Seismic Design of Rigid 

Wall-Flexible Diaphragm 

Buildings: An Alternate 

Procedure 

FEMA P-1026/March 2015 

FEMA
 

Seismic Design of 

Rigid Wall-Flexible 

Diaphragm Buildings: 

An Alternate 

Procedure 

FEMA P-1026/March 2015 

Prepared for the Federal Emergency Management Agency of the 

U.S. Department of Homeland Security 

by the Building Seismic Safety Council of the 

National Institute of Building Sciences 

The Building Seismic Safety Council 

A council of the National Institute of Building Sciences 

Washington, DC 
NOTICE: Any opinions, findings, conclusions, or recommendations expressed in this publication do 

not necessarily reflect the views of the Federal Emergency Management Agency. Additionally, neither 

FEMA nor any of its employees make any warranty, expressed or implied, nor assume any legal liability 

or responsibility for the accuracy, completeness, or usefulness of any information, product, or process 

included in this publication. 

The Building Seismic Safety Council (BSSC) was established in 1979 under the auspices of the National 

Institute of Building Sciences as a forum-based mechanism for dealing with the complex regulatory, 

technical, social, and economic issues involved in developing and promulgating building earthquake 

hazard mitigation regulatory provisions that are national in scope. By bringing together in the BSSC all 

of the needed expertise and all relevant public and private interests, it was believed that issues related 

to the seismic safety of the built environment could be resolved and jurisdictional problems overcome 

through authoritative guidance and assistance backed by a broad consensus. 

The BSSC is an independent, voluntary membership body representing a wide variety of building 

community interests. Its fundamental purpose is to enhance public safety by providing a national forum 

that fosters improved seismic safety provisions for use by the building community in the planning, design, 

construction, regulation, and utilization of buildings. 

This report was prepared under Contract HSFEHQ-09-D-0417 between the Federal Emergency 

Management Agency and the National Institute of Building Sciences. 

For further information on Building Seismic Safety Council activities and products, see the Council’s 

website (www.bssconline.org) or contact the Building Seismic Safety Council, National Institute of Building 

Sciences, 1090 Vermont, Avenue, N.W., Suite 700, Washington, D.C. 20005; phone 202-289-7800; fax 

202-289-1092; e-mail bssc@nibs.org. 

This report can be obtained free of charge from the the FEMA Publication Distribution Center at 1-800-

480-2520. The report can also be downloaded in pdf form from the BSSC website at www.bssconline.org. 

The National Institute of Building Sciences and its Building Seismic Safety Council caution users 

of this document to be alert to patent and copyright concerns especially when applying prescriptive 

requirements. 
Foreword 

The Federal Emergency Management Agency (FEMA) of Department of Homeland Security has 

committed under the National Earthquake Hazard Reduction Program (NEHRP) to support 

implementation of new knowledge and research results for improving seismic design and 

building practices in the nation. This FEMA NEHRP document, Seismic Design of Rigid WallFlexible Diaphragm Buildings: An Alternate Procedure is a new design resource that applies 

recent research and testing results in addressing the seismic performance issue of “big box” 

buildings. This type of buildings is typically used for warehouses or retail stores and has been 

reported for numerous earthquake damage or collapses in the past. 

FEMA and the project officer wish to express the gratitude to the members of the Project 

Workgroup, the Project Management Committee, the Project Review Panel and BSSC Board 

of Direction, management, and staff for the development, review and completion of this 

alternate design procedure of rigid wall flexible diaphragm buildings. We are also delighted to 

see that this alternate procedure has also been adopted in Part III of the 2015 NEHRP 

Recommended Provisions for trial use by the design community and hopefully to be adopted 

by the national standards and code in the future. 

Federal Emergency Management Agency 

Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure i 
Preface 

Single-story buildings with rigid walls and flexible diaphragms (RWFD buildings) are common 

throughout the United States and are often used for warehouse buildings and “big box” retail 

stores. These buildings have stiff walls constructed of reinforced concrete or masonry, or braced 

frames of structural steel, and relatively flexible diaphragms of metal deck or wood structural 

panels. The seismic response of this type of structure is dominated by the deformation of the 

large and relatively flexible diaphragms. The standard design methods used in current seismic 

codes for all building types, however, assume primary response occurs in deformation of the 

vertically oriented lateral force resisting elements - moment frames, braced frames, or shear 

walls. A design approach for the RWFD building type that is more technically correct than 

current code design methods, and that can be shown to meet accepted code performance, has 

been sought for some time. 

This publication is the result of a Simplified Design Program study funded by the Federal 

Emergency Management Agency (FEMA) and administered by the National Institute of Building 

Sciences’ Building Seismic Safety Council. For the RWFD building type, this study 

demonstrates that design provisions narrowly directed at a single building type can not only be 

simpler, but provide designs that more consistently meet expected performance objectives. The 

study also has formed the basis for developing improved design provisions for Part 3 of the 2015 

edition of the NEHRP Provisions [FEMA, 2015]. 

With the alternate design provisions provided in this report, the seismic design community will 

be afforded a far greater understanding of the seismic response of RWFD buildings. It is 

anticipated that this methodology will be incorporated into future seismic design codes and 

standards. Until this occurs, some aspects of the alternate design method can be implemented 

within the context of current code procedures. 

I wish to thank the subject matter experts listed in the Acknowledgments, who were instrumental 

in conducting the RWFD study and producing this publication. 

Jim Sealy 

Chair, Building Seismic Safety Council Board of Direction 

ii Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure 
FEDERAL EMERGENCY MANAGEMENT AGENCY

Acknowledgments 

Principal Authors 

John Lawson, California Polytechnic State University, San Luis Obispo 

Dominic J. Kelly, Simpson Gumpertz & Heger Inc. 

Contributing Authors 

Andre Filiatrault, University at Buffalo, New York 

Maria Koliou, University at Buffalo, New York 

Reviewers 

Kelly Cobeen, Wiss, Janney, Elstner Associates, Inc. 

David McCormick, Simpson Gumpertz & Heger Inc. 

Project Management Committee 

William Holmes, Rutherford and Chekene (Chair) 

James R. Harris, JR Harris & Company 

John D. Hooper, Magnusson Klemencic Associates 

Dominic J. Kelly, Simpson Gumpertz & Heger Inc. 

Barry H. Welliver, BHW Engineers, L.L.C. 

Project Review Panel 

Ryan Kersting, Buehler & Buehler Structural Engineers, Inc. 

James Kramer, MHP Structural Engineers 

Trent Nagele, VLMK Consulting Engineers 

Joe Steinbicker, Steinbicker & Associates, LLC 

Doug Thompson, STB Structural Engineers, Inc. 

Project Review Panel Workshop Participants 

Thomas Gangel, Wallace Engineering (Walmart) 

Nathan Hauer, Structural Engineering Group, Target Stores 

Philip Line, American Wood Council 

Bonnie Manley, American Iron and Steel Institute 

Lawrence Novak, Portland Cement Association 

Project Oversight 

Mai Tong, Federal Emergency Management Agency 

Robert D. Hanson, Federal Emergency Management Agency 

Philip Schneider, National Institute of Building Sciences 

Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure iii 

Table of Contents 

Foreword ................................................................................................................................................i
 

Preface...................................................................................................................................................ii
 

Acknowledgments ............................................................................................................................... iii
 

Chapter 1	 Introduction..................................................................................................... 1
 

1.1	 The Need for a New Design Procedure for RWFD Buildings....................................................2
 

1.2	 Purpose of Report ......................................................................................................................2
 

1.3	 Introduction to the Alternate Procedure and Comparison to Current
 

Design Practice ..........................................................................................................................3
 

1.4	 Implementation of the Alternate Design Procedure....................................................................6
 

1.5	 Scope and Limitation of the Alternate Procedure.......................................................................6
 

1.6	 Overview of Report Contents.....................................................................................................7
 

Chapter2	 Description of RWFD Buildings and Their Performance
 

in Earthquakes .............................................................................................. 11
 

2.1	 Description of Typical RWFD Structures................................................................................. 11
 

2.2	 Seismic Performance History...................................................................................................12
 

Chapter 3	 Current Design Practice Example ............................................................... 17
 

3.1	 Example Building Description (current practice).....................................................................17
 

3.2	 Determine Design Spectral Response Accelerations SDS and SD1 (current practice).............19
 

3.3	 Determine Fundamental Building Period (current practice).....................................................19
 

3.4	 Base Shear Using the ELF Procedure (current practice)..........................................................20
 

3.5	 Diaphragm Design Forces Using the ELF Procedure (current practice) ..................................21
 

3.6	 North/South Diaphragm Shear Design (current practice).........................................................25
 

3.7	 North/South Diaphragm Chord Design (current practice)........................................................30
 

3.8	 East/West Diaphragm Shear Design (current practice) ............................................................31
 

3.9	 East/West Diaphragm Chord Design (current practice)............................................................32
 

3.10	 Shear Wall Force Using the ELF Procedure (current practice) ................................................33
 

3.11	 Shortcomings of Current Practice ............................................................................................36
 

Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure v 
Chapter 4 Development of an Alternate Seismic Design Procedure.......................... 37
 

4.1 Determination of Building and Diaphragm Period...................................................................38
 

4.2	 Response Modification Coefficient, R, Selection .....................................................................41
 

4.3	 Deflection Amplification Factor, C Selection ........................................................................45
 d,

4.4	 Overstrength Factor, Ω , Selection...........................................................................................45
 o

4.5 Overview of the Alternate Seismic Design Procedure .............................................................46
 

Chapter 5	 Implementation of the Alternate Seismic Design Procedure..................... 49
 

5.1 A Two-Stage ELF Procedure....................................................................................................49
 

5.2 First Stage – Diaphragm Design ..............................................................................................50
 

5.3	 Diaphragm Design Coefficient Cs Using the ELF Procedure...................................................50
 

5.4 Diaphragm Forces Using the ELF Procedure...........................................................................54
 

5.5 North/South Diaphragm Shear Design.....................................................................................57
 

5.6 North/South Diaphragm Shear Transfer to Walls.....................................................................62
 

5.7 North/South Diaphragm Chord Design....................................................................................62
 

5.8 East/West Diaphragm Shear Design.........................................................................................63
 

5.9 East/West Diaphragm Shear Transfer to Walls.........................................................................64
 

5.10 East/West Diaphragm Chord Design........................................................................................65
 

5.11 Second Stage – Shear Wall Design ..........................................................................................65
 

5.12 Shear Wall Force Using the ELF Procedure.............................................................................66
 

5.13 Limitations and Adaptations of the Alternate Design Procedure..............................................71
 

Chapter 6		 Diaphragm Deflection Check ....................................................................... 73
 

6.1	 Deflection of North/South Diaphragm .....................................................................................73
 

6.2	 Deflection of North/South Walls..............................................................................................77
 

6.3	 Limits on Diaphragm Deflection – Deformation Compatibility...............................................79
 

6.4	 Limits on Diaphragm Deflection – Second Order Effects and P-Δ Instability..........................79
 

6.5	 Limits on Diaphragm Deflection – Building Separations and Setbacks...................................81
 

Chapter 7	 Comparison of Designs Using Current Practice and Alternate
 

Design Procedure ......................................................................................... 83
 

vi 
Chapter 8 Future Studies for Design of RWFD Buildings ........................................... 87
 

8.1 Steel Deck Diaphragms............................................................................................................87
 

8.2 Out-of-Plane Top of Wall Anchorage Forces ...........................................................................87
 

8.3 In-Plane Wall Yielding/Rocking...............................................................................................88
 

8.4	 Irregular Plan Shapes and Abrupt Changes along Exterior Walls.............................................88
 

8.5	 Combining Connector Forces from Shear Acting in Two Orthogonal Directions....................89
 

8.6 Forces on Continuity Ties........................................................................................................89
 

8.7	 Three-Dimension Modeling Calibrated to the Response of Buildings and Tests .....................89
 

8.8	 Deflection of Wood Diaphragms..............................................................................................89
 

8.9	 Applicability to Buildings with Lightweight Enclosures and Steel Bracing ............................90
 

8.10	 Applicability to Multi-Story Buildings....................................................................................90
 

8.11	 Implications of Diaphragm Deflections on Structural and Nonstructural Elements.................90
 

8.12 Large-Scale Diaphragm Tests ..................................................................................................91
 

Chapter 9 Conclusions .................................................................................................. 93
 

References ....................................................................................................................... 95
 

Appendices 

A. Alternate Design Procedure Discussion and Commentary.......................................................99
 

A.1 Commentary on Alternate Design Procedure with Diaphragm Yielding ...........................99
 

A.2 Limitations of the Alternate Design Procedure ...............................................................103
 

A.3 Applicability of Alternate Design Procedure to RWFD Buildings with

Steel Deck Diaphragms..........................................................................................................104
 

A.4 Discussion of Diaphragm Yielding..................................................................................105
 

A.5 Quality of Design, Construction and Inspection..............................................................105
 

A.6 Diaphragm Modifications and Deterioration ...................................................................106
 

A.7 Possible Code Provisions................................................................................................106
 

B. Evaluating RWFD Buildings Using FEMA P695 Methodology ............................................ 111
 

B.1 Modeling Framework ...................................................................................................... 113
 

B.2 Modeling Framework Validation..................................................................................... 116
 

vii 
C.	 List of Connectors in Database .............................................................................................. 119
 

D. Evaluation of Current Design Procedure................................................................................121
 

D.1 Description of Archetypes...............................................................................................121
 

D.2 Summary of FEMA P695 Analysis Results for Current Design ......................................123
 

D.3 Fundamental Period of the Archetypes............................................................................126
 

E. Description of Archetypes for Current Design Procedure ......................................................129
 

F. FEMA P695 Evaluation Results for Current Design Procedure .............................................137
 

G. Evaluation of Alternate Design Procedure .............................................................................145
 

G.1 Description of Archetypes...............................................................................................145
 

G.2 Summary of FEMA P695 Analysis Results for the Alternate Design Procedure .............145
 

G.3 Overstrength and Deflection Amplification Factors for the Diaphragm ..........................147
 

H. Description of Archetypes for Alternate Design Procedure....................................................149
 

I. FEMA P695 Evaluation Results for Alternate Design Procedure...........................................153
 

J. Out-of-plane Wall Anchorage Forces.....................................................................................157
 

J.1 Out-of-Plane Wall and Wall Anchorage Forces; Current Design ......................................157
 

J.2 Out-of-Plane Wall Anchorage Force Study.......................................................................158
 

J.3 Stiffness of Wall Anchorage Connectors ..........................................................................161
 

J.4 Transfer of Wall Anchorage Forces to Continuous Diaphragm Ties.................................161
 

K. Analysis of Archetypes Using Uniform Nailing.....................................................................163
 

viii Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure
List of Tables 

Table 3.1	 Diaphragm Nailing Schedule (Cases 2 and 4) ...........................................................28
 

Table 3.2	 Diaphragm Nailing Zone Shear Checks.....................................................................29
 

Table 3.3	 Diaphragm Nailing Zone Shear Checks.....................................................................32
 

Table 5.1	 Diaphragm Nailing Schedule (Cases 2 and 4) ...........................................................59
 

Table 5.2	 Diaphragm Nailing Zone Shear Checks.....................................................................61
 

Table 5.3	 Diaphragm Nailing Zone Shear Checks.....................................................................64
 

Table 6.1	 Shear Deformation and Nail Slip Computation Table................................................75
 

Table 7.1	 Common Features for Example Buildings.................................................................83
 

Table 7.2	 Comparison of Diaphragm Design Using Current Practice and
 

Alternate Design Procedure.......................................................................................83
 

Table 7.3	 Comparison of Shear Wall Design Forces Using Current Practice

and Alternate Design Procedure ................................................................................85
 

Table B1	 FEMA P695 Earthquake Ground Motion Ensemble ................................................ 112
 

Table B2	 Beta factors for determining acceptable collapse margin ratios............................... 113
 

Table C1	 Cyclic test data for nails.......................................................................................... 119
 

Table C2	 Cyclic test data for steel deck sidelap connectors.................................................... 119
 

Table C3	 Cyclic test data for steel deck framing connectors...................................................120
 

Table D1	 Summary of collapse margin ratio results for wood diaphragm
 

archetype performance groups for current design....................................................125
 

Table D2	 Summary of collapse margin ratio results for steel deck diaphragm

archetype performance groups.................................................................................125
 

Table D3	 Summary of Elastic Periods for Archetypes............................................................126
 

Table E1	 Archetype Descriptions for Wood Diaphragms .......................................................129
 

Table E2	 Archetype Descriptions for Steel Diaphragms for High-Seismic
 

Risk – Existing Design ............................................................................................130
 

Table E3	 Archetype Descriptions for Steel Diaphragms for ModerateSeismic Risk – Existing Design...............................................................................133
 

Table F1	 Summary of collapse results for RWFD buildings incorporating

wood roof diaphragm archetype designs .................................................................138
 

ix 
Table F2	 Adjusted collapse margin ratios and acceptable collapse margin

ratios for RWFD buildings incorporating wood roof diaphragm

archetype designs ....................................................................................................139
 

Table F3	 Summary of collapse results for RWFD buildings incorporating

steel roof diaphragm archetype designs...................................................................140
 

Table F4	 Computed and acceptable adjusted collapse margin ratios for
 

RWFD buildings incorporating steel roof diaphragm archetype designs.................143
 

Table G1	 Summary of collapse margin ratio results for wood structural panel

diaphragm archetype performance groups...............................................................146
 

Table G2	 Summary of Elastic Periods for Archetypes Designed Using the

Alternative Design Procedure..................................................................................146
 

Table G3	 Range of building drift ratios (BDRs) for the wood diaphragm

performance groups.................................................................................................147
 

Table H1	 Archetype Descriptions for Wood Diaphragms for High- and

Moderate-Seismic Risk – Alternate Design .............................................................149
 

Table I1	 Summary of collapse results for RWFD buildings incorporating

wood roof diaphragm archetype designs .................................................................153
 

Table I2	 Adjusted collapse margin ratios and acceptable collapse margin

ratios for RWFD buildings incorporating wood roof diaphragm

archetype designs ....................................................................................................154
 

Table I3	 Overstrength and Deflection Amplification Parameters for the

Alternate Design Procedure.....................................................................................155
 

Table I4	 Ratio of the medial diaphragm drift caused by the design level

ground motion to the median diaphragm drift at the “code” level force ..................156
 

Table K1	 Comparison of archetypes .......................................................................................163
 

x Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure
List of Figures 

Figure 1.1 Comparison of design steps for the alternate and current procedures..........................5
 

Figure 2.1	 Collapse of RWFD Buildings at Elmendorf Air Force Base, 1964 ............................13
 

Figure 2.2 Partial Collapse of a RWFD Building with a steel deck diaphragm 

in Yucca Valley, 1992 ................................................................................................14
 

Figure 2.3	 Partial Collapse of a RWFD Building in the Northridge Earthquake, 1994...............14
 

Figure 2.4 Evolution of Wall Anchorage Code Provisions..........................................................15
 

Figure 3.1 Example RWFD Building..........................................................................................17
 

Figure 3.2	 Diaphragm Loading Model (both orthogonal directions shown) ...............................23
 

Figure 3.3	 Diaphragm Shear Distribution in both Orthogonal Directions...................................25
 

Figure 3.4 Sheathing Layout and Nailing for a Panelized Roof System .....................................27
 

Figure 3.5	 North/South Nailing Zone Layout .............................................................................29
 

Figure 3.6 Diaphragm Chord Forces...........................................................................................30
 

Figure 3.7	 North/South and East/West Nailing Zones Combined ...............................................32
 

Figure 3.8 North/South Lateral Design Forces acting on the Shear Walls (Lines A & J)............35
 

Figure 3.9 East/West Lateral Design Forces acting on the Shear Walls (Lines 1 & 5)................35
 

Figure 5.1 Diaphragm Loading Model (Alternate Procedure) ....................................................55
 

Figure 5.2	 Diaphragm Shear Distribution...................................................................................57
 

Figure 5.3 Shear Diagrams for the Diaphragm Design with the 1.5x Factor ..............................58
 

Figure 5.4	 North/South Nailing Zone Layout .............................................................................61
 

Figure 5.5	 North/South and East/West Nailing Zones Combined Layout...................................64
 

Figure 5.6 North/South Lateral Design Forces acting on the Shear Walls (Lines A & J)............70
 

Figure 5.7 East/West Lateral Design Forces acting on the Shear Walls (Lines 1 & 5)................71
 

Figure A1	 Amplified Shear Boundary Zones for the Alternate Procedure................................102
 

Figure A2	 Deformations and Change in Angle between Roof Diaphragm and Wall ................103
 

Figure B1 Three-step modeling framework.............................................................................. 114
 

Figure B2	 Illustration of hysteretic models: (a) Wayne-Stewart and (b) CUREE-SAWS......... 114
 

Figure B3 Comparison of hysteretic response for 10d common nail and wood
 

deck: (a) example of experimental data and (b) best fit numerical
 

model based on data from several tests.................................................................... 115
 

xi 
Figure B4	 Comparison of hysteretic response for 2-ply-22-gauge framing 

welds to 0.25 in. plate: (a) experimental and (b) fitted optimal

hysteretic models..................................................................................................... 115
 

Figure B5	 In-plane displacement components of the analytical inelastic roof
 

diaphragm model..................................................................................................... 116
 

Figure B6	 Illustration of a simplified rigid wall flexible diaphragm (RWFD)

building model developed in the RUAUMOKO2D platform .................................. 116
 

Figure B7 Validation/comparison of inelastic roof diaphragm for monotonic loading............. 117
 

Figure B8 Validation/comparison of inelastic roof diaphragm for cyclic loading .................... 117
 

Figure B9 Incremental dynamic analysis results/comparison................................................... 118
 

Figure D1 Archetype Naming Convention ...............................................................................122
 

Figure D2 Comparison of fundamental periods from analyses of wood panel
 

archetypes to those predicted by the proposed formula, ASCE 7-10
 

equations, a best fit curve, and those proposed by Freeman et. al............................127
 

Figure D3	 Comparison of fundamental periods from analyses of steel deck 

archetypes to those predicted by the proposed formula, ASCE 7-10
 

equations, and	a	best	fit	curve ..................................................................................128
 

Figure J1 Median out-of-plane wall anchorage force for transverse direction of loading .......159
 

Figure J2 Median out-of-plane wall anchorage force for longitudinal direction of loading ....160
 

xii 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Acronyms
 

ACI American Concrete Institute 

ACMR adjusted collapse margin ratio 

ASCE American Society of Civil Engineers 

ASD allowable stress design 

AWC American Wood Council 

BDR building drift ratio 

CMR collapse margin ratio 

CUREE Consortium of Universities for Research in Earthquake Engineering 

DDR diaphragm drift ratio 

DE Design Earthquake 

DF/L Douglas-Fir/Larch 

DM damage measure 

EERI Earthquake Engineering Research Institute 

ELF Equivalent Lateral Force 

FEMA Federal Emergency Management Agency 

g gravity 

IBC International Building Code 

ICBO International Conference of Building Officials 

ICC International Code Council 

IDA incremental dynamic analysis 

IM intensity measure 

MCE Maximum Considered Earthquake 

NEHRP National Earthquake Hazards Reduction Program 

NIST National Institute of Standards and Technology 

NOAA National Oceanic and Atmospheric Administration 

NRC National Research Council of National Academy of Sciences 

o.c. on center 

OSB oriented-strand board 

P-Δ axial load-deflection 

PCF pounds per cubic foot 

PEER Pacific Earthquake Engineering Research Center 

PG performance group 

xiii 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

PGA peak ground acceleration 

Plf pounds per linear foot 

PSI pounds per square inch 

RWFD rigid wall-flexible diaphragm 

SAWS Seismic Analysis of Woodframe Structures 

SDC Seismic Design Category 

SDI Steel Deck Institute 

SDPWS Special Design Provisions fo Wind and Seismic 

SEAOC Structural Engineers Association of California 

SEAONC Structural Engineers Association of Northern California 

sec seconds 

SFRS Seismic-Force-Resisting System 

SRSS square root sum of the squares 

SSC Seismic Safety Commission of the State of California 

SSF spectral shape factor 

UBC Uniform Building Code 

WDR wall drift ratio 

WR Deck wide rib deck 

xiv 
FEDERAL EMERGENCY MANAGEMENT AGENCY

Chapter 1 Introduction 

This report presents a proposed alternate design procedure for earthquake resistance of one-story 

buildings with stiff and strong concrete or masonry wall elements coupled with flexible roof 

diaphragms. In this report, these buildings are referred to as rigid wall-flexible diaphragm (RWFD) 

buildings. 

This alternate design procedure resulted from one of three studies that were part of the Building Seismic 

Safety Council’s Simplified Design Program, a larger project to explore means of simplifying the 

seismic design of buildings. The other two studies in this program were stand-alone seismic design 

provisions for Seismic Design Category (SDC) B structures and further simplification of the existing 

simplified procedure in Section 12.14 of ASCE 7 (ASCE, 2010). The goal of the RWFD study was to 

determine whether a set of stand-alone design provisions could be created for a single building type, in 

this case a “box” or RWFD building. This topic had the added potential to directly address the behavior 

of RWFD buildings that often includes yielding of the diaphragm rather than in-plane yielding of the 

walls. 

The objectives of the study were: 

•	 To develop an alternate design methodology for the horizontal roof diaphragm and the vertical 

elements of the seismic-force-resisting system (SFRS) that is relatively simple yet appropriately 

captures the unique behavior of single-story RWFD buildings in which a building’s response is 

dominated by the diaphragm instead of the vertical portion of the SFRS, and 

•	 To base the alternate design procedure on design parameters that are representative of the 

diaphragms response such as a period, a ductility coefficient, and an overstrength factor that 

account for diaphragm flexibility and performance. 

The alternate design procedure was developed and evaluated using the procedure of Quantification of 

Building Seismic Performance Factors (FEMA P695) [FEMA, 2009] to confirm it would meet the intent 

of current code provisions. The results of these evaluations are presented in the appendices to this 

report. 

In addition to this report, a preliminary version of the alternative procedure is included in Part 3 of the 

2015 NEHRP Provisions [FEMA, 2015]. It is intended that the alternative design procedure be proposed 

for incorporation into a future edition of Minimum Design Loads for Buildings and Other Structures 

(ASCE 7) [ASCE, 2010]. 

Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure 1 
FEDERAL EMERGENCY MANAGEMENT AGENCY

 

1.1 The Need for a New Design Procedure for RWFD Buildings 

Single-story buildings with concrete or masonry walls supporting lightweight wood or steel roof 

diaphragms are a very common building type across North America and other parts of the world. The 

walls are strong and stiff in their plane in comparison to the strength and stiffness of the diaphragm in its 

plane. The current building code provisions most frequently used for these buildings are those of the 

equivalent lateral force procedure in ASCE 7-10 (ASCE, 2010). This procedure, applicable to all 

buildings, incorporates the assumption that the primary flexibility and ductility occur in the vertical 

elements of the SFRS. The flexibility drives the dynamic amplification of the ground motion, and the 

ductility drives the dissipation of the energy of the dynamic response. The actual seismic behavior of 

these Rigid Wall-Flexible Diaphragm (RWFD) buildings is quite different. Evidence indicates that the 

dynamic behavior is largely dominated by the diaphragm’s response instead of the walls’ response. This 

is a significant departure from the underlying assumptions of the widely used equivalent lateral force 

procedure. 

The past performance of RWFD buildings when subjected to moderate to strong earthquake shaking has 

demonstrated weaknesses. Building code design provisions have addressed specific known weaknesses 

of RWFD buildings, and in particular, the connections between the tops of walls and the diaphragms. 

Provisions specific to these buildings have evolved mostly as reactions to observed damage with little 

stated recognition of how these buildings respond differently to earthquakes than multi-story frame 

buildings or one-story buildings with rigid diaphragms. The RWFD buildings have diaphragms that 

often yield and dominate the building behavior while the walls typically remain mostly in the elastic 

range for in-plane loading. 

There is a need to address the diaphragm yielding of RWFD buildings in applicable design 

requirements. Several design approaches were considered including a displacement based design 

approach, which would not have fit into the current framework of ASCE 7. However, the resulting 

alternate design procedure ended up being well aligned with current provisions of ASCE 7-10, but with 

the diaphragm yielding specifically considered. Many of the current provisions are still applicable when 

implementing the alternate design procedure. As such it is better suited for incorporation into ASCE 7 

rather than being in a stand-alone document. 

1.2 Purpose of Report 

The purpose of this report is to present an alternate seismic design procedure for RWFD buildings that 

better captures actual building behavior, and in particular accounts for yielding of the diaphragm being 

predominant, rather than yielding in the vertical elements of the SFRS. The target audience is practicing 

engineers that design and retrofit this type of building. The intention of this report is to convey design 

principles to these practicing engineers that they may use in their designs to improve the seismic 

performance of RWFD buildings. 

2 Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure
FEDERAL EMERGENCY MANAGEMENT AGENCY

1.3	 Introduction to the Alternate Procedure and Comparison to 

Current Design Practice 

The alternate procedure is force based like existing design requirements for this type of building; 

however, unlike current provisions, the magnitude of the diaphragm design forces in the alternate 

procedure depends more on diaphragm properties than those of the vertical in-plane wall elements. The 

alternate procedure is similar to the two-staged analysis procedure of a multiple story building with a 

flexible upper portion and a stiff lower portion; however, for the one-story RWFD building, the 

diaphragm is the flexible upper portion, and the in-plane walls are the stiff lower portion. 

In the alternate procedure, the diaphragm is designed using the equivalent lateral force procedure but 

with a period applicable to the diaphragm alone and a response modification coefficient applicable to the 

diaphragm, Rdiaph. This is a departure from current design practice in which the diaphragm forces are 

computed using a period and response modification coefficient applicable to the vertical wall system. 

Also, the alternate procedure requires designing the end regions of a diaphragm for an amplified shear to 

better spread diaphragm yielding. Diaphragm chords are designed using forces computed with Rdiaph but 

without the amplification in the end regions. Collectors for buildings assigned to SDC C to F are 

designed for a diaphragm force amplified by the diaphragm overstrength factor, Ωo. At this time the 

alternative is limited to buildings constructed with wood structural panel diaphragms nailed to wood 

framing members or wood nailers. 

The walls are then designed using a period appropriate for the in-plane walls and a response 

modification, Rwall, applicable to the wall SFRS. The period for the walls is based on an approximate 

period equation, Equation 12.8-10, in ASCE 7-10 applicable to masonry and concrete shear walls. Note 

that this is a different approximate period equation than equation 12.8-7 of ASCE 7-10 that is commonly 

used for this type of building. In addition, the value of Rwall/ρwall cannot be greater than Rdiaph/ρdiaph; and 

if it is less, then the diaphragm force applied to the walls must be amplified by the ratio of 

(Rdiaph×ρwall)/(Rwall×ρdiaph). Currently, the redundancy factor ρdiaph is permitted to equal 1.0 per ASCE 7-

10 Section 12.3.4.1. These variables are defined in Chapters 4 and 5 of this report. 

In addition to designing the diaphragm and walls for lateral forces, the in-plane deflections of the 

diaphragm and walls must be checked. The diaphragm deformations are computed using the equation 

from the SDPWS-2008 (AWC, 2009) using a force level consistent with the design force level and then 

amplified by a defection amplification coefficient, Cd, applicable to the diaphragm. The wall 

deformations can be computed using their design level forces and then amplified by the Cd factor 

appropriate for the wall SFRS. These deflections are used to check deformation compatibility, P-Δ

instability, and building separation or setbacks. 

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The alternate design procedure is outlined in Figure 1.1 along with an outline for current design practice. 

The list of design steps demonstrates both similarities and differences between the alternate design 

procedure and current design practice. Many of the difference have been discussed above. The 

similarities are substantial in that both procedures are force based and the steps for each procedure can 

be aligned with one another. Many provisions such as those for out-of-plane wall forces, wall anchorage 

and diaphragm cross-ties are essentially identical for larger diaphragms under current practice. 

4 Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure
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Period determination:

T

diaph

= 0.002L

f

T

walls

= !.!!"#

!!!

h!

Equivalent Lateral Force Procedure:

Using	
  R

diaph

= 4.5 and T

diaph

Determine	
  diaphragm shears:

• Create a diaphragm with	
  nailing zones using

SDPWS-­‐2008

• Amplify shears in end 10% region by 1.5

Design	
  diaphragm chords

Design	
  diaphragm collector using force amplified by Ωo

for

the diaphragm

Alternate	
  Design Procedure

• Force Based

• Two-­‐stage Analysis Equivalent

Determine	
  wall	
  shears:

• Equivalent lateral force procedure

with	
  R

wall

≤ R

diaph

• Amplify force from diaphragm

!!"#$h!!"!!

!!"##!!"#$h

≥ 1.0

Deformation compatibility, P-­‐Δ stability, and structural

separation:

Compute diaphragm and	
  wall deflections

• SDPWS-­‐2008 formula and amplify by C

d

for the	
  

diaphragm

• Typical approach	
  for walls amplified	
  by C

d

of the

wall system

ASCE 7-­‐10 Provisions for:

• Out-­‐of-­‐plane wall	
  force

• Top of wall anchorage force

• Diaphragm Ties

Current Design Procedure

• Force Based

• Based on wall	
  yielding

Period determination for building:

T

a

= !!h!⬚

!

Where C

T

= 0.02 and x = 0.75

Equivalent Lateral	
  Force	
  Procedure:

Using	
  R for the SFRS and T

a

Determine	
  diaphragm shears:

• Create a diaphragm with	
  nailing zones using

SDPWS-­‐2008

Design	
  diaphragm chords

Design diaphragm collector using force amplified by Ωo

for

the walls

Determine	
  wall	
  shears:

• Equivalent lateral force procedure

with	
  R for SFRS

Deformation compatibility, P-­‐Δ stability, and structural

separation:

Diaphragm and	
  wall deflections are often not computed,

deformation	
  compatibility is rarely checked, P-­‐Δ is typically

not checked, and structural separation	
  is handled

conservatively or sometimes deflections are computed for

this purpose

ASCE 7-­‐10 Provisions for:

• Out-­‐of-­‐plane wall	
  force

• Top of wall anchorage force

• Diaphragm Ties

Figure 1.1 – Comparison of design steps for the alternate and current procedures 

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1.4 Implementation of the Alternate Design Procedure 

 

The alternative procedure has yet to be considered for adoption by building code or standard writing 

organizations. As such, it is not adopted by any building code at this time. Use of the alternate procedure 

for new construction could be permitted by the building official on a case by case basis, as allowed for 

in Section 11.1.4 Alternate Materials and Methods of Construction and the last paragraph of Section 

12.2.1 of ASCE 7-10. Use of the alternate procedure for voluntary seismic strengthening of RWFD 

buildings should be permissible under current building code provisions. 

Although designs using the alternate procedure will likely not meet current code requirements, some of 

the principles can be implemented within current design requirements of ASCE 7-10. For example, the 

concept of having a stronger diaphragm end region that will be introduced in this report can be 

implemented by using current diaphragm required strength, while increasing the end regions of the 

diaphragm above current diaphragm strength requirements. 

The principles of the alternate procedure can also be implemented as part of voluntary seismic 

strengthening projects. For example, rather than strengthening an entire existing diaphragm that is too 

weak by today’s standards, increasing the nailing only in the end regions may move the location of first 

yielding away from the ends of the diaphragm and improve the overall behavior when subjected to 

strong earthquake shaking. Doing so would also require strengthening diaphragm-to-ledger and ledgerto-wall connections as well, but it would limit the strengthening to the perimeter regions of the 

diaphragm rather than the entire diaphragm. Also, the use of the two-stage procedure with a period of 

the diaphragm will reduce the design forces on large span diaphragms. Note that it would be more 

difficult to apply this procedure to existing building code upgrades in accordance with Seismic 

Evaluation and Retrofit of Existing Buildings (ASCE 41-13) [ASCE, 2013]. 

1.5 Scope and Limitations of the Alternate Procedure 

The alternate design procedure presented in this report is applicable to the design of new and the retrofit 

of existing RWFD buildings with wood structural panel diaphragms in which diaphragm yielding is 

expected. The diaphragm must be rectangular in shape or consist of a multi-span diaphragm able to be 

separated into rectangular portions laterally supported on all four edges of each rectangular segment. 

The wood structural panels must be nailed to wood framing members or wood nailers. It does not apply 

to buildings in which the vertical wall elements are anticipated to experience significant yielding under 

the design earthquake. 

At this time the alternate design procedure is not intended to apply to RWFD buildings with steel deck 

diaphragms. There are several reasons for not recommending its use even though use of the procedure 

for steel deck diaphragms has been studied (Koliou, 2014). Reasons include (1) tests results of a large 

6 Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure
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scale diaphragm showed significantly less distribution of yielding than the analyses show when loaded 

parallel to deck edges (Massarelli, et al., 2012), (2) steel deck diaphragms have not been envisioned to 

be yielding elements, and as such design strengths are based on monotonic tests, (3) data for reverse 

cyclically loaded connections is sparse and missing for many commonly used deck gages, (4) the postyield stiffness of connectors is positive for only a small deformation, 1 to 2 mm, (5) few reverse 

cyclically loaded diaphragm tests have been performed while FEMA P695 requires comprehensive test 

data, and (6) many diaphragms in high seismic regions are designed using proprietary sidelaps for which 

no test data was available to include in the study. Additionally, end lap connectors that are expected to 

resist diaphragm shears in a ductile manner, while at the same time resisting out-of-plane wall anchorage 

forces in an elastic manner must be further studied and understood. This issue will likely require design 

limitations that have yet to be identified. These limitations demonstrate the high priority for further 

research on the seismic capabilities of steel deck diaphragms. 

