seismic behavior of base-level diaphragm anchorage of ... · component-level investigations 1.4.1.1...

2003

CUREE Publication No. W-24

Earthquake Hazard Mitigation of Woodframe ConstructionFunded by the Federal Emergency Management Agency through a Hazard Mitigation Grant Program

award administered by the California Governor’s Office of Emergency ServicesCUREE

the CUREE-Caltech Woodframe Project

Seismic Behavior of Base-Level DiaphragmAnchorage of Hillside Woodframe Buildings

Yan XiaoLi Xie

The CUREE-Caltech Woodframe Project is funded by the Federal Emergency Management Agency(FEMA) through a Hazard Mitigation Grant Program award administered by the CaliforniaGovernor’s Office of Emergency Services (OES) and is supported by non-Federal sources fromindustry, academia, and state and local government. California Institute of Technology (Caltech)is the prime contractor to OES. The Consortium of Universities for Research in EarthquakeEngineering (CUREE) organizes and carries out under subcontract to Caltech the tasks involv-ing other universities, practicing engineers, and industry.

the CUREE-Caltech Woodframe Project

CUREE

Disclaimer

The information in this publication is presented as apublic service by California Institute of Technology andthe Consortium of Universities for Research in EarthquakeEngineering. No liability for the accuracy or adequacy ofthis information is assumed by them, nor by the FederalEmergency Management Agency and the CaliforniaGovernor’s Office of Emergency Services, which providefunding for this project.

CUREe

CUREEConsortium of Universities for Research in Earthquake Engineering

1301 S. 46th St.Richmond, CA 94804-4698

tel.: 510-231-9557 fax: 510-231-5664e-mail: [email protected] website: www.curee.org

Seismic Behavior of Base-Level DiaphragmAnchorage of Hillside Woodframe Buildings

CUREE Publication No. W-24

2003

Yan XiaoLi Xie

Department of Civil EngineeringUniversity of Southern California

ISBN 1-931995-17-6

First Printing: February 2003

Printed in the United States of America

Published byConsortium of Universities for Research in Earthquake Engineering (CUREE)1301 S. 46th Street, Richmond, CA 94804-4698www.curee.org (CUREE Worldwide Web site)

CUREE

Preface | iii

Preface The CUREE-Caltech Woodframe Project originated in the need for a combined research and implementation project to improve the seismic performance of woodframe buildings, a need which was brought to light by the January 17, 1994 Northridge, California Earthquake in the Los Angeles metropolitan region. Damage to woodframe construction predominated in all three basic categories of earthquake loss in that disaster:

§ Casualties: 24 of the 25 fatalities in the Northridge Earthquake that were caused by building damage occurred in woodframe buildings (1);

§ Property Loss: Half or more of the $40 billion in property damage was due to damage to woodframe construction (2);

§ Functionality: 48,000 housing units, almost all of them in woodframe buildings, were rendered uninhabitable by the earthquake (3).

Woodframe construction represents one of society’s largest investments in the built environment, and the common woodframe house is usually an individual’s largest single asset. In California, 99% of all residences are of woodframe construction, and even considering occupancies other than residential, such as commercial and industrial uses, 96% of all buildings in Los Angeles County are built of wood. In other regions of the country, woodframe construction is still extremely prevalent, constituting, for example, 89% of all buildings in Memphis, Tennessee and 87% in Wichita, Kansas, with "the general range of the fraction of wood structures to total structures...between 80% and 90% in all regions of the US….” (4). Funding for the Woodframe Project is provided primarily by the Federal Emergency Management Agency (FEMA) under the Stafford Act (Public Law 93-288). The federal funding comes to the project through a California Governor’s Office of Emergency Services (OES) Hazard Mitigation Grant Program award to the California Institute of Technology (Caltech). The Project Manager is Professor John Hall of Caltech. The Consortium of Universities for Research in Earthquake Engineering (CUREE), as subcontractor to Caltech, with Robert Reitherman as Project Director, manages the subcontracted work to various universities, along with the work of consulting engineers, government agencies, trade groups, and others. CUREE is a non-profit corporation devoted to the advancement of earthquake engineering research, education, and implementation. Cost-sharing contributions to the Project come from a large number of practicing engineers, universities, companies, local and state agencies, and others. The project has five main Elements, which together with a management element are designed to make the engineering of woodframe buildings more scientific and their construction technology more efficient. The project’s Elements and their managers are:

1. Testing and Analysis: Prof. André Filiatrault, University of California, San Diego, Manager; Prof. Frieder Seible and Prof. Chia-Ming Uang, Assistant Managers

2. Field Investigations: Prof. G. G. Schierle, University of Southern California, Manager 3. Building Codes and Standards: Kelly Cobeen, GFDS Engineers, Manager; John Coil and

James Russell, Assistant Managers 4. Economic Aspects: Tom Tobin, Tobin Associates, Manager 5. Education and Outreach: Jill Andrews, Southern California Earthquake Center, Manager

iv | Seismic Behavior of Base-Level Diaphragm Anchorage of Hillside Woodframe Buildings

The Testing and Analysis Element of the CUREE-Caltech Woodframe Project consists of 23 different investigations carried out by 16 different organizations (13 universities, three consulting engineering firms). This tabulation includes an independent but closely coordinated project conducted at the University of British Columbia under separate funding than that which the Federal Emergency Management Agency (FEMA) has provided to the Woodframe Project. Approximately half the total $6.9 million budget of the CUREE-Caltech Woodframe Project is devoted to its Testing and Analysis tasks, which is the primary source of new knowledge developed in the Project.

Woodframe Project Testing and Analysis Investigations Task # Investigator Topic

Project-Wide Topics and System-level Experiments

1.1.1 André Filiatrault, UC San Diego

Kelly Cobeen, GFDS Engineers

Two-Story House (testing, analysis)

Two-Story House (design)

1.1.2 Khalid Mosalam, Stephen Mahin, UC Berkeley Bret Lizundia, Rutherford & Chekene

Three-Story Apt. Building (testing, analysis) Three-Story Apt. Building (design)

1.1.3 Frank Lam et al., U. of British Columbia Multiple Houses (independent project funded separately in Canada with liaison to CUREE-Caltech Project)

1.2 Bryan Folz, UC San Diego International Benchmark (analysis contest)

1.3.1 Chia-Ming Uang, UC San Diego Rate of Loading and Loading Protocol Effects

1.3.2 Helmut Krawinkler, Stanford University Testing Protocol

1.3.3 James Beck, Caltech Dynamic Characteristics

Component-Level Investigations

1.4.1.1 James Mahaney; Wiss, Janney, Elstner Assoc. Anchorage (in-plane wall loads)

1.4.1.2 Yan Xiao, University of Southern California Anchorage(hillside house diaphragm tie-back)

1.4.2 James Dolan, Virginia Polytechnic Institute Diaphragms

1.4.3 Rob Chai, UC Davis Cripple Walls

1.4.4.4 Gerard Pardoen, UC Irvine Shearwalls

1.4.6 Kurt McMullen, San Jose State University Wall Finish Materials (lab testing)

1.4.6 Gregory Deierlein, Stanford University Wall Finish Materials (analysis)

1.4.7 Michael Symans, Washington State University Energy-Dissipating Fluid Dampers

1.4.8.1 Fernando Fonseca, Brigham Young University Nail and Screw Fastener Connections

1.4.8.2 Kenneth Fridley, Washington State University Inter-Story Shear Transfer Connections

1.4.8.3 Gerard Pardoen, UC Irvine Shearwall-Diaphragm Connections

Analytical Investigations

1.5.1 Bryan Folz, UC San Diego Analysis Software Development

1.5.2 Helmut Krawinkler, Stanford University Demand Aspects

1.5.3 David Rosowsky, Oregon State University Reliability of Shearwalls

Preface | v

Not shown in the tabulation is the essential task of managing this element of the Project to keep the numerous investigations on track and to integrate the results. The lead management role for the Testing and Analysis Element has been carried out by Professor André Filiatrault, along with Professor Chia-Ming Uang and Professor Frieder Seible, of the Department of Structural Engineering at the University of California at San Diego. The type of construction that is the subject of the investigation reported in this document is typical “two-by-four” frame construction as developed and commonly built in the United States. (Outside the scope of this Project are the many kinds of construction in which there are one or more timber components, but which cannot be described as having a timber structural system, e.g., the roof of a typical concrete tilt-up building). In contrast to steel, masonry, and concrete construction, woodframe construction is much more commonly built under conventional (i.e., non-engineered) building code provisions. Also notable is the fact that even in the case of engineered wood buildings, structural engineering analysis and design procedures, as well as building code requirements, are more based on traditional practice and experience than on precise methods founded on a well-established engineering rationale. Dangerous damage to US woodframe construction has been rare, but there is still considerable room for improvement. To increase the effectiveness of earthquake-resistant design and construction with regard to woodframe construction, two primary aims of the Project are:

1. Make the design and analysis more scientific, i.e., more directly founded on experimentally and theoretically validated engineering methods and more precise in the resulting quantitative results.

2. Make the construction more efficient, i.e., reduce construction or other costs where possible,

increasing seismic performance while respecting the practical aspects associated with this type of construction and its associated decentralized building construction industry.

The initial planning for the Testing and Analysis tasks evolved from a workshop that was primarily devoted to obtaining input from practitioners (engineers, building code officials, architects, builders) concerning questions to which they need answers if they are to implement practical ways of reducing earthquake losses in their work. (Frieder Seible, André Filiatrault, and Chia-Ming Uang, Proceedings of the Invitational Workshop on Seismic Testing, Analysis and Design of Woodframe Construction, CUREE Publication No. W-01, 1999.) As the Testing and Analysis tasks reported in this CUREE report series were undertaken, each was assigned a designated role in providing results that would support the development of improved codes and standards, engineering procedures, or construction practices, thus completing the circle back to practitioners. The other elements of the Project essential to that overall process are briefly described below. To readers unfamiliar with structural engineering research based on laboratory work, the term “testing” may have a too narrow a connotation. Only in limited cases did investigations carried out in this Project “put to the test” a particular code provision or construction feature to see if it “passed the test.” That narrow usage of “testing” is more applicable to the certification of specific models and brands of products to declare their acceptability under a particular product standard. In this Project, more commonly the experimentation produced a range of results that are used to calibrate analytical models, so that relatively expensive laboratory research can be applicable to a wider array of conditions than the single example that was subjected to simulated earthquake loading. To a non-engineering bystander, a “failure” or “unacceptable damage” in a specimen is in fact an instance of successful experimentation if it provides a valid set of data that builds up the basis for quantitatively predicting how wood components and systems of a wide variety will perform under real earthquakes. Experimentation has also been conducted to improve the starting point for this kind of research: To better define what specific kinds of simulation in the laboratory best represent the real conditions of actual buildings subjected to earthquakes, and to develop protocols that ensure data are produced that serve the analytical needs of researchers and design engineers.

vi | Seismic Behavior of Base-Level Diaphragm Anchorage of Hillside Woodframe Buildings

Notes (1) EQE International and the Governor’s Office of Emergency Services, The Northridge Earthquake of January

17, 1994: Report of Data Collection and Analysis, Part A, p. 5-18 (Sacramento, CA: Office of Emergency Services, 1995).

(2) Charles Kircher, Robert Reitherman, Robert Whitman, and Christopher Arnold, “Estimation of Earthquake

Losses to Buildings,” Earthquake Spectra, Vol. 13, No. 4, November 1997, p. 714, and Robert Reitherman, “Overview of the Northridge Earthquake,” Proceedings of the NEHRP Conference and Workshop on Research on the Northridge, California Earthquake of January 17, 1994, Vol. I, p. I-1 (Richmond, CA: California Universities for Research in Earthquake Engineering, 1998).

