TRUNG TÂM ĐÀO TẠO XÂY DỰNG VIETCONS
CHƯƠNG TRÌNH MỖI NGÀY MỘT CUỐN SÁCH

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DESIGN OF
REINFORCED
MASONRY
STRUCTURES
Narendra Taly, Ph.D., P.E., F.ASCE
Professor Emeritus
Department of Civil Engineering
California State University, Los Angeles

Second Edition

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To my wife, Trish, for her high-limit state of endurance,
to my daughters, Neena and Beena, for their love of teaching,
and to the memory of my parents, Sundar Bai and Bhagwan Das Taly,
this book is dedicated.

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ABOUT THE AUTHOR
Narendra Taly, Ph.D., P.E., F.ASCE, is a professor (emeritus) of civil engineering at
California State University, Los Angeles. He has more than 50 years of experience in the
fields of civil and structural engineering design. Dr. Taly is the author of Loads and Load
Paths in Buildings: Principles of Structural Design and Design of Modern Highway Bridges.
He is a co-author of Reinforced Concrete Design with FRP Composites and has written
several technical papers in the field of structural engineering.


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CONTENTS

Preface to the Second Edition xiii
Preface to the First Edition xvii
Acknowledgments xix
Notation xxi
Acronyms xxvii

Chapter 1. Introduction
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8

1.1

What Is Masonry? / 1.1
Plain and Reinforced Masonry / 1.1
A Brief History of Masonry Construction / 1.2
Evolution of Reinforced Masonry / 1.3
Unreinforced and Reinforced Masonry / 1.5

Historical Development of Building Codes and Standards for Masonry Construction / 1.6
Design Methods / 1.9
Load Combinations / 1.11
References / 1.14

Chapter 2. Masonry Units: Applications, Types, Sizes, and Classification
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
2.14

Introduction / 2.1
Application of Masonry Units in Construction / 2.1
General Description of Masonry Units / 2.2
Clay Building Brick / 2.4
Functional Aspects / 2.15
Concrete Masonry Units / 2.23
Bonds and Patterns in Masonry Work / 2.35
Structural Requirements for Masonry in Stack Bond /
Mortar Joints / 2.42

Types of Wall Construction / 2.43
Glass Unit Masonry / 2.46
Mortarless Block Systems / 2.51
Prefabricated Masonry / 2.51
Autoclaved Aerated Concrete / 2.54
References / 2.55

2.41

Chapter 3. Materials of Masonry Construction
3.1
3.2
3.3
3.4
3.5
3.6
3.7

Introduction / 3.1
Mortar / 3.1
Grout / 3.6
Differences between Mortar, Grout, and Concrete / 3.11
Compressive Strength of Masonry / 3.12
Steel Reinforcement / 3.15
Modulus of Elasticity of Masonry Materials / 3.22

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ix


2.1

3.1


x

CONTENTS

3.8 Thermal Effects on Masonry / 3.23
3.9 Influence of Moisture on Masonry: Shrinkage / 3.25
3.10 Creep of Masonry / 3.27
References / 3.28

Chapter 4. Design of Reinforced Masonry Beams
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
4.14

4.15
4.16
4.17
4.18
4.19
4.20
4.21

4.1

Introduction / 4.1
Historical Development / 4.2
Strength Design Philosophy / 4.2
Assumptions in Strength Design Philosophy / 4.5
Analysis of Rectangular Sections in Flexure / 4.7
Modulus of Rupture and Nominal Cracking Moment of a Masonry Beam /
Design of Masonry Beams / 4.31
Procedure for Flexural Design of Beams / 4.41
Overreinforced Beams / 4.53
Design for Shear in Reinforced Masonry Beams / 4.56
Lateral Support of Masonry Beams / 4.69
Analysis of Doubly Reinforced Masonry Beams / 4.69
Lintels / 4.74
Masonry Wall Beams (Deep Wall Beams) / 4.101
Bond Beams / 4.109
Diaphragm Action / 4.111
Flexural Strength of a Wall due to In-Plane Loads / 4.115
Development Lengths for Reinforcing Bars / 4.117
Serviceability Criteria for Beams / 4.119
Service Load Analysis of Reinforced Masonry Beams / 4.120

