

90.083

OK

D38

34.11

6.056

21

127.17

OK

D40

7.97

6.056

21

127.17

OK

322

B

(A)

IO

Z

LS

X

CP

C

D

E

(B)

FIG. 5.12 Plastic hinges formation in the infill walls in the main building under PY1. (A) Contour. (B) Force-displacement diagram.

Advanced Design Examples of Seismic Retrofit of Structures

Y

X

B

(A)

IO

LS

CP

C

D

Y

E

(B)

FIG. 5.13 Plastic hinges formation in the infill walls in the main building under PX2. (A) Contour. (B) Force-displacement diagram.

Example of a Steel Frame Building Retrofitted Chapter

Z

5

323

324

Advanced Design Examples of Seismic Retrofit of Structures

TABLE 5.19 Initial Stiffness, Base Shear Corresponding to the Target Displacement, and Yield Strength of the Main Building Load Pattern

Ki (ton/cm)

Ke (ton/cm)

Vt (ton)

Vy (ton)

Vt > 0.8Vy

Te (s)

PX1

161.4

126.8

109.8

67.2

OK

0.55

PY1

80

74.82

282.86

252.9

OK

0.43

PX2

140.35

89.3

121.44

70.1

OK

0.61

PY2

79.02

76.98

288.46

249.44

OK

0.427

PX3

169.63

140.83

110.87

67.6

OK

0.53

PY3

108.1

101.16

279.02

243.8

OK

0.43

PX4

155.86

118.27

122.41

68.6

OK

0.56

PY4

106.74

99.51

285.2

244.8

OK

0.43

TABLE 5.20 Control of the Upper and Lower Truss Ridges in the Sports Building Truss

Fa (kg/cm2)

PCL (ton)

PUF (ton)

DCR

B1

377.98

24.67

7.85

0.32

B2

377.98

24.67

7.08

0.29

B3

377.98

24.67

21.62

0.88

B4

377.98

24.67

12.96

0.53

B5

575.02

53.76

3.32

0.06

B6

575.02

53.76

17.70

0.33

B7

575.02

53.76

3.62

0.07

B8

575.02

53.76

17.67

0.33

B9

575.02

53.76

3.32

0.06

B10

575.02

53.76

17.70

0.33

B11

377.98

24.67

7.85

0.32

B12

377.98

24.67

7.08

0.29

B13

377.98

24.67

21.62

0.88

B14

377.98

24.67

12.96

0.53

Example of a Steel Frame Building Retrofitted Chapter

5

325

5.8.5 Braces Brace actions are classified as deformation-controlled actions which are evaluated based on Eqs. (5.32) and (5.33) for braces in compression and tension, respectively. The results of the control of the braces in the sports building in the linear static method are presented in Table 5.21. Plastic hinges formation in the braces in the sports building under PX1 shown in Fig. 5.14. The results of the nonlinear analysis on the sports building is presented in Table 5.22. PCEðCÞ ¼ 1:7
0Fas
A B ðFas ¼ B:Fa Þ, B @B ¼ 

1

C C λ A 1+ 2Cc sffiffiffiffiffiffiffiffiffiffi 2π 2 E Cc ¼ Fy 1

(5.32)

PCEðT Þ ¼ A:Fye

(5.33)

where: PCE(C) ¼ expected strength of the brace in compression; PCE(T ) ¼ expected strength of the brace in tension; Fas ¼ allowable compressive stress in braces; and B ¼ coefficient for reduction in stress. We have 1:0
692 ¼ 284:77 2:43 6025 λ < pffiffiffiffiffiffiffi ! 284 > 124:04 Fye 1 ¼ 0:482 B¼ 284:77 1+ 265:2   105
105 kg ¼ 129:47 Fa ¼ cm2 ð284:77Þ2 λ¼



kg Fas ¼ Fa  B ¼ 129:47
0:482 ¼ 62:4 cm2



5.8.6 Foundation Based on ASCE 41 [3], prescriptive expected capacities shall be used where construction documents or previous geotechnical reports for the existing building are available and provide information on foundation soil design parameters.

326

Brace

QUD(C) (ton)

QUD(T ) (ton)

QCE(C) (ton)

QCE(T ) (ton)

mc

mt

mcκQCE(C)

mtκQCE(T )

DCR (T)

DCR (C)

D51

87.18

82.05

1.034

29.02

3

6

3.102

174.12

0.47

28.10

D52

91.58

84.42

1.034

29.02

3

6

3.102

174.12

0.48

29.52

D53

87.18

82.05

1.034

29.02

3

6

3.102

174.12

0.47

28.10

D54

91.58

84.42

1.034

29.02

3

6

3.102

174.12

0.48

29.52

Advanced Design Examples of Seismic Retrofit of Structures

TABLE 5.21 Control of the Braces in the Sports Building

3

4

5

X

1

2

Z

B

(A)

IO

LS

CP

C

D

E

(B)

FIG. 5.14 Plastic hinges formation in the braces in the sports building under PX1. (A) Contour. (B) Force-displacement diagram.

Example of a Steel Frame Building Retrofitted Chapter

Y

5

327

328

Advanced Design Examples of Seismic Retrofit of Structures

TABLE 5.22 Initial Stiffness, Base Shear Corresponding to the Target Displacement, and Yield Strength of the Sports Building Load Pattern

Ki (ton/cm)

Ke (ton/cm)

Vt (ton)

Vy (ton)

Vt > 0.8Vy

Te (s)

PX1

0.871

0.832

9.324

9.573

OK

2.36

PY1

1.98

1.98

9.91

9.91

OK

0.31

PX2

1.003

0.88

13.48

11.95

OK

2.46

PY2

2.34

2.34

11.62

11.62

OK

0.31

PX3

0.878

0.823

9.405

9.702

OK

2.38

PY3

2.0

2.0

9.98

9.98

OK

0.31

PX4

1.011

0.899

13.6

12.54

OK

2.45

PY4

2.36

2.36

11.72

11.72

OK

0.31

The prescriptive expected bearing capacity, qc, for a spread footing shall be calculated using Eq. (8.1): qc ¼ 3qallow

(5.34)

where qallow ¼ allowable bearing pressure specified in available documents for the gravity load design of shallow foundations (dead plus live loads). Based on geotechnical tests and field observations, the soil design parameters for the foundations of the two example buildings are derived and presented in Table 5.23. The geometrical characteristics of the foundation of the example buildings are presented in Fig. 5.15.

TABLE 5.23 Soil Design Parameters Based on Geotechnical Tests and Field Observations Pad Foundation

Strip Footing

Width (m)

qa (kg/cm2)

qallow 5 3 × 2 × qa

Width (m)

qa (kg/cm2)

qallow 5 3 × 2 × qa

1.0

1.682

10.092

0.8

1.467

8.802

1.7

1.797

10.782

1.6

1.633

9.798

2.2

1.88

11.28

Example of a Steel Frame Building Retrofitted Chapter

FIG. 5.15 Geometrical characteristics of the foundation of the example buildings. (A) The main building.

5

329

330 Advanced Design Examples of Seismic Retrofit of Structures

FIG. 5.15—CONT’D (B) The sports building.

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5

331

Based on ASCE 41, soil actions are considered as deformation-controlled actions which are determined according to Section 5.5.5.1. The results indicate the vulnerability of the foundation of the main building in terms of soil pressure and foundation uplift as the example contours of two load combinations shown in Figs. 5.16 and 5.17. Neither soil nor the foundation in the sports building show any form vulnerability (see Fig. 5.18 as an example). The required reinforcement for the foundation derived from modeling (Fig. 5.19) is also less than the existing reinforcement found in the field observations.

5.9 RETROFIT OPTIONS Based on the results of the evaluation of the building, apart from the fact that both buildings, at least in one direction, lack any lateral load-bearing element, different structural elements are vulnerable, and hence the building should undergo retrofit. The approaches of the retrofit measures can be as follows:

5.9.1 Local Retrofit of the Vulnerable Structural Elements Although there are several vulnerable structural elements including columns, infill walls, braces, and foundation, because the buildings lack any lateral load-bearing element, local retrofit of the vulnerable structural elements cannot be regarded as the final solution.

5.9.2 Elimination or Reduction in the Building’s Irregularity The results of the studies in Section 5.5.1 indicate both buildings are irregular in plan but regular in height. As previously stated, the buildings lack lateral loadbearing elements, and adding a new lateral load-bearing system is thus necessary. It is imperative to arrange the lateral load-bearing elements with the aim more uniform demand forces distribution on these elements which per se originated from reduction of the irregularity of the building to as little as possible.

5.9.3 Providing Lateral Stiffness to the Building The lateral stiffness in the main building is provided by masonry infill walls only. In the sports building in the transverse direction, the lateral stiffness of the building is provided by braces. As a result, a system should be added to both buildings to provide lateral stiffness. This can be done by one of the following methods.

5.9.3.1 Concentric Braces One of the main problems in adding braces to the building is architectural concerns. In the example buildings, there are few bays that can be considered for adding concentric braces without conflict to a lesser degree with the view and

332 Advanced Design Examples of Seismic Retrofit of Structures

FIG. 5.16 Soil pressure (kg/cm2) of the main building. (A) 1.1(DL + LL) + EPX.

Example of a Steel Frame Building Retrofitted Chapter

FIG. 5.16—CONT’D (B) 1.1(DL + LL) + EPY.

5

333

334

Advanced Design Examples of Seismic Retrofit of Structures

FIG. 5.17 Foundation uplift (cm) of the main building. (A) 1.1(DL + LL) + EPX. (B) 1.1(DL + LL) + EPY.

functionality of the building. The foundation adequacy to resist the considerable forces from the braces also play an important role in the design process of the retrofit.

5.9.3.2 Eccentric Braces Similar to the concentric braces, adding eccentric braces to the existing buildings leads to architectural concerns. One of the advantages of this method over concentric braces is the ability to control the failure mode from the braces to the link beam. The design of this beam can be done with the aim of flexural or shear failure preceding the failure in braces. The ductile failure of the link beam can provide large energy dissipation capacity compared with buckling of the

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335

FIG. 5.18 Soil pressure (kg/cm2) of the sports building. (A) 1.1(DL + LL) + EPX. (B) 1.1(DL + LL) + EPY.

FIG. 5.19 Required foundation reinforcement of the sports building. (A) X-direction. (B) Y-direction.

336

Advanced Design Examples of Seismic Retrofit of Structures

Existing beam

New beam

Link beam Eccentric braces

FIG. 5.20 Adding new beams to the building with eccentric braces.

concentric braces. Because the existing beams of the building are not able to resist the considerable demands from the braces in this method, new beams may be added to the building; this adds to the complexity of the retrofit system (see Fig. 5.20).

5.9.3.3 Steel Shear Walls The results of several experimental studies indicate that steel shear walls show an acceptable seismic performance in terms of providing significant stiffness, strength, ductility, and energy dissipation to the buildings. They have small strength and stiffness degradation, and hence provide the building with a stable seismic response. Adding steel shear walls to the existing building necessitates strength of the beams and columns, inclusion of the boundary elements, and strengthening of the foundation.

5.9.4 Providing Lateral Strength to the Building Similar to the methods in Section 5.11.3, adding braces or steel shear walls can be regarded as good solutions in providing the buildings with strength.

5.9.5 Reduction of Mass In many cases, reducing the mass of a building leads to the reduction of seismic demands. This can be done by reduction of the number of stories, modifications of the roof and floor system to reduce dead loads, changing the functionality of the building to reduce live loads (e.g., from educational to residential), and rearrangement and reduction of the partition walls. None of these methods can

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337

result in a considerable reduction in seismic forces in the example buildings, because the diaphragms are not heavy and the buildings are low-rise.

5.9.6 Completion of the Load Transfer Routes In the example buildings, there is no discontinuity in the load transfer routes.

5.9.7 Changing the Functionality of the Building This can be done with the aim of reduction of the target retrofit level. Because the required target retrofit level by the owner of the buildings is basic, no lesser target retrofit level can be considered for the building, even by changing its functionality.

5.9.8 Dampers By dissipation of energy, dampers can reduce damage to structural members. There are various types of dampers including viscoelastic, friction, and metallic yield dampers; each has their distinctive features, pros, and cons. Adding dampers to buildings is usually achieved by installation of these parts on braces. Also, dampers should be used in conjunction with other lateral load-bearing elements such as braces.

5.9.9 Base Isolation Base isolation is one of the major methods in significant reduction of seismic demands. However, application of this system to the existing buildings can become very expensive. Also, considering that the example buildings do not possess any lateral load-bearing element, even when base-isolated, proper lateral load-bearing system should be provided for these buildings.

5.10 PRELIMINARY ASSESSMENT OF THE THREE RETROFIT OPTIONS In order to compare in more detail the three preferred retrofit strategies, preliminary evaluation of the building retrofitted by each of these methods is performed.

5.10.1 Concentric Braces The preliminary design of the concentric braces is made in the bays at which it conflicts least with the architecture and functionality of the building. The design method is according to Section 5.8.5. It is noteworthy that in the sports building, the beams of the lightweight diaphragm of the main building at the first story

338

Advanced Design Examples of Seismic Retrofit of Structures

have to be tied with BOX100
100 mm. In addition, the vulnerable braces in the sports building have to be replaced by the newly designed profiles. There are eight beams which have to be added to the sports building to form the load transfer route from the diaphragm to the foundation. The results of the evaluation indicate there is no need to add piles to the foundations. However, the foundation under the columns adjacent to the braces needs to be retrofitted. The columns of the building adjacent to the braces need to be retrofitted, but other columns of the building are not vulnerable because they have no contribution to lateral load-bearing. The location of the added concentric braces is shown in Fig. 5.21. The designed profiles of the concentric braces are presented in Table 5.24. As an example, the results of the evaluation of the buildings in terms of DCR of the structural members in the retrofitted model by concentric braces are shown in Fig. 5.22. Based on the geotechnical studies, the allowable soil pressures for the example buildings are determined based on the relations below. For the pad foundation and strip footing with depths of 60 and 75 cm, respectively, the allowable soil pressures for various foundation widths are listed in Table 5.25. qa ¼ 12.34 + 4.71D + 1.65B For pad foundation (main building) qa ¼ 9.49 + 4.71D + 2.07B Forstrip footing (sports building) where B ¼ foundation width and D ¼ foundation depth. Soil pressure in the retrofitted main building by concentric braces under critical load combinations is shown in Fig 5.23. As can be seen, in some 100 cm
100 cm foundations, the soil pressure is higher than the allowable soil pressure according to Table 5.25. Also, some foundation of the main building is vulnerable against punching shear, as shown in Fig 5.24. The required reinforcement in the retrofitted main building by concentric braces, which are shown in Fig 5.25, is also higher than the existing reinforcement in those foundations, hence indicating the need for retrofit. Soil pressure in the retrofitted sports building by concentric braces under critical load combinations is shown in Fig. 5.26. As can be seen, the soil pressure is not higher than the allowable soil pressure according to Table 5.25. The foundation of the sports building is adequate against punching shear as shown in Fig. 5.27. The required reinforcement in the retrofitted sports building by concentric braces which are shown in Fig. 5.28 is not higher than the existing reinforcement in the foundation. As a result, the foundation in the sports building is not vulnerable.

5.10.2 Eccentric Braces Compared to concentric braces with the behavior factor of 5.5, the behavior factor of the frame buildings with eccentric braces is 7.0, which leads to 27% reduction on the design seismic loads, according to Standard 2800 [2]. However, as stated in Section 5.9.3.2, there is a need to add new beams to the buildings to resist the considerable forces from the braces. The results of the analyses

1

2

3

4

5

6

B C

D E

F G H

I

J K

(A) FIG. 5.21 Location of the added concentric braces. (A) Floor story.

8

9

10

11

12

13

14

Example of a Steel Frame Building Retrofitted Chapter

A

7

5

339

340

FIG. 5.21—CONT’D (B) First story.

Advanced Design Examples of Seismic Retrofit of Structures

(B)

14 13 12 11 10 9 8 7 6 5 4

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5

341

TABLE 5.24 Designed Concentric Braces Brace Name

Story Number

Profile

Main building (X-direction)

1

2UNP80

Floor

2UNP100

1

2UNP80

Floor

2UNP140

Floor

2UNP80

Main building (Y-direction)

Sports building

show that due to high forces acting in the beams, plate girders should be used as link beams. This adds to the costs and complexity of the retrofit method. Similar to the building retrofitted with concentric braces, the columns of the building adjacent to the braces need to be retrofitted; however, other columns of the building are not vulnerable because they have no contribution in lateral load-bearing. Location of the added eccentric braces is shown in Fig. 5.29. The designed profiles of the concentric braces are presented in Table 5.26. As can be seen, larger profiles are needed for the eccentric braces compared with the corresponding concentric braces. The designed section of the link beams are presented in Table 5.27. The length of the link beams in all the bays is assumed to be 60 cm. As an example, the results of the evaluation of the buildings in terms of DCR of the structural members in the retrofitted model by eccentric braces are shown in Fig. 5.30. As stated, because the existing beams in the buildings cannot resist the forces from the eccentric braces, new beams have to be added beneath the existing beams (see Fig. 5.20). At each bay, the significant shear forces in the distance between the existing and the added beams which represents the short column behavior should be checked. Based on the Iranian National Building Code; Part 10: Steel Building [6], the compressive sections experiencing considerable shear forces  have shear strengths determined based on Eq. (5.35), if 3185 ffiffiffiffi. the section satisfies thw  p Fy

Fv ¼ 0:4Fy

(5.35)

The demand shear force and the shear capacity of the column section are 6.9 and 30.2 ton, respectively; hence, the short columns between the existing and added beams are not vulnerable in shear. The short columns should also be checked for web local yielding. Based on the Iranian National Building Code; Part 10: Steel Building [6], when the

342 Advanced Design Examples of Seismic Retrofit of Structures

FIG. 5.22 Examples of DCR of the structural members in the retrofitted model by concentric braces. (A) Main building (axis 1). (Continued)

Example of a Steel Frame Building Retrofitted Chapter

FIG. 5.22—CONT’D (B) Main building (axis A). (C) Sports building (axis 1).

5

343

344

Advanced Design Examples of Seismic Retrofit of Structures

TABLE 5.25 Allowable Soil Pressure (kg/cm2) B (m)

Pad Foundation

Strip Footing

0

15.17

13.02

0.5

15.99

14.06

0.8

16.49

14.68

1

16.82

15.09

1.5

17.64

16.13

1.6

17.81

16.33

1.7

17.97

16.54

2

18.47

17.16

2.2

18.80

17.58

2.5

19.29

18.20

3

20.12

19.23

concentrated force to be resisted is applied at a distance from the member end that is greater than the depth of the member d, the section should satisfy Eq. (5.36). R  0:66Fy tw ðN + 5kÞ

(5.36)

where: k ¼ distance from outer face of the flange to the web toe of the fillet; N ¼ length of bearing (not less than k for end beam reactions); and tw ¼ web thickness. For the short column, we have:     6:9
103 kg kg ¼ 1346:34  1557:6 0:5ð2 + 5
1:65Þ cm2 cm2 As a result, the short column satisfies the requirements for web local yielding. As an example, the details of column strengthening A-1 are shown in Fig. 5.31. The results of the foundation evaluation of the main and sports buildings retrofitted with eccentric braces are not presented here, for brevity. Similar to the results of the buildings retrofitted with concentric braces, the foundations

Example of a Steel Frame Building Retrofitted Chapter 5

345

FIG. 5.23 Soil pressure in the retrofitted main building by concentric braces (kg/cm2). (A) 0.75DL + 0.75LL + 0.75EX + 0.225EY. (B) 0.75DL + 0.75LL + 0.75EX  0.225EY. (C) 0.75DL + 0.75LL + 0.75EY + 0.225EX. (D) 0.75DL + 0.75LL + 0.75EY  0.225EX.

346 Advanced Design Examples of Seismic Retrofit of Structures

FIG. 5.24 Punching shear in the retrofitted main building by concentric braces.

Example of a Steel Frame Building Retrofitted Chapter

FIG. 5.25 Required reinforcement in the retrofitted main building by concentric braces (foundations with red circles are vulnerable). (A) X-direction. (Continued)

5

347

348 Advanced Design Examples of Seismic Retrofit of Structures

FIG. 5.25—CONT’D (B) Y-direction.

Example of a Steel Frame Building Retrofitted Chapter

5

349

FIG. 5.26 Soil pressure in the retrofitted sports building by concentric braces (kg/cm2). (A) 0.75DL + 0.75LL + 0.75EX + 0.225EY. (B) 0.75DL + 0.75LL + 0.75EX  0.225EY. (C) 0.75DL + 0.75LL + 0.75EY + 0.225EX. (D) 0.75DL + 0.75LL + 0.75EY  0.225EX.

of the main building are vulnerable. The required reinforcement of the foundation is higher than that in the buildings retrofitted with concentric braces.

5.10.3 Crossed Braces The behavior factor of the buildings with crossed braces is the same as for the buildings with concentric braces. However, according to Standard 2800 [2], the buildings with crossed braces should be designed against 1.5 times of the designed seismic actions. This causes larger brace profiles compared with concentric braces. In this method, the columns of the building adjacent to the braces need to be retrofitted; however, other columns of the building are not

350

Advanced Design Examples of Seismic Retrofit of Structures

FIG. 5.27 Punching shear in the retrofitted sports building by concentric braces.

FIG. 5.28 Required reinforcement in the retrofitted sports building by concentric braces. (A) X-direction. (B) Y-direction.

1

2

3

4

5

6

B C

D E

F G H

I

J K

(A) FIG. 5.29 Location of the added eccentric braces. (A) Floor story.

8

9

10

11

12

13

14

Example of a Steel Frame Building Retrofitted Chapter

A

7

5

351

Advanced Design Examples of Seismic Retrofit of Structures

FIG. 5.29—CONT’D (B) First story.