(3) Jeanne B. Perkins, John Boatwright, and Ben Chaqui, “Housing Damage and Resulting Shelter Needs: Model

Testing and Refinement Using Northridge Data,” Proceedings of the NEHRP Conference and Workshop on Research on the Northridge, California Earthquake of January 17, 1994, Vol. IV, p. IV-135 (Richmond, CA: California Universities for Research in Earthquake Engineering, 1998).

(4) Ajay Malik, Estimating Building Stocks for Earthquake Mitigation and Recovery Planning, Cornell Institute

for Social and Economic Research, 1995.

Acknowledgements | vii

Acknowledgements

This research project was carried out as part of the CUREE-Caltech Woodframe

Research Program (Task 1.4.1-2) sponsored by the Federal Emergency Management Agency

(FEMA). The authors would like to thank the program coordinators and the funding agency. The

inputs provided by the following individuals are warmly appreciated: Mr. Nicolino G. Delli

Quadri (LA City DBS) Mr. S.L. Perlof (S. Perlof Consulting Structural Engineers), Mr. Steve

Pryor (Simpson Strong-Tie), Mr. N. Roselund (Roselund and Assoc.), Mr. J. Russell, Mr. R.P.

Sonntag (Sonntag and Assoc.), Ms.Vida Tarasyoly (Rubicon, Inc.), Prof. Chia-Ming Uang

(UCSD). In particular, Mr. Russell provided careful and in-depth reviews on the previous

versions of the project report, helping the authors to improve the quality of the report. Thanks are

also due to Mr. H. Wu, and Mr. A. Esmaeily-Ghasemabadi, graduate research assistants of USC

for their helps during the project.

viii | Seismic Behavior of Base-Level Diaphragm Anchorage of Hillside Woodframe Buildings

Abstract

This report summarizes an experimental and analytical program on seismic behavior of

the base-level diaphragm anchorage of hillside wood-frame buildings. The background of

practice in the construction of hillside buildings as well as the current code requirements for

earthquake resistance was reviewed and an experimental program with testing of primary and

secondary anchors under simulated seismic loading was carried out. Analytical models were

developed for pushover analysis of the base-level diaphragm in both the downhill direction and

the cross downhill direction.

Table of Contents | ix

Table of Contents Preface iii

Acknowledgements vii

Abstract viii

Table of Contents ix

List of Tables xi

List of Figures xii

Chapter 1 Introduction 1 Chapter 2 Background 3

2.1 Characteristics of Hillside Buildings 3

2.2 Retrofit Ordinance of the City of Los Angeles 10

2.3 Review of a Retrofit Example 15

Chapter 3 Experimental Program 25

3.1 Specimen Details 25

3.2 Test Setup 31

3.3 Instrumentation 38

3.4 Loading Protocol 41

Chapter 4 Experimental Results 43

4.1 General Observation 43

4.2 Force-Displacement Responses 55

4.3 Deformations 63

x | Seismic Behavior of Base-Level Diaphragm Anchorage of Hillside Woodframe Buildings

Chapter 5 Analytical Study 79

5.1 General 79

5.2 Model Building 80

5.3 Analytical Models 82

5.4 Analytical Procedures 92

5.5 Analytical Results and Discussion 95

5.6 Push-Over Analysis Based on Incremental Linear Procedure 98

5.7 Comments on Performance Based Design Criteria 100

Chapter 6 Summary 103

References 105

List of Tables | xi

List of Tables 3.1 Test matrix 25

4.1 Test results 45

5.1 Details of Components and Diaphragm of Model Building 81

5.2 Nailing Schedule of Diaphragm Specimens 85

5.3 Mechanical Properties of Diaphragm Specimens 86

xii | Seismic Behavior of Base-Level Diaphragm Anchorage of Hillside Woodframe Buildings

List of Figures 2.1 One Story Hillside Building 5

2.2 Two Story Hillside Building 5

2.3 One Story Hillside Building with Another Story Down 5

2.4 Hillside Building with Garage at Same Level 6

2.5 Hillside Building with Garage at Basement 6

2.6 A Box Type Building on Level Ground 7

2.7 A Box Type Hillside Building 7

2.8 Deflection under Downhill Earthquake Forces 8

2.9 Rotation under Cross Downhill Earthquake Forces 8

2.10 Damage to Connections on Sill Plates 9

2.11 Damage to Connections on Ledges 9

2.12 Plot Plan 18

2.13 Ground Floor Plan 18

2.14 Foundation Plan 19

2.15 Roof Plan 19

2.16 South Elevation 20

2.17 North Elevation 20

2.18 East Elevation 21

2.19 West Elevation 21

2.20 New Foundation Plan (After Retrofit) 22

2.21 Section A (After Retrofit) 22

2.22 Secondary Anchors 23

List of Figures | xiii

3.1 Specimen details 26

3.2 Test setup 32

3.3 A Specimen in Test 37

3.4 Strain Gauges applied at Plywood and Collectors/Joists 38

3.5 Loading Procedure 42

4.1 General Observation for Specimen SA-1 46



4.4 General Observation for Specimen PA-1 51

4.5 General Observation for Specimen PA-2 53

4.6 Force-Displacement Response of Specimen SA-1 56



4.9 Force-Displacement Response of Specimen PA-1 58

4.10 Force-Displacement Response of Specimen PA-2 58

4.11 Envelope Curve of Force-Displacement Response, Specimen SA-1 59



4.14 Envelope Curve of Force-Displacement Response, Specimen PA-1 60

4.15 Envelope Curve of Force-Displacement Response, Specimen PA-2 61

4.16 Hysteresis Loop Model 62

4.17 Parameter Input and Numeric Result of Hysteresis Loops of HD5 Anchor Assembly

Following an Arbitrary Load History 62

4.18 Displacement Distribution, Specimen SA-1 64



4.21 Displacement Distribution, Specimen PA-1 65

4.22 Displacement Distribution, Specimen PA-2 66

4.23 Joist Strain Distribution, Specimen SA-1 67


xiv | Seismic Behavior of Base-Level Diaphragm Anchorage of Hillside Woodframe Buildings


4.26 Joist Strain Distribution, Specimen PA-1 70

4.27 Joist Strain Distribution, Specimen PA-2 71

4.28 Plywood Strain Distribution, Specimen SA-2 72

4.29 Plywood Strain Distribution, Specimen PA-1 72

4.30 Strain Gauge Response, Specimen SA-1 73



4.33 Strain Gauge Response, Specimen PA-1 76

4.34 Strain Gauge Response, Specimen PA-2 77

5.1 Plan and Side View of Model Building 80

5.2 Floor Framing Plan of Base-Level Diaphragm 81

5.3 Analytical Model of Base-Level Diaphragm in Downhill Direction 83

5.4 Analytical Model of Base-Level Diaphragm Normal to Downhill Direction 83

5.5 Framing Configuration of Diaphragm Specimens RD1, RD2 and RD3 87

5.6 Load-Displacement Curve of Specimen RD1 87



5.9 Load-Displacement Curve of Shear Wall Specimen 90

5.10 Force-Displacement Curve of Nonlinear Spring for Shear Walls 90

5.11 Force-Displacement Curve of Nonlinear Spring for Primary Anchors 91

5.12 Force-Displacement Curve of Nonlinear Spring for Secondary Anchors 91

5.13 Finite Element Model for Downhill Direction 93

5.14 Element Numbering for Downhill Direction 93

5.15 Finite Element Model for Normal to Downhill Direction 94

5.16 Element Numbering for Normal to Downhill Direction 94

5.17 Force-Displacement Curve in Downhill Direction 96

5.18 Force-Displacement Curve in Normal to Downhill Direction 96

5.19 Reaction-Displacement Curves in Downhill Direction 97

5.20 Reaction-Displacement Curves in Normal to Downhill Direction 97

List of Figures | xv

5.21 Flow Chart of Incremental Linear Analysis 98

5.22 Input and Output at First Yield 99

5.23 Force-Displacement Curve of the Diaphragm by VisualAnalysis 100

xvi | Seismic Behavior of Base-Level Diaphragm Anchorage of Hillside Woodframe Buildings

Introduction | 1

Chapter 1 Introduction

Hillside dwellings are popular in the west coast of the United States. There are many reasons

why people prefer hillside homes. The followings are a few (Levin, 1999):

(1) More privacy than in the crowded cities or the usual suburb.

(2) Attractive country atmosphere.

(3) Spectacular view.

(4) Abundant wildlife nearby, etc.

Although the cost of construction on the hills is generally higher than that on level

grounds, high profits can be achieved if the land is carefully selected and the design and

development are intelligently done.

However, there is ample evidence indicating a need for retrofit of existing hillside

buildings in high seismic regions such as in California, especially those designed under the

guidance of older codes. After the 1994 Northridge Earthquake, an effort was devoted to

establish standards for retrofit of hillside buildings in the City of Los Angeles. However, there is

still a lack of sufficient experimental data to verify the performance and reliability of hillside

buildings after retrofit. Further experimental and analytical investigations on seismic

performance of woodframe hillside buildings are needed.

This report summarizes an investigative program on seismic behavior of the base-level

diaphragm anchorage of hillside wood-frame buildings. The specific research objectives include:

i. To provide a literature review on the practice of construction and retrofit of hillside

buildings, existing research, and code requirements or guidelines.

ii. To define and conduct an experimental program to provide information on the seismic

behavior of hillside buildings.

iii. To develop analytical methods for evaluating the performance of hillside buildings and

their key structural elements.

2 | Seismic Behavior of Base-Level Diaphragm Anchorage of Hillside Woodframe Buildings

Chapter 2: Background | 3

Chapter 2 Background

2.1 Characteristics of Hillside Buildings

The January 17, 1994 Northridge alerted society and the engineering profession about the

seismic vulnerability of hillside constructions of woodframe buildings (“Northridge” 1995;

“Woodframe” 2001). In the 1994 Northridge earthquake more than 300 hillside woodframe

dwellings suffered structural damage, including destructive collapse of 14 hillside buildings with

the loss of five lives (Roselund, 1996). It is estimated that there are approximately 10,000

existing hillside buildings in the City of Los Angeles. Some of them might be hazardous and

susceptible to life-threatening collapse or severe structural damage in event of a major

earthquake.

Illustrations of different types of hillside buildings are shown in Fig. 2.1 to Fig. 2.5. The

spaces below the base-level diaphragm can be enclosed or open, and occupied or not. One of the

common characteristics of structural damage unique to hillside buildings is related to the

connections between the grade beams at the uphill side and the base-level diaphragms. The

difference between hillside buildings and buildings that are on level grounds is apparent by a

comparison of sketches of a simple box type building with flexible shear walls below the lowest

diaphragm (Fig. 2.6) and a similar hillside building (Fig. 2.7). Deformation characteristics of the

hillside building under two types of earthquake forces are briefly reviewed in the following.

2.1.1 Earthquake Forces Acting in Downhill Direction

Compared with the flexible wood shear walls and diaphragms, concrete grade beams can

be deemed as rigid. The horizontal deflection of the flexible base-level diaphragm under

earthquake forces in the downhill direction is not compatible with the deflection of the rigid

uphill grade beam, as shown in Fig. 2.8. Thus, it leads to internal forces in the connections

between the base-level diaphragm and the grade beam. When the internal forces exceed the

capacities of the connections, damage occurs. Several types of damage to the connections are

shown in Fig. 2.10 to Fig. 2.11 (Roselund, 1996). Damage to these elements may lead to loss of

vertical support for the framing at the uphill side. This weakness can be compounded by damage


to the connections due to deterioration of the wood and the metal connectors: rotted wood and

corroded anchor bolts and nails caused by water from many years of poor yard drainage or heavy

garden irrigation.