Deflections of Reinforced Masonry Beams / 4.126
References / 4.139

Chapter 5. Columns

4.26

5.1

Introduction / 5.1
Behavior of Axially Loaded Columns / 5.4
Axial Strength of Reinforced Masonry Columns / 5.7
MSJC Code Provisions for Reinforced Masonry Columns / 5.10
Analysis of Reinforced Masonry Columns / 5.16
Design Procedure for Reinforced Masonry Columns / 5.21
Columns under Combined Axial Load and Bending / 5.28
Discussion and Interpretation of the Axial Load-Bending Moment Interaction
Diagrams / 5.57
5.9 Interaction Diagram for a Wall under Combined Loading
(Axial Load and Bending) / 5.58
5.10 Shear Strength of Masonry Columns / 5.60
5.11 Masonry Piers / 5.64
References / 5.68
5.1
5.2
5.3
5.4
5.5
5.6
5.7

5.8

Chapter 6. Walls under Gravity and Transverse Loads
6.1
6.2
6.3
6.4
6.5

Introduction / 6.1
Types of Masonry Walls / 6.1
Bond Patterns in Masonry Walls / 6.16
Analysis of Walls under Gravity and Transverse Loads /
Out-of-Plane Loads on Walls / 6.25

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6.23

6.1


xi

CONTENTS

6.6
6.7
6.8

6.9
6.10

Analysis of Masonry Walls for Out-of-Plane Loads / 6.38
Design of Walls for Gravity and Transverse Loads / 6.44
Axial Loads on Walls Subjected to Out-of-Plane Loads / 6.69
Pilasters / 6.69
Nonload-Bearing Walls / 6.77
References / 6.86

Chapter 7. Shear Walls
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
7.11
7.12
7.13

7.1

Introduction / 7.1
Fundamental Concepts / 7.2
Types of Shear Walls / 7.6

Rigidity and Relative Rigidity of a Shear Wall / 7.10
Rigidity of a Shear Wall with Openings / 7.17
Determination of Seismic Lateral Forces in Shear Walls / 7.39
Horizontal Diaphragms / 7.50
Influence of Building Configuration on Lateral Force Distribution in Shear Walls / 7.57
Analysis of Shear Walls and Diaphragms under Direct Shear and Torsional Moments / 7.69
Design Considerations for Shear Walls / 7.81
Analysis of Shear Walls under Flexure and Axial Loads / 7.95
Design of Multistory Shear Walls / 7.108
Failure Modes of Shear Walls / 7.110
References / 7.121

Chapter 8. Retaining and Subterranean Walls
8.1
8.2
8.3
8.4
8.5
8.6
8.7

Introduction / 8.1
Principal Types of Retaining Walls / 8.2
Lateral Pressures on Retaining Walls / 8.9
External Stability of a Retaining Wall / 8.25
Design Procedure for Masonry Retaining Walls /
Subterranean or Basement Walls / 8.35
Construction Considerations / 8.42
References / 8.48


8.29

Chapter 9. Construction Aspects
9.1
9.2
9.3
9.4
9.5
9.6
9.7

9.1

Introduction / 9.1
Placement of Steel Reinforcement / 9.2
Grouting / 9.7
Movements of Construction Materials, Their Causes and Effects / 9.23
Control of Cracking and Movement Joints / 9.33
Quality Assurance / 9.42
Flashing for Masonry Construction / 9.43
References / 9.46

Chapter 10. Anchorage to Masonry
10.1
10.2
10.3
10.4

8.1


Introduction / 10.1
Types of Anchor Bolts / 10.1
Placement and Embedment of Anchor Bolts in Masonry Grout / 10.2
Nominal Strength of Anchor Bolts / 10.3

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10.1


xii

CONTENTS

10.5 Nominal Axial Strength of Anchor Bolts Loaded in Tension and in Combined
Tension and Shear / 10.5
10.6 Nominal Shear Strength of Headed and Bent-Bar Anchor Bolts in Shear / 10.14
10.7 Headed and Bent-Bar Anchor Bolts in Combined Axial Tension and Shear / 10.15
10.8 Structural Walls and Their Anchorage Requirements / 10.16
References / 10.27

Appendix Design Aids: Tables
Glossary G.1
Index I.1

A.1

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PREFACE TO THE
SECOND EDITION

Why write?
I hear, I forget;
I see, I remember;
I write, I understand.
A Chinese proverb