352

(B)

14 13 12 11 10 9 8 7 6 5 4

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5

353

TABLE 5.26 Designed Eccentric Braces Brace Name

Story Number

Profile

Main building (X-direction)

1

2UNP80

Floor

2UNP120 2UNP140

Main building (Y-direction)

Sports building

1

2UNP80

Floor

2UNP140

Floor

2UNP120

TABLE 5.27 Designed Section of the Link Beams Story

V (kg)

Fv (kg/cm2)

Av (cm2)

Profile

Floor (X-direction)

11,610

944

12.3

IPE 330

Floor (X-direction) H-I

43,180

944

45.74

IPE 500

1st (X-direction)

3960

944

4.19

IPE 200

Floor (Y-direction)

16,800

944

17.8

IPE 330

1st (Y-direction)

6140

944

6.5

IPE 200

Sports building

10,900

944

11.55

IPE 330

vulnerable because they have no contribution to lateral load-bearing. The location of the added crossed braces is similar to those in previous methods. The designed profiles of the crossed braces are presented in Table 5.28. As can be seen, larger profiles are needed for the crossed braces compared with the corresponding concentric and eccentric braces. As an example, the results of the evaluation of the buildings in terms of DCRs of the structural members in the retrofitted model by eccentric braces are shown in Fig. 5.30. The results of the foundation evaluation of the main and sports buildings retrofitted with crossed braces are not presented here, for brevity. Similar to the results of the buildings retrofitted with concentric and eccentric braces, the foundations of the main building are vulnerable. The required reinforcement of the foundation is higher than that in the buildings retrofitted with concentric and eccentric braces.

354 Advanced Design Examples of Seismic Retrofit of Structures

FIG. 5.30 Examples of DCRs of the structural members in the retrofitted model by eccentric braces. (A) Main building (axis 1). (Continued)

Example of a Steel Frame Building Retrofitted Chapter

FIG. 5.30—CONT’D (B) Main building (axis A). (C) Sports building (axis 1).

5

355

356

Advanced Design Examples of Seismic Retrofit of Structures

FIG. 5.31 Details of column strengthening.

TABLE 5.28 Designed Crossed Braces Brace Name

Story Number

Profile

Main building (X-direction)

1

2UNP100

Floor

2UNP160

1

2UNP100

Floor

2UNP160

Floor

2UNP80

Main building (Y-direction)

Sports building

Example of a Steel Frame Building Retrofitted Chapter

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357

5.10.4 Conclusions A comparison of the three considered retrofit options in various important aspects is made in Table 5.29 and Fig. 5.32. It is noteworthy that the grand total cost of the retrofit method by concentric braces is $119,000, but it greatly depends on many factors including material costs, workmanship cost, etc. It can be concluded that the method of adding concentric braces to the building is marginally superior to the other two candidates, and hence is selected as the preferred retrofit solution to the example buildings.

5.11 EVALUATION OF THE RETROFITTED BUILDING BY THE PREFERRED METHOD In this part, the building retrofitted by concentric braces as the preferred retrofit method in Section 5.10 is evaluated in detail.

5.11.1 Irregularity Similar to Section 5.5.1, the necessary controls for determination of the irregularity of the retrofitted example buildings in plan and in height are presented briefly. For brevity, the controls which are the same as those for the unretrofitted building are excluded from this section and only those with new results are mentioned. The complete set of requirements of determination of the irregularity of the buildings in plan and height are presented in Section 2.5.4 in Chapter 2. l

l

l

Coordinates of center of mass (CoM) and center of rigidity (CoR) of the retrofitted buildings are shown in Table 5.30. Based on the results of this table, the distances of the main and sports buildings’ CoM and CoR are less than 20% of the external dimension of the buildings in each direction. According to Table 5.31, the maximum inter-story displacement (by inclusion of accidental torsion) of the main and sports buildings is less than 20% of the average inter-story displacement of the two story ends. For the main and the sports buildings, the lateral load-bearing elements are the added braces, existing braces, and infill walls. Based on the results in Table 5.32, the story stiffness in the floor story is not less than 70% of that in the first story or 80% of the average story stiffness. The single-story sports building is not subjected to irregularity in height.

5.11.2 Diaphragms According to the procedure in Section 5.5.2, the results of the diaphragms’ flexibility for the example buildings retrofitted by concentric braces are presented in

358

Construction Cost

Construction Complexity

Performance Improvement

Construction Time

Architectural Conflicts

Concentric braces

Moderate

Moderate

High

Low

High

Eccentric braces

High

High

High

Moderate

Moderate

Crossed braces

High

High

High

Moderate

Moderate

Option

Advanced Design Examples of Seismic Retrofit of Structures

TABLE 5.29 Comparison of the Retrofit Options

Example of a Steel Frame Building Retrofitted Chapter

5

359

Cost of retrofit/cost of reconstruction

40% 35% 30% 25% 20% 15% 10% 5% 0% Concentric braces

(A)

Eccentric braces Retrofit option

Crossed braces

88

Construction time, days

86 84 82 80 78 76 Concentric braces

(B)

Eccentric braces Retrofit option

Crossed braces

FIG. 5.32 Comparison of the retrofit options. (A) Construction cost. (B) Construction time.

Table 5.33. Based on these results, the diaphragm in the floor story of the main building is semi-rigid and the diaphragm of the sports building is rigid.

5.11.3 Torsion The procedure is similar to that in Section 5.5.3.

5.11.4 Soil-Structural Interaction The procedure is similar to that in Section 5.5.4.

360

Story

Diaphragm

Mass X (kg)

XCM (m)

YCM (m)

XCR (m)

YCR (m)

(XCM-XCR) (m)

(YCM-YCR) (m)

Main building 1st

D2

22526

12.6

7.6

11.2

7.7

1.4

0.0

Floor

D1

64757

15.3

7.6

10.7

7.6

4.7

0.0

17420

4.21

8

5.0

7.9

0.82

0.0

Sports building 1

D1

Advanced Design Examples of Seismic Retrofit of Structures

TABLE 5.30 Coordinates of Center of Mass and Center of Rigidity of the Retrofitted Building

Story

Drift Ratio Under EPX (%) Maximum

Drift Ratio Under EPY (%)

Drift Ratio Under ENX (%)

Drift Ratio Under ENY (%)

1.2 × Mean

Maximum

1.2 × Mean

Maximum

1.2 × Mean

Maximum

1.2 × Mean

Main building 2

0.2

0.2

0.1

0.1

0.2

0.2

0.1

0.1

1

0.3

0.3

0.8

0.8

0.3

0.4

0.7

0.9

0.3

0.2

0.2

0.2

0.3

0.2

0.2

Sports building 1

0.2

Example of a Steel Frame Building Retrofitted Chapter

TABLE 5.31 Maximum and Mean Drift Ratio of the Retrofitted Buildings

5

361

362

Advanced Design Examples of Seismic Retrofit of Structures

TABLE 5.32 Comparison of the Story Stiffness With That in the Adjacent Stories Direction

Story

Ki (MN/m)

70% Ki (MN/m)

80% Average Ki (MN/m)

Result

X

1st

714

500

571

OK

Floor

2500

–

–

OK

1st

263

184

210

OK

Floor

909

–

–

OK

Y

5.11.5 Analysis Procedure 5.11.5.1 Demand Forces Calculations The procedure is similar to that in Section 5.6.1. Based on the derived natural periods from the model, we have: - For the main building: 0:7  0:21 0:7  0:24 ¼ 1:41, C1ðyÞ ¼ 1 + ¼ 1:38  C1ðxÞ ¼ 1 + 1:4  0:2 1:4  0:2 VðXÞ ¼ 1:16W C2 ¼ 1:0 ) V ðY Þ ¼ 1:14W Cm ¼ 1:0 SaðxÞ ¼ SaðyÞ ¼ 0:3
2:75 ¼ 0:825 - For the sports building: 0:7  0:17 C1ðxÞ ¼ C1ðyÞ ¼ 1 + ¼ 1:44  1:4  0:2 VðXÞ ¼ 1:19W C2 ¼ 1:0 ) V ðY Þ ¼ 1:19W Cm ¼ 1:0 SaðxÞ ¼ SaðyÞ ¼ 0:3
2:75 ¼ 0:825

5.11.5.2 Target Displacement The procedure is similar to that in Section 5.5.3. We have: ð0:21Þ2
9:81 ¼ 1:84ðcmÞ
1:5 ¼ 2:75ðcmÞ 39:43 2 and ð0:24Þ
9:81 ¼ 2:35ðcmÞ
1:5 ¼ 3:53ðcmÞ δtðxÞ ¼ 1:2
1:4
1:2
0:825
39:43 For the main building;

δtðxÞ ¼ 1:2
1:4
1:2
0:825


TABLE 5.33 Determination of the Diaphragms’ Flexibility in the Floor Story of the Retrofitted Buildings

Building

t (cm)

H(m)

I (cm4)

H (m)

Main

11

6.1

2160

Sports

11

16.0

1000

E (GPa)

Fpx (ton)

Fpy (ton)

ωx (MPa)

ωy (MPa)

Ix (m4)

Iy (m4)

α

1.3

3.3

1369

1256

35

73

92.4

2.1

1.5

1.3

3.3

241

246

24

15

91.7

37.5

1.5

L (m)

Ax (m2)

Ay (m2)

G (GPa)

17

39

2.37

0.67

16

10

11.00

1.76

Δax (cm)

Δay (cm)

Δfx (cm)

Δfy (cm)

ΔDx (cm)

ΔDx (cm)

ΔSx (cm)

ΔSx (cm)

Main

1.02

0.61

0.32

0.19

1.34

0.80

0.94

1.38

Sports

0.32

0.33

0.10

0.10

0.43

0.44

1.28

1.10

If (ΔD/ΔS)0.5 then rigid

ΔD If ( )2.0 ΔS then flexible

ΔDx ΔSx

ΔDy ΔSy

1.43

0.57

0.33

0.39

364

Advanced Design Examples of Seismic Retrofit of Structures

δtðxÞ ¼ δtðyÞ ¼ 1:0
1:43
1:2
0:825
For the sports building:

ð0:17Þ2 39:43
9:81 ¼ 1:03ðcmÞ
1:5 ¼ 1:53ðcmÞ

5.11.6 Concurrent Seismic Effects The procedure is similar to that in Section 5.5.4.

5.11.7 Actions Calculations The procedure is similar to that in Section 5.5.5.

5.11.8 Overturning Effects The procedure is similar to that in Section 5.5.6. As the results of the evaluation of the overturning effects presented in Table 5.34 show, the retrofitted buildings adequately resist the overturning moments.

5.11.9 Modeling Assumptions The procedure is similar to that in Section 5.5.7. The plastic hinge characteristics of different structural members of the retrofitted buildings are shown in Figs. 5.33–5.36.

5.11.10 Capacity Forces Calculations 5.11.10.1 Linear Static Procedure Beams The procedure is similar to that in Section 5.7.1.1. Columns The procedure is similar to that in Section 5.7.1.2. The lower-bound axial capacities of columns in the retrofitted buildings are presented in Table 5.35.

5.11.10.2 Nonlinear Static Procedure The procedure is similar to that in Section 5.7.2.

5.11.11 Acceptance Criteria The procedure is similar to that in Section 5.8.

5.11.12 Results Examples of the results of nonlinear static analysis on the main retrofitted building are shown in Figs. 5.37 and 5.38 and Tables 5.36 and 5.37. The example

TABLE 5.34 Results of the Evaluation of the Overturning Effects for the Retrofitted Buildings (Units: ton, m) Building

Story

Vx

Vy

H

WI

Dx

Dy

C1x

C1y

C2

J

ROT

Main

1st

461

461

7.1

99

15.6

7.5

1.4

1.3

1

2

8

Floor

793

793

3.7

720

19.2

7.5

1.3

1.3

1

2

8

Floor

248

248

5.5

174

5.0

8.0

1.4

1.4

1

2

8

MOTX

MOTY

MSTX

MSTY

MSTX > MOTX/ (C1xC2J)

MSTY > MOTY/ (C1yC2J)

0.9 MSTX > MOTX/ (C1xC2 ROT)

0.9 MSTY > MOTY/ (C1yC2 ROT)

Main

6250

6250

15446

6191

2219

2259

554

564

Sports

1377

1377

871

1393

477

477

119

119

Sports

366

Advanced Design Examples of Seismic Retrofit of Structures

FIG. 5.33 Plastic hinge characteristic of brace 675
12 in the sports building.

FIG. 5.34 Plastic hinge characteristic of braces 480
10 in the main building.

Example of a Steel Frame Building Retrofitted Chapter

FIG. 5.35 Plastic hinge characteristic of girders ridge in the sports building.

FIG. 5.36 Plastic hinge characteristic of column C12 in the sports building.

5

367

368

Advanced Design Examples of Seismic Retrofit of Structures

TABLE 5.35 Lower-Bound Axial Capacity of Columns in the Retrofitted Buildings Profile

r (cm)

A (cm2)

λ

FS

Fa (kg/cm2)

QCL (ton)

2IPE140  E10 (Story-1)

5.7

32.8

65.8

1.83

1107

61.7

2IPE140  E10 (Story-2)

5.7

32.8

58.8

1.83

1131

63.1

2IPE160  E15 (Story-1)

7.7

90.2

48.7

1.80

1204

184.7

2IPE160  E15 (Story-2)

7.7

90.2

43.5

1.80

1215

186.3

2IPE160 + 2PL30
1 (Story-1)

7.8

100.2

48.2

1.79

1231

209.7

2IPE160 + 2PL30
1 + 2PL20
1 (Story-2)

7.3

140.2

46.1

1.79

1242

296.0

2IPE160 + 2PL30
1 + 2PL20
1 (Story-1)

7.3

140.2

51.6

1.80

1214

289.3

2IPE160  E10 (sports building)

6.6

40.2

84.5

1.86

1001

68.4

results related to the sports retrofitted building are presented in Figs. 5.39 and 5.40 and Tables 5.38 and 5.39. As can be seen, no plastic hinges rotation exceed the allowable rotation related of LS. Examples of the details of the braces and the base plates are shown in Figs. 5.41–5.43. The design procedure for the gusset plates, their connections to the frame members, and the base plates’ adequacy and strengthening in the form of adding extra bolts to the base plate are excluded here, for brevity. Examples of construction stages in adding the braces to the building are shown in Figs. 5.44 and 5.45. The adequacy of the cradle-type connections against the vertical shear forces is made using Code 324 [9]. Based on this code, the capacity of the lower steel angle against vertical shear forces can be determined according to Eq. (5.37). Control of the vertical shear adequacy of the cradle-type connections

B

(A)

IO

Z

LS

X

CP

C

D

E

(B)

FIG. 5.37 Plastic hinges formation in the main retrofitted building under PX1. (A) Contour. (B) Force-displacement diagram.

Example of a Steel Frame Building Retrofitted Chapter

Y

5

369

370

B

(A)

IO

Z

LS

X

CP

C

D

E

(B)

FIG. 5.38 Plastic hinges formation the main retrofitted building under PY1. (A) Contour. (B) Force-displacement diagram.

Advanced Design Examples of Seismic Retrofit of Structures

Y

TABLE 5.36 The Results of Plastic Hinges in the Main Retrofitted Building Under PX1 Displacement

Base Force

A-B

B-IO

IO-LS

LS-CP

CP-C

C-D

D-E

≥E

Total

0

0.0016

0

52

0

0

0

0

0

0

0

52

1

2.77E 04

117,069.7734

49

3

0

0

0

0

0

0

52

2

0.0015

196,824.9219

44

4

4

0

0

0

0

0

52

3

0.0042

319,873.3125

39

5

8

0

0

0

0

0

52

4

0.0076

462,290.7813

38

6

8

0

0

0

0

0

52

5

0.0094

538,479.75

38

5

9

0

0

0

0

0

52

6

0.0112

613,619.5625

34

6

12

0

0

0

0

0

52

7

0.0133

691,679.0625

31

9

12

0

0

0

0

0

52

8

0.014

711,515.6875

29

10

13

0

0

0

0

0

52

9

0.0154

730,432.8125

29

5

18

0

0

0

0

0

52

10

0.0168

739,888.6875

52

0

0

0

0

0

0

0

52

Example of a Steel Frame Building Retrofitted Chapter

Step

5

371

372

Step

Displacement

Base Force

A-B

B-IO

IO-LS

LS-CP

CP-C

C-D

D-E

≥E

Total

0

1.88E 04

0

50

2

0

0

0

0

0

0

52

1

0.0025

122,714.7188

50

0

2

0

0

0

0

0

52

2

0.0049

202,692.8438

47

3

2

0

0

0

0

0

52

3

0.0056

226,348.8125

43

7

2

0

0

0

0

0

52

4

0.008

298,510.2188

41

7

4

0

0

0

0

0

52

5

0.0126

420,228.3438

38

7

7

0

0

0

0

0

52

6

0.014

458,527.0625

36

7

9

0

0

0

0

0

52

7

0.0162

492,245.4375

36

5

11

0

0

0

0

0

52

8

0.0185

507,845.8438

36

3

13

0

0

0

0

0

52

9

0.0209

523,461.6563

36

1

15

0

0

0

0

0

52

10

0.0232

539,065.125

36

1

15

0

0

0

0

0

52

11

0.0237

542,236.1875

52

0

0

0

0

0

0

0

52

Advanced Design Examples of Seismic Retrofit of Structures

TABLE 5.37 The Results of Plastic Hinges in the Main Retrofitted Building Under PY1

(B)

FIG. 5.39 Plastic hinges formation in the sports retrofitted building under PX1. (A) Contour. (B) Force-displacement diagram.

Example of a Steel Frame Building Retrofitted Chapter

(A)

5

373

374 Advanced Design Examples of Seismic Retrofit of Structures

(A)

(B)

FIG. 5.40 Plastic hinges formation the sports retrofitted building under PY1. (A) Contour. (B) Force-displacement diagram.

TABLE 5.38 The Results of Plastic Hinges in the Sports Retrofitted Building Under PX1 Displacement

Base Force

A-B

B-IO

IO-LS

LS-CP

CP-C

C-D

D-E

≥E

Total

0

7.50E 04

0

145

0

0

0

0

0

0

0

145

1

7.88E 04

24,161.041

144

1

0

0

0

0

0

0

145

2

0.0018

40,498.3047

142

3

0

0

0

0

0

0

145

3

0.0036

56,508.4141

142

1

2

0

0

0

0

0

145

4

0.0051

68,828.9766

142

1

2

0

0

0

0

0

145

5

0.0067

81,149.6563

141

1

3

0

0

0

0

0

145

6

0.0082

93,470.4375

141

1

3

0

0

0

0

0

145

7

0 0097

105,764.2109

140

2

3

0

0

0

0

0

145

8

0.0104

110,665.7109

139

2

4

0

0

0

0

0

145

9

0.0119

114,275.625

139

1

5

0

0

0

0

0

145

10

0.0134

114,430.5078

139

1

5

0

0

0

0

0

145

11

0.0146

114,550.8984

145

0

0

0

0

0

0

0

145

Example of a Steel Frame Building Retrofitted Chapter

Step

5

375

376

Step

Displacement

Base Force

A-B

B-IO

IO-LS

LS-CP

CP-C

C-D

D-E

≥E

Total

0

0.0015

0

145

0

0

0

0

0

0

0

145

1

2.10E 05

32,436.1523

141

4

0

0

0

0

0

0

145

2

1.97E 04

36,141.7813

141

4

0

0

0

0

0

0

145

3

0.0017

52,596.2969

141

0

4

0

0

0

0

0

145

4

0.0033

69,053.3359

141

0

4

0

0

0

0

0

145

5

0.0048

85,521.9609

140

1

4

0

0

0

0

0

145

6

0.0073

111,257.9219

140

1

4

0

0

0

0

0

145

7

0.0088

127,268.0469

140

0

5

0

0

0

0

0

145

8

0.0103

143,280.6875

140

0

5

0

0

0

0

0

145

9

0.0119

159,306.875

137

3

5

0

0

0

0

0

145

10

0.0134

174,674.7031

137

3

5

0

0

0

0

0

145

11

0.0139

176,281.0781

145

0

0

0

0

0

0

0

145

Advanced Design Examples of Seismic Retrofit of Structures

TABLE 5.39 The Results of Plastic Hinges in the Sports Retrofitted Building Under PY1

Example of a Steel Frame Building Retrofitted Chapter

PL200x80x10 (New) 7(New) STIFFENER 150 2x2x1 / 2PL100x80x10 (New) STIFFENER 7(New) 850

5

377

2IPE160+ 2PL 250x10 (New)

A –

A – 2UNP160[BOX] (NEW)

275

7(New) 300

50

PL–1 850x550x10 (New)

PL400x80x10 (New) STIFFENER

7(New) 400

7(New)

DETAIL

A –

2x2x1/2PL100x80x10 (New) 150

400 2UNP160[BOX] (NEW)

150

7(New) 300 for Br. 2IPE160+ 2PL 250x10 (New)

PL–1 850x550x10(New) PL–1 850x550x10 (New) PL400x80x10 (New) STIFFENER

700

7(New) 400 for Stiff.

SECTION

7(New) 7(New) 850

A –

SPACER PL 200x100x10@750mm (New)

2UNP160[BOX] (New)

–

B

7(New)

2UNP160[BOX] (New)

B

7(New) 100

–

7(New) 300

2UNP160[BOX] (New) SPACER PL 200x100x10@750mm (New) 7(New) 2UNP160[BOX] (New) 2UNP160[BOX] (New) PL 800x500x10 (New)

7–100(New)

SECTION

B –

DETAIL

D –

FIG. 5.41 Details of the braces in bay J/7-8 floor story in the main building.

is shown in Table 5.40. As can be seen, all the beam-column connections can resist the shear forces.     bfb L 2 L (5.37) t1 + + 0:7 t2wb + 2t2fb R1 ¼ fy bfb  2t1 2bfb 2bfb where: fy ¼ expected yield strength of material; bfb ¼ flange width of the beam; tfb ¼ flange thickness of the beam; twb ¼ web thickness of the beam; t1 ¼ flange thickness of the angle; and

378

Advanced Design Examples of Seismic Retrofit of Structures

7(New) 150–400

PL 250x100x8@500 mm

2UNP80[BOX] (NEW) 7(New) PL140x80x10 (New) 140 STIFFENER

7(NEW)

7(New) 340

2x1/2PL100x80x10 (New) STIFFENER

7(New) 100

7(NEW) 170

PL–3 400x400x10(New) PL140x80x10 (New) STIFFENER 7(New) 140 PL420x350x10 (New) 7(New) PL540x400x10 (New) 340

IPE140 2INP240 7(New)

7(New) 400

7(NEW)

PL250x80x10 (New) STIFFENER PL–3 400x400x10(New)

PL140x80x10 (New) STIFFENER 7(New) 7(New) 340 100

2x1/2PL100x80x10 (New) STIFFENER 7(New) 300

2IPE160+ 2PL 250x10 (New)

PL–2 450x450x10 (New)

2x1/2PL100x80x10 (New) STIFFENER

7(New) 140

170

PL200x80x10 (New) 7(New) STIFFENER 200 7(New) 390

7(New) 340

7(New)

2IPE140

170

7(New) 350

2IPE160 PL 250x100x8@500 mm

2UNP80[BOX] (New)

PL200x80x10 (New) STIFFENER 7(New) 200

DETAIL

C –

7(New) 390 2UNP160[BOX] (NEW) 90 B –

250

340

90

DETAIL

390

250

PL–3 400x400x10(New)

325

60

60

60

125

340

60

390

125

PL–2 450x450x10(New)

325

SPACER PL 120x100x10@750mm (NEW)

2UNP80[BOX] (NEW)

–

C

7(New)

2UNP80[BOX] (NEW) 7(New) 100 –

C

7(New) 100

2UNP80[BOX] (NEW) SPACER PL 120x100x10@750mm (NEW)

7(New) 2UNP80[BOX] (NEW)

2UNP80[BOX] (NEW) PL 300x200x10 (NEW) 7(New) 100

SECTION

DETAIL C –

E –

FIG. 5.42 Details of the braces in bay J/7-8 first story in the main building.