The building examples presented and the supporting analytical modeling use a SFRS consisting of 

concrete shear walls. It is believed that the alternate design procedure is equally suited for masonry 

shear wall systems. At this time the procedure presented in this report is not expressly intended to apply 

to braced frame buildings with flexible roof diaphragms; however, many of the concepts are expected to 

be relevant to this building type. In contrast to RWFD buildings, structures with a perimeter braced 

frame SFRS often do not have heavy walls, and the proposed period equation presented in this report 

and the buildings modeled behavior may not be applicable. Large RWFD buildings that use interior 

braced frames to reduce the roof diaphragm spans to manageable distances are a possible exception; the 

alternate procedure and its period assumptions are likely applicable. 

1.6 Overview of Report Contents 

The following is an overview of the contents of this report. 

Chapter 2 provides a description of RWFD buildings and the performance of these buildings in past 

earthquakes. 

Chapter 3 describes current design practice through the use of a design example and finishes with a 

discussion of the shortcomings of current design practice. The current code design procedure is 

presented before the alternate procedure, so that shortcomings of current practice can be brought to light 

and addressed with the alternate procedure. 

Chapter 4 describes the basis for development of an alternate procedure to the design of RWFD 

buildings. It presents an estimated period formula applicable to a flexible diaphragm and discusses 

computation of the overall building fundamental period. It recommends the use of a diaphragm 

response modification coefficient and provides values for a diaphragm deflection amplification factor 

and a diaphragm overstrength factor. It also demonstrates that increasing the diaphragm strength in the 

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end regions of the diaphragm results in better distribution of diaphragm yielding. The final section of 

this chapter summarizes the steps required to implement the alternate design procedure. 

Chapter 5 describes in detail implementation of the alternate design procedure. It describes a two-stage 

equivalent lateral force procedure in which the diaphragm is designed using the diaphragm’s response 

modification coefficient and the diaphragm’s period, and then the walls are designed using the response 

modification coefficient and period applicable the vertical elements of the SFRS. It uses the same 

building considered in Chapter 3 for current practice and redesigns it with the alternate procedure. 

Chapter 6 demonstrates computation of the diaphragms deflection. It then describes use of the 

diaphragm deflection to check for deformation compatibility, second order effects and P-Δ instability, 

and building separation or setback. 

Chapter 7 provides a comparison of key design results from current practice relative to the alternate 

design procedure. This includes a comparison of the required diaphragm nailing for each procedure. 

Chapter 8 provides a list of future studies recommended on this topic in order to extend the use of the 

alternate procedure and develop a comprehensive set of seismic design provisions for RWFD buildings. 

Chapter 9 provides conclusions. 

The appendices provide background information on the analyses performed on archetypes designed 

using current practice. The analyses demonstrate the need for modified design requirements and the 

improvement in performance of archetypes designed with the alternate procedure. Appendix A provides 

commentary, discussion, and limitations of the alternate design procedure. Appendix B describes use of 

the FEMA P695 [FEMA, 2009] methodology to evaluate RWFD buildings for acceptable seismic 

performance. Appendix C includes a list of connectors used for flexible diaphragms that have been 

cyclically tested. 

Evaluation of the current design procedure for RWFD buildings is described and the results presented in 

Appendices D to F. Appendix D describes how the current design approach was evaluated and provides 

summary results for archetype performance groups. It also provides information of how the period 

formulas were determined for RWFD buildings and diaphragms. Appendix E describes the archetypes, 

and Appendix F includes detailed FEMA P695 analysis results. 

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Evaluation of the alternate design procedure for RWFD buildings is described and the results presented 

in Appendices G to I. Appendix G includes summary results for the archetype performance groups, 

period information, and overstrength and deflection amplification factors. Appendix H describes the 

archetypes, and Appendix I includes detailed analysis results. 

Appendix J includes information of a study on out-of-plane wall anchorage forces, and Appendix K 

includes analysis results of archetypes with uniform nailing over the entire span to determine the 

sensitivity to the spread of yielding if the shear amplification factor is applied over the entire diaphragm 

span. 

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Chapter 2	 Description of RWFD Buildings and 

Their Performance in Earthquakes 

RWFD buildings have been a common building type for many decades, particularly in the western U.S. 

where seismic hazards are greatest. The performance of and damage to these buildings during major 

earthquakes have been recorded or documented in many reports and papers. Past performance indicates 

that special vulnerabilities have existed in this building type; however. Recent code changes 

implemented to address these vulnerabilities have not yet been tested by a major earthquake. 

2.1 Description of Typical RWFD Structures 

Structures containing rigid walls with flexible diaphragms are ubiquitous across our urban environment. 

Often labeled as “big-box” buildings, these structures are the mainstay for retail, storage and distribution 

facilities for North America’s large companies. These buildings are favored by developers and owners 

for providing the most cost effective approach to enclosing large floor spaces while providing durable 

and secure perimeters. 

RWFD buildings incorporate concrete or masonry walls, which are considered rigid in-plane, with 

flexible horizontal in-plane wood or steel roof diaphragm systems. These rigid walls act as shear walls 

to provide seismic shear resistance. Concrete wall systems are most often site-cast precast panels, 

usually referred to as tilt-up or tilt-wall panels [ACI 551, 2010]. These highly cost-efficient and versatile 

enclosures are common in many markets across North America, including in high seismic zones. Plantcast precast concrete walls and concrete block masonry are also very popular perimeter shear wall 

systems enclosing these structures; the relative popularity varies significantly from one regional market 

to another. These rigid wall systems inherently contain large perimeter seismic masses relative to the 

roof diaphragm seismic mass. Details of how these buildings are constructed can be found in 

Engineering Tilt-Up [Mays and Steinbicker, 2013]. 

Roof diaphragms in these buildings consist either of a wood structural panel diaphragm or a steel deck 

diaphragm depending upon the regional preferences. Wood structural panel diaphragms are very 

common in the Western and Southwestern United States, especially in high seismic regions. Plywood, or 

more recently oriented strand board (OSB), is fastened with nails to wood framing to provide a 

structural diaphragm as well as a roofing substrate. More commonly encountered today, these wood 

structural panels are fastened to wood nailer plates that are factory installed on top of steel joist and 

joist-girder roof support structure. The speed and cost-efficiency of combining the wood-based 

diaphragm with a steel support structure make this “hybrid” system very popular in RWFD buildings in 

California, Nevada, Arizona, Oregon and Washington. The in-plane shear strength and stiffness of these 

diaphragms are a function of the wood structural panel thickness and grade, as well as nail size and 

spacing. The wood structural panel diaphragms are relatively flexible, weak, and lightweight compared 

with the surrounding stiff, strong, and heavy walls. 

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Steel deck diaphragms are more popular in Canada, Mexico, as well as the United States outside of the 

West and Pacific Northwest. The steel decking is fastened to supporting open web steel joists and 

adjacent deck panels with welds or screws, and sometimes with an assortment of proprietary fasteners. 

The in-plane shear strength and stiffness of these diaphragms are a function of the steel deck gage, deck 

profile, joist spacing, and fastener type and spacing [SDI, 2004]. Unlike composite steel decking topped 

with concrete, a popular floor and roof system in multistory buildings, untopped steel deck diaphragms 

are relatively lightweight, weak, and flexible in-plane compared with the surrounding walls. 

A similar seismic response is also possible from buildings that incorporate rigid braced frames instead of 

concrete or masonry walls as the vertical elements of the SFRS. In very large distribution warehouses, 

interior braced frames are commonly used to reduce the horizontal roof diaphragm spans. The design 

methodology presented herein is believed to be equally applicable to these situations. The principal 

difference is that, unlike concrete or masonry walls, the braced frames often are not much stronger than 

the diaphragm. The reason is that the proportions of the walls are driven more by the need for functional 

enclosure of the space than for adequate out-of-plane strength. These reasons usually drive the design to 

a solution that has in-plane strength far in excess of code demands. The same is generally not true for 

steel braced frames. 

Potentially, some metal building structures could also be included in a broader definition of RWFD 

buildings. The important factor to consider is the relative horizontal stiffness or period of vibration of 

the roof diaphragm compared to the vertical elements of the SFRS. Metal buildings with X-braced 

perimeter systems and a large steel deck diaphragm will possibly also have seismic behavior dominated 

by the diaphragm; however, metal buildings with repetitive steel frames and/or X-braced roof 

diaphragms likely will not be dominated by diaphragm behavior to the extent assumed in this alternate 

design methodology. 

2.2 Seismic Performance History 

The seismic performance of RWFD buildings in the past has often been poor. The first documented 

failures of a RWFD building due to seismic ground motions were warehouses at Elmendorf Air Force 

Base near Anchorage, Alaska in 1964. Designed in 1951 for a lateral force of only 8-percent of gravity 

under an allowable stress design approach [NRC, 1973], a partial steel rod X-braced diaphragm below a 

wood roof structure failed at the diaphragm boundaries due to inadequate shear transfer, causing two 

buildings to completely collapse (Figure 2.1). A few years later, the 1971 San Fernando earthquake 

tested this building type again with strong seismic ground motions. Because of the high density of 

RWFD buildings in the region, coupled with poor out-of-plane wall anchorage practices, significant 

failures caught the attention of the engineering community and quickly resulted in new code provisions. 

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Figure 2.1: Collapse of RWFD Buildings at Elmendorf Air Force Base, 19 64 (Source: U.S. Air Force ) 

Thus far, the performance history of RWFD buildings has largely been dominated by the poor 

performance of the out-of-plane anchorage attaching the heavy walls to the lightweight roof diaphragms 

[SEAONC, 2001]. Wall-to-roof separations and partial collapses have been documented in the 1971 San 

Fernando earthquake [NOAA, 1973], 1984 Morgan Hill earthquake [EERI, 1985], 1987 Whittier 

Narrows earthquake [EERI, 1988], 1989 Loma Prieta earthquake [Phipps M, et. al., 1990], 1992 

Landers/Big Bear earthquakes (Figure 2.2) [Shipp, 2010], and the 1994 Northridge earthquake (Figure 

2.3) [SSC, 1995]. Because the earthquakes in which wall anchorage failures have been observed have 

occurred in California, and because the RWFD building roof systems in California are predominately 

wood structural panel, observed wall anchorage failures have historically been in wood diaphragms. The 

smaller number of steel deck diaphragm failures [Shipp, 2010; Brandow, 2010] observed to date could 

simply be associated with the limited inventory of this roof system where strong ground motions have 

occurred to date. 

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Figure 2.2: Partial Collapse of a RWFD Building with a steel deck diaphragm in Yucca Valley, 1992 

(Source: Gregg Brandow) 

Figure 2.3: Partial Collapse of a RWFD Building in the Northridge Earthquake, 1994 (Source: EERI) 

14 Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure
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In reaction to the repeated failures of the wall anchorage system in these buildings in the western United 

States, the Uniform Building Code (UBC) provisions have, multiple times, become more stringent and 

required higher design forces for out-of-plane wall anchorage (Figure 2.4). Based on observations 

following the Northridge earthquake, the current wall anchorage provisions referenced by the 2012 

International Building Code (IBC) [ICC, 2012] are contained in ASCE 7-10 Section 12.11.2 [ASCE, 

2010] and prescribe maximum expected design forces without relying upon connection ductility 

[SEAOC, 1999]. These design force levels and detailing requirements for out-of-plane wall anchorage 

have remained largely unchanged since they were introduced into the 1997 Uniform Building Code 

[ICBO, 1997]. Since that time, the current practice and force levels of anchoring heavy walls to the 

flexible diaphragms have not been tested by a strong earthquake event. 

Figure 2.4: Evolution of Wall Anchorage Code Provisions (Source: John Lawson SE) 

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Observation of earthquake damage to the in-plane rigid shear walls or the main flexible roof diaphragm 

has been rare, except for collateral damage from the out-of-plane wall anchorage issues. The perimeter 

shear walls often consist of largely solid wall portions with relatively few penetrations, resulting in inplane lateral strength significantly in excess of that required for seismic forces. This inherent 

overstrength of the shear walls transfers the inelastic building behavior into the diaphragm. It is 

important to consider that the out-of-plane detachment of the heavy walls from the diaphragm in the past 

may have protected the diaphragm from experiencing in-plane seismic forces which could have led to 

global failure. The overstrength of the walls, combined with the code required higher wall anchorage 

and collector force levels, could potentially make diaphragm yielding, foundation rocking or sliding, and 

global response more critical for RWFD buildings in future earthquakes. 

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Chapter 3 Current Design Practice Example 

While the out-of-plane wall anchorage provisions have dramatically evolved after each damaging 

earthquake, code-based seismic design methodologies for the diaphragm and vertical elements of the 

SFRS have remained fairly consistent. For RWFD buildings, the past and current practices are to 

engineer the SFRS using the equivalent lateral force (ELF) procedure of ASCE 7-10 Section 12.8. This 

procedure assumes the predominant structural response is closely associated with the vertical elements 

of the SFRS. Under the ELF procedure, seismic forces are based on the assumption of lumped masses at 

story levels, supported on flexible elements that represent the lateral stiffness of shear walls or frames 

traditionally defining the SFRS. The period of the SFRS is key to determine the code-based seismic 

forces. Additionally, overstrength factor, Ωo, and deflection amplification factor, Cd, are currently both 

determined based on the vertical elements of the SFRS. 

3.1 Example Building Description (current practice) 

To illustrate the concepts presented in this report, design of an example building is presented. The 

example building represents a common concrete tilt-up wall building with a low-sloped wood structural 

panel roof diaphragm. See Figure 3.1. 

Figure 3.1: Example RWFD Building 

Codes and Standards 

2012 International Building Code (IBC) 

Minimum Design Loads for Buildings and Other Structures (ASCE 7-10) 

2008 Special Design Provisions for Wind and Seismic (SDPWS-2008) 

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Seismic-force-resisting system 

Bearing-wall system consisting of intermediate precast concrete shear walls supporting a flexible 

diaphragm of wood structural panel construction. 

Seismic and site data 

Mapped spectral accelerations for the site SS = 1.5 and S1 = 0.6 

Site Class = D 

Risk Category = II (ASCE 7-10 Table 1.5-1) 

Redundancy Factor ρ = 1.0 (computed for the walls and given for the diaphragm in accordance 

with ASCE 7-10 Section 12.3.4.1) 

Wind: Assumed not to govern the design 

Perimeter Walls 

Wall Thickness = 9.25 inches of concrete (150 pcf, f’c = 4000 psi) 

Height = 30 feet to roof with another 3-foot for the parapet 

Roof Structure 

Panelized hybrid roof structure [Lawson J, 2013] 

Structural-I sheathing (15/32” OSB wood structural panel) 

Pre-engineered/pre-manufactured open-web steel joists and joist-girders with full-width wood 

nailers (popular hybrid system). 

All wood is Douglas-fir/Larch (DF/L), S-Dry 

Roof Dead Load = 12 psf assumed as a design load 

Following common practice, the equivalent lateral force (ELF) procedure and the provisions of the 2012 

IBC and ASCE 7-10 will be utilized for this design example unless otherwise noted. 

Typically, the building inventory comprising RWFD buildings consists of concrete or masonry shear 

walls. In SDC C and higher, the permitted types of concrete and masonry shear wall systems are: 

intermediate precast concrete shear walls, special reinforced concrete shear walls, and special reinforced 

masonry shear walls. While special reinforced concrete and special masonry shear walls benefit from 

higher response modification coefficients, additional detailing and analysis provisions are applicable, so 

they are less frequently used. As a result, in one-story tilt-up concrete buildings, intermediate precast 

shear wall systems are most common. In SDC D and above, this lateral-force-resisting system has a 

height limitation of 40 feet, except in single-story storage warehouses where the limitation extends to 45 

feet, per ASCE 7-10 Table 12.2-1. The use of the intermediate precast shear wall system will be 

illustrated for this building example. 

18 Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure
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3.2	 Determine Design Spectral Response Accelerations SDS and SD1

(current practice) 

The short and long period site coefficients Fa and Fv are used to modify the mapped spectral 

accelerations SS and S1 to determine the design spectral response accelerations. Using the given mapped 

spectral accelerations SS = 1.5 and S1 = 0.6 and site class D, the following site coefficients are 

determined from IBC Tables 1613.3.1 (1) and (2). ASCE 7-10 Tables 11.4-1 and 11.4-2 may also be 

consulted. 

Fa = 1 (short period) 

Fv = 1.5 (1-second period) 

Using these site coefficients, the site-adjusted spectral accelerations are determined:

!!" = !!!! = 1.0 1.5 = 1.5 (short period) IBC Eq. 16-37

!!! = !!!! = 1.5 0.6 = 0.9 (1-second period) IBC Eq. 16-38 

The design spectral response accelerations are obtained as follows: 

!!" = !

!!" = 1.0 (short period) IBC Eq. 16-39

!!! =

!

!

!

!!! = 0.6 (1-second period) IBC Eq. 16-40 

Using the design spectral response accelerations and the risk category, the next step is to determine the 

appropriate Seismic Design Category from IBC Tables 1613.3.5 (1) and (2). With S1

 less than 0.75, both 

the short-period and 1-second-period design categories are level D; thus, SDC D governs. 

Short-period category = D IBC T 1613.3.5(1) 

1-second-period category = D IBC T 1613.3.5(2) 

Governing SDC = D 

Using ASCE 7-10 Section 12.6 in conjunction with Table 12.6-1, the equivalent lateral-force (ELF) 

procedure of Section 12.8 is most commonly used to determine the seismic base shear coefficient. 

3.3	 Determine Fundamental Building Period (current practice) 

For a concrete shear wall building, the approximate fundamental period, Ta, under current practice is 

obtained using ASCE 7-10 Equation 12.8-7 with CT = 0.020 and x = 0.75. For this building, the average 

roof height, hn , is 30 feet. 

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3/4 0.75 

Ta = CThn = (0.02)30 = 0.26 seconds ASCE 7-10 Eq. 12.8-7 

Alternatively, Equation 12.8-9 could have been used. 

Because this example involves a regular structure five stories or fewer in height having a period, Ta , less 

than 0.5 seconds, the base shear coefficient, Cs, can be based on an SDS that need not exceed the value 

calculated using a value of 1.5 for SS (Section 12.8.1.3). However, in our example SS already does not 

exceed 1.5, thus the design spectral response accelerations and SDC remain as originally calculated. 

S = 1.0 (short period) DS design 

S = 0.6 (1-second period) D1 design 

SDC = D 

3.4 Base Shear Using the ELF Procedure (current practice) 

ASCE 7-10 Section 12.8.1 defines the seismic base shear as 

V = CsW ASCE 7-10 Eq. 12.8-1 

where 

!! = !

!!" ASCE 7-10 Eq. 12.8-2

!!

Because these tilt-up concrete walls will be considered load-bearing, intermediate precast shear walls, 

the following seismic performance factors are applicable to the building: 

R = 4 Response modification coefficient ASCE 7-10 T 12.2-1 

Ωo = 21⁄2 Overstrength factor 

Cd = 4 Deflection amplification factor 

In addition, the importance factor described in ASCE Section 11.5 is obtained from Table 1.5-2 based 

on the building’s given Risk Category II: 

Ie = 1.0 ASCE 7-10 T 1.5-2 

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Therefore, per Eq. 12.8-2

!! 1.0

! "

! = = = 0.25 ! 4

!! 1.0

Checking the maximum limit for Cs with Eq. 12.8-3 where T ≤ TL 

! !

!" = !!

! = !.!

! # ! = 0.58 > 0.25 OK

! !.!" !! !.!

Checking the minimum allowed value for Cs, ASCE 7-10 Equations 12.8-5 and 12.8-6 are applicable. 

In this example, S1 is equal to 0.6g: therefore, Equation 12.8-6 is also required to check the minimum 

allowed Cs

. 

!! !"# = 0.044!!"!! = 0.044 1.0 1.0 = 0.044 < 0.25 OK ASCE 7-10 Eq. 12.8-5 

Cs min = 0.01 < 0.25 OK ASCE 7-10 Eq. 12.8-5

! = !.!!! = !.!(!.!)

! !"# ! ! = 0.075 < 0.25 OK ASCE 7-10 Eq. 12.8-6 

!! !.!

The calculated value for Cs = 0.25 is between the maximum and minimum allowed values. 

Cs governs = 0.25 

Substituting into Equation 12.8-1, we obtain the base shear equation for the building for each orthogonal 

axis direction of the structure, which is used to determine the design forces in the shear walls. 

V = Cs

W = 0.25W 

3.5 Diaphragm Design Forces Using the ELF Procedure (current practice) 

Because the current code practice is based on a classical vibration model using lumped masses (at the 

diaphragm) elevated on a flexible column (frames or shear walls), the diaphragm’s forces are assumed to 

be closely associated with the response of the vertical elements of the SFRS. 

The following formula is used in current practice to determine the total seismic force F

px

 on the 

diaphragm at a given level of a building in each direction. 

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!

! !!! !!

!" = ! !!" ASCE 7-10 Eq. 12.10-1

!!! !!

As determined, the base shear for this building is V = 0.25W. Because it is a one-story building, 

Equation 12.10-1 simply becomes the following

!!" = 0.25!!"

F

px

 shall not be less than

0.2!!"!!!!" = 0.2 1.0 1.0 !!" = 0.2!!" ASCE 7-10 Eq. 12.10-2 

But need not exceed 

0.4!!"!!!!" = 0.4 1.0 1.0 !!" = 0.4!!" ASCE 7-10 Eq. 12.10-3 

Based on the criteria given in Section 12.10.1.1, Fpx= 0.25wpx. 

Therefore, current practice dictates for diaphragm design in each direction to use F

p 

= 0.25w

p. 

Using a flat-beam analogy, where the diaphragm is idealized as a simply-supported beam spanning 

between supporting walls, north/south seismic forces are resisted by shear walls on grid lines A and J, 

and east/west seismic forces are resisted by shear walls on grid lines 1 and 5. For this building, it is not 

required to combine both orthogonal directions based on ASCE 7-10 Sections 12.5.3 and 12.5.4. Each 

orthogonal uniform load across this flat-beam model is illustrated in Figure 3.2. 

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Figure 3.2: Diaphragm Loading Model (both orthogonal directions shown) 

The uniformly distributed loads wNS and wEW applied laterally to the diaphragm are computed using the 

diaphragm lengths and unit weights and the tributary wall heights and unit weights: 

Roof dead load = 12 psf 

Wall dead load = 116 psf (91⁄4” thick at 150 pcf) 

Roof height = 30’-0” (above floor) 

Top of wall = 33’-0” (above floor) 

33′ 1

!!" = 0.25 12!"# 200′ + 2 0.25 116!"# 33′ = 1653!"# 2 30′

33′ 1

!!" = 0.25 12!"# 400′ + 2 0.25 116!"# 33′ = 2253!"# 2 30′

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The maximum design shears are now computed using simple statics on the uniformly loaded flat beam 

model. Because of the building’s regular shape and uniformly distributed mass, the loading diagram will 

be uniform and the reactions VNS at grid lines A and J will be equal. See Figure 3.3. 

North-south diaphragm shear: 

!!" = !!"

400

2

ft = 1653400

2

ft = 330,600 !"#, !"#$!%!

North-south unit shear: 

= 330, ! 200

!!"

ft 200

600

ft !" = = 1653 !"#, !"#$!%!

East-west diaphragm shear: 

!!" = !!"

200

2

!" = 2253 !"#200

2

!" = 225,300 !"#, !"#$!%!

East-west unit shear: 

400

300

ft ! 400

!!"

ft = 225, !" = = 563 !"#, !"#$!%!

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Figure 3.3: Diaphragm Shear Distribution in both Orthogonal Directions 

3.6 North/South Diaphragm Shear Design (current practice) 

In Section 3.5, the maximum diaphragm shears were determined for each orthogonal direction. ASCE 7-

10 Section 12.5 does not require simultaneous load from two directions in this building. The highest unit 

shear demand is in the north/south direction with vNS = 1653 plf (unfactored). The nominal diaphragm 

shear capacities are provided in Special Design Provisions for Wind and Seismic (SDPWS-2008) 

[AWC, 2008] Tables 4.2A and 4.2B for a wide range of blocked diaphragm conditions. Panelized roof 

systems are commonly blocked based on their modular arrangement. Many engineers still use the 

Allowable Stress Design (ASD) format for timber design, even though the published nominal resistance 

values for diaphragms can be easily converted to strength format. This example will follow ASD 

convention for the timber diaphragm design. 

The basic loading combinations are given in IBC Section 1605.3.1 and those involving earthquake 

loading have been simplified in ASCE 7-10 Section 12.4.2.3, where load combination (5) will govern 

the design. 

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(1.0 + 0.14SDS)D + H + F + 0.7ρQE ASCE 7-10 Sec. 12.4.2.3 

When considering horizontal wind or seismic loads on a structural diaphragm, the vertical loading is not 

considered when evaluating the lateral diaphragm unit shear stress. Thus, the applicable load 

combination is simplified using D = 0, H = 0, F = 0 and L = 0. Additionally, the redundancy factor ρ is 

set to 1.0 for typical diaphragms per ASCE 7-10 Section 12.3.4.1. Therefore, the applicable basic load 

combination reduces to 0.7QE. 

!!" (!"#) = 0.7!!" = 0.7 1653 = 1157 plf 

!!"(!"#) = 0.7!!" = 0.7 563 = 394 plf 

Using these unit shear values, the designer may enter either SDPWS-2008 Table 4.2A or 4.2B to select a 

diaphragm assembly with an appropriate shear capacity. 15/32-inch Structural I sheathing is traditionally 

used as a minimum thickness in panelized construction [Lawson J, 2013]. The panelized sheathing 

system is inherently fully blocked and typically follows layout Case 2 (east/west loading) and 4 

 

 

 

 

(north/south loading) illustrated in SDPWS-2008 Tables 4.2A and 4.2B. SDPWS-2008 Tables 4.2A and 

4.2B are at a nominal strength level, and ASD design values are obtained by dividing by a factor of two 

in accordance with SDPWS-2008 Section 4.2.3. 

In the north/south direction, the ASD unit shear demand is greater than the maximum ASD capacities 

obtained from SDPWS-2008 Table 4.2A, thus reference to the high-load diaphragm shears in Table 

4.2B will be necessary. The on-center (o.c.) nail spacing shown here requires thicker framing to prevent 

splitting. The capacity is reduced from the table nominal strength value to allowable stress design value 

by dividing in half per SDPWS-2008 Section 4.2.3. 

15/32”-thick Structural I sheathing 

10d nails in 2 lines at 

2 1⁄2” (o.c.) boundaries and continuous north/south edges 

3” o.c. other edges 

10d nails in 1 line at 

12” o.c. intermediate (field) 

4x framing width at adjoining edges CAPACITY = 2580/2 = 1290 plf (ASD) 

!!" (!"#) = 0.7!!" = 0.7 1653 = 1157 plf < 1290 plf OK 

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The construction of this diaphragm system is illustrated in Figure 3.4. 

Figure 3.4: Sheathing Layout and Nailing for a Panelized Roof System [Lawson J, 2013] 

For a building this size, it is not efficient to install the heavy diaphragm nailing required at the boundary 

over the entire roof structure. Because the shear demands diminish towards the center of the diaphragm 

span, it is permitted to reduce the nailing and subpurlin widths as the corresponding unit shears also 

reduce. For this example, Table 3.1 identifies various diaphragm nailing configurations from the 

SDPWS-2008 that will be utilized at different portions of this building. The ASD shear values are 

simply the nominal strengths listed in SDPWS-2008 Tables 4.2A and 4.2B divided by a factor of two 

per Section 4.2.3. For a panelized roof structure, layout case 2 and 4 are applicable. 

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Table 3.1 – Diaphragm Nailing Schedule (Cases 2 and 4) 

15/32” Structural I OSB Sheathing (DOC PS 2 [NIST, 2004]) 

with 10d nails (0.148” dia x 2” long minimum)

Zone Framing Width	
  

at Adjoining

Edges

Lines of

Nails

Nailing per line at

Boundary &

Continuous Edges

Nailing per line at

Other Edges

ASD Allowable

Shear

(plf)

1 2x 1 6” o.c. 6” o.c. 320

2 2x 1 4” o.c. 6” o.c. 425

3 2x 1 21⁄2” o.c. 4” o.c. 640

4 3x 1 2” o.c. 3” o.c. 820

5 4x 2 21⁄2” o.c. 4” o.c. 1005

6 4x 2 21⁄2” o.c. 3” o.c. 1290

At the diaphragm boundaries (grid lines A and J), Nailing Zone 6 was determined to be acceptable. 

At some location inward as the diaphragm shears diminish, Nailing Zone 5 will become 

acceptable. The transition from Nailing Zone 6 to Nailing Zone 5 may be solved using statics as 

follows: 

Shear Demand (ASD) = Shear Capacity (ASD) 

0.7[330,600 lbs – (1653 plf)x] = 1005 plf (200 ft) 

where 

x = the demarcation distance from the diaphragm boundary. 

Solving for x obtains 

x = 26.3 ft 

Because a panelized roof system typically consists of 8-foot wide wood structural panels, the joist 

spacing module is also 8 feet, and the transition should be increased to the next 8-foot increment. 

In this case, it is increased to x = 32 feet.
 

The transition locations between Zones 5 and 4, Zones 4 and 3, Zones 3 and 2, and Zones 2 and 1 

for the north-south loading direction are found using the same process resulting in Table 3.2. 

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Table 3.2 – Diaphragm Nailing Zone Shear Checks 

Nailing Zone Distance from 

Boundary 

Strength Level 

Unit Shear 

ASD 

Unit Shear 

Allowable Shear 

Capacity 

6 0 feet vmax = 1653 plf vASD = 1157 plf 1290 plf 

5 32 feet vmax = 1389 plf vASD = 972 plf 1005 plf 

4 64 feet vmax = 1124 plf vASD = 787 plf 820 plf 

3 96 feet vmax = 860 plf vASD = 602 plf 640 plf 

2 128 feet vmax = 595 plf vASD = 417 plf 425 plf 

1 152 feet vmax = 397 plf vASD = 278 plf 320 plf 

The resulting nailing zone layout for the north/south loading is shown in Figure 3.5. 

Figure 3.5: North/South Nailing Zone Layout 

An additional check when designing wood diaphragms is to check their plan aspect ratios against the 

limitations in the SDPWS-2008 Table 4.2.4. For blocked diaphragms such as those that occur in 

panelized construction, the maximum aspect ratio is L/W = 4:1. In this example, the north/south loading 

direction is the critical L/W ratio. 

L/W = 400/200 = 2.0 < 4 Okay 

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3.7 North/South Diaphragm Chord Design (current practice) 

Recall that a flexible diaphragm may be thought of as a flat horizontal beam where the shear resistance 

is obtained by the wood structural panel sheathing across the roof surface. However, tensile forces from 

horizontal bending are not considered to be resisted by the sheathing, but by perimeter chords acting in 

tension and compression instead. 

To resist bending efficiently, the diaphragm chords are traditionally placed at the extreme sides of the 

diaphragm. In buildings with masonry or concrete perimeter walls, these chords are often steel ledger 

angles or channels at the roof line. Chord forces are determined using simple statics as illustrated in 

Figure 3.6. Maximum chord forces will occur at the center of the diaphragm’s span where the maximum 

moment occurs. 

Figure 3.6: Diaphragm Chord Forces 

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Using the equations in Figure 3.6, the maximum tensile chord force for our building example is 

determined: 

! ! 1653 = !"!! !"# 400 !

! = = = 165,300 !"# ! 8! 8 200

The chord is designed here using strength design with ASTM A36 Steel (Fy = 36 ksi). Consulting IBC 

Section 1605.2, the applicable load factor for seismic forces is 1.0. The area of steel required is:

! 165.3

! = = = 5.10 !"!

! ∅!! 0.9 36

Using a L5x5x5/8 rolled steel angle satisfies this chord demand. 

L5x5x5/8 Steel Area AS = 5.90 in2 > 5.10 in2 

3.8 East/West Diaphragm Shear Design (current practice) 

Similar to the north/south loaded direction, the orthogonal east/west direction will also require 

consideration using the same sequential process. In Section 3.6, the maximum diaphragm shear in the 

east/west direction was determined to be vEW = 563 plf (unfactored); and converting to allowable stress 

design (ASD), the maximum diaphragm shear is as follows: 

!!"(!"#) = 0.7!!" = 0.7 563 = 394 plf 

As before, SDPWS-2008 Table 4.2A is used to select diaphragm nailing with an appropriate shear 

capacity. In the north/south loaded direction, Case 4 is the loading configuration, but for the east/west 

direction this becomes a Case 2 configuration. The applicable Case determines the nail spacing along the 

continuous adjoining panel edges in the direction parallel to load. Comparing the diaphragm’s shear 

demand with Table 1 of Section 3.6, Nailing Zone 2 is selected:

!!"(!"#) = 394 !"# < 425 !"# (!"#$#%& !"#$ 2)

At some distance away from the diaphragm boundary (walls at grid lines 1 and 5), Nailing Zone 1 in 

Table 1 will be acceptable due to the diminishing unit diaphragm shears. Using the same approach as 

done in the north/south direction, the location of the nailing zone transition from Zone 2 to 1 is found 

and Table 3.3 is developed. 

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Table 3.3 – Diaphragm Nailing Zone Shear Checks 

Nailing Zone Distance from 

Boundary 

Strength Level 

Unit Shear 

ASD 

Unit Shear 

Allowable Shear 

Capacity 

2 0 feet vmax = 563 plf vASD = 394 plf 425 plf 

1 20 feet vmax = 451 plf vASD = 315 plf 320 plf 

Combining the nailing requirements for the north/south loading with the east/west loading results in 

Figure 3.7. 

Figure 3.7: North/South and East/West Nailing Zones Combined 

3.9 East/West Diaphragm Chord Design (current practice) 

With the diaphragm chords placed at the extreme sides of the diaphragm, the maximum chord forces in 

the east/west loaded direction are computed as follows: 

! ! !

!"! 2253 !"# 200 !

! = = = = 28,100 !"# ! 8! 8 400

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The required area of the steel chord is:

! 28.1

!! = = = 0.87 !"!

∅!! 0.9 36

Using an L4x4x1/4 rolled steel angle as a practical minimum size satisfies this chord demand. 

L4x4x1/4 Steel Area AS = 1.93 in2

 > 0.87 in2 

3.10 Shear Wall Force Using the ELF Procedure (current practice) 

For a single-story building, the diaphragm’s support reactions are the basis of the applied loads to the 

shear wall lines. The flexible diaphragm with its tributary mass will generate a lateral force near the top 

of the wall, Fv1. Additionally, the rigid concrete in-plane walls have significant self-weight that will also 

generate lateral forces near their center of mass, Fv2. See Figures 3.8 and 3.9. 

As determined previously in Section 3.5, the diaphragm reactions to the shear walls based on ρdiaph = 1.0 

are as follows: 

North/South Diaphragm Reactions 

Fp = VNS = 330,600 lbs 

East/West Diaphragm Reactions 

Fp = VEW = 225,300 lbs 

These diaphragm reaction forces need to be amplified to an appropriate shear wall design force if the 

redundancy factor for the SFRS is greater than 1.0.

! ! !"##

!! = !!×

!!"#$!

where for this example ρwall = 1.0 (computed) and ρdiaph = 1.0 (ASCE 7-10 Section 12.3.4.1) 

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Therefore, the shear wall design force from the diaphragm in each orthogonal direction are as follows: 

North/South 

Fv1 = 330,600 lbs 

East/West 

Fv1 = 225,300 lbs 

Next, the lateral seismic force generated from the walls’ self-weight must be included for design. 

Because this is a single-story building, the self-weight seismic force Fv2 is simply the wall line’s selfweight multiplied by the base shear coefficient Cs and any applicable redundancy factor ρ for the 

building. The base shear coefficient Cs for both axes of the building was determined in Section 3.4. 

Fv2 = CsW = 0.25Wp-wall 

For the north/south direction, the wall’s self-weight Wp-wall is computed as

!!!!"## = 116 !"#×200 !"×33 !" = 765,600 !"#

Therefore 

Fv2 = 0.25Wp-wall = 0.25(765,600) = 191,400 lbs 

Therefore, the total shear wall design force Fv for the north/south direction is 

Fv = Fv1 + Fv2 = 330,600 + 191,400 

Fv = 522,000 lbs or 522 kips 

For the east/west direction, the wall’s self-weight Wp-wall is computed as

!!!!"## = 116 !"#×400 !"×33 !" = 1,531,200 !"#

Therefore 

Fv2 = 0.25Wp-wall = 0.25(1,531,200) = 382,800 lbs 

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Therefore, the total shear wall design force Fv for the east/west direction is 

Fv = Fv1 + Fv2 = 225,300 + 382,800 

Fv = 608,100 lbs or 608 kips 

Figures 3.8 and 3.9 illustrate the forces acting on the shear walls providing lateral resistance in the 

north/south and east/west directions respectfully. The design forces at the base of the shear walls are 552 

kips north/south and 608 kips east/west. These forces include the entire weight of the walls and are 

appropriate for the design of shear forces that transfer to the slab on ground or foundation. In-plane 

shear design considerations for tilt-up concrete shear walls may be found in other sources [Mays and 

Steinbicker, 2013]. 

Figure 3.8: North/South Lateral Design Forces acting on the Shear Walls (Lines A & J) 

Figure 3.9: East/West Lateral Design Forces acting on the Shear Walls (Lines 1 & 5) 

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3.11 Shortcomings of Current Practice 

The simplistic model assumed by the ELF procedure fails to capture the actual behavior of RWFD 

buildings. The ELF procedure assumes that the seismic response consists primarily of deforming vertical 

elements and that the horizontal diaphragm is rigid, i.e. deformation of the diaphragm is not considered. 

However, for most RWFD structures the primary seismic response is dominated by the deformation of 

the horizontal flexible diaphragm. A more accurate structural model is needed to capture the flexible 

diaphragm potentially dominating the response. 