The writing of this book was motivated by a professional need to update changes in the
reinforced masonry design philosophy that have occurred as a result of incorporation
of strength design philosophy in the 2008 Building Code Requirements for Masonry
Structures reported by the Masonry Standards Joint Committee (referred to in this book as
the MSJC-08 Code) and corresponding requirements of the 2009 International Building
Code (2009 IBC), and to update changes brought out by the ASCE/SEI 7-05 Standard,
Minimum Design Loads for Buildings and Other Structures (referred to in this book as
ASCE 7-05 Standard). While the fundamental principles of designing reinforced masonry
structures discussed in the first edition (2001) of this book remain valid, revisions in
codes, specifications, and reference standards applicable to design and construction of
masonry structures that have since occurred required updating that book in the form of this
second edition.
The allowable stress design (ASD) method of designing reinforced masonry structures
presented in the first edition of this book is still acceptable, and is expected to remain so for
the foreseeable future. However, the general trend in the structural engineering profession
is to move toward using the strength design philosophy for the design of concrete structures,
and load and resistance factor design (LRFD) for the design of steel structures. Readers of
the first edition of this book will note that the topic of strength design of reinforced masonry
was briefly covered in App. D. This second edition is a natural, follow-up publication that

focuses exclusively on strength design philosophy for reinforced masonry structures. In
addition, a new chapter on anchorage to masonry (Chap. 10) has been introduced.
Consistent with the first edition, this edition of the book is written in a stand-alone
format and independent of the ASD philosophy. While knowledge of and familiarity with
the strength design principles for design of reinforced concrete structures would enable
readers to quickly grasp the fundamentals of strength design of reinforced masonry, neither
that knowledge nor that of allowable stress design of masonry are considered prerequisites
for understanding the discussion presented herein. Each chapter of the book presents the
theory based on first principles and is supported by references and followed by numerous
examples that illustrate its application.
Like the first edition of this book, this edition is written for use by students and professionals of reinforced masonry design and construction. It is written in a simple, practical,
and logical manner, and is styled to suit as a text for teaching reinforced masonry design
and construction in a classroom environment at senior/graduate level. Frequent references
to the MSJC-08 Code and ASCE/SEI 7-05 Standard are made throughout all discussions
and examples in this book to acquaint readers with the design and specification requirements
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xiv

PREFACE TO THE SECOND EDITION

that must be followed; readers will find it helpful to keep copies of these two references
handy while reading this book.
Chapter 1 introduces the topic of masonry design and constructionfrom ancient times
to modern timesa practice that began as the art of construction and evolved into the
modern engineered construction. Also presented in the chapter are brief discussions of the

governing building codes and specifications for masonry structures, and governing provisions of ASCE/SEI 7-05 Standard that form the basis of load calculations for analysis and
design.
Masonry structures are built from units that are fabricated in production plants from
clay and concrete, and hand-laid by skilled masons, one unit at a time. Chapter 2 is devoted
to a detailed discussion of both clay and concrete units with respect to industry standards,
product availability, modular sizes, design properties, and applicable ASTM Standards.
Chapter 3 presents a discussion on materials of masonry construction: masonry units,
mortar, grout, and steel reinforcing bars. Reinforced masonry structures are built from
placing masonry units with mortar between them, placing horizontal and vertical reinforcements, and grouting the cells of masonry units to accomplish the desired design objectives.
Adherence to the specifications of these materials is the key to acceptable performance of
as-built structures, hence the importance of this chapter.
Chapters 4 through 10 present analysis and design of masonry structures subjected to
flexure, shear, compression, and combined axial compression and flexure; walls subjected
to out-of-plane loads; shear walls (walls subjected to in-plane loads); retaining walls; and
anchorage to masonry.
Chapter 4 presents an exhaustive discussion of fundamentals of strength design philosophy and their application to flexural analysis and design of masonry structures. This is the
longest and also the most important chapter in the book for it embodies principles of strain
compatibility and ductility, and requirements of the MSJC-08 Code pertaining to design for
flexure, shear, deflection, and cracking moment, concepts which are used in later chapters
of the book. The author has provided in-depth explanation of fundamental principles of
strength design in this chapter, followed by numerous examples designed to satisfy the
many what if questions and curiosities of readers, particularly students. The purpose
of this chapter is to encourage discussion and to develop confidence in understanding the
ramifications of improper designs.
Chapter 5 is devoted to design of compression membersreinforced masonry columns
loaded axially or in combination with bending. Many examples are presented to illustrate
the design concepts and alternatives. An in-depth discussion of interaction diagrams for
columns subjected to combined axial load and bending, including detailed, step-by-step
calculations for developing such diagrams, forms the highlight of this chapter.
Chapter 6 presents analysis and design of reinforced masonry walls subjected to out-ofplane loads due to wind or earthquakes. The chapter presents a discussion and calculation