L ¼ length of the angle. The evaluation of the retrofitted foundation based on the details shown in Figs. 5.46 and 5.47 is made here. Based on ASCE 41, if the base of the structure is assumed to be completely rigid, then the base reactions for all foundations shall be classified as force controlled, in accordance with Section 5.5.5.2, and shall not exceed upper-bound component capacities. The J-factor in determination of the actions calculations is selected as the minimum DCR of the braces, as presented in Table 5.41. The soil pressure in the retrofitted main building and the required reinforcement are shown in Figs. 5.48 and 5.49, respectively. Some construction stages in the foundation retrofit process are shown in Fig. 5.50.

Example of a Steel Frame Building Retrofitted Chapter

5

2 STIFF PL 500x250x12(New) 500 160

170

12

170

–

GAP

2mm

240

4 STIFF PL 250x160x12(New)

330 310

20

2PL 500x330x20(New) POS A

90

130

POS A

2IPE 160+ 2PL250x10 at flange + 2PL200x10 at web(New)

410

8

500

B –

500

130

6ø22 (New) HOLE ø24

4 STIFF PL 250x80x12(New)

POS A A –

170

2IPE 160+ 2PL250x10 at flange + 2PL200x10 at web(New)

2 STIFF PL 500x250x12(New)

2PL A 500x330x20(New) 8 95

T.O.F.New=–30 2 PL–B STIFFENER

PL–C Cut from PL–B

8 24

156

24 8

24

2L60´60´6 L=12 cm

–

BOLT ø20

PL500´400´15

View

22

A

2IPE 160+ 2PL250x10 at flange + 2PL200x10 at web(New) 4 STIFF PL 250x80x12(New)

4 STIFF PL 250x160x12(New)

8

2 STIFF PL 500x250x12(New) 2PL A 500x330x20(New)

8 T.O.F.New=–30 2 PL–B STIFFENER

–

BOLT ø22 & 2Nut22 (New)

T.O.F.=–55

2L60x60x6 L=25 cm

–

BOLT ø20

PL500x400x15

View

FIG. 5.43 Details of the base plate.

PL–B t=10mm

90

2L60´60´6 L=25 cm

B –

25

T.O.F.=–55

65

95

2IPE160

379

380

Advanced Design Examples of Seismic Retrofit of Structures

FIG. 5.44 Demolition of infill walls. (A) External view. (B) Internal view. (Photos taken by A.S. Moghadam.)

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5

381

FIG. 5.45 Adding braces to the building. (A) External view. (B) Internal view. (Photos taken by A.S. Moghadam.)

382

Section 2INP240 + 2L140
140
14

fy (kg/cm2)

bfb (cm)

tfb (cm)

t1 (cm)

twb (cm)

L (cm)

R (kg)

MAX (VDL+ LL) (kg)

DCR

2400

10.6

1.31

1.4

0.87

20

21282

6530

0.31

Advanced Design Examples of Seismic Retrofit of Structures

TABLE 5.40 Control of the Vertical Shear Adequacy of the Cradle-Type Connections

Example of a Steel Frame Building Retrofitted Chapter

I+I

I+I

I+I

360

14

I+I

I+I

I+I

I+I

I+I

I+I

I+I

I+I

I+I

I+I

I+I I+I

I+I

I+I

I+I

I+I

I+I

I+I

I+I

I+I

I+I

I+I

I+I

I+I

I+I

I+I

I+I

I+I

I+I

I+I

I+I

I+I

I+I

I+I

I+I

I+I

115

I+I

4

365

5

360

6

360

7

365

8

360

9

351

10

615

11

355

12

365

13

I+I

I+I I+I

I+I

I+I

I+I

I+I

I+I

510

3

I+I

I+I

504

2

I+I

358 J K

H

E

D

B C

247 158 137

FIG. 5.46 Plan of the retrofitted foundation.

I+I

40

232

105 A

I+I

I

63 314

I+I

G

32

I+I

F

1

I+I

5

383

Advanced Design Examples of Seismic Retrofit of Structures

22

21 ø20@20cm (New) 20 Continuous

ø12@25cm (New) 22 L=290cm

15 260 15

25

ø12@25cm (New) 4 L=80cm

15

170 130 270

50 70

50 70

T.O.F=–55 ø20@20cm (New) Continuous ø20@20cm (New) Continuous

(New) 8 ø12@25cm L=125cm

ø12@25cm (New) L=125cm

10 105 10 8

10 105 10 8

115

21 ø20@20cm (New) 20 Continuous

ø12@25cm (New) 22 L = 640cm

610 15

40 270

115

T.O.F(NEW)=–30

25

T.O.F=–55

1

3 ø[email protected] (New) 1 Continuous

ø[email protected] (New) Continuous ø12@25cm (New) 4 L=110cm

ø12@25cm (New) 4 L=110cm

10 90 10 4

15

50

T.O.F(NEW)=–30

ø20@20cm (New) 5 Continuous

10 60 10 4

15

90

ø20@20cm (New) 5 Continuous

90 50

50

3 ø[email protected] (New) 1 Continuous

(New) 4 ø12@25cm L=80cm 10 60 10 4

(New) 6 ø20@20cm Continuous

T.O.F=–55

90

2 (New) 1 ø[email protected] Continuous

ø12@25cm (New) 22 L=290cm

T.O.F(NEW)=–30

25

15 260 15

15

384

130 150 570

170 110

50 100

10 145 10 4

170 110

10 90 10 4

50 100

ø12@25cm (New) 4 L=165cm ø[email protected] (New) 1 Continuous

21 15 610 15

ø20@20cm (New) 20 Continuous

ø12@25cm (New) 22 L=640cm

25 50 15

90

T.O.F(NEW)=–30 T.O.F=–55

1

ø[email protected] (New) Continuous 4 ø12@25cm (New) L=145cm 10 125 10 4

110

250

50

50

110

ø[email protected] (New) Continuous

3 1

ø12@25cm (New) L=145cm

4

10 125 15 4

570 10 240 10 4

ø12@25cm (New) 4 L=260cm ø[email protected] (New) Continuous

1

FIG. 5.47 Details of the retrofitted foundation.

TABLE 5.41 Minimum DCRs of the Braces Brace Section

L (m)

Max (PUF) (ton)

PCL (ton)

Min (DCR)

2UNP120

5.5

106.37

42.66

2.49

6.95

97.57

26.82

3.90

4.8

147.73

80.85

1.83

5.25

112.52

75.92

1.48

7.15

165.82

51.85

3.20

2UNP160

Based on Standard 2800 [2], the beams in jack-arch roofs should be tied together by bars or steel strips to provide the integrity of the roof. The added crossed elements in each panel tying these beams should not exceed the area larger than 25 m2, and the ratio of the length to width of these panels should be larger than 1.5. Details of providing the jack-arch roof with uniformity are shown in Fig. 5.51. Views of the building after retrofit process are illustrated in Fig. 5.52.

5

FIG. 5.48 Soil pressure in the retrofitted main building by concentric braces with retrofitted foundation (kg/cm2). (A) 1.1(DL + LL) + EX + 0.3EY. (B) 1.1(DL + LL)  EX + 0.3EY. (C) 1.1(DL + LL) + EY + 0.3EX. (D) 1.1(DL + LL)  EY + 0.3EX.

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FIG. 5.49 Required reinforcement in the retrofitted main building by concentric braces with retrofitted foundation. (A) X-direction. (B) Y-direction.

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5

387

(A)

(B) FIG. 5.50 Foundation retrofit process. (A) Removing the floor, and drilling the dowel bars between in the existing foundation. (B) Installation of the reinforcement grid. (Photos taken by A.S. Moghadam.)

Advanced Design Examples of Seismic Retrofit of Structures

L

388

FIG. 5.51 Details of providing the jack-arch roof with uniformity.

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389

FIG. 5.52 The building after retrofit process. (A) Internal view. (B) External view. (Photos taken by A.S. Moghadam.)

REFERENCES [1] Instruction for Seismic Rehabilitation of Existing Buildings (No. 360), Management and Planning Organization of fice of Deputy for Technical Affairs, Iran, (2014) (in Persian). [2] Iranian Code of Practice for Seismic Resistant Design of Buildings (Standard 2800). Fourth Revision, Building and Housing Research Center, Iran (in Persian).

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[3] FEMA-310, Handbook for the Seismic Evaluation of Buildings—A Prestandard, American Society of Civil Engineers, Washington, DC, 1998. [4] NEHRP Handbook for the Seismic Evaluation of Existing Buildings (FEMA 178), Building Seismic Safety Council, 1992. [5] W.W. El-Dakhakhni, M. Elgaaly, A.A. Hamid, Three-strut model for concrete masonry-infilled steel frames, J. Struct. Eng. 129 (2) (2003) 177–185. [6] Iranian National Building Code; Part 10: Steel Buildings, 2014. [7] ASCE, Seismic Evaluation and Retrofit of Existing Buildings, ASCE/SEI 41-13, American Society of Civil Engineers, Reston, VA, 2014. [8] AISC Committee, Specification for Structural Steel Buildings (ANSI/AISC 360-10), American Institute of Steel Construction, Chicago, IL, 2010. [9] Instruction for Design of Buildings With Cradle-type Connections (No. 324), Management and Planning Organization of fice of Deputy for Technical Affairs, Iran, (2006) (in Persian).

Chapter 6

Examples of Nonengineered Buildings Mohammad Yekrangnia Department of Civil Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran

Aims By reading this chapter, you are introduced to: l l l l l l

adobe buildings characteristics and failure modes; introduction to several simple, feasible and economical retrofitting techniques suitable for adobe buildings; good experiences from around the world in seismic retrofit of adobe buildings; an introduction and implementation of the “stability-based” retrofit method; comparison of seismic performance of several test specimens retrofitted with various methods; and performance of the retrofitted adobe buildings in past earthquakes.

6.1 INTRODUCTION The term “nonengineered” buildings refers to buildings with poor seismic performance which cannot meet codes’ minimum requirements. These buildings are usually constructed by common-practice and their material properties and constructional details vary significantly. Construction of nonengineered houses has been among the most typical construction technique in many third-world countries. Also, there are numerous cases of old buildings which had been constructed at the time when no seismic design code was available; hence they are categorized as nonengineered buildings. The collapse of these buildings has been and still remains as one of the main causes of loss of human lives and of economic devastation following strong earthquakes [1]. An example of large-scale collapse of these nonengineered houses after the 2008 Ziarat earthquake in Pakistan is shown in Fig. 6.1. Nonetheless, observations from past earthquakes, for example, the 2003 Bam earthquake in Iran, prove that if these nonengineered buildings are constructed according to the uniformly accepted construction concepts with good-quality materials and workmanship, their seismic performance is superior Advanced Design Examples of Seismic Retrofit of Structures. https://doi.org/10.1016/B978-0-08-102534-5.00006-4 © 2019 Elsevier Ltd. All rights reserved.

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FIG. 6.1 Total collapse of adobe houses during the Ziarat earthquake in 2008. (Permission from Dr. Hashmat Lodi [2].)

to those “engineered” buildings that cannot meet the design codes’ requirements. An example is shown in Fig. 6.2 in which an adobe building with lower vulnerability and a collapsed RC building are compared after the 2003 Bam earthquake. Many years of research have succeeded in developing improved construction techniques and the related codes for building design and construction has been adopted in some countries, for example, Peru; however, these efforts are not directly applicable to existing nonengineered constructions, which represent a real seismic risk [3]. Considering that there are too many structures of this kind throughout many developing and underdeveloped countries and a majority of their residents have little financial affordability, seismic retrofitting of these buildings should be taken as a priority rather than reconstruction. It is obvious that the proposed retrofitting technique should be simple, feasible, and economical, as well. Therefore, it is imperative to find low-cost retrofitting alternatives, capable of providing these buildings with sufficient confinement and integrity as to withstand severe earthquakes without collapse [4]. In the case of old buildings, which are usually of historical value, the implemented methods should also have no conflicts with the appearance and character of these buildings. Unlike other more commonly used structural systems—that is, brick masonry, steel, and reinforced concrete structures for which regulations exist for their seismic retrofit—a lack of retrofit codes, or even construction design codes in many countries, makes retrofitting of nonengineered buildings more challenging. In the absence of robust design procedure for seismic retrofit of these buildings, reliance on experience, available tests results, and, more importantly, engineering judgments plays a significant role. Apart from the fact that nonengineered buildings cover a large spectrum of structural systems, for example, stone masonry, adobe buildings, etc., the construction details and materials of each particular structural system can be very divergent in different regions.

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FIG. 6.2 An example comparing damage to a properly constructed “nonengineered” building and an improperly constructed “engineered” building. (A) An adobe building with slight damage. (B) A collapsed RC frame; the structural deficiencies include, but are not limited to, passing column bars outside the beam bars in the connection zone, wrongly-located split point in the column; very poor construction quality of split point in terms of bonding of concrete; and low-quality concrete. ((A) Photo taken by Mohammad Yekrangnia. (B) Permission from Dr. A.S. Moghadam.)

This variety results in different behavioral characteristics, failure modes, and different performance levels during earthquakes. An example of two different failure modes caused from different construction details of adobe buildings in two different parts of the world is shown in Fig. 6.3. As a result, a particular retrofit scheme which suits a building type in one region may not be beneficial for the same structural system which is found in another part of the world; hence retrofit methods and especially details for each structural system is subjective to a specific details practiced in a particular region. Consequently, the contents of this chapter are presented in the form of major successful experiences from several countries that contributed to seismic retrofit of nonengineered buildings. Among the various structural types which are categorized as nonengineered buildings, adobe buildings constitute one of the most abundant and vulnerable construction types. Adobe as the main construction material of the early construction was available in the region and easily worked by local masons. Adobe has many promising features for construction in arid regions; it provides effective thermal insulation, the clay-type soil from which adobe blocks are made is

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FIG. 6.3 Comparison of different construction details and failure modes of two buildings, both of which are categorized as adobe buildings. (A) Adobe building with very slender walls and very light inclined roof after the 2009 Yunnan, China earthquake. (B) Adobe building with thick short walls and very heavy arched roof after the 2003 Bam, Iran earthquake. ((A) Permission from EERI. (B) Photo taken by Mohammad Yekrangnia.)

found in many parts of the world, minimal skill and experience required for building adobe structures is required; and it is among the most energy-saving building construction [5]. Compared to brick-masonry buildings, adobe buildings are generally regarded as inferior in terms of seismic performance. However, thin-walled masonry structures can easily fail due to gravitational effects shortly after experiencing low to moderate seismic actions, whereas thick-walled adobe buildings can exhibit significant structural ductility even though the building’s construction material itself is brittle [6]. The main cause of severe damage and collapse of adobe buildings is lack of integrity of different structural parts including weak connection between perpendicular walls and also poor seismic performance of wall-to-roof connection, both of which endanger the “box-like” behavior of such buildings [4]. In this chapter, examples of various retrofitting methods and successful national experiences on risk reduction of adobe buildings are presented.

6.2 RETROFIT APPROACHES Structural stability is fundamental for the adequate performance of adobe buildings during major earthquakes and for designing appropriate retrofit measures. The walls of adobe buildings will crack during moderate to large earthquakes because massive adobe walls activate significant amounts of inertial forces, and both adobe blocks and mud mortar are low-strength materials. After cracks have developed, it is essential that the cracked elements of the structure remain stable, upright, and able to carry vertical loads. Compared to the more traditional force-based approach, which aims at increasing structural elements strength, the stability-based, retrofit design

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approach which was proposed by Tolles et al. [5] attempts to mobilize adobe’s favorable post-cracking, energy-dissipation characteristics while limiting relative displacements between adjacent cracked blocks. The purpose of this approach is, while accepting a level of damage in moderate to high earthquakes, to prevent severe structural damage and collapse. Thick adobe walls are inherently stable and have great potential for absorbing energy. These stability and energy-absorption characteristics can be enhanced by the application of a number of simple seismic improvement methods, as described in the following section.

6.3 RETROFIT METHODS In this part, a brief review is made on the commonly used retrofit methods for seismic performance improvements of adobe buildings around the world. The more comprehensive review on various retrofit methods for masonry construction can be found in Chapter 2.

6.3.1 Bond Beam on Top of the Walls Perhaps the most widely proposed method of strengthening adobe houses is the placement of bond beams in the upper perimeter of the walls [7] (Fig. 6.4) and confinement [8], as shown in Fig. 6.4. Nonetheless, this method requires severe intervention and sophisticated execution for the existing buildings, which makes it suitable for construction of new earthquake-resisting houses, not as a retrofitting solution.

6.3.2 Mesh on Walls Surfaces Reinforcing adobe walls with mesh grids has proved an effective technique for seismic retrofit of adobe buildings in the past earthquakes and by many

FIG. 6.4 Construction of bond beam. (Permission from Ms. Rachel Chapman (Ethnos 360))

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previously performed tests. The performance of the retrofitting mesh depends heavily on several parameters including the material (e.g., high carbon steel, tensioned steel, plastic, polymer), the type of mesh joints (i.e., solid, pressed), the shape of the mesh cells, the size of the cells, the diameter of the mesh elements, the material and thickness of the covering layer, and the mechanism and distance of the connections. Some experiments show the effectiveness of the polymer grids in providing the masonry and adobe walls with integrity and homogeneity [9–13]. Although stiff pre-stretched polymers are available, the hyper-elastic nature of some polymers which requires considerable deformations for the polymer to be activated in the load-bearing process can be a disadvantage. Apart from their high costs, polymer grids are vulnerable against ultra violet (UV) waves from the sun, especially in the long term. On the other hand, steel welded mesh, if coated with proper insulation against corrosion, has been adopted by some regions to be widely used for rural houses, for example, in Peru [14]. This kind of mesh also showed satisfactory improvement in the seismic performance of adobe and masonry buildings [15–17]. Nevertheless, the woven type of steel mesh which has pin connection between the mesh elements is not recommended for retrofit because it has no shear stiffness to prevent widening of diagonal shear cracks in masonry walls [14]. Plastic mesh [15] is usually used as fencing. Using chicken wire [18] and gypsum coating [19] can also provide acceptable integrity for adobe buildings; however, these solutions can meet lower performance levels, for example, collapse prevention for adobe buildings during moderate earthquakes when compared to other surface reinforcement options, for example, shotcrete. Examples of various types of mesh which can be used in retrofit of adobe buildings are shown in Fig. 6.5.

6.3.3 Straps and Reinforcing Bars Using vertical and horizontal rubber or steel straps on adobe and masonry walls in order to tie the discrete masonry blocks together is another method for seismic performance improvement of these buildings (Fig. 6.6A). Drilling the walls from the top at subsequent distances and filling the holes with rods and grout greatly increases the shear strength of such walls. Moreover, the reinforcement of walls can be done by tying the vertical retrofitting components to the walls by nylon threads. The rods can be in the form of steel bars, fiber reinforced polymer (FRP), cane, or bamboo (Fig. 6.6B, C). In the case of using straps, these elements can be prestressed in order to increase walls’ tensile and shear resistance. Some studies on the aforementioned retrofit systems are [6, 20–22].

6.4 GOOD EXPERIENCES Speaking of adobe buildings, robust formulations and modeling details in the design procedure for seismic retrofit of these buildings are absent. Unlike other structural systems that have been addressed in seismic design codes, for

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FIG. 6.5 Various types of mesh. (A) Steel woven mesh. (B) Steel welded mesh. (C) Steel bar grids with large cells. (D) Polymer mesh with diamond-shape cells. (E) Chicken wire. (F) Plastic meh with hexagon-shape cells.

example, ASCE 41, seismic retrofit of adobe buildings relies greatly on engineering judgment, experience, and authentic experimental data. In the following, several years of research and experience from around the world in the area of seismic retrofit of adobe buildings are presented.

6.4.1 US Experiences 6.4.1.1 Introduction Many of the early structures that date back to the Spanish colonial period in the southwestern United States were built of mud brick, or adobe. Approximately 900 adobes were originally constructed in the San Francisco Bay Area alone; the number had dropped to about 65 by the 1940s. Today, fewer than 350

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Advanced Design Examples of Seismic Retrofit of Structures

FIG. 6.6 Examples of using straps and reinforcing bars on adobe walls. (A) Prestressed tire straps [22]. (B) Effectiveness of external bamboo bars in stabilizing cracks [23]. (C) Internal FRP bars. ((B) Permission from Taylor and Francis. (C) Permission from Dr. Nanni.)

historic adobes remain in California. These buildings are among the most vulnerable buildings during earthquakes. For instance, the 1971 San Fernando earthquake in Los Angeles County destroyed the San Fernando Mission church, which was the largest and most elaborately decorated residential adobe structure in California [5]. The Getty Seismic Adobe Project (GSAP) initiative, first discussed in 1990 following the 1989 Loma Prieta earthquake in California which had severely damaged or destroyed historic adobe buildings in the area, was formed with the aim of minimizing the earthquake-caused damage to historic adobe buildings in seismic areas of the southwestern region of the United States as much as possible. Because the earthquake codes for seismic stability in California and elsewhere require intrusive retrofitting to stabilize historic structures, the primary objective of the GSAP initiative was to find technologically sympathetic and minimally invasive methods of stabilizing these structures. The objective was not to make adobes “earthquake-proof,” but rather to ensure safety by preventing the overturning of walls during a seismic event. In this part, US

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experiences in seismic retrofitting of adobe buildings which centers on several years of research by GSAP are presented [5]. The objectives of seismic retrofit measures that satisfy conservation criteria are ranked in order of importance are: (a) provisions for life safety during the most severe earthquakes; (b) limitation of damage to repairable levels during the most severe earthquakes; and (c) minimizing damage during moderate earthquakes. It is noteworthy that different retrofit measures may be used to satisfy each of these objectives. The life-safety objective must be ranked first, but the second and third objectives are interchangeable depending on the goals of the decision makers [5]. Although this part can be considered as examples of conservation of historic buildings, the methods and approach implemented here can be easily extended to other residential buildings of this kind.