The ELF procedure also inappropriately assumes that the primary inelastic behavior is in the vertical 

wall or frame system, instead of the roof diaphragm. The seismic response modification coefficient, R, 

the overstrength factor Ωo, and the deflection amplification factor Cd in ASCE 7-10 Table 12.2-1 are 

utilized to estimate the strength demands, capacities and deflections on systems that are designed using 

linear methods while responding in the nonlinear range. Currently, the selection of R, Ωo and Cd for 

design is solely based on the performance characteristics of the SFRS’s vertical elements. In reality, the 

inelastic behavior is likely to be in the horizontal diaphragm and the current ELF procedure fails to 

characterize this diaphragm response adequately. Currently, wood and steel flexible diaphragms and 

rigid concrete diaphragms are all designed as if they have the same seismic response and performance. 

In current practice the seismic diaphragm shears used for design are directly related to the type of 

vertical elements used in the SFRS. In fact, some engineers routinely select special reinforced concrete 

shear walls (R=5) in their design (instead of intermediate precast, R=4) to reduce the diaphragm design 

shears and allow the diaphragm to span farther. The same motive drives some engineers to place girder 

support columns adjacent to the intermediate precast shear walls, converting the bearing wall system 

(R=4) to a building frame system (R=5) in one direction. The selection of the SFRS solely driven by a 

desired diaphragm load outcome is not a desirable practice, because it fails to recognize the likely 

building behavior. Current seismic design provisions in ASCE 7-10 may unintentionally encourage this 

practice. 

Because RWFD buildings typically have excessive strength in the shear walls as compared with the 

diaphragm, it is unrealistic to expect the yielding to be in the walls instead of the diaphragm; despite the 

fact that the response modification coefficient R is selected based on that assumption. Past failures have 

typically been out-of-plane wall detachments, and building codes have responded to these failures by 

increasing the out-of-plane wall anchorage design force. Assuming that failure of out-of-plane wall 

anchorage is prevented, diaphragm yielding and potential failure may become the critical behavior. The 

ELF procedure of ASCE 7-10 as currently applied to RWFD buildings does not account for this 

diaphragm behavior. 

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Chapter 4	 Development of a n Alternate Seismic Design 

Procedure 

With seismic response dominated by the horizontal diaphragm in RWFD structures, it is more realistic 

that design forces be developed around the diaphragm’s behavior. Furthermore, because the inelastic 

behavior in a RWFD building is typically located in the diaphragm, it is more realistic that the seismic 

system capacity be developed around the overstrength and ductility of the diaphragm, rather than of the 

vertical elements of the SFRS. An alternate procedure based on the diaphragm’s response would be 

more realistic and has the potential to better permit evaluation of a structure’s margin against collapse. 

A more accurate method of establishing seismic design loads for buildings dominated by diaphragm 

response is to consider the diaphragm’s period relative to the design spectral acceleration. As an 

example, ASCE 41-13 [ASCE, 2013] provides the Linear Static Procedure to rehabilitate existing onestory RWFD buildings by estimating the diaphragm-dominated building period and then establishing a 

pseudo-lateral force on the system. A number of other sources have proposed other methods of 

estimating flexible diaphragm periods and their corresponding pseudo-lateral force [Freeman et. al., 

2002; PEER, 2004; SEAONC, 2001]. With a more accurate period of the dominating response, the 

force-based procedures of ASCE 7 can be used more appropriately. Furthermore, the use of an ELF 

approach with a response modification coefficient R, an overstrength factor Ωo, and a deflection 

amplification factor Cd, related to the diaphragm’s design, construction and detailing, is expected to 

produce more rational results. 

Both the inelastically acting horizontal diaphragm and the SFRS’s vertical elements need a unified 

design methodology. The fact that RWFD buildings have a flexible upper portion (the diaphragm) 

supported in series with a rigid lower portion (the walls) make them ideally suited to be designed similar 

to the two-staged ELF procedure that currently exists within ASCE 7-10 Section 12.2.3.2. This approach 

is often used for residential podium type structures where three or four story wood shear wall buildings 

are supported on masonry or concrete shear wall parking structures. This approach encourages the two 

portions to be analyzed for seismic loading independently, and then combined as appropriate. As the 

seismic forces are handed off from one portion to another, they are adjusted to reflect the next portion’s 

expected seismic performance influenced by its period and stipulated R-coefficient. 

Chapter 4 provides background on key parameters incorporated into the alternate procedure for RWFD 

buildings. For simplicity, it is reasonable to develop a methodology for RWFD structures that can fit 

within the existing code framework already familiar to practitioners, yet providing a more rational 

approach than currently exists. 

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4.1 Determination of Building and Diaphragm Period 

As mentioned previously, a primary objective of an alternate design methodology is a design 

considering seismic response and seismic performance factors uniquely associated with a building 

dominated by the flexible diaphragm instead of the vertical portion of the SFRS. The diaphragm period 

Tdiaph is a very important parameter in determining a more realistic seismic response. 

A number of approaches have been proposed in the past to more accurately estimate the periods of 

various flexible diaphragm dominated buildings [Koliou, 2014]. One approach in current use for seismic 

evaluation is the fundamental period equation within ASCE 41-13 for one-story buildings with flexible 

diaphragms. 

!! = 0.1∆! + 0.078∆! ASCE 41-13 Eq. 7-19 

where 

!!= fundamental period in sec. in the direction of consideration. 

∆w = maximum in-plane wall displacement in inches at 1.0g 

∆d = maximum diaphragm displacement in inches at 1.0g 

While this equation has credibility from the fact that it is formally adopted in an ASCE standard, it has 

been criticized as being derived from an improper flexural beam idealization for the diaphragm instead 

of a more realistic shear beam idealization. Wilson et. al.[Wilson, 2013] derived an equation based on 

shear beam behavior and recommends that the diaphragm component (0.078∆d)

0.5 be revised to 

(0.066∆d)

0.5 within the ASCE 41-13 procedure. With this modification, the following equation for the 

fundamental period of one-story buildings with flexible diaphragms becomes: 

!! = 0.1∆! + 0.066∆! Equation (1) 

Equation (1) is mathematically derived and provides a valuable approach provided that accurate wall 

and diaphragm displacements can be computed. However, this equation is better suited for analyzing 

existing structures than it is for design because it requires one to compute the wall and diaphragm 

deflections. For design, an estimate of the period is needed to establish wall and diaphragm design 

forces. One cannot compute the deflections of the walls and diaphragm until after these elements have 

been designed, which is typical of most design problems 

To meet the objective of developing a design methodology that is simple to implement and accounts for 

diaphragm flexibility, a simple period approximation, Ta, was desired. The research conducted in 

conjunction with this report developed simple separate period formulas, Ta, for RWFD buildings with 

wood or steel deck diaphragms based on a semi-empirical analysis using a special numerical model of 

23 archetypes designed under ASCE 7-10.The design seismic demand was based on the upper bound of 

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design spectral response accelerations for Seismic Design Category D, designated as SDC Dmax. For the 

purposes of creating archetypes for evaluation under FEMA P695, this period Ta was selected to be the 

algebraic sum of Tdiaph and Twalls. In the case of the wood diaphragm, the period formula Ta = Tdiaph + 

Twalls tracks very closely with the formula, Equation (1), developed by Wilson et. al [Wilson, 2013] for 

diaphragms less than 250-ft long. For lengths over 250 feet, the proposed formulas provide a smaller 

period than Wilson’s equation [Koliou, 2014]. The approximate period equations represent the elastic 

building period at an applied load approximately equal to code level forces prior to a shift in the period 

due to inelastic behavior. More information on the development of these formulas is provided in 

Appendix D Section D.2 and Appendix G Section G.1.2. 

The following equations were developed empirically from the results obtained from 23 archetype 

building configurations involving 33-ft high concrete tilt-up walls 91⁄4” thick in a high seismic hazard 

region. Generally speaking, situations with more or less mass will have a corresponding diaphragm 

design with more or less stiffness, thus directly offsetting the mass variation. Therefore, the proposed 

period formulas are independent of mass. Additionally, because the diaphragm deformations were 

found to be overwhelmingly shear dominated, the diaphragm’s aspect ratio does not significantly affect 

the period. Tdiaph is simply based on the diaphragm’s span Lf, and Twalls is based on current ASCE 7-10 

provisions for concrete or masonry shear wall buildings. The reader is cautioned that the equation for 

Twalls was developed for shear wall buildings of various heights and with heavy floor and roof masses, 

and will probably overestimate the period for this type of building, but it serves a useful purpose for this 

discussion. 

For wood structural panel diaphragms [Koliou, 2014]: 

!!"#$! = 0.002!! Equation (2) 

!!"##$ = !.!

!

!

!

"# h! ASCE 7-10 Eq. 12.8-9 

For steel deck diaphragm [Koliou, 2014]:

!!"#$! = 0.001!! Equation (3) 

! !.!!"#

!"##$ = h! ASCE 7-10 Eq. 12.8-9 !!

where 

Lf = The span, in feet, of the horizontal flexible diaphragm being considered; the span is measured 

between vertical elements that provide lateral support to the diaphragm in the direction 

considered. 

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hn = The structural height defined in ASCE 7-10 Section 11.2. 

Cw = Shear wall coefficient for concrete and masonry walls per ASCE 7-10 Equation 12.8-10. 

!

100 h !

! ! !!

! = !! h ! ! h! !!! 1 + 0.83 !!

AB = area of base of structure, ft2 

A 2 

i = web area of shear wall i in ft

Di = length of shear wall i in ft 

hi = height of shear wall i in ft 

x = number of shear walls in the building effective in resisting lateral forces in the direction 

under consideration 

For our example wood diaphragm building, Equation 2 will be used to estimate the diaphragm’s 

approximate period, Tdiaph, and ASCE 7-10 Eq. 12.8-9 will be used to estimate the walls’ approximate 

period, Twalls; however, the two periods will not be combined to estimate a building period, Ta, out of 

concern that this will overestimate the building period and underestimate the seismic load effect. 

!!"#$! = 0.002!!

0.0019

!!"##$ = h! !!

Compute building area AB 

!! = 200!!×400!" = 80,000!"!

This building is comprised of a series of equal 25-ft long concrete tilt-up wall panels acting as shear 

walls around the building perimeter. Thus all parameters for each wall i are the same. 

9.25!"

!! = 25!"× = 19.3!!!/!"## 12

!! = 25!"

h! = 30!"

In the transverse direction (north/south) there are eight wall panels along each line of resistance, or a 

total of sixteen panels in the considered direction (x = 16). Similarly, in the longitudinal direction 

(east/west) there are thirty-two panels total in the considered direction (x = 32). Thus the shear wall 

coefficient Cw is different in each orthogonal direction. 

40 Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure
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North/South: 

100 30 ! 19.3

!! = 16 .176 80,000 30 30 ! = 0

1 + 0.83 25

!!"#$! = 0.002 400!" = 0.800 !"#

0.0019

!!"##$ = 30!" = 0.136 !"#

0.176

Using this alternative approach, the diaphragm period alone is estimated at 0.800 seconds compared 

with the code’s current approximate period of 0.26 seconds for the building using ASCE 7-10 Equation 

12.8-7 or 0.136 seconds using Equation 12.8-9. 

East/West: 

100 30 ! 19.3

!! = 32 0 , ! . 80 30 30 = 352 000

1 + 0.83 25

!!"!"! = 0.002 200!" = 0.400 !"#

0.0019

!!"##$ = 30!" = 0.096 !"#

0.352

Using this alternative approach, the diaphragm period is estimated at 0.400 seconds compared with the 

code’s current approximation for the building of 0.26 seconds using ASCE 7-10 Equation 12.8-7 or 

0.096 seconds using Equation 12.8-9. Determination of periods used when implementing the alternate 

RWFD procedure is further discussed in Chapter 5 of this report. 

4.2 Response Modification Coefficient, R, Selection 

As previously stated, a primary objective is to identify seismic response and seismic performance factors 

considering response dominated by the flexible diaphragm instead of the vertical elements of the SFRS. 

The structural response modification coefficient, R, is an important parameter to estimate strength 

demands on systems that are designed using linear methods, such as the ELF procedure, but may 

respond in the nonlinear range when subject to strong ground motions. R coefficients currently in ASCE 

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7 are largely based on judgment. Historically, validation of seismic performance factors was simply 

based on observations following major earthquakes. 

While learning from earthquakes is invaluable when validating current design factors, a more systematic 

form of validation is needed when proposing new R coefficients and new design procedures. The 

methodology contained in FEMA P695 [FEMA, 2009] was developed specifically to provide a means to 

evaluate a SFRS proposed for adoption into building codes, but can be used to evaluate proposed design 

procedures as well. The primary objectives of a FEMA P695 study	
  are to obtain	
  an acceptably	
  low	
  

probability of collapse of the SFRS under maximum considered earthquake	
  (MCE)	
  ground motions

and to provide a uniform protection against	
  collapse across various structural	
  systems. An

appropriate P695	
  evaluation must develop a representative nonlinear model that	
  includes both

detailed design information of the system as well as comprehensive	
  test data on the post-­‐yield	
  

performance of system components and subassemblies. The procedure evaluates	
  the probability

of collapse during	
  strong	
  earthquake	
  shaking while accounting	
  for a variety of possible ground

motions, uncertainties, and a range of building configurations representing the design space. The

building example being illustrated in this report	
  is an example of just one of the archetypes

evaluated as part	
  of the RWFD study introduced in	
  Section 1.0.

An appropriate	
  response modification coefficient unique to the diaphragm,	
  Rdiaph, was determined

using	
  a trial-­‐and-­‐error	
  process using FEMA P695.	
  The first trial evaluated existing ASCE	
  7-­‐10

designs using intermediate precast (tilt-­‐up) concrete	
  shear walls (R = 4) with	
  both	
  wood	
  and	
  steel

deck diaphragms for their acceptability. As expected, the	
  results	
  showed	
  the	
  inelastic	
  behavior	
  

was clearly	
  in the	
  diaphragms instead of the in-­‐plane walls, confirming the need for a diaphragm-­‐

based approach.	
  Even though the diaphragm design capacity was intentionally stepped down to 

efficiently follow the shear demand reduction towards the diaphragm interior as is often done in 

practice, the analysis results indicate that the inelastic response of the diaphragm is concentrated 

adjacent to the supporting shear walls. 

Because the inelastic behavior was not well distributed across the diaphragm, the localized inelastic 

response near the shear wall supports was quickly overwhelmed by the limited ability of the connectors 

to dissipate large amounts of energy, and led to global building failure. This phenomenon was observed 

in both the steel and wood deck diaphragm analyses. The FEMA P695 analysis results for archetypes 

using R equal to 4 for the intermediate precast wall system did not meet the required margin against 

collapse required by the FEMA P695 methodology, thus indicating revised R-coefficients are necessary.

A detailed description of the implementation of FEMA P695 evaluations	
  for use	
  on this	
  project and

the numerical computer model are contained	
  in Appendix B.

A direct approach to resolve the deficient	
  margin against collapse	
  identified for RWFD buildings

designed using existing practice is to design the flexible diaphragms using	
  a response modification

coefficient, Rdiaph, that represents the ductility and overstrength of the diaphragm	
  instead of the

42 Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure
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walls.	
   Two approaches could be taken	
  to assigning	
  a value or values to Rdiaph, either (1) assign	
  a

single	
  value	
  and design the diaphragm assuming a linear distribution	
  of design shear along	
  the

diaphragm’s span length or (2) assign	
  a value to Rdiaph but amplify the design shear	
  in targeted	
  

zones	
  within the	
  diaphragm,	
  to encourage the spread of yielding	
  across more of the diaphragm’

length.	
  Based on	
  the P695	
  results	
  for the	
  current design procedure,	
  approach	
  (1) requires an Rdiaph

value	
  significantly	
  less	
  than	
  4 to obtain acceptable performance during a maximum considered

earthquake	
  (MCE)	
  event if design shear	
  is assumed to be distributed	
  linearly	
  along the diaphrag

span	
  length.	
  Approach	
  (2) in which	
  the	
  inelastic	
  diaphragm behavior is spread away from the

diaphragm boundaries by designing	
  for amplified shear in targeted zones has	
  the	
  potential of

requiring a less punitive Rdiaph over much of a diaphragm’s span	
  length.	
   Such an approach	
  is

discussed	
  in the	
  following	
  subsection.

4.2.1 Encouraging Distributed Inelastic Behavior 

Analytical studies have demonstrated that the performance of a diaphragm during strong earthquake 

shaking can be improved if yielding is spread over a large portion of a diaphragm’s span instead of 

focused at the boundary. The spread of diaphragm yielding is improved if the location of initial yielding 

is shifted away from the boundaries of the diaphragm. Surprisingly, this can be achieved either by 

intentionally weakening a portion the diaphragm’s interior areas below current building code levels, or 

by increasing the strength-to-demand ratio of the diaphragm near its boundaries. 

Distributing the inelastic behavior deeper into the diaphragm also requires that the diaphragm 

connectors that yield first exhibit sufficient positive post-yield stiffness behavior. In other words, once 

the critical connectors begin to yield, they need to resist increasing load rather than maintaining the 

initial yield load so connectors elsewhere in the diaphragm also reach their yield load. The connectors 

that yield must also have sufficient post-yield deformability so the diaphragm as a whole has adequate 

post-yield deformability to provide the required collapse resistance. The overall diaphragm 

deformability increases if connector yielding spreads over a large portion of the diaphragm. Also, the 

spread of yielding reduces the deformation demand on individual connectors. The hysteretic responses 

of the nail connectors in the wood structural panel diaphragms have sufficient positive post-yield 

stiffness to effectively move the location of first yield away from the diaphragm boundaries and spread 

the yielding over a large portion of the diaphragm’s span. In the case of steel deck diaphragms, 

insufficient data is available to make that determination. Thus, the recommendations for spreading 

diaphragm yielding are limited to wood structural panel diaphragms at this time. An alternative for steel 

deck diaphragms could involve simply using a smaller Rdiaph until sufficient data is obtained to justify an 

approach that distributes inelastic behavior. An appropriate Rdiaph for steel deck diaphragms where the 

spreading of inelastic behavior is beyond the scope of this report. 

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Using the numerical model developed for the FEMA P695 evaluation, several archetypes were designed 

with varying degrees of weakening below current code level design forces at interior diaphragm span 

locations. A series of incremental dynamic analyses were conducted and the results were promising. It 

was observed that indeed relative weakening of the diaphragm interior assists in protecting the perimeter 

boundary areas from excessive inelastic demand, and increases the overall margin against building 

collapse. Additional information on these studies is contained in Koliou [2014]. Similar results were 

obtained using a combination of weakening interior portions of the diaphragm below current code level 

forces and amplifying the design shear forces in the end regions of the diaphragm, which is the approach 

used for the alternate design procedure proposed in this report. 

In the development of the alternate design procedure, it was recognized that often in smaller buildings 

with low shear demands a minimum fastener size at maximum spacing is provided uniformly across the 

entire diaphragm, thus not permitting intentional weakening. Partially to address this situation, a shear 

amplification factor is applied to increase the design shear of the diaphragm’s boundary areas to 

improve the spread of diaphragm yielding away from diaphragm boundaries. In this approach, the 

diaphragm boundary areas are designed the same as the diaphragm interior but with an applied shear 

amplification factor. In diaphragms where a designer simply elects to apply the boundary’s shear 

amplification factor across the entire wood diaphragm, acceptable performance will still be achieved but 

the performance will be reduced as discussed in Appendix K. 

One potential concern with the spread of diaphragm yielding is its impact on the cost of repair. If 

diaphragm yielding occurs over a larger percentage of the roof area, a larger area of the diaphragm may 

require repair following an earthquake. A potential tradeoff between improved collapse resistance and 

cost of repairs may exist. For buildings in which higher potential repair costs are a concern, designing 

the diaphragm for higher forces or trying to force the yielding into the vertical wall elements may be 

desirable. 

4.2.2 Diaphragm Response Modification Coefficient and Shear Amplification 

As discussed above in Section 4.2, an assumed linear distribution of design shear along the diaphragm 

span requires Rdiaph to be less than 4, but as discussed in Section 4.2.1, Rdiaph could potentially be 

increased if design shear is increased in targeted areas near the diaphragm supports to spread yielding 

within the diaphragm. 

Based on this premise, a FEMA P695 study was conducted on a set of archetype buildings with 

weakened interior portions of a diaphragm; trial and error was used to evaluate different values of Rdiaph 

with different nonlinear shear distribution along the length of the diaphragm span. From this study the 

alternative procedure was developed for one-story RWFD buildings. The FEMA P695 evaluation 

included a set of buildings of various sizes, shapes and seismic exposures, designed by incorporating a 

new approximate building period (Equations 2, 4, 6), reducing the strength of the interior diaphragm 

portions with a response modification coefficient Rdiaph = 4.5 (instead of 4), and strengthening the 

44 Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure
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diaphragm boundary regions (a minimum width of 10% of the diaphragm span at each end) with 50% 

more capacity. With this alternate design procedure, the FEMA P695 evaluation showed a significant 

improvement in the collapse capacity and met all collapse margin targets required to show equivalency 

to the seismic performance intent of the current building code. 

4.3 Deflection Amplification Factor, Cd , Selection 

Deflections are used in design to check for deformation compatibility, second order effects, P-Δ

stability, property line setbacks, and separation at seismic joints. These are required to be checked at the 

design earthquake force level. Diaphragms in RWFD buildings are expected to go into the inelastic 

range during a design earthquake; however, the design forces used to compute diaphragm deflections are 

based on elastic behavior. Thus the computed elastic deformations must be amplified to get realistic 

values. Essentially, this amplification is reversing the process that the response modification coefficient, 

R, provided to the design level forces. 

The value of Cd computed in accordance FEMA P695 assuming 2% damping, is equal to 1.25 times the 

value of response modification coefficient, R. See Appendix Section G.3. However, the ratio of mean 

diaphragm deflection for design earthquake shaking to the diaphragm deflection due to design forces 

reduced by R computed for the archetypes as part of this study indicate that a deflection amplification 

factor, Cd, equal to the response modification coefficient, R, for the corresponding structural system is 

appropriate. The basis for Cd diaph is presented in Appendix G Section G.3. 

The diaphragm deflection for design earthquake shaking can be obtained by first computing the elastic 

deflection for design earthquake forces using the equations of the Special Design Provisions for Wind 

and Seismic with Commentary (SDPWS-2008) [AWC, 2009] and then multiplying this value by Cd. 

4.4 Overstrength Factor, Ωo, Selection 

For design of a limited number of critical elements, the building code dictates using special load 

combinations with overstrength to prevent these critical elements from being the weak link. The 

overstrength factor, Ωo, is used to increase the design forces to appropriate design levels for this 

purpose. When conducting a study under FEMA P695 to evaluate a proposed response modification 

coefficient, R, a suitable overstrength factor, Ωo, can be determined for the proposed structural system 

being considered. 

Because the diaphragm is expected to be where the inelastic behavior occurs, the use of a unique 

overstrength factor, Ωo, tied to the diaphragm is more appropriate for the design of diaphragm collectors 

and their connections than the current procedure which uses the shear wall system’s Ωo. For this study a 

diaphragm overstrength value of 2 was computed in accordance with FEMA P695. 

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4.5 Overview of the Alternate Seismic Design Procedure 

The alternate design procedure can be thought of as a two-stage approach to designing a RWFD 

building: first, the diaphragm is designed using its own response modification coefficient, period and 

detailing rules, and second, the vertical elements of the SFRS are designed using the existing design 

provisions of ASCE 7-10 with minor modifications. 

The alternate design procedure is only permitted to be used when all of the following conditions apply: 

•	 The building is single-story, 

•	 The perimeter walls are concrete or masonry, 

•	 The diaphragm is wood structural panel, nailed to wood framing or wood nailers, 

•	 The diaphragm is rectangular or can be divided into rectangular plan areas that are laterally 

supported on each edge, 

•	 The value of Tdiaph is greater than or equal to 3 times the value of period of the walls, Twalls, 

computed using ASCE 7-10 Eq. 12.8-9 as indicated in Step 8, and 

•	 The approximate period, Ta, computed using ASCE 7-10 Equation 12.8-9 for the shear walls is 

small enough to be in the constant acceleration portion of the design spectrum. 

The following provides an overview of the steps required to implement the alternate procedure: 

1.	 A response modification coefficient of the diaphragm, Rdiaph equal to 4.5 is assigned. 

2.	 The wood diaphragm period is determined using Equation (3):

!!"#$! = 0.002!!

where 

Lf = the span, in feet, of the horizontal flexible diaphragm being considered; the span is 

measured between vertical elements that provide lateral support to the diaphragm in the 

direction being considered. 

The value of Tdiaph shall be greater than or equal to 3 times the value of period of the walls, 

Twalls, computed using ASCE 7-10 Eq. 12.8-9 as indicated in Step 8. Although it is believed 

that the equation for Twalls will overestimate the actual period, this limitation is to remain 

consistent with the comparative range of building responses investigated in this study. 

3.	 Cs is determined in accordance with the equivalent lateral force procedure in Section 12.8.1 of 

ASCE 7-10 but using Rdiaph in place of R and Tdiaph in place of Ta computed in accordance 

ASCE 7-10 Eq. 12.8-7 or Eq. 12.8-9. 

4.	 Diaphragm design shears are computed using the following force acting on the diaphragm 

46 Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure
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!! = !!!!

where

!!= the force acting on the diaphragm per unit length.

!!= the tributary seismic weight applicable per unit length of diaphragm including the 

tributary weight of the walls acting out-of-plane. 

5.	 The diaphragm design shears are increased by a shear amplification factor of 1.5 for the end 

10% of the diaphragm span length at each end of the diaphragm span. 

6.	 Diaphragm chords are designed for the diaphragm flexure resulting from diaphragm loads 

computed using Fp in Step 4 without the amplification in Step 5. 

7.	 Collectors and their connections are designed for the forces computed from the design 

diaphragm shears collected and amplified by a diaphragm overstrength factor, Ωo diaph, equal to 

2. 

8.	 The vertical elements of the SFRS, i.e., shear walls, are designed for in-plane forces using the 

equivalent lateral force procedure of ASCE 7-10 Section 12.8 but with the force from the 

diaphragm as computed in Step 4 amplified by (Rdiaph/ρdiaph)/(Rwall/ρwall) but not less than 1.0. 

The response modification coefficient, Rwall, is assigned the value for the type of vertical 

system being engineered but not greater than Rdiaph. The approximate period, Ta, is computed 

using ASCE 7-10 Equation 12.8-9 for the shear walls. This period, for the type of building 

envisioned, should always be small enough to be in the constant acceleration portion of the 

design spectrum. Acceleration computed using Rwall and Ta is applied to the seismic mass of the 

in-plane walls. The detailing requirements and system limitations of ASCE 7-10 Table 12.2-1 

apply even though the Rwall may have been reduced to be less than or equal to Rdiaph. 

9.	 Deflections are computed for the diaphragm and the wall system. Elastic diaphragm deflection, 

δe diaph, is computed using the force level, Fp, in Step 4 and Equation 4.2-1 in SDPWS-2008 

Section 4.2.2. The elastic diaphragm deflection should be amplified by a deflection 

amplification factor for the diaphragm, Cd diaph, equal to 4.5 and a formula similar to ASCE 7-

10 Equation 12.8-15.

!!"#$! = !! !"#$!

!!

!! !"#$!

Deflection of the wall system should be computed for design level forces and amplified by Cd 

for the wall system. 

!!"##	 

!! !"##

!!

!! !"## =

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The computed deflection is used to check that the interconnection of structural wall elements 

and connections to supporting framing systems have sufficient ductility and rotational capacity 

in accordance with ASCE 7-10 Section 12.11.1. For SDC D to F, the computed deflection is 

also used to check that the permissible deflection of attached elements is not exceeded in 

accordance with ASCE 7-10 Section 12.12.2. If appropriate, the computed deflections are used 

to determine required seismic separations or property setbacks in accordance with ASCE 7-10 

Section 12.12.3. 

10.	 Second order/P-Δ effects for the building are checked in accordance with ASCE 7-10 

Section 12.8.7 but both diaphragm and wall deflections should be included. The diaphragm 

deflection component can be reduced to approximately two-thirds of the maximum diaphragm 

deflection because the diaphragm tributary seismic weight on average moves approximately 

two-thirds of the diaphragm deflection plus the deflection of the in-plane walls. 

11.	 Out-of-plane wall forces and out-of-plane top-of-wall anchorage forces and detailing 

requirements are designed in accordance with Sections 12.11.1 and 12.11.2 of ASCE 7-10 

except that ka is set equal to 2 for all diaphragm spans in Equation 12.11-1. Appendix J 

provides addition information regarding this. 

Information on the study that demonstrates the adequacy of this alternate seismic design procedure is 

provided in Appendices A and G to I. A more specific description of this design method in code-based 

language is also provided in Appendix A to this report. 

48 Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure
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Chapter 5	 Implementation of the Alternate Seismic 

Design Procedure 

Explanation of how to implement the alternate design procedure listed in Section 4.5 is provided in this 

chapter. Redesign of the example building introduced in Chapter 3 is used to demonstrate and explain 

the procedure. 

5.1 A Two-Stage ELF Procedure 

Conceptually, a RWFD building is simply a flexible diaphragm structure supported by a more rigid wall 

structure below. In regards to the seismic load path, the flexible diaphragm is in series with the rigid 

walls, and could conceivably be viewed in part as a vertical combination of SFRS under ASCE 7-10 

Section 12.2.3.1. If viewed as an upper flexible diaphragm supported by a lower rigid shear wall system, 

this is similar to today’s common podium buildings with a flexible SFRS at the upper floors supported 

on a rigid SFRS at the lower floors. 

The two-stage ELF procedure of ASCE 7-10 Section 12.2.3.2, first introduced into the 1988 Uniform 

Building Code [ICBO, 1988], is commonly used in practice today for podium structures. This 

philosophy is adapted for use in the alternate procedure for RWFD buildings. When an upper flexible 

portion is supported by a lower rigid portion, a two-stage procedure encourages the use of two different 

periods T and two different response modification coefficients R in series within the same building to 

determine the applied seismic design forces to each portion. Furthermore, two separate overstrength 

factors, Ωo, and deflection amplification factors, Cd, may be utilized when appropriate, one pair of Ωo 

and Cd values for the diaphragm and another for the walls. 

Currently, the two-stage analysis procedure within ASCE 7-10 Section 12.2.3.2 limits its applicability to 

situations where the period of the entire structure is not greater than 1.1 times the period of the upper 

portion considered as a separate structure. Additionally, applicability is also limited to situations where 

the lower portion is at least ten times stiffer than the upper portion. These limitations were placed to 

account for the uncertainty of the structure’s behavior when the differences in the stiffnesses or periods 

are small. However, these limitations are deemed to not be necessary to the alternate design 

methodology presented here, because this procedure was validated through FEMA P695 with a wide 

range of diaphragm and wall stiffnesses as well as diaphragm and building periods that often fell 

significantly below the stiffness ratio thresholds. Thus, some influence or interaction between the walls 

and diaphragm due to stiffnesses or periods that begin to approach each other is already reflected in the 

FEMA P695 validation. The alternate procedure should be valid as long as the approximate period of 

the diaphragm computed in accordance with Equation (2) is at least three times the approximate period 

of the walls computed using ASCE 7-10 Equation 12.8-9. 

Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure 49 
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5.2 First Stage – Diaphragm Design 

The first stage of the analysis involves design of the diaphragm as a separate structure using an ELF 

procedure in each direction. As previously discussed, special seismic response modification coefficients, 

overstrength factors and deflection amplification factors have been established for the flexible 

diaphragm comprised of wood structural panels. Additionally, a comparison of the periods for the 

diaphragm and the in-plane shear walls is necessary to verify that the alternative design procedure is 

valid. 

!!"#$! = 0.002!! Equation (2) 

!!"##$ = !.!!"# h! ASCE 7-10 Equation 12.8-9 !!

where 

Cw and hn are per ASCE 7-10 Section 12.8.2.1 

Seismic Performance Factors: 

Rdiaph = 4.5 provided an amplified shear boundary zone is incorporated into the diaphragm 

Ωo diaph = 2.0 for the design of collectors, etc. (See Section 4.4) 

Cd diaph = 4.5 for the calculation of diaphragm deflections (See Section 4.3) 

ρ = 1.0 (ASCE 7-10 Section 12.3.4.1) 

The design spectral accelerations will be the same as current practice. As previously determined: 

SDS design = 1.0 (short period)

SD1 design = 0.6 (1-second period)

SDC = D 

5.3 Diaphragm Design Coefficient Cs Using the ELF Procedure 

ASCE 7-10 Section 12.8.1 defines the seismic base shear as 

V = CsW ASCE 7-10 Eq. 12.8-1 

where 

50 Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure
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! !"

! = !

! ASCE 7-10 Eq. 12.8-2

!!

Because the flexible diaphragm is supported by the significantly stiffer rigid shear walls, the diaphragm 

will be viewed as a separate structure with its base at the roof-to-wall interface. Thus using Equation 

12.8-1 the diaphragm force Fp will be represented as 

Fp = Cswp 

Now with the ability to differentiate between the wall’s and diaphragm’s response modification 

coefficients, a unique CS is initially obtained for the diaphragm. Per Equation 12.8-2 

!

! = !" 1.0 ! = = 0.222 !!"#$! 4.5

! 1.0 !

With the greater flexibility of the diaphragm compared to the walls, it is now possible that the upper 

bound for Cs using Equation 12.8-3 may govern, indicating that the seismic response is off the plateau of 

the design spectrum. 

Before the upper bound for Cs can be computed, the approximate fundamental period of the diaphragm 

in each orthogonal axis direction must be considered. The north/south (transverse) loading direction will 

be considered first, followed by the east/west (longitudinal) loading direction. 

North/South Direction: 

As previously determined in Section 4.1:

!!"#$! = 0.800 !"#

!!"## = 0.136 !"#

For engineers using ASCE 41-13 to evaluate RWFD buildings, standard practice has been to use the 

building’s period Ta from ASCE 41-13 Eq. 7-19 to develop pseudo forces for the diaphragm. However, 

engineers using ASCE 7-10’s two-stage procedure typically design the upper flexible portion 

considering its own isolated period. There is some inconsistency between how the period is selected 

between these two approaches. 

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In this study, the numerical model analyzed 54 building archetypes whose diaphragms were designed 

using the building’s full period Ta = Tdiaph + Twalls, similar to the ASCE 41-13 approach; and the results 

were found to be acceptable under the FEMA P695 validation. However, situations where the walls may 

behave more like frames could cause the design forces to become unconservative due to the longer 

design period utilized. It is recommended and will be illustrated in this example to design the 

diaphragm for its own approximate period using Equations (2) and (3), instead of including the walls’ 

contribution. This will result in a smaller period causing the diaphragm design forces to potentially 

increase for very large buildings whose spectral design acceleration is off the constant acceleration 

plateau. 

At this point it is also necessary to compare the ratio of diaphragm period (0.800 sec) to wall period 

(0.136 sec). By definition, RWFD buildings require the vertical portions of the SFRS to be relatively 

stiffer than the horizontal diaphragm. This study investigated archetypes with ratios that got within 3 

when considering ASCE 7-10 Equation 12.8-9, and thus recommend that this alternative procedure be 

limited to those situations where diaphragm-to-wall period ratio exceeds 3. For the north/south direction, 

this ratio is equal to 5.9, thus acceptable. 

Returning back to the computation of Cs for the purposes of determining the diaphragm’s design force, a 

check of the upper limit for Cs is necessary where T ≤ TL . Using the building period Tdiaph = 0.800

seconds, the following is determined: 

! = !!! !.!

! !"# ! = !.! = 0.167 < 0.222 ASCE 7-10 Eq. 12.8-3 ! !.!"" !! !.!

The fundamental period is longer than the transition period, Ts, equal to 0.6 seconds so the fundamental 

period is off the design spectrum’s constant acceleration plateau and in the 1/T region of the spectrum. 

Thus, preliminarily Cs equals 0.167. Checking the minimum allowed value for Cs, ASCE 7-10 Equations 

12.8-5 and 12.8-6 are applicable. In this example, S1 is equal to 0.6g: therefore, Equation 12.8-6 is valid 

to check the minimum allowed Cs. 

!! !"# = 0.044!!"!! = 0.044 1.0 1.0 = 0.044 < 0.167 OK ASCE 7-10 Eq. 12.8-5 

Cs min = 0.01 < 0.167 OK ASCE 7-10 Eq. 12.8-5

! !.!!! !.!(!.!)

! !"# = ! = !.! = 0.067 < 0.167 OK ASCE 7-10 Eq. 12.8-6

!! !.!

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The calculated value of Cs = 0.167 is above all the minimum allowed values. 

Cs governs = 0.167 

Substituting into Equation 12.8-1, we obtain the diaphragm force equation for the north/south direction 

of the structure, which is used to determine the design forces acting on the diaphragm. 

Fp = VN/S = CsW 

Fp = 0.167wp 

East/West Direction: 

As previously determined in Section 4.1:

!!"#$! = 0.400 !"#

!!"## = 0.096 !"#

By definition, RWFD buildings require the vertical portions of the SFRS to be relatively stiffer than the 

horizontal diaphragm, and a limitation of this procedure is that the ratio of diaphragm period to wall 

period be at least equal to 3, when Twalls is evaluated using ASCE 7-10 Equation 12.8-9. For this 

example building, the diaphragm period (0.400 sec) to wall period (0.096 sec) ratio is equal to 4.2, thus 

acceptable. 

Checking the upper limit for C T s where ≤ TL 

! !!! !.!

! !"# = ! = !.! = 0.333 > 0.222 ASCE 7-10 Eq. 12.8-3 ! !.!"" !! !.!