of these forces based on ASCE/SEI 7-05 Standard. Also presented in this chapter are many
different types of masonry walls and their uses.
Chapter 7 deals with an all-important topic of analysis and design of reinforced masonry
shear walls which are used as systems for resisting lateral forces in building structures
either as the main wind forceresisting systems (MWFRS) or as the seismic forceresisting
systems (SFRS). Because of the extreme importance of this topic, this chapter provides an
in-depth discussion of seismic load provisions of ASCE 7-05 Standard and design requirements pertaining to the many different types of shear walls as classified and permitted by the
standard for use as lateral forceresisting systems.
Chapter 8 describes analysis and design of reinforced masonry earth-retaining walls and
basement walls which are commonly used in practice.
Chapter 9 provides a discussion of masonry construction practices, with an emphasis
on grouting practices. Masonry construction involves hand placement of brick or concrete

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PREFACE TO THE SECOND EDITION

xv

masonry units interfaced with mortar, and then providing reinforcing bars as specified and
followed by grouting. Following recommended procedures for all of these facets of construction is important to ensure intended performance of the as-built masonry structures.
Connection between masonry and other structural components, such as ledger beams
or other load-carrying elements that are required to transfer forces through connections, is
accomplished by anchorage. Chapter 10 is devoted to analysis and design of anchorage to
masonry. The discussion in this chapter presents the various limit states that govern design
of bolted connections to masonry.
The examples in each chapter are presented in a comprehensive, step-by-step manner
that is easy to understand. Every step is worked out from first principles. Typical problems

are provided at the ends of Chaps. 4 to 8 and 10 for readers practice to develop confidence
in understanding the subject matter.
The appendix provides many helpful tables that make analysis and design of masonry
quick, efficient, and interesting, thus avoiding the drudgery of longhand calculations. Use
of these tables is explained in the many examples presented in this book.
As with any professional book, readers will find many new terms introduced. A glossary
of terms used in this book is provided following the appendix.
Narendra Taly, Ph.D., P.E., F.ASCE

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PREFACE TO THE
FIRST EDITION

Reinforced masonry design and construction is both an art and science. Truly recognized as
the oldest building material known to man, masonry has been used in one form or another
since the dawn of history. The Sphinx, Coliseum (the Flavian Amphitheater in Rome),
Parthenon, Roman aqueducts, the Great Wall of China, and many castles, cathedrals, temples,
mosques, and dams and reservoirs all over the world stand as a testimony of enduring and
aesthetic quality of masonry. Masonry construction continues to be used for many types
of buildings, ranging from multistory high-rises to low-income apartment buildings. This
book is intended for engineers, architects, builders, manufacturers of masonry products,
and students who wish to engage in planning, design, construction, and acquire knowledge
of masonry. It can be used as a useful reference volume by engineering professionals as
well as a suitable textbook for students of masonry design and construction.
The book is the outgrowth of authors combined professional and teaching experience of
40 years. Its development began with a set of notes prepared for an senior/graduate course
at the California State University, Los Angeles, beginning 1987 when the author developed

a new course titled Timber and Masonry Design, which he has been teaching ever since.
These notes were expanded and periodically updated with the Uniform Building Code,
which was revised every 3 years. No originality is claimed in writing this book, however.
I acknowledge my debt to the numerous authors and organizations whose work I have
quoted.
The book presents a comprehensive discussion on both theory and design of masonry
structures built from clay and concrete masonry. Each chapter begins with introduction
followed by discussion of theory of structural design using masonry as a structural material, which is quite general and not code-specific. The discussion is supplemented by several examples to illustrate the application of the principles involved. Engineering practice
requires that structures be universally built according to building codes, which continue
to change. Theory and examples presented in this book are referenced to building codes
used in the United States. Because of the heavy use of the Uniform Building Code (UBC
1997) and its strong emphasis on reinforced masonry, it has been referenced in detail in
this book. Considerable space has been given to discussion of earthquake loads and computational methods as specified in the UBC 1997. However, in text as well as in examples,
pertinent references to the International Building Code (IBC 2000, the new code that will
soon be adopted nationally), and the Masonry Standards Joint Committee (MSJC) Code
(ACI 530-99/ASCE 5-99/TMS 402-99) have also been given. Wherever possible, all three
codes have been referenced in the book. Equations and formulas have also been identified
with proper references to the UBC, IBC, and MSJC Code for the use and convenience of a
broad spectrum of readers.
Written for use by professionals of reinforced masonry design and construction, this
book is written in a simple, practical and logical manner, and is formatted to suit as a
text for teaching masonry design and construction in a classroom environment. Because
of the practical nature of the subject, the first three chapters are devoted to a comprehensive discussion on masonry products, materials of construction, and building codes and
ASTM Standards. Chapters 4 (flexural analysis and design of masonry beams), 5 (columns),
xvii