6.4.1.2 Law Enforcement and Retrofit Measures In California, construction of new unreinforced masonry buildings was prohibited in 1933, and state law (enacted in 1986) required seismic retrofitting of existing structures. Nowadays, most URM buildings have undergone retrofitting [24]. There is particular cause for concern in regions which can generate strong earthquakes, but only rarely. Such regions may not have regulations limiting the construction of URMs, or have only implemented them recently. For example, the Wasatch Fault in the US state of Utah closely parallels the state’s most populous metropolitan area, the Wasatch Front. This has a population of 2 million, and contains 200,000 URMs compared with the entire state of California’s 25,000 [25]. Utah has recently retrofitted many public URMs to withstand earthquakes better, but most URMs in the state are private homes. 6.4.1.3 Survey of Damage to Adobe Buildings The 1994 Northridge earthquake offered a rare opportunity to observe the huge loss that could occur to the remaining historic adobe buildings in California. The field data collected following this earthquake has led to a better general understanding of the seismic performance of adobe buildings. A total of 19 historic adobe buildings were surveyed after the earthquake and the observed structural damage were classified into several groups according to Table 6.1. Examples of damage to the surveyed buildings are presented in Fig. 6.7. The GSAP team also classified the severity of the different damage types in terms of their effect on both life safety and the historic fabric of the building. More information about this damage may be found elsewhere [26]. The extent of damage to an adobe structure subjected to an earthquake is a function of four major factors: (a) the severity of the ground motion;

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TABLE 6.1 Historic Adobe Earthquake Damage Typologies [26] Type Out-ofplane

Abbreviation

Description

Gable end failure

(DT-1)

Gable-end walls suffer severe cracking that often leads to instability. Gable-end walls are tall, poorly attached to the building, have large slenderness ratios, and carry no vertical loads

Flexural cracks and collapse

(DT-2)

Flexural cracks begin as vertical cracks at transverse walls, extend downward vertically or diagonally to the base of the wall, and extend horizontally to the next perpendicular wall. The existence of cracks does not necessarily mean that a wall is unstable. Walls can rock without becoming unstable. After cracks have developed, the out-of-plane stability of a wall is dependent on the slenderness ratio, connection to the structure, vertical loads, and the condition of the wall at its base

Mid-height cracks

(DT-3)

Long, tall, and slender single-wythe walls, or long, tall, double-wythe walls with no header courses interconnecting the wythes are susceptible to mid-height horizontal cracking from out-of-plane ground motion

(DT-4)

Classic X-shaped or simple diagonal cracks are caused by in-plane shear forces

Vertical

(DT-5)

Vertical cracks can develop at corners in one or both planes of intersecting walls

Diagonal

(DT-6)

Diagonal cracks that extend diagonally from the bottom to the top of a wall at a corner may be caused by in-plane shear forces or out-of-plane flexural forces

Cross

(DT-7)

A diagonal crack extending from the bottom corner can combine with a diagonal crack from the top corner forming a wedge-shaped section

In-plane

Corner damage

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TABLE 6.1 Historic Adobe Earthquake Damage Typologies—cont’d Type

Abbreviation

Description

Cracks at openings

(DT-8)

Cracks often begin at the tops of doors and openings and propagate upward vertically or at a diagonal. Cracks can also develop at the lower corners of windows. These cracks may be caused by in-plane or out-ofplane motion

Damage at intersection of perpendicular walls

(DT-9)

Perpendicular walls can separate from each other and cause damage by pounding

Slippage between walls and wood framing

(DT-10)

Roof, ceiling, and floor framing often slips at the interface with the adobe walls. Wood framing is often not or inadequately attached to the adobe walls in historic adobe buildings

Damage at anchorage and cross-ties

(DT-11)

Crack damage often propagates from structural anchorage and crossties. It is difficult to avoid stress concentrations at these locations which generally lead to cracks and other damage such as crushing of material

Local section instability

(DT-12)

Local wall sections can become unstable as the result of cracks that develop at corners of buildings and/ or window and door openings

Horizontal upper-wall cracks

(DT-13)

Horizontal cracks may develop near the tops of walls when there is a bond beam or the roof is anchored to it. These cracks are caused by the combination of horizontal forces and the small vertical compressive stresses near the top of the wall

Moisture damage contributions to instability

(DT-14)

Moisture damage at the base of a wall can result in wall instability. In some cases, the wall may collapse out-of-plane because one side of the wall has been weakened or eroded. In other cases, saturation or repeated wet/dry cycles can weaken the lower adobes causing weakened slip-planes at the base of the wall along which the wall can slip and collapse

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Vertical corner crack Cross cracks at corners

Local section instability

Horizontal upper-wall crack

Damage at openings Diagonal corner crack

Gable-end wall collapse

Damage at intersection of perpendicular walls

FIG. 6.7 Typical failure typologies observed in historic adobe buildings after the Northridge earthquake [27]. (Permission from Getty Adobe.)

(b) the geometrical characteristics of the structure, that is, the configuration of the adobe walls, roof, floors, openings, and foundation; (c) the existence and effectiveness of seismic retrofit measures; and (d) the condition of the building at the time of the earthquake [26]. Geometry plays an important role in determination of seismic response of adobe buildings. For example, thin adobe walls with a high slenderness (height-to-thickness) ratio will perform differently than a thick wall with a small slenderness ratio. A freestanding adobe wall will show different response characteristics compared to that in a wall buttressed by perpendicular walls. The existence of openings greatly changes the adobe walls failure patterns compared to that in a corresponding solid wall. In many cases, previously installed seismic retrofit measures have a positive effect on the seismic performance of an adobe building. Bond beams, buttresses, tie-rods, and other structural elements that add resilience and/or continuity to a structural system are beneficial. Roof and mid-height flooring/ceiling systems can significantly affect the overall performance. Good connections between adobe walls and the roof and floor can greatly improve the seismic performance by providing integrity. Negative effects can also result from seismic retrofit measures by creating stress concentrations leading to other types of damage [26]. The condition of a building at the time of an earthquake plays a significant role in its performance. Preexisting cracks, perhaps resulting from previous

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FIG. 6.8 Poor bonding of a brick masonry wall. (Photo taken by Mohammad Yekrangnia.)

earthquakes, may isolate a wall section, causing it to act as a freestanding wall; other walls may be leaning, affecting their stability. Water damage is perhaps the most important existing condition that affects the performance of an adobe building: it can alter the strength of adobe to such an extent that a wall may be unable to support its own weight. The integrity of the adobe blocks also influences seismic performance of adobe buildings. Masonry integrity is a function of the bonding pattern and the cohesion between the adobe blocks and mortar. When there is poor bonding (Fig. 6.8), the walls may not behave monolithically as well-constructed adobe walls typically do. In addition, the effects of preexisting conditions in terms of moisture and unrepaired cracks can have profound effects on seismic response of adobe buildings. Moisture rising from the base of adobe walls can drastically reduce the compressive and shear strength of adobe material. Also, the previouslyinitiated and developed cracks and generally any form of structural damage can have a moderate to high negative influence on the performance of adobe buildings during earthquakes. The summary of the field observation of the extent of damage to adobe buildings after the Northridge earthquake is shown in Fig. 6.9. In this figure, the qualitative damage states proposed by Earthquake Engineering Research Institute (EERI) presented in Table 6.2 were used for determination of damage severity to the surveyed adobe buildings. Nonetheless, the more detailed damage classification by post-earthquake rapid assessment can be found in ATC 20 [28], AeDES [29], and other related documents.

6.4.1.4 Experimental Studies In order to understand better the common vulnerability of adobe houses and the effectiveness of different retrofit measure on the seismic performance

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Advanced Design Examples of Seismic Retrofit of Structures

EERI damage level

(E)

4

(D)

3

(C)

2

(B)

1

(A)

0

Good precondition, unretrofitted tted Poor precondition Retrofitted

Moderate damage- Cracks open

Severe damage- Large motion of cracked block section and potentioal collapse

Slight damageCrack initiation

0

0.1

0.2

0.3

0.4

0.5

0.6

PGA, g FIG. 6.9 Damage level versus estimated horizontal peak ground acceleration for historic adobe buildings after the 1994 Northridge earthquake (for damage states, refer to Table 6.2).

improvement of such buildings, the results of 10 years of research in the form of shaking table tests on nine small-scale (1:5) adobe specimens are presented in this section. This research was conducted by GSAP with the help of an international group of specialists and earthquake engineers, which was performed first on small-scale models at Stanford University [5]. Specimens’ Description The description of the small-scale model buildings are shown in Table 6.3. Listings of the 10 simulated earthquake motions based on the 1952 Taft earthquake in Kern County, California are presented in Table 6.4. The estimated peak ground acceleration (EPGA) is similar to the actual peak ground acceleration (PGA), except that the EPGA is determined from the response spectrum between 0.125 and 0.5 s. All models were shaken in a uniaxial east-west direction. The concept of Model 8 was to add further retrofit measures to minimize the extent of damage during very strong ground motions. That is because in some cases it is necessary to reduce intermediate levels of damage and to ensure that a building remains reparable. The tests on Models 4, 5, and 6 were performed to determine the effects of wall thickness on seismic behavior. As shown by the results of this study which are presented in the following, the specific retrofit system used was the dominant factor in the performance of these models and walls slenderness ratio was of secondary importance. The retrofit system used on Model 8 was similar to that of Model 7, except fiberglass center-core rods were installed in two adjacent walls. In general, the retrofit systems used in models 7 and 8 were extremely effective and greatly improved the overall seismic response. Further information about the specimens may be found elsewhere [5].

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TABLE 6.2 Standardized Damage States Damage State A None B Slight

C Moderate

D Extensive

E Complete

EERI Description

Commentary on Damage to Adobe Buildings

No damage, but room contents could be shifted. Only incidental hazard

No damage or evidence of new cracking

Minor damage to nonstructural elements

Preexisting cracks have opened slightly. New hairline cracking may have begun to develop at the corners of doors and windows or the intersection of perpendicular walls

Building may be temporarily closed but could probably be reopened after minor cleanup in less than one week. Only incidental hazard Primarily nonstructural damage; there also could be minor but nonthreatening structural damage; building probably closed for 2–12 weeks

Cracking damage throughout the building

Extensive structural and nonstructural damage. Long-term closure should be expected due either to amount of repair work or uncertainty of economic feasibility of repair. Localized, life-threatening situations would be common

Extensive crack damage throughout the building. Crack offsets are large in many areas, cracked wall sections are unstable, vertical support for the floor and roof framing is hazardous

Complete collapse or damage that is not economically repairable. Life-threatening situations in every building of this category

Very extensive damage. Collapse or partial collapse of much of the structure. Due to extensive wall collapse, repair of the building requires reconstruction of many of the walls

Cracks at the expected locations (opening, wall intersections, slippage between framing and walls). Offsets at cracks are small. None of the wall sections is unstable

(Adapted from E.L. Tolles, F.A. Webster, A. Crosby, E.E. Kimbro, Survey of Damage to Historic Adobe Buildings After the January 1994 Northridge Earthquake, Getty Conservation Institute, 1996.)

Retrofit Measures The retrofit measures on the model buildings included horizontal elements and, usually, vertical elements. The horizontal elements were nylon straps, a bond beam, or a partial wood diaphragm. The vertical elements were nylon straps, center-core rods, or local ties.

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TABLE 6.3 Description of Getty Seismic Adobe Project (GSAP) Small-Scale Model Buildings Model No.

Walls’ Slenderness Ratio

Walls

Type and Location of Retrofit

Simple model: Four walls with no roof system 1

7.5

NE

Upper horizontal strap

SW

Upper and lower horizontal straps Bond beam and center cores

2

7.5

NE SW

Bond beam plus vertical and horizontal straps

3

7.5

NE

Bond beam, center cores, and saw cuts; lower horizontal strap only in west pier of north wall

SW

4

5.0

NE SW

5

11.0

NE SW

6

11.0

NE SW

Bond beam, center cores, and internal lower horizontal straps Upper strap Upper and lower straps Control model, not retrofitted Control model, not retrofitted Bond beam, lower horizontal straps, and vertical straps Bond beam, lower horizontal strap, and local ties

Tapanco-style model: Gable-end walls with attic floor and roof system 7

5.0

NE SW

8

7.5

NE SW

9

7.5

NE SW

Partial diaphragms applied on attic-floor and roof framing; upper and lower horizontal and vertical straps Same as the NW walls, except vertical straps placed only on the piers between the door and window of the north wall Partial diaphragms applied on attic-floor and roof framing; upper and lower horizontal and vertical straps Partial diaphragms applied on attic-floor and roof framing; upper and lower horizontal straps and vertical straps; no lower horizontal strap on west wall; center-core rods Control model, not retrofitted Control model, not retrofitted

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TABLE 6.4 Simulated Earthquake Motions for Testing (Dimensions in the Prototype Domain) Test Level

Maximum EPGA (g)

PGD (cm)

I

0.12

2.54

II

0.18

5.08

III

0.23

7.62

IV

0.28

10.16

V

0.32

12.70

VI

0.40

15.88

VII

0.44

19.05

VIII

0.48

25.40

IX

0.54

31.75

X

0.58

38.10

The wood bond beams used on Models 3 and 6 were made of Douglas fir and were 3.8 cm wide and 1.0 cm thick. The bond beams were anchored to the walls with 0.3 cm diameter by 8.9 cm long coarse-threaded screws. The holes for the screws were predrilled before placement. The vertical and horizontal straps in the form of a 0.3 cm wide, flexible, and woven nylon strap typically used for a bootlace formed a loop either around the entire building or around an individual wall. The straps were passed through small holes in the wall and the two ends were knotted together. It is noteworthy that exterior straps were found to have been useful for stabilizing some Guatemalan adobes following the major earthquake in that region in 1976 [30]. Crossties in the form of 0.16 cm diameter nylon cord were installed to reduce the relative displacement across cracks. Moreover, when vertical and horizontal straps were installed on both sides of a wall, crossties were added to provide a through-wall connection and were inserted through small holes in the wall to reduce the out-of-plane displacement of the wall. Flat nylon straps that are commonly used in electrical work and referred to as cable ties were also used as crossties [5]. Although stresses in the crossties and vertical or horizontal straps were not measured on the models, none of the straps or crossties failed during any of the tests. The static breaking loads of the nylon straps and the cable ties were 102 and 27 kg, respectively. The center-core elements used in Models 2 and 3 were 0.3 cm diameter steel drill rods. The rods were directly drilled into the wall after flattening each end into a V-shaped form. These rods, which were left in place after drilling,

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Advanced Design Examples of Seismic Retrofit of Structures

functioned well throughout the testing sequence and were adequate for providing shear dowels between the cracked sections of the walls, especially for thick adobe walls. The center-core elements in Model 8 were 0.48 cm diameter steel rods anchored with an epoxy grout. The holes were drilled with a 0.6 cm diameter drill bit; however, because of the coarseness of the sand in the adobe mixture, the actual diameter of the holes was approximately 1.0 cm. All center-core rods were located entirely within the adobe wall and were not connected to the concrete base. When used in conjunction with wood bond beams, the rods were anchored to the bond beam with an epoxy resin [5]. As an example of the retrofit details, Fig. 6.10 shows the retrofit measures applied to Model 7 walls which consists of horizontal and vertical nylon straps with crossties. In this model, the south wall has only one vertical strap, and the east wall has none, whereas the north and west walls have four vertical straps each. Furthermore, partial diaphragms applied on attic-floor and roof framing in order to enhance adobe walls monolithic response. Details of retrofit measures applied at floor level of this model are shown in Fig. 6.11A, B. The attic-floor joists were anchored to the walls with small-diameter through-wall ties that were threaded through small holes in the center of the attic-floor joist, as shown in in Fig. 6.11C. The cord was passed through the wall on both sides of the joist and was attached to the horizontal strap on the wall’s exterior surface. Also, the roof rafters were anchored with screws to the bearing plates, and blocking was placed between each of the roof rafters (Fig. 6.11D). On the nonload-bearing walls, the roof rafters were placed directly on the wall’s both sides and tied together with bolts through the wall. The partial roof diaphragm was attached to the tops of the roof rafters. Coarse-thread screws 15 cm long extended through the roof diaphragm and blocking into the wall (Fig. 6.11E, F). These details were used to anchor the tops of the gable-end walls to the roof system. These connections worked well and did not fail during the tests [5]. The section sketch of retrofit measure on a wall-roof connection of Model 7 for load-bearing and nonload-bearing walls are shown in Fig. 6.12A, B, respectively. In part B of this figure, the nylon crosstie connects the horizontal perimeter strap to the floor joist through holes in the wall and joist. Roof framing in historic adobe buildings in the USA is often only lightly attached to the walls. Very often, the framing is not actually attached at all and just rests on top of the wall, and hence the roof framing can slide relative to the wall or can dislodge bricks at the top of the wall. Also, floor-to-wall connections can show unsatisfactory responses during earthquakes. As a solution, an exterior continuous plate can be attached to the through-wall floor joists. Lag screws are anchored into the end grain of the joist (Fig. 6.13) to prevent the relative movement of the walls and the floor joists. Bolting into the end grain of a joist is not generally recommended, but in this case, the joint had sufficient strength to prevent relative movement during the earthquake.

Single vertical strap on south wall

Note: Vertical straps on both sides of walls. Lower horizontal straps on both sides of walls. Upper horizontal strap on exterior only.

12 in. Slope 8 in. 12½ in.

Nylon straps around exterior 6 in.

58½ in.

24 in.

58½ in.

South elevation

Crosstle locations shown by black dots

Vertical nylon straps on the north and west walls

Examples of Nonengineered Buildings Chapter

Nylon straps on both sides of lower wall

42½ in.

6

West elevation

FIG. 6.10 Retrofit measures applied to Model 7 walls. (Adapted from E.L. Tolles, E.E. Kimbro, F.A. Webster, W.S. Ginell, Seismic Stabilization of Historic Adobe Structures, The Getty Conservation Institute, Los Angeles, 2000.)

409

North elevation

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Advanced Design Examples of Seismic Retrofit of Structures

Horizontal strap around exterior Partial wood diaphragm Through-wall ties around the horizontal strap and through joists or around ledger (nylon string)

(B)

(A)

(C)

(E)

(D)

(F)

FIG. 6.11 Retrofit measures on Model 7 roof. (A) Attic-floor framing and partial diaphragm, made of wood. (B) Attic plan, showing retrofit measures applied at floor level. (C) Inside of attic floor, showing through-ties connecting joist and wall. (D) Roof line of load-bearing wall. (E) Detail at east gable-end wall, showing anchor bolts and one-half of partial diaphragm exposed. (F) Completed roof system. (Adapted from E.L. Tolles, E.E. Kimbro, F.A. Webster, W.S. Ginell, Seismic Stabilization of Historic Adobe Structures, The Getty Conservation Institute, Los Angeles, 2000.)

Details of vertical retrofit elements on adobe wall are shown in Fig. 6.14. The diameter of center-core rods used in full-scale walls can range from 12 to 25 mm, and the rods should be inserted in holes that are sized according to the needs of the material used for anchoring the center-core rods. The GSAP research was based on a prototype adobe wall that was 41 cm thick, and 17 mm diameter center-core rods worked well even when used without grout. Smalldiameter rods and holes less than 50 mm in diameter should be used because

(B)

FIG. 6.12 Section sketch of retrofit measure on of wall-roof connection of Model 7. (A) Load-bearing wall, roof, and attic floor, showing retrofit measures. (B) Nonload-bearing wall. (Adapted from E.L. Tolles, E.E. Kimbro, F.A. Webster, W.S. Ginell, Seismic Stabilization of Historic Adobe Structures, The Getty Conservation Institute, Los Angeles, 2000.)

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(A)

6

411

412

Wood ledger

Floor sheathing

Floor joist

Threaded lag screw, anchored into end grain of floor joists

(A)

(B)

FIG. 6.13 Floor-to-wall connection. (A) Side of wall showing continuous ledger and lag screws driven into the end of a joist [5]. (b) Details showing lag screw, ledger, and joist [5]. (Permission from Getty Adobe.)

Advanced Design Examples of Seismic Retrofit of Structures

Adobe wall Stucco

Examples of Nonengineered Buildings Chapter

Wood top plate

6

413

Wood top plate

Vertical nylon straps

Center-core rods

Nylon crossties

Oversized holes for placement of center-core rods

Adobe wall

Adobe wall Buckles

Plastic pipes at base of wall

Drill holes to foundation level

(A)

(B)

FIG. 6.14 Details of vertical retrofit elements on adobe wall. (A) Straps and crossties. (B) Centercore rods. (Adapted from E.L. Tolles, E.E. Kimbro, W.S. Ginell, Planning and Engineering Guidelines for the Seismic Retrofitting of Historic Adobe Structures, The Getty Conservation Institute, Scientific Reports Series, Los Angeles, California, 2002.)

(A)

(B)

FIG. 6.15 Implementation of center-core on Model 8. (a) Center-core holes being drilled in the west gable-end wall. (b) Epoxy resin grout being injected into model. (Adapted from E.L. Tolles, E.E. Kimbro, F.A. Webster, W.S. Ginell, Seismic Stabilization of Historic Adobe Structures, The Getty Conservation Institute, Los Angeles, 2000. (A, B) Permission from Getty Adobe.)

larger-diameter center-core elements may act as “hard spots” and serve to split the low-strength adobe wall [6]. The two main steps of implementation of center-core are shown in Fig. 6.15 which was constructed on Model 8. Injection of Epoxy resin grout was used to attain continuity between the center-core rods and the adobe wall. Results The results of the study by GSAP indicate using vertical straps was most effective for reducing the risk of out-of-plane wall collapse. Vertical straps had a

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Advanced Design Examples of Seismic Retrofit of Structures

negligible effect on the initiation and early development of cracks in the walls. However, strapping system controlled the relative displacement of cracked sections of walls with more significant displacements or offsets. In-plane damage was much less affected by vertical straps. This is largely because in-plane offsets are smaller and can benefit from the considerable residual strength in this direction. Similar to their effects on out-of-plane motion of the walls, straps can only prevent large displacements and crack offsets, as well as preventing piers from becoming unstable. Moreover, vertical center-core rods were found to be very influential in delaying and limiting the damage to walls under both in-plane and out-of-plane directions. Contrary to straps which were ineffective in delaying the initiation of cracks, the center-core rods were pretty effective in this regard. Epoxy grout surrounding the rods which was soaked into the adobe unevenly provided effective shear transfer between the adobe and the steel rods. Some cracks in the in-plane walls that started at the corners of the door and window openings propagated to a center-core rod and then were arrested, thus indicating the rods acted as dowel pins that minimized the relative motion of adobe blocks. The cracks never became severe [5]. Also, the center-core rods acted as reinforcing elements in the out-of-plane walls. Generally speaking, the effects of slenderness ratio were noticeable in outof-plane response of the walls, whereas this parameter had negligible effects on the walls’ in-plane performance. The thin walls easily rocked about their bases (Fig. 6.16a), and the principal lateral support was provided by the bond beam. This behavior was not observed in the walls of moderate thickness with the same bond beam because the thickness of the wall did not permit easy rocking about the base (Fig. 6.16b). In addition, the out-of-plane motion at the top of the walls was not amplified as it was in the thinner walls. The effectiveness of the retrofit measures during test level VI is shown by the performance of Models 8 and 9. The out of plane unretrofitted gable-end walls collapsed during test level VI (Fig. 6.17A). The retrofitted gable-end walls

(A)

(B)

FIG. 6.16 Comparison of damage in the East wall (out-of-plane direction) after test level VII. (A) Model 6 (SL:11). (B) Model 2 (SL:7.5). (Adapted from E.L. Tolles, E.E. Kimbro, F.A. Webster, W.S. Ginell, Seismic Stabilization of Historic Adobe Structures, The Getty Conservation Institute, Los Angeles, 2000.)