Horizontal deflections of the base-level diaphragm are mainly contributed by the

following two sources:

(1) Flexibility in the diaphragm

As the diaphragm deflects between the vertical shear resisting elements below it, the mid-

span of the uphill edge of the diaphragm may deflect away from its support at the uphill side.

(2) Flexibility in the shear walls or other vertical supports below the diaphragm

The entire diaphragm may deflect away from its support at the uphill side due to drift or

damage in the vertical bracing elements below the diaphragm. Typical vertical bracing elements

that produce damaging drift include the following three types:

(a). Tension-only rod bracing that yields or fails due to fracture;

(b). Flexible wood-framed shear walls that allow excessive drift;

(c). Weak shear walls that fail in shear resulting in excessive drift.

Shear walls on stepped footings belong to weak shear walls of 2(c). The damage found in

earthquake-shaken hillside buildings has shown that those shear walls may be subjected to non-

uniform distribution of internal forces. The highest internal forces will be produced in the nails

and anchor bolts at the uphill step due to its greater stiffness, which is a phenomenon similar to

the short columns in a frame structure. If failure occurs in the most highly loaded uphill

connectors, progressive damage quickly extends into the adjacent down-slope wall segment as

forces are redistributed within the shear wall assembly.

2.1.2 Earthquake Forces Acting Normal to Downhill Direction

Due to the relatively larger flexibility in the vertical bracing system along the downhill

side under the base-level diaphragm, earthquake forces acting normal to downhill direction lead

to rotation of the base-level diaphragm, as shown in Fig. 2.9. Rotation of the diaphragm also

leads to differential deformations that can result in damage to the connections along the grade

beam at the uphill side, similar to those discussed above.


Fig. 2.1 One Story Hillside Building Fig. 2.2 Two Story Hillside Building

Fig. 2.3 One Story Hillside Building with Another Story Down


Fig. 2.4 Hillside Building with Garage at Same Level

Fig. 2.5 Hillside Building with Garage at Basement


Fig. 2.6 A Box Type Building on Level Ground

Fig. 2.7 A Box Type Hillside Building


Fig. 2.8 Deflection under Downhill Earthquake Forces

Fig. 2.9 Rotation under Cross Downhill Earthquake Forces


Fig. 2.10 Damage to Connections on Sill Plates

Fig. 2.11 Damage to Connections on Ledgers


2.2 Retrofit Ordinance of the City of Los Angeles

The Voluntary Existing Hillside Buildings Retrofit Ordinance (1996) of the city of Los

Angeles (referred to Ordinance below) was proposed after the 1994 Northridge earthquake. The

goal of retrofit is to identify structural hazards and to mitigate the hazards at reasonable cost. The

seismic response of an existing hillside building can be greatly improved by strengthening the

connections between the base-level diaphragm and the uphill foundation and by reducing the

flexibility and improving the strength of the vertical bracing system under the base-level

diaphragm. The main features of the Ordinance are provided in the following sections.

2.2.1 Scope

The retrofit Ordinance is applicable to all existing buildings on or into slopes steeper than

3 horizontal to 1 vertical, constructed on either uphill or downhill sites. Such buildings have been

recognized as life hazardous as a result of partial or complete collapse that occurred during the

Northridge earthquake. Seismic strengthening constructed prior to the effective date of the

Ordinance shall also be evaluated and modified in accordance with the provisions of this

Ordinance.

2.2.2 Definitions

Certain terms are defined in the Ordinance as follows:

Base-level diaphragm: The floor at or closest to the top of the highest level of the

foundation.

Diaphragm anchors: Assemblies that connect a diaphragm to the adjacent foundation at

the uphill diaphragm edge.

Primary anchors: Diaphragm anchors from a diaphragm strut or collector, providing a

direct connection between the base-level diaphragm and the foundation at the uphill side. The

diaphragm strut or collector must engage the full width of the diaphragm, thus forming the edge

of the diaphragm or dividing the diaphragm into panels.


Secondary anchors: Other diaphragm anchors that provide a redundant interconnection

between the base-level diaphragm and the foundation at the uphill side.

2.2.3 Degree of Hazard

Existing hillside buildings are categorized in the Ordinance according to degree of hazard

as follows:

Category I: the most hazardous category includes rod-braced buildings; buildings with no

shear walls below the base-level diaphragm and no primary anchors connecting the diaphragm to

the foundations; and buildings with no apparent lateral force resistance.

Category II: those downhill buildings including buildings with sloped sill plates;

buildings without foundation anchor bolts; non-shear wall buildings with connections at the

foundation critical to the lateral force resistance such as braced frames or moment frames.

Category III: all other downhill buildings not listed in category one or two, such as

downhill buildings with stepped sill plates.

Category IV: the least hazardous category that covers all other uphill buildings not listed

in category one, including non-shear wall buildings with connections at the foundation critical to

the lateral force resistance such as braced frames or moment frames.

2.2.4 Analysis and Design

2.2.4.1 Base for Seismic Design

The base for seismic design is defined as follows:

A. Downhill Direction:

For seismic forces acting in the downhill direction, the base of the building is defined as

the floor at or closest to the top of the highest level of the foundation.

B. Normal to Downhill Direction:

For seismic forces acting normal to the downhill direction, the base of the building is

defined as the lowest level of the foundation. The distribution of seismic forces over the height

of the building needs to be determined. Retrofitting, however, shall only be required at the base

level and below.


2.2.4.2 Base Shear

The base level lateral force for allowable stress design shall be that required at the time of

the original building permit, but not less than V=0.133W, where, W is the weight of the entire

building.

2.2.4.3 Downhill Base Shear Resistance

Downhill base shear, including forces from the base-level diaphragm, shall be resisted by

primary anchors between the diaphragm and the uphill foundation. Primary anchors are intended

to provide the principal connections of the building to its foundation and are thus in the primary

load path of seismic forces from the foundation into the superstructure. Therefore, primary

anchors are designed to resist 125% of the tributary seismic forces in the downhill direction and

to be spaced at a maximum 30 ft on center. The foundation must be shown to be adequate to

resist the concentrated loads from the primary anchors.

Secondary anchors are intended to reduce the flexibility of the diaphragm. They shall be

uniformly distributed along the uphill diaphragm edge and shall be spaced a maximum of 4 ft on

center. Secondary anchors at the base level are designed for a uniformly distributed minimum

force equal to the total primary anchorage design force at that level divided by the length of the

uphill diaphragm edge, but not less than 300 pounds per lineal foot. The load path for secondary

anchors need not be developed beyond the connection to the foundation. Secondary anchors are

not required in the following special cases:

A. Foundations in the downhill direction spaced no more than 30 ft apart, that extend up

to and are directly connected to the base-level diaphragm for at least 70 percent of the diaphragm

depth.

B. The diaphragm is separated from the sill plate at the uphill foundation by a cripple

wall which has anchor bolts and is braced in the plane of the wall and constructed with studs that

are not less than 12 inches in height. Primary anchors are spaced at a maximum of 20 ft on

center.

C. Deflection of the plywood floor diaphragm between adjacent primary anchors is

calculated to be less than ¼ inch.


Wood diaphragm struts, collectors and other wood members connected to primary

anchors shall not be less than 3X members or doubled 2X members fastened together. Secondary

anchors may be developed through 2X framing members. All primary and secondary anchorages

including struts, splices and collectors must be designed for 125% of the tributary force.

The seismic load factor shall be 1.7 for steel elements when using strength design, and

concrete embedment anchorage shall use a load factor of 2.0 for strength design method is used.

For materials using allowable stress design method, the one-third allowable stress increase is not

permitted.

2.2.4.4 Systems Normal to Downhill Direction

Vertical bracing system normal to the downhill direction below the base-level diaphragm

at the downhill side is required to limit diaphragm rotation under the seismic forces normal to the

downhill direction. The inter-story drift below the base-level diaphragm shall not exceed 0.5% of

the story height. The total drift from the base level diaphragm to the foundation shall not exceed

¾ inch. The story height along a stepped foundation shall be measured from the average height

of the top of the foundation to the base level diaphragm.

2.2.4.5 Alternate Lateral Force Resisting Systems

As an alternative to providing primary anchor connections from the diaphragm to the

foundation in the downhill direction and as options for resisting lateral forces normal to the

downhill direction, the following systems may be used:

A. Wood Structural Panel Shear Walls:

Wood structural panel shear walls may be used provided:

a. The minimum length of shear wall shall be 8 ft.

b. The minimum level length between steps in the shear wall sill shall be 8 ft and the

maximum step height between adjacent sills shall be 2'-8".

c. Sill plates do not slope and they bear on a level surface.

d. The design lateral forces shall be distributed to lateral force-resisting elements of

varying heights in accordance with the stiffness of each individual element. The stiffness of a

stepped wood shear wall may be determined by dividing the wall into adjacent rectangular


elements, subject to the same top deflection. Sheathing and fastening requirements for the stiffest

section shall be used for the entire wall. Each section of wall shall be anchored for shear and

uplift at each step as an independent shear wall.

e. The drift is limited to a maximum of 0.5% of the story height.

B. Braced Frames:

Structural steel braced frames with concentric connections may be used as part of the

lateral force-resisting system. All members in braced frames shall be designed to resist tension

and compression forces. Seismic forces shall not induce flexural stresses in any member of the

frame, in diaphragm struts, or in the connectors.

C. Rod-Braced Frames:

Tension-only bracing performed very poorly during the Northridge earthquake. Existing

tension-only bracing may be included in the lateral load resisting system provided its

components are exposed and tested to confirm their capacity to resist 5 times the design force

and that the connections have the capacity to resist the yield strength of the bracing.

D. Steel Moment Frames:

Lateral force-resisting systems normal to the downhill direction may include steel

moment frames in addition to those mentioned above provided the drift does not exceed 0.5% of

the story height.

2.2.4.6 Diaphragms

Diaphragms at the base level and below may be of straight 1x6 or 2x6 sheathing provided

downhill vertical lateral force-resisting elements or primary anchors are spaced no more than 20

ft apart and the diaphragm shear forces do not exceed 100 pounds per lineal foot. Existing

plywood and diagonally sheathed diaphragms need not be investigated. Existing cantilevered

wood diaphragms are acceptable provided they do not cantilever more than one half of the

diaphragm back span (anchor span).


2.2.4.7 Foundations

All intersecting foundations shall be positively anchored where separation has occurred.

Damaged foundations shall be evaluated by the engineer or architect and, if found to reduce the

capacity of the vertical and lateral force-resisting system, be repaired or replaced. Metal

connectors shall not be in contact with, or below earth unless the connectors are hot dipped

galvanized and further protected from earth with 4 inches of concrete.

2.3 Review of a Retrofit Example

An earlier retrofit project of a hillside residential house (Sonntag, 1989) is reviewed in

this section, in the light of the retrofit Ordinance (1996). This retrofit project was completed in

1990, prior to the effective date of the retrofit Ordinance. The house was located in the City of

Los Angeles and sustained certain damage during the 1987 Whittier earthquake. Plans and

elevations of the existing house are shown in Fig. 2.12 to Fig. 2.19.

The degree of hazard of the existing building falls in category III based on the LA

Ordinance. The downhill slope is approximately 1:2. Some cracks were observed in walls and

foundations around the interconnection between the original house and the addition. The existing

footing was replaced by reinforced concrete grade beams with six piles below them. The new

foundation plan is shown in Fig. 2.20. A section of the house after retrofit is shown in Fig. 2.21.