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xviii

PREFACE TO THE FIRST EDITION

6 (walls subjected to axial and out-of-plane loads), 7 (shear walls), and 8 (retaining and
subterranean walls) cover theory of design, followed by code requirements, and detailed
examples. Chapters 6 and 7 introduce design for wind and earthquake loads with a comprehensive discussion of the seismic design provisions of 97-UBC. The examples in each
chapter are presented in a comprehensive, step-by-step manner that is easy to understand.
Every step is worked out from first principles.
Reinforced masonry consists of four different materials: masonry units, mortar, reinforcement, and grout. Masonry derives its strength from the assemblage of these four elements when they are laid together carefully by skilled masons. Therefore, construction
procedures used in masonry work are just as important as design. In recognition, Chap. 9
is devoted to a comprehensive discussion on various aspects of masonry construction that
include placement of reinforcement, mortar joints, grouting, curing, movement joints, and
water-penetration resistance. Chapter 10 presents brief case studies of many masonry highrise buildings to inform readers of the potential of masonry as versatile building material.
This is followed by a discussion on planning and layout of masonry load-bearing building systems, and design example of a four-story concrete masonry shear wall building.
Component design for masonry buildings is covered in Chaps. 4 through 8.
An extensive glossary of terms related to masonry has been provided following Chap. 10
for readers quick reference.
The appendices in the book provide rich information. Appendix A presents 24 design
tables referred to throughout the book. These are gathered together for easy reference,
which makes it possible to use the book in design offices or teaching courses without the
need for a handbook.
This book makes frequent references to Chaps. 16 (Structural Design Requirements)
and 21 (Masonry) of the 97-UBC. These two chapters are provided in Apps. B1 and C,
respectively, for ready reference. Appendix B2 presents a comprehensive discussion and
examples of load combinations as specified in IBC 2000 and 1999-ACI Code. These load
combinations are referred to throughout many examples in the book.
The design of masonry structures presented in this book is based on the allowable stress
design (ASD) principles. Appendix D presents a comprehensive discussion on the strength
design philosophy for masonry structures. Concepts of load factors, strength reduction

factors, and slender wall, and the strength design provisions of the 97-UBC for masonry
structures have been introduced. Detailed examples, including design of slender wall, based
on the strength design principles have been presented in this appendix.

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ACKNOWLEDGMENTS

The author is grateful for the help and assistance provided by many individuals with whom
he had numerous discussions about the interpretation and the intent of the MSJC-08 Code
during the writing of this book. Notably, these include Dr. Richard Bennett, Department
of Civil Engineering, University of Tennessee, Knoxville, Tenn.; Dr. Dave McLean,
Department of Civil Engineering, Washington State University, Pullman, Wash.; and
Mr. Jason Thompson, Director of Engineering, National Concrete Masonry Association
(NCMA), Herndon, Va.
Many individuals have contributed to this book by generously providing permission to
use information and illustrations from their publications. These include Jason Thompson,
Director of Engineering, National Concrete Masonry Association (NCMA); Brian Trimble,
Sr. Director Engineering Services and Architectural Outreach, Brick Industry Association
(BIA); Jamie Farny, Portland Cement Association (PCA); Neal S. Anderson, Vice President
of Engineering, Concrete Reinforcing Steel Institute (CRSI); Kurt Siggard, Executive
Director, Concrete Masonry Association of California and Nevada (CMACN); and many
others. The author is thankful to his student Edward Perez for his help in providing many
of the computer-generated line drawings for this book.
The author appreciates the patience and understanding of the senior acquisitions editor
of this book, Larry Hager, McGraw-Hill, and is thankful to Mark Johnson, Vice President,
International Code Council, for advice and encouragement provided during the writing of
this book.