Examples of Nonengineered Buildings Chapter

(A)

(B)

(C)

(D)

6

415

FIG. 6.17 Comparison of control Model 9 and retrofitted Model 8 after test level VI. (A) East wall of Model 9. (B) East wall of Model 8. (C) North wall of Model 9. (D) North wall of Model 8. (Adapted from E.L. Tolles, E.E. Kimbro, F.A. Webster, W.S. Ginell, Seismic Stabilization of Historic Adobe Structures, The Getty Conservation Institute, Los Angeles, 2000.)

experienced some cracks, but the model was very stable (Fig. 6.17B). Damage to the in-plane unretrofitted walls was similar (Fig. 6.17C), and those in the retrofitted model (Fig. 6.17D) suffered some additional cracks not observed in the unretrofitted model. These further cracks can be justified, by the additional load transferred through the partial diaphragms and upper horizontal straps. The light retrofit system used on the thin south and west walls of Model 6, which consisted of a bond beam and vertical local ties, acceptably withstood the motions of test level VII, but the out-of-plane wall collapsed during test level VIII (Fig. 6.18A). By comparison, the opposite walls of the same model were stable during this test level (Fig. 6.18B), a result that can be attributed to the effectiveness of the vertical straps. Similarly, moderately thick walls with a bond beam and center-core rods also responded well during test level VIII (Fig. 6.18C). Test level IX was even more of a challenge to some of the lightly retrofitted model buildings. A large part of the in-plane thin wall with bond beam and local ties collapsed during this test (Fig. 6.19A). Again, the light retrofit system used on this thin wall was not sufficient to provide resistance to the major dynamic

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Advanced Design Examples of Seismic Retrofit of Structures

(A)

(B)

(C) FIG. 6.18 Comparison of out-of-plane performance after test level VIII. (A) Lightly retrofitted walls (Model 6, West wall). (B) More complete retrofits that included vertical straps (Model 6, East wall). (C) Center cores (Model 2, East wall). (Adapted from E.L. Tolles, E.E. Kimbro, F.A. Webster, W.S. Ginell, Seismic Stabilization of Historic Adobe Structures, The Getty Conservation Institute, Los Angeles, 2000.)

(A)

(B)

(C) FIG. 6.19 Comparison of in-plane performance after test level IX. (A) Lightly retrofitted walls (Model 6, South wall). (B) More complete retrofits that included vertical straps (Model 6, North wall). (C) Center cores (Model 2, North wall). (Adapted from E.L. Tolles, E.E. Kimbro, F.A. Webster, W.S. Ginell, Seismic Stabilization of Historic Adobe Structures, The Getty Conservation Institute, Los Angeles, 2000.)

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417

demands. Compared to local ties, the addition of vertical straps better improved the performance of the thin walls. The condition of the two in-plane walls shows the difference between the use of local ties (Fig. 6.19A) and the use of vertical straps (Fig. 6.19B). Good behavior was also observed in the moderate walls with a bond beam and center cores during test level IX (Fig. 6.19C). In addition to the partial diaphragms on each building, the minimum retrofits for out-of-plane gable-end walls of the tapanco-style models were upper and lower horizontal straps. The only gable-end wall that did not have lower horizontal straps was the west wall of Model 8 (Fig. 6.20D), which had center-core rods. In Model 7, the thick East wall (Fig. 6.20A) which remained stable had only upper and lower straps. There was a large offset at the mid-height horizontal crack, because there was little restraint across this crack plane. Vertical straps provided additional restraint that minimized the extent of residual crack offsets. In Model 7, the performance of the West wall (Fig. 6.20B) was better than that of the East wall, because the vertical straps provided restraint for block movements along horizontal and diagonal cracks.

(A)

(B)

(C)

(D)

FIG. 6.20 Comparison of the out-of-plane wall performance with differing retrofit systems after test level X. (A) East wall of Model 7. (B) West wall of Model 7. (C) East wall of Model 8. (D) West wall of Model 8. (Adapted from E.L. Tolles, E.E. Kimbro, F.A. Webster, W.S. Ginell, Seismic Stabilization of Historic Adobe Structures, The Getty Conservation Institute, Los Angeles, 2000.)

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Advanced Design Examples of Seismic Retrofit of Structures

The retrofit system used on Model 8 was modified slightly to try to decrease the amount of offset at horizontal cracks. The East wall (Fig. 6.20C) had vertical straps, and the wall crossties were spaced closely together to limit the relative displacement between adjacent blocks. The displacements in the gable-end wall were limited to small amounts, which was an improvement over the performance of Model 7, but was not as dramatic as that achieved by the installation of center-core rods. The performance of the West wall of Model 8 proved the effectiveness of center-core rods in reducing the offset across cracks during out-of-plane ground motions (Fig. 6.20D). Most of this wall, which was retrofitted with epoxied center-core rods, experienced minimal cracks and no visible offsets across center-core rods. On the other hand, severe damage to this wall occurred near the base in the area where the center-core rods did not extend; this indicates considerable energy dissipation in the areas outside of the center-core rods. If the center-core rods had extended into the foundation, there may have been additional damage in the upper part of the wall, since there would have been no clear area for energy dissipation [5]. In the in-plane direction, center-core rods were also most effective at preventing permanent offsets. In general, the cracks expanded moderately in each of the walls except where epoxied center-core rods were installed (Fig. 6.21). The horizontal straps restrained the development of permanent offsets in the

(A)

(B)

(C)

(D)

FIG. 6.21 Comparison of the in-plane wall performance with differing retrofit systems after test level X. (A) South wall of Model 7. (B) North wall of Model 7. (C) North wall of Model 7. (D) South wall of Model 7. (Adapted from E.L. Tolles, E.E. Kimbro, F.A. Webster, W.S. Ginell, Seismic Stabilization of Historic Adobe Structures, The Getty Conservation Institute, Los Angeles, 2000.)

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419

walls but still allowed displacements of the blocks. Stiffer straps may have been used to provide greater restraint against damage, but two factors would need to be taken into account: (1) a failure plane might develop just above the strap that would permit slippage; or (2) the strap may dig into the adobe material and loosen, even with a stiffer strap. To try to control the latter, a wire-mesh screen was added at the exposed corners. However, the straps were still able to dig into the adobe at the through-wall holes. Minimal damage was observed in the in-plane wall of Model 9, where the vertical center-core rods were used (Fig. 6.21D) [5]. The summary of all the results for tested wall pairs are presented in Table 6.5.

TABLE 6.5 Summary of Results for Wall Pairs After GSAP Tests [5] Model No. and Walls

Collapse Level

Principal Retrofit Measures

Comments

5

VII

None (control model)

Complete collapse

4 NE

No collapse

Upper horizontal strap

Basically stable with substantial block offsets

1 NE

X

Upper horizontal strap

Out-of-plane collapse that may have been prevented by more closely spaced crossties

4 SW

No collapse

Upper and lower horizontal straps

Basically stable with substantial block offsets

1 SW

No collapse

Upper and lower horizontal straps

Close to collapse during final test

6 SW

VIII

Bond beam, lower horizontal straps, and local ties at piers between the door and windows

Collapse of out-of-plane west wall during test level VIII; collapse of most of south wall during test level IX

6 NE

No collapse

Bond beam, lower horizontal straps, and vertical straps

Out-of-plane walls near collapse; center pier dislodged

2 NE

No collapse

Bond beam and centercore rods

Stable behavior in all tests

2 SW

No collapse

Bond beam, lower internal horizontal straps, and vertical straps

Stable behavior in all tests Continued

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Advanced Design Examples of Seismic Retrofit of Structures

TABLE 6.5 Summary of Results for Wall Pairs After GSAP Tests—cont’d Model No. and Walls

Collapse Level

Principal Retrofit Measures

3 NE

No collapse

Bond beam, lower internal horizontal straps, and vertical center-core rods

Stable behavior in all tests

3 SW

No collapse

Bond beam, lower internal horizontal straps, and vertical center-core rods

Stable behavior in all tests

9

VI

None (control model)

Complete collapse of gable-end walls

8 NE

No collapse

Partial wood diaphragms—upper strap at attic-floor level, lower straps, and vertical straps

Stable behavior in all tests

8 SW

No collapse

Partial wood diaphragms—upper strap at attic-floor level, lower straps, and vertical centercore rods; no lower strap on west wall

Stable behavior in all tests

7 NE

No collapse

Partial wood diaphragms—upper strap at attic-floor level, lower straps, and vertical straps

Stable behavior in all tests

7 SW

X

Partial wood diaphragms—upper strap at attic-floor level and lower straps; no vertical straps

Partial collapse of south (in-plane) wall during test level X

Comments

6.4.1.5 Comparison of Test Results and Field Observations Comparison of laboratory tests and field observations of the Northridge earthquake show good correlation. The important observations can be summarized as follows: l

l

Below 0.15 g, little or no damage was observed in adobe buildings with good conditions. Starting around 0.2 g, minor and more severe cracks were observed in intact buildings and previously damaged structures, respectively.

Examples of Nonengineered Buildings Chapter

l

l

6

421

From 0.25 to 0.35 g, damage became increasingly severe. The number and length of cracks increased throughout the structure, and some permanent offsets were observed. Above 0.35 g, severe damage occurred throughout the structure, and in some cases, wall instability was observed.

In general, the overall crack patterns observed in the model buildings were similar to those found in historic adobe buildings after the Northridge earthquake.

6.4.1.6 General Remarks General recommendation for retrofit of adobe buildings are as follows: l

l

l

Minimum levels of intervention: for structures that have moderately thick or thick walls, it may be possible to attain reasonable levels of seismic safety and significantly reduce the life-safety hazard simply by using anchors at the tops of walls. Moderate levels of security and intervention: a more detailed design may include vertical and horizontal straps, structural redundancy, strengthening of the roof system, and/or addition of bond beams. High levels of security and damage control: center-core rods coupled with other retrofit measures can be used to increase levels of safety greatly, reduce the potential hazard to the historic fabric, and reduce the likelihood of severe structural damage.

Recognition of global design issues is the starting point in the design process. The basic elements of global design are as follows: l

l

l

Upper-wall horizontal elements (Fig. 6.22A): these are used to prevent outof-plane overturning and in-plane offsets. These can be a bond beam, straps in conjunction with the floor or roof system, or a partial diaphragm. Because of their importance in seismic improvement of adobe buildings, these elements are mandatory in all the retrofit projects. They provide anchorage to the roof or floor, increase out-of-plane strength and stiffness, and provide in-plane continuity. Lower-wall horizontal elements (Fig. 6.22B): these prevent displacements at the base of the walls stop cracked wall sections from “kicking out” in plane. They can consist of straps or cable elements or even buttresses. The use of these elements is also optional. Vertical wall elements (Fig. 6.22C): these add resilience and redundancy to the structural system and restrict the displacement of cracked wall sections. These can be surface straps or internal center-core rods. They are optional except for thin-walled structures. These elements can greatly increase the ductility of the walls. The need for vertical wall elements is most important for thinner adobe walls to minimize the possibility of out-of-plane failure. For thicker adobe walls, center-core elements tend to act as shear dowels rather than as flexural reinforcements.

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Advanced Design Examples of Seismic Retrofit of Structures

(A)

(B)

(C) FIG. 6.22 Horizontal and vertical elements. (A) Upper-wall horizontal elements. (B) Upper and lower horizontal elements. (C) Vertical elements in conjunction with upper and lower horizontal elements. (Adapted from E.L. Tolles, E.E. Kimbro, W.S. Ginell, Planning and Engineering Guidelines for the Seismic Retrofitting of Historic Adobe Structures, The Getty Conservation Institute, Scientific Reports Series, Los Angeles, California, 2002.)

6.4.2 Iranian Experiences 6.4.2.1 Introduction More than 95% of almost 4 million rural houses in Iran, housing more than 20 million people, have no lateral load-bearing elements and are vulnerable even to moderate earthquakes [31]. In Iran, one of the most dramatic examples is the 2003 Bam earthquake in which more than 40,000 people were buried under heavy masonry and adobe ruins. Based on the study by Ghannad et al. [32] from several field inspections throughout Iran, nine types of rural houses were recognized as representatives of existing rural houses. Examples of these structures together with brief description about each are presented in Table 6.6. Fig. 6.23 shows the distribution of these types in the whole country. This classification has been done according to the structural elements of rural houses consisting of roofs and walls. As can be seen, adobe buildings constitute 13% of all rural buildings in Iran. 6.4.2.2 Characteristics of Iranian Adobe Buildings Similar to other countries around the world, the construction practice of adobe buildings in Iran dates back centuries ago because of the available local material, that is, soil, its feasibility and low prices, and last but not least, compatibility of adobe properties with the local environmental demands. Iranian adobe

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TABLE 6.6 Typology of Rural Houses of Iran Type 1: Adobe walls with wooden flat roofs Location: Very popular, usually found in mountainous areas of north eastern and north western Iran. It is the dominant type of rural construction in Khorasan, Azerbaijan, and Ardebil. Description: Poor beam to wall, beam to column (in balconies) and wall to wall connections; no longitudinal or transverse anchorage at bearing supports of beams on the adobe walls, and inappropriate foundation. Walls are about 35–90 cm thick and weigh about 900–1200 kg/m2. Roofs are about 20–40 cm thick (excluding timbers) and weigh about 300–600 kg/m2; diameter of timbers is about 5–20 cm. Type 2: Adobe walls with arched roof Location: Arid and semiarid regions especially the deserts in central Iran, provinces: Kerman, Yazd, and south of Khorasan. Description: Several layers of mud-straw cover the roof making it too heavy; collapse of structure can be prevented if the supporting walls are maintained sound. Walls are about 40–120 cm thick and weigh about 900–1500 kg/m2. Roofs are about 30–50 cm thick and weigh about 450–750 kg/m2. Continued

TABLE 6.6 Typology of Rural Houses of Iran—cont’d Type 3: Stone walls with wooden flat roof Location: Mountainous and cold regions, provinces: Fars, Azerbaijan, and Khorasan. Description: Very heavy walls with poor wall to wall connection; the roof is covered with mud-straw every 2 or 3 years that makes it heavy; weak beam to wall connections; the mortar is mud, gypsum or sometimes no mortar is used; stone and mud mortar are not consistent materials. Walls are about 40–60 cm thick, more than 2 m high and weigh about 1000–1500 kg/m2. Type 4: Wooden walls (Zegali/ Zogmei) with inclined roof Location: Caspian coast in north of Iran, provinces: Gilan, Mazandaran, and Golestan. Description: Roof covering of this two-story building is of thatch while galvanized iron, mission tile or asbestos is also used widely; thatch is a good heat insulator; the structure of the roof is a truss built from wood and sometimes steel that results in a light roof. Walls are about 25–30 cm thick and weigh about 250 kg/m2. Type 5: Cement block walls with inclined roof Location: Caspian coast in north of Iran, provinces: Gilan, Mazandaran, and Golestan. Description: The structure of the roof and its cover are similar to Type 4. The walls are made of cement blocks about 22 cm thick.

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TABLE 6.6 Typology of Rural Houses of Iran—cont’d Type 6: Brick/cement block walls with wooden flat roof Location: Like other types with wooden flat roof, usually found in regions that wood is available. Description: Unreinforced masonry building with large openings and weak roof to wall connection. The walls are made of brick or cement blocks about 22 cm thick and weigh about 380 kg/m2. Type 7: Brick/cement block walls with arched roof Location: Arid and semiarid regions. Description: The roof is built with brick and covered with mud-straw. Wall to wall connection is limited to laying bricks alternatively in two perpendicular directions.

Type 8: Brick/cement block walls with jack-arch roof (without tie-beams) Location: In almost all rural regions. This type is built with industrial materials and as a result is not restricted to one specific climate. Description: Unreinforced masonry buildings, weak even against moderate earthquakes. Among problems: large openings, too much spacing between bearing beams, lack of technical know-how (e.g., using mud mortar instead of sand-cement mortar), and low ductility. Continued

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TABLE 6.6 Typology of Rural Houses of Iran—cont’d Type 9: Brick/cement block walls with jack-arch roof (with tie-beams) Location: In almost all rural regions. This type is built with industrial materials and as a result is not restricted to one specific climate. Description: Unreinforced masonry buildings, weak even against moderate earthquakes. Among problems: large openings, too much spacing between bearing beams, lack of technical know-how (e.g., using mud mortar instead of sand-cement mortar), and low ductility.

Adobe walls - wooden flat roof

6%

Adobe walls - arched roof

11% 2%

Stone walls - wooden flat roof

20% 14%

Wooden walls - inclined roof Concrete block walls - inclined roof

4%

5%

Brick/concrete block walls - wooden flat roof Brick/concrete block walls - arched roof

13% 25%

Brick/concrete block walls - jack arched roof (without tie-beam) Brick/concrete block walls - jack arched roof (with tie-beam)

FIG. 6.23 Distribution of Types of Rural Houses in Iran.

buildings are usually found in arid and semi-arid areas, mostly in rural regions. Although recently, the majority of large cities in Iran have undergone great changes with respect to construction types and development, some adobe buildings can still be found in urban and especially suburban areas [33]. Foundation, in its best form, is limited to about 50 cm of digging the ground and filling it with lime-sand mortar and stone or the wall materials up to ground level [32]. Generally, foundation construction is mostly affected by the topography of the site

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(A)

(B)

(C)

(D)

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FIG. 6.24 Examples of cluster arched roof adobe buildings in arid areas. (A) Yazd province. (B) Kerman province. (C) Khorasan province. (D) Kerman province. (Photos taken by Mohammad Yekrangnia.)

and the soil condition, and it is not considered serious, unless in regions having very loose soils such as organic soils. Adobe buildings in Iran usually constitute 1–20 units in each building (Fig. 6.24). Since these buildings are found in arid and semi-arid areas in the middle of deserts, cluster houses which are concentrated around a main yard are common [33]. The walls of these buildings are built by sun-dried adobe blocks with mud mortar in the bed joints. In some regions, depending on the available material, goats’ hair, palm leaves, or sand are added to the blocks and/or mortar to enhance their mechanical properties. The thick adobe walls which range from 0.6 to 1.8 m (shown in Fig. 6.25) ensure good insulation against the hot days and cold nights common in those regions. The average walls density in these buildings is 6%–14%. Generally speaking, the roof system of Iranian adobe buildings can be either wooden or arched. In mountainous regions and also those regions having access to wood, flat roofs are quite common. In this type of roof, wooden beams are used to carry the load of the roof, and then mud and branches of trees are used to cover the roof. These roofs are 20–40 cm in thickness and have mass per unit area from 300 to 600 kg/m2. The clear story height in these buildings is 2.7–3.0 m. The typical span of wooden flat roof is 2.5–4.0 m. An example of a wooden roof in Iranian adobe buildings together with the details is shown in Fig. 6.26.

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(A)

(B)

(C) FIG. 6.25 Examples of thick adobe walls in Iranian adobe buildings. (A) 87 cm. (B) 52 cm. (C) 73 cm. (Photos taken by Mohammad Yekrangnia.)

(A)

(B)

FIG. 6.26 Wooden flat roof. (A) Details. (B) An example. (Photo taken by Mohammad Yekrangnia.)

Arched roofs can be in the form of barrel, dome, polygonal, crescent, and complex (Tagh-o-Lenge), as depicted in Fig. 6.27. All of these roofs are made of smaller adobe blocks, gypsum-mud mortar, and, in some cases, wood timbers. These roofs are 30–50 cm in thickness and have mass per unit area of 450–750 kg/m2. Over time, several additional protective layers are mounted

adapted from Alalhesabi [34]

(A)

(Photo taken by Mohammad Yekrangnia)

adapted from Alalhesabi [34] (Photo taken by Mohammad Yekrangnia)

(B)

(C)

adapted from Zamrashidi [35]

(Photo taken by Mohammad Yekrangnia)

(Photo taken by Mohammad Yekrangnia) from http://www.calearth.org

(D) FIG. 6.27 Different types of adobe arched roofs in Iran. (A) Polygonal. (B) Barrel. (C) Crescent. (D) Dome. (E) Complex (Tagh-o-lengeh). ((A) Adapted from M. Alalhesabi, “Patterns of rural houses”, Housing Foundation of Islamic Revolution, Tehran, Iran, 1993 (photo taken by Mohammad Yekrangnia). (B) Adapted from M. Alalhesabi, “Patterns of rural houses”, Housing Foundation of Islamic Revolution, Tehran, Iran, 1993 (photo taken by Mohammad Yekrangnia). (Continued)

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(B)

(Photo taken by Mohammad Yekrangnia) adapted by Zamrashidi [35]

(E) FIG. 6.27, CONT’D (C) Adapted from H. Zamrashidi, “Architecture of Iran—Construction of Traditional Houses”, Zomorrod Publications, Tehran, Iran, 1995 (photo taken by Mohammad Yekrangnia). (D) From http://www.calearth.org (photo taken by Mohammad Yekrangnia). (E) Adapted by H. Zamrashidi, “Architecture of Iran—Construction of Traditional Houses”, Zomorrod Publications, Tehran, Iran, 1995 (photo taken by Mohammad Yekrangnia).)

