analysis irregular shaped structures diaphandshearwalls

The Analysis of Irregular Shaped

Structures

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StructuresDiaphragms and Shear Walls

R. Terry Malone, P.E., S.E.

Robert W. Rice, CBO

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Dedicated to, and in appreciation of, those who inspire us.

To our families, especially our wives:

JerriLisa

And to our mentors:

Noel R. Adams, S.E., Brad Crawford, P.E.

This page intentionally left blank

About the AuthorsR. Terry Malone, P.E., S.E., performs third-party struc-tural plan reviews and presents structural-related semi-nars at state and local International Code Council (ICC) chapters and professional engineering organizations. He was a practicing structural engineer in Tacoma, Washington, for 17 years, after which he was a principal in consulting structural engineering firms in Washing-ton and Oregon from 1985 to 2004. Mr. Malone also served as a faculty member at St. Martins College in Lacey, Washington. He is currently licensed as a Profes-sional Engineer in Washington, Oregon, and Arizona.

Robert W. Rice, CBO, is Building Safety Director for Josephine County, Oregon. He holds numerous Oregon/ICC certifications and is a member of ICCs Building Codes Action Committee. Mr. Rice is currently the Secretary/Treasurer of the Oregon Building Officials Association, serves as Chair of the Codes Committee, and was the 2010 Oregon Building Official of the Year. Prior to pursuing a career in building code administra-tion, he worked as a structural designer for engineering firms in southern Oregon for 10 years. Mr. Rice has been a part-time instructor in the Construction Technology Department at Rogue Community College since 1997.

Acknowledgment and appreciation for help in reviewing and providing comments on the contents of this book are given to Ed Keith and B. J. Yeh of the APAThe Engineered Wood Association; Hamid Naderi and John Henry of the International Code Council; and Timothy Mays, Ph.D., Associate Professor, The Citadel.

This publication reproduces excerpts from the 2009 International Building Code, published by the International Code Council, Inc., Washington, D.C. Reproduced with permission. All rights reserved.

This publication reproduces excerpts from Acceptance Criteria for Steel Deck Roof and Floor Systems (AC 43), published by ICC Evaluation Service, LLC, Whittier, California. Reproduced with permission. All rights reserved. ICC-ES Acceptance Criteria are developed for use solely by ICC-ES for purposes of issuing ICC-ES evaluation reports. There is no warranty by ICC Evaluation Service, LLC, express or implied, as to any finding or other matter in the Acceptance Criteria, or as to any product covered under the Acceptance Criteria.

Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiNomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

1 Code Sections and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 IBC 2009 Code Sections Referencing Wind and Seismic . . . . . . 3 1.3 ASCE 7-05 Sections Referencing Seismic . . . . . . . . . . . . . . . . . . . 5 1.4 AF&PA-SDPWS 2008 Sections Referencing

Wind and Seismic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Complete Load Paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.6 Methods of Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.7 References Containing Analysis Methods for Complex

Diaphragms and Shear Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2 Diaphragm Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.2 The Basic Lateral-Force-Resisting System . . . . . . . . . . . . . . . . . . 23 2.3 Load Distribution into a Diaphragm . . . . . . . . . . . . . . . . . . . . . . 27 2.4 Diaphragm Boundary Elements . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.5 Drag Struts and Collectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.6 Chord and Strut Discontinuities . . . . . . . . . . . . . . . . . . . . . . . . . . 60 2.7 Subdiaphragms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 2.8 Introduction to Transfer Diaphragms . . . . . . . . . . . . . . . . . . . . . 70 2.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

3 Diaphragms With End Horizontal Offsets . . . . . . . . . . . . . . . . . . . . . . 83 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 3.2 Method of Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 3.3 Diaphragm Deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 3.4 Single Offset Diaphragms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 3.5 Double Offset Diaphragms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 3.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

4 Diaphragms With Intermediate Offsets . . . . . . . . . . . . . . . . . . . . . . . . 161 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 4.2 Intermediate Offset, Transverse Loading . . . . . . . . . . . . . . . . . . . 161 4.3 Optional Layouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 4.4 Diaphragm Deflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 4.5 Intermediate Offset, Longitudinal Loading . . . . . . . . . . . . . . . . . 170 4.6 Diaphragms With Offsets at the End Wall . . . . . . . . . . . . . . . . . 180 4.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

ix

5 Diaphragms With Openings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 5.2 Method of Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 5.3 Single Opening in Diaphragm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 5.4 Diaphragm Deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 5.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

6 Open Front and Cantilever Diaphragms . . . . . . . . . . . . . . . . . . . . . . . 209 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 6.2 Open Front One Side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 6.3 Diaphragm Deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 6.4 Open Front Both Sides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 6.5 Cantilever Diaphragm One Side . . . . . . . . . . . . . . . . . . . . . . . . . . 223 6.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232