The author is very thankful to Preeti Longia Sinha, Glyph International, the project
manager for this book, for her professionalism, insight, suggestions, guidance, and, above
all, patience, provided through endless e-mails during the production phase of this book.
Great care has been exercised in organizing and presenting the material in this book,
including giving due credit for permission. However, in spite of numerous proofreadings,
it is inevitable that some errors and omissions will still be found. The author would be
grateful to readers for conveying to him any errors they might find, and for any suggestions
or comments offered.

xix

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NOTATION

The following notation has been used in this book. Much of this notation is in conformance
with IBC 2009, Chap. 21, Sec. 2102.2, and MSJC-08, Chap. 1, Sec. 1.5.
= cross-sectional area of anchor bolt, in.2 (mm2)
= effective cross-sectional area of masonry, in.2 (mm2)
= gross cross-sectional area of masonry, in.2 (mm2)
= net cross-sectional area of masonry, in.2 (mm2)
= projected area on the masonry surface of a right circular cone for anchor bolt

allowable shear and tension calculations, in.2 (mm2)
Aps = area of prestressing steel, in.2 (mm2)
Apt = projected area on masonry surface of right circular cone for calculating tensile
breakout capacity of anchor bolts, in.2 (mm2)
Apv = projected area on masonry surface of one-half of a right circular cone for calculating tensile breakout capacity of anchor bolts, in.2 (mm2)
As = effective cross-sectional area of reinforcement, in.2 (mm2)
As = effective cross-sectional area of compression reinforcement in a flexural member,
in.2 (mm2)
Av = area of steel required for shear reinforcement perpendicular to the longitudinal
reinforcement, in.2 (mm2)
A1 = bearing area, in.2 (mm2)
A2 = effective bearing area, in2 (mm2)
Ast = total area of laterally tied longitudinal reinforcing steel in a reinforced masonry
column or pilaster, in.2 (mm2)
a = depth of an equivalent compression zone (rectangular stress block) at nominal
strength, in. (mm)
Ba = allowable axial force on an anchor bolt, lb (N)
Bab = allowable axial force on an anchor bolt when governed by masonry breakout,
lb (N)
Ban = nominal axial strength of an anchor bolt, lb (N)
Banb = nominal axial force on an anchor bolt when governed by masonry breakout, lb
(N)
Banp = nominal axial force on an anchor bolt when governed by anchor pullout, lb (N)
Bans = nominal axial force on an anchor bolt when governed by steel yielding, lb (N)
Bap = allowable axial force on an anchor bolt when governed by anchor pullout,
lb (N)
Bas = allowable axial force on an anchor bolt when governed by steel yielding, lb (N)
Bv = allowable shear force on an anchor bolt, lb (N)

Ab

Ae
Ag
An
Ap

xxi

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xxii

Bvb
Bvc
Bvn
Bvnb
Bvnc
Bvns
Bvpry
Bvnpry
Bvs
b
ba
baf
bv
bvf
bw
Cd
c

D
d
db
dv
E
EAAC
Em
Es
Ev
e
eb
eu
F
Fa
Fb
Fs

NOTATION

= allowable shear load on an anchor bolt when governed by masonry breakout,
lb (N)
= allowable shear load on an anchor bolt when governed by masonry crushing,
lb (N)
= nominal shear load on an anchor bolt, lb (N)
= nominal shear strength of an anchor bolt when governed by masonry breakout,
lb (N)
= nominal shear strength of an anchor bolt when governed by masonry crushing,
lb (N)
= nominal shear strength of an anchor bolt when governed by steel yielding,
lb (N)

= allowable shear load on an anchor bolt when governed by anchor pryout,
lb (N)
= nominal shear strength of an anchor bolt when governed by anchor pryout,
lb (N)
= allowable shear load on anchor bolt when governed by steel yielding
= width of section, in. (mm)
= total applied design axial force on an anchor bolt, lb (N)
= factored axial force in an anchor bolt, lb (N)
= total applied design shear force on an anchor bolt, lb (N)
= factored shear force in an anchor bolt, lb (N)
= width of wall beam
= deflection amplification factor
= distance from the neutral axis to extreme compression fiber, in. (mm)
= dead load or related internal forces and moments
= distance from the extreme fibers of a flexural member to the centroid of longitudinal tension reinforcement, in. (mm)
= diameter of the reinforcing bar or anchor bolt, in. (mm)
= actual depth of masonry in the direction of shear considered, in. (mm)
= load effects of earthquake or related internal forces and moments
= modulus of elasticity of AAC masonry in compression, psi (MPa)
= modulus of elasticity of masonry in compression, psi (MPa)
= modulus of elasticity of steel, psi (MPa)
= modulus of rigidity (shear modulus) of masonry, psi (MPa)
= eccentricity of axial load, in. (mm)
= projected leg extension of bent bar anchor, measured from inside edge of anchor
at bend to farthest point of anchor in the plane of the hook
= eccentricity of Puf , in. (mm)
= lateral pressure of liquids or related internal forces and moments
= allowable compressive stress due to axial load only, psi (MPa)
= allowable compressive stress due to flexure only, psi (MPa)
= allowable tensile or compressive stress in reinforcement, psi (MPa)