Thatch

32 cm Mud Stone Adobe

FIG. 6.28 Placement of several layers insulation on a complex roof which makes it heavy.

on top of these roofs which make them heavier by aging (Fig. 6.28). The height of the wall up to the pivot of arch is 2.0–2.8 m. The typical span of dome arched roof is 4.0–5.0 m, while for barrel vault roof it ranges between 2.8 m and 3.6 m. Also for the latter, the longitudinal span can be greater than 5.0 m. The height of the arch usually ranges from 0.7 m to 1.5 m. Based on the study by Mousavi Eshkiki et al. [34], who surveyed eight seismic prone provinces in Iran, the average areas of doors, windows, and shelves are 1.9, 2.2, and 2.1 m2, respectively. There are two types of openings in Iranian adobe buildings: one type is wooden lintel and the other, which is more common for arched roof adobe buildings, is an arched shape without any lintel

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FIG. 6.29 Different types of opening. (A) Arched without lintel. (B) Rectangular with wooden lintel. (Photos taken by Mohammad Yekrangnia.)

(Fig. 6.29). Although in some cases, deterioration of the shallow foundations was observed if there was any, no damage due to insufficient foundation specifications were reported.

6.4.2.3 Survey of Damage to Adobe Buildings Observations from past earthquakes indicate that adobe buildings are among the most vulnerable structures in Iran, claiming more than 30,000 lives in earthquakes like 2003 Bam and 2005 Zarand. The main reason of this seismic weakness is detachment of the perpendicular walls and spoiling “box-like” behavior of buildings, which results in the collapse of the roof (Fig. 6.51). In addition, the thick walls impose considerable inertia forces during even moderate earthquakes which may surpass the strength of a typical building of this kind. As a result, construction of adobe buildings was abandoned in seismic regions by the first Iranian Code of Practice for Seismic Resistant Design of Buildings in 1988. The thick walls of adobe buildings, however, possess significant outof-plane capacity due their low slenderness ratio. Moreover, due to the larger weight of these walls, considerable in-plane shear resistance can be activated from the frictional mechanism. Examples of damage to adobe arched roofs during the 2005 Zarand earthquake are shown in Fig. 6.30. Typical failure modes of Iranian adobe buildings are more or less similar to those in the USA, which are shown in Fig. 6.7. There have been several earthquakes which, on a large scale, resulted in total destruction and major damage to adobe buildings in Iran; chief among them are 2003 Bam and 2005 Zarand. Unfortunately, no major systematic attempt was made to document the damage specifically to the adobe buildings in the affected areas. Moreover, the mentioned Iranian earthquakes were so severe that many buildings including the majority of the adobe buildings could not withstand them. As a result, there is no available document which classifies in detail the damage to Iranian adobe

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(A)

(B)

(C) FIG. 6.30 Examples of damage to adobe arched roof during the 2005 Zarand earthquake. (A) Partial collapse of the roof due to out-of-plane motions of the support wall. (B) Complete collapse of the roof. (C) Cracks in the roof caused by unbalanced motions of the support walls. (Photos taken by Mohammad Yekrangnia.)

buildings. Nevertheless, there are several cases in which out-of-plane failure of adobe walls resulted in loss of life of the residents of these buildings (Fig. 6.31).

6.4.2.4 Experimental Studies This section is dedicated to several years of research on seismic performance improvement of adobe buildings through static-cyclic and shaking table tests. These tests were performed by a team of researchers from the Sharif University of Technology (SUT), Tehran, Iran with the financial aid of Housing Foundation of Iran. The static-cyclic tests were performed in a structural laboratory at the Building and Housing Research Center (BHRC) in Iran and the shaking table tests were carried out at the Earthquake Engineering Research Center (EERC) of the SUT. Specimens’ Description and Retrofit Measures Static Cyclic Tests Fig. 6.32 shows the geometry of 12 2:3 scale wall specimens for static cyclic tests together with their name for static cyclic tests. In all the specimens, the thickness of walls is 42 cm with 1-cm mud mortar

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(A)

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433

(B)

FIG. 6.31 Out-of-plane collapse of nonload-bearing walls in barrel adobe roofs. (A) After 2003 Bam earthquake. (B) After 2005 Zarand earthquake. (Photos taken by Mohammad Yekrangnia.)

between bed joints only. In order to study different possible failure modes, walls with various opening configuration are considered. One group of the specimens is solid walls; the other group has a large central window and the other has a door and a small side window. The dimensions of the openings were selected based on the data from the previously performed field study of numerous adobe buildings throughout Iran by the SUT team. As shown in Fig. 6.32, three methods of retrofit for the specimens were considered, as follows: (i) The first method included installing welded steel mesh connected to the wall by through-wall connections at appropriate locations. The steel mesh had a 5 cm cell and consisted of 4 mm elements. The mesh was not attached to the foundation and it was extended up to 25 cm lower than the base of the windows. (ii) The second method included using steel strips with the connection details similar to that in the first method. The patterns of these strips, which included horizontal, vertical, and diagonal elements, were based on the observed crack pattern of the corresponding unretrofitted specimens. The width of all the strips was 10 cm and the thicknesses of the horizontal and vertical strips and diagonal stripes were 1 and 2 mm, respectively. (iii) In the third method, chicken wire was used together with 0.5 mm thickness, 50 mm wide steel stripes. Compared with the second method, the diagonal stripes were removed and the connection of the stripes which confined the chicken wire to the wall was made by nails without the need for drilling, hence its implementation was considerably simpler and faster. It is noteworthy that in all the implemented retrofit methods, both surfaces of the walls were retrofitted. As the results of the shaking table tests in the next section prove, there is no need to cover both faces of the adobe walls in practice. Covering both faces of the walls in the static cyclic tests was done in order to

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Advanced Design Examples of Seismic Retrofit of Structures

(A-I)

(B-I)

(C-I)

(A-II)

(B-II)

(C-II)

(A-III)

(B-III)

(C-III)

(A-IV)

(B-IV)

(C-IV)

FIG. 6.32 Wall specimens for static cyclic tests (dimensions in cm) [35]. (A-I) URA-WO. (B-I) URA-LW. (C-I) URA-DW. (A-II) SMRA-WO. (B-II) SMRA-LW. (C-II) SMRA-DW. (A-III) SSRA-WO. (B-III) SSRA-LW. (C-III) SSRA-DW. (A-IV) CWRA-WO. (B-IV) CWRA-LW. (C-IV) CWRA-DW.

maintain symmetry and prevent eccentricity of the walls with respect to in-plane axis. The details of through-wall connections used in methods i and ii are shown in Fig. 6.33. These connections are key in providing the thick double-wythe adobe walls integrity while experiencing severe ground motions. If the 8 mm connection rods are extended less than the whole wall’s thickness and are not anchored at the opposite face of the walls, they can only interlock some adobe blocks, and hence their efficiency would decrease. Fig. 6.34 shows the necessary steps of retrofitting adobe walls by steel wire mesh. As can be seen, this method does not require shotcreting or placing any form of mortar in order to increase the strength and stiffness of the retrofit elements. However, in order to prevent steel corrosion and invasion to the esthetics of the walls, mud-straw mortar or other similar coatings can be added to the

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FIG. 6.33 Schematic view of through-wall connections of mesh to the walls.

(A)

(B)

(C)

(D)

(E)

(F)

(G)

(H)

(I)

FIG. 6.34 Retrofitting steps by steel wire mesh. (A) Placement of mesh on wall. (B) Fixing mesh position by nailing. (C) Tying overlapping mesh sheets. (D) Drilling at intended locations. (E) Cutting in the shear keys. (F) Insertion of the connection rod. (G) Removing mud from threaded rod. (H) Using washer and tightening nots. (I) Completed retrofit scheme. (Photos taken by Mohammad Yekrangnia.)

mesh. Also, the mesh does not cover lower parts of the walls, and hence any requirement to strengthen the foundation of these buildings in order to transfer properly the forces from the mesh to the ground will be eliminated. The reason behind not extending the mesh to the base of the walls was based on the significant mass of adobe wall which ensures huge shear capacity, especially at the lower parts of these walls. As a result, the main target of using mesh with the

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details shown in Fig. 6.32 was transferring the cracks from the more dangerous upper parts of the wall to the lower parts in which initiation and propagation of cracks due to considerable shear capacity of the walls can be minimized. The only problem that may arise is the necessity of cutting through the shear key in areas where two mesh sheets overlap, in order to fit the steel box shown in Fig. 6.34E in one of the mesh cells. The steps for strengthening of adobe walls by steel strips are presented in Fig. 6.35. The necessary step in this retrofit procedure is initially to drill the positions of the connection rods with smaller drill. Then, after assembling the strips on the wall, these holes are widened by a larger drill which goes into the adobe wall. Similar to the steel mesh method, retrofitting adobe walls by steel strips does not require any form of mortar. Also, none of these strips is attached to the foundation of the wall. The main difficulty regarding implementation of this method is mapping the connection precise position on the overlapping areas of the strips; otherwise, the connection rod cannot pass through the eccentric holes on the two overlapping strips. The retrofitting steps by chicken wire with light steel strips are shown in Fig. 6.36. The main steps are tying several layers of chicken wire if necessary,

(A)

(B)

(C)

(D)

FIG. 6.35 Retrofitting steps by steel strips. (A) Mapping the strips on wall. (B) Initial drilling of the strips. (C) Final drilling of the strips. (D) Completed retrofit scheme. (Photos taken by Mohammad Yekrangnia.)

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FIG. 6.36 Retrofitting steps by chicken wire with light steel strips. (A) Tying the mesh sheets. (B) Installation on wall with nails. (C) Cutting the mesh at unwanted locations. (D) Placing the thin steel strips with nails. (E) Placing the thick steel strips with nails. (F) Completed retrofit scheme. (Photos taken by Mohammad Yekrangnia.)

installation of the layers on the wall by means of nails, cutting the nails with scissors at the intended locations (e.g., openings or ends of the walls), and placement of light steel strips at the intended locations which are connected to the walls by nails. A comparison of the implemented retrofit methods is provided in Table 6.7. As can be seen, using steel mesh is marginally cheaper and faster than the other methods. Also, because chicken wire requires considerable deformation to contribute in load-bearing, it is expected to provide integrity for the adobe blocks and prevent them from falling. As a result, this retrofit method can be regarded as a solution to the minimum requirement for retrofitting adobe buildings. Shaking Table Tests Two 2:3 scale specimens representing a common practice of dome-roof adobe buildings were tested on the shaking table. The first building was the unretrofitted control specimen, and the other, exactly duplicating the first one, was retrofitted. The specimens consisted of four types of walls having various types of openings which were exactly duplicating the wall specimens in static cyclic tests in “Static-Cyclic Tests” section. The geometrical characteristics of the specimens are shown in Fig. 6.37. The longitudinal and transverse components of the 2005 Zarand earthquake, Chatrood Station, are chosen as input excitations of shaking table tests. The two input components were scaled up in an equal ratio so that peak ground acceleration (PGA) of both components (in east-west direction) is scaled to 0.35 g, entitled 100% as of design earthquake based on the Iranian Code of Practice

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TABLE 6.7 Comparison of the Implemented Retrofit Methods

Retrofit Method

Cost Per Unit Wall Area ($/m2)

Construction Time for a 25 m2 Wall (day)

Steel mesh

6.5

2.0

Requires cutting through some shear keys

Steel strips

7.8

2.5

Requires re-drilling strips and locating the drilling position exactly at some locations

Chicken wire with light steel strips

6.9

2.2

Nailing is not as much effective as through-wall connection; chicken wire can only provide integrity during severe damage and does not contribute in enhancement of stiffness and strength

Problems

for Seismic Resistant Design of Buildings (Standard 2800) [36]. These specimens were subjected to sequential excitations with increasing intensity. The details of the sequential excitation in the specimens are shown in Table 6.8. Following the observations from the failure mode of the first specimen, retrofitting of the second specimen for shaking table tests followed these strategies: (i) preventing out-of-plane failure of the walls, even the small outof-phase movements of top of the walls and in doing so, preventing collapse of the roof; and (ii) minimizing initiation and propagation of the in-plane cracks at the upper parts of the walls and transferring them into the lower parts which possess higher levels of shear strength. From the previously performed shaking table tests, it was shown that only small forces were required to prevent the out-of-plane displacement of moderate to thick adobe walls. Simply anchoring the tops of the walls to the roof prevented collapse of out-of-plane walls, and thus the horizontal stiffness that could be imparted by a diaphragm was not needed. As noted by Tolles et al., the addition of only minor additional horizontal stiffness prevents the out-ofplane failure of adobe walls at high levels of acceleration and larger displacements [6]. However, this is not the case in the dome-roof specimens because even small out-of-phase displacement of the support walls results in the collapse of the roof. In the current study, in order to prevent out-of-phase movement of the walls and ultimately out-of-plane failure of these walls, four rods were drilled the upper parts of each wall which were passed through inside the

(D)

(C)

6

FIG. 6.37 Wall Specimens for Shaking Table Tests (Dimensions in cm) [4]. (A) Southern wall. (B) Northern wall. (C) Western wall. (D) Eastern wall.

(B)

(A)

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TABLE 6.8 Sequential Excitation in the Specimens (PGA Excitation to the Prototype is Scaled to 0.35 g) Step No.

Unretrofitted Specimen

Retrofitted Specimen

1

25%

25%

2

75%

100%

3

100%

125%

4

125% (collapsed)

150%

5

–

175%

60

60

110

60

60

specimen and anchored at the other end of the parallel wall. Details of using horizontal steel rods tying the parallel walls are shown in Fig. 6.38. In order to ensure the contribution of the rods even during small to moderate seismic actions, slight pre-stressing on the rods together with using spring washers at the anchorage location is recommended.

60

60

110

60

60

Plates and nuts

(A)

Steel horizontal rods

Washer and spring washer Nut Thread Horizontal steel rod (φ22 mm)

(B)

Steel plate

FIG. 6.38 Horizontal steel rods tying the parallel walls (dimensions in cm). (A) Plan view. (B) Details of connection to the walls.

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FIG. 6.39 Inertia forces and reactions on walls. (Adapted from K. Doherty, M.C. Griffith, N. Lam, J. Wilson, Displacement-based seismic analysis for out-of-plane bending of unreinforced masonry walls, Earthq. Eng. Struct. Dyn. 31(4) (2002) 833–850.)

When designing the rods which maintain the box-like behavior of the specimen and hence prevent the roof from falling down, the minimum section area can be calculated based on the force necessary to prevent the simultaneous out-of-plane failure of the two parallel walls. Based on Doherty et al. [37], and considering inverse triangular distribution of the induced accelerations across the wall 2 (Fig. 6.39),
gt the resultant of critical force acting at 3 wall’s height equals F0 ¼ Me H where Me is the active wall’s mass in the first mode which equals 34 M. Xn 2 m δ i i i¼1 Me ¼ Xn (6.1) m δ2 i¼1 i i where mi and δi are mass and displacement of the ith finite element in the wall. By taking the moment at the wall’s toe, the rod’s minimum diameter is calculated. In determining the minimum diameter of the rods, it was conservatively assumed that the two parallel walls react completely out-of-phase and, as a result, the design force of the rods is two times larger than that of a single wall. In addition, the effect of openings in reducing the wall’s mass was conservatively neglected.   gt2  2 H ¼ 4FH ð2 wallsÞ  F0 H ¼ ð4 rodsÞFH ! 2Me 3 H 3     3 gt 2 H ¼42F ! ρLtH 4 H 3 0 1  10 m  0:52m   2 3 kg A 2  2:00m  1800 3  3:6mm  0:52m  2:0m @ s 2:00m 4 m 3
 ¼ 4  2  F ! F ¼ 4:4kN, 0:6fy Ar ¼ 4:4kN ;4φ6mm fy ¼ 240MPa



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Advanced Design Examples of Seismic Retrofit of Structures

(A)

(B)

(C)

(D)

FIG. 6.40 Retrofitting steps by tying parallel walls. (A) Drilling in the desired location. (B) Insertion of the rod. (C) Tightening the nuts. (D) Completed retrofit scheme. (Photos taken by Mohammad Yekrangnia.)

Although computed as 6 mm, the diameter of the steel rods is conservatively selected as 22 mm because the force method approach in this case requires large deformation of the steel rods which can endanger the stability of the roof. It is worth mentioning that in the unretrofitted specimen, the roof collapsed because of the walls’ slight out-of-plane displacement. Therefore, the sensitivity of the roof stability to its boundary conditions movement is very high in the studied specimens compared to other adobe buildings tested previously [5,38]. This necessitates using retrofitting elements with significant stiffness in order to reduce relative movements and the selection of rods with larger diameter is justifiable in this regard. The steps for retrofitting the specimen by tying parallel walls are shown in Fig. 6.40. These include precise drilling of the walls at the intended locations, passing the steel rods between the parallel walls, placing the steel plates on the external face of the walls to prevent stress concentration on the walls from the rods, installation of washers, and tying the nuts with slight pre-stress. When the box-like behavior of the specimen is provided by the aforementioned rods, the in-plane resistance of the adobe walls needs to be improved. Among the three retrofitting methods studied during static cyclic testing, using steel welded mesh on one face of the walls was selected. The details of retrofit of the specimen using welded mesh and also four rods which tie parallel walls are schematically shown in Fig. 6.41. A view of both the shaking table specimens before testing is depicted in Fig. 6.42.

6

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100

85

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Plates for horizontal steel rods Mesh on both sides of wall

(B)

100

85

(A)

Splice and overlapping area of mesh sheets

Mesh shear connection

(C)

(D)

FIG. 6.41 Schematic view of mesh dimensions and connections position (dimensions in cm). (A) Southern wall. (B) Northern wall. (C) Western wall. (D) Eastern wall.

(A)

(B)

FIG. 6.42 South-east view of the shaking table specimens. (A) Unretrofitted. (B) Retrofitted. (Photos taken by Mohammad Yekrangnia.)

Results Static-Cyclic Tests Failure modes of all the wall specimens of static cyclic testing introduced in Fig. 6.32 are shown in Fig. 6.43. Comparison of parts A-I, B-I, and C-I of this figure indicates that existence of openings can greatly influence the crack pattern of the adobe walls. Openings corners and pier between openings are more susceptible of experiencing shear cracks even at initial stages of testing.

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FIG. 6.43 Failure modes of wall specimens after static cyclic testing. (A-I) URA-WO. (B-I) URALW. (C-I) URA-DW. (A-II) SMRA-WO. (B-II) SMRA-LW. (C-II) SMRA-DW. (A-III) SSRA-WO. (B-III) SSRA-LW. (C-III) SSRA-DW. (A-IV) CWRA-WO. (B-IV) CWRA-LW. (C-IV) CWRADW. (Photos taken by Mohammad Yekrangnia.)

Comparison of parts A-I and A-II of this figure shows the effects of adding steel mesh, with detachments of the walls in the retrofitted specimen compared to the major shear sliding crack in the corresponding specimen. The main weakness of specimen SMRA-WO is therefore detachment of the perpendicular walls. Although the steel mesh was bent to cover this critical section, a better response improvement in this location can be achieved by installing steel L-shaped or box profiles at the intersection of the perpendicular walls in order to prevent detachment of these walls. This detail was implemented in the other

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FIG. 6.44 Details for tying perpendicular masonry walls by DRES.

retrofitted specimens and led to satisfactory results. In addition, an example of the details of similar concept which was implemented by the Organization for Development, Renovation and Equipping Schools of Iran (DRES) are shown in Fig. 6.44. Also, cracks are more uniformly propagated and are narrower in part B-II and C-II of this figure compared to part B-I and C-I, respectively, which proves the effects of welded steel mesh in controlling the cracks from further widening. The only vulnerable area in specimen SMRA-LW was at the both sides of the opening. This area was partly unconfined by the existence of the opening and hence it is harder to maintain its integrity. A solution which can be considered for this specimen is folding back the steel mesh in such a way that the mesh “embraces” the end of the piers in the vicinity of the opening [39] (Fig. 6.45). A comparison of the results in part A-III of this figure with those in part A-I indicates the ability of the retrofit method consisting of steel strips in further propagation of damage throughout the wall’s surface and, in doing so, minimizing the severity of cracks. The major weakness of specimen SSRA-LW was transforming the shear-dominated failure mode into toe-crushing. Nonetheless, the maximum strength capacity of the retrofitted specimen was significantly higher than that in the corresponding unretrofitted specimen, and considerable ductility and energy dissipation was achieved before occurrence of this failure mode.

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(A)

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(B)

FIG. 6.45 Cutting and folding the grid on each side of the opening [39]. (A) Both vertical sides. (B) Below.

Some in-depth observations of damage of wall specimens after static cyclic testing are presented in Fig. 6.46. In a specimen SMRA-WO (part A), there was a sliding-rocking crack exactly at the level in which the steel mesh was cut. This indicates the successful strategy of transferring the cracks from the more dangerous upper parts of the wall to the more stable lower parts. As previously mentioned, the main weakness of this specimen was detachment the intersection of perpendicular walls, which in some locations resulted in rupture of the steel mesh (part B). Some local buckling of the steel mesh were observed in specimen SMRA-LW (part C) mainly because of local instability around the opening; however, because the mesh was not expected to carry compressive forces, this behavior was considered as a weakness in the response of the specimen. Moreover, after removing the mesh from the specimen upon completion of the test, the specimen collapsed (part D). As a result, it can be concluded that the steel mesh not only improved the lateral response of the specimen to a large degree, but also prevented the wall from collapse under vertical direction. The same behavior was found in specimen SSRA-WO (parts E and F). In some cases, excessive forces acted on the connections, which resulted in permanent deformation of these parts (part G). A comparison of response characteristics of walls models in static cyclic testing is provided in Fig. 6.47. As can be seen, the openings have marginal effect on the maximum strength of the adobe walls; however, retrofit measures have led to considerable difference in the ductility of walls with different opening configurations. In general, retrofit methods increased the ductility of the walls from two to five times. Shaking Table Tests The unretrofitted specimen was severely damaged and collapsed during the 100% and 125% levels of excitation, respectively. Although the walls experienced major shear cracking, the main cause of collapse of the roof was in-balanced movement of the support walls which was from out-of-phase motions of the parallel walls in out-of-plane direction.

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FIG. 6.46 Some in-depth observations of damage of wall specimens after static cyclic testing. (A) SMRA-WO (showing sliding crack). (B) SMRA-WO (showing mesh rupture). (C) SMRA-LW (showing mesh buckling). (D) SMRA-LW (showing collapse of the specimen). (E) SSRA-WO (showing strip buckling). (F) SSRA-WO (showing collapse of the specimen). (G) SSRA-WO (showing bearing failure at one of the holes). (Photos taken by Mohammad Yekrangnia.)