The fundamental period is short enough to be on the design spectrum’s plateau, thus preliminarily Cs = 

0.222. Checking the minimum allowed value for Cs

, ASCE 7-10 Equations 12.8-5 and 12.8-6 are 

applicable. In this example, S1 is equal to 0.6g: therefore, Equation 12.8-6 is valid to check the minimum 

allowed Cs. 

!! !"# = 0.044!!"!! = 0.044 1.0 1.0 = 0.044 < 0.222 OK ASCE 7-10 Eq. 12.8-5 

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Cs min = 0.01 < 0.222 OK ASCE 7-10 Eq. 12.8-5

! = !.!!! = !.!(!.!)

! !"# ! !.! = 0.067 < 0.222 OK ASCE 7-10 Eq. 12.8-6

!! !.!

The calculated value of Cs = 0.222 is above all the minimum allowed values. 

Cs governs = 0.222 

Substituting into Equation 12.8-1, we obtain the diaphragm force equation for the north/south direction 

of the structure, which is used to determine the design forces in the diaphragm. 

Fp = VE/W = Cs

W 

Fp = 0.222wp 

Each of the uniformly distributed diaphragm design loads 0.167wp and 0.222wp in the north/south and 

east/west directions respectfully are different than the current practice value of 0.25wp. These 

differences are attributed to recognition of the longer period of the long spanning diaphragm in the 

north/south direction and better distribution of yielding along the diaphragm spans reflected in the 

response modification coefficient (R=4.5 instead of 4). However, this increase in R also requires an 

amplification of design shear in the end regions of the diaphragm that will be explained in Section 5.5. 

This amplification of the diaphragm design shears is effectively a local reduction of Rdiaph relative to a 

value of 4.5 in the diaphragm end regions. 

5.4 Diaphragm Forces Using the ELF Procedure 

Using our flat-beam analogy, north/south seismic forces are resisted by shear walls on grid lines A and 

J, and east/west seismic forces are resisted by shear walls on grid lines 1 and 5. A uniformly distributed 

load across this flat-beam is illustrated in Figure 5.1. 

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The uniform loads wNS and wEW applied laterally to the diaphragm are computed using the diaphragm 

lengths and unit weights and the tributary wall heights and unit weights: 

Roof dead load = 12 psf 

Wall dead load = 116 psf (91⁄4” thick at 150 pcf) 

Roof height = 30’-0” 

Top of wall = 33’-0” (above floor) 

33′ 1

!!" = 0.167 12!"# 200′ + 2 0.167 116!"# 33′ = 1104!"# 2 30′

33′ 1

!!" = 0.222 12!!" 400′ + 2 0.222 116!"# 33′ = 2000!"# 2 30′

The maximum design shears are now computed using simple statics on the uniformly loaded flat beam 

model. Because of the building’s symmetry, VNS at grid lines A and J will be equal. See Figure 5.2. 

Figure 5.1: Diaphragm Loading Model (Alternate Procedure) 

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North-south diaphragm shear: 

! 400 ft

!!" = !!" = 1104 = 220,800 !"# 2 2

North-south unit shear: 

! 800

!!" = !" 220, = = 1104 !"# !"#$!%! 200 ft 200 ft

East-west diaphragm shear:

! 200 ft

!!" = !!" = 2000 = 200,000 !"# 2 2

East-west unit shear: 

! 200 = !" ,000

!!" = = 500 !"#, !"#$!%! 400 ft 400 ft

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Figure 5.2: Diaphragm Shear Distribution 

5.5 North/South Diaphragm Shear Design 

The diaphragm design for the shears follows a similar approach as that outlined in Section 3.6, which 

illustrates current practice. In Section 5.4 above, the maximum diaphragm shears were determined for 

each orthogonal direction; but as mentioned earlier, performance was found to improve in the computer 

model’s FEMA P695 analyses when inelastic behavior was better distributed, and this was accomplished 

in part by providing overstrength in the amplified shear boundary zones of the diaphragm. More 

specifically, the ten-percent of the diaphragm’s length 0.10L at each end is designed for 1.5 times more 

diaphragm shear than otherwise would have been computed. Figure 5.3 illustrates the design shear 

distribution across the diaphragm in each direction. 

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As observed in Figure 5.3, the worst unit shear demand is in the north/south direction with vNS = 

1104x1.5 = 1656 plf (unfactored). The nominal diaphragm shear capacities are provided in SDPWS2008 Tables 4.2A and 4.2B for a wide range of blocked diaphragm conditions. As done in Section 3.6 

for current design, an ASD approach using the blocked panelized roof system will be followed.

!!" (!"#) = 0.7!!" = 0.7 1656 = 1159 plf 

!!"(!"#) = 0.7!!" = 0.7 750 = 525 plf 

Using these unit shear values, the designer enters either SDPWS-2008 Table 4.2A or 4.2B to select a 

diaphragm assembly with an appropriate shear capacity for 15/32-inch Structural I sheathing with 10d 

nails. 

Figure 5.3 – Shear Diagrams for the Diaphragm Design with the 1.5x Factor. 

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In the north/south direction, the ASD unit shear demand is greater than the maximum ASD capacities 

obtained from SDPWS-2008 Table 4.2A, thus reference to the high-load diaphragm shears in Table 

4.2B will be necessary. The on-center (o.c.) nail spacing shown here requires thicker framing to prevent 

splitting. The capacity has been reduced from the table nominal strength value to an allowable stress 

design value by dividing in half per SDPWS-2008 Section 4.2.3. 

15/32”-thick Structural I sheathing 

10d nails in 2 lines at 

 2 1⁄2” (o.c.) boundaries and continuous north/south edges 

 3” o.c. other edges 

10d nails in 1 line at 

 12” o.c. intermediate (field) 

4x framing width at adjoining edges CAPACITY = 2580/2 = 1290 plf (ASD) 

!!" (!"#) = 0.7!!" = 0.7 1656 = 1159 plf < 1290 plf OK 

The construction of this diaphragm system is illustrated in Figure 3.4: 

The nailing and subpurlin widths may be reduced as the corresponding unit shears also reduce. For this 

example, Table 5.1 identifies various diaphragm nailing configurations from the SDPWS-2008 that will 

be utilized at different portions of this building. The ASD shear values are simply the nominal strengths 

listed in SDPWS-2008 Tables 4.2A and 4.2B divided by a factor of two per Section 4.2.3. Note that the 

framing and nailing listed for Zones 1 to 6 in Table 5.1 are the same as those listed for Zones 1 to 6 in 

Table 3.1 for the current practice design example in Chapter 3. 

 

 

 

 

Table 5.1 – Diaphragm Nailing Schedule (Cases 2 and 4) 

15/32” Structural I OSB Sheathing (DOC PS 2 [NIST, 2004]) 

with 10d nails (0.148” dia x 2” long minimum)

Zone Framing Width 

at Adjoining 

Edges 

Lines of 

Nails 

Nailing per line at 

Boundary & 

Continuous Edges 

Nailing per line 

at Other Edges 

ASD Allowable 

Shear 

(plf) 

1 2x 1 6” o.c. 6” o.c. 320 

2 2x 1 4” o.c. 6” o.c. 425 

3 2x 1 21⁄2” o.c. 4” o.c. 640 

4 3x 1 2” o.c. 3” o.c. 820 

5 4x 2 21⁄2” o.c. 4” o.c. 1005 

6 4x 2 21⁄2” o.c. 3” o.c. 1290 

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At the diaphragm boundaries (grid lines A and J), Nailing Zone 6 was determined to be acceptable. 

At some location inward as the diaphragm shears diminish, Nailing Zone 5 will become 

acceptable. The transition from Nailing Zone 6 to Nailing Zone 5 may be located using statics as 

follows: 

Shear Demand (ASD) = Shear Capacity (ASD) 

0.7[VNS – (wNS)x](1.5) = (1005 plf)B Equation (7) 

0.7[220,800 lbs – (1104 plf)x](1.5) = 1005 plf (200 ft) 

where 

x = the demarcation distance from the diaphragm boundary. 

Solving for x obtains 

x = 26.6 ft 

Because a panelized roof system typically consists of 8-foot wide wood structural panels, the joist 

spacing module is also 8 feet, and the transition should be increased to the next 8-foot increment. 

In this case, it is increased to x =32 feet; however, this leaves only 8 feet more until the shear 

demand dramatically reduces at 0.1L = 40-ft from the boundary as seen in Figure 5.3. Therefore it 

is elected to provide Nailing Zone 6 across the entire amplified shear boundary zone of the 

diaphragm. 

It is important to observe that the potential transition location from nailing Zone 6 to Zone 5 

selected occurs within the 0.1L or 40-ft wide boundary strip, thus Equation 7 is still valid with the 

1.5 factor included. For the first nailing zone transition at or past 0.1L from the boundary shear 

element, the 1.5 shear amplification factor in Equation (7) may be omitted. 

Latitude in the locating potential nailing zone transitions further away from the diaphragm 

boundary is possible within the end regions where shear is amplified, at the transition between 

amplified and non-amplified shear, and within the interior portions of the diaphragm where shear 

is not amplified. The basis for this latitude is the results of analyses of archetypes in which the 

nailing pattern at the boundary is used for the entire diaphragm span. Although these archetypes 

did not perform as well as the archetypes with multiple nailing zones, they met the acceptable 

performance criteria. 

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After 0.1L, the shear demand drops dramatically and some nailing zone assemblies may be skipped 

entirely. The transition locations between Zones 5 and 4, Zones 4 and 3, Zones 3 and 2, and Zones 

2 and 1 for the north-south loading direction are found using the same process resulting in the 

following Table; however, it is important to recognize that the 1.5 shear amplification factor is 

only on the outer 0.1L portions. 

Because the shear diagram (Figure 5.3) has a large stepped reduction in the design shear at 0.1L, 

nailing zones 5 and 4 are not utilized. This significant transition in nailing from zone 3 to 6 may 

catch framers by surprise; or worse it could be confusing and lead to field errors. As such, 

engineers should consider this construction aspect in their structural observation program. 

Table 5.2 – Diaphragm Nailing Zone Shear Checks 

Nailing Zone Distance from 

Boundary 

Maximum 

Unit Shear 

ASD 

Unit Shear 

Allowable Shear 

Capacity 

6 0 feet vmax = 1656 plf vASD = 1159 plf 1290 plf 

5 --- --- --- 1005 plf 

4 --- --- --- 820 plf 

3 40 feet vmax = 883 plf vASD = 618 plf 640 plf 

2 96 feet vmax = 574 plf vASD = 401 plf 425 plf 

1 120 feet vmax = 442 plf vASD = 309 plf 320 plf 

The resulting nailing zone layout for the north/south loading is shown in Figure 5.4. 

Figure 5.4: North/South Nailing Zone Layout 

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When designing wood diaphragms, the diaphragm aspect ratio must also be checked against the 

limitations in the SDPWS-2008 Table 4.2.4. For blocked diaphragms such as those that occur in 

panelized construction, the maximum aspect ratio is L/W = 4:1. In this example, the north/south loading 

direction is the critical L/W ratio. 

L/W = 400/200 = 2.0 < 4 Okay 

5.6 North/South Diaphragm Shear Transfer to Walls 

As the diaphragm shears reach the diaphragm boundary, this seismic force must be transferred to the 

vertical SFRS, or as in this example the concrete shear walls. Traditionally, this transfer has been 

through a wood ledger at the inside face of wall. Occasionally, no parapets are utilized in the 

architectural design and a wood nailer is provided at the top of wall in place of a ledger. With the 

alternate design procedure, the diaphragm boundary nailing to the wood ledger/nailer and the 

ledger/nailer’s bolting to the shear walls are designed using the diaphragm shear force with the 1.5 shear 

amplification factor to encourage the spreading of yielding within the diaphragm. 

This example utilizes steel ledgers as discussed in Section 3.7. Steel ledgers have become very popular 

in large RWFD buildings, utilizing steel angles or channels bolted to the inside face of the shear walls. 

When these steel ledgers are combined with wood nailers on the top flange at the diaphragm interface, 

the provisions mentioned above for wood ledgers/nailers still apply. However, it has also become 

popular to omit the wood nailer and directly fasten the wood structural panel to the steel ledger with 

pneumatically driven steel pins. These proprietary pins typically have an ICC ES approval and can 

usually be driven through 3/8” thick steel, however there is no cyclic test data available to evaluate the 

post-yield behavior. Therefore, the pin design forces are designed with an overstrength factor, Ωo, 

associated with the diaphragm. 

Ledger bolting capacities into the concrete or masonry shear walls shall comply with ACI 318-11 or 

TMS 402-13 provisions respectfully. 

5.7 North/South Diaphragm Chord Design 

Recall that a flexible diaphragm may be thought of as a flat horizontal beam where the shear resistance 

is obtained by the wood structural panel sheathing across the roof surface and the flexural resistance is 

obtained from perimeter chords. As illustrated in the current-practice design of Section 3.7, these chords 

are steel ledger angles at the roof line. Chord forces are determined using simple statics as shown in 

Figure 3.6, and the design force is a uniformly distributed load without the 1.5 shear amplification 

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design factor. Maximum chord forces will occur at the center of the diaphragm’s span where the 

maximum moment occurs. 

The maximum tensile chord force for our building example is determined as follows: 

! ! !"# = !"!! 1104 400 !

! = = = 110,400 !"# ! 8! 8 200

The chord is designed here using strength design with ASTM A36 Steel (Fy = 36 ksi). Consulting IBC 

Section 1605.2, the applicable LRFD load factor for seismic forces is 1.0. The area of steel required is:

! 110.4

!! = = = 3.41 !"!

∅!! 0.9 36

Using an L5x5x3/8 rolled steel angle satisfies this chord demand. 

L5x5x3/8 Steel Area A 2

S = 3.65 in > 3.41 in2 

5.8 East/West Diaphragm Shear Design 

Similar to the north/south loaded direction, the orthogonal east/west direction will also require 

consideration using the same sequential process. In Section 5.5, the maximum diaphragm shear in the 

east/west direction was determined to be vEW = 750 plf (unfactored) including the 1.5 shear 

amplification factor; and converting to allowable stress design (ASD), the maximum diaphragm shear is 

as follows: 

!!"(!"#) = 0.7!!" = 0.7 750 = 525 plf 

As before, SDPWS-2008 Table 4.2A is used to select diaphragm nailing with an appropriate shear 

capacity. In the north/south loaded direction, Case 4 is the loading configuration, but for the east/west 

direction this becomes a Case 2 configuration. The applicable Case determines the nail spacing along the 

continuous adjoining panel edges in the direction parallel to load. Comparing the diaphragm’s shear 

demand with the capacities of Section 5.5’s Table 5.1, Nailing Zone 3 is selected:

!!"(!"#) = 525 !"# < 640 !"# (!"#$#%& !"#$ 3)

At some distance away from the diaphragm boundary (walls at grid lines 1 and 5), Nailing Zone 2 in 

Table 5.1 will be acceptable due to the diminishing unit diaphragm shears. With the dramatic drop in 

design shear at 0.1L = 20-ft, Nailing Zone 2 can be skipped altogether. Using the same approach as done 

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in the north/south direction, the locations of the nailing zone transition from Zone 3 to 2, and Zone 2 to 1 

are found and shown in Table 5.3. 

Table 5.3 – Diaphragm Nailing Zone Shear Checks 

Nailing Zone Distance from 

Boundary 

Maximum 

Unit Shear 

ASD 

Unit Shear 

Allowable Shear 

Capacity 

3 0 feet vmax = 750 plf vASD = 525 plf 640 plf 

2 --- --- --- 425 plf 

1 20 feet vmax = 400 plf vASD = 280 plf 320 plf 

Combining the nailing requirements for the north/south loading with the east/west loading results in 

Figure 5.5. 

Figure 5.5: North/South and East/West Nailing Zones Combined Layout 

5.9 East/West Diaphragm Shear Transfer to Walls 

Similar to the north/south diaphragm force design, the seismic diaphragm shears must be transferred to 

the vertical concrete shear walls. As discussed in Section 5.6, the shear transfer is designed with the 1.5 

shear amplification factor, with an additional diaphragm overstrength factor Ωo at locations where 

proprietary pin fasteners are used at steel ledgers. 

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Unlike the north/south force direction, the diaphragm boundaries resisting east/west seismic forces along 

grid lines 1 and 5 do not have uniform boundary nailing. While most of the length contains nailing zone 

3 requirements, the first and last 40-ft of this wall line contain nailing zone 6 requirements, whose 

stiffness may attract more load. In this example, there is a belief that the shear transfer to the steel ledger 

is non-uniform; however, the steel ledger was designed as the diaphragm chord in Section 5.7 and 

contains sufficient capacity to drag and redistribute the shear load appropriately to the shear wall 

elements. This is especially true when the diaphragm chord design is based on the maximum force at 

midspan, yet the chord design remains consistent along the entire shear wall line. 

5.10 East/West Diaphragm Chord Design 

With the diaphragm chords placed at the extreme sides of the diaphragm, the maximum chord forces in 

the east/west loaded direction are computed in a similar fashion as the north/south direction: 

! ! ! 2000 !"# 200 !

! = = !"! = = 25,000 !"# ! 8! 8 400

The required area of the steel chord is:

! 25.0

! !

! = = = 0.77 !" ∅!! 0.9 36

Using an L4x4x1/4 rolled steel angle as a practical minimum size satisfies this chord demand. 

L4x4x1/4 Steel Area AS = 1.93 in2

 > 0.77 in2 

5.11 Second Stage – Shear Wall Design 

The second stage of the analysis involves the design of the heavy in-plane shear walls, whose period 

does not involve the diaphragm component, and is thus comparatively small. However, it does include 

the diaphragm mass as well as a portion of the perpendicular out-of-plane walls and in-plane walls. 

Additionally, the response modification coefficient R and redundancy factor ρ for the design of the inplane walls will be as currently specified within ASCE 7-10 for that specific shear wall system. 

Determining the lateral design forces for the in-plane shear walls involves a conversion of the 

diaphragm design forces based on Rdiaph and ρdiaph (ρdiaph equal to 1.0) into the shear wall design forces 

based on Rwall and ρwall, where the determination of ρ remains unchanged from ASCE 7-10 Section 

12.3.4. This conversion design philosophy is also found in ASCE’s two-stage analysis procedure of 

Section 12.2.3.2. 

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It should be noted that the current design philosophy embedded within the code is that when two 

different SFRS’s are in a vertical combination (Section 12.2.3.1), the lower system’s response 

modification coefficient R is not to rise above that of the upper system’s. In other words, the lower 

SFRS’s design force shall not be reduced more than the upper system’s design force, due to system 

ductility and overstrength. This philosophy is additionally included in ASCE’s two-stage analysis 

procedure in Section 12.2.3.2 which also includes consideration of different redundancy factors that may 

occur in the upper and lower systems. Thus the diaphragm design force conversion to the shear wall 

design force is always an amplification, and this design philosophy will be maintained in this report. In 

summary, Rwall /ρwall used in the shear wall design shall always be less than or equal to Rdiaph/ρdiaph. 

Note that the 1.5 shear amplification factor applied to the design of the diaphragm end regions is not 

included in the conversion to wall forces. 

The following sections illustrate this design procedure in each orthogonal direction on the example 

building: 

5.12 Shear Wall Force Using the ELF Procedure 

Because the building is being evaluated as two different seismically behaving portions, the force to the 

in-plane shear walls will have two significant components. The flexible diaphragm with its tributary 

mass will generate a lateral force near the top of the wall, Fv1. Additionally, the rigid concrete in-plane 

walls have significant self-weight that will also generate lateral forces near their center of mass, Fv2. 

First, diaphragm forces imparted into the shear walls will be converted to be consistent with the 

expected seismic performance of an intermediate precast shear wall system. The diaphragm forces used 

for the design of the shear walls below will not include the 1.5 amplification factor used to design the 

diaphragm end regions. 

As determined previously in Section 5.4, the diaphragm reactions to the shear walls based on Rdiaph = 4.5 

and ρdiaph = 1.0 are as follows: 

North/South Diaphragm Reactions 

Fp = VNS = 220,800 lbs 

East/West Diaphragm Reactions 

Fp = VEW = 200,000 lbs 

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These diaphragm reaction forces need to be amplified to an appropriate shear wall design force. 

North/South 

!!"#$!

! ! = ! × !"#$!

!! ! !!"##

!!"##

where 

!!"#$! 4.5 !!"#$! 1.0 = = 1.125 > 1.0 ... .!" !!"## 4

!!"## 1.0

!!! = 220,800×1.125

!!! = 248,400 !"#

East/West 

!!"#$!

! ! !!× !"#$!

!! = !!"##

!!"##

where 

!!"#$! 4.5 !!"#$! 1.0 = = 1.125 > 1.0 ... .!" !!"## 4

!!"## 1.0

!!! = 200,000×1.125

!!! = 225,000 !"#

Second, the lateral seismic force generated from the walls’ self-weight must be included for design. The 

walls’ self-weight will have a seismic response unique to its period of vibration, therefore the ELF 

procedure’s base shear equation will be revisited. 

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ASCE 7-10 Section 12.8.1 defines the seismic base shear as 

V = CsW ASCE 7-10 Eq. 12.8-1 

where 

! !!"

! = ! ASCE 7-10 Eq. 12.8-2

!!

Now working with the intermediate precast concrete shear walls (R = 4) instead of the diaphragm (Rdiaph 

= 4.5), a unique CS is obtained for the shear wall design. Per Equation 12.8-2 

! .0

!! = !" 1 = = 0.25 ! 4

!! 1.0

An upper bound for Cs must now be computed using the approximate period of the rigid shear walls 

using Equation 12.8-3. As previously determined, the approximate Twalls is different in each orthogonal 

direction when using Equation 12.8-9. The north/south (transverse) loading direction will be considered 

first, followed by the east/west (longitudinal) loading direction. 

North/South Direction:

!! = !!"##$ = 0.136 !"#

Checking the upper limit for Cs where T ≤ TL 

!! = !!!

!"# = !.!

! ! = 1.10 > 0.25 ASCE 7-10 Eq. 12.8-3 ! !.!"# !! !.!

As expected for rigid shear walls, the fundamental period is short enough to be on the design spectrum’s 

constant acceleration plateau, thus preliminarily Cs equals 0.25. Checking the minimum allowed value 

for Cs

, ASCE 7-10 Equations 12.8-5 and 12.8-6 are applicable. In this example, S1 is equal to 0.6g: 

therefore, Equation 12.8-6 is valid to check the minimum allowed Cs. 

!! !"# = 0.044!!"!! = 0.044 1.0 1.0 = 0.044 < 0.25 OK ASCE 7-10 Eq. 12.8-5 

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! = !.!!! !

# = .!(!.!)! !" ! ! = 0.075 < 0.25 OK ASCE 7-10 Eq. 12.8-6

!! !.!

The calculated value of Cs = 0.25 is above all the minimum allowed values. 

Cs governs = 0.25 

Substituting into Equation 12.8-1, we obtain the lateral force Fv2 equation for the shear wall’s selfweight, Wp-wall, for the north/south direction of the structure. 

Fv2 = CsW = 0.25Wp-wall 

The wall self-weight Wp-wall is computed as

!!!!"## = 116!"#×200!"×33!" = 765,600 !"#

Therefore 

Fv2 = 0.25Wp-wall = 0.25(765,600) = 191,400 lbs 

 

 

Therefore, the total shear wall design force Fv for the north/south direction is 

Fv = Fv1 + Fv2 = 248,400 + 191,400 

Fv = 439,800 lbs or 440 kips 

East/West Direction 

Because the east/west load direction has the same Rwall, ρwall, and because Ta is smaller than in the 

north/south direction, the seismic response coefficient, Cs, is still on the constant acceleration plateau, 

Fv2 = 0.25Wp-wall. 

Fv = Fv1 + Fv2 = 225,000 + 0.25Wp-wall 

The wall self-weight Wp-wall is computed as

!!!!"## = 116!"#×400!"×33!" = 1,531,200 !"#

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Therefore 

Fv2 = 0.25Wp-wall = 0.25(1,531,200) = 382,800 lbs 

Therefore, the total shear wall design force Fv for the east/west direction is 

Fv = Fv1 + Fv2 = 225,000 + 382,800 

Fv = 607,800 lbs or 608 kips 

Figures 5.6 and 5.7 illustrate the forces acting on the shear walls providing lateral resistance in the 

north/south and east/west directions respectfully. The design forces at the base of the shear walls are 440 

kips north/south and 608 kips east/west. These forces include the entire weight of the walls and are 

appropriate for the design of shear forces that transfer to the slab on ground or foundation. 

Figure 5.6: North/South Lateral Design Forces acting on the Shear Walls (Lines A & J) 

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Figure 5.7: East/West Lateral Design Forces acting on the Shear Walls (Lines 1 & 5) 

5.13 Limitations and Adaptations of the Alternate Design Procedure 

The alternate design methodology was presented for a very basic single story, rectangular building with 

solid walls and no interior vertical SFRS elements. Often the design of much larger buildings is 

necessary, and these situations often require interior shear walls or braced frames to keep the diaphragm 

shears manageable. For these one-story buildings with multiple-span diaphragm, each diaphragm span 

can be evaluated separately, and appropriately combined and adjusted as the design load is brought to 

the shear walls. 

Situations involving two or more stories, non-rectangular plans, diaphragm materials outside the typical 

nailed wood structural panel, and vertical SFRS other than concrete or masonry have not been properly 

evaluated to determine whether the alternate design procedure is applicable. Caution is needed before 

this design procedure is applied to situations that fall outside of the archetype inventory created for this 

project. Some areas of further study are listed in Section 8 of this report. 

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Chapter 6 Diaphragm Deflection Check 

Seismic ground motion typically causes more lateral deformation in the diaphragm than in the walls of 

RWFD buildings. The magnitude of the diaphragm deflections can be large enough to impact the 

building’s structural integrity, compromise the attached non-structural elements, or cause the building to 

pound against adjacent structures. Large diaphragm deflections may also result in excessive secondorder loading P-delta effects, causing instability that leads to collapse. 

ASCE 7-10 Section 12.12.2 limits diaphragm deflections to the amount that will permit the attached 

elements to maintain their structural integrity and to continue supporting their prescribed loads. The 

intent is to prevent substantial damage to structural elements and their connections, the failure of which 

can lead to local structural collapse. This requirement is also intended to prevent excessive PΔ effects 

that could lead to a sidesway collapse. For non-structural elements, the intent is to prevent failure of 

connections or to compromise the self-integrity that could result in a localized falling hazard. In order to 

evaluate these aspects of structural design, the engineer needs to compute the approximate building 

deformation as a combination of the deflection of the diaphragm and vertical elements of the SFRS. 

6.1 Deflection of North/South Diaphragm 

For the building example, the diaphragm deflection in the north/south direction will be greater than that 

in the east/west direction, and thus only the north/south direction will be checked. Procedures for 

computing horizontal diaphragm deflections under lateral loading are found in SDPWS-2008 Section 

4.2.2. Equation 4.2-1 provides a simplified method of computing deflections of wood structural panel 

diaphragms by considering the contribution of flexural bending, shear deformation, nail slip and chord 

slip. 

!!!!

! !.!"!" !∆!

!"# = + + SDPWS Eq. 4.2-1 !!"# !"""!! !!

where 

δdia = maximum mid-span diaphragm deflection determined by elastic analysis, in 

v = Maximum diaphragm shear, ft (assuming a uniformly loaded rectangular diaphragm) 

L = horizontal span of diaphragm, ft 

W = diaphragm span depth, ft 

E = chord’s modulus of elasticity, psi 

A = cross sectional area of chord, in2 

Ga = apparent diaphragm shear stiffness, kips/in 

Δc = chord slip at each connection, in 

x = distance from chord splice to nearest support, ft 

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For our diaphragm example, the following parameters are determined below: 

v = 1104 plf (Section 5.4) 

L = 400 ft 

W = 200 ft 

E = 29,000,000 psi 

A = L5x5x5x3/8 = 3.65 in2 (Section 5.6) 

Ga = 24 kips/in Zone 1 (SDPWS-2008 Table 4.2A) 

= 15 kips/in Zone 2 (SDPWS-2008 Table 4.2A) 

= 20 kips/in Zone 3 (SDPWS-2008 Table 4.2A) 

= 51 kips/in Zone 6 (SDPWS-2008 Table 4.2B) 

Δc = 0 (Welded chord connections assumed, and have no slip) 

The contribution from flexural deformation !!!!

 is derived from a horizontal beam with a uniformly !!"#

applied distributed load. The term EA will represent in this example the steel chord stiffness; however, 

the concrete walls themselves will also provide significant flexural stiffness to the diaphragm. 

Therefore, this equation generally overestimates the flexural contribution to diaphragm displacement. 

5!!! 5 1104!"# 400!" !

!!"# !"#$%&# = = = 2.09 !" 8!"# 8 29,000,000!"# 3.65!!! 200!"

The shear deformation and nail slip contribution !.!"!" is derived from a horizontal beam with a 

!"""!!

uniformly applied distributed load, uniform shear stiffness and uniform diaphragm nailing. In general, 

the shear deformation between two points, Li apart, under constant shear, v, is simply vLi/Ga. In a simply 

supported beam with a uniformly distributed load, the shear is not constant but decreases linearly and 

thus the average shear, vave, between the two points is applicable, vaveLi/Ga. Because the average shear is 

half the maximum shear 

!!"# = 0.5!

and the distance to the maximum deformation at midspan, Li, is half the total span L 

!! = 0.5!

With the apparent shear stiffness Ga in kips/inch, the shear deformation contribution becomes

!

! !"#! = ! 0.5! 0.5! 0.25!"

!"# !!!"# = = 1000!! 1000!! 1000!!

and this matches the shear deformation term in SDPWS-2008 Eq. 4.2-1. 

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For efficiency reasons, large diaphragms seldom have uniform diaphragm nailing across the building 

and thus the shear deformation term needs to be modified. For a diaphragm with various strips of 

different nailing zones, there are several approaches to this modification. As previously discussed, the 

shear deformation between two points at distance Li apart under an average shear of vave is 

!

"# # = !"#!

! !

! !!!" !!

With multiple nailing zone strips of width Li, and apparent shear stiffness Gai in kips/inch, and average 

shears vi ave, the total shear deformation at midspan can be computed as the summation of each strip’s 

contribution between the edge and the midspan of the diaphragm: 

! !"#!

! ! !

!"# !!!"# = 1000!!"

where 

vi ave = the average diaphragm shear within each shear stiffness (nailing) zone 

Li = the length of each shear stiffness zone measured perpendicular to loading 

Gai = the apparent shear stiffness of each shear stiffness zone being considered 

This approach assumes the nailing zones are continuous strips oriented from north to south as illustrated 

in Figure 5.4; however, the east/west diaphragm design caused Nailing Zone 3 to wrap around Nailing 

Zone 1 as illustrated in Figure 5.5. To simplify the analysis, the additional nailing from Zone 3 (north 

and south of Zone 1) will be ignored which will result in an overestimate of diaphragm deformation 

(conservative). Table 6.1 provides an organized approach to the computation working from grid A to the 

midspan. This format allows each different nailing zone strip to be evaluated separately. 

Table 6.1 – Shear Deformation and Nail Slip Computation Table 

Zone vleft vright vi ave Li Ga 

!! !"#!!

1000!!"

6 1104 883 994 40 51 0.78 in 

3 883 574 729 56 20 2.04 in 

2 574 442 508 24 15 0.81 in 

1 442 0 221 80 24 0.74 in 

∑ = 4.37 in 

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!! !"#!

! !

!"# !!!"# = = 4.37 !" 1000!!"

The chord slip contribution to diaphragm deformation !∆! is assumed to be zero because of the use of

!!

welded chord splices (Δc = 0).

!∆

! = !

!"# !!!"# !"#$ = 0 !" 2!

Considering all the diaphragm deflection contributions we obtain 

!!"# = !!"# !"#$%&# + !!"# !!!"# + !!"# !!!"# !"#$ = 2.09 + 4.37+ 0 = 6.48 in 

Because the applicable load combination involves 1.0E, this unfactored diaphragm deflection is also the 

deflection at strength-based design loads. But recall that the seismic coefficient Cs in Section 5.3 

involves dividing the maximum expected building response by the diaphragm’s response modification 

coefficient Rdiaph. To properly estimate the diaphragm’s maximum expected deflection, the earlier 

effects of dividing by R must be reversed, and this is accomplished with the use of the deflection 

amplification factor Cd. ASCE 7-10 Equation 12.12-1 (or 12.8-15) may be used to compute the 

maximum expected diaphragm deflection δmax. 

!

! = !!!"#

! !!

Cd = 4.5 (Section 4.5) 

δmax = 6.48 in (an elastic response under strength-level forces) 

Ie = 1.0 (importance factor) 

! ! 4.5 6.48

!!!!"#$! = ! !"# = = 29.2 !" !! 1

The computed elastic deflection (δmax) of the diaphragm allows one to estimate the period of the 

diaphragm using Wilson’s shear beam formula (Equation 1) as a guide. In this instance, the result can be 

approximated as Tdiaph = (0.066δmax) 0.5 where δmax is based on 1.0g of acceleration, and results in a 

period significantly larger than the 0.800 seconds. At this time, this alternative design procedure is based 

upon using Tdiaph = 0.002L for wood structural panel diaphragms, and a larger period computed by other 

methods is not permitted for design. 

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6.2 Deflection of North/South Walls 

It is anticipated that the diaphragm deflection will be the majority of the overall structural deformation; 

however, shear wall deflection should be added to the diaphragm deflection to obtain the total 

deformation used to evaluate its impact. The deflection of a cantilever shear wall has two components: a 

flexural component and a shear component from the following equation. 

!!"## = !!"## !"#$%&# + !!"## !!!"#

!h! 1.2!h

!!"## = + 3!" !"

The adjusted load onto the shear wall was computed in Section 5.10 as 440 kips, but a portion of this 

was from the diaphragm acting at the roof (Fv1 = 248.4 kips), and a portion was from the wall’s selfweight effectively acting at the mid-height (Fv2 = 191.4 kips). One approach to approximate the 

combined effect of these two forces is to place half the wall force at the roof height with the diaphragm 

force. 

191.4

! = 248.4 + = 344 !"#$ 2

h = 30 !"

The material properties and section properties are computed for the eight 25-ft long concrete shear walls 

(91⁄4” thick, f’c = 4000 psi) 

! = 57 ! ′ = 57 4000 = 3.6×10! ! !"#

! 3.6×10!

! = = = 1.50×10! !"# 2 1 + ! 2 1 + 0.2

!h! 9.25 25×12 !

!! = = ×8 !"##$ = 166.5×10! !"!

12 12

!! = !" = 9.25 !"(25 !"×12)×8 !"##$ = 22,200 !"!

The section properties Ig and Ag are for the gross section, but it is possible that the concrete members 

will crack, which will reduce the effective stiffness of the shear walls. ACI 318-11 Section 8.8.2(b) 

[ACI, 2011] gives some guidance on approximating the reduced stiffness to determine lateral deflections 

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in concrete members. More specifically, without a more accurate analysis, half the stiffness obtained 

from the gross section properties may be considered. 

!h! 1.2!h

!!"## = +

3! 0.5!! ! 0.5!!

344 30×12 ! 1.2(344)(30×12) !!"## = 3 3.6×10! + 0.5×166.5×10! 1.5×10!(0.5×22,200)

!!"## = 0.018 + 0.009 = 0.027 !"

To properly estimate the shear walls’ maximum expected deflection, the earlier effects of dividing by 

response modification coefficient, R, must be reversed, and this is accomplished with the use of the 

deflection amplification factor Cd. ASCE 7-10 Equation 12.12-1 (or 12.8-15) may be used to compute 

the maximum expected wall deflection δM-wall. 

!

! !!!"##

!!!"## = !!

Cd = 4.0 (ASCE 7-10 Table 12.2-1) 

δwall = 0.027 in (an elastic response under strength-level forces) 

I = 1.0 (importance factor)

! !

! = ! !"## 4.0 0.027

!!!"## = = 0.11 !! ! 1

The total system displacement is the sum of the two deflection components.

!! = !!!!"#$! + !!!!"## = 29.2 + 0.11 = 29.3 !"

This is the total anticipated inelastic deformation during the design seismic forces. It is observed that the 

contribution from the shear walls is very small, and could have been neglected in this situation. One of 

the prime characteristics of RWFD buildings is that the diaphragm dominates the response of the 

building, and this is surely evident here. 

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6.3	 Limits on Diaphragm Deflection – Deformation Compatibility 

In order to prevent damage to attached structural elements or any non-structural elements and their 

attachments, the engineer should be familiar with the expected building deflection and whether portions 

of the building are compatible with that deformation. ASCE 7-10 Section 12.12.2 and SDPWS-2008 

Section 4.2.1 both state the following in terms of maintaining structural integrity during diaphragm 

deflections: 

“Permissible deflection shall be that deflection that will permit the diaphragm and any 

attached elements to maintain their structural integrity and continue to support their 

prescribed loads as determined by the applicable building code or standard.” 

No prescriptive limits on deformation compatibility are given in either the 2012 IBC or the ASCE 7-10, 

instead it is left to the structural engineer’s judgment. 

RWFD buildings typically occur in masonry or concrete shear wall buildings, and thus the diaphragm 

deflection results in the columns and perpendicular walls rotating about their bases due to diaphragm 

translation at the top. This rotation is likely acceptable if the columns and walls were modeled with 

pinned bases during their individual design, even if some unintentional fixity exists. 

