Advanced Design Examples of Seismic Retrofit of Structures

By Mohammad Yekrangnia

Advanced Design Examples of Seismic Retrofit of Structures provides insights on the problems associated with the seismic retrofitting of existing structures. The authors present various international case studies of seismic retrofitting projects and the different possible strategies on how to handle complex problems encountered. Users will find tactics on a variety of problems that are commonly faced, including problems faced by engineers and authorities who have little or no experience in the practice of seismic retrofitting.

• Provides several examples of retrofitting projects that cover different structural systems, from non-engineered houses, to frame buildings
• Presents various retrofitting methods through examples
• Provides detailed, step-by-step design procedures for each example
• Includes real retrofit projects with photos of the details of various retrofitting techniques
• Contains several modeling details and hints making use of various software in this area

• Language: English
• Publisher: Elsevier Science
• Release date: Sep 13, 2018
• ISBN: 9780081025352

Mohammad Yekrangnia

Mohammad Yekrangnia, is a faculty member of Civil Engineering Department, Shahid Rajaee University. Since 2008, he has been a senior technical advisor at the retrofit office of the Organization for Development, Renovation and Equipping Schools of Iran (DRES). He was a Visiting Fellow at The Pacific Earthquake Engineering Research Center (PEER), UC Berkeley, CA, USA. He co-authored two books and published over 50 peer-reviewed papers in reputed international journals and conferences. Also, he contributed in publishing more than 10 international and national reports and had a major role in development of several national standards and instructions. His research interests include seismic retrofit of buildings, masonry buildings, seismic risk analysis, infilled frames, and historic buildings. He specialized in advanced numerical modelling of structures and also various types of laboratory and in-situ testing methods.

Book preview

Advanced Design Examples of Seismic Retrofit of Structures

First Edition

Mohammad Yekrangnia

Table of Contents

Cover image

Title page

Copyright

Contributors

Preface

Chapter 1: Introduction

Abstract

1.1 Introduction

1.2 Seismic Risk Reduction Strategies

1.3 Performance-Based Earthquake Engineering

1.4 Basic Terminology in Seismic Retrofit Standards

1.5 Review of Common Retrofit Options

1.6 Future Directions; Toward Seismic Resilience

1.7 The Organization of the Book Chapters

Chapter 2: Example of a Two-Story Unreinforced Masonry Building Retrofitted by Shotcrete☆

Abstract

2.1 Introduction

2.2 Assumptions

2.3 Factors Influencing URM Seismic Damage

2.4 Damage Classification

2.5 Building Configuration

2.6 Demand-to-Capacity Parameters

2.7 Analysis Procedure

2.8 Retrofit Measures

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

Abstract

3.1 Introduction

3.2 Qualitative Evaluation

3.3 Quantitative Evaluation (Phase-2, Stage-1)

3.4 Preliminary Design and Study of the Possible Retrofit Methods (Phase-1, Stage-2)

3.5 Detailed Design of the Selected Retrofit Method (Phase-2, Stage-2)

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

Abstract

4.1 Introduction

4.2 Assumptions

4.3 Damage Classification

4.4 Evaluation of the Building

4.5 Isolation of Infill Walls Not Meeting Infill Panel Requirements From the Frame

Chapter 5: Example of a Steel Frame Building Retrofitted with Concentric Braces☆

Abstract

5.1 Introduction

5.2 Assumptions

5.3 Field Testing

5.4 Modeling of the Building

5.5 Analysis Procedure

5.6 Capacity Forces Calculations

5.7 Acceptance Criteria

5.8 Results

5.9 Retrofit Options

5.10 Preliminary Assessment of the Three Retrofit Options

5.11 Evaluation of the Retrofitted Building by the Preferred Method

Chapter 6: Examples of Nonengineered Buildings

Abstract

6.1 Introduction

6.2 Retrofit Approaches

6.3 Retrofit Methods

6.4 Good Experiences

Index

Copyright

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

Preface

Mohammad Yekrangnia

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 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. For the study and design of seismic vulnerability and also construction of retrofit projects for nearly 130,000 classrooms in Iran, more than 100 private-sector 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.

Chapter 1

Introduction

Mohammad Yekrangnia⁎; Salar Arian†    ⁎ Department of Civil Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran

† International Institute of Earthquake Engineering and Seismology (IIEES), Tehran, Iran

Abstract

The seismic retrofit process involves several steps: developing knowledge of as-built conditions, determination of parameters affecting the seismic response, creation of numerical/mathematical model, carrying out analysis, assessment of acceptability, and selection of proper retrofit strategy. Generally, each step includes specific topics of engineering challenges, which are briefly discussed in this chapter. The development of a proper retrofit strategy in accordance with available standards and guidelines is also included. Many parts of earthquake engineering are directly related to seismic retrofit, including performance-based design, determination of seismic hazard, and retrofit costs. These subjects and their relationship to risk and resilience are briefly addressed. Finally, a summary of future directions in earthquake engineering toward seismically resilient built environment is presented.

Keywords

Seismic retrofit; Performance-based earthquake engineering; Resilience

Aims

By reading this chapter, you are introduced to:

•seismic risk reduction strategies;

•performance-based earthquake engineering;

•basic terminology in seismic retrofit standards; and

•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 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-to-same-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 performance-related 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, 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 performance-based 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.

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

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):

   (1.1)

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 | EDP) denotes the probability of exceeding LS conditioned on the value of EDP; and G(EDP | IM) 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 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.

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.

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].

Table 1.1

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 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:

•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 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