Figs. 6.48 and 6.49 show the collapse of the unretrofitted specimen from side and above viewports, respectively. The thick walls, however, were stable after the tests and none of them collapsed. Seismic performance of the retrofitted specimen significantly improved thanks to the retrofit measures in the form of using rods tying parallel walls and also welded steel mesh on the upper parts of the walls. As a result, the failure mode of this specimen changed from the premature failure observed in the unretrofitted specimen to shear cracks from the torsion in this specimen. This torsion was because of the eccentricity of the center of mass with respect to the center of rigidity of the building specimen (Fig. 6.50). As can be seen in part C of Fig. 6.50, the steel mesh has successfully controlled the stepped-diagonal shear cracks in the Eastern wall. As shown in Fig. 6.50 part D, the local falling down of adobe blocks occurred, which was also observed in the wall specimens from static cyclic test in Fig. 6.43B-II.

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60 WO LW

Maximum strength, kN

50

DW 40 30 20 10 0 Unretrofitted

(A)

Steel mesh Steel strips Retrofit method

Chicken wire

30 WO 25

LW DW

Ductility

20

15 10 5 0

Unretrofitted

(B)

Steel mesh

Steel strips

Chicken wire

Retrofit method

FIG. 6.47 Comparison of response characteristics of wall models. (A) Maximum strength. (B) Ductility.

6.4.2.5 Comparison of Test Results and Field Observations As previously mentioned, the main cause of collapse of the tested building during shaking table tests was in-balanced motions of the support walls in out-of-plane direction. The out-of-plane movement and eventually failure of adobe walls is among the most frequent and serious cause of partial and total collapse of such buildings. This failure mode is not limited to adobe buildings in Iran; it was also reported as a serious and life-threatening damage by Tolles et al. (2003) [6]. Examples of this failure mode in the 2005 Zarand earthquake together with the associated failure mode in the unretrofitted specimen are shown in Fig. 6.51. As shown in Fig. 6.29, two types of openings, in terms of the shape of the upper part and securing the wall on top of the opening, are found in Iranian adobe buildings. The dome-roof adobe buildings usually have arched-shape

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FIG. 6.48 Collapse of unretrofitted specimen at 125% level of excitation (South view). (Photos taken by Mohammad Yekrangnia.)

openings. Contrary to the rectangular opening in which shear cracks are initiated and propagated from their corners, the main weakness of arched-shape openings is the crown part of the opening. Observations from past earthquakes indicate that during ground motions, the adobe blocks start to loosen in this area. Examples of these observations together with the corresponding failure mode in the presented shaking table specimen are presented in Fig. 6.52. The previous parts proved the efficiency of the retrofit measures in preventing collapse of the tested adobe building and effectively reducing the in-plane cracks. In the implemented strategies for retrofit, the rods tying parallel walls which maintained box-like behavior of the building play a more important role because they directly deal with preventing the collapse of the roof. These rods, however, had been previously considered for several adobe walls in Iran, and also for masonry arches and vaults in other parts of the world (Fig. 6.53). Examples of these retrofit measures are shown in Fig. 6.54. Spectral accelerations of the square root of the sum (SRSS) of the two components of the applied excitation of the 2005 Zarand earthquake at 100% and 175% of the excitation levels are shown in Fig. 6.55. The spectrum related to 100% of excitation level is compared with 130% (as recommended for spectral scaling of two component excitations) of the codified spectrum of Standard 2800 over soil type A according to this standard. This spectrum represents the Design Based Earthquake (DBE) with the return period of 475 years (or 10%

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FIG. 6.49 Collapse of the unretrofitted specimen at 125% level of excitation (plan view). (Photos taken by Mohammad Yekrangnia.)

probability of occurrence in 50 years’ lifetime of the building). Also, the spectrum related to 175% of excitation level is compared with 150% of the codified DBE spectrum which represents the Maximum Credible Earthquake (MCE) with the return period of 2475 years (or 2% probability of occurrence in 50 years’ lifetime of the building). For the tested building model in shaking table tests, the natural period of the first mode of the building (noted as T1 in Fig. 6.55) was 0.11 s. Based on the codified spectral scaling procedure for performing time history analysis, the excitation spectrum intensity should not be lower than 0.9 of the codified spectrum between 0.2T1 and 1.5T1 [36]. Based on this procedure, the spectra of 100% and 175% of excitation levels meet the requirements for scaling according to DBE and MCE, respectively. Based on this figure, the unretrofitted specimen did not satisfy the Life Safety (LS) Performance Level during DBE. However, thanks to the implemented retrofit measures, the corresponding retrofitted specimen not only satisfied the LS during DBE, but also met the requirement of the Collapse Prevention (CP) Performance Level during MCE.

FIG. 6.50 Damage to the retrofitted specimen at 175% level of excitation. (A) Shear cracks at the base of the door. (B) Shear cracks at the wall’s corner. (C) Torsional shear crack at the east wall. (D) Local cracks around the window in the east wall. (Photos taken by Mohammad Yekrangnia.)

FIG. 6.51 Detachment of perpendicular walls and spoiling box-like behavior. (A) External view after the 2005 Zarand earthquake. (B) Internal view after the 2005 Zarand earthquake. (C) Shaking table tests by Bakhshi et al. (2015) [4]. (Photos taken by Mohammad Yekrangnia.)

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(A)

(B)

(C) FIG. 6.52 Comparison of common cracks around adobe arched openings in the past earthquakes and experimental results. (A) 2005 Zarand earthquake. (B) A recent undocumented earthquake. (C) Shaking table tests by Bakhshi et al. (2015) [4]. ((A) Photo taken by Mohammad Yekrangnia. (B) Permission from DRES. (C) Photo taken by Mohammad Yekrangnia.)

(A)

(B)

FIG. 6.53 Examples of using tie-rods in stabilization of arches and vaults in historic masonry structures. (A) An example of a European cathedral (permission from Dr. Gentilini). (B) Sforza Castle, Milan, Italy [40]. (permission from Mr. Chuck LaChiusa; www.buffaloah.com)

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(C)

(D)

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FIG. 6.54 Using steel rods and welded steel mesh for enhancing seismic performance of adobe walls in out-of-plane and in-plane directions. (A) In a dome-roof building. (B) In a damaged dome-roof building after the 2005 Zarand earthquake; note the undamaged adjacent roof. (C) In a flat-roof building after the 2005 Zarand earthquake. (D) In a cylindrical-roof building after the 2005 Zarand earthquake. (Photos taken by Mohammad Yekrangnia.)

FIG. 6.55 Spectral acceleration of the applied excitation during shaking table tests.

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1

1 Level 100%

Level 125%

Level 125%

0.6

D.I.

D.I.

0.8

0.8

0.4

0.4

0.2

0.2

Level 175%

0

0 1

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Level 150%

0.6

2

3

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5

Location

6

7

8

9

1

10

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2

3

4

5

6

7

8

9

10

Location

FIG. 6.56 Damage index proposed by Bakhshi et al. (2015) [4] in different test steps and in different parts of the shaking table models. (A) Unretrofitted specimen. (B) Retrofitted specimen.

For comparison purposes, the quantitative damage severity of the two models tests on the shaking table are compared in Fig. 6.56 based on the damage index proposed by Bakhshi et al. (2015) [4]. As can be seen, the retrofitted model experienced considerable lower levels of damage even at 175% excitation level. This proves the effectiveness of the implemented retrofit technique not only in preventing the building from collapse, but also in reducing the damage in different parts of the building. Similar results can also be found in the vulnerability functions used by JICA in 2000 in seismic risk assessment in Greater Tehran as the capital of Iran, shown in Fig. 6.57. In this figure, adobe buildings as the most vulnerable type of building in Tehran are noted by class number (9). Comparison of the results of Figs. 6.56 and 6.57 indicate that the

(A)

(B) FIG. 6.57 Vulnerability functions of residential buildings in Greater Tehran, Iran applied by JICA (2000) [40]. (A) versus PGA. (B) versus seismic intensity, MMI.

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vulnerability of the retrofitted adobe building is comparable with higher-quality steel and reinforced concrete (RC) building noted by class number (2), (3), (4). Descriptions about seismic intensities, MMI against which the vulnerability functions of buildings are plotted in part B of this figure, are found in Table 6.9.

TABLE 6.9 The Modified Mercalli Intensity Scale [41] Level

Description

I

Not felt except by a very few under favorable circumstances

II

Felt only by a few persons at rest, especially on the upper floors of buildings. Suspended objects may swing

III

Felt quite noticeably indoors, especially on upper floors of office buildings, but not necessarily recognized as an earthquake. Standing cars may rock slightly. Vibration similar to that of a passing truck

IV

If during the day, felt indoors by many, outdoors by few. If at night, few awakened. Dishes, windows, and doors rattle, walls creak. A sensation such as a heavy truck striking the building. Standing cars rock noticeably

V

Felt by nearly everyone, many awakened. Some dishes and windows broken, some plaster cracked, unstable objects overturned. Disturbance to trees, poles, and other tall objects. Pendulum clocks may stop

VI

Felt by all; many people run outdoors. Fallen plaster, minor chimney damage. Movement of moderately heavy furniture

VII

Everyone runs outdoors. Damage negligible in buildings of good design and construction; slight to moderate in well-built ordinary structures; considerable in poorly built or badly designed structures. Some chimneys broken. Noticed by persons driving cars

VIII

Damage light in specially designed structures; considerable in ordinary substantial buildings. Panel walls thrown out of frame structures. Chimneys, factory stacks, monuments, walls, and columns fall. Heavy furniture overturned and damaged. Changes in well water. Sand and mud ejected in small amounts. Persons driving in cars are disturbed

IX

Damage considerable in specially designed structures; well-designed frame structures thrown out of plumb; great damage in substantial buildings, which suffer partial collapse. Buildings shifted off foundations, ground noticeably cracked, underground pipes broken

X

Some well-built wooden structures destroyed, most masonry structures destroyed, foundations ruined, ground badly cracked. Rails bent. Considerable land-slides from steep slopes and river banks. Water splashed over banks. Shifted sand and mud

XI

Few, if any, masonry structures remain standing. Bridges destroyed. Broad fissures in ground. Under-ground pipes out of service. Earth slumps and land slips in soft ground. Rails bent greatly

XII

Total damage. Waves are seen on ground surface. Lines of sight and level are distorted. Objects thrown into the air

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REFERENCES [1] J. Kuroiwa, A regional earthquake scenario in south peru, in: The 11th World Conference on Earthquake Engineering (11WCEE), Acapulco, Mexico, Acapulco, Mexico, 1996. [2] L.S. Hashmat, A.J. Sangi, A. Abdullah, “Adobe houses”, World Housing Encyclopedia, Earthquake Engineering Research Institute (EERI) and International Association for Earthquake Engineering (IAEE), Report#166, 2012. [3] L. Zegarra, A. San Bartolome, D. Quiun, Reconditioning of existing adobe houses to mitigate earthquake effects, in: The 11th World Conference on Earthquake Engineering (11WCEE), Acapulco, Mexico, 1996. [4] A. Bakhshi, M.A. Ghannad, M. Yekrangnia, H. Masaeli, Shaking table tests on dome-roof adobe houses. J. Earthq. Eng. Struct. Dyn. (2016). https://doi.org/10.1002/eqe.2800. [5] E.L. Tolles, E.E. Kimbro, F.A. Webster, W.S. Ginell, Seismic Stabilization of Historic Adobe Structures, The Getty Conservation Institute, Los Angeles, 2000. [6] E.L. Tolles, E.E. Kimbro, W.S. Ginell, Planning and Engineering Guidelines for the Seismic Retrofitting of Historic Adobe Structures, The Getty Conservation Institute, Scientific Reports Series, Los Angeles, California, 2002. [7] M. Blondet, F. Ginocchio, C. Marsh, G. Ottazzi, G. Villa Garcia, J. Yep, Shaking table test of improved adobe masonry houses, in: The 9th World Conference on Earthquake Engineering (9WCEE), Tokyo-Kyoto, Japan, 1988. [8] R. Vera, S. Miranda, Experimental study of retrofitting techniques for adobe walls, in: The 13th World Conference on Earthquake Engineering (13WCEE), Vancouver, B.C., Canada, 2004. [9] M. Blondet, G. Villa Garcia, S. Brzev, Earthquake-Resistant Construction of Adobe Buildings: A Tutorial, Earthquake Engineering Research Institute, IAEE, Oakland, California/Tokyo, Japan, 2003 (EERI adobe tutorial). [10] E. Juhasova, R. Sofronie, R. Bairrao, Stone masonry in historical buildings-ways to increase their resistance and durability, Eng. Struct. 30 (8) (2008) 2194–2205. [11] K. Meguro, P. Mayorca, R. Guragain, N. Shathiparan, N. Nesheli, Shaking table experiment on masonry buildings and effectiveness of PP-band retrofitting technique, 生産研究 57 (6) (2005) 534–537. [12] R. Meli, O. Hernandez, M. Padilla, Strengthening of adobe houses for seismic actions, in: The 7th World Conference on Earthquake Engineering (7WCEE), Istanbul, Turkey, 1980. [13] R.A. Soforonie, R. Crisan, M. Toanchina, Retrofitting the masonry of cultural heritage buildings, in: The 5th National Conference on Earthquake Engineering, Istanbul, Turkey, 2003. [14] M. Yekrangnia, Evaluation of Seismic Performance of Adobe Dome-roof Structures Retrofitted by Steel Rods and Mesh Using Shaking Table Facility (MSc thesis), Sharif University of Technology, Tehran, Iran, 2009 (in Persian). [15] M. Blondet, G.V. Garcia, Earthquake resistant earthen buildings? in: The 13th World Conference on Earthquake Engineering (13WCEE), Vancouver, B.C., Canada, 2004. [16] San Bartolome A, Quiun D, Zegarra L, Effective system for seismic reinforcement of adobe houses, The 13th World Conference on Earthquake Engineering (13WCEE), Vancouver, BC, Canada. [17] Yamin LE, Phillips CA, Reyes JC, Ruiz DM, Seismic behavior and rehabilitation alternatives for adobe and rammed earth buildings, The 13th World Conference on Earthquake Engineering (13WCEE), Vancouver, BC, Canada.

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[18] F. Somi, M. Yekrangnia, A. Bakhshi, M.A. Gannad, S.E. Hashemi-Rafsanjani, Study of in-plane behavior of adobe walls with cyclic tests, in: The 6th International Conference on Seismology and Earthquake Engineering (SEE-6), May 16–18, Tehran, Iran, 2011. [19] T.-G. Zhou, X. Hu, C.-X. Yu, Shaking table model test and engineering practice of a new gypsum-adobe walls dwelling in Xinjiang autonomous region, China, Acta Seismol. Sin. 21 (3) (2008) 319–324. [20] D. Abrams, T. Smith, J. Lynch, S. Franklin, Effectiveness of rehabilitation on seismic behavior of masonry piers, J. Struct. Eng. 133 (1) (2007) 32–43. [21] D.M. Dowling, B. Samali, Low-cost, low-tech means of improving the earthquake resistance of adobe-mud brick houses, in: International Conference on Earthquake Engineering (ICEE 2006), Lahore, Pakistan, 2006. [22] A. Turer, S.Z. Korkmaz, H.H. Korkmaz, Performance improvement studies of masonry houses using elastic post-tensioning straps, Earthq. Eng. Struct. Dyn. 36 (2007) 683–705. [23] D. Dowling, B. Samali, J. Li, An Improved Means of Reinforcing Adobe Walls-External Vertical Reinforcement, University of Technology, Sydney, Australia, 2005. [24] R. Selna, 150 S.F. brick buildings yet to be reinforced, San Francisco Chronicle, 2008, p. A14. [25] Deseret News article, http://www.deseretnews.com/article/635199749/Its-2008–and-the-bigone-slams-Utah.html. [26] E.L. Tolles, F.A. Webster, A. Crosby, E.E. Kimbro, Survey of damage to historic adobe buildings after the January 1994 Northridge earthquake, Getty Conservation Institute, 1996. [27] E.L. Tolles, Survey of damage to historic adobe buildings after the January 1994 Northridge earthquake, Getty Conservation Institute, 1996. [28] ATC 20; Applied Technology Council, Procedures for Postearthquake Safety Evaluation of Buildings, Applied Technology Council, CA, USA, 1989. [29] C. Baggio, A. Bernardini, R. Colozza, L. Corazza, M. Della Bella, G. Di Pasquale, et al., Field Manual for Post-Earthquake Damage and Safety Assessment and Short Term Countermeasures (AeDES), (2007). European Commission—Joint Research Centre—Institute for the Protection and Security of the Citizen, EUR, 22868. [30] M.E. Molino de Garcia, in: Prevencio´n sı´smica en las construcciones de adobe, en la cuidad de Guatemala despues de los terremotos de 1917–1918, Paper Presented at the Sixth International Conference on the Conservation of Earthen Architecture, Las Cruces, N.Mex., October 14–19, 1990. [31] Housing Foundation of Iran, Rural Houses Specifications Count, 2003. [32] M.A. Ghannad, A. Bakhshi, S.E. Mousavi Eshkiki, A. Khosravifar, Y. Bozorgnia, A.A. Taheri Behbahani, in: A study on seismic vulnerability of rural houses in Iran, Proceedings of the First European Conference on Earthquake Engineering and Seismology, paper (No. 680), 2006. [33] M. Yekrangnia, A. Bakhshi, M.A. Ghannad, A. Khosravifar, E. Mousavi Eshkiki, H. Masaeli, “Adobe Arched-Roof”, World Housing Encyclopedia, Earthquake Engineering Research Institute (EERI) and International Association for Earthquake Engineering (IAEE), Report#177, 2014. [34] S.E. Mousavi Eshkiki, A. Khosravifar, M.A. Ghannad, A. Bakhshi, A.A. Taheri Behbahani, Y. Bozorgnia, Structural typology of traditional houses in iran based on their seismic behavior, in: Proceedings of the 8th U.S. National Conference on Earthquake Engineering, April 18–22, San Francisco, California, USA, 2006. [35] F. Somi, Investigation of Cyclic Behavior of Adobe Walls Strengthened With Various Retrofitting Methods (M.Sc. Thesis), Sharif University of Technology, December, Tehran, Iran, 2010.

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[36] Standard 2800-05. Iranian Code of Practice for Seismic Resistant Design of Buildings. third revision, Building and Housing Research Center, Iran (in Persian). [37] K. Doherty, M.C. Griffith, N. Lam, J. Wilson, Displacement-based seismic analysis for out-ofplane bending of unreinforced masonry walls, Earthq. Eng. Struct. Dyn. 31 (4) (2002) 833–850. [38] M. Blondet, D. Torrealva, J. Vargas, in: Seismic reinforcement of adobe houses using external polymer mesh, The 1st European Conference on Earthquake Engineering and Seismology (1ECESS), Geneva, Switzerland, 2006. [39] J. Vargas, D. Torrealva, M. Blondet, Building Hygienic and Earthquake-Resistant Adobe Houses Using Geomesh Reinforcement. For Arid Zones. Spanish and English, Catholic University of Peru, Fondo Editorial, Lima, Peru, 2007. [40] C. JICA, The Study on Seismic Microzoning of the Greater Tehran Area in the Islamic Republic of Iran. Pacific Consultants International Report, OYO Cooperation, Japan, 2000. [41] H.O. Wood, F. Neumann, Modified Mercalli Intensity scale of 1931, Bull. Seismol. Soc. Am. 20 (1931) 277–283.

FURTHER READING [42] M. Alalhesabi, “Patterns of rural houses”, Housing Foundation of Islamic Revolution, Tehran, Iran, 1993. [43] H. Zamrashidi, “Architecture of Iran—Construction of Traditional Houses”, Zomorrod Publications, Tehran, Iran, 1995.

Index Note: Page numbers followed by f indicate figures and t indicate tables.

