Earthquake engineering : application to design

EARTHQUAKE ENGINEERING

EARTHQUAKE

ENGINEERING

Application to Design

CHARLES K. ERDEY

Northern Arizona University

Formerly Adjunct Professor, California State University Long Beach

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Library of Congress Cataloging-in-Publication Data:

Erdey, Charles K., 1931–

Earthquake engineering: application to design/Charles K. Erdey.

p. cm.

ISBN-13: 978-0-470-04843-6 (cloth)

ISBN-10: 0-470-04843-3 (cloth)

1. Earthquake engineering. I. Title.

TA654.6.E73 2006

624.1
762—dc22

2006011329

Printed in the United States of America

10 9 8 7 6 5 4 3 2 1

v

CONTENTS

PREFACE xi

ACKNOWLEDGMENTS xiii

NOTATION xv

1 OVERVIEW 1

1.1 Introduction / 1

1.2 Concepts, Terminology, and Source of Earthquakes / 2

1.3 Wave Propagation and Velocities / 5

1.4 Magnitude of Earthquakes / 7

1.5 Building Damage / 7

1.6 Structural Failures: Overall Failure / 10

1.7 Component or Joint Failure / 17

1.8 Code Design Forces: Reserve Strength to Counter

Extreme Forces / 21

2 SEISMIC DESIGN REGULATIONS 25

2.1 Building Codes / 25

2.2 UBC 1997: A Model Code / 26

2.3 Interaction of Building Codes and Other Standards / 27

2.4 IBC 2006 / 29

vi CONTENTS

3 REINFORCED-CONCRETE STRUCTURES 36

3.1 Introduction / 36

3.2 Shearing Resistance of RC Beams / 40

3.3 Development Length / 45

3.4 Northridge Experience / 49

3.5 Case 1: Reinforced-Concrete Parking Garage / 50

3.6 Case 2: Reinforced-Concrete Retaining Wall

System / 62

References / 67

4 SEISMIC STEEL DESIGN: SMRF 68

4.1 Design of SMRF Structure: LRFD Method / 68

4.2 Design Steps / 69

4.3 Project Description: Four-Story Office Building / 70

4.4 Project Layout and Typical SMRF per UBC 1994 / 70

4.5 1994 Design / 71

4.6 Wind Analysis: 1997 UBC, CHAPTER 16, DIV. III / 72

4.7 Example: Wind Analysis of Four-Story Building / 73

4.8 Seismic Zones 3 and 4 / 75

4.9 Earthquake Analysis of Four-Story Office Building / 76

4.10 Design for Earthquake / 79

4.11 Significant Changes in 1997 Design / 84

4.12 1997 versus 1994 Design / 86

4.13 Summary of Procedure / 87

4.14 Design Strategies / 89

4.15 Design of Beams: Code Requirements / 89

4.16 Second-Floor Beam / 91

4.17 Beam-to-Column Joint / 92

4.18 Flexural Resistance of Beam-to-Column Joint / 92

4.19 Shear Tab Design / 96

4.20 Shear Tab-to-Beam Welded Connection / 99

4.21 Second-Floor Panel Zone / 99

4.22 Third-Floor Beam / 102

4.23 Third-Floor Shear Tab Connection / 103

4.24 Third-Floor Beam-to-Column Moment Connection / 107

4.25 Third-Floor Panel Zone / 108

4.26 Design of Columns / 109

CONTENTS vii

4.27 Column Final Design Data / 115

4.28 First-Story Column Design for Compression: Major

Axis / 116

4.29 Column Design Flowchart / 120

4.30 Design of Third-Story Column for Compression / 120

4.31 Design of Third-Story Column Splice / 120

4.32 Reexamination of Pre- and Post-Northridge Research

and Literature / 124

References / 126

5 SEISMIC STEEL DESIGN: BRACED FRAMES 128

5.1 Introduction / 128

5.2 Project Description: Four-Story Library Annex / 129

5.3 Wind Analysis / 129

5.4 Earthquake Analysis / 130

5.5 Wind and Earthquake Loads / 135

5.6 Response of Braced Frames to Cyclic Lateral

Loads / 135

5.7 1997 UBC Provisions / 138

5.8 Rules Applicable to Bracing Members / 139

5.9 Column Strength Requirements / 141

5.10 Design for Earthquake / 141

5.11 Strategies for Brace Member Design / 142

5.12 Brace Members 2 and 3 / 144

5.13 Brace Members 3 and 2: First Story / 144

5.14 Design of Fillet Weld Connection / 148

5.15 Design of Gusset Plate: First and Second Stories / 149

5.16 Brace Member 13: Third Story / 152

5.17 Fillet Weld Design: Third and Fourth-Story Gusset

Plates / 154

5.18 Gusset Plate Design: Third and Fourth Stories / 155

5.19 Vertical Component / 156

5.20 Column Design / 157