Perimeter walls that have significant fixity at the base, often because they are anchored to the floor slab 

and foundation, should be evaluated as to their ability to yield and rotate at their base. The governing 

building codes for concrete and masonry slender wall design (ACI 318 and TMS 402) require these 

slender walls to be tension-controlled flexural members. This allows the walls to better accommodate 

any out-of-plane localize yielding at the base while continuing to carry vertical loads. The assumption of 

plastic hinges forming at the base of various elements prior to reaching the maximum displacement, δM, 

is acceptable provided that these hinges do not result in an unstable structural mechanism or a loss of 

vertical support. 

6.4	 Limits on Diaphragm Deflection – Second Order Effects and P-Δ

Instability 

One potential safety concern with large flexible diaphragms that have large deflections is the rise in 

second order effects including P-Δ instability. As the roof translates, the tops of columns and walls also 

translate, resulting in a leaning gravity system that generates additional lateral forces further 

exacerbating the deflection. 

One simple method to evaluate this concern is through the stability coefficient, θ, of ASCE 7-10 Section 

12.8.7. Although this stability coefficient, θ, was not originally intended to be used to evaluate 

diaphragm deformations, with some simple adjustments it is a useful tool to investigate the diaphragm 

system stability under P-Δ effects. 

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! !!∆! = !	 ASCE 7-10 Eq. 12.8-16 !!!!"!!

where 

Px = the vertical gravity load acting on the translating system, kips 

Δ = the weighted average horizontal translation, inches 

Ie = importance factor 

Vx = the seismic shear force acting on the translating system under consideration, kips 

hsx = the height of the translating system under consideration, inches 

Cd = the dynamic amplification factor. Because the overwhelming majority of the horizontal 

translation is from the diaphragm, this factor may be based on the diaphragm’s Cd. 

This equation evaluates the relative magnitude of the horizontal load added to the lateral force resisting 

system at the system’s maximum expected deformation. An increase of 10% or less (θ ≤ 0.10) is 

considered tolerable under ASCE 7-10 without a more detailed investigation. 

The vertical gravity load acting on the translating system, Px, has a component from the roof weight, Px 

roof, and a component from the wall weight, Px wall. As indicated by the applicable load combinations, the 

roof live load is excluded from the weight of the translating roof system. Because the wall’s center of 

mass between the roof and slab on ground is only translating approximately half of the roof’s 

translation, the Px wall may be computed as the upper half of the wall plus any parapet. The load factors 

are 1.0 for this investigation. 

Px roof = 12 psf (400 ft)(200 ft) = 960 kips 

9.25 !" 30!" !! !"## = 150 !"# + 3!" 400!" 2 !"#$! = 1,665 !"#$ 12 2

Px = Px roof + Px wall = 960 + 1,665 = 2625 kips 

Δ = the average horizontal translation. A deflecting flexible diaphragm will approximate a 

parabolic shape, and thus the average translation of the roof and perpendicular walls will be 

two-thirds the maximum translation. 

! = !! !

! = 29.3 !" = 19.5 !"

! !

Vx = the seismic shear force acting on the translating system under consideration

!! = 1104 !"# 400 !" = 442 !"#$

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hsx = the height of the translating system under consideration

h!" = 30 !" ×12 = 360 !"

Cd = 4.5 

!!∆!

!

0 = ! 2625 19.5 1. = = 0.071 ≤ 0.10 !"#$ !!h!"!! 442 360 4.5

Because the stability coefficient is less than 10%, the P-Δ effects on story shears, moments, and drifts 

need not be considered further. 

It is worth mentioning here that diaphragm deflection is not included when evaluating the story drift 

limits of ASCE 7-10 Section 12.12.1. These limitations on building drift were developed primarily for 

the classic flexible frame system with a rigid diaphragm to prevent excessive distortion within the plane 

of the frame or shear wall. In masonry and concrete tilt-up buildings, the vertical elements deflect very 

little in-plane, with the bulk of translation occurring in the diaphragm. The story drift limits of the 

building code do not apply to the diaphragm deflection. 

6.5 Limits on Diaphragm Deflection – Building Separations and Setbacks 

Another diaphragm deflection limitation that must be investigated is building setbacks from property 

lines or adjacent buildings per ASCE 7-10 Section 12.12.3. For this investigation, the total δM is 

computed as the sum of the shear walls’ in-plane drift and the diaphragm’s in-plane deflection. 

However, the in-plane drift of the stiff concrete or masonry shear walls is usually insignificant compared 

with the diaphragm, and so is often ignored. 

At property lines, the required building setback is δM. When evaluating two buildings on the same 

property, the required separation between those two buildings may be evaluated as the square-root-ofthe-sum-of-the-squares (SRSS) of the two independent δM’s per ASCE 7-10 Equation 12.12-2. 

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Chapter 7	 Comparison of Designs Using Current Practice 

and Alternate Design Procedure 

This chapter presents a comparison of key design computations and results of the Chapter 3 design in 

accordance with current practice, compared to equivalent computations and results of the alternate 

design procedure presented in Chapter 5. A list of common design features is provided in Table 7.1, a 

comparison of the diaphragm designs is provided in Table 7.2, and a comparison of the shear wall 

designs is provided in Table 7.3. Comparison of design forces in Table 7.2 indicates that in general the 

alternate design procedure requires the diaphragm to be designed for lower forces. The exceptions are 

that the shear amplification for the north-south direction (transverse loading) results in essentially 

equivalent design force at the diaphragm edge and end 10% regions and that the shear amplification in 

the east-west direction (longitudinal loading) results in higher diaphragm design forces along the edge 

and end 10% regions. These observations are reflected in the nailing patterns that show that the 

alternate design procedure has less stringent nailing requirements in the interior of the diaphragm, the 

same nailing requirement in the zone along the east and west edges, and more stringent nailing along the 

mid length of the north and south edges. 

Table 7.1 Common Features for Example Buildings 

Diaphragm: Wood structural panel diaphragm 

Plan dimensions: 200 ft north-south x 400 ft east-west 

Wall thickness: 9-1/4 in. 

Wall height: 30 ft from slab on ground to diaphragm plus 3 

ft tall parapet 

Roof design dead load: 12 psf 

Spectral parameters SDS = 1.0 and SD1 = 0.6 

Seismic Design Category D 

Table 7.2 Comparison of Diaphragm Designs Using Current Practice and Alternate 

Design Procedure 

Current Practice Design Alternate Design Procedure 

R = 4, Ωo = 2.5, and Cd = 4 Rdiaph = 4.5, Ωo diaph = 2.0, and Cd diaph = 4.5 

Ta = CThn 

3/4 

= (0.02)30 

0.75 

= 0.26 seconds 

ASCE 7-10 Eq. 12.8-7 

!!"#$! 0.002 400!" 0.800 !"#

!!"##$ = 0.0019

0.176

30!" = 0.136 !"#

!! = !

!!

!!

= 1.0

4

1.0

= 0.25 North-South 

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Current Practice Design Alternate Design Procedure 

!! = !!!

!!"#$!

!

!!

= 0.6

0.800 4.5

1.0

= 0.167

East-West

!! = !!"

!!"#$!

!!

= 1.0

4.5

1.0

= 0.222

F

p 

= 0.25w

p 

North-South: F

p 

= 0.167w

p 

East-West: F

p 

= 0.222w

p 

!!" 1653!"#

!!" = 2253!"#

!!" 1104!"#

!!" = 2000!"#

Unit shear at diaphragm edge:

!!" = 1653 !"#

!!" = 563 !"#

Unit shear at diaphragm edge (amplified x 1.5):

!!" = 1104 !"# (1656 !"#)

!!" = 500 !"# (750 !"#)

Diaphragm nailing pattern current practice 

from Figure 3.7 

Diaphragm nailing pattern alternate design 

from Figure 5.5 

North-south diaphragm chords 

As required = 5.10 in2 

L5x5x5/8 steel angle, As = 5.90 in2 

East-west diaphragm chords 

As required = 0.87 in2 

L4x4x1/4 steel angle, As = 1.93 in2 

North-south diaphragm chords 

As required = 3.41 in2 

L5x5x3/8 steel angle, As = 3.65 in2 

East-west diaphragm chords 

As required = 0.77 in2 

L4x4x1/4 steel angle, As = 1.93 in2 

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Table 7.3 Comparison of Shear Wall Design Forces Using Current Practice and Alternate 

Design Procedure 

Current Practice Design Alternate Design Procedure 

R = 4, Ωo = 2.5, and Cd = 4 Rwall = 4, Ωo wall = 2.5, and Cd wall = 4 

Ta = CThn 

3/4 

= (0.02)30 

0.75 

= 0.26 seconds 

ASCE 7-10 Eq. 12.8-7 

!!"#$! 0.002 400!" 0.800 !"#

!!"##$ = 0.0019

0.176

30!" = 0.136 !"#

!! = !

!!

!!

= 1.0

4

1.0

= 0.25 North-South

!! = !!"

!!"##

!!

= 1.0

4

1.0

= 0.25

East-West

!! = !!"

!!"##

!!

= 1.0

4

1.0

= 0.25

In-plane shear at base of shear walls: 

!!" = 552 !"#$

!!" = 608 !"#$

In-plane shear at base of shear walls: 

!!" = 440 !"#$

!!" = 608 !"#$

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Chapter 8 Future Studies for Design of RWFD Buildings 

The investigation and modeling performed to develop the alternate design procedure assumed a 

rectangular building with solid walls. Additional studies would be valuable for bringing the design 

procedure described in this report into ASCE 7. The following discussion describes some additional 

work that would give greater insight into the design of these buildings. 

8.1 Steel Deck Diaphragms 

The design example provided in this report illustrated design of a wood structural panel diaphragm 

nailed to wood member. A similar approach might be applicable to a steel deck diaphragm; however, 

additional studies are needed to develop an appropriate response modification coefficient R, considering 

connector ductility and the system behavior in each orthogonal direction relative to the deck orientation. 

In addition, the encouragement of spreading the inelastic behavior across greater portions of the 

diaphragm to improve margins against collapse needs additional study for the steel deck. This concept of 

spreading ductility needs a sufficient positive post-yield slope in the assembly behavior, and further 

studies are necessary to determine whether steel decking can satisfy this. 

8.2 Out-of-Plane Top of Wall Anchorage Forces 

The results of an out-of-plane wall study [Koliou 2014] indicate that the current wall anchorage 

provisions in ASCE 7-10 are likely adequate except the ka term applicable to shorter diaphragm spans 

should be eliminated and the factor of 0.4 should become 0.8. The study also showed that there are 

corner affects that can occur. Additional studies should focus on the following: 

1.	 Determine whether the out-of-plane design forces are large enough in situations where the 

diaphragm might remain elastic due to excess diaphragm strength provided to meet 

strength demands in the orthogonal direction. 

2.	 Determine the forces on parapets, particularly taller parapets that are common at the front 

of big-box retail stores, 

3.	 Determine whether top of wall anchorage near building corners needs to be designed for 

higher forces as discussed in Appendix J, 

4.	 Determine whether there is a need to combine the design for out-of-plane wall forces with 

in-plane diaphragm shears, 

5.	 Determine whether shears in a subdiaphragm should be combined with the main diaphragm 

shears. 

6.	 Determine the effect of non-parallel (skewed) walls on out-of-plane wall forces. 

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Items 1, 2, and portions of 4 and 5 can be studied with the simplified numerical model developed for this 

project. Items 3, portions of 4 and 5, and 6 are best studied using three-dimensional nonlinear models. 

The portion of 4 that is best studied with a three dimensional nonlinear diaphragm model is determining 

how to combine the connector forces from out-of-plane wall anchorage for which the connection is 

expected to remain elastic and main diaphragm shears for which the connection is expected to become 

inelastic. 

8.3 In-Plane Wall Yielding/Rocking 

In this report, a procedure is presented for the common situation where the horizontal diaphragm is 

expected to yield prior to yield occurring in the vertical shear walls or braced frames. However, if a 

RWFD building is designed for the vertical elements of the seismic-force-resisting system to yield inplane and the diaphragm to remain elastic, the nonlinear displacement demands on the vertical elements 

need to be established. The in-plane yielding of the walls can occur due to “frame” action of a wall 

panel with large openings, rocking of the wall, or yielding at wall-to-slab or wall-to-foundation shear 

transfer connections. 

Although ASCE 7-10 has response modification coefficients for the wall systems that in theory account 

for wall yielding and rocking, the appropriateness of these values should be studied because they were 

set based on committee opinion rather than rigorous analyses. A disconnect exists because the same 

response modification coefficients have been used to date for wall systems with either rigid or flexible 

diaphragms even though the flexible diaphragms have the potential to increase inelastic displacement 

demand on the walls. 

If the walls, geometry, and masses of two buildings are equal but one has a rigid diaphragm and the 

other has a flexible diaphragm, the building with the flexible diaphragm will have a greater spectral 

displacement than that for the building with a rigid diaphragm. For the elastic range of motion, 

displacements occur in both the diaphragm and the walls. Once the walls yield, the displacement 

contribution of the diaphragm will be limited to the displacement associated with the overstrength of the 

wall system. At accelerations greater than that associated with the wall overstrength, the displacement 

will increase in the wall system but not the diaphragm. This has the potential to drive additional 

nonlinear displacements into the wall system relative to the building with a completely rigid diaphragm. 

The displacement demands on the vertical elements of the seismic-force-resisting system can be studied 

using the simplified numerical model developed in conjunction with this project. 

8.4 Irregular Plan Shapes and Abrupt Changes along Exterior Walls 

RWFD often have re-entrant corners and other abrupt changes in geometry. For example, small wall 

pop-outs of about 3-ft provide architectural relief for long walls. The effect of re-entrant corners, small 

wall pop-outs, and other abrupt changes would benefit from a study that looks at how these conditions 

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affect forces acting on nearby diaphragm connectors and the effect on diaphragm chords and collectors. 

These issues are best studied with three-dimensional models. 

8.5	 Combining Connector Forces from Shear Acting in Two Orthogonal 

Directions 

Diaphragm shears from two orthogonal directions both load a diaphragm connector. ASCE 7-10 does 

not require that connectors be designed for forces from orthogonal shears acting simultaneously. A 

study using three-dimensional nonlinear response models of diaphragms with individual diaphragm 

connectors modeled could be used to determine if these forces should be combined at the connector 

level. If so, then the models could be used to study how best to combine the forces. 

8.6	 Forces on Continuity Ties 

Steel deck panels often serve as the wall anchorage continuity ties in the direction that the deck spans. 

At end laps continuity tie forces are transferred through the framing connectors that attach the ends of 

deck panels to one another and to the support framing. These same connectors resist shear forces from 

the main diaphragm shear. Clarification of how exactly to combine forces to the connectors from the 

diaphragm shear and continuity tie forces would be beneficial. 

8.7	 Three-Dimensional Modeling Calibrated to the Response of Buildings 

and Tests 

Several instrumented RWFD buildings have been exposed to strong ground shaking, and several 

nonlinear response analyses by others have been performed in an attempt to replicate the measured 

response. Several of these analyses have been relatively successful, but more detailed models that 

include individual nonlinear connector response would be useful. Most, if not all, of the instrumented 

RWFD buildings have wood diaphragms. For RWFD buildings with steel deck, there is no response 

data with strong motions. For steel deck diaphragms, a three-dimensional model could be compared to 

the approximately 70-ft long diaphragms tested by Massarelli, et al [Massarelli, et. al, 2012]. Also, 

instrumentation of additional RWFD buildings including ones with wood diaphragms and ones with 

steel deck diaphragms is desirable. 

8.8	 Deflection of Wood Diaphragms 

A simple means of computing or estimating the diaphragm deflection could likely be obtained from the 

analysis results performed to date. In comparison to the analyses of the archetypes, deflections 

computed in accordance with the 2008 SDPWS appear to overestimate diaphragm displacement. 

Although overestimating deflection is conservative for computing second order effects and building 

separations, it would be unconservative if one used it to compute a period and used that period to 

determine design forces. This is the reason that in Section 6.1, the estimated period of the diaphragm 

Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure 89 
FEDERAL EMERGENCY MANAGEMENT AGENCY

using Wilson’s shear beam formula (Equation 1, Tdiaph = (0.066δmax) 0.5 where δmax is based on 1.0g of 

acceleration), which is more than Tdiaph = 0.002L for wood structural panel diaphragms, or other means 

of computing the period should not be used to determine design forces. The data from the archetype 

analyses could be studied to develop a means of estimating the diaphragm displacement at the design 

level and maximum considered earthquakes. The results could be compared to analysis results of the 

three-dimensional model described in Section 8.7. 

8.9	 Applicability to Buildings with Lightweight Enclosures and Steel 

Bracing 

The archetypes developed in conjunction with this project were selected to represent typical RWFD 

buildings in the United States. It is recognized that the alternate design methodology may apply to other 

systems not necessarily modeled, such as stiff braced frame buildings with steel stud and/or steel siding 

envelopes. It would be beneficial to conduct further studies with these other building types to better 

evaluate their performance under this alternate design procedure. Many of the concepts of the alternate 

procedure are expected to be relevant; however, the lightweight wall typically used with braced frames 

may require a period equation different than the period equation presented in this report. Also, the 

significant difference in mass due to the lightweight walls may lead to different behavior than that of the 

archetypes modeled in the studies that led to the alternate design procedure. 

8.10	 Applicability to Multi-Story Buildings 

The principles discussed under this design methodology could also be transferred to certain multi-story 

buildings, but with caution. Often two-story tilt-up concrete or masonry buildings are built with large 

flexible diaphragms, and their behavior may be similar to that modeled under this project. Higher mode 

shapes and interaction between the two diaphragms remain a concern and should be studied further 

before extrapolating this alternate design procedure to multiple stories. 

8.11	 Implications of Diaphragm Deflections on Structural and 

Nonstructural Elements 

Buildings with large flexible diaphragms can experience portions of the building displacing significant 

distances horizontally compared with buildings with rigid diaphragms. In buildings with rigid 

diaphragms, the diaphragm’s horizontal displacement is likely only a little larger than the supporting 

frame or shear wall system; and the drift of these supporting SFRS’s is limited by ASCE 7-10. 

Therefore, internal horizontal displacements of the rigid diaphragms are indirectly controlled. 

However, the limitations on flexible diaphragm displacements are less prescriptive than the drift limits 

for the SFRS, relying much upon the engineer’s judgment of deformation compatibility discussed in 

Section 6.3. Furthermore as demonstrated in Section 6.4, investigating second-order effects (P-∆) due to 

90 Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure
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large diaphragm displacements involves modifying existing code provisions not originally intended for 

horizontal diaphragms usage. 

While the mainstay of RWFD buildings has traditionally been warehouse shells, their use in office 

buildings or commercial retailing with numerous tenant improvements and partitions has become very 

common. The susceptibility of these two different building inventories to damage due to large 

displacements is quite different, and limitations will likely be warranted. 

8.12 Large-Scale Diaphragm Tests 

Large-scale cyclically loaded diaphragm tests or diaphragms tests for response to earthquake records 

could be performed to better understand the behavior of flexible diaphragms. Tests are desirable for 

both wood and steel deck diaphragms. The effect of connection ductility on global diaphragm ductility 

could be explored along with means of improving the spread of ductility. The location of first yield and 

how to control this location could also be explored. Deformation compatibility issues could also be 

explored along with the diaphragm tests though focused sub-assemblage tests are likely also needed. 

Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure 91 
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Chapter 9 Conclusions 

This report has presented an alternate procedure to design single-story RWFD buildings with wood 

structural panel diaphragms within the existing framework of the current 2012 IBC and ASCE 7-10. The 

alternate design procedure presented is relatively simple to implement and is based on yielding and 

energy dissipation in the diaphragm rather than yielding, rocking, or sliding of the walls. FEMA P695 

based analytical studies have demonstrated improved seismic performance of buildings designed using 

the alternate procedure, beyond the seismic performance anticipated using currently adopted seismic 

design provisions. 

The flow of goods and the sale of goods in the United States is heavily dependent upon RWFD 

buildings. Big box retail stores and logistical storage facilities can be at risk if the building code 

provisions that govern seismic design do not appropriately address how earthquakes affect them. With 

this disconnect between the intent of the provisions and the behavior of these buildings, difficulty exists 

in evaluating this building stock for seismic vulnerabilities. The alternate procedure presented in this 

report is intended to fill this gap. 

At this time, the alternate seismic design procedure is not adopted by a building code or included in 

ASCE 7-10. Designs using this alternate design procedure may not comply with IBC 2012 and ASCE 

7-10. For an existing building, using this procedure may not result in a building that complies with 

ASCE 41-13. For new buildings the Alternate Materials and Methods of Construction of ASCE 7-10 

Section 11.1.4, could be used but would require approval from the authority having jurisdiction. 

Although strictly following the alternative design procedure may not meet current code, the principles 

could be applied to a building that meets current code by modifying the procedure to include 

strengthening above current code requirements in the end zones (amplified shear boundary zones) 

without including reduction of the design forces in the other areas of the diaphragm. 

A version of the alternate design procedure presented herein has been adopted by the 2015 NEHRP 

Provisions [FEMA, 2015] as a Part 3 resource paper. Eventually, this procedure or a version of it will 

be proposed as a change to a future edition of ASCE 7. It was not brought forward in the current 

standard update cycle in order to allow designers of these buildings to gain trial experience with the 

procedure, and so that relevant issues as discussed in Chapter 8 could be further discussed. 

Recommendations for future study and research are provided in Chapter 8. The intention of including 

these recommendations is to provide focus to future studies and research so it directly benefits 

development of design provisions for RWFD buildings. 

Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure 93 
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98 Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure
 

APPENDIX A Alternate Design Procedure Discussion 

and Commentary 

An alternate procedure for design of rigid wall-flexible diaphragm buildings for earthquake effects is 

proposed in Section 4.5 of this report. When using this procedure, diaphragm yielding is expected. The 

alternate procedure requires proportionally strengthened end regions of the diaphragm, which 

encourages the spread of yielding within the diaphragm as described in Section A.4. The alternate 

procedure is based on the results of a study in which the performance of archetype buildings was 

improved by weakening the diaphragm away from the end region Koliou, et al. (2014). At this time, the 

alternate design procedure is meant to apply to RWFD buildings with wood structural panel diaphragms 

nailed to wood framing. 

The alternate design procedure is one of three design paths applicable to buildings with rigid walls and 

flexible diaphragms. The three design paths are: 

1.	 Yielding and energy dissipation of a ductile diaphragm is expected with the walls remaining 

essentially elastic, 

2.	 Yielding and energy dissipation of the vertical elements is expected with the diaphragm 

remaining essentially elastic, and 

3.	 The location of yielding and energy dissipation is not specifically determined and may occur in 

either the diaphragm or walls, or both. 

In this report, only Path 1 is addressed. Path 2 is difficult to achieve because of the inherent in-plane 

strength and stiffness of the walls relative to the strength and stiffness of the diaphragm. Path 3 could 

have design requirements based on the equivalent lateral force procedure and a two-stage approach 

similar to that proposed for Path 1. However, a response modification coefficient applicable to the 

diaphragm, Rdiaph, is likely required in the range of 2 to 3.5. This is based on fewer restrictions on 

diaphragm geometry than Path 1 and a projection of the results of the analyses of diaphragms with only 

one nailing pattern throughout as presented in Appendix K. Path 3 would require confirmation 

analyses. An engineer would choose the design path based on the expected behavior of the diaphragm 

relative to the wall. At this time, only Path 1 is fully developed, so the remainder of this Appendix only 

addresses Path 1. 

A.1 Commentary on Alternate Design Procedure with Diaphragm Yielding 

Two-stage analysis procedure: RWFD buildings with the flexible diaphragm supported by much stiffer 

perimeter walls are similar to podium buildings for which a flexible wood framed upper structure is 

supported by a much stiffer podium structure of reinforced concrete with concrete or masonry shear 

walls. The two-stage analysis procedure of Section 12.2.3.2 of ASCE 7-10, is often used to design 

podium structures. The alternate design procedure proposed in Section 4.5 of this report is a two-stage 

analysis procedure: first, design the diaphragm using its own period, response modification coefficient 

Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure 99 
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and detailing rules, and second, design the vertical elements using the existing design provisions of 

ASCE 7-10 with minor modifications. 

The listed commentary statements below match the alternate design procedure steps presented in Section 

4.5. 

C.1	 Response modification coefficient: A response modification coefficient for the diaphragm was 

determined based on a FEMA P695 evaluation of the alternate procedure. The evaluation is 

described in Appendix G, Archetype building types are described in Appendix H, and the analysis 

results are presented in Appendix I. 

C.2	 Period for the wood diaphragm: The formula for the wood diaphragm is obtained from 

Appendix D, Section D.3. It is based on diaphragms designed for high-seismicity using the 

current design procedure and was confirmed to be valid with this alternate procedure at all 

seismic hazard levels. The formula yields a shorter period than would be obtained for diaphragms 

designed for moderate seismicity so it can conservatively be applied to all levels of seismicity. 

The period of the diaphragm alone, i.e. without the period lengthening effect of including wall 

flexibility, is used rather than the total building period to be conservative in picking the spectral 

acceleration for the diaphragm design. The analyses demonstrated that the diaphragm periods 

were substantially independent of diaphragm depth. Alternate procedures that compute a 

diaphragm period that is longer than the period obtained from the proposed equation should not 

be used. 

C.3	 Seismic response coefficient, Cs: The seismic response coefficient is determined in accordance 

with the equivalent lateral force procedure in Section 12.8.1 of ASCE 7-10 but using Rdiaph in 

place of R and Tdiaph in place of Ta. For large diaphragm spans, Tdiaph is typically longer than Ta 

computed in accordance with Eq. 12.8-7 of ASCE 7-10 and will often be longer than the 

transition period, Ts, resulting in spectral accelerations that are in the constant velocity portion of 

the design spectrum. 

C.4	 Diaphragm design shears: In general, diaphragm design shears are less than those computed 

using the current practice for intermediate precast concrete shear wall buildings, except along the 

10% edge regions of the diaphragm. 

C.5	 Shear amplification in edge regions: Diaphragm design shears are increased by an amplification 

factor of 1.5 for the end 10% of the diaphragm span length (amplified shear boundary zone). This 

is shown in Figure A1. The value of 1.5 was confirmed with the analyses presented in 

Appendices G, H and I. 

C.6	 Diaphragm Chords: The diaphragm chords required with this alternate design procedure are 

generally smaller than those designed using current practice because the seismic response 

coefficient, Cs, is generally lower for the alternate design procedure. 

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C.7	 Collectors: The design of collectors and their connections for buildings assigned to SDC C and 

higher requires that the collected force be amplified by an overstrength factor. The diaphragm 

overstrength factor, Ωo diaph, should be used rather than the wall overstrength factor because the 

diaphragm rather than the walls limit the strength of the system. 

C.8	 Vertical elements of the SFRS: The vertical elements of the SFRS, i.e., shear walls, are designed 

as Stage 2 of the two-stage analysis procedure. Forces from the diaphragm are amplified by the 

ratio (Rdiaph/ρdiaph)/(Rwall/ρwall) as they are applied to the walls. This is similar to the requirement 

of Item d of the Two-Stage Analysis Procedure in Section 12.2.3.2 of ASCE 7-10. The response 

modification coefficient, R, is assigned the value for the type of vertical system being engineered 

but not greater than Rdiaph to ensure that the diaphragm will yield first. The approximate period 

for the walls is computed using ASCE 7-10 Equation 12.8-9 for the walls. This formula typically 

results in a period that is less than that computed using ASCE 7-10 Equation 12.8-7. This results 

in design forces for wall mass based on a spectral acceleration that is almost always on the plateau 

of the design spectrum, i.e. the constant acceleration portion of the design spectrum. 

C.9	 Deflections: Deflection computations are required to confirm that structural integrity of attached 

structural elements is maintained, attached or supported nonstructural items are not damaged to 

the point of causing falling hazards, and the structure does not pound against adjacent structures. 

For example, diaphragm deflection may cause prying at perimeter roof connections, as shown in 

Figure A2, and in current practice, this condition is not accounted for. Although study is required 

to determine how critical this is, it does demonstrate the type of concern that should be addressed. 

The elastic diaphragm deflection is amplified by a deflection amplification factor for the 

diaphragm, Cd diaph. The basis for Cd diaph = 4.5 is presented in Appendix G Section G.3. 

C.10	 Second order/P-Δ effects: Both diaphragm and wall deflections should be considered when 

checking for second-order or P-Δ effects. The diaphragm deflection component can be reduced to 

approximately two-thirds of the maximum diaphragm deflection because the diaphragm tributary 

seismic weight on average moves approximately two-thirds of the diaphragm deflection plus the 

deflection of the walls. 

C.11	 Out-of-plane wall forces and out-of-plane top-of-wall anchorage forces: Out-of-plane wall 

forces and out-of-plane wall anchorage are in accordance with current code requirements except 

as that ka is set equal to 2 for all diaphragm spans. The basis for this change is described in 

Appendix J. 

Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure 101 
C.12	 Additional requirements. As Discussed in Section 5.6, two additional design requirements apply 

to transfer of shear between the diaphragm and vertical element of the SFRS. First, the amplified 

unit shear stress (in plf) in the diaphragm end zone is to be used for design of the shear connection 

between the diaphragm and the vertical elements. Second, where wood structural panel sheathing 

is fastened directly to a wood ledger, the unit shear stress (in plf) is required to be further 

amplified by Ω0. 

C.13 

Figure A1. Amplified Shear Boundary Zones for the Alternate Procedure 

V computed

using Rdia= 4.5

V amplified

1.5x

0.1Le-­‐w

0.1Le-­‐w

0.8Le-­‐w

0.1Ln-­‐s 0.8Ln 0.1Ln-­‐s

102 Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure
 

Figure A2. Deformations and Change in Angle between Roof Diaphragm and Wall 

A.2 Limitations of the Alternate Design Procedure 

The alternate design procedure is limited to one-story buildings whose plan geometry can be divided 

into self-supported rectangular diaphragm segments. Each diaphragm segment must be supported 

laterally on all four sides, i.e., this does not apply to diaphragms that cantilever or resist load in rotation, 

but can apply to multi-span diaphragm systems. The alternate procedure is not applicable to irregularshaped diaphragms that are not devisable into rectangular sections because defining how to spread 

ductility in a non-rectangular diaphragm configuration is beyond the scope of the study reported in this 

report. For buildings with irregular configurations or as an alternative for rectangular-shaped 

diaphragms, a design procedure in which Rdiaph on the order of 2 to 3.5 is used without strengthened 

edges, Design Path 3 listed in Section A.1 might be appropriate but would require additional analyses to 

confirm the adequacy of such a procedure. 

The alternate procedure is only applicable to diaphragms that will perform equivalent to the diaphragms 

studied to develop the alternate design procedure. For wood diaphragms, the connectors studied were 

common nails that connect the wood structural panels to wood framing members or nailers on steel 

framing. Steel deck diaphragms were also studied but as will be discussed in Section A.3, the alternate 

procedure should not be used for them at this time. 

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A.3 Applicability of Alternate Design Procedure to RWFD Buildings with Steel Deck 

Diaphragms 

At this time the alternate design procedure is not intended to apply to RWFD buildings with steel deck 

diaphragms. There are several reasons for not recommending its use even though it has been studied 

(Koliou, 2014). Reasons include (1) test results of a large scale diaphragm show significantly less 

distribution of yielding than the analytical results show when loaded parallel to deck edges (Massarelli, 

et al., 2012), (2) steel deck diaphragms were never intended to be yielding elements as such design 

strengths are based on monotonic tests, (3) data for reverse cyclically loaded connections is sparse and 

missing for many commonly used deck gages, (4) the post-yield stiffness of connectors is positive for 

only a short deformation, 1 to 2 mm, (5) few reverse cyclically loaded diaphragm tests have been 

performed while FEMA P695 requires comprehensive test data, and (6) many diaphragms in high 

seismic regions are designed using proprietary sidelap connections for which no test data was available 

to include in the study. Additionally, the behavior of connectors simultaneously resisting forces from 

diaphragm shear for which ductile connector behavior is expected and forces from out-of-plane wall 

anchorage for which elastic connector behavior is expected must be understood. This issue will likely 

require design limitations that have yet to be identified. 

Archetypes studied and reported by Koliou included 20 and 22 ga steel deck diaphragms with puddle 

welds, powder actuated fasteners and self-drilling screws for framing connectors. Sidelap connectors 

included in the study were button punches, self-drilling screws, and top seam welds. There is a potential 

that the alternate design procedure could be applied to 20 and 22 ga diaphragms with the connectors 

studied. However, the concern of yielding not spreading as reported by Massarelli, et al. (2012) for 

diaphragms loaded parallel to the direction that the deck sheets span must be understood and addressed. 

It could also be applied to new or proprietary connectors with positive post-yield stiffness to an 

acceptable deformation limit. Currently that limit is not known exactly but a value of 10 mm is likely 

sufficient. 

Once a set of non-proprietary connections can be shown to result in acceptable diaphragm performance, 

additional connectors could be approved using the procedures of FEMA P795 (2011) Quantification of 

Building Performance Factors: Component Equivalency Methodology. 

If the alternate design procedure were to be applicable to diaphragms with welded connections the weld 

quality must be consistent with the weld quality used for the cyclic testing that led to the applicability. 

Detailed welding requirements would be required as part of the procedure. Recommendations for 

welding are provided in Guenfoud, et al. (2010). The factors to control for arc-spot welds (puddle 

welds) are high current setting, electrode type (ASTM E6011), and proper welding technique. 

Recommendations are made to increase the welding times relative to those recommended in SDI Manual 

(2004) for 1/8 in. electrodes. 

104 Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure
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A.4 Discussion of Diaphragm Yielding 

Use of the alternate procedure has the potential to provide improved diaphragm yielding relative to that 

of a diaphragm designed with current design procedures. However, the degree of improvement is 

dependent on how diaphragm shear strength is distributed for each design. 

Diaphragm yielding spreads towards the center of the diaphragm span because of the post-yield strength 

characteristics of common nails used as connectors. Common nails connecting wood structural panels 

to wood framing or wooden nailers exhibit positive post-yield stiffness that results in substantial 

increases in strength above its yield strength. This strength gain above the yield strength allows higher 

forces and yielding to develop in the diaphragm in the direction toward the center of the diaphragm 

span. 

The spread of yielding also depends on the nonlinear distribution of shears in the diaphragm. The 

degree to which the yielding spreads towards the diaphragm center depends on the distribution of 

diaphragm shears for a particular time-history and the changes in diaphragm nailing along the length of 

the diaphragm. A diaphragm with many nailing zones that approximately follow a linearly varying 

distribution of diaphragm shear strength will distribute yielding more than a diaphragm with fewer 

nailing zones between the amplified shear end regions. 

A.5 Quality of Design, Construction and Inspection 

Like many seismic-force-resisting systems, the effectiveness of the alternate design procedure will 

depend on how well the design requirements are met. Fortunately, the design requirements are 

relatively simple in comparison to many other systems. The main change from current design practice is 

how shear strength is proportioned along the diaphragm span. As described in Section A.4, improved 

distribution of yielding can be obtained by using multiple zones of diaphragm strength but the procedure 

is not dependent on providing multiple zones of yielding. 

Diaphragm designs using the alternate design procedure are no more likely to be constructed improperly 

than current diaphragm designs. A common concern is the use of the wrong nailing patterns or wrong 

nail type. If this is a concern, inspection of the nailing pattern and type of nails should be included in 

the project inspection requirements or structural observation program. Special inspection is already a 

requirement for most diaphragms in SDC C and above and for high-load wood diaphragm designs 

utilizing Table 4.2B in the SDPWS in all SDCs. 

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A.6 Diaphragm Modifications and Deterioration 

After initial construction, diaphragm strength can be affected by modifications and deterioration. The 

most common modification that reduces strength is adding openings through the diaphragm, which will 

reduce the strength approximately in proportion to the size of the openings in a line relative to the 

overall depth of the diaphragm. Large openings or many small ones can further reduce the strength and 

cause a concentration of deformations. This is also a concern with current practice, and is usually 

addressed by the engineer by adding extra diaphragm strength to offset the weakening from the 

penetrations [Lawson J, 2013]. Openings near the center of the diaphragm are likely to have little or no 

effect on performance. Openings at the transition between unamplified and amplified shears or close to 

this transition but towards the center of the diaphragm span will have a detrimental effect as this region 

is likely to have the greatest yielding. Openings within the amplified shear end regions are also likely to 

have a detrimental effect, particularly if they are near the diaphragm ends where weakening can result in 

a concentration of yielding at the diaphragm end. 

Deterioration of a diaphragm can occur due to roof leaks or moisture condensation. These can lead to 

damage to wood structural panels and to corrosion of nails or steel deck diaphragms. Roof leak damage 

is usually concentrated at or near the diaphragm-to-wall connections and at openings through the 

diaphragm. Deterioration is a concern but it is no greater for the alternate design than it is for current 

practice. 

A.7 Possible Code Provisions 

12.2 STRUCTURAL SYSTEM SELECTION 

12.2.1 Selection and Limitations 

The basic lateral and vertical seismic force-resisting system shall conform to one of the types indicated in Table 12.2-1 or a 

combination of systems as permitted in Sections 12.2.2, 12.2.3, and 12.2.4. Each type is subdivided by the types of vertical elements 

used to resist lateral seismic forces. The structural systems used shall be in accordance with the structural system limitations and the 

limits on structural height, hn, contained in Table 12.2-1. The appropriate response modification coefficient, R; overstrength factor, 

Ω0; and the deflection amplification factor, Cd, indicated in Table 12.2-1 shall be used in determining the base shear, element design 

forces, and design story drift. 

Single-story buildings with a flexible wood structural panel diaphragm and reinforced-concrete or reinforced-masonry shear walls 

that meet the restrictions of 12.15.* are permitted to be designed using the two-stage analysis procedure of Section 12.15. 

Each selected seismic force-resisting system shall be designed and detailed in accordance with the specific requirements for the 

system as set forth in the applicable reference document listed in Table 12.2-1 and the additional requirements set forth in 

Chapter 14. 