All existing shear walls below the base-level diaphragm were replaced with new wood shear

walls, which function as an alternative of the primary anchors.

The maximum distance between lateral force-resisting elements (shear walls) in the

downhill direction before retrofit was 37 ft, larger than 30 ft (the maximum distance permitted by

the Ordinance). After retrofit, the maximum distance was 25 ft, satisfying the requirement of the

Ordinance.

There was no secondary anchor in the existing building. New secondary anchors were

added and spaced 32 inches apart, less than 48 inches per the requirement of the Ordinance. Fig.


2.22 is an illustration of the secondary anchor at the uphill diaphragm edge, not necessarily a

proper way to install a PA anchor.

For a preliminary check of this retrofit project, appropriate values are assumed for the

dead loads of the roof, floor, and the exterior and inner walls as shown below:

Roof dead load:

15 psf on a horizontal plane

Floor dead load:

20 psf

Exterior wall dead load:

15 psf

Inner wall dead load:

10 psf

Weight of the roof:

24x62x15 = 22320 pounds

Weight of the floor:

21x60x20 = 25200 pounds

Weight of exterior walls in half a story above the base level:

162x8.5/2x15 = 10328 pounds

Weight of exterior walls in half a story below the base level:

81x12.75/2x15 = 7746 pounds

Weight of inner walls in half a story above the base level:

124x8.5/2x10 = 5270 pounds

Weight of inner walls in half a story below the base level:

56x12.75/2x10 = 3570 pounds

Lumped weight at the roof level:

W2 = 22320+10328+5270 = 37918 pounds

Lumped weight in the floor level:

W1 = 25200+10328+7746+5270+3570 = 52114 pounds

Total weight:

W = 37918+52114 = 90032 pounds


(1) Base shear in downhill direction:

hn = 8.5 ft

T = 0.02x(hn)3/4 = 0.1 sec

Ca = 0.44

Cv = 0.64

Ts = Cv/(2.5Ca) = 0.58 sec > T = 0.1 sec

R = 4.5

I = 1.0

V = (2.5CaI/R)W/1.4 = 0.174W > 0.133W

V = 0.174x90032 = 15700 pounds

When the allowable stress design method is used, the total design base shear for the

secondary anchors or the wood shear walls below the base-level diaphragm in the downhill

direction is

Vd = 1.25x15700 = 19625 pounds

(2) Base shear normal to the downhill direction:

hn = 21.3 ft

T = 0.02x(hn)3/4 = 0.2 sec

Ts = 0.58 sec > T = 0.2 sec

V = 0.174x90032 = 15700 pounds

The total design base shear is the same as that in the downhill direction.

The capacity of each secondary anchor may be estimated as 900 pounds and there were at

least 25 secondary anchors. So, the total capacity of secondary anchors is 22500 pounds > 19625

pounds, sufficient as a redundant measure. The wood shear walls below the base-level

diaphragm (an alternative of the primary anchors) can also be shown to have sufficient capacity

to resist the design base shears. However, it should be pointed out that considering the projected

capacity of the bent PA18 anchors, these secondary anchors would be insufficient for resisting

the base shear. More over, in current design practice, there is no consideration of the possible

performance and failure mode of the hillside structures and their components. These should be

addressed in the research program.


Fig. 2.12 Plot Plan

Fig. 2.13 Ground Floor Plan


Fig. 2.14 Foundation Plan

Fig. 2.15 Roof Plan


Fig. 2.16 South Elevation

Fig. 2.17 North Elevation


Fig. 2.18 East Elevation

Fig. 2.19 West Elevation


Fig. 2.20 New Foundation Plan (After Retrofit)

Fig. 2.21 Section A (After Retrofit)


Fig. 2.22 Secondary Anchors

Chapter 3: Experimental Program | 25

Chapter 3 Experimental Program

3.1 Specimen Details

An experimental program was carried out to define and evaluate the seismic characteristics

including force-displacement response, capacities and failure modes of anchorage for a base

level diaphragm. The experimental program included testing subassemblies of a portion of base-

level diaphragm with primary or secondary anchors. Although in an actual retrofit project,

engineers have the option to use standard anchor products or custom-built ones, only standard

anchors manufactured by the Simpson StrongTie Company were tested to limit the variety of the

specimens. Two model specimens were tested for primary anchors, HD15 and PHD8, and three

specimens were tested for secondary anchors, HD5, PHD5 and HTT22. The specimen details are

given in Table 3.1 and Fig. 3.1.

Table 3.1 Test Matrix

Specified Capacities by Manufacturer Specimen Anchor Joist/

Collector Allowable Capacity Qa (kips)

Yield Capacity Qy (kips)

PA-1 HD15 6x6 15.305 34.5

Prim

ary

Anc

hors

PA-2 PHD8 6x6 6.730 15.2

SA-1 HD5 (2)2x8 3.705 8.4

SA-2 PHD5 (2)2x8 4.685 10.6

Seco

ndar

y A

ncho

rs

SA-3 HTT22 (2)2x6 5.250 9.9

Note: 1. All specimens use non-symmetric (single anchor) connection; 2. Allowable capacity refers to the

allowable stress design (ASD); 3. Qy = k Qa / 1.33, where k = 2.5 for HTT22, 3.0 for other anchors.

Each specimen can be considered as a portion of the base level diaphragm, with a 4’x6’

sheet of plywood nailed on joists/collectors and an anchor connected to the uphill footing. The

width of the plywood of the specimen was 4ft., while the center distance of the joists was 16in.,

simulating an anchor spacing of 2x16=32in. The length of the specimens was determined by


considering the dimension of the loading frame. Three identical anchors were used at the other

end to simulate distributed earthquake forces. For convenience of test setup, the specimens were

designed to be identical at both testing and loading ends.

1. ALL JOISTS AND BEAMS USE DOUGLAS FIR NO. 2

2. DIAPHRAGM SHEATHING USES 5/8" PLYWOOD, STRUCT. I (STD. INDEX #32/16)

3. BOLT SIZE: ANCHOR BOLTS: 1 1/4" DIA. STUD BOLTS: 1" DIA.

3 1/2"

8"16

"16

"8"

48"

16"

NAILS AT 4" O.C. TO BOUNDARY BEAMS, AND 3" O.C. TO FIELD JOISTS. INDEX #32/16.

PLAN VIEW OF SPECIMEN PA-1

4x4"=16"

72"

4x4"=16"7"

6"x6"

3 1/2"

12 7

/8"

7"

1 1/16" DIA. BOLT HOLES

4"x6"

1 5/16" DIA. BOLT HOLES

U66

3 1/

8"16

"

4"x6"

5/8" PLYWOOD

SIDE VIEW

NOTES:

NAILED WITH 10d COMMON

(a)

Fig. 3.1 Specimen Details: (a) Specimen PA-1

All the anchors used in the testing were supplied by the manufacturer, while the timbers,

hangers, nails and threaded bolts used in constructing the specimens were purchased from a local construction supply shop. Details of specific materials are described in Fig.3.1(a) to (e) for the five specimens, respectively. The specimens were assembled at the laboratory by the second author with the assistance from others.


3. BOLT SIZE: ANCHOR BOLTS: 7/8" DIA.



3 1/2"

8"16

"16

"8"

48"

16"

PLAN VIEW OF SPECIMEN PA-2

72"

6"x6"

3 1/2"

12 1

/8"

4"x6"

15/16" DIA. BOLT HOLES

3 7/

8"16

"

4"x6"

U66

5/8" PLYWOOD

SIDE VIEW

NOTES:

NAILED WITH 10d COMMON

NAILS AT 4" O.C. TO BOUNDARY BEAMS, AND 3" O.C. TO FIELD JOISTS.

(b)

Fig. 3.1 (Continued) Specimen Details: (b) Specimen PA-2


3. BOLT SIZE: ANCHOR BOLTS: 5/8" DIA. STUD BOLTS: 3/4" DIA.

8"16

"16

"8"

48"

3"

16"

PLAN VIEW OF SPECIMEN SA-1

72"

3"5 1/4"

(2)2"x8"

11 1

1/16

"

5 1/4"3" 3"

(2)2"x8"



4 5/

16"

16"

(2)2"x8"

LUS26-2

5/8" PLYWOOD

SIDE VIEW

NOTES:



NAILED WITH 10d COMMON NAILS AT 4" O.C. TO BOUNDARY BEAMSAND 6" O.C. TO FIELD JOISTS.

(c)

Fig. 3.1 (Continued) Specimen Details: (c) Specimen SA-1


8"16

"16

"8"

48"

3"

16"


72"

(2)2"x8"

10 7

/8"

3"

(2)2"x8"


16"

(2)2"x8"

LUS26-2

5 1/

8"

5/8" PLYWOOD

SIDE VIEW


NOTES:



NAILED WITH 10d COMMON NAILS AT 4" O.C. TO BOUNDARY BEAMS, AND 6" O.C. TO FIELD JOISTS.

(d)

Fig. 3.1 (Continued) Specimen Details: (d) Specimen SA-2


8"16

"16

"8"

48"

3 1/2"

16"


72"

(2)2"x6"

10 7

/8"

3 1/2"

4"x6"


16"

4"x6"

LUS26-2

5 1/

8"

5/8" PLYWOOD

SIDE VIEW


NAILED WITH 10d COMMON NAILS AT 4" O.C. TO BOUNDARY BEAMS, AND 6" O.C. TO FIELD JOISTS.



NOTES:

(e)

Fig. 3.1 (Continued) Specimen Details: (e) Specimen SA-3


3.2 Test Setup

After extensive discussions with the advisory committee to the project, the objective of

the testing was focused to investigate the hysteretic responses of the anchors in a subassembly

including a portion of a full-scale base-level diaphragm. The test setups for the five model

specimens were illustrated in Fig. 3.2(a) to Fig. 3.2(e), including side and top view. Fig. 3.3

shows a photograph of an overall view of a specimen in test.

Since the study was focused on the behavior of the anchor assembly, the uphill

foundation was not specifically simulated, instead it was represented by a stiff concrete block,

which was post-tensioned to the reaction floor beam. The specimen was horizontally placed

between the stiff concrete block and a 300-kip capacity actuator. The actuator applied push/pull

cyclic forces to the specimen through a steel tube distribution beam connected to the back end of

the specimen by three identical anchors as the testing unit that connected the front end to the

concrete block. Dead load effect of the base-level diaphragm was not specifically simulated. The

subassembly specimen was supported on Teflon bearings and rollers to eliminate the friction

forces. Thus, the force recorded by the load cells of the horizontal actuator can be considered as

the applied force to the anchor under test. Before the testing, the model specimen was placed in between the actuator and the

concrete block. The actuator was pushed to close the gaps between the ends of the specimen and

the concrete block as well as the distribution beam. Then the anchors connecting the back end of

the specimen and the distribution beam were tightened, while the testing unit anchor at the front

end of the specimen was snugly tightened.