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NOTATION

xxiii

= allowable shear stress in masonry, psi (MPa)
= calculated compressive stress in masonry due to axial load only, psi (MPa)
= calculated compressive stress in masonry due to flexure only, psi (MPa)
= specified compressive strength of AAC, the minimum compressive strength for
a class of AAC as specified in ASTM C1386, psi (MPa)
f g = specified compressive strength of grout, psi (MPa)
f m = specified compressive strength of masonry, psi (MPa)
f mi = specified compressive strength of masonry at the time of prestress transfer, psi
(MPa)
fps = stress in prestressing tendon at nominal strength, psi (MPa)
fpu = specified tensile strength of prestressing tendon, psi (MPa)
fpy = specified yield strength of prestressing tendon, psi (MPa)
fr
= modulus of rupture, psi (MPa)
frAAC = modulus of rupture of AAC, psi (MPa)
fs
= calculated tensile or compressive stress in reinforcement, psi (MPa)
fse = effective stress in prestressing tendon after all prestress losses have occurred, psi
(MPa)
ftAAC = splitting tensile strength of AAC as determined in accordance with ASTM C1006
fv

= calculated shear stress in masonry, psi (MPa)
fy
= specified yield strength of steel for reinforcement and anchors, psi (MPa)
H = lateral pressure of soil or related forces and moments
= effective height of column, wall, or pilaster, in. (mm)
h
hw = height of entire wall or segment of wall considered, in. (mm)
Icr = moment of inertia of cracked cross-sectional area of member, in.4 (mm4)
Ieff = effective moment of inertia of member, in.4 (mm4)
Ig
= moment of inertia of gross (or uncracked) cross-sectional area of member, in.4
(mm4)
= ratio of distance between centroid of flexural compressive forces and centroid of
j
tensile forces to depth, d
= dimension used to calculate reinforcement development length, in. (mm)
K
KAAC = dimension used to calculate reinforcement development length for AAC masonry,
in. (mm)
Kc = coefficient of creep of masonry, per psi (MPa)
ke = coefficient of irreversible moisture expansion of clay masonry
kt
= coefficient of thermal expansion of masonry, per degree Fahrenheit (degree
Celcius)
= live load or related forces and moments
L
= clear span between supports, in. (mm)
l
lb
= effective embedment length of plate, headed or bent anchor bolts, in. (mm)

lbe = anchor bolt edge distance, measured in the direction of load, from edge of
masonry center of cross section of anchor bolt, in. (mm)
ld
= development length or lap length of straight reinforcement, in. (mm)
Fv
fa
fb
f AAC

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xxiv

le
lp
lw
M
Ma
Mcr
Mn
Mser
Mu
n
Nu
Nv
P
Pa
Pe

Pn
Pps
Pu
Puf
Puw
Q
QE
R
r
S
Sn
s
T
t
U
v
V
VAAC

NOTATION

= equivalent embedment length provided by standard hooks measured from the
start of the hook (point of tangency), in. (mm)
= clear span of prestressed member in the direction of prestressing tendon, in.
(mm)
= length of the entire wall or of segment of wall considered in the direction of
shear force
= maximum moment in section under consideration, in.-lb (N-mm)
= maximum moment in member due to the applied loading for which deflection
is considered, in.-lb (N-mm)