5.21 Column Splice Design: Third Floor / 166

5.22 Beam Design / 167

5.23 Column Base-Plate Design / 174

5.24 Summary of Design Procedures / 180

viii CONTENTS

5.25 SEAOC Blue Book and the Code / 180

References / 182

6 IBC SEISMIC DESIGN OF SMRF STRUCTURES 184

6.1 IBC Setup of Seismic Design Forces / 184

6.2 Design Example / 184

6.3 IBC Building Categories / 187

7 MASONRY STRUCTURES 191

7.1 Introduction / 191

7.2 Case 1: Retaining Wall System / 193

7.3 Case 2: Seismic versus Wind / 206

7.4 Case 3: Design of CMU Wall and Precast Concrete

Plate / 214

7.5 Case 4: Retail Store, Masonry and Steel / 217

References / 226

8 WOOD-FRAMED BUILDINGS 227

8.1 Introduction / 227

8.2 Northridge Lesson / 228

8.3 Case 1: Steel-Reinforced Wood-Framed Building / 237

8.4 Case 2: Wood-Framed Two-Story Home / 247

8.5 Case 3: Steel-Reinforced Two-Story Duplex / 252

8.6 Case 4: Wood-Framed Commercial Building / 256

8.7 Case 5: Wood-Framed Residential Building / 264

8.8 Case 6: Wood-Framed Garage and Workshop / 273

8.9 Light-Gauge Steel as Alternative to Wood

Framing / 277

8.10 Case 7: Light-Gauge Steel in Multistory Project / 278

Appendix / 283

References / 289

9 MATRICES IN ENGINEERING 290

9.1 Use of Matrices in Engineering / 290

9.2 Matrix Addition and Multiplication / 292

9.3 Matrix Forms / 294

9.4 Transposition / 295

9.5 Minor and Cofactor Matrices / 295

CONTENTS ix

9.6 Determinant of a Matrix / 296

9.7 Inverse of a Matrix / 297

9.8 Linear Systems of Equations / 298

9.9 Elementary Row Operations / 301

9.10 Summary of Matrix Operations / 302

10 DIFFERENTIAL EQUATIONS 303

10.1 Basic Concepts / 303

10.2 First-Order Differential Equations / 304

10.3 Separation of Variables / 304

10.4 Exact Equations / 305

10.5 Integrating Factor / 307

10.6 Second-Order Linear Equations / 309

10.7 Homogeneous Differential Equations / 313

10.8 Characteristic Equation / 313

11 NUMERICAL METHODS AND ENGINEERING APPLICATIONS 314

11.1 Introduction to Dynamic Analysis / 314

11.2 Equation of Motion / 315

11.3 Damping: Damped Free Vibration / 321

11.4 Free Vibrations: Two-Degree Systems / 323

11.5 Eigenvalues and Eigenvectors / 323

11.6 Modeling Actual Structures / 327

11.7 Three-Degree Systems / 329

11.8 Existence and Uniqueness Theory: Wronskian / 334

11.9 Driving Function (Ft

): Seismic Ground Motion

as Ft / 334

12 METHODS AND TOOLS TO UNRAVEL SECRETS OF

EARTHQUAKES 336

12.1 Elements of an Earthquake / 336

12.2 Vertical-Acceleration Component / 339

12.3 New Method of Dynamic Analysis / 339

12.4 Background of Research / 340

12.5 Analysis of Actual Structure / 342

12.6 Results and Findings / 344

12.7 Nature and Causes of Joint Failure / 344

References / 348

x CONTENTS

13 RECENT AND FUTURE DEVELOPMENTS IN SEISMIC

DESIGN 349

13.1 Tests on Joints / 349

13.2 Dogbone Experiment / 350

13.3 Joint Strain Hardening: Speed Straining / 350

13.4 Mechanism of Joint Degradation / 350

13.5 Conclusions / 351

13.6 New Trends / 352

13.7 Seismic Isolation / 353

13.8 Engineered Damping / 357

References / 358

ACRONYMS 359

GLOSSARY 361

References / 370

APPENDIX: COMPUTER ANALYSIS 371

A. SMRF Project Part I / 372

B. SMRF Project Part II / 388

C. Braced-Frame Project / 399

INDEX 423

xi

PREFACE

The primary motivation for writing this book is the causes of structural fail￾ures—what went wrong—during the earthquakes that hit the western states

in the last decades.

In view of the relatively large number of steel moment-resisting frames

damaged during the Northridge earthquake, the book expands on the evalu￾ation and performance of structures of this type. The pre- and post-Northridge

experimental research and new design strategies to improve moment connec￾tions for new buildings are also discussed, keeping in mind basic building

code concepts to demonstrate the application of general strength-level load

combinations.