Rea

ctio

nFr

ame

3 to

n

2x3

ton

Mon

orai

l Cra

ne S

yste

m

Act

uato

rs+l

oad

cells

Act

uato

rs+l

oad

cells

Anc

hor H

D15

to b

e te

sted

Anc

hors

for l

oadi

ng

Spec

imen

PA

-1 (4

'x6'

)

Lin

ear P

oten

tiom

eter

s

(a)

Fig

.3.2

Tes

t Set

up :

(a) S

peci

men

PA

-1


Rea

ctio

nFr

ame

3 to

n

2x3

ton

Mon

orai

l Cra

ne S

yste

m

Act

uato

rs+l

oad

cells

Act

uato

rs+l

oad

cells

Anc

hor P

HD

8to

be

test

edA

ncho

rsfo

r loa

ding

Spec

imen

PA

-2 (4

'x6'

)

Lin

ear P

oten

tiom

eter

s

(b)

Fig

. 3.2

(Con

tinu

ed) T

est S

etup

: (b

) Spe

cim

en P

A-2


Rea

ctio

nFr

ame

3 to

n

2x3

ton

Mon

orai

l Cra

ne S

yste

m

Act

uato

rs+l

oad

cells

Act

uato

rs+l

oad

cells

Anc

hor

HD

5to

be

test

edA

ncho

rsfo

r loa

ding

Spec

imen

SA

-1 (4

'x6'

)

Lin

ear P

oten

tiom

eter

s

(c)

Fig

.3.2

(Con

tinu

ed) T

est S

etup

: (c

) Spe

cim

en S

A-1


Rea

ctio

nFr

ame

3 to

n

2x3

ton

Mon

orai

l Cra

ne S

yste

m

Act

uato

rs+l

oad

cells

Act

uato

rs+l

oad

cells

Anc

hor P

HD

5to

be

test

edA

ncho

rsfo

r lo

adin

g

Spec

imen

SA

-2 (4

'x6'

)

Lin

ear P

oten

tiom

eter

s

(d)

Fig

. 3.2

(Con

tinu

ed) T

est S

etup

: Sp

ecim

en S

A-2


Rea

ctio

nFr

ame

3 to

n

2x3

ton

Mon

orai

l Cra

ne S

yste

m

Act

uato

rs+l

oad

cells

Act

uato

rs+l

oad

cells

Anc

hor H

TT

22to

be

test

edA

ncho

rsfo

r lo

adin

g

Spec

imen

SA

-3 (4

'x6'

)

Lin

ear P

oten

tiom

eter

s

(e)

Fig

. 3.2

(Con

tinu

ed) T

est S

etup

: Sp

ecim

en S

A-3


Fig. 3.3 A Specimen in Test


3.3 Instrumentation

Three linear potentiometers were installed at the testing end at the locations of the three

joists/collectors. The middle one was used to control the loading history, while the other two

were added to measure the deformation of the diaphragm, due to the so-called shear lag effects.

Strain gauges were attached to the diaphragm plywood and the joists or collectors. It was

intended to investigate the strain responses of the plywood (marked with “-S” plus numbers) and

the joists/collectors (marked with “-J” plus numbers). The information provided by these

instrumentations may be useful for future calibration of detailed analysis using FEM with the test

results. Fig. 3.4 illustrates the locations and notations of the strain gauges applied on the plywood

and the joists or collectors.

3 1/2"

8"16

"16

"8"

48"

P1-S3

16"

P1-J6

4x4"=16"

72"

4x4"=16"7"

P1-S5

P1-J3

P1-S4

3 1/2"7"

12 7

/8"

30"

P1-J4~P1-J6

P1-J5

P1-J4

30"

P1-S2

P1-J2

P1-J1

P1-S1

P1-J1~P1-J3

P1-S1~P1-S5

3 1/

8"16

"

(a)

Fig. 3.4 Strain Gauges applied at Plywood and Collectors/Joists

(a) Specimen PA-1


3 1/2"

16"

48"

16"

8"8"

16"

72"

P2-J6P2-J3

P2-S5

P2-S4

P2-S3

3 1/2"

12 1

/8"

25"

P2-J5

P2-J4

P2-J4~P2-J6

25"

P2-S2

P2-J2

P2-S1

P2-J1

P2-S1~P2-S5

P2-J1~P2-J3

3 7/

8"16

"

(b)

(c)

Fig. 3.4 (Continued) Strain Gauges applied at Plywood and Collectors/Joists

(b) Specimen PA-2; (c) Specimen SA-1


8"16

"16

"8"

48"

3"

16"

72"

S2-S3

S2-S4

S2-J3S2-S5

3"

S2-J6

10 7

/8"

17"

S2-J1S2-S1

S2-S2

S2-J2

S2-S1~S2-S5

S2-J1~S2-J3

17"

16"

S2-J5

S2-J4

S2-J4~S2-J6

5 1/

8"

(d)

(e)

Fig. 3.4 (Continued) Strain Gauges applied at Plywood and Collectors/Joists

(d) Specimen SA-2; (e) Specimen SA-3


3.4 Loading Protocol

The loading procedure is shown in Fig. 3.5, which was modified from a loading protocol

proposed for the wood-frame project (Krawinkler, 2000). The loading was divided into two

stages. A force-controlled loading was applied until the nominal yield displacement (defined

below) was reached. Loading increments in push and pull were the same in the first loading

stage, even though anchor behaviors under tension and compression were quite different. Once

the nominal yield displacement was reached, loading in pull direction (anchors in tension) was

switched to the displacement control according to multiples of the nominal yield displacement,

while loading in push was kept in force control.

The nominal yield displacement was generally defined as the displacement at the

specified yield capacity. When the actual yield capacity was observed to be lower than the

specified capacity, the nominal yield displacement was defined by the following equation:

11

yy Q

Q∆=∆ (3.1)

where

y∆ = nominal yield displacement

yQ = specified yield capacity by manufacturer

1Q = an intermediate load, such as yQ5.0

1∆ = measured displacement at 1Q

The determination of nominal yield displacement for specimens PA-1 and PA-2 followed this

definition.

The loading was considered as quasi-static, with a slow actuator piston speed of about 0.5

to 1 in. per minute. The testing for each specimen took approximately two hours to complete.


1.0Q y , 1.0D y

0.7Q y

0.5Q y

1.5D y

2.0D y

3.0D y

-1.0Q y

FORCECONTROL

DISPLACEMENTCONTROL IN PULL

-0.5Q y

-0.7Q y

Qy = Specified Yield Capacity Dy = Nominal Yield Displacement

Fig. 3.5 Loading Procedure

Chapter 4: Experimental Results | 43

Chapter 4 Experimental Results

4.1 General Observation

Table 4.1 shows the test results of the yield, maximum and ultimate capacities, and

corresponding displacements of all specimens. As shown in the table, specimens simulating

secondary anchors SA-1, SA-2 and SA-3 achieved a maximum capacity of about 30% higher

than their specified yield capacities. Primary anchor specimen PA-2 achieved a maximum

capacity close to its specified yield capacity, while specimen PA-1 only achieved a maximum

capacity of about 90% of its specified yield capacity. Specimens PA-2 (PHD8) and SA-2

(PHD5) developed a nominal yield displacement of about a quarter of an inch, while the other

three specimens developed a nominal yield displacement of about half an inch. Specimens SA-1

(HD5) and SA-2 (PHD5) achieved their maximum capacities at a displacement of about three

times of their nominal yield displacements, while the other three specimens achieved their

maximum capacities at a displacement of about two times of their nominal yield displacements.

SA-1 (HD5): Severe deformation was observed in the anchor HD5 in specimen SA-1 and

a crack initiated in the joist from the holes of the anchor bolts when the specimen was loaded to a

displacement twice of its nominal yield displacement, as shown in Fig. 4.1(a). Fig. 4.1(b) and (c)

show the specimen loaded to a displacement three times of its nominal yield displacement (front

and back views). As shown in the front view, the crack width in the joist almost reached half an

inch. Thus, it was deemed that the ultimate capacity of the specimen was approached. Fig. 4.1(d)

shows the localized deformation of the joist (back view) after the test, while Fig. 4.1(e) shows

the anchor HD5 after test, compared with a new anchor HD5.

SA-2 (PHD5): Severe deformation was observed in the anchor PHD5 in specimen SA-2

when the specimen was loaded to its specified yield capacity, as shown in Fig. 4.2(a). Fig. 4.2(b)

shows the specimen at failure. As shown in the figure, two cracks were generated along the two

rows of wood screws. At the same time, the wood screws were severely bent. Fig. 4.2(c) shows

the anchor PHD5 and some wood screws broken in the test, compared with a new anchor PHD5

and new wood screws.

SA-3 (HTT22): A crack initiated at the end of the HTT22 anchor when specimen SA-3

was loaded to a displacement one and a half time of its nominal yield displacement, as shown in

Fig. 4.3(a). Fig. 4.3(b) shows the specimen at failure when it was loaded to a displacement three

times of its nominal yield displacement. As shown in the figure, fracture occurred at a cross


section of the anchor where the holes for nailing made it a critical cross section. As further

deformation occurred at the end of the anchor, the initial crack became stable and it had no effect

on the maximum capacity of the specimen. No damage was observed in the joist. Fig. 4.3(c)

shows the anchor HTT22 after test, compared with a new anchor HTT22.

PA-1 (HD15): A crack initiated in the collector from the hole of the primary anchor bolt

when specimen PA-1 was loaded to a force of 0.9 times of its specified yield capacity, as shown

in Fig. 4.4(a). After the cracking, a sudden drop in force occurred. Fig. 4.4(b) shows a front view

of the specimen at failure. As shown in the figure, the initial crack was further developed to split

the collector and generate a slip of about half an inch. However, the anchor itself did not

demonstrate any deformation. It implied that the 6x6 collector was not strong enough to match

the specified yield capacity of the anchor HD15. Fig. 4.4(c) shows a back view of the specimen

at failure, in which a rotation of the stud bolts was clearly demonstrated.

PA-2 (PHD8): A crack appeared along the top row of the wood screws on the side of the

anchor PHD8 when specimen PA-2 was loaded to its specified yield capacity, as shown in Fig.

4.5(a). Fig. 4.5(b) illustrated the specimen loaded to a displacement three times of its nominal

yield displacement. As shown in the figure, the collector was fractured along the two rows of

wood screws and the wood screws were severely bent and pulled outward. Fig. 4.5(c) shows the

specimen loaded to a displacement four times of its nominal yield displacement. As shown in the

figure, some wood screws were broken and one of them fell out.


Table 4.1 Test Results

Yield Capacity

Maximum Capacity

Ultimate Capacity

Specimen Anchor Qy

(kips) Dy

(in) Qm

(kips) Dm (in)

Qu (kips)

Du (in)

PA-1 HD15 28.10# 0.4912 31.23 0.7337 20.17 1.5570

Prim

ary

Anc

hors

PA-2 PHD8 15.02# 0.3368 16.33 0.7535 7.16 1.4296

SA-1 HD5 8.40 0.4928 10.83 1.4878 10.83 1.4878

SA-2 PHD5 10.60 0.2756 13.84 0.7102 7.45 1.2353

Seco

ndar

y A

ncho

rs

SA-3 HTT22 9.90 0.6104 14.20 1.3529 7.04 1.4826

# For PA-1 and PA-2, Yield Capacities were lower than the specified yield capacities by

manufacturer; For other specimens, the specified yield capacities were defined as Yield

Capacities.