= nominal cracking moment strength, in.-lb (N-mm)
= nominal moment strength, in.-lb (N-mm)
= service moment at midheight of a member, including P-delta effects, in.-lb (Nmm)
= factored moment, in.-lb (N-mm)
= modular ratio = Es/Em
= factored compressive force acting normal to shear force that is associated with
Vu loading combination case under consideration, in.-lb (N-mm)
= compressive force acting normal to shear surface, lb (N)
= axial load, lb (N)
= allowable axial compressive force in reinforced member, lb (N)
= Eulers buckling load, lb (N)
= nominal axial strength, lb (N)
= prestressing tendon force at time and location relevant for design, lb (N)
= factored axial load
= factored axial load from tributary floor or roof areas under consideration, lb (N)
= factored weight of wall area tributary to wall section under consideration, lb (N)
= first moment about the neutral axis of an area between the extreme fibers and
the plane at which the shear stress is being calculated, in.3 (mm3)
= the effect of horizontal seismic (earthquake) forces
= seismic response modification factor
= radius of gyration, in. (mm)
= section modulus of the gross cross-sectional area of a member, in.3 (mm3)
= section modulus of the net cross-sectional are of a member, in.3 (mm3)
= spacing of reinforcement, in. (mm)
= forces and moments caused by restraint of temperature, creep, and shrinkage, or
differential settlement
= nominal thickness of a member, in. (mm)
= required strength to resist factored loads, or related internal moments and
forces
= shear stress, psi (MPa)

= shear force, lb (N)
= shear strength provided by AAC masonry, lb (N)

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NOTATION

Vm.
Vn
Vnm
Vns
Vu
W
wstrut
wu
a
b
bb
g

a
d
dne
ds
du
ecs
emu
es

ey
mAAC
f
r
rb
rmax

xxv

= shear strength provided by masonry, lb (N)
= nominal shear strength, lb (N)
= nominal shear strength provided by masonry, lb (N)
= nominal shear strength provided by shear reinforcement, lb (N)
= factored shear force, lb (N)
= wind load or related internal forces and moments
= horizontal projection of the width of the diagonal strut, in. (mm)
= out-of-plane distributed load, lb/in. (N/mm)
= tension reinforcement strain factor
= 0.25 for fully grouted masonry or 0.15 for other than fully grouted masonry
= ratio of area of reinforcement cut off to total area of tension reinforcement at a
section
= reinforcement size factor
= calculated story drift, in. (mm)
= allowable story drift, in. (mm)
= moment magnification factor
= displacements computed using code prescribed seismic forces and assuming
elastic behavior
= horizontal deflection at midheight under service loads, in. (mm)
= deflection due to factored loads, in. (mm)
= drying shrinkage of AAC

= maximum usable compressive strain of masonry
= strain in steel reinforcement
= yield strain in steel reinforcement
= coefficient of friction of AAC
= strength reduction factor
= reinforcement ratio
= reinforcement ratio producing balanced strain conditions
= maximum flexural reinforcement ratio

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ACRONYMS

The following is a list of acronyms/abbreviations frequently used in this text:
AASHTO
ACI
AISC
AISCM
AISCS
AISI
AITC
ANSI

APA
ASCE
ASD
ASTM
B&S
BIA
BOCA
CABO
CMACN
CRC
CRSI
FEMA
IBC
ICBO
IMI
LF
LFD
LRFD
MIA
MSJC
NCMA
NDS
NEHRP
PCA
PCI

American Association of State Highway and Transportation Officials
American Concrete Institute
American Institute of Steel Construction
American Institute of Steel Construction Manual

American Institute of Steel Construction Specifications
American Iron and Steel Institute
American Institute of Timber Construction
American National Standards Institute
American Plywood Association
American Society of Civil Engineers
allowable stress design
American Society for Testing and Materials
beams and stringers
Brick Institute of America, also Brick Industry Association
Building Officials and Code Administrators International
Council of American Building Officials
Concrete Masonry Association of California and Nevada
Column Research Council
Concrete Reinforcing Steel Institute
Federal Emergency Management Agency
International Building Code
International Conference of Building Officials
International Masonry Institute
light framing
load factor design
load and resistance factor design
Masonry Institute of America
Masonry Standards Joint Committee
National Concrete Masonry Association
National Design Specifications for Wood Construction
National Earthquake Hazard Reduction Program
Portland Cement Association
Prestressed Concrete Institute
xxvii


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xxviii

PD
P&T
SBCCI
SCPI
SCR
SEI
SSRC
TCM
TMS
UBC
W
WSD
WWPA

ACRONYMS

plastic design
posts and timbers
Southern Building Code Congress International
Structural Clay Products Institute (now BIA)
structural clay (trademark of Structural Clay Products Institute, now BIA)
Structural Engineering Institute
Structural Stability Research Council

Timber Construction Manual
The Masonry Society
Uniform Building Code
wide flange shape
working stress design
Western Wood Products Association

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DESIGN OF
REINFORCED
MASONRY
STRUCTURES

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