Topics relevant to seismic design in other areas of engineering, such as

concrete, masonry, and wood-framed buildings, are also included. An attempt

has been made to maintain a practical approach. In lieu of problem-solving,

single design issues, the book walks the reader through step-by-step design

of actual projects in moderate-to-high seismicity areas in compliance with

building regulations.

Chapter 12 introduces a new method of dynamic analysis and discusses

the causes of joint failure in steel design. Subjects like matrices, differential

equations, numerical analysis, and engineering applications are presented for

completeness and ready reference for the reader.

It is hoped that the book will help practicing engineers not yet fully familiar

with seismic design and graduating students to use the building codes in their

seismic design practice.

xiii

ACKNOWLEDGMENTS

The author gratefully acknowledges the comments and suggestions of Tom

King, professor of mathematics, California State Polytechnic University, Po￾mona, and John G. Shipp, S.E., senior member of SEAOC, for their sugges￾tions, and to Victor F. Sanchez, P.E., for his valuable comments. Thanks are

also due to Ernest Pappas, former plan examiner, Mohave County, for his

contribution on some topics, Alex Zupanski, CSULB graduate student for

facilitating the inputting of the author’s mathematical formulas into the com￾puter, and to Alice H. Zwiller for assisting with proofreading.

xv

NOTATION

A
cross-sectional area (in.2

)

AB
ground-floor area

Agt
gross area subjected to tension (in.2

)

Agv
gross area subjected to shear (in.2

)

Ant
net area subjected to tension

Anv
net area subjected to shear (in.2

)

Aw
effective area of weld (in.2

)

Ax
torsional amplification factor (level x)

bƒ
flange width of column

B
width of base plate (in.)

B1, B2
factors used to determine Mu for combined bending

and axial forces

Ca, Cv
seismic coefficients

Ce
height, exposure, and gust factor coefficient

Cq
pressure coefficient subject to function, geometry,

and location of structure or element

D
dead load on structural element

d
depth of column

db
nominal bolt diameter (in.)

dc
column depth (in.)

E, Eh, Ev
earthquake design components

E
modulus of elasticity of steel (29,000 ksi)

Ec
modulus of elasticity of concrete (ksi)

FEXX
strength of weld metal (ksi)

Fi

, Fn, Fx
design seismic forces applied to each level

xvi NOTATION

ƒ

c
strength of concrete

Fp
design seismic force applied to part of structure

Ft
V portion of base shear on top of structure

Fu
specified minimum tensile strength of steel used (ksi)

Fy
specified minimum yield stress of steel used (ksi)

G
shear modulus of elasticity of steel (11,200 ksi)

g
acceleration due to gravity (386 in./s2

)

H
average story height (above and below beam-to￾column connection)

I
seismic importance factor related to Occupancy Cat￾egory; moment of inertia (in.4

)

Iw
importance factor subject to occupancy or function

of building

K
coefficient for estimating natural frequency of beam

(AISC Specification)

L
live load on a structural element; unbraced length

(compression or bracing member)

Lb
laterally unbraced length

Lp
limiting laterally unbraced length

M
maximum moment magnitude

Mmax
value of maximum moment in unbraced segment of

beam (kip-in.)

MA
absolute value of moment at quarter point of un￾braced beam segment (kip-in.)

MB
absolute value of moment at half point of unbraced

beam segment (kip-in.)

MC
absolute value of moment at three-quarter point of

unbraced beam segment (kip-in.)

Mp
plastic moment of resistance of beam

Mu
required flexural strength (kip-in. or kip-ft)

Na, Nv
near-source factors

P
design wind pressure; concentrated load (kips)

Pp
bearing load on concrete (kips)

Pu
required axial strength (kips)

QE
effect of horizontal seismic forces

qs
basic wind pressure subject to basic wind speed

R
numerical coefficient applied to lateral-force-resisting

systems

r
ratio used in determining

RI
response modification factor

Rp
component response modification factor

SA, SB, SC, SD, SE, SF
types of soil profiles

T
elastic fundamental period of vibration; tension force

due to service loads (kips)

tp
thickness of base plate (in.)

NOTATION xvii

tp
panel zone thickness including doubler plates (in.)

U
reduction coefficient

V
total design lateral force (of shear)

Vn
shear force component (kips)

W
total seismic dead load (UBC 1997, Section

1630.1.1)

wz
width of panel zone between column flanges

Z
seismic zone factor; plastic section modulus (in.3

)

fraction of member force transferred across a partic￾ular net section

M
Maximum Inelastic Response Displacement

S
Design-level Response Displacement


deflection (in.)

Redundancy/Reliability Factor


resistance factor

b
resistance factor for flexure

c
resistance factor for axially loaded composite col￾umns

c
resistance factor for compression

t
resistance factor for tension

v
resistance factor for shear

w
resistance factor for welds

0
Seismic Force Amplification Factor