Seismic force-resisting systems not contained in Table 12.2-1 are permitted provided analytical and test data are submitted to the 

authority having jurisdiction for approval that establish their dynamic characteristics and demonstrate their lateral force resistance 

and energy dissipation capacity to be equivalent to the structural systems listed in Table 12.2-1 for equivalent values of response 

modification coefficient, R; overstrength factor, Ω0; and deflection amplification factor, Cd. 

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The following is the proposed addition of Section 12.15 to ASCE 7-10. The content of this section is all 

new text so strikeout and underline formatting is not used. 

12.15 TWO-STAGE DESIGN PROCEDURE SINGLE-STORY BUILDINGS WITH FLEXIBLE WOOD 

STRUCTURAL PANEL DIAPHRAGMS AND WITH A REINFORCED-CONCRETE OR REINFORCED-MASONRY 

SHEAR WALL SYSTEM 

12.15.1 Restrictions 

Single-story buildings with flexible wood structural panel diaphragms and with a reinforced-concrete or reinforced-masonry 

shear wall system shall be permitted to be designed in accordance with the Two-Stage Design Procedure of Section 12.15.2 

to 12.15.* if the following restrictions are met. 

1.	 The wood structural panel diaphragm is without rigid topping, and is designed with nail fasteners in conformance with the 

2008 NDS Special Design Provisions for Wind and Seismic [AWC, 2008]. 

2.	 The vertical elements are intermediate or special reinforce concrete shear walls or special reinforced masonry shear walls. 

3.	 The diaphragm is without horizontal structural irregularities except for Type 2 in accordance with Table 12.3-1. 

4.	 The diaphragm can be divided into rectangular segments with lateral support at each edge. 

5.	 The period of the diaphragm, Tdiaph, computed in accordance with 12.15.2.2 is greater than or equal to 3 times the period of 

the wall system, Twalls, computed in accordance with 12.15.2.3. 

6.	 Cs wall falls on the plateau of the response spectrum. 

12.15.2 Stage One – Diaphragm Design 

12.15.2.1 Design Coefficients and Factors for Diaphragm 

The diaphragm is assigned a response modification coefficient, Rdiaph equal to 4.5, an overstrength factor, Ωo diaph, equal to 2, and a 

deflection amplification factor, Cd, equal to 4.5. 

12.15.2.2 Diaphragm Period 

1.	 The wood diaphragm period is determined using Eq. 12.15-1. 

2. !!"#$! = 0.002!!	 (12.15-1) 

3.	 where 

4.	 Lf = the span, in feet, of the horizontal flexible diaphragm being considered; the span is measured between vertical 

elements that provide lateral support to the diaphragm in the direction being considered. 

12.15.2.3 Diaphragm Design Force 

Design forces for the diaphragm shall be computed in accordance with Sections 12.15.3.1 to 12.15.3.*. 

12.15.2.3.1 Calculation of Seismic Response Coefficient 

The seismic response coefficient, Cs, is determined in accordance with the equivalent lateral force procedure in Section 12.8.1 of 

ASCE 7-10 but using Rdiaph in place of R and Tdiaph in place of T. 

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12.15.2.3.2 In-plane Diaphragm Force 

The in-plane diaphragm force shall be in accordance with Eq. 12.15-2. 

!! = !!!! (12.15-2) 

where 

!!= the force acting on the diaphragm per unit length. 

!!= the tributary seismic weight applicable per unit length of diaphragm including the tributary weight of the out-of-plane walls. 

12.15.2.3.3 Direction of Loading 

The seismic design forces are permitted to be applied independently in each of two orthogonal directions and orthogonal interaction 

effects are permitted to be neglected. 

12.15.2.3.4 Diaphragm Shears 

The diaphragm design shear shall be computed using the force computed with Eq. 12.15-2. For shear design of the diaphragm, the 

design shears in the end 10% regions of the diaphragm span in each orthogonal direction shall be amplified 1.5 times. 

12.15.2.3.5 Diaphragm Chords and Chord Forces 

Diaphragm chords shall be located at opposite edges to resist the diaphragm’s flexural forces.. Flexural moments in the diaphragm 

shall be computed using forces computed in accordance with Eq. 12.15-2. The chord axial force shall be determined assuming a 

force couple develops between the chords at opposite edges of the diaphragm segment. 

12.15.2.3.6 Collector Elements and Their Connections 

Collector elements shall be provided that are capable of transferring the seismic forces originating in other portions of the structure 

to the vertical wall elements providing the resistance to those forces. Structures assigned to Seismic Design Categories C through F 

shall be designed to resist the forces calculated using the seismic load effects including overstrength factor of Section 12.4.3 but 

using Ωo diaph for the overstrength and using the seismic forces determined from Eq. 12.15-2. 

12.15.3 Stage Two – Wall System Design 

12.15.3.1 Design Coefficients and Factors for Shear Walls 

A seismic force-resisting system that includes reinforced-concrete or reinforced-masonry shear walls and is listed in Table 12.2-1 

shall be assigned seismic parameters in accordance with Section 12.2.1. The appropriate response modification coefficient, R, 

overstrength factor, Ωo, and deflection amplification factor shall be in accordance with the value assigned in Table 12.2-1 except 

that R shall not be greater than Rdiaph. The response modification coefficient, R, shall be referred to as Rwall, the overstrength factor, 

Ωo, shall be referred to as Ωo wall, and the deflection amplification factor, Cd, shall be referred to as Cd wall. The detailing requirements 

and system limitations of Table 12.2-1 apply even though the Rwall may have been reduced to be less than or equal to Rdiaph. 

12.15.3.2 Period for Walls 

The period of the wall system, Twall, shall be computed assuming the diaphragm is rigid and using Eq. 12.8-9. 

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12.15.3.3 Design Force for Wall System 

The vertical wall elements of the seismic force-resisting system shall be designed for in-plane forces using the equivalent lateral 

force procedure of Section 12.8 but with the force from the diaphragm amplified by (Rdiaph/ρdiaph)/(Rwall/ρwall) but not less than 1.0, 

Rwall in place of R, and Twall in place of T. 

12.15.4 Deflections 

12.15.4.1 Diaphragm Deflection 

Elastic diaphragm deflection, δe diaph, shall be computed using the force level, Fp, in Section 12.15.2.3.2. The maximum inelastic 

diaphragm deflection, δdiaph, shall be computed using Eq. 12.15-3. 

!!"#$! = !! !"#$!

!!

!! !"#$! (12.15-3) 

12.15.4.2 In-Plane Wall Deflection 

Elastic in-plane wall deflection, δe wall, shall be computed using the force level in Section 12.15.3.3. The maximum inelastic wall 

deflection, δwall, shall be computed using Eq. 12.15-4. 

!!"## = !! !"#

!

#

!

!! !"## (12.15-4) 

12.15.4.3 P-Delta Effects 

P-∆ effects on diaphragm shear shall be investigated in accordance with 12.8-7. The design story drift, Δ, shall equal two-thirds of 

the maximum diaphragm displacement δdiaph computed in accordance with Eq. 12.15-3 plus the deflection of the wall system δwall 

computed in accordance with Eq. 12.15-4. 

12.15.4.4 Deflection Limitation 

The maximum inelastic deflection equal to the in-plane deflection of the diaphragm, δdiaph, plus the in-plane deflection of the wall 

system, δwall, in the direction under consideration shall not exceed the permissible deflection of the attached elements. Permissible 

deflection shall be that deflection that will permit the attached element to maintain its structural integrity under the individual 

loading and continue to support the prescribed loads. 

12.15.4.5 Structural Separation 

Structural separations shall be computed in accordance with 12.12.3 except that the maximum inelastic response displacement , δM, 

shall be a combination of the diaphragm plus in-plane wall displacements (δdiaph + δwall). 

12.15.5 Structural Walls and Their Anchorage 

The walls and their anchorages shall be designed in accordance with Section 12.11 except that ka shall be assigned a value of 2.0 for 

all diaphragm span lengths. 

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APPENDIX B Evaluating RWFD Buildings Using FEMA P695 

Methodology 

The FEMA P695 methodology is used to reliably quantify building system performance and provide 

guidance in the selection of appropriate design criteria when ASCE 7-10 linear design methods are 

applied. The primary objectives of FEMA P695 are to obtain an acceptably low probability of collapse 

of the SFRS under maximum considered earthquake (MCE) ground motions, and to provide uniform 

protection against collapse across various structural systems. An appropriate P695 evaluation must use 

a representative nonlinear model that includes both detailed design information of the system as well as 

comprehensive test data on the post-yield performance of system components and subassemblies. 

When using FEMA P695, a structural system and design methodology are evaluated through the use of 

collapse fragility curves. Incremental Dynamic Analyses (IDA) are conducted on a representative 

sample of nonlinear numerical building models that account for the range of the design space using a 

pre-determined ensemble of earthquake ground motions. Collapse fragility curves are then developed 

from the IDAs. The number of archetypes selected is based on building an appropriate representation of 

typical RWFD buildings including the range of variation reasonably expected and likely to affect 

performance. The archetypes are assigned to performance groups for the evaluation process. 

Evaluations of archetypes are performed for seismicity levels being considered for a building system. 

For RWFD buildings archetypes are designed for high and moderate seismic risk. For the evaluations, 

high-seismic risk is defined as having design acceleration parameters SDS equal to 1.0 and SD1 equal to 

0.60. These acceleration parameters are used for the SDC Dmax evaluation in accordance with FEMA 

P695. Moderate-seismic risk is defined as having design acceleration parameters SDS equal to 0.499 and 

SD1 equal to 0.199, which are the boundary values for SDCs C and D and is referred to SDC Cmax for the 

evaluations. 

For this study, the FEMA P695 Far Field Ground Motion Set (FEMA P695, 2009) was used. This set 

contains twenty-two historical ground motions listed in the table below from all over the world with two 

horizontal components each recorded at the same station. This results in 

forty-four ground motion records to use to analyze each archetype. This ground motion ensemble is 

considered representative of the seismicity in the Western United States. 

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Table B1 – FEMA P695 Earthquake Ground Motion Ensemble 

EQ. 

Index 

Earthquake Event 

Recording Station PGA(g)* Name Year Mw EQ_ID. Earthquake 

1 12011 Northridge 1994 6.7 Beverly Hills – Mulhol 0.52 

2 12012 Northridge 1994 6.7 Canyon Country–WLC 0.48 

3 12041 Duzce, Turkey 1999 7.1 Bolu 0.82 

4 12052 Hector Mine 1999 7.1 Hector 0.34 

5 12061 Imperial Valley 1979 6.5 Delta 0.35 

6 12062 Imperial Valley 1979 6.5 El Centro Array#11 0.38 

7 12071 Kobe, Japan 1995 6.9 Nishi – Akashi 0.51 

8 12072 Kobe, Japan 1995 6.9 Shin – Osaka 0.24 

9 12081 Kocaeli, Turkey 1999 7.5 Duzce 0.36 

10 12082 Kocaeli, Turkey 1999 7.5 Arcelik 0.22 

11 12091 Landers 1992 7.3 Yermo Fire Station 0.24 

12 12092 Landers 1992 7.3 Coolwater 0.42 

13 12101 Loma Prieta 1989 6.9 Capitola 0.53 

14 12102 Loma Prieta 1989 6.9 Gilroy Array#3 0.56 

15 12111 Manjil, Iran 1990 7.4 Abbar 0.51 

16 12121 Superstition Hills 1987 6.5 El Centro Imp. Co. 0.36 

17 12122 Superstition Hills 1987 6.5 Poe Road (temp) 0.45 

18 12132 Cape Mendocino 1992 7.0 Rio Dell Overpass 0.55 

19 12141 Chi-Chi, Taiwan 1999 7.6 CHY 101 0.44 

20 12142 Chi-Chi, Taiwan 1999 7.6 TCU045 0.51 

21 12151 San Fernando 1971 6.6 LA – Hollywood Stor. 0.21 

22 12171 Friuli, Italy 1976 6.5 Tolmezzo 0.35 

The collapse margin ratio (CMR) is determined from the IDA and fragility curves. It is defined as the 

median spectral collapse intensity at the fundamental elastic period of the building archetype under 

analysis, SCT[T] obtained from nonlinear dynamic analyses divided by the ground motion spectral 

demand SMT[T] at the maximum considered earthquake (MCE) intensity level at the same fundamental 

elastic period. The collapse margin ratio is multiplied by a spectral shape factor (SSF) to obtain an 

adjusted collapse margin ratio (ACMR). The spectral shape factor is a function of the fundamental 

period, the period-based ductility, μT, and the applicable seismic design category of the archetype under 

analysis. The ACMR for both individual archetypes and the archetype performance groups are 

compared to acceptable ACMRs that account for uncertainties judged to be within the evaluation 

process. The acceptable ACMR for a performance group targets less than 10% probability of collapse in 

an MCE event, and the acceptable ACMR for individual archetypes targets less than 20% probability of 

collapse in an MCE event. 

For this study, the acceptable ACMRs are computed using the uncertainty (beta) factors listed in Table 

B2. Note that the value for the design requirement uncertainty is based on an assumed improved design 

procedure so a larger value might be more appropriate for evaluating the current design procedure. The 

combined uncertainty, βTotal, is computed as the square root sum of the squares of the individual 

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uncertainties. For βTotal equal to 0.66, the acceptable ACMR is 1.73 and 2.30 for 20% and 10% 

probability of collapse at Maximum Considered Earthquake (MCE) ground motion, respectively. The 

acceptable ACMR applicable for the performance of individual archetypes is 1.73, and the acceptable 

ACMR of performance groups is 2.30. 

Table B2. Beta factors for determining acceptable collapse margin ratios. 

Description Beta factor Value of β

Record-to-record uncertainty βTR 0.40 

Design requirements uncertainty ΒDR 0.20 

Test data uncertainty βTD 0.35 

Modeling uncertainty ΒMDL 0.35 

Combined uncertainty βTotal 0.66 

B.1 Modeling Framework 

Large wood structural panel and steel deck diaphragms can have thousands of connectors. Yielding of 

these connectors is the primary means of obtaining ductility and dissipating energy. Although modeling 

the nonlinear behavior of all or many of these connectors in a detailed three-dimensional analysis would 

be the ideal means of evaluating RWFD systems, taking this approach is unrealistic at this time given 

the thousands of hours of computer run time it would require. For example, such a model took more 

than three hours to run one-half of a comparatively short record. Because the computer run time 

necessary to perform nonlinear response history analyses of detailed three dimensional models is too 

long, a modeling framework was developed that allows for a relatively simplified model to be used. 

The modeling framework developed to analyze RWFD buildings includes three steps as illustrated in 

Figure B1. These three steps are as follows: 

1.	 Create a database of connectors that have been cyclically tested. Based on the test results, determine 

the hysteretic parameters of Wayne-Stewart (Stewart 1987) or SAWS (Folz and Filiatrault, 2001) 

nonlinear cyclic springs for each connector. A representation of the parameters for the WayneStewart and SAWS springs are shown in Figure B2. Examples for nailed and welded framing 

connectors are illustrated in Figures B3 and B4. 

2.	 Create a mathematical model in MATLAB of one-half of each archetype’s diaphragm that accounts 

for the stiffness of the panels, diaphragm chords, and each diaphragm connector. Divide the 

diaphragm model into horizontal segments and load the diaphragm by a cyclic point load at its midspan. Combine the response of the elements and connectors within each diaphragm segment to form 

a single nonlinear hysteretic spring that represents the cyclic response of the segment. This step is 

illustrated in Figure B5. Variable connector spacing is accounted for in this model. 

3.	 Create a model in RUAUMOKO2D (Carr, 2007) that consists of one-half of the archetype and 

includes a spring and mass for each horizontal diaphragm segment, beam elements with nonlinear 
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hinges to represent the out-of-plane wall response, and springs and masses to represent the in-plane 

wall at the end of the diaphragm. A representation of the simplified model is shown in Figure B6. 

P-delta effects are incorporated into the model by applying the roof weight on leaning columns 

between the ground and the roof diaphragm. Localized effects that account for shear concentration 

in subdiaphragms, at corners, at openings, or at regions receiving wall anchorage forces are not 

accounted for in this analysis. This model also cannot account for loading from the two orthogonal 

directions acting simultaneously. 

Figure B1. Three-step modeling framework. 

(a) (b) 

Figure B2. Illustration of hysteretic models: (a) Wayne-Stewart (Stewart, 1987) and (b) CUREE-SAWS 

(Folz and Filiatrault, 2001). 

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2000
 

1000
 

Force [lbs] Force [lbs] Force [lbs] 

0

-1000

-2000-1 -0.5 0 0.5 1

Displacement [in] 

2000

2000 1000

0

1000 -1000

Wayne-Stewart model 

CUREE-SAWS model 

-2000-1 -0.5 0 0.5 1

Force [lbs] 

Displacement [in] 

2000

0 

1000 -1000 

0

-2000 

-1 -0.5 0 0.5 1 -1000

-2000 Displacement [in] -1 -0.5 0 0.5 1

Displacement [in] 

-1 -0.5 0 0.5 1

Displacement [in] 

(a) (b) 

-2000

-1000

0

1000

2000

Force [lbs] 

Figure B4. Comparison of hysteretic response for 2-ply-22-gauge framing welds to 0.25 in. plate: (a) experimental 

(Guenfoud, et. al., 2010) and (b) fitted optimal hysteretic models 

(a) (b) 

Figure B3. Comparison of hysteretic response for 10d common nail and wood deck: (a) example of experimental data 

(Coyne, 2007) and (b) best fit numerical model based on data from several tests (Koliou, 2014). 

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δpanels δconnectors F

d

Cchord T M=Tchord X d chord

F

Chord

Connectors

Panel 1

Panel 2

Panel 3

Panel 4

Center	
  of roof	
  diaphragm δflexure@chord

Figure B5. In-plane displacement components of the analytical inelastic roof diaphragm model. 

(a) (b)

Figure B6. Illustration of a simplified rigid wall flexible diaphragm (RWFD) building model developed in the 

RUAUMOKO2D platform. 

Cyclic test data for the 10d common nails are from Coyne (2007), Fonseca and Campbell (2002), and 

Christovasilis, et al (2009). Cyclic data for button punch, screw, and top seam weld sidelap connectors 

between deck sheets are from Rogers and Tremblay (2003b). Cyclic data for welds, powder actuated 

fasteners, and screws that connect steel deck to steel plates are from Guenfoud, et al. (2010) and from 

Rogers and Tremblay (2003a). A list of the database of cyclic test data for nails and steel deck 

connectors is included in Tables C1, C2, and C3 of Appendix C. 

B.2 Modeling Framework Validation 

The two-dimensional model of the diaphragm, Step 2, was validated by comparing predicted results to 

cyclic diaphragm test results of Tremblay et al. (2004). The predicted and tested shear for monotonic 

loading are normalized to the applicable maximum shear and compared in Figure B7. The results of 

shear versus deformation for one main cycle predicted by the diaphragm sub model versus the test 

results are compared in Figure B8. Results for the simplified model, Step 3, are compared to those of a 

detailed finite element model by Olund (2009). 

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The periods are obtained from eigenvalue analyses using the simplified building model and are initial 

elastic periods. The natural periods of the simplified model for the first and second modes are about 3% 

longer than those predicted by Olund’s detailed model. 

Figure B7. Validation/comparison of inelastic roof diaphragm for monotonic loading. 

Figure B8. Validation/comparison of inelastic roof diaphragm for cyclic loading (one main cycle). 

The collapse assessment of the rigid wall flexible diaphragm (RWFD) building was evaluated by 

conducting Incremental Dynamic Analyses (IDA) (Vamvatsikos and Cornell, 2002) using the FEMA 

P695 Far Field Ground Motion Ensemble (FEMA P695, 2009) and computing the median collapse 

intensity. To monitor the state of the structure at the end of each nonlinear time history dynamic 

analysis, the diaphragm (roof) drift ratio was considered as the damage measure (DM), while the 

intensity measure (IM) was defined by the spectral acceleration (Sa(T1)) at the fundamental period of the 

RWFD building; T1 is the fundamental period obtained from eigenvalue analyses of the initially elastic 

simplified building model. Olund (2009) set the limit state for a RWFD as a roof drift equal to 3%. For 

the purpose of comparing results of Olund’s detailed model to those of the simplified building model the 

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1 

0.8 

0.6 

0.4 

0.2 

0 

IM = Sa (T1) [g] 

Figure B9. Incremental dynamic analysis results/comparison. P[Roof drift > 3%]

FEM model (Olund, 2009) 

2D building model 

2D model building data 

Median(μ) 

FEM model (Olund, 2009)=1.5 

2D building model=1.36 

0 1 2 3 4 5 6 7 

limit state is set equal to 3% diaphragm drift, but for analysis results for the FEMA P695 evaluations, 

the limit state is equated to a load-displacement (P-delta) sidesway instability. As shown in Figure B9, 

the simplified building model slightly underestimates (by approximately 9%) the median collapse 

intensity compared to the detailed FEM developed by Olund (2009). 

A limitation of the modeling framework is that it cannot account for the simultaneous loading of framing 

connectors at ends of steel deck sheets from the in-plane diaphragm shears and the continuity tie or outof-plane wall anchorage forces. Therefore, the archetypes designed and analyzed are based on the 

requirements to resist shear only. However, the magnitudes of these two sources of loading are not 

compatible with one another. Specifically, out-of-plane wall forces are not reduced to account for 

ductility and the connections supporting the wall are expected to behave elastically, while the forces 

acting on these same connectors from diaphragm shear resistance are based on an assumption that the 

connections will yield. There seems to be a philosophical conflict in the intended behavior of the 

fastener when exposed to both diaphragm shear forces and wall anchorage forces, which occur 

simultaneously in some regions of the diaphragm. For steel deck diaphragms, consideration should be 

given to supporting the out-of-plane wall forces with separate continuity ties rather than transferring 

them into the deck sheets. Further analyses beyond those for the FEMA P695 evaluations are 

recommended to study this issue. Studying this issue will require nonlinear response history analyses of 

detailed, three-dimensional models with nonlinear connections, but it will be unrealistic to apply the 

entire suite of time-histories typically used for FEMA P695 evaluations. 

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APPENDIX C List of Connectors in Database 

Cyclic test data are essential for analyzing flexible diaphragms. At this time, the data for common nail 

connectors are relatively complete. More cyclic test data of steel deck diaphragm connectors is needed. 

The connections included in the database assembled by Koliou (2014) and the sources of the test data 

are included in Tables C1, C2, and C3. The fitted parameters for the Wayne-Stewart hysteretic model 

and the CUREE-SAWS hysteretic model are included in Chapter 3 of Koliou (2014). 

Table C1. Cyclic test data for nails 

Connection type Specimen 

characteristics 

Number of 

specimens 

tested 

Source 

6d common nails 

(d=0.113in, l=2.0in) 

7/16 OSB std. 10 Coyne (2007) 

8d common nails 

(d=0.113in, l=2.5in) 

2x4 Hem Fir. & 

7/16 OSB std. 

19 

Christovasilis et al. 

2x6 Hem Fir. & (2009) 

7/16 OSB std. 

17 

8d common nails 

(d=0.131in, l=2.5in) 

7/16 OSB std. 10 

Coyne (2007) 10d common nails 

(d=0.148in, l=3.0in) 

7/16 OSB std. 10 

5/8 OSB std. 10 

3/4 OSB std. 10 

10d box nails 

(d=0.131in, l=3.0in ) 

DF-L & 19/32 

T&G 

20 

Fonseca et al. (2002) 

DF-L & 19/32 

OSB std. 

20 

#10 Rolled – Hardened 

screws 

(d=0.113in, l=2.0in) 

DF-L & 7/16 

OSB std. 

20 

Table C2. Cyclic test data for steel deck sidelap connectors 

Connection type Specimen 

characteristics 

Number of 

specimens tested 

Corresponding 

Publication 

Button punch (0.39in. 22 ga deck 2 

Rogers and Tremblay 

(2003b) 

diameter) 20 ga deck 2 

Screws (10-14x7/8 in.) 22 ga deck 2 

20 ga deck 2 

Welds (1.38in. length) 22 ga deck 2 

Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure 119 
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Table C3. Cyclic test data for steel deck framing connectors 

Connection type Specimen characteristics Number of 

specimens tested 

Corresponding 

Publication 

Powder-Actuated 

Fasteners (Hilti 

EDNK22-THO12 and 

Buildex BX12) 

22 ga deck to 0.12 in. plate 4 

Rogers and Tremblay 

(2003a) 

20 ga deck to 0.12 in. plate 4 

Powder-Actuated 

Fasteners 

(Hilti ENPH2-21-L15 

and Buildex BX14) 

22 ga deck to 0.79 in. plate 4 

20 ga deck to 0.79 in. plate 4 

Buildex Screws 

(12-14x in.) 

22 ga deck to 0.12 in. plate 2 

20 ga deck to 0.12 in. plate 2 

Hilti Screws 

(12-24x7/8 in.) 

22 ga deck to 0.12 in. plate 2 

20 ga deck to 0.12 in. plate 2 

Welds (0.63 in. arc spot) 

& Washer 22 ga deck to 0.12 in. plate 1 

Welds (0.63 in. arc spot) 

22 ga deck to 0.12 in. plate 2 

22 ga deck to 0.79 in. plate 1 

20 ga deck to 0.12 in. plate 2 

Welds (0.63in. – 0.75in. 

arc spot) 

2 ply – 16 ga deck to 0.25 

in. plate 

4 

Guenfoud, Tremblay & 

Rogers (2010) 

2 ply – 18 ga deck to 0.25 

in. plate 

4 

2 ply – 20 ga deck to 0.25 

in. plate 

4 

2 ply – 22 ga deck to 0.25 

in. plate 

4 

4 ply – 16 ga deck to 0.25 

in. plate 

4 

4 ply – 18 ga deck to 0.25 

in. plate 

3 

4 ply – 20 ga deck to 0.25 

in. plate 

4 

4 ply – 22 ga deck to 0.25 

in. plate 

4 

120 Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure
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APPENDIX D Evaluation of Current Design Procedure 

Although the current design procedure is based on the assumption of inelastic response in the vertical 

elements (walls, rigid frames), yielding of the diaphragm commonly dominates the inelastic response of 

the buildings to earthquakes. Archetype buildings using the current design procedure were designed and 

P695 analyses (FEMA P695, 2009) were applied to these designs to provide a baseline of performance 

and to demonstrate that changes to the design procedure are necessary. 

D.1 Description of Archetypes 

Evaluations were performed on archetypes as described for high and moderate risk. For these 

evaluations, archetypes were designed with either steel deck or wood structural panel diaphragms. The 

archetype naming convention is shown in Figure D1. Summary tables and tables with detailed 

descriptions of diaphragm zones for the archetypes are in Appendix E. The walls for these archetypes 

are reinforced-concrete wall panels 25 ft in width, 33 ft tall measured from the top of the slab-on-grade, 

and 9-1/4 in. thick for high seismic risk and 7-1/4 in. thick for moderate seismic risk. The roof level is 

at 30 ft above the top of the slab-on-grade with the walls cantilevering as a parapet 3 ft higher than the 

roof level. 

The archetypes are grouped by diaphragm type, either wood or steel deck, and whether the diaphragm is 

relatively large or small. The archetypes have plan aspect ratios of 1:1, 2:1 and 1:2. Large diaphragms 

are 400 ft long and either 400 ft or 200 ft wide. The small diaphragms with aspect ratios of 2:1 and 1:2 

are 200 ft long by 100 ft wide, and for the 1:1 aspect ratios the diaphragms are 100 ft by 100 ft. The 

wood diaphragms are wood structural panels nailed to wood nailers that are attached to open web steel 

joists, commonly called a hybrid panelized roof structure. The steel deck diaphragms are attached to the 

joists with arc spot welds, powder actuated fasteners, or self-drilling screws. Adjacent steel deck sheets 

are attached along their sides (sidelaps) with top seam welds, button punches, or self-drilling screws. 

Many steel deck diaphragms include proprietary sidelap connections in the western portion of the U.S., 

which includes regions of high seismicity. Archetypes are not included with the proprietary sidelap 

connections because cyclic test data for the response of these connectors is not available. The steel deck 

diaphragms were designed using 22 and 20 gage deck because connection data was available for 

connectors with these deck gages. Note that thicker gage deck results in less ductile connections so the 

steel deck diaphragm results presented herein are limited to only diaphragms with 22 or 20 gage deck. 

Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure 121 
Figure D1. Archetype Naming Convention. 

The archetypes were designed as intermediate precast shear walls with a response modification 

coefficient of 4. The period for each direction of each archetype was computed using the approximate 

period equation, ASCE 7-10 Eq. 12.8-7, for Ta, which is consistent with current practice. For the 30 ft 

roof height of the archetypes, the approximate period is 0.26 seconds. This value is less than the 

transition period, Ts, equal to 0.60 seconds for high-seismic risk (SDC D) archetypes and 0.40 seconds 

for moderate seismic-risk (SDC Cmax) archetypes. Therefore, the archetypes for the existing design 

procedure, i.e., current code, are designed using a base shear coefficient of 0.25 for the high-seismic risk 

(SDC D) archetypes and for a base shear coefficient of 0.125 for the moderate seismic risk (SDC Cmax) 

cases. 

The diaphragms for the archetypes are zoned with different fastener spacings similar to zoning 

commonly used in practice. For the wood diaphragms, the diaphragms are zoned as follows: 

122 Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure
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•	 Large wood diaphragms with 1:1 aspect ratio – four zones of concentric squares for highseismic risk and two zones of concentric squares for moderate seismic risk. 

•	 Large wood diaphragm with 2:1 and 1:2 aspect ratio for high-seismic risk – six zones 

total with the first two zones near the center of diaphragm as concentric rectangles and 

the remaining zones banded for loading in the transverse direction 

•	 Large wood diaphragm with 2:1 and 1:2 aspect ratio for moderate seismic risk – three 

banded zones for loading in the transverse direction 

•	 Small wood diaphragm with 1:1 aspect ratio – two zones of concentric squares 

•	 Small wood diaphragms with 2:1 and 1:2 aspect ratio – five banded zones for highseismic risk and two banded zones for moderate seismic risk for loading in the transverse 

direction 

For the steel deck diaphragms, the diaphragms are zoned as follows: 

•	 Large steel deck diaphragm with 1:1 aspect ratio – three zones of concentric squares 

•	 Large steel deck diaphragm with 2:1 and 1:2 aspect ratio – three zones banded for 

transverse direction loading 

•	 Small steel deck diaphragms with 1:1 aspect ratio – one zone used for entire diaphragm 

•	 Small steel deck diaphragms with 2:1 and 1:2 aspect ratio – two zones banded for 

transverse direction loading 

D.2 Summary of FEMA P695 Analysis Results for Current Design 

Incremental Dynamic Analyses (IDA) (Vamvatsikos and Cornell, 2002) using the FEMA P695 Far Field 

Ground Motion Ensemble (FEMA P695, 2009) were performed using the simplified building models to 

compute the median collapse intensity. For the analysis results, the median collapse intensity is defined 

as the median spectral intensity at the fundamental period that causes side-sway P-delta instability. 

Summaries of collapse results for individual wood and steel deck diaphragm archetypes are included in 

Appendix F. Values for the median collapse intensity, SCT[T], ground motion spectral demand, SMT[T], 

building drift ratios (BDR) for the design level earthquake and maximum considered earthquake, the 

spectral shape factor (SSF), fundamental elastic period, and period based ductility, μT, are provided. 

The BDR, which equals the sum of the wall drift ratio (WDR) and the diaphragm drift ratio (DDR), is 

used as measure of building damage for this study. Collapse margin ratios (CMRs), adjusted collapse 

margin ratios (ACMRs), and acceptable ACMRs for the individual archetypes and the archetype groups 

are also included in Appendix F. The acceptable ACMR applicable for the performance of individual 

archetypes is 1.73, and the acceptable ACMR of performance groups is 2.30. Summaries of the collapse 

margin ratio results for the performance groups of wood and steel archetypes are provided in Tables D2 

and D3. 

Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure 123 
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The current design procedure did not pass the FEMA P695 collapse criteria for the small archetype 

performance groups with wood diaphragms. Each small wood diaphragm archetype had an individual 

ACMR that exceeded the acceptable value of 1.73 indicating each archetype passed the criterion. 

However, the small archetype performance groups for both high- and moderate-seismic risk had ACMR 

values of 2.11 and 1.98, respectively, which is less than the acceptable ACMR of 2.30, so these 

performance groups did not pass the criterion. The small archetypes had short periods and remained in 

the short period range as yielding occurred. In this region, period shifts can result in resonance with 

large spikes in the short period range that can lead to much larger spectral accelerations and 

displacements than predicted using the design spectrum plateau. This issue of short-period structures 

having higher seismic demands leading to the lowest level of collapse performance has been well 

documented, starting with Newmark and Hall (1973). Section 9.5.1 of FEMA P695 (2009) describes 

this issue with short-period structures in greater detail. 

The larger archetype wood diaphragm performance groups had ACMRs of 2.68 and 2.80 for the highand moderate risk performance groups, which exceed the acceptable ACMR of 2.30 to pass the criteria. 

Each large wood diaphragm archetype had an individual ACMR that exceeded the acceptable value of 

1.73. The large wood archetypes performed better because the elastic periods were often off of the 

design response spectrum’s plateau but the diaphragm was designed as though it was on the plateau of 

the spectrum. Also, as the diaphragm yields its period lengthens, which in general leads to lower forces. 

Both the large and small steel deck diaphragm performance groups did not pass the criteria. For 

individual archetypes with high-seismic risk 5 of 7 large archetypes and 1 of 9 small archetypes had 

ACMRs less than the acceptable ACMR of 1.73, and for individual archetypes with moderate-seismic 

risk 3 of 12 large archetypes and 3 of 9 small archetypes had ACMRs less than acceptable. The ACMRs 

for the large archetype groups of 1.71 and 1.87 for high-seismic risk and 1.95 and 1.88 for moderate 

seismic risk performed slightly worse than the small archetype groups. The small archetype groups had 

values of 2.23 and 1.92 for high-seismic risk and a value of 1.86 for moderate seismic risk. The reason 

for the difference relative to what was observed for the wood diaphragms is that the larger steel 

diaphragms were relatively stiffer than the larger wood diaphragms and had periods that were on or 

close to the design spectrum plateau. Differences in ACMRs of the archetypes with various 

combinations of welds, PAFs, screws and button punches were not significant enough to distinguish 

definitive differences in performance of the connectors.

124 Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure
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Table D1. Summary of collapse margin ratio results for wood diaphragm archetype

performance groups for current design 

Performance 

Group 

Seismicity Size Computed ACMR Acceptable 

ACMR 

Pass/Fail 

PG-1E High Large 2.68 Pass 

PG-2E High Small 2.11 2.30 Fail 

PG-3E Moderate Large 2.80 Pass 

PG-4E Moderate Small 1.98 Fail 

Table D2. Summary of collapse margin ratio results for steel deck diaphragm archetype

performance groups 

Performance 

Group 

Seismicity Size Framing 

Connectors 

Sidelaps Comput 

ed 

ACMR 

Accept 

able 

ACMR 

Pass/Fail 

PG-5E High Large Welds Welds / 

button 

punches 

1.71 

2.30 

Fail 

PG-6E High Large PAFs / screws Screws 1.87 Fail 

PG-7E High Small Welds Button 

punches 

2.23 Fail 

PG-8E High Small PAFs / screws Screws 1.92 Fail 

PG-9E Moderate Large Welds / PAFs/ 

screws 

Screws 1.95 Fail 

PG-10E Moderate Large Welds / PAFs/ 

screws 

Welds 1.88 Fail 

PG-11E Moderate Small Welds /PAFs / 

screws 

Screws 1.86 Fail 

The results indicate that the current design rules are not adequate based on the FEMA P695 

methodology for both wood structural panel and steel deck diaphragms. Therefore, a modified or new 

design procedure is needed. The results also indicate that if a single response modification coefficient 

were to be used for the diaphragm parallel to current design of SFRS, its value would need to be less 

than 4. For the wood diaphragms, considering that the lowest ratio of ACMR to acceptable ACMR 

(1.98/2.3) is 0.86 leads to the expectation that current design using a response modification coefficient R 

(0.86x4) of about 3 to 3.5 is appropriate. For steel deck diaphragms, consider that the lowest ratio of 

ACMR to acceptable ACMR (1.71/2.3) is 0.74 leads to the expectation that current design using an Rcoefficient of about 2.5 to 3 may be appropriate for 20 and 22 ga steel deck diaphragms. However, 

analyses should be performed to determine the appropriate R values. This expectation is not appropriate 

for steel deck diaphragms with gages of 18 or thicker as they are anticipated to result in less ductile 

diaphragms. 

Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure 125 
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The analysis results also showed that the diaphragm’s inelastic behavior was concentrated at the ends of 

the diaphragm. The global ductility of the diaphragm is lower than the ductility of the connectors 

because connector yielding is not spreading well into the diaphragm. Response of these buildings would 

improve if a means of spreading connection yielding deeper into the diaphragm were developed. For the 

steel deck diaphragms, the response would also be improved if the post-yield stiffness of the connector 

were positive to a larger displacement value. Tests indicate positive post-yield stiffness only to 1 or 2 

mm. The exact displacement needed for improved behavior is not known at this time but a value such as 

10 mm is expected to be more than adequate. 

D.3 Fundamental Period of the Archetypes 

The results of the simplified building model analyses show that the fundamental period of each 

archetype is dominated by the diaphragm response. The elastic fundamental periods for the archetypes 

were obtained from the analyses and are included in Tables F1 and F3 of Appendix F. A summary of 

the elastic periods are included in Table D3. 