(a)

(b)

Fig. 4.1 General Observation for Specimen SA-1

(a) Loaded to 2Dy, Front View; (b) Loaded to 3Dy , Front View


(c)

(d)

Fig. 4.1(Continued) General Observation for Specimen SA-1

(c) Loaded to 3D0 , Back View; (d) After Test , Back View


(e)


(e) Comparison between Pre-Test and Post-Test Anchors

(a)


(a) Loaded to Qy , Front View


(b)

(c)


(b) Loaded to Failure , Front View;

(c) Comparison between Pre-Test and Post-Test Anchors


(a)

(b)


(a) Loaded to 1.5Dy , Front View; (b) Loaded to Failure , Front View


(c)


(c) Comparison between Pre-Test and Post-Test Anchors

(a)

Fig. 4.4 General Observation for Specimen PA-1

(a) Loaded to 0.9Qy , Front View


(b)

(c)

Fig. 4.4 (Continued) General Observation for Specimen PA-1

(b) Loaded to Failure , Front View; (c) Loaded to Failure , Back View


(a)

(b)

Fig. 4.5 General Observation for Specimen PA-2

(a) Loaded to Qy , Front View; (c) Loaded to 3Dy , Front View


(c)

Fig. 4.5 (Continued) General Observation for Specimen PA-2

(c) Loaded to 4Dy , Front View


4.2 Force-Displacement Responses

The force-displacement responses of the five specimens are given in Fig. 4.6 to Fig. 4.10,

in which the specified allowable and yield capacities by manufacturer are also given for

comparison. The envelope curves of the force-displacement responses are given in Fig. 4.11 to

Fig. 4.15. Several features can be observed for all the test results:

i. Since the anchors were initially snug-tightened, a gap existed before the anchors started

to take any tension load.

ii. The responses for pull (simulating downhill loading) and push (simulating uphill loading)

were significantly different. This was expected since the pull load was carried by the

anchor only, while the push load was transferred by the joists in bearing to the concrete

block.

iii. The capacity in the push direction was not reached for the reasons that the uphill

foundation was not specifically simulated in the testing, as described previously. The

capacity in the pull loading direction was determined by the capacity of the anchor

assembly. In reality, potential failure modes should also include the failure of the anchor

due to pull-out from the uphill foundation. Again, this was not simulated for the reasons

stated previously.

iv. The first pull loading cycle had larger stiffness than the subsequent cycles. The first pull

cycle loop enclosed a small area indicating some energy dissipation, however, the

subsequent cycles at the same peak load essentially demonstrated little energy

dissipation, similar to the so-called slip type hysteresis loop. Similar features also existed

in the cycles corresponding to larger peak displacement.

v. In the push loading direction, the load-displacement relationship was essentially linear

with little enclosed loop area. However, some drifts were seen between different cycles,

reflecting slight progressive changes in the specimen, probably due to the bearing

deterioration of the wood joists.

vi. All the three model specimens simulating base-level diaphragms with secondary anchors

developed the manufacturer specified load carrying capacity, before failure or

termination of loading. For specimen SA-1, the ultimate capacity was not obtained since


the peak load carrying capacity continued to grow corresponding to the increase of the

induced displacement.

vii. For the specimen simulating primary anchor PA-1, the manufacturer specified anchor

capacity was not developed due to a wood splitting failure described previously.

Specimen PA-2 experienced a drop in the peak load at a displacement of about 0.2 in.,

however, the load carrying capacity recovered and the specified capacity was developed

at the peak corresponding to a displacement of 0.75 in. before failure described in

previous section.

-15

-10

-5

0

5

10

15

-20 0 20 40 60 80 100 120 140 160

Displacement (x10 -2 in)

Fo

rce

(kip

s)

test allowable capacity yield capacity

Pull Push

Fig. 4.6 Force-Displacement Response of Specimen SA-1


-15

-10

-5

0

5

10

15

-20 0 20 40 60 80 100 120 140 160


Fo

rce

(kip

s)


Pull Push


-15

-10

-5

0

5

10

15

20

-20 0 20 40 60 80 100 120 140 160


Fo

rce

(kip

s)


Pull Push



-40

-30

-20

-10

0

10

20

30

40

-20 0 20 40 60 80 100 120 140 160


Fo

rce

(kip

s)


Pull Push

Fig. 4.9 Force-Displacement Response of Specimen PA-1

-20

-15

-10

-5

0

5

10

15

20

-20 0 20 40 60 80 100 120 140 160


Fo

rce

(kip

s)


Pull Push

Fig. 4.10 Force-Displacement Response of Specimen PA-2


-15

-10

-5

0

5

10

15

-20 0 20 40 60 80 100 120 140 160

Displacement (x10-2 in)

Fo

rce

(kip

s)


Pull Push

Fig. 4.11 Envelope Curve of Force-Displacement Response, Specimen SA-1

-15

-10

-5

0

5

10

15

-20 0 20 40 60 80 100 120 140 160


Forc

e (k

ips)


Pull Push



-15

-10

-5

0

5

10

15

-20 0 20 40 60 80 100 120 140 160


Forc

e (k

ips)


Pull Push


-40

-30

-20

-10

0

10

20

30

40

-20 0 20 40 60 80 100 120 140 160


Forc

e (k

ips)


Pull Push

Fig. 4.14 Envelope Curve of Force-Displacement Response, Specimen PA-1


-20

-15

-10

-5

0

5

10

15

20

-20 0 20 40 60 80 100 120 140 160


Fo

rce

(kip

s)


Pull Push

Fig. 4.15 Envelope Curve of Force-Displacement Response, Specimen PA-2

Based on the previous discussions on the hysteretic response of the model specimens, a

simple hysteresis loop model consisting of linear segments is proposed to simulate the behavior

of primary and secondary anchor assemblies. As shown in Fig.16, the model has the following

10 parameters, defining various characteristic deformations, capacities and stiffness.

Dmax: maximum tensile displacement

Pmax: capacity corresponding to maximum tensile displacement

Dmin: maximum compressive displacement

Pmin: capacity corresponding to maximum compressive displacement

Dg: displacement gap before compressive resistance to be activated

P1: first yield capacity, about 70% of estimated capacity

D1: displacement corresponding to first yield capacity

P2: estimated capacity by manufacturer

D2: displacement corresponding to estimated capacity

Ku: unloading and reloading stiffness

As a by-product of other research, a program for examining hysteresis loop models,

USC-Hysteresis Viewer Vision 1.0 was developed. As an example, the parameters and the


numeric results of the hysteresis response to an arbitrarily input load history are shown in Fig.17

for anchor assembly HD5.

Fig. 4.16 Hysteresis loop model

Fig. 4.17 Parameter input and numeric result of hysteresis loops of HD5 anchor

assembly following an arbitrary load history

O

P

G J M1 2 max

P1

PmaxP2

gmin

Pmin

KuF

HA

B LC

D

E


4.3 Deformations

The displacement distributions for the five specimens are given in Fig. 4.18 to Fig. 4.22.

In the figures, P0.5 and P0.7 refer to load steps at 50% and 70% of the specified yield capacity,

while D1.0 and D2.0 refer to load steps at the nominal yield displacement and two times of the

nominal yield displacement.

Joist strain distributions are shown in Fig. 4.23 to Fig. 4.27. In the figures, section 1 is the

section with strain gauges J1, J2 and J3, while section 2 is the section with strain gauges J4, J5

and J6. As shown in the figures, the tensile strain in the middle joist was much higher than that in

the side joists.

Typical plywood strains distributions are shown in Fig. 4.28 and Fig. 4.29 for specimen

SA-2 and PA-1. As compared to joist strains, plywood strains were much smaller.

Typical plywood and joist strain gauge responses at selected locations are shown in Fig.

4.30 to Fig. 4.34.

Note that the information on the strain responses may be useful for future calibration of

detailed analysis using sophisticated tools, such as FEM. In this report, only test results are

provided without further discussions.


0

40

80

120

-16 -8 0 8 16

Distance (in)

Dis

pla

cem

ent

(x10

-2in

)

D2.0D1.0P0.7P0.5

Fig. 4.18 Displacement Distribution, Specimen SA-1

0

20

40

60

80

-16 -8 0 8 16

Distance (in)

Dis

pla

cem

ent

(x10

-2 in

)

P0.5P0.7D1.0D2.0



0

40

80

120

-16 -8 0 8 16

Distance (in)

Dis

pla

cem

ent

(x10

-2in

)D2.0D1.0P0.7P0.5


0

50

100

150

-16 -8 0 8 16

Distance (in)

Dis

pla

cem

ent

(x10

-2in

)

D2.0D1.0P0.7P0.5

Fig. 4.21 Displacement Distribution, Specimen PA-1


0

25

50

75

100

-16 -8 0 8 16 Distance (in)

Dis

pla

cem

ent

(x10

-2 in

)

D2.0 D1.0 P0.7 P0.5

Fig. 4.22 Displacement Distribution, Specimen PA-2


0

800

1600

-16 -8 0 8 16

Distance (in)

Str

ain

(x1

0-6)

D2.0D1.0P0.7P0.5

(a)

0

800

1600

-16 -8 0 8 16

Distance (in)

Str

ain

(x1

0-6)

D2.0D1.0P0.7P0.5

(b)

Fig. 4.23 Joist Strain Distribution, Specimen SA-1

(a) Section 1; (b) Section 2


0

600

1200

1800

-16 -8 0 8 16

Distance (in)

Str

ain

(x1

0-6)

P0.5P0.7D1.0

(a)

0

600

1200

1800

-16 -8 0 8 16

Distance (in)

Str

ain

(x1

0-6)

P0.5P0.7D1.0

(b)




0

900

1800

-16 -8 0 8 16

Distance (in)

Str

ain

(x1

0-6)

D2.0D1.0P0.7P0.5

(a)

0

800

1600

-16 -8 0 8 16

Distance (in)

Str

ain

(x1

0-6)

D2.0D1.0P0.7P0.5

(b)




0

200

400

600

800

-16 -8 0 8 16

Distance (in)

Str

ain

(x1

0-6)

P0.7

P0.5

(a)

0

100

200

300

400

-16 -8 0 8 16

Distance (in)

Str

ain

(x1

0-6)

P0.7

P0.5

(b)

Fig. 4.26 Joist Strain Distribution, Specimen PA-1



0

800

1600

-16 -8 0 8 16

Distance (in)

Str

ain

(x1

0-6)

D1.0

P0.7

P0.5

(a)

0

400

800

-16 -8 0 8 16

Distance (in)

Str

ain

(x1

0-6)

D1.0

P0.7

P0.5

(b)

Fig. 4.27 Joist Strain Distribution, Specimen PA-2

Section 1; (b) Section 2


-125

0

125

250

-16 -8 0 8 16

Distance (in)

Str

ain

(x1

0-6)

P0.5D1.0D2.0D4.0

Fig. 4.28 Plywood Strain Distribution, Specimen SA-2

-100

0

100

200

300

-16 -8 0 8 16

Distance (in)

Str

ain

(x10

-6)

P1.0P0.7P0.5

Fig. 4.29 Plywood Strain Distribution, Specimen PA-1


-200

0

200

400

600

800

1000

-40 -20 0 20 40 60 80 100 120


Fo

rce

(kip

s)

PullPush

(a)

0

200

400

600

800

1000

1200

1400

1600

-20 0 20 40 60 80 100 120 140 160


Str

ain

(x1

0-6)

PullPush

(b)

Fig. 4.30 Strain Gauge Responses, Specimen SA-1:

(a) S1-S3, top of plywood at center joist; (b) S1-J2, Joist at center


-300

-200

-100

0

100

200

300

-40 -20 0 20 40 60 80 100 120


Str

ain

(x1

0-6)

PullPush

(a)

-200

0

200

400

600

800

1000

1200

1400

1600

1800

-30 0 30 60 90 120


Str

ain

(x1

0-6)

PullPush

(b)

Fig. 4.31 Strain Gauge Responses, Specimen SA-2:

(b) S2-S3, top of plywood at center joist; (b) S2-J2, center joist.