A Acceptance criteria ASCE41-13, 308 deformation-controlled actions, 79–81 force-controlled actions, 81 linear static procedure deformation-controlled actions, 308–310, 309t, 312t force-controlled actions, 310 nonlinear static procedure deformation-controlled actions, 310–311, 312–314t force-controlled actions, 311 Adobe buildings. See Nonengineered buildings Analytic hierarchy process (AHP) scoring table, of retrofit strategies, 148, 150t Arched roofs, 428–430 Attic-floor joists, 408

B Bam earthquake, 422 Bars, characteristics, 126–127 Beams, flexural strength of, 214–215, 214t Bond beam on top of the walls, 395 Building and Housing Research Center (BHRC), 432

C Capacity forces deformation-controlled actions, 300 force-controlled actions, 300 linear static procedure beams, 303–306, 305–306t columns, 306–307, 307t nonlinear static procedure, 307, 307f Capacity forces calculations, 75–79 Center-core rods, 94 Center of mass (CoM) coordinates, 287, 288t Center of rigidity (CoR) coordinates, 287, 288t Chicken wire, 395, 397f, 436–437, 439f Cluster arched roof adobe buildings, 427f Coarse-thread screws, 408

Collapse prevention (CP) performance level, 449–450 Columns characteristics, 132–133t flexural strength and axial strength, 215–217 and shear strength, 215, 216t results and observations from sondage, 130–131f shear walls and diaphragm plan and observations, 129f Compound cracks, 29–30 Concentric braces, retrofit options DCR, structural members, 337–338, 342–343f designed profiles, 337–338, 341t lateral stiffness, 331–334 location of added concentric braces, 337–338, 339–340f punching shear main building, 338, 346f sports building, 338, 350f required reinforcement main building, 338, 347–348f sports building, 338, 350f soil pressure main building, 338, 344t, 345f sports building, 338, 344t, 349f Concrete, compressive strength of, 126, 127t Concurrent seismic effects, 296 Confining ties, 19 Construction quality, 19 Cradle-type connections beams with, 311–314, 315–316f, 317–318t vertical shear adequacy of, 368–377, 382t Crossed braces, retrofit options, 349–356, 354–355f, 356t

D Damage classification steel frame building with masonry infill walls corner-crushing failure, 205–206, 207f ductility demand for elasto-plastic system, 204–205, 206f

459

460 Index Damage classification (Continued) equivalent strut model, 204, 205f failure mode of infill walls, 205–206, 207f interaction with braces, 205, 207f out-of-plane failure, 207, 208f shear and flexural failure, 204f shear-sliding failure, 205–206, 207f soft/weak stories, 205, 206f unreinforced masonry collapse of parapet walls and facades, 22–24 common types of damage, 39 dome roofs, 36 in-plane damage of walls, 24–25 mid-height flexural out-of-plane cracks, 22 nonstructural components, 37–38 out-of-plane failure of URM walls, 20–21 partial collapse of jack-arch roofs, 35–36 soil and foundation condition, 31–35 surrounding walls, 22 ties in confined masonry buildings, 30 walls corners, 27–30 walls-roof connection, 31 walls supports, 25–27 Deformation-controlled actions, 73–74 acceptance criteria linear static procedure, 308–310, 309t, 312t nonlinear static procedure, 310–311, 312–314t capacity forces, 300 Demand forces calculations, 52–55 distribution in height, 294 effective mass factor, 293 modification factors, 292–293, 295t natural periods, 293–294 seismic demand force, 291 Demand-to-capacity parameters, URM load transfer between the walls, 50–51 mortar shear strength, 49–50 seismicity and soil conditions, 50 Design Based Earthquake (DBE), 449–450 Design, seismic retrofit standards, 6 Diagonal cracks, 27–28 Diaphragms, 40–41 connection of, 169–171 design control, 169–171 filling openings, 180–184 flexible diaphragm, 291 flexural deformation, 287–290 with horizontal deformation, 287–290

inertial force, 290 in-plane shear, 169 rigidity, 16 semi-rigid diaphragm, 287–290 shear deformation, 287–290 Dome roofs, 36

E Earthquake, 18–19 record characteristics, 17 Earthquake Engineering Research Center (EERC), 432 Earthquake Engineering Research Institute (EERI), 403 Eccentric braces, retrofit options behavior factor, 338–341 column strengthening details, 344, 356f DCR of structural members, 341, 354–355f demand shear force, 341 designed profiles, 341, 353t designed section, link beams, 341, 353t foundation evaluation results, 344–349 lateral stiffness, 331–334, 336f location of added eccentric braces, 341, 351–352f shear capacity, 341 short columns, 341–344 Elastic base shear capacity, 53 Engineering process, of risk assessment/retrofit, 3f Epoxy injection, 92–93 Estimated peak ground acceleration (EPGA), 404 Expected flexural capacity of beams, 305, 305t Expected shear capacity of beams, 306, 306t External bamboo bars, 395–396, 398f External reinforcement, 93–94

F Facades, 22–24 Failure modes diagonal tension, 107–108 flexural, 105–107 m-factors for linear static analysis, 108 sliding, 108 Ferrocement covering of the walls, 91–92 Fiber reinforced polymer (FRP), 396 Filler-joist diaphragm, 40 Flat nylon straps, 407 Flexible diaphragms with horizontal ties, 72

Index without horizontal ties, 72–73 Flexural strength of beams, 214–215, 214t of columns and axial strength, 215–217 and shear strength, 215, 216t Floor-to-wall connection, 412f Force-controlled actions, 74 acceptance criteria linear static procedure, 310 nonlinear static procedure, 311 capacity forces, 300 Foundations control and design, 172–180 control of structural adequacy under gravitational loads flexural behavior of foundation section, 177, 177f loads combinations, 175 soil pressure control, 175 soil settlement control, 175–176 plan and observations, 128f retrofit design, 177–180, 186f connection bars details, 185f controlling soil pressure, 177–179 flexural capacity, 181f negative moments, 182f new foundation design, 180 positive moments, 183f reinforcement details, 184f soil design parameters foundation uplift, 331, 334f geometrical characteristics, 328, 329–330f geotechnical tests and field observations, 328, 328t prescriptive expected bearing capacity, 325–328 required foundation reinforcement, 331, 335f soil pressure of main building, 331, 332–333f of sports building, 331, 335f Friction shear capacity, of shear walls, 173–174t

G Gable-end walls, 21 Getty Seismic Adobe Project (GSAP) initiative, 398–399 small-scale model buildings, 404, 406t Grout injection, 90, 91f, 92–93

461

H Historic adobe earthquake damage typologies, 399, 400–401t Horizontal distribution of demand forces, 56–73 Horizontal ties, 51

I Incremental seismic rehabilitation (ISR), 89–90 In-plane bed-joint sliding strength of URM walls and piers, 76–77 In-plane rocking strength of URM walls and piers, 75–76 Instruction for Seismic Rehabilitation of Existing Buildings, 43–45 Internal FRP bars, 395–396, 398f Intersecting walls, 21 Iranian adobe buildings characteristics, 422–431 comparison of test results and field observations, 448–455 experimental studies, 432–447 shaking table tests, 437–442, 446–447 static cyclic tests, 432–437, 443–446 survey of damage, 431–432 Iranian Code of Practice for Seismic Resistant Design of Buildings, 36, 50 Irregularity, 43–49 steel frame building elimination/reduction, 331 requirements, 285–287, 288–289t

J Jack-arch diaphragm, 40–41 Jack-arch roofs, 35–36

L Linear static procedure acceptance criteria deformation-controlled actions, 308–310, 309t, 312t force-controlled actions, 310 capacity forces beams, 303–306, 305–306t columns, 306–307, 307t steel frame building with masonry infill walls base shear, 228–231 deformation-controlled actions, 232–233 demand capacity ratios, 231 force-controlled actions, 233–234

462 Index Linear static procedure (Continued) in-plane discontinuity irregularity, 231 natural period of building, 223–228 non-orthogonal lateral-force-resisting system, 232 out-of-plane discontinuity irregularity, 231 torsional strength irregularity, 232 vertical stiffness irregularity, 232 weak story irregularity, 231–232 Load-bearing vs. nonload-bearing walls, 21 wall, 21, 23f Lower-bound axial capacity of columns, 307, 307t URM walls and piers in-plane diagonal tension strength of, 78 in-plane toe-crushing strength of, 77–78 in-plane vertical compressive strength of, 78–79 Lower-wall horizontal elements, 421

M Masonry integrity, 403 Maximum and mean drift ratio, 287, 289t Maximum Credible Earthquake (MCE), 449–450 Mid-height flexural out-of-plane cracks, 22 Model 7 roofs, 410f Model 7 walls, 409f Modern portfolio theory (MPT), 9–10 “Modification of the Stiffness Relations for Piers in Single-Story Buildings” section, 63 Mortar shear strength, 49–50 Multi-degree-of-freedom (MDOF) system, 294–295

N Nonengineered buildings adobe, 393–394 construction details and failure modes, 392–393, 394f vs. “engineered” building, 391–392, 393f Iranian experiences characteristics, 422–431 comparison of test results and field observations, 448–455 experimental studies, 432–447 shaking table tests, 437–442, 446–447 static cyclic tests, 432–437, 443–446 survey of damage, 431–432

retrofit approaches, 394–395 retrofit methods bond beam on top of the walls, 395 mesh on walls surfaces, 395–396 straps and reinforcing bars, 396 seismic risk, 392 US experiences comparison of test results and field observations, 420–421 experimental studies, 403–419 general recommendation, 421 law enforcement and retrofit measures, 399 objectives of seismic retrofit measures, 399 results, 413–419 survey of damage to adobe buildings, 399–403 Ziarat earthquake, 391, 392f Nonlinear static procedure acceptance criteria deformation-controlled actions, 310–311, 312–314t force-controlled actions, 311 capacity forces, 307, 307f Nonload-bearing wall, 21, 23f “Nonparallel” load-bearing components, 47 Nonstructural components, 37–38 Northridge earthquake, 399

O Organization for Development, Renovation and Equipping Schools of Iran (DRES), 444–445, 446f Out-of-plane failure of URM walls, 20–21 Out-of-plane flexural cracks, 21 Overturning of walls, 21

P Pacific Earthquake Engineering Research (PEER) center framework, 4 Paralleled walls, 92 Parapet walls, 22–24 Participation factor, 73 Peak ground acceleration (PGA), 404 Performance-based earthquake engineering (PBEE), 1 first generation, 4–5, 5f probabilistic seismic demand analysis, 4 Perpendicular walls, 21, 23f Plastic mesh, 395, 397f

Index Polymer mesh, 395, 397f Posttensioning, 95 Preexisting cracks, 402–403 Prestressed tire straps, 395–396, 398f Probabilistic earthquake hazard levels, 6

Q Qualitative evaluation, of RC building, 122–127 as-built sketches, preparation of, 127, 134–140f bars, characteristics of, 126–127 columns characteristics of, 132–133t results and observations from sondage of, 130–131f shear walls and diaphragm plan and observations, 129f concrete, compressive strength of, 126, 127t field testing, 125–127 foundation plan and observations, 128f material testing, 125, 126t results of, 125, 125t Quantitative evaluation, of RC building assumed conditions, 127–134 center of mass and rigidity coordinates, 137–138, 142f lateral displacements, 136–137, 141f retrofit solutions, 141–142 three-dimensional modeling, 134–135 vulnerability causes, 138–139, 143t

R Rehabilitation objective, seismic retrofit standards, 6 Reinforced concrete (RC) building designing retrofit system, 120–121 overall plan, 121f performance objective determination of, 123–124t enhanced, 120–121 qualitative evaluation, 122–127 as-built sketches, preparation of, 127, 134–140f bars, characteristics of, 126–127 columns, characteristics of, 132–133t columns, shear walls and diaphragm plan and observations, 129f concrete, compressive strength of, 126, 127t field testing, 125–127

463

foundation plan and observations, 128f material testing, 125, 126t results of, 125, 125t sondage of columns, results and observations from, 130–131f quantitative evaluation (Phase-2, Stage-1) (see Quantitative evaluation, of RC building) retrofit solutions (Phase-1, Stage-2) AHP scoring table, 148, 150t isolation and decreasing stiffness of building parts, 146–148 isolation and increasing stiffness of building parts, 144–146 proper connection of two building parts, 143–144 selected retrofit method, design of (Phase-2, Stage-2) assumed material properties, 151–154, 154t connections, 172 dead and live loads, 154, 154t deformation-controlled actions, 156–157 diaphragms design control, 169–171 diaphragms-to-shear walls connections, 172 dividing shear walls, 148, 153f filling diaphragms openings, 180–184 flexural design, of RC shear walls, 160–163 force-controlled actions, 157–158 foundation control and design, 172–180 loads combinations, 158, 158–159t MATLAB code, 160–161 new building parts, design of, 185–198 new shear walls-to-existing shear walls connections, 172 partial demolition, of shear wall, 148, 152f seismic forces coefficients, 156, 156t seismic loads, 155–156 shear wall design, algorithm for, 163 tasks, 148 views of, 119–120, 120f vulnerability assessment phase, 120–121 Repointing, 92 Retrofit actions, classification of connectivity, 8 improvement of global behavior, 8–9 local behavior, 9 Retrofit measures, URM adding tie columns, 92

464 Index Retrofit measures, URM (Continued) center-core rods, 94 external reinforcement, 93–94 ferrocement covering of the walls, 91–92 grout and epoxy injection, 92–93 incremental seismic rehabilitation, 89–90 placement of steel, polymer, or plastic grids, 96–97 posttensioning, 95 repointing, 92 safe room, 95–96 shotcrete, 90–91, 97–115 strength vs. stability-based design approach, 86–88 tying paralleled walls, 92 Retrofit methods, nonengineered buildings bond beam on top of the walls, 395 mesh on walls surfaces, 395–396 straps and reinforcing bars, 396 Retrofit options, 6–9 lateral stiffness concentric braces, 331–334 eccentric braces, 331–334, 336f in main building, 331 in sports building, 331 steel shear walls, 336 lateral strength, 336 load transfer routs completion, 337 local retrofit, vulnerable structural elements, 331 preliminary assessment, 337 comparison, 357, 358t, 359f concentric braces (see Concentric braces, retrofit options) construction cost and construction time, 357, 359f crossed braces, 349–356, 354–355f, 356t eccentric braces (see Eccentric braces, retrofit options) reduction of mass, 336–337 steel frame building base isolation, 337 changing building functionality, 337 dampers, 337 elimination/reduction in building’s irregularity, 331 Retrofit solutions, steel frame building with masonry infill walls axial and flexural strength of columns, 215–217 cradle-type beam-to-column connections, 221, 221f

dead loads, 217–220, 220t effective width, 222–223 expected shear strengths of infill panels, 223, 227–228t flexural and shear strength of columns, 215, 216t flexural strength of beams, 214–215, 214t infill panels, 221–223, 224–226t live loads, 217–220, 221t longitudinal direction, 217 lower-bound values, of strength, 215–217, 218–219t material properties, 213 thickness, 223 3D model building, 217–220, 220f transverse direction, 217 Retrofitted building, concentric braces acceptance criteria, 364 action calculations, 364 analysis procedure demand forces calculations, 362 target displacement, 362–364 capacity forces calculations linear static procedure, 364, 368t nonlinear static procedure, 364 concurrent seismic effects, 364 diaphragms, 357–359, 363t irregularity, 357, 360–362t modeling assumptions, 364, 366–367f overturning effects, 364, 365t results adding braces to the building, 368, 381f base plate details, 368, 379f braces in bay J/7-8 first story in main building, 368, 378f braces in bay J/7-8 floor story in main building, 368, 377f building after retrofit process, 384, 389f demolition of infill walls, 368, 380f foundation retrofit process, 378, 387f jack-arch roof with uniformity, 384, 388f minimum DCRs of e braces, 378, 384t plan of the retrofitted foundation, 378, 383f plastic hinges formation in main building under PX1, 364–368, 369f, 371t plastic hinges formation in main building under PY1, 364–368, 370f, 372t plastic hinges formation in sports building under PX1, 364–368, 373f, 375t plastic hinges formation in sports building under PY1, 364–368, 374f, 376t

Index required reinforcement with retrofitted foundation, 384, 386f retrofitted foundation details, 378, 384f soil pressure with retrofitted foundation, 384, 385f vertical shear adequacy of cradle-type connections, 368–377, 382t soil-structural interaction, 359–361 torsion, 359 Retrofitted gable-end walls, 414–415 Rigid diaphragms center of rigidity, 60–64 controlling torsional vulnerability, 66 determination of center of mass, 56–59 determination of torsional force, 66–72 piers above the floor story, 63–64 piers in the floor story, 63 shear demand calculation results, 64–66 stiffness relations for piers in multistory buildings, 63–64 stiffness relations for piers in single-story buildings, 61–62 Roof and mid-height flooring/ceiling systems, 402 Roof rafters, 408

S Safe room, 95–96 Seismic damage losses from, 1 unreinforced masonry condition of building during earthquake, 18–19 construction quality, 19 geometrical characteristics, 17–18 seismic intensity and other strong-motion characteristics, 17 seismic rehabilitation elements, 18 soil and foundation condition, 19 Seismic Evaluation and Retrofit of Existing Buildings, ASCE 41, 14 Seismic-force-resisting system stiffness, 49 Seismicity and soil conditions, 50 Seismic loads, 155–156 Seismic rehabilitation elements, 18 Seismic resilience, 9–10 Seismic retrofit standards, 6 Seismic risk reduction strategies, 2–3 Shaking table tests, 437–442, 446–447 Shotcrete, 90–91 acceptance criteria, 104–108 failure modes

465

diagonal tension, 107–108 flexural, 105–107 m-factors for linear static analysis, 108 sliding, 108 of infill panels in transverse direction, 250–253, 254–255t, 256f selection of the walls, 98–99 steel frame building with masonry infill walls, 256f walls stiffness, 99–104 Simulated earthquake motions for testing, 404, 407t Single-degree-of-freedom (SDOF) system, 294–295 Single-stage seismic rehabilitation (SSR), 89 Site topography, 19 Slenderness ratio, 21 Soil and foundation condition, 19 damage due to damped bases, 31–33 damage due to foundation settlement, 34–35 Soil-structural interaction (SSI), 53, 291 Stability-based retrofit design approach, 394–395 Standardized damage states, 403, 405t Static cyclic tests, 432–437, 443–446 Steel bar grids, 395, 397f Steel frame building acceptance criteria ASCE41-13, 308 linear static procedure, 308–310 nonlinear static procedure, 310–311 capacity forces deformation-controlled actions, 300 force-controlled actions, 300 linear static procedure, 303–307, 305–307t nonlinear static procedure, 307, 307f concurrent seismic effects, 296 demand force distribution in height, 294 effective mass factor, 293 modification factors, 292–293, 295t natural periods, 293–294 seismic demand force, 291 external and internal infill walls thickness, 280 field testing, 285, 286t height-to-thickness ratios, 280 infill wall in main building, 300, 301f interface between two building parts, 280, 280f main building and sports building models, 300, 304f

466 Index Steel frame building (Continued) modeling diaphragms, 287–291 irregularity, 285–287, 288–289t primary members, 285 secondary members, 285 SSI, 291 torsion, 291 nonstructural parts evaluation, 285 overturning effects, 298–300 plan of example building, 280, 282–283f plastic hinge characteristic in sports building of braces, 300, 302f of columns, 300, 301f of girders, 300, 302–303f preliminary assessment, 285 results beams with cradle-type connections, 311–314, 315–316f, 317–318t braces, 325, 326t, 327f, 328t columns, 314, 319–321t foundation soil, 325–331, 328t, 329–330f, 332–335f infill walls, 314, 321t, 322–323f, 324t upper and lower truss ridges, 314–324, 324t retrofit options (see Retrofit options, steel frame building) section of example building, 280, 284f seismic actions deformation-controlled action, 296–297 force-controlled action, 296–297 load combinations, 298, 298t seismic hazard, 285 soil and site characteristics, 280, 281t target displacement, 294–296, 295t target retrofit, 285 Steel frame building with masonry infill walls acceptance criteria deformation-controlled actions, 234–235 force-controlled actions, 235 ASCE 41 and ICERIFB evaluation activation conditions, 210–213 brickwork, mechanical properties of, 209–210 frames, 208–209 walls, 209, 210f assumptions, 203 damage classification corner-crushing failure, 205–206, 207f ductility demand for elasto-plastic system, 204–205, 206f

equivalent strut model, 204, 205f failure mode of infill walls, 205–206, 207f interaction with braces, 205, 207f out-of-plane failure, 207, 208f shear and flexural failure, 204f shear-sliding failure, 205–206, 207f soft/weak stories, 205, 206f evaluation of beam and columns, 253–258, 258f, 260–263t beams against gravitational loads, 264–266, 268–270t checking compact sections of columns, 236, 240–244t frame connections, 266–267 infill walls in out-of-plane direction, 258–264, 265t results of infill panels, 236–250, 237–239t, 245–248t isolation design procedure, 267–276 linear static procedure base shear, 228–231 deformation-controlled actions, 232–233 demand capacity ratios, 231 force-controlled actions, 233–234 in-plane discontinuity irregularity, 231 natural period of building, 223–228 non-orthogonal lateral-force-resisting system, 232 out-of-plane discontinuity irregularity, 231 torsional strength irregularity, 232 vertical stiffness irregularity, 232 weak story irregularity, 231–232 m-factors, 235t, 249t plan and section, 202, 202–203f retrofit solutions axial and flexural strength of columns, 215–217 cradle-type beam-to-column connections, 221, 221f dead loads, 217–220, 220t effective width, 222–223 expected shear strengths of infill panels, 223, 227–228t flexural and shear strength of columns, 215, 216t flexural strength of beams, 214–215, 214t infill panels, 221–223, 224–226t live loads, 217–220, 221t longitudinal direction, 217 lower-bound values, of strength, 215–217, 218–219t

Index material properties, 213 thickness, 223 3D model building, 217–220, 220f transverse direction, 217 shotcreting of infill panels in transverse direction, 250–253, 254–255t, 256f Steel strips, 436, 437f Steel welded mesh, 395, 397f Steel wire mesh, 434–436, 436f Steel woven mesh, 395, 397f Straps and reinforcing bars, 396 Strength vs. stability-based design approach, 86–88 Strong-motion characteristics, 17 Structural and nonstructural components, 39–40 Surrounding walls, 22

T Target building performance level, 6, 7t Target displacement, 294–296, 295t Through-wall connections, 434, 435f Ties columns, 16, 92 in confined masonry buildings, 30 Torsion, steel frame building, 291

U Unreinforced masonry (URM) analysis procedure acceptance criteria, 79–81 capacity forces calculations, 75–79 deformation-controlled actions, 73–74 demand forces calculations, 52–55 force-controlled actions, 74 horizontal distribution of demand forces, 56–73 vertical distribution of demand forces, 55–56 assumptions, 14–17 building configuration diaphragms, 40–41 irregularity, 43–49 structural and nonstructural components, 39–40 walls in longitudinal (X) and transverse (Y) directions, 41–42 damage classification collapse of parapet walls and facades, 22–24 common types of damage, 39 dome roofs, 36

467

in-plane damage of walls, 24–25 mid-height flexural out-of-plane cracks, 22 nonstructural components, 37–38 out-of-plane failure of URM walls, 20–21 partial collapse of jack-arch roofs, 35–36 soil and foundation condition, 31–35 surrounding walls, 22 ties in confined masonry buildings, 30 walls corners, 27–30 walls-roof connection, 31 walls supports, 25–27 demand-to-capacity parameters load transfer between the walls, 50–51 mortar shear strength, 49–50 seismicity and soil conditions, 50 isolation of the adjacent building, 16, 16f plan, 13, 14f retrofit measures adding tie columns, 92 center-core rods, 94 external reinforcement, 93–94 ferrocement covering of the walls, 91–92 grout and epoxy injection, 92–93 incremental seismic rehabilitation, 89–90 placement of steel, polymer, or plastic grids, 96–97 posttensioning, 95 repointing, 92 safe room, 95–96 shotcrete, 90–91, 97–115 strength vs. stability-based design approach, 86–88 tying paralleled walls, 92 risks, 13–14 sections, 13, 15f seismic damage condition of building during earthquake, 18–19 construction quality, 19 geometrical characteristics, 17–18 seismic intensity and other strong-motion characteristics, 17 seismic rehabilitation elements, 18 soil and foundation condition, 19 view, 13, 15f Upper-wall horizontal elements, 421 URM. See Unreinforced masonry (URM) US adobe buildings comparison of test results and field observations, 420–421 experimental studies, 403–419

468 Index US adobe buildings (Continued) general recommendation, 421 law enforcement and retrofit measures, 399 objectives of seismic retrofit measures, 399 results, 413–419 survey of damage to adobe buildings, 399–403

V Vertical center-core rods, 414 Vertical cracks, 29 Vertical distribution of demand forces deformation-controlled demand force, 55 force-controlled demand force, 55–56 Vertical wall elements, 421

W Walls corners, 27–30 Walls-roof connection, 31 Walls supports, 25–27 Water damage, 402–403 Wood bond beams, 407 Wooden flat roof, 427, 428f

Z Zarand earthquake, 430–431, 432f Ziarat earthquake, 391, 392f