Table D3. Summary of Elastic Periods for Archetypes 

Wood diaphragm span length Period for high-seismic 

archetypes 

Period for moderate-seismic 

archetypes 

400 ft 0.85 to 0.87 sec 0.90 to 0.92 sec 

200 ft 0.49 to 0.54 sec 0.55 to 0.58 sec 

100 ft 0.36 to 0.38 sec 0.43 to 0.45 sec 

Steel diaphragm span length 

400 ft 0.49 to 0.56 sec 0.61 to 0.73 sec 

200 ft 0.35 to 0.42 sec 0.51 to 0.59 sec 

100 ft 0.21 to 0.26 sec 0.28 to 0.33 sec 

Using the elastic periods from the analyses of the high-seismic wood diaphragm archetypes and the 

high-seismic steel deck diaphragm archetypes, empirical formulas were developed for the fundamental 

periods of wood and steel deck diaphragms, respectively. The following formula is proposed for 

computing the fundamental period, Twood, of the wood diaphragm buildings with concrete or masonry 

shear walls. 

! = !.!!"#

!""# h! + 0.002!f Equation (D1) !!

126 Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure
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Where, Lf is the diaphragm span in feet between vertical elements of the seismic-force-resisting system, 

Cw is a coefficient defined by Equation 12.8-10 in ASCE 7-10 

!! = !"" ! !!

!!! ! ! Equation (D2) !! !!!.!" !

!!

A is the web area of the in-plane shear wall i in ft2

B is the area of the base of the building in ft2

, Ai , Di is 

the length of the in-plane shear wall i in ft2, and h 2

i is the height of the in-plane shear wall i in ft , hn is 

the height of the roof framing in ft. 

The following formula is proposed for computing the fundamental period, Tsteel, of the steel deck 

diaphragm buildings. 

! = !.!!"#

!"##$ h! + 0.001!f Equation (D3) !!

The proposed period equations are plotted along with the periods determined from the simplified 

building model analyses in Figure D2 for the wood diaphragm archetypes and in Figure D3 for the steel 

diaphragm archetypes. Although the periods are derived from analyses of single-span diaphragms, the 

deformations were shear dominated. Therefore, the period equations are valid for multi-span 

diaphragms. The archetypes used to develop these formulas included heavy walls. A study on the 

applicability of these formulas to buildings with light walls is recommended. 

Figure D2. Comparison of fundamental periods from analyses of wood panel archetypes to those predicted by 

the proposed formula (Equation D1), ASCE 7-10 equations, a best fit curve, and those proposed by Freeman et. 

al (1995). 

Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure 127 
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Figure D3. Comparison of fundamental periods from analyses of steel deck archetypes to those predicted by 

the proposed formula (Equation D3), ASCE 7-10 equations, and a best fit curve. 

128 Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure
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APPENDIX E Description of Archetypes for Current Design 

Procedure 

Refer to Koliou (2014) for additional information about the archetypes. 

Table E1. Archetype Descriptions for Wood Diaphragms 

Archetype ID Diaphragm 

construction 

Building 

size 

Diaphragm 

aspect 

ratio 

Building 

dimensions 

(ft) 

Connector 

type 

(F=framing 

S=sidelap) 

Seismic 

design 

category 

HWL_21_N_OSB_RW4_04 Wood Large 2:1 400x200 Common 

nails Dmax 

HWL_12_N_OSB_RW4_02 Wood Large 1:2 200x400 Common 

nails Dmax 

HWL_11_N_OSB_RW4_01 Wood Large 1:1 400x400 Common 

nails Dmax 

HWS_21_N_OSB_RW4_01 Wood Small 2:1 200x100 Common 

nails Dmax 

HWS_12_N_OSB_RW4_01 Wood Small 1:2 100x200 Common 

nails Dmax 

HWS_11_N_OSB_RW4_01 Wood Small 1:1 100x100 Common 

nails Dmax 

HWS_11_N_OSB_RW4_02 Wood Small 1:1 100x100 Common 

nails Dmax 

MWL_11_N_OSB_RW4_01 Wood Large 1:1 400x400 Common 

nails Cmax 

MWL_21_N_OSB_RW4_01 Wood Large 2:1 400x200 Common 

nails Cmax 

MWL_12_N_OSB_RW4_01 Wood Large 1:2 200x400 Common 

nails Cmax 

MWS_11_N_OSB_RW4_01 Wood Small 1:1 100x100 Common 

nails Cmax 

MWS_21_N_OSB_RW4_01 Wood Small 2:1 200x100 Common 

nails Cmax 

MWS_12_N_OSB_RW4_01 Wood Small 1:2 100x200 Common 

nails Cmax 

Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure 129 
FEDERAL EMERGENCY MANAGEMENT AGENCY

Table E2. Archetype Descriptions for Steel Diaphragms for High-Seismic Risk – 

Existing Design Archetype Designation Diaphragm Dimensions Zone Zone Width (ft) Connector Pattern / Deck Gage Framing Connectors Sidelap Connectors Sidelap Spacing High Seismicity – Large Buildings HSL_11_P_S_RW4 400 x 400 ft 3 56 36/11 – 22 ga PAF #10 screw 6 in. 2 24 36/9 – 22 ga PAF #10 screw 9 in. 1 120 36/9 – 22 ga PAF #10 screw 18 in. 

HSL_11_W_WB_RW4 400 x 400 ft 3 56 36/7 – 22 ga 1/2 in. dia. welds TSW 12 in. 

2 24 36/7 – 22 ga 1/2 in. dia. welds BP 12 in. 

1 120 36/7 – 22 ga 1/2 in. dia. welds BP 24 in. 

HSL_21_W_WB_RW4_01 400 x 200 ft 3 50 36/7 – 22 ga 

1/2 in. dia. Effective 

area welds (5/8 and

3/4 in. dia. at the 

surface) 

TSW 6 in. 

2 54 36/7 – 22 ga 

1/2 in. dia. Effective 

area welds (5/8 and

3/4 in. dia. at the 

surface) 

TSW 12 in. 

1 96 36/7 – 22 ga 

1/2 in. dia. Effective 

area welds (5/8 and

3/4 in. dia. at the 

surface) 

BP 12 in. 

HSL_21_P_S_RW4_01 400 x 200 ft 3 50 36/9 – 20 ga PAF #10 screws 3 in. 

2 60 36/9 – 22 ga PAF #10 screws 6 in. 

1 90 36/5 – 22 ga PAF #10 screws 6 in. 

HSL_11_S_S_RW4 400 x 400 ft 3 66 36/11 – 22 ga 

#12 or #14 HWH

self-drilling screws by

Hilti 

#10 screws 3 in. 

2 24 36/9 – 22 ga 

#12 or #14 HWH

self-drilling screws by

Hilti 

#10 screws 6 in. 

130 
Table E2. Archetype Descriptions for Steel Diaphragms for High-Seismic Risk – 

Existing Design (cont.) Archetype Designation Diaphragm Dimensions Zone Zone Width (ft) Connector Pattern / Deck Gage Framing Connectors Sidelap Connectors Sidelap Spacing 1 120 36/9 – 22 ga #12 or #14 HWH self-drilling screws by Hilti #10 screws 9 in. HSL_12_W_WB_RW4 Refer to HSL_21_W_WB for design HSL_12_P_S_RW4 Refer to HSL_21_P_S for design High Seismicity – Small Buildings

HSS_11_W_B_RW4 100 x 100 ft 3 50 36/5 – 22 ga 

1/2 in. dia effective 

welds (5/8 in. and 3/4 

in. at the surface) 

BP 12 in. 

2 50 36/5 – 22 ga 

1/2 in. dia. effective 

welds (5/8 in. and 3/4 

in. at the surface) 

BP 12 in. 

1 50 36/5 – 22 ga 

1/2 in. dia. effective 

welds (5/8 in. and 3/4 

in. at the surface) 

BP 12 in. 

HSS_21_W_WB_RW4 200 x 100 ft 3 0 36/7 – 22 ga 

1/2 in. dia. effective 

welds (5/8 in. and 3/4 

in. dia. puddle welds

at the surface) 

TSW 9 in. 

2 40 36/7 – 22 ga 

1/2 in. dia. effective 

welds (5/8 in. and 3/4 

in. dia. puddle welds

at the surface) 

TSW 9 in. 

131 
Table E2. Archetype Descriptions for Steel Diaphragms for High-Seismic Risk – 

Existing Design (cont.) Archetype Designation Diaphragm Dimensions Zone Zone Width (ft) Connector Pattern / Deck Gage Framing Connectors Sidelap Connectors Sidelap Spacing 1 60 36/7 – 22 ga 1/2 in. dia. effective welds (5/8 in. and 3/4 in. dia. puddle welds at the surface) BP 12 in. HSS_12_W_WB_RW4 Refer to HSS_21_W_WB_RW4 HSS_11_P_S_RW4 100 x 100 ft 3 0 36/9 – 22 ga PAF #10 screws 18 in. 

2 0 36/9 – 22 ga PAF #10 screws 18 in. 

1 50 36/9 – 22 ga PAF #10 screws 18 in. 

HSS_11_S_S_RW4 100 x 100 ft 3 0 36/9 – 22 ga #12 #10 screws 9 in. 

2 0 36/9 – 22 ga #12 #10 screws 9 in. 

1 50 36/9 – 22 ga #12 #10 screws 9 in. 

HSS_21_P_S_RW4 200 x 100 ft 3 0 36/9 – 22 ga PAF #10 screws 3 in. 

2 40 36/9 – 22 ga PAF #10 screws 3 in. 

1 60 36/9 – 22 ga PAF #10 screws 9 in. 

HSS_12_P_S_RW4 Refer to HSS_21_P_S_RW4HSS_21_S_S_RW4 200 x 100 ft 3 0 36/11 – 20 ga #12 #10 screws 3 in. 

2 40 36/11 – 20 ga #12 #10 screws 3 in. 

1 60 36/9 – 22 ga #12 #10 screws 6 in. 

HSS_12_S_S_RW4 Refer to HSS_21_S_S_RW4 

132 
Table E3. Archetype Descriptions for Steel Diaphragms for Moderate-Seismic Risk – 

Existing Design Archetype Designation Diaphragm Dimensions Zone Zone Width (ft) Connector Pattern / Deck Gage Framing Connectors Sidelap Con- nectors Sidelap Spacing Moderate Seismicity – Large Buildings MSL_21_P_S_RW4 400 x 200 ft 3 32 36/9 – 22 ga PAF #10 screws 15 in. 2 36 36/9 – 22 ga PAF #10 screws 27 in. 1 132 36/5 – 22 ga PAF #10 screws 15 in. 

MSL_12_P_S_RW4 Refer to MSL_21_P_S_RW4MSL_21_S_S_RW4 400 x 200 ft 3 32 36/9 – 22 ga #12 Hilti HWH

screws 

#10 screws 6 in. 

2 36 36/9 – 22 ga #12 Hilti HWH

screws 

#10 screws 12 in. 

1 132 36/5 – 22 ga #12 Hilti HWH

screws 

#10 screws 9 in. 

MSL_12_S_S_RW4 Refer to MSL_21_S_S_RW4MSL_21_W_S_RW4 400 x 200 ft 3 32 36/7 – 22 ga 3/4 in. welds #10 screws 6 in. 

2 36 36/7 – 22 ga 3/4 in. welds #10 screws 12 in. 

1 132 36/5 – 22 ga 5/8 in. welds #10 screws 9 in. 

MSL_12_W_S_RW4 Refer to MSL_21_W_S_RW4MSL_11_P_S_RW4 400 x 400 ft 3 32 36/5 – 22 ga PAF #10 screws 12 in. 

2 36 36/5 – 22 ga PAF #10 screws 21 in. 1 132 36/5 – 22 ga PAF #10 screws 36 in. 

MSL_11_S_S_RW4 400 x 400 ft 3 32 36/5 – 22 ga #12 Hilti HWH

screws 

#10 screws 9 in. 

2 36 36/5 – 22 ga #12 Hilti HWH

screws 

#10 screws 12 in. 

1 132 36/5 – 22 ga #12 Hilti HWH

screws 

#10 screws 21 in. 

MSL_11_W_S_RW4 400 x 400 ft 3 32 36/5 – 22 ga 5/8 in. dia. welds #10 screws 9 in. 

2 36 36/5 – 22 ga 5/8 in. dia. welds #10 screws 18 in. 1 132 36/5 – 22 ga 5/8 in. dia. welds #10 screws 21 in. 

MSL_21_W_W_RW4_01 400 x 200 ft 3 40 36/7 – 22 ga 3/4 in. dia. welds TSW 18 in. 

133 
Table E3. Archetype Descriptions for Steel Diaphragms for Moderate-Seismic Risk – 

Existing Design (cont.) Archetype Designation Diaphragm Dimensions Zone Zone Width (ft) Connector Pattern / Deck Gage Framing Connectors Sidelap Con- nectors Sidelap Spacing 2 40 36/5 – 22 ga 3/4 in. dia. welds TSW 24 in. 1 120 36/5 – 22 ga 3/4 in. dia. welds TSW 36 in. MSL_12_W_W_RW4_01 Refer to MSL_21_W_W_RW4_01 MSL_11_W_W_RW4_01 400 x 400 ft 3 40 36/5 – 22 ga 3/4 in. dia. welds TSW 36 in. 2 40 36/4 – 22 ga 3/4 in. dia. welds TSW 36 in. 1 120 36/4 – 22 ga 3/4 in. dia. welds TSW 72 in. Moderate Seismicity – Small Buildings

MSS_11_S_S_RW4 100 x 100 ft 3 0 36/5 – 22 ga #12 HWH Hilti screw #10 screws 36 in. 

2 0 36/5 – 22 ga #12 HWH Hilti screw #10 screws 36 in. 1 50 36/5 – 22 ga #12 HWH Hilti screw #10 screws 36 in. 

MSS_11_P_S_RW4 100 x 100 ft 3 0 36/5 – 22 ga PAF #10 screws 36 in. 

2 0 36/5 – 22 ga PAF #10 screws 36 in. 1 50 36/5 – 22 ga PAF #10 screws 36 in. 

MSS_11_W_S_RW4 100 x 100 ft 3 0 36/5 – 22 ga 5/8 in. puddle welds #10 screws 36 in. 

2 0 36/5 – 22 ga 5/8 in. puddle welds #10 screws 36 in. 1 50 36/5 – 22 ga 5/8 in. puddle welds #10 screws 36 in. 

MSS_21_S_S_RW4 200 x 100 ft 3 22 36/7 – 22 ga #12 HWH Hilti screw #10 screws 9 in. 

2 0 36/5 – 22 ga #12 HWH Hilti screw #10 screws 12 in. 1 78 36/5 – 22 ga #12 HWH Hilti screw #10 screws 12 in. 

MSS_12_S_S_RW4 Refer to MSS_21_S_S_RW4MSS_21_P_S_RW4 200 x 100 ft 3 22 36/7 – 22 ga PAF #10 screws 12 in. 

2 0 36/5 – 22 ga PAF #10 screws 21 in. 1 78 36/5 – 22 ga PAF #10 screws 21 in. 

MSS_12_P_S_RW4 Refer to MSS_21_P_S_RW4MSS_21_W_S_RW4 200 x 100 ft 3 22 36/7 – 22 ga 5/8 in. puddle welds #10 screws 9 in. 

2 0 36/5 – 22 ga 5/8 in. puddle welds #10 screws 12 in. 1 78 36/5 – 22 ga 5/8 in. puddle welds #10 screws 12 in. 

MSS_12_W_S_RW4 Refer to MSS_21_W_S_RW4MSL_21_P_S_RW4 400 x 200 ft 3 32 36/9 – 22 ga PAF #10 screws 15 in. 

134 
Table E3. Archetype Descriptions for Steel Diaphragms for Moderate-Seismic Risk 

– Existing Design (cont.) Archetype Designation Diaphragm Dimensions Zone Zone Width (ft) Connector Pattern / Deck Gage Framing Connectors Sidelap Con- nectors Sidelap Spacing 2 36 36/9 – 22 ga PAF #10 screws 27 in. 1 132 36/5 – 22 ga PAF #10 screws 15 in. MSL_12_P_S_RW4 Refer to MSL_21_P_S_RW4 MSL_21_S_S_RW4 400 x 200 ft 3 32 36/9 – 22 ga #12 Hilti HWH screws #10 screws 6 in. 2 36 36/9 – 22 ga #12 Hilti HWH screws #10 screws 12 in. 1 132 36/5 – 22 ga #12 Hilti HWH

screws 

#10 screws 9 in. 

MSL_12_S_S_RW4 Refer to MSL_21_S_S_RW4MSL_21_W_S_RW4 400 x 200 ft 3 32 36/7 – 22 ga 3/4 in. welds #10 screws 6 in. 

2 36 36/7 – 22 ga 3/4 in. welds #10 screws 12 in. 

1 132 36/5 – 22 ga 5/8 in. welds #10 screws 9 in. 

MSL_12_W_S_RW4 Refer to MSL_21_W_S_RW4 

135 
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APPENDIX F – FEMA P695 Evaluation Results for Current Design Procedure 

Results for the FEMA P695 collapse analyses for the current design procedure are presented in 

this appendix. The following notations and abbreviations are used in the tables: 

ACMR Adjusted Collapse Margin Ratio where: ACMR = SSFi × CMRi

BDR Building Drift Ratio where: BDR(%) = DDR(%) + WDR(%)

CMR Collapse Margin Ratio where: CMRi =

SCT

SMT

DE Design Earthquake

DDR Diaphragm Drift Ratio (%) where: DDR(%) =

Xmid,roof

Lf

2

⁄

× 100

Xmid,roof is the diaphragm deflection at mid length

Lf is the diaphragm span in feet

MCE Maximum Considered Earthquake

SSF Spectral Shape Function

SCT [T] Median collapse intensity obtained from nonlinear dynamic analysis at the fundamental 

elastic period

SMT [T] Ground motion spectral demand at maximum considered earthquake (MCE) intensity 

level at the fundamental elastic period

WDR(%) In-plane Wall Drift Ratio where: WDR(%) =

Xin−plane walls

hwall

× 100

Xin-plane walls is the deflection at the roof level of the in-plane walls

hwall is the height of roof above the foundation

μT Period based ductility where: μT =

δu

δy,eff

u is the ultimate building drift ratio (BDR)

y,eff is the effective yield building drift ratio (BDR)

Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure 137 
Table F1. Summary of collapse results for RWFD buildings incorporating wood roof 

diaphragm archetype designs Archetype ID Design configuration Pushover and IDA results Relevant analysis parameters Building size Diaphragm aspect ratio Diaphragm construction Seismic SDC S MT [T] (g) S CT [T] (g) CMR Period (sec) Median BDR @ DE (%) Median BDR @ MCE (%) Performance Group No. PG-1E (Wood, Large Building, Existing Design) HWL_21_N_OSB_RW4_07 Large 2:1 Wood Panelized D max 1.06 2.00 1.89 0.85 0.29 0.55 HWL_12_N_OSB_RW4_02 Large 1:2 Wood Panelized D max 1.50 3.36 2.24 0.49 0.42 0.64 HWL_11_N_OSB_RW4_01 Large 1:1 Wood Panelized D max 1.05 1.68 1.60 0.87 0.32 0.53 

Performance Group No. PG-2E (Wood, Small Building, Existing Design)

HWS_21_N_OSB_RW4_01 Small 2:1 Wood Panelized D max 1.41 1.98 1.40 0.54 0.56 1.16 

HWS_12_N_OSB_RW4_01 Small 1:2 Wood Panelized D max 1.50 2.64 1.76 0.38 0.72 1.72 HWS_11_N_OSB_RW4_01 Small 1:1 Wood Panelized D max 1.50 2.21 1.47 0.36 0.65 1.68 HWS_11_N_OSB_RW4_02 Small 1:1 Wood Panelized D max 1.50 2.32 1.55 0.37 0.68 1.63 

Performance Group No. PG-3E (Wood, Large Building, Existing Design)

MWL_21_N_OSB_RW4_01 Large 2:1 Wood Panelized C max 0.50 1.28 2.56 0.90 0.31 0.52 

MWL_12_N_OSB_RW4_01 Large 1:2 Wood Panelized C max 0.75 1.75 2.33 0.55 0.39 0.63 MWL_11_N_OSB_RW4_01 Large 1:1 Wood Panelized C max 0.51 1.09 2.14 0.92 0.35 0.55 

Performance Group No. PG-4E (Wood, Small Building, Existing Design)

MWS_21_N_OSB_RW4_01 Small 2:1 Wood Panelized C max 0.75 1.15 1.50 0.58 0.51 0.89 

MWS_12_N_OSB_RW4_01 Small 1:2 Wood Panelized C max 0.75 1.35 1.72 0.43 0.55 0.98 MWS_11_N_OSB_RW4_01 Small 1:1 Wood Panelized C max 0.75 1.47 1.96 0.45 0.59 1.15 

138 
Table F2. Adjusted collapse margin ratios and acceptable collapse margin ratios for 

RWFD buildings incorporating wood roof diaphragm archetype designs Archetype ID Design configuration Collapse margin parameters Acceptance check Building size Diaphragm aspect ratio Diaphragm construction Seismic SDC CMR μ Τ SSF ACMR Accept. ACMR Pass/Fail Performance Group No. PG-1E (Wood, Large Building, Existing Design) HWL_21_N_OSB_RW4_07 Large 2:1 Wood D max 1.89 8.07 1.43 2.70 1.73 Pass HWL_12_N_OSB_RW4_02 Large 1:2 Wood D max 2.24 8.95 1.36 3.05 1.73 Pass HWL_11_N_OSB_RW4_01 Large 1:1 Wood D max 1.60 8.42 1.43 2.29 1.73 Pass Mean of Performance Group: 1.91 8.48 1.41 2.68 2.30 Pass Performance Group No. PG-2E (Wood, Small Building, Existing Design) HWS_21_N_OSB_RW4_01 Small 2:1 Wood D max 1.40 7.20 1.31 1.84 1.73 Pass HWS_12_N_OSB_RW4_01 Small 1:2 Wood D max 1.76 8.95 1.36 2.39 1.73 Pass HWS_11_N_OSB_RW4_01 Small 1:1 Wood D max 1.55 8.32 1.36 2.10 1.73 Pass HWS_11_N_OSB_RW4_02 Small 1:1 Wood D max 1.55 8.51 1.36 2.11 1.73 Pass Mean of Performance Group: 1.57 8.25 1.35 2.11 2.30 Fail Performance Group No. PG-3E (Wood, Large Building, Existing Design) MWL_21_N_OSB_RW4_01 Large 2:1 Wood C max 2.56 8.15 1.14 2.92 1.73 Pass MWL_12_N_OSB_RW4_01 Large 1:2 Wood C max 2.33 8.79 1.14 2.66 1.73 Pass MWL_11_N_OSB_RW4_01 Large 1:1 Wood C max 2.14 8.54 1.14 2.44 1.73 Pass Mean of Performance Group: 2.34 8.49 1.14 2.67 2.30 Pass Performance Group No. PG-4E (Wood, Small Building, Existing Design)

MWS_21_N_OSB_RW4_01 Small 2:1 Wood C max 1.50 8.05 1.16 1.74 1.73 Pass MWS_12_N_OSB_RW4_01 Small 1:2 Wood C max 1.72 8.49 1.14 1.96 1.73 Pass 

MWS_11_N_OSB_RW4_01 Small 1:1 Wood C max 1.96 8.09 1.14 2.23 1.73 Pass 

Mean of Performance Group: 1.73 8.21 1.15 1.98 2.30 Fail

139 
Table F3. Summary of collapse results for RWFD buildings incorporating steel roof 

diaphragm archetype designs Archetype ID Design configuration Pushover and IDA results Relevant analysis pa- rameters Building size Diaphragm aspect ratio Diaphragm construction Seismic SDC S MT [T] (g) S CT [T] (g) CMR Period (sec) Median BDR @ DE (%) Median BDR @ MCE (%) Performance Group No. PG-5E (Steel, Large Building, Welds and Button Punches as sidelap Connectors, Existing Design) HSL_21_W_WB_RW4_01 Large 2:1 Steel (WR Deck) D max 1.50 1.56 0.99 0.52 0.19 0.45 HSL_12_W_WB_RW4_01 Large 1:2 Steel (WR Deck) D max 1.50 2.85 1.90 0.39 0.28 0.71 HSL_11_W_WB_RW4_01 Large 1:1 Steel (WR Deck) D max 1.50 1.43 0.95 0.49 0.13 0.42 

Performance Group No. PG-6E (Steel, Large Building, Screws as sidelap Connectors, Existing Design)

HSL_21_P_S_RW4_01 Large 2:1 Steel (WR Deck) D max 1.50 1.85 1.23 0.54 0.15 0.33 

HSL_12_P_S_RW4_01 Large 1:2 Steel (WR Deck) D max 1.50 3.10 2.07 0.41 0.25 0.56 

HSL_11_P_S_RW4_01 Large 1:1 Steel (WR Deck) D max 1.50 1.69 1.13 0.56 0.18 0.34 HSL_11_S_S_RW4_01 Large 1:1 Steel (WR Deck) D max 1.50 1.73 1.15 0.51 0.16 0.29 

Performance Group No. PG-7E (Steel, Small Building, Button Punches as sidelap Connectors, Existing Design)

HSS_11_W_B_RW4_01 Small 1:1 Steel (WR Deck) D max 1.50 2.59 1.73 0.21 0.17 0.39 

HSS_21_W_B_RW4_01 Small 2:1 Steel (WR Deck) D max 1.50 2.13 1.42 0.35 0.21 0.44 HSS_12_W_B_RW4_01 Small 1:2 Steel (WR Deck) D max 1.50 2.85 1.90 0.26 0.15 0.35 

Performance Group No. PG-8E (Steel, Small Building, Screws as sidelap Connectors, Existing Design)

HSS_11_P_S_RW4_01 Small 1:1 Steel (WR Deck) D max 1.50 2.33 1.55 0.23 0.16 0.41 

HSS_11_S_S_RW4_01 

Small 

1:1 

Steel

(WR Deck) D max 1.50 2.15 1.43 0.25 0.14 0.36 

140 
Table F3. Summary of collapse results for RWFD buildings incorporating steel roof 

diaphragm archetype designs (cont.) Archetype ID Design configuration Pushover and IDA results Relevant analysis pa- rameters Building size Diaphragm aspect ratio Diaphragm construction Seismic SDC S MT [T] (g) S CT [T] (g) CMR Period (sec) Median BDR @ DE (%) Median BDR @ MCE (%) HSS_21_P_S_RW4_01 Small 2:1 Steel (WR Deck) D max 1.50 1.99 1.33 0.37 0.19 0.35 HSS_12_P_S_RW4_01 Small 1:2 Steel (WR Deck) D max 1.50 2.56 1.71 0.24 0.17 0.31 HSS_21_S_S_RW4_01 Small 2:1 Steel (WR Deck) D max 1.50 1.87 1.25 0.42 0.15 0.42 HSS_12_S_S_RW4_01 Small 1:2 Steel (WR Deck) D max 1.50 2.13 1.42 0.22 0.14 0.39 Performance Group No. PG-9E (Steel, Large Building, Screws as sidelap Connectors, Existing Design)

MSL_21_P_S_RW4_01 Large 2:1 Steel (WR Deck) D max 0.68 0.93 1.35 0.66 0.29 0.41 

MSL_12_P_S_RW4_01 Large 1:2 Steel (WR Deck) D max 0.75 1.50 2.01 0.53 0.19 0.33 MSL_21_S_S_RW4_01 Large 2:1 Steel (WR Deck) D max 0.63 0.96 1.52 0.71 0.22 0.35 MSL_12_S_S_RW4_01 Large 1:2 Steel (WR Deck) D max 0.75 1.41 1.88 0.55 0.21 0.32 MSL_21_W_S_RW4_01 Large 2:1 Steel (WR Deck) D max 0.62 1.15 1.41 0.73 0.20 0.31 MSL_12_W_S_RW4_01 Large 1:2 Steel (WR Deck) D max 0.75 1.47 1.96 0.52 0.23 0.34 MSL_11_P_S_RW4_01 Large 1:1 Steel (WR Deck) D max 0.70 1.27 1.81 0.65 0.24 0.39 

MSL_11_S_S_RW4_01 Large 1:1 Steel (WR Deck) D max 0.70 1.10 1.58 0.65 0.21 0.45 

MSL_11_W_S_RW4_01 Large 1:1 Steel (WR Deck) D max 0.67 1.11 1.66 0.68 0.25 0.47 

141 
Table F3. Summary of collapse results for RWFD buildings incorporating steel roof 

diaphragm archetype designs (cont.) Archetype ID Design configuration Pushover and IDA results Relevant analysis pa- rameters Building size Diaphragm aspect ratio Diaphragm construction Seismic SDC S MT [T] (g) S CT [T] (g) CMR Period (sec) Median BDR @ DE (%) Median BDR @ MCE (%) Performance Group No. PG-11E (Steel, Small Building, Screws as sidelap Connectors, Existing Design) Performance Group No. PG-10E (Steel, Large Building, Welds as sidelap Connectors, Existing Design) MSL_21__W_W_RW4_01 Large 2:1 Steel (WR Deck) C max 0.73 1.02 1.39 0.62 0.19 0.35 MSL_12__W_W_RW4_01 Large 1:2 Steel (WR Deck) C max 0.75 1.50 1.99 0.51 0.24 0.41 MSL_11__W_W_RW4_01 Large 1:1 Steel (WR Deck) C max 0.74 1.13 1.52 0.61 0.18 0.36 Performance Group No. PG-11E (Steel, Small Building, Screws as sidelap Connectors, Existing Design)

MSS_11_S_S_RW4_01 Small 1:1 Steel (WR Deck) C max 0.75 1.26 1.67 0.32 0.15 0.36 

MSS_11_P_S_RW4_01 Small 1:1 Steel (WR Deck) C max 0.75 1.34 1.78 0.30 0.17 0.41 MSS_11_W_S_RW4_01 Small 1:1 Steel (WR Deck) C max 0.75 0.98 1.30 0.28 0.14 0.37 MSS_21_S_S_RW4_01 Small 2:1 Steel (WR Deck) C max 0.75 1.05 1.39 0.54 0.19 0.48 MSS_12_S_S_RW4_01 Small 1:2 Steel (WR Deck) C max 0.75 1.39 1.85 0.31 0.15 0.29 MSS_21_P_S_RW4_01 Small 2:1 Steel (WR Deck) C max 0.75 1.17 1.55 0.59 0.20 0.44 MSS_12_P_S_RW4_01 Small 1:2 Steel (WR Deck) C max 0.75 1.48 1.97 0.28 0.16 0.32 MSS_21_W_S_RW4_01 Small 2:1 Steel (WR Deck) C max 0.75 1.08 1.43 0.55 0.18 0.36 MSS_12_W_S_RW4_01 Small 1:2 Steel (WR Deck) C max 0.75 1.28 1.71 0.33 0.17 0.31 

142 
Table F4. Computed and acceptable adjusted collapse margin ratios for RWFD 

buildings incorporating steel roof diaphragm archetype designs Archetype ID Design configuration Collapse margin parameters Acceptance check Building Size Diaphragm aspect ratio Diaphragm construction Seismic SDC CMR μ Τ SSF ACMR Accept. ACMR Pass/Fail Performance Group No. PG-5E (Steel, Large Building, Welds and Button Punches as sidelap Connectors, Existing Design) HSL_21_W_WB_RW4_01 Large 2:1 Steel D max 0.99 8.09 1.34 1.33 1.73 Fail HSL_12_W_WB_RW4_01 Large 1:2 Steel D max 1.90 8.26 1.33 2.53 1.73 Pass HSL_11_W_WB_RW4_01 Large 1:1 Steel D max 0.95 8.16 1.33 1.27 1.73 Fail Mean of Performance Group: 1.28 8.17 1.33 1.71 2.30 Fail Performance Group No. PG-6E (Steel, Large Building, Screws as sidelap Connectors, Existing Design) HSL_21_P_S_RW4_01 Large 2:1 Steel D max 1.23 8.24 1.35 1.67 1.73 Fail HSL_12_P_S_RW4_01 Large 1:2 Steel D max 2.07 8.14 1.33 2.75 1.73 Pass HSL_11_P_S_RW4_01 Large 1:1 Steel D max 1.13 8.26 1.36 1.53 1.73 Fail HSL_11_S_S_RW4_01 Large 1:1 Steel D max 1.15 8.01 1.33 1.53 2.73 Fail Mean of Performance Group: 1.40 8.16 1.34 1.87 2.30 Fail Performance Group No. PG-7E (Steel, Small Building, Button Punches as sidelap Connectors, Existing Design) HSS_11_W_B_RW4_01 Small 1:1 Steel D max 1.73 7.94 1.32 2.28 1.73 Pass HSS_21_W_B_RW4_01 Small 2:1 Steel D max 1.42 8.05 1.33 1.89 1.73 Pass HSS_12_W_B_RW4_01 Small 1:2 Steel D max 1.90 7.91 1.32 2.51 1.73 Pass Mean of Performance Group: 1.68 7.97 1.32 2.23 2.30 Fail Performance Group No. PG-8E (Steel, Small Building, Screws as sidelap Connectors, Existing Design)

HSS_11_P_S_RW4_01 Small 1:1 Steel D max 1.55 8.02 1.33 2.07 1.73 Pass 

HSS_11_S_S_RW4_01 Small 1:1 Steel D max 1.43 8.15 1.33 1.91 1.73 Pass HSS_21_P_S_RW4_01 Small 2:1 Steel D max 1.33 8.33 1.33 1.76 1.73 Pass HSS_12_P_S_RW4_01 Small 1:2 Steel D max 1.71 8.25 1.33 2.27 1.73 Pass HSS_21_S_S_RW4_01 Small 2:1 Steel D max 1.25 7.85 1.32 1.65 1.73 Fail 

HSS_12_S_S_RW4_01 Small 1:2 Steel D max 1.42 8.06 1.33 1.89 1.73 Pass 

Mean of Performance Group: 1.45 8.11 1.33 1.92 2.30 Fail 

143 
Table F4. Computed and acceptable adjusted collapse margin ratios for RWFD buildings 

incorporating steel roof diaphragm archetype designs (cont.) Archetype ID Design configuration Collapse margin parameters Acceptance check Building Size Diaphragm aspect ratio Diaphragm construction Seismic SDC CMR μ Τ SSF ACMR Accept. ACMR Pass/Fail Performance Group No. PG-9E (Steel, Large Building, Screws as sidelap Connectors, Existing Design) v MSL_21_P_S_RW4_01 Large 2:1 Steel C max 1.35 8.32 1.15 1.55 1.73 Fail MSL_12_P_S_RW4_01 Large 1:2 Steel C max 2.01 7.85 1.13 2.27 1.73 Pass MSL_21_S_S_RW4_01 Large 2:1 Steel C max 1.52 8.02 1.18 1.80 1.73 Pass MSL_12_S_S_RW4_01 Large 1:2 Steel C max 1.88 8.38 1.15 2.16 1.73 Pass MSL_21_W_S_RW4_01 Large 2:1 Steel C max 1.41 8.20 1.18 1.66 1.73 Fail MSL_12_W_S_RW4_01 Large 1:2 Steel C max 1.96 8.02 1.15 2.25 1.73 Pass MSL_11_P_S_RW4_01 Large 1:1 Steel C max 1.81 7.99 1.15 2.08 1.73 Pass MSL_11_S_S_RW4_01 Large 1:1 Steel C max 1.58 8.15 1.15 1.81 1.73 Pass MSL_11_W_S_RW4_01 Large 1:1 Steel C max 1.66 8.22 1.17 1.94 1.73 Pass Mean of Performance Group: 1.69 8.13 1.16 1.95 2.30 Fail Performance Group No. PG-10E (Steel, Large Buildings, Welds as Sidelap connectors, Existing Design) MSL_21__W_W_RW4_01 Large 2:1 Steel C max 1.39 7.76 1.15 1.59 1.73 Fail MSL_12__W_W_RW4_01 Large 1:2 Steel C max 1.99 8.15 1.14 2.27 1.73 Pass MSL_11__W_W_RW4_01 Large 1:1 Steel C max 1.52 8.09 1.16 1.76 1.73 Pass Mean of Performance Group: 1.63 8.00 1.15 1.88 2.30 Fail Performance Group No. PG-11E (Steel, Small Building, Screws as sidelap Connectors, Existing Design) MSS_11_S_S_RW4_01 Small 1:1 Steel C max 1.67 8.15 1.14 1.91 1.73 Pass 

MSS_11_P_S_RW4_01 Small 1:1 Steel C max 1.78 8.26 1.14 2.03 1.73 Pass MSS_11_W_S_RW4_01 Small 1:1 Steel C max 1.30 7.78 1.13 1.47 1.73 Fail 

MSS_21_S_S_RW4_01 Small 2:1 Steel C max 1.39 8.05 1.15 1.60 1.73 Fail MSS_12_S_S_RW4_01 Small 1:2 Steel C max 1.85 8.56 1.14 2.11 1.73 Pass 

MSS_21_P_S_RW4_01 Small 2:1 Steel C max 1.55 8.12 1.16 1.80 1.73 Pass MSS_12_P_S_RW4_01 Small 1:2 Steel C max 1.97 7.88 1.14 2.25 1.73 Pass MSS_21_W_S_RW4_01 Small 2:1 Steel C max 1.43 7.97 1.15 1.65 1.73 Fail 

MSS_12_W_S_RW4_01 Small 1:2 Steel C max 1.71 8.02 1.14 1.95 1.73 Pass 

Mean of Performance Group: 1.63 8.09 1.14 1.86 2.30 Fail 

144 
APPENDIX G Evaluation of Alternate Design Procedure 

To validate the alternate design procedure, archetype buildings were designed and P695 analyses were 

performed. 