-150

-100

-50

0

50

100

-20 0 20 40 60 80 100 120


Fo

rce

(kip

s)

PullPush

(a)

-200

0

200

400

600

800

1000

1200

1400

1600

1800

2000

-20 0 20 40 60 80 100 120 140 160


Str

ain

(x1

0-6)

PullPush

(b)

Fig. 4.32 Strain Gauge Responses, Specimen SA-3

(c) S3-S3, top of plywood at center joist; (b) S3-J2, center joist


-1400

-1200

-1000

-800

-600

-400

-200

0

200

400

-20 0 20 40 60 80 100 120 140 160


Fo

rce

(kip

s)

PullPush

(a)

-200

-100

0

100

200

300

400

500

600

700

800

-20 0 20 40 60 80 100 120 140 160


Str

ain

(x1

0-6)

PullPush

(b)

Fig. 4.33 Strain Gauge Responses, Specimen PA-1

(d) P1-S3, top of plywood at center; (b) P1-J2, center joist


-500

-400

-300

-200

-100

0

100

200

-30 0 30 60 90 120 150


Fo

rce

(kip

s)

PullPush

(a)

-400

-200

0

200

400

600

800

1000

1200

1400

1600

-20 0 20 40 60 80 100 120 140 160


Str

ain

(x1

0-6)

PullPush

(b)

Fig. 4.34 Strain Gauge Responses, Specimen PA-2

(e) P2-S3, top of plywood at center; (b) P2-J2, center joist

Chapter 5: Analytical Study | 79

Chapter 5 Analytical Study

5.1 General

As discussed in Chapter 2, significant variations exist in hillside buildings. For the

purpose of analytical study, it was attempted to define a model building that possesses the key

features of typical hillside wood-frame buildings.

To perform a push over analysis, the mechanical characteristics of the structural

components need to be defined based on experimental data. Due to the limited information of

relevant research at the stage when the analytical phase of the project was carried out, only test

data available in two reports (Pardoen, 1999, EQE, 1999) were utilized to define the mechanical

properties of shear wall and diaphragm of the model building. The experimental results as

described in the previous chapter were employed to define the mechanical characteristics of the

primary and secondary anchors.

Recently, as parts of the CUREE-Caltech Woodframe project, Uang et al. tested shear

wall specimens at UCSD, and, Chai et al. provided experimental information on seismic

behavior of stepped cripple walls. However, due to the constraint of time, these new findings

have not been included into the analytical studies described in this chapter. It should be pointed

out that the analytical methods including the models described in this report are only the first

step to conceptually demonstrate the validity of a special push-over analysis, which may be a

useful tool for seismic design of the hillside buildings in the light of the performance based

design. To further refine the analytical method is the continued task for the authors.


5.2 Model Building

A one-story model building is defined as shown in Fig. 5.1. The model building is a two-

bedroom house with a basement. The plan size of the building is 20 x 30 feet. The floor-framing

plan of the base-level diaphragm is shown in Fig. 5.2. The floor joists are 2x8 @16” O.C. along

the downhill direction. Primary and secondary anchors are placed at the uphill side. Shear walls

below the diaphragm are arranged at the other three sides, as illustrated in the figure. Table 5-1

summarizes the details of components of the base-level diaphragm.

Balcony

Bath

CLO

CLO

Bedroom

BedroomLiving Room

Kitchen

C LO

GradeBeam

Fig. 5.1 Plan and Side View of Model Building


8' 8'Shear Wall Shear Wall

FJ2x

8@16

"O.C

.

Prim

ary

Anc

hor

Secondary Anchors

8' A

A

Prim

ary

Anc

hor

Grade Beam

A 8'

A

Fig. 5.2 Floor Framing Plan of Base-level Diaphragm

Table 5.1 Details of Components and Diaphragm of Model Building

Sheathing ½ ” Structural I Plywood

Joist 2” x 8” @16” O.C. Diaphragm

Chord 2-2” x 6”

Shear Wall 8’ x 8’, Details refer to [3]

Primary Anchor HD15

Secondary Anchor HD5


5.3 Analytical Models

For the model building described in the previous section, the analytical models for the

base-level diaphragm under horizontal earthquake forces in the downhill direction and normal to

downhill direction are given in the following.

5.3.1 Model for Downhill Direction

The analytical model is illustrated in Fig. 5.3. The base-level diaphragm is modeled as a

flexural-shear beam. The primary and secondary anchors, and shear walls are modeled as

springs. It is assumed that the downhill earthquake forces are uniformly distributed along the

diaphragm. Note that additional springs can be added to represent the flexibility of the uphill

foundation, if necessary.

5.3.2 Model for Normal to Downhill Direction

The analytical model is illustrated in Fig. 5.4. The contributions of the base-level

diaphragm in the downhill direction and normal to downhill direction are represented separately

by two flexural-shear beams. A rigid beam is added to convert the end moment of the

perpendicular beam into a couple of forces acting at the two ends of the parallel beam, at the

locations where the diaphragm chords are placed. This is to represent the fact that the chords

tend to collect more forces in a diaphragm. Of course, if such a chord effect is conceived as not

applicable, a different model should be considered. The primary anchors, secondary anchors, and

the shear walls are represented by springs. It is assumed that the earthquake forces are uniformly

distributed along the perpendicular beam.


Downhill Earthquake Forces

Diaphragm

Secondary

AnchorPrimary Anchors

Shear Wall

AnchorPrimary

Shear Wall

Fig. 5.3 Analytical Model of Base-level Diaphragm in Downhill Direction

Rigid Link

& Shear WallPrimary Anchor Anchors

Secondary

Diaphragm(Parallel)

Rigid Beam

Primary Anchor& Shear Wall

LongitudinalShear Walls

Cro

ss D

ownh

ill D

irec

tion

Ear

thqu

ake

Forc

es

Dia

phra

gm(P

erpe

ndic

ular

)

Fig. 5.4 Analytical Model of Base-level Diaphragm Normal to Downhill Direction


5.3.3 Mechanical Properties of Base-Level Diaphragm

In Pardoen’s report (Pardoen, 1999), five diaphragm specimens were tested under cyclic

loading. All specimens were 16’x20’ in plan size, and sheathed by ½” Structural I plywood with

10d common nails. The nailing schedule is given in Table 5.2. Test data of specimens RD1, RD2

and RD3 (Fig. 5.5) were considered in this study, for only those specimens having the same joist

spacing as the model building.

Specimens RD1 and RD3 were tested by racking the 16’ edge, whereas specimen RD2

was tested by racking the 20’ edge. The load-displacement curves of RD1, RD2 and RD3 are

shown in Fig. 5.6 to Fig. 5.8. The yield capacities, ultimate capacities and corresponding

displacements of the three specimens are given in Table 5.3.

It is well known that the displacement of a diaphragm is composed of four components:

bending displacement, shear displacement, displacement due to nail slip and displacement due to

slip in chord connection splices. The latter three components are assumed to be proportional to

the shear force. So, when the diaphragm is model by a flexural-shear beam, those displacement

components are combined together and referred to as shear displacement.

It can be verified that the bending stresses in the chord members were small for the

diaphragm specimens as mentioned above. That is to say, the non-linear deformation of

diaphragms mainly results from the shear deformation, while the bending deformation can be

assumed to be in the elastic range. Therefore, the shear displacement can be calculated by the

total displacement minus the bending displacement, which can be calculated based on mechanics

of materials. Following that, the shear stiffness of the specimens can be further defined as given

in Table 5.3.

As shown in Table 5.3, the initial shear stiffness was almost the same for all three

specimens. It was perhaps owing to the fact that the sheathing plywood and joist spacing were

the same for the three specimens. The post-yield shear stiffness of specimen RD3 was about

twice of the average post-yield shear stiffness of specimens RD1 and RD2. That should be due to

the fact that the edge nailing spacing of specimen RD3 was about half of the edge nailing

spacing of specimens RD1 and RD2.

For simplicity in this study, a linear elastic beam model was adopted for the diaphragm of

the model building. The moment of inertia of the cross section of the equivalent beam could be


defined by taking into account the diaphragm chords only. The effective area of cross section for

shear resistance in horizontal and vertical sections could be defined based on the initial shear

stiffness, which was assumed to be the same as the average initial shear stiffness of specimens

RD1, RD2 and RD3, as follows:

025.0)15003/()20.2046.2054.15(2E/sK2G/sKwt =×++×=== in

0.9360025.0bwtshA =×=×= in2

0.6240025.0hwtsvA =×=×= in2

in which the poison’s ratio was assumed to be zero.

If a nonlinear beam model was to be used, the shear resistance of the diaphragm could be

represented by a nonlinear shear spring added to the flexural beam element representing the

flexural stiffness of the diaphragm.

Table 5.2 Nailing Schedule of Diaphragm Specimens

Sample Height x width Edge Nailing Continuous Edge Nailing

RD1 20’ x 16’ 6” O.C. 6” O.C.

RD2 16’ x 20’ 6” O.C. 6” O.C.

RD3 20’ x 16’ 3” O.C. 2” O.C.


Table 5.3 Mechanical Properties of Diaphragm Specimens

RD1 RD2 RD3

Plan size (b x h) 16’x20’ 20’x16’ 16’x20’

Chord size (A) 40.25 in2 61.5 in2 40.25 in2

Moment of Inertia (I=A.b2/2) 741888 in4 1771200 in4 741888 in4

E 1500 ksi 1500 ksi 1500 ksi

Yield Capacity (Py)

6.5 kips 10.0 kips 15.0 kips

Ultimate Capacity (Pu)

16.0 kips 22.0 kips 26.0 kips

Yield Displacement (Dy)

0.55” 0.40” 0.99”

Ultimate Displacement (Du)

4.04” 3.91” 3.49”

Bending Displ. At Yield (Dby=Pyh

3/3EI) 0.027” 0.009” 0.062”

Bending Displ. At Peak (Dbu=Puh

3/3EI) 0.066” 0.020” 0.108”

Shear Displ. At Yield (Dsy=Dy-Dby)

0.523” 0.391” 0.928”

Shear Displ. At Peak (Dsu=Du-Dbu)

3.974” 3.890” 3.382”

Initial Shear Stiffness (Ks=Pyh/Dsyb) 15.54 kips/in 20.46 kips/in 20.20 kips/in

Post Yld Shear Stiffness (Ks=[Pu-Py]h/[Dsu-Dsy]b) 3.44 kips/in 2.74 kips/in 5.60 kips/in


Fig. 5.5 Framing Configuration of Diaphragm Specimens RD1, RD2 and RD3 (Pardoen,

1999)

Fig. 5.6 Load – Displacement Curve of Specimen RD1 (Pardoen, 1999)


5.3.4 Mechanical Properties of Shear Wall

Shear wall test data (EQE, 1999), as shown in Fig. 5.9, were utilized to define the

mechanical properties of the equivalent nonlinear spring representing a shear wall. Each of the

four pieces of shear walls in the model building below the base-level diaphragm was assumed to

have the same size and same details as the shear wall specimen defined in reference report (EQE,

1999). The force-displacement curve of the nonlinear spring is shown in Fig. 5.10.

5.3.5 Mechanical Properties of Primary Anchor

Based on the envelope curve as given in Fig. 4.25 for primary anchor HD15, the force-

displacement curve of the equivalent nonlinear spring is shown in Fig. 5.11.

5.3.6 Mechanical Properties of Secondary Anchor

Based on the envelope curve as given in Fig. 4.22 for secondary anchor HD5, the force-

displacement curve of the equivalent nonlinear spring is shown in Fig. 5.12.