G.1	 Description of Archetypes 

Evaluations were performed on archetypes designed for high and moderate seismic risk as defined 

in Appendix B. For these evaluations, archetypes were designed with either steel deck or wood panel 

diaphragms. Summary tables with detailed descriptions of diaphragm zones for the archetypes are in 

Appendix H for the wood diaphragms. The results of the steel deck diaphragms are included in Koliou 

(2014). The walls for these archetypes are reinforced-concrete wall panels 25 ft in length, 33 ft tall 

measured from the top of slab-on-grade, and 

9-1/4 in. thick for high seismic risk and 7-1/4 in. thick for moderate seismic risk. The roof level is at 30 ft 

above the top of slab-on-grade with parapet walls cantilevering 3 ft higher than the roof level. 

The archetypes are grouped by whether the diaphragm is large or small. The archetypes have plan aspect 

ratios of 1:1, 2:1 and 1:2. Large diaphragms are 400 ft long and either 400 ft or 200 ft wide. The small 

diaphragms with aspect ratios of 2:1 and 1:2 are 200 ft long by 100 ft wide, and for the 1:1 aspect ratios the 

diaphragms are 100 ft by 100 ft. The wood diaphragms are wood structural panels nailed to wood nailers 

that are attached to open web steel joists. 

G.2	 Summary of FEMA P695 Analysis Results for the Alternate Design 

Procedure 

Incremental Dynamic Analyses (IDA) (Vamvatsikos and Cornell, 2002) using the FEMA P695 Far Field 

Ground Motion Ensemble (FEMA P695, 2009) were performed using the simplified models to compute 

the median collapse intensity. Summaries of collapse results for individual wood diaphragm archetypes 

are included in Appendix I. Adjusted collapse margin ratios (ACMR) and acceptable ACMR values for 

the individual archetypes and the archetype groups are also included in Appendix I. The acceptable 

ACMR values are computed using the beta factors listed in Table D1. The combined uncertainty, βTotal, is 

computed as the square root sum of the squares of the individual uncertainties. For βTotal equal to 0.66, 

the acceptable ACMR is 1.73 and 2.30 for 20% and 10% probability of collapse at Maximum Considered 

Earthquake (MCE) ground motion, respectively. The acceptable ACMR applicable for the performance of 

individual archetypes is 1.73, and the ACMR of performance groups is 2.30. Summaries of the adjusted 

collapse margin ratio results for the performance groups of wood archetypes are provided in Table G1. 

The acceptable ACMR of at least 2.30 is achieved for each performance group. 

145 
Table G1. Summary of collapse margin ratio results for wood structural panel diaphragm archetype performance groups 

Performance 

Group Seismicity Size Computed ACMR Acceptable ACMR Pass/Fail 

PG-1N High Large 3.68 Pass 

PG-2N High Small 2.51 2.30 Pass 

PG-3N Moderate Large 3.90 Pass 

PG-4N Moderate Small 3.07 Pass 

The elastic periods for the archetypes designed in accordance with the alternate design procedure are 

listed in Table G2. In almost all cases the range of periods are 0 to 20% longer than the computed 

equivalent periods in Table D3 for the archetypes designed using the current code design procedure. 

The archetypes with larger diaphragms did better than the archetypes with small diaphragms, and the 

archetypes designed for moderate seismicity performed better than the ones designed for high seismicity. 

The small archetypes designed for high seismicity had the lowest ACMR. The range of fundamental 

elastic periods indicated in Table G2 is less than the transition period of 0.6 sec. for most of these 100 

and 200 ft long diaphragms. Thus, these archetypes are experiencing the short period issue described in 

Section D.1.2 regarding the FEMA P695 analyses for the archetypes using the current design procedure. 

The ACMR for small archetypes designed for moderate seismicity have longer periods than those 

designed for high seismicity and the transition period is only 0.4 sec. The short period issue is less of a 

factor for the small buildings designed for moderate seismicity. The elastic period values in Table G2 are 

all well above the transition period for the wood archetypes that are 400 ft long, thus, the high ACMRs 

for the large wood diaphragm performance groups, PG1 and PG3. 

Table G2. Summary of Elastic Periods for Archetypes Designed Using the Alternate 

Design Procedure 

Wood diaphragm span length Period for high-seismic archetypes 

Period for moderate-seismic archetypes 

400 ft 0.92 to 0.96 sec 0.92 to 0.93 sec 

200 ft 0.53 to 0.65 sec 0.57 to 0.61 sec 

100 ft 0.39 to 0.42 sec 0.45 to 0.46 sec 

The ranges of building drift ratios (BDR) for the performance groups are provided in Table G3. The BDR 

is the sum of the wall drift ratio (WDR) and the diaphragm drift ratio (DDR) and serves as a damage 

index. The WDR is computed as the in-plane wall deformation divided by the height of the roof, and the 

DDR is computed as the diaphragm displacement divided by one-half of the diaphragm span. In general 

shorter diaphragm spans result in larger BDRs, especially for the wood diaphragms. This likely results 

from the wall drift ratio (WDR) being a larger percentage of the BDR for the smaller buildings. 

146 
	 	 	 	 	 	 	

Table G3. Range of building drift ratios (BDRs) for the wood diaphragm performance 

groups 

Performance 

Group Seismicity Size Median BDR @ DE (%) Median BDR @ MCE (%) 

PG-1N High Large 0.34 to 0.52 0.54 to 0.81 

PG-2N High Small 0.79 to 0.85 1.14 to 1.31 

PG-3N Moderate Large 0.34 to 0.39 0.55 to 0.65 

PG-4N Moderate Small 0.53 to 0.61 0.90 to 1.21 

G.3	 Overstrength and Deflectio Amplificatio Factors for the Diaphragm

Values for the overstrength factor, Ωo, and deflection amplification factor, Cd, computed from the 

analysis results are included in Table I3. The smallest overstrength factor of all performance groups 

proposed for the system equal to 1.70, but rounded to half unit intervals, it would be equal to 2.0. The 

deflection amplification was computed as 5.6 in accordance with FEMA P695. Normally, deflection 

amplification factors are not taken greater than the response modification coefficient, R; however, in this 

case, an amplification factor higher than R was required because only 2% damping was assumed. An 

initial stiffness damping value of 2% of critical damping was chosen rather than the commonly assumed 

value of 5% for buildings because these buildings generally incorporate fewer non-structural components 

than conventional frame and wall buildings. Additional explanation is provided in Koliou [2014]. The 

deflection amplification factor was computed as Rdiaph/0.8 to account for the low damping. For Rdiaph 

= 4.5, Cd = 5.6. To test the validity of this value, the ratio of the median diaphragm drift caused by the 

design level ground motion to the median diaphragm drift at the “code” level force was computed for 

each archetype. The results are presented in Table I4. The mean ratio for Performance Group 1, which 

is large footprints and high seismic risk, was 3.3, which was the highest value for any of the performance 

groups. The highest ratio for an individual archetype was 4.3. These results indicate that the damping 

was more than 2% and that Cd equal to Rdiaph is appropriate. 

147 
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Appendix H Description of Archetypes for the Alternate Design 

Procedure 

H.1 Description of Archetypes for the Alternate Design Procedure 

Table H1. Archetype Descriptions for Wood Diaphragms for High- and ModerateSeismic Risk – Alternate Design Archetype ID Diaphragm Dimensions Zone Zone Width (ft) Sheathing 10d Common Nail Spacing Boundaries and Contin- uous Edges Other Edges Intermediate Field Area High-Seismicity Wood, Large Buildings HWL_21_N_OSB_RD4.5-1.5_01 HWL_12_N_OSB_RD4.5-1.5_01 400 x 200 ft End 40 ft 15/32” OSB 2 in. o.c. 3 in. o.c. 12 in. o.c. Middle 320 ft 15/32” OSB 2-1/2 in. o.c. 4 in. o.c. 12 in. o.c. HWL_21_N_OSB_RD4.5-1.5_02 HWL_12_N_OSB_RD4.5-1.5_02 400 x 200 ft End 40 ft 15/32” OSB 2 lines each at 2-1/2 in. o.c. 2 lines each at 4 in. o.c.* 12 in. o.c. Middle 320 ft 15/32” OSB 2-1/2 in. o.c. 4 in. o.c. 12 in. o.c. HWL_21_N_OSB_RD4.5_1.5_03 400 x 200 ft End 40 ft 15/32” OSB 2 lines each at 2-1/2 in. o.c. 2 lines each at 3 in. o.c.* 12 in. o.c. Middle 320 ft 15/32” OSB 2 in. o.c. 3 in. o.c. 12 in. o.c. HWL_21_N_OSB_RD4.5_1.5_04 400 x 200 ft End 40 ft 15/32” OSB 2 lines each at 2-1/2 in. o.c. 2 lines each at 4 in. o.c.* 12 in. o.c. Middle 320 ft 15/32” OSB 2-1/2 in. o.c. 4 in. o.c. 12 in. o.c. HWL_11_N_OSB_RD4.5-1.5_01 400 x 400 ft End 40 ft 15/32” OSB 2 in. o.c. 3 in. o.c.** 12 in. o.c. 

Middle 320 ft 15/32” OSB 4 in. o.c. 6 in. o.c. 12 in. o.c. 

149 
Table H1. Archetype Descriptions for Wood Diaphragms for High- and ModerateSeismic Risk – Alternate Design (cont.) Archetype ID Diaphragm Dimensions Zone Zone Width (ft) Sheathing 10d Common Nail Spacing Boundaries and Con- tinuous Edges Other Edges Intermediate Field Area High-Seismicity Wood, Large Buildings HWL_21_N_OSB_RD4.5-1.5_01 HWL_12_N_OSB_RD4.5-1.5_01 400 x 200 ft End 40 ft 15/32” OSB 2 in. o.c. 3 in. o.c. 12 in. o.c. Middle 320 ft 15/32” OSB 2-1/2 in. o.c. 4 in. o.c. 12 in. o.c. HWL_21_N_OSB_RD4.5-1.5_02 HWL_12_N_OSB_RD4.5-1.5_02 400 x 200 ft End 40 ft 15/32” OSB 2 lines each at 2-1/2 in. o.c. 2 lines each at 4 in. o.c.* 12 in. o.c. Middle 320 ft 15/32” OSB 2-1/2 in. o.c. 4 in. o.c. 12 in. o.c. HWL_21_N_OSB_RD4.5_1.5_03 400 x 200 ft End 40 ft 15/32” OSB 2 lines each at 2-1/2 in. o.c. 2 lines each at 3 in. o.c.* 12 in. o.c. Middle 320 ft 15/32” OSB 2 in. o.c. 3 in. o.c. 12 in. o.c. HWL_21_N_OSB_RD4.5_1.5_04 400 x 200 ft End 40 ft 15/32” OSB 2 lines each at 2-1/2 in. o.c. 2 lines each at 4 in. o.c.* 12 in. o.c. Middle 320 ft 15/32” OSB 2-1/2 in. o.c. 4 in. o.c. 12 in. o.c. HWL_11_N_OSB_RD4.5-1.5_01 400 x 400 ft End 40 ft 15/32” OSB 2 in. o.c. 3 in. o.c.** 12 in. o.c. Middle 320 ft 15/32” OSB 4 in. o.c. 6 in. o.c. 12 in. o.c. HWL_11_N_OSB_RD4.5-1.5_02 400 x 400 ft End 40 ft 15/32” OSB 2 lines each at 2-1/2 in. o.c. 2 lines each at 4 in. o.c.* 12 in. o.c. Middle 320 ft 15/32” OSB High-Seismicity Wood, Small Buildings HWS_21_N_OSB_RD4.5-1.5_01

HWS_12_N_OSB_RD4.5-1.5_01 200 x 100 ft End 20 ft 15/32” OSB 2 lines each at 2-1/2 in. o.c. 2 lines each at 3 in. o.c.* 12 in. o.c. 

Middle 160 ft 15/32” OSB 2 in. o.c. 3 in. o.c.** 12 in. o.c. 

150 
Table H1. Archetype Descriptions for Wood Diaphragms for High- and ModerateSeismic Risk – Alternate Design (cont.) Archetype ID Diaphragm Dimensions Zone Zone Width (ft) Sheathing 10d Common Nail Spacing Boundaries and Con- tinuous Edges Other Edges Intermediate Field Area HWS_11_N_OSB_RD4.5_1.5_01 100 x 100 ft End 10 ft 15/32” OSB 2-1/2 in. o.c. 4 in. o.c. 12 in. o.c. Middle 80 ft 15/32” OSB 4 in. o.c. 6 in. o.c. 12 in. o.c. Moderate-Seismicity Wood, Large Buildings MWL_21_N_OSB_RD4.5-1.5_01 MWL_12_N_OSB_RD4.5-1.5_01 400 x 200 ft End 0 ft 15/32” OSB 6 in. o.c. 6 in. o.c. 12 in. o.c. Middle 400 ft 15/32” OSB 6 in. o.c. 6 in. o.c. 12 in. o.c. MWL_11_N_OSB_RD4.5-1.5_01 400 x 400 ft End 0 ft 15/32” OSB 6 in. o.c. 6 in. o.c. 12 in. o.c. Middle 400 ft 15/32” OSB 6 in. o.c. 6 in. o.c. 12 in. o.c. Moderate-Seismicity Wood, Small Buildings MWS_21_N_OSB_RD4.5-1.5_01 MWS_12_N_OSB_RD4.5-1.5_01 200 x 100 ft End 20 ft 15/32” OSB 4 in. o.c. 6 in. o.c. 12 in. o.c. Middle 160 ft 15/32” OSB 6 in. o.c. 6 in. o.c. 12 in. o.c. MWS_11_N_OSB_RD4.5-1.5_01 100 x 100 ft End 0 ft 15/32” OSB 6 in. o.c. 6 in. o.c. 12 in. o.c. Middle 100 ft 15/32” OSB 6 in. o.c. 6 in. o.c. 12 in. o.c. *Special 4x4 subpurlins at other edges in lieu of 2x4s **Special 3x4 subpurlins at other edges in lieu of 2x4s 

151 
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Appendix I FEMA P695 Evaluation Results for the 

Alternate Design Procedure 

I.1 FEMA P695 Evaluation Results for Alternate Design Procedure 

Table I1. Summary of collapse results for RWFD buildings incorporating wood roof 

diaphragm archetype designs Archetype ID Design Configuration Pushover and IDA Results Relevant Analysis Parameters Building Size Diaphragm Aspect Ratio Diaphragm Const. Seismic SDC SMT[T] (g) SCT[T] (g) CMR Period (sec) Median BDR @ DE (%) Median BDR @ MCE (%) Performance Group No. PG-1N (Wood, Large Building, New Design) HWL_21_N_OSB_RD4.5-1.5_01 Large 2:1 Wood D max 0.95 2.56 2.69 0.93 0.44 0.60 HWL_21_N_OSB_RD4.5-1.5_02 Large 2:1 Wood D max 0.92 2.91 3.16 0.94 0.41 0.56 HWL_21_N_OSB_RD4.5-1.5_03 Large 2:1 Wood D max 0.96 2.65 2.59 0.92 0.43 0.60 HWL_21_N_OSB_RD4.5-1.5_04 Large 2:1 Wood D max 0.94 2.94 3.13 0.94 0.42 0.54 HWL_12_N_OSB_RD4.5-1.5_01 Large 1:2 Wood D max 1.50 3.65 2.43 0.53 0.51 0.78 

HWL_12_N_OSB_RD4.5-1.5_02 Large 1:2 Wood D max 1.50 3.63 2.42 0.55 0.52 0.81 HWL_11_N_OSB_RD4.5-1.5_01 Large 1:1 Wood D max 0.91 2.11 2.32 0.96 0.34 0.57 HWL_11_N_OSB_RD4.5-1.5_02 Large 1:1 Wood D max 0.93 2.15 2.39 0.95 0.35 0.59 

Performance Group No. PG-2N (Wood, Small Building, New Design)

HWS_21_N_OSB_RD4.5-1.5_01 Small 2:1 Wood D max 1.36 2.45 1.80 0.65 0.83 1.14 

HWS_12_N_OSB_RD4.5-1.5_01 Small 1:2 Wood D max 1.50 2.95 1.97 0.42 0.85 1.24 HWS_11_N_OSB_RD4.5-1.5_01 Small 1:1 Wood D max 1.50 2.84 1.89 0.39 0.79 1.31 

Performance Group No. PG-3N (Wood, Large Building, New Design)

MWL_21_N_OSB_RD4.5 -1.5_01 Large 2:1 Wood C max 0.49 1.68 3.43 0.92 0.34 0.55 MWL_12_N_OSB_RD4.5 -1.5_01 Large 1:2 Wood C max 0.75 2.08 2.77 0.57 0.41 0.65 MWL_11_N_OSB_RD4.5-1.5_01 Large 1:1 Wood C max 0.48 1.76 3.52 0.93 0.39 0.57 

Performance Group No. PG-4N (Wood, Small Building, New Design)

MWS_21_N_OSB_RD4.5-1.5_01 Small 2:1 Wood C max 0.74 1.61 2.18 0.61 0.53 0.90 MWS_12_N_OSB_RD4.5-1.5_01 Small 1:2 Wood C max 0.75 2.08 2.77 0.45 0.67 0.99 MWS_11_N_OSB_RD4.5-1.5_01 Small 1:1 Wood C max 0.75 2.35 3.13 0.46 0.61 1.21 

153 
Table I2. Adjusted collapse margin ratios and acceptable collapse margin ratios for 

RWFD buildings incorporating wood roof diaphragm archetype designs Archetype ID Design Configuration Collapse Margin Parameters Acceptance Check Building Size Diaphragm Aspect Ratio Diaphragm Construction Seismic SDC CMR 

μΤ SSF ACMR Accept. ACMR Pass/Fail 

Performance Group No. PG-1N (Wood, Large Building, New Design)

HWL_21_N_OSB_RD4.5-1.5_01 Large 2:1 Wood D max 2.69 8.44 1.45 3.91 1.73 Pass HWL_21_N_OSB_RD4.5-1.5_02 Large 2:2 Wood D max 3.16 8.37 1.45 4.59 1.73 Pass HWL_21_N_OSB_RD4.5-1.5_03 Large 2:1 Wood D max 2.65 8.43 1.45 3.84 1.73 Pass HWL_21_N_OSB_RD4.5-1.5_04 Large 2:1 Wood D max 3.13 8.35 1.45 4.54 1.73 Pass HWL_12_N_OSB_RD4.5-1.5_01 Large 1:2 Wood D max 2.43 8.84 1.34 3.26 1.73 Pass HWL_12_N_OSB_RD4.5-1.5_02 Large 1:2 Wood D max 2.45 8.87 1.34 3.29 1.73 Pass HWL_11_N_OSB_RD4.5-1.5_01 Large 1:1 Wood D max 2.32 8.34 1.45 3.36 1.73 Pass HWL_11_N_OSB_RD4.5-1.5_02 Large 1:1 Wood D max 2.39 8.38 1.45 3.46 2.73 Pass 

Mean of Performance Group: 2.58 8.50 1.42 3.68 2.58 8.50 

Performance Group No. PG-2N (Wood, Small Building, New Design)

HWS_21_N_OSB_RD4.5-1.5_01 Small 2:1 Wood D max 1.80 7.59 1.35 2.43 1.73 Pass HWS_12_N_OSB_RD4.5-1.5_01 Small 1:2 Wood D max 1.97 8.15 1.33 2.62 1.73 Pass HWS_11_N_OSB_RD4.5-1.5_01 Small 1:1 Wood D max 1.89 8.44 1.33 2.52 1.73 Pass 

Mean of Performance Group: 1.88 8.06 1.34 2.51 2.30 Pass 

Performance Group No. PG-3N (Wood, Large Building, New Design)

MWL_21_N_OSB_RD4.5-1.5_01 Large 2:1 Wood C max 3.42 8.22 1.22 4.18 1.73 Pass MWL_12_N_OSB_RD4.5-1.5_01 Large 1:2 Wood C max 2.77 8.87 1.15 3.19 1.73 Pass MWL_11_N_OSB_RD4.5-1.5_01 Large 1:1 Wood C max 3.52 8.64 1.23 4.33 1.73 Pass 

Mean of Performance Group: 3.23 8.58 1.20 3.90 2.30 Pass 

Performance Group No. PG-4N (Wood, Small Building, New Design) 

MWS_21_N_OSB_RD4.5-1.5_01 Small 2:1 Wood C max 2.18 8.16 1.16 2.49 1.73 Pass MWS_12_N_OSB_RD4.5-1.5_01 Small 1:2 Wood C max 2.77 8.54 1.14 3.16 1.73 Pass MWS_11_N_OSB_RD4.5-1.5_01 Small 1:1 Wood C max 3.13 8.25 1.14 3.57 1.73 Pass 

Mean of Performance Group: 2.69 8.32 1.15 3.07 2.30 Pass 

154 
Table I3. Overstrength and Deflection Amplification Parameters for the Alternate Design 

Procedure Archetype ID Design configuratio Building Size Diaphragm aspect ratio Diaphragm construction Seismic SDC Ω Cd Performance Group No. PG-1N (Wood, Large Building, Alternate Design)

HWL_21_N_OSB_RD4.5-1.5_01 Large 2:1 Wood Dmax 2.46 5.625 

HWL_21_N_OSB_RD4.5-1.5_02 Large 2:1 Wood Dmax 2.44 5.625 

HWL_21_N_OSB_RD4.5-1.5_03 Large 2:1 Wood Dmax 2.44 5.625 

HWL_21_N_OSB_RD4.5-1.5_04 Large 2:1 Wood Dmax 2.45 5.625 

HWL_12_N_OSB_RD4.5-1.5_01 Large 1:2 Wood Dmax 1.58 5.625 

HWL_12_N_OSB_RD4.5-1.5_02 Large 1:2 Wood Dmax 1.61 5.625 

HWL_11_N_OSB_RD4.5-1.5_01 Large 1:1 Wood Dmax 2.25 5.625 

HWL_11_N_OSB_RD4.5-1.5_02 Large 1:1 Wood Dmax 2.20 5.625 

Mean 2.18 N/A 

Performance Group No. PG-2N (Wood, Small Building, Alternate Design)

HWS_21_N_OSB_RD4.5-1.5_01 Small 2:1 Wood Dmax 1.68 5.625 

HWS_12_N_OSB_RD4.5-1.5_01 Small 1:2 Wood Dmax 1.71 5.625 

HWS_11_N_OSB_RD4.5-1.5_01 Small 1:1 Wood Dmax 1.70 5.625 

Mean 1.70 N/A 

Performance Group No. PG-3N (Wood, Large Building, Alternate Design)

MWL_21_N_OSB_RD4.5-1.5_01 Large 2:1 Wood Cmax 4.68 5.625 MWL_12_N_OSB_RD4.5-1.5_01 Large 1:2 Wood Cmax 2.77 5.625 MWL_11_N_OSB_RD4.5-1.5_01 Large 1:1 Wood Cmax 4.32 5.625 

Mean 3.92 N/A 

Performance Group No. PG-4N (Wood, Small Building, Alternate Design)

MWS_21_N_OSB_RD4.5-1.5_01 Small 2:1 Wood Cmax 2.65 5.625 MWS_12_N_OSB_RD4.5-1.5_01 Small 1:2 Wood Cmax 2.22 5.625 MWS_11_N_OSB_RD4.5-1.5_01 Small 1:1 Wood Cmax 2.25 5.625 

Mean 2.37 N/A 

155 
Table I4. Ratio of the medial diaphragm drift caused by the design level ground motion 

to the median diaphragm drift at the “code” level force 

Archetype ID Cd 

Performance Group No. PG-1N 

HWL_21_N_OSB_RD4.5-1.5_01 4.0 

HWL_21_N_OSB_RD4.5-1.5_02 3.4 

HWL_21_N_OSB_RD4.5-1.5_03 4.3 

HWL_21_N_OSB_RD4.5-1.5_04 4.0 

HWL_12_N_OSB_RD4.5-1.5_01 2.2 

HWL_12_N_OSB_RD4.5-1.5_02 2.3 

HWL_11_N_OSB_RD4.5-1.5_01 3.4 

HWL_11_N_OSB_RD4.5-1.5_02 2.5 

Mean of Performance Group: 3.3 

Performance Group No. PG-2N 

HWS_21_N_OSB_RD4.5-1.5_01 3.8 

HWS_12_N_OSB_RD4.5-1.5_01 2.1 

HWS_11_N_OSB_RD4.5-1.5_01 2.0 

Mean of Performance Group: 2.6 

Performance Group No. PG-3N 

MWL_21_N_OSB_RD4.5-1.5_01 3.4 

MWL_12_N_OSB_RD4.5-1.5_01 1.9 

MWL_11_N_OSB_RD4.5-1.5_01 3.3 

Mean of Performance Group: 2.8 

Performance Group No. PG-4N 

MWS_21_N_OSB_RD4.5-1.5_01 3.5 

MWS_12_N_OSB_RD4.5-1.5_01 3.4 

MWS_11_N_OSB_RD4.5-1.5_01 2.4 

Mean of Performance Group: 3.1 

156 
APPENDIX J Out-of-Plane Wall and Wall Anchorage Forces 

The wall’s out-of-plane force level and force level for anchorage of the wall to the diaphragm are 

separately derived and account for amplified ground accelerations as identified by Bouwkamp, et al. 

(1994) and Celebi, et al. (1989), observed failures, and consideration of whether yielding should be 

allowed. While some out-of-plane yielding of the wall is considered acceptable, top of wall anchorage 

forces are expected to be resisted by connections and members that behave nearly elastically. 

J.1 Out-of-Plane Wall and Wall Anchorage Forces; Current Design 

During an earthquake, the ground shakes and moves the base of walls in-plane and out-of-plane, which 

generates inertial forces in the wall. The wall movement causes the diaphragm to move, which 

generates inertial forces in the diaphragm. The diaphragm movement causes movement of the tops of 

the walls, which also leads to inertial forces generated in the walls. These out-of-plane wall anchorage 

forces can be much larger as determined by the percentage of effective mass than the overall forces for 

the SFRS. 

ASCE 7-10 requires that walls be designed for an out-of-plane force, Fp, in accordance with the 

following formula.

!! = 0.4!!"!!!! ≥ 0.1!! ASCE 7-10, Section 12.11-1 

Where Wp is the weight of the wall. 

ASCE 7-10 requires that the anchorage of walls and transfer of forces into the diaphragm be designed 

for an out-of-plane wall force in accordance with the following formulas. 

!! = 0.4!!"!!!!!! ≥ 0.2!!!!!! ASCE 7-10, Section 12.11-1 

!! = 1.0 +

!

!

"

!

" ≤ 2.0 ASCE 7-10, Section 12.11-2 

Where ka is an amplification factor for diaphragm flexibility, and 

Lf is the span, in feet, of a flexible diaphragm between resisting walls or rigid frames. 

In ASCE 7-10, Section 12.11-1 and 12.11-2, ka and Lf account for diaphragm flexibility. If a diaphragm 

is rigid, Lf equals 0 but if it is flexible, Lf equals the span length. For many buildings with rigid walls 

and flexible roof diaphragms, the diaphragm span between supporting walls or frames will be longer 

than 100 ft so ka will often be equal to 2.0. For diaphragms in which ka equals 2.0, the acceleration 

parameter used to compute the out-of-plane wall anchorage force is 0.8SDS, which is 80% of the 

maximum design spectral acceleration parameter. The intent is that the wall anchorage force is resisted 

Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure 157 
elastically for a force level computed using the maximum design spectral acceleration. The 0.8 factor is 

included to recognize that some connection and member overstrength may be relied upon to resist the 

top of wall anchorage force [SEAOC Seismology Committee, 1999]. 

ASCE 7-10, Section 12.11-1 allows for top of wall anchorage forces less than those computed using the 

maximum design response spectrum parameter for cases in which the diaphragm span is less than 100 ft. 

This reduction is inconsistent with the common condition in which a short span diaphragm often has 

significant overstrength that can result in greater forces developing at the top of wall support. 

J.2 Out-of-plane Wall Anchorage Force Study 

A study was performed to determine the magnitude of the force required to anchor the top of walls for 

out-of-plane forces. Archetype HSL_21_W_WB_RW4 was analyzed to determine the out-of-plane wall 

forces. This archetype is 400 ft long by 200 ft wide with the roof height at 30 ft. The wall panels are 9-

1/4 in. thick and 33 ft tall. The roof diaphragm is steel deck with welded framing connectors, top seam 

weld sidelap connectors in the outer two zones and button punches at the center zone. The top of wall 

anchorage force computed in accordance with ASCE 7-10 Eq. 12.11-1, is 1,680 lbs/ft, which is based on 

the design level earthquake. The model of the archetype was loaded with the forty-four ground-motion 

records from FEMA P695 and incrementally amplified to spectral acceleration intensities up to 2.5g. 

The median out-of-plane wall anchorage forces for the forty-four records at the roof level are shown in 

Figures J1 and J2 respectively for the transverse and longitudinal direction of loading. In the figures, the 

solid blue lines represent out-of-plane anchorage forces for analyses that account for wall flexibility and 

the solid red lines represent out-of-plane anchorage forces for analyses that have infinitely rigid walls. 

The out-of-plane wall anchorage forces that include wall flexibility in the analyses, solid blue lines, 

should be referred to for determining the median out-of-plane wall anchorage force. The analyses with 

infinitely rigid walls, red lines, are used to help understand the amplified forces near corners, which is 

discussed later in this section. The MCE intensities are where the dashed vertical blue lines cross the 

curves. 

158 Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure
Figure J1. Median out-of-plane wall anchorage force for transverse direction of loading.

Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure 159 
Figure J2. Median out-of-plane wall anchorage force for longitudinal direction of loading.

The study showed that anchorage forces are higher for walls loaded out-of-plane when the diaphragm is 

loaded in the longitudinal direction than they are for walls loaded out-of-plane when the diaphragm is 

loaded in the transverse direction. At the center of the diaphragm span, the out-of-plane wall anchorage 

forces are about 1.2 kips/ft for the transverse direction loading and 1.5 kips/ft in the longitudinal 

direction loading for MCE level of shaking. Out-of-plane anchorage forces in the longitudinal direction 

are likely greater than in the transverse direction because the diaphragm has more overstrength in the 

longitudinal versus the transverse direction. 

The study also showed that anchorage forces were higher at the corners than in the middle of the 

diaphragm. This occurs because input motions between the bottom and the top of the wall panels are 

more likely to be in-phase adjacent to the corners, which dynamically amplifies the wall accelerations 

near the corner. This dynamic amplification is evident in the comparison of the out-of-plane anchorage 

forces for analyses that include wall flexibility, solid blue line, and those that assume the wall is rigid, 

solid red line. Near corners eliminating wall flexibility greatly reduces the out-of-plane anchorage 

forces but has little effect near the center of the diaphragm span. Also, the magnitude of the panel 

flexibility affects the load developed near the corners more than away from the corners. 

Median forces generated in the analyses are less than the required design forces computed in accordance 

with ASCE 7-10 using Eq. 12.11-1 except at the corner in the longitudinal direction. The results suggest 

160 Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure
that overstrength in the diaphragm and corner conditions result in higher out-of-plane anchorage forces. 

Therefore, smaller footprint buildings, which often have significant diaphragm overstrength, may 

generate higher forces than obtained with the formula for out-of-plane wall anchorage. 

J.3 Stiffness of Wall Anchorage Connections 

The stiffness of wall-to-diaphragm connections is also considered in design. In previous earthquakes 

wall-to-diaphragm connections have experienced premature failures and loss of wall support. Strap 

anchors have buckled and fractured prematurely. Also, as the straps elongate, wood ledgers have been 

loaded in cross grain bending from the diaphragm nailing. A similar issue occurs with hold-down wall 

anchors that have oversized bolt holes. The slip that occurs as the hold-down moves to engage the bolt 

can also allow the diaphragm nailing to load the wood ledger board in cross grain bending. When using 

wood ledgers, designs should include wall-to-diaphragm anchorage connections that have adequate 

stiffness to avoid cross grain bending of wood ledger boards, buckling and subsequent fracture of straps, 

and other detrimental effects of connections that are too flexible. 

Current practice for connecting diaphragms to walls avoids some of the potential problems. For 

example, steel angles have largely replaced wood ledgers. This eliminates the possibility of ledger cross 

grain bending. The popularity of the hybrid panelized roof system in parts of the United States has 

significantly reduced the number of diaphragms with wood framing, thus reducing the use of holddowns. For steel deck diaphragms, the welded connections are stiff. Although other issues may exist 

with the improved connections, such issues may not become evident until the next major earthquake 

occurs. 

J.4 Transfer of Wall Anchorage Forces to Continuous Diaphragm Ties 

Although the interaction of the diaphragm and walls is dynamic in nature, following the flow of forces 

as if only static forces were involved makes it easier to understand how the connections and roof 

elements should be designed for support of the walls out-of-plane. For wood diaphragms, the static 

simplification of the load path for support of out-of-plane wall forces has wall anchorage forces being 

transferred to sub-diaphragms in the end regions of the diaphragm that transfer anchorage forces into 

continuity ties that distribute forces into the main diaphragm. Current practice is for the sub-diaphragm 

to be designed for the top of wall anchorage forces but the shears generated within the sub-diaphragm 

are not combined with the shears from the main diaphragm even though they occur simultaneously. For 

steel deck diaphragms, some designers use sub-diaphragms similar to the approach used for wood 

diaphragms. More commonly for steel deck diaphragms, the static simplification of the load path for 

support of out-of-plane wall forces has wall anchorage forces transferred to the end of the deck sheets 

for out-of-plane forces parallel to the direction that the deck sheets span and into the joists for out-ofplane forces perpendicular to the direction that the joists span. 

Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure 161 
For buildings with concrete and masonry walls, Section 12.11.2.2 of ASCE 7-10 requires continuous 

diaphragm ties that resist the out-of-plane top of wall connection forces. Many engineers interpret the 

provision to require that the force at the edge of the wall be transferred across the entire diaphragm 

through the continuity ties. Other engineers interpret the requirement as allowing the force in the 

continuity tie to be reduced as the force is transferred into the main diaphragm. This approach is very 

common when analyzing existing buildings. If using this approach of variable tie force, the required tie 

strength is small near the center of the diaphragm assuming equal wall mass at each diaphragm edge 

acting with motions in phase. To address the small tie force, engineers should use a minimum tie force 

equal to that required by Section 12.1.3 (SEAOC 2008 and SEAOC 2010). 

Section 12.1.3 ASCE 7-10 requires that all parts of buildings between seismic separation joints be 

interconnected. If the minimum force level determined using this section is applied, the ties must also 

be designed for a seismic force, Fp, equal to 0.133 times short period acceleration, SDS, times the weight 

of the smaller portion of the building being connected to the larger portion but not less than 5% of the 

weight of the smaller portion. For one-story buildings, the weight includes the wall and roof weights. 

Therefore, the maximum tie force will be located where the weight to each side of the tie is equal. For 

symmetrical buildings, this will be the center of the diaphragm. 

162 Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure
 

 

APPENDIX K Analysis of Archetypes Using Uniform Nailing

Table K1 includes a comparison of archetypes designed using the alternate design procedure versus 

those using uniform nailing. For the archetypes with uniform nailing, the nailing in the edge zone, 

where the shear is amplified by 1.5, was extended across the diaphragm. This is essentially designing 

for Rdiaph equal to 3.0 without reducing the nailing across the diaphragm. This nailing is likely to cause a 

concentration of yielding along the diaphragm edge with little opportunity for yielding to spread into the 

diaphragm. For the archetypes studied, the less desirable nailing lowered the ACMR but in no case did 

it reduce it below the acceptable level of 1.73 for an individual archetype. This result indicates that 

adequate overstrength and ductility exists for this less than desirable nailing. It also means that the 

location of the transition of amplified shear to unamplified can be extended toward the center of the 

diaphragm if necessary with only modest reductions in the seismic performance. 

Table K1. Comparison of archetypes 

Performance

group	
  ID

Design	
  Configuration Collapse margin

Pass/Fail Archetype ID Building Size Diaphragm

Construction Seismic SDC ACMR AcceptableACMR

PG-­‐1

HWL_12_N_OSB_RD4.5-­‐1.5_01 Large Wood Panelized Dmax 3.26 1.73 Pass

HWL_12_N_OSB_RD3_01 Large Wood Panelized Dmax 2.93 Pass

Perfomance Group	
  (ACMR=3.78) Projected ACMR of PG=ACMR*(2.93/3.26) 3.40 2.30 Pass

PG-­‐2

HWS_21_N_OSB_RD4.5-­‐1.5_01 Small Wood Panelized Dmax 2.43 1.73 Pass

HWS_21_N_OSB_RD3_01 Small Wood Panelized Dmax 2.25 Pass

Perfomance Group	
  (ACMR=2.52) Projected ACMR of PG=ACMR*(2.11/2.43) 2.33 2.30 Pass

PG-­‐3

MWL_12_N_OSB_RD4.5-­‐1.5_01 Large Wood Panelized Cmax 3.19 1.73 Pass

MWL_12_N_OSB_RD3_01 Large Wood Panelized Cmax 2.76 Pass

Perfomance Group	
  (ACMR=3.90) Projected ACMR of PG=ACMR*(2.76/3.19) 3.37 2.30 Pass

PG-­‐4

MWS_21_N_OSN_RD4.5-­‐1.5_01 Small Wood Panelized Cmax 2.49 1.73 Pass

MWS_21_N_OSN_RD3_01 Small Wood Panelized Cmax 2.05 Pass

Perfomance Group	
  (ACMR=3.07) Projected ACMR of PG=ACMR*(2.05/2.49) 2.53 2.30 Pass

Seismic Design of Rigid Wall-Flexible Diaphragm Buildings: An Alternate Procedure 163 
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