Fig. 5.9 Load – Displacement Curve of Shear Wall Specimen (EQE, 1999)

Force-Displacement Curve of Nonlinear Spring for Shear Walls

-10

-5

0

5

10

-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0

Displacement (in)

Fo

rce

(kip

)

Fig. 5.10 Force-Displacement Curve of Nonlinear Spring for Shear Walls


Force-Displacement Curve of Nonlinear Spring for Primary Anchors

-40

-20

0

20

40

-0.5 0.0 0.5 1.0 1.5 2.0

Displacement (in)

Fo

rce

(kip

)

Fig. 5.11 Force-Displacement Curve of Nonlinear Spring for Primary Anchors

Force-Displacement Curve of Nonlinear Spring for Secondary Anchors

-15

-10

-5

0

5

10

15

-0.5 0.0 0.5 1.0 1.5 2.0

Displacement (in)

Fo

rce

(kip

)

Fig. 5.12 Force-Displacement Curve of Nonlinear Spring for Secondary Anchors


5.4 Analytical Procedures

Software ADINA (900 node Version) was used to perform the pushover analysis for the

base-level diaphragm under uniform loading in the downhill direction and the normal to

downhill direction. The analytical procedure applying ADINA to the pushover analysis is

straightforward.

In the downhill direction, the finite element model with line loading and boundary

conditions is shown in Fig. 5.13. The diaphragm was represented by 33 beam elements (Fig.

5.14) with cross section defined by moment of inertia (475200in4) and effective shear area

(6.0in2). The diaphragm was assumed to be in elastic range for simplicity. The shear wall,

primary anchor and secondary anchor were represented by nonlinear springs with mechanical

properties as defined in the previous section.

In the normal to downhill direction, the finite element model with line loading and

boundary conditions is given in Fig. 5.15. The contribution of the diaphragm in the cross

downhill direction was modeled by 15 beam elements with moment of inertia of 1069200in4 and

effective shear area of 9.0in2 (Fig. 5.16). The contribution of the diaphragm in downhill direction

was modeled by 33 beam elements with moment of inertia of 475200in4 and effective shear area

of 6.0in2. The rigid beam was represented by two beam elements with section properties all set to

1010. The rigid links were modeled by truss elements with area of cross section set to 1010.

In order to get a descending branch for the force-displacement curve, the built-in collapse

analysis in ADINA was selected for the pushover analysis. It uses an arch length control solution

procedure, and the software itself adjusts the arch length.


Fig. 5.13 Finite Element Model for Downhill Direction

Fig. 5.14 Element Numbering for Downhill Direction


Fig. 5.15 Finite Element Model for Normal to Downhill Direction

Fig. 5.16 Element Numbering for Normal to Downhill Direction


5.5 Analytical Results and Discussion

The force-displacement curves for the base-level diaphragm under uniform loading in

downhill direction and normal to downhill direction are shown in Fig. 5.17 and Fig. 5.18,

respectively. Displacements shown in Fig. 5.17 and Fig. 5.18 are the mid-span displacement of

the diaphragm for the downhill direction model and the displacement at the downhill side of the

diaphragm for the normal to downhill direction model. In Fig. 5.17 and Fig. 5.18, SA means

secondary anchor; PA means primary anchor; SW means shear wall along downhill direction;

NSW means shear wall along the normal to downhill direction.

As shown in Fig. 5.17 and Fig. 5.18, the diaphragm in downhill direction is much

stronger and stiffer than in normal to downhill direction. For downhill direction loading, the

secondary anchors play an important role for the behavior of the diaphragm. The diaphragm

reached its maximum capacity when the primary and secondary anchors reached their maximum

capacities almost at the same time. Apparently, the secondary anchors have a significant

contribution to the maximum capacity of the diaphragm in downhill direction, although they are

designed as redundant elements for earthquake resistance.

For the normal to downhill direction loading, the shear walls along the downhill side

yielded and failed before the base-level diaphragm reached its maximum capacity. The

secondary anchors have some contribution to the maximum capacity of the diaphragm, but not as

significant as in downhill direction.

Variations of the reaction forces in the primary, secondary anchors and shear walls with

diaphragm displacements are shown in Fig. 5.19 and Fig. 5.20.


0

40

80

120

160

200

0.0 0.5 1.0 1.5 2.0 2.5 Diaphragm Midspan Displacement (in)

Tota

l Bas

e-le

vel F

orce

(kip

)

SA First Yield

PA&SW First Yield

PA Failure

PA Reach Maximum Followed by SA failure

SW Failure

Fig. 5.17 Force-Displacement Curve in Downhill Direction

0

30

60

90

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Displacement along Downhill side(in)

To

tal B

ase-

leve

l Fo

rce

(kip

)

NSW First Yield

NSW Reach Maximum & Failure

PA(in pull) Reach MaximumSW&SA(in pull side) Yield

PA(in pull) Failure Followed by SW&SA(in pull side) Failure

SA(close to push side) Pull Failure

Fig. 5.18 Force-Displacement Curve in Normal to Downhill Direction


0

10

20

30

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Diaphragm Midspan Displacement (in)

An

cho

r/S

hea

r W

all F

orc

e (k

ip)

PASWSA

Fig. 5.19 Reaction-Displacement Curves in Downhill Direction

0

10

20

30

0.0 1.0 2.0 3.0 4.0 5.0


An

cho

r/S

hea

r W

all F

orc

e (k

ip)

PASWNSWSA

Fig. 5.20 Reaction-Displacement Curves in Normal to Downhill Direction


5.6. Push-Over Analysis Based on Incremental Linear Procedure

A push over analysis can be also performed in a step by step procedure by adjusting the

stiffness of the components as well as the boundary conditions at each step. Fig. 5.21 shows a

flow chart of the procedure. Such a procedure is suitable for problems involving a relatively

small number of elements and limited calculation steps. Engineers may choose this relatively

simple procedure to perform the push-over analysis with demonstrating major physical changes

in the structural system. Any structural analysis program or spread sheet based procedures which

have a linear analysis feature can be employed. In this study, an educational version of

VisualAnalysis was used. Only the downhill loading case was analyzed with VisualAnalysis.

The analytical model and results are shown in figures 5.22 and 5.23, respectively. Results are

identical with those obtained using ADINA program.

Start

Load Increment w

Linear Static Analysis

Compare spring displacement with critical displacement cr (at yield,

maximum strength and rupture)

i cr

Adjust Stiffness or Boundary

w' wcr j

j cr min

No Yes

If a member reaches rupture, then, remove the member and applying its internal force to the remaining structure. Progressive failure

occures if not stablized

Fig.5.21. Flow Chart of Increment Linear Analysis


Fig. 5.22. Input and Output at First Yield


Pushover Analysis of Base-level Diaphragm by Incremental Linear Analysis

0

25

50

75

100

125

150

175

200

0 0.25 0.5 0.75 1 1.25 1.5


To

tal B

ase-

leve

l Fo

rce

(kip

)

Downhill DirectionFirst secondary anchor yield

Shear wall yield

First secondary anchor reaches maximum strength

First secondary anchor rupture

Fig. 5.23. Force-Displacement Curves of the Diaphragm by VisualAnalysis

5.7 Comments on Performance Based Design Criteria

The push over analysis described in this report can be used in performance-based design

for hillside buildings. The following criteria are suggested to define the performance levels for

the base level diaphragms of hillside buildings, similar to FEMA-273 (1997).


Operational Level:

All major force-resisting elements are in elastic.

Intermediate Level:

In downhill loading direction, primary anchors and shear walls are in elastic, secondary

anchors may be yielded but not reaching ultimate.

In cross downhill loading direction, shear walls at the downhill side may yielded but not

reaching ultimate.

Life Safety Level:

In downhill loading direction, primary anchors and shear walls may be yielded, but none

of them reaching ultimate, and no more than 25% of secondary anchors reaching

ultimate.

In cross downhill loading direction, primary and secondary anchors at uphill side and

shear walls in downhill direction may yielded but not reaching ultimate.

Collapse Prevention Level:

In both loading directions, primary anchors and shear walls in downhill direction may be

yielded, but at least one of these two systems not reaching ultimate.

Chapter 6: Summary | 103

Chapter 6 Summary

The background on retrofit of hillside buildings for earthquake resistance is reviewed in

this report. The structural characteristics that make hillside buildings hazardous, and the main

regulations and important concepts in the Los Angeles City Voluntary Existing Hillside

Buildings Retrofit Ordinance (1995) are discussed. A retrofit project on a hillside house in the

City of Los Angeles is reviewed.

An experimental program on primary and secondary anchorage was designed and

completed. The experimental findings of the anchorage test were presented in this report.

Specimens SA-1, SA-2 and SA-3, simulating base-level diaphragms with secondary anchors, all

achieved a maximum capacity of about 30% higher than their specified yield capacities

according to the manufacturer’s specifications. However, severe deformation or fracture was

observed in the anchors. Specimens PA-1 and PA-2, representing primary anchors, only

achieved a maximum capacity of about 90% and 100% of their specified yield capacities,

respectively. No deformation was observed in the anchors. This implies that the 6x6 collector is

not strong enough to match the maximum capacity of the primary anchors.

All of the five specimens demonstrated a slip type response in tension and behaviors in

tension (downhill loading) and compression (uphill loading) were quite different. An initial slip

was observed for all of the five specimens. The gap between the specimen and the reaction block

was a major factor for the value of the initial slip. The energy dissipating capacities of all the

specimens were small. But all of them demonstrated substantial deformability. The values of the

initial stiffness, unloading and reloading stiffness depend on the anchor types. The hysteresis

loops of the anchor assemblies can be simulated by a 10-parameter model consisting of linear

segments.

Finally, analytical models were established for push over analysis of the base-level

diaphragms of typical hillside wood-frame buildings in both downhill direction and normal to

downhill direction. Analytical results demonstrate that secondary anchors play an important role

in the behavior of the diaphragms in downhill direction. The analysis clearly demonstrated that

the contributions of each force resisting element are not activated or engaged simultaneously,

and the progress failure may be possible, resulting unsatisfactory seismic performance. The

proposed analytical models and the procedures are useful for seismic design of hillside buildings.


It was recognized that the research described in this report might be the first experimental

and analytical attempt to deal with the seismic design of hillside woodframe buildings. Thus,

there are still many outstanding problems that need to be addressed in future. The followings are

some of the suggested future research topics:

i. More tests on anchor assemblies should be carried out to enlarge the performance

database. Testing scope should be expanded to reflect the varieties of the types of

anchors, such as custom-built anchor details, anchors from other manufacturers, etc.

ii. Loading rate effects on performance of anchor assemblies should be considered in future

tests by possible dynamic testing.

iii. Investigations on system performance of base-level diaphragms or overall hillside

buildings should be carried out by using either laboratory models tests or in-situ tests.

iv. Detailed analysis such as using FEM should be performed to calibrate the method with

the detailed strain responses observed in the tests.

v. Time history analysis of hillside buildings should be carried out.

vi. Performance based design guidelines should be established.

References | 105

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Plywood Shear Walls with USP Lumber Connector Hold-Downs – SEAOSC Testing

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FEMA-273, (1997), “NEHRP Guidelines for the Seismic Rehabilitation of Buildings”, Federal

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CUREE Publication No. W-02.

Levin, Arthur H. (1999), “Hillside Building - Design and Construction,” 2nd Edition, Builder's

Book Inc.

Los Angeles City (1996), “Voluntary Existing Hillside Buildings Retrofit Ordinance.”

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Earthquake Engineering Research Institute, 95-03, J. Hall, Editor, Oakland, Calif., April.

Pardoen, et al (1999), “Stiffness of Timber Diaphragms and Strength of Timber Connections”,

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Roselund, Nels (1996), "Retrofit of Hillside Dwellings for Earthquake Resistance".

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Rehabilitation", Project Documents.

“Woodframe Project – Testing and Analysis Literature Reviews.” (2001), CUREE Publication

No. W-03, Andre Filiatrault, editor. Richmond, California.

Xiao, Yan and Xie, Li (2000), “Experimental Program to Study Anchorage of Hillside

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SERP 2000-3.

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