7 Diaphragms With Vertical Offsets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 7.2 Method of Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 7.3 Single Vertical Offset in Diaphragm . . . . . . . . . . . . . . . . . . . . . . 244 7.4 Multiple Vertical Offsets in Diaphragm . . . . . . . . . . . . . . . . . . . . 260 7.5 Alternate Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 7.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

8 Complex Diaphragms With Combined Openings and Offsets . . . 273 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 8.2 Loads and Load Paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 8.3 Analysis in the Transverse Direction . . . . . . . . . . . . . . . . . . . . . . 280 8.4 Analysis in the Longitudinal Direction . . . . . . . . . . . . . . . . . . . . 301 8.5 Alternate Layouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323

9 Standard Shear Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 9.2 Shear Wall BasicsStandard and Sloped Walls . . . . . . . . . . . . . 325 9.3 Hold-Down Anchors and Boundary Members . . . . . . . . . . . . . . 333 9.4 Shear Wall Sheathing Combinations . . . . . . . . . . . . . . . . . . . . . . 337 9.5 Shear Wall Aspect Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 9.6 Shear Wall Rigidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342 9.7 Multistory Shear Wall Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 9.8 Interior Shear Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350 9.9 Shear Wall and Foundation Issues . . . . . . . . . . . . . . . . . . . . . . . . 3609.10 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367

10 Shear Walls With Openings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36910.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36910.2 Perforated Shear Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37010.3 Shear Walls With Force Transfer Around an Opening . . . . . . . 37610.4 Shear Walls With OpeningsThe Cantilever Method . . . . . . . 39210.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402

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11 Discontinuous Shear Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40511.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40511.2 In-Plane Offset Shear Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40511.3 Vertically Discontinuous Shear Walls . . . . . . . . . . . . . . . . . . . . . . 42611.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438

12 Horizontally Offset Shear Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43912.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43912.2 In-Line, Out-of-Line Shear Wall Layouts . . . . . . . . . . . . . . . . . . . 43912.3 Offset Walls in the Same Line of Resistance . . . . . . . . . . . . . . . . 44012.4 Offset Walls Not in the Same Line of Resistance . . . . . . . . . . . . 458

13 The Portal Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46313.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46313.2 Testing and Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46613.3 Foundation Issues and Inflection Points . . . . . . . . . . . . . . . . . . . 46913.4 Force Transfer Around an Opening Method . . . . . . . . . . . . . . . . 47913.5 Alternate Frame Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48013.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483

14 Rigid Moment-Resisting Frame Walls: The Frame Method of Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485

14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48514.2 Method of Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48914.3 Composite Glued Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49614.4 Design of Wall Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50114.5 Nailed-Only Partially Composite Sections . . . . . . . . . . . . . . . . . 50614.6 The Portal Frame Wall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50914.7 Frames Utilizing Glu-lam Beam Members . . . . . . . . . . . . . . . . . 52814.8 Special Wall Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52814.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539

Preface

Residential and commercial buildings have become more complex than structures built only a few decades ago. Horizontal and vertical offsets in the diaphragms, multiple reentrant corners, multiple irregularities, and fewer vertical lateral-force-resisting elements are commonplace. The structural configurations of many modern buildings require very complex lateral load paths. Most texts and publications available today only address simple rectangular diaphragms and shear walls. Methods of analysis for these simpler diaphragms and shear walls do not easily adapt to complex diaphragms and shear wall layouts in irregular shaped structures. Calculating the forces that are to be transferred across multiple discontinuities and detailing the design requirements on the construction documents can be very challenging and time-consuming. Various methods of analyzing the distribution of lateral loads in complex structures were developed in the early 1980s, based largely on work done by the Applied Technology Council,1 the APAThe Engineered Wood Association,2 and Edward F. Diekmann,3 among others. But the distribution of this information has been limited, making some of the material hard to find. The purpose of this publication is to consolidate much of that information into one source to provide a comprehensive coverage of the analysis of modern irregular shaped structures through numerous step-by-step examples, and to bring it to the forefront of the engineering and code official communities. A secondary objective is to reemphasize the need for complete lateral load paths through shear wall and diaphragm discontinuities.

The complex diaphragm, shear wall, and load path issues addressed in this book are representative of todays demand on design professionals and code officials. The diaphragms are considered to be flexible using wood sheathing or steel decking. The shear walls are also considered to be flexible using wood or cold-formed steel framing with wood sheathing. The information is presented as a guideline for recognizing irregularities and developing the procedures necessary to resolve the forces along complicated load paths. The code is, and has been, clear that lateral forces must be transferred across all discontinuities and that continuous load paths must be established and maintained down to the foundation. Forces at discontinuities must be dissipated into diaphragms and shear walls within their shear and tension capacities. That being stated, there have been few or no examples as to what the actual code requirements mean. The examples included in this book provide progressive coverage from basic to very complex illustrations of load paths in the complicated structures that have become increasingly popular. Most of the examples presented throughout the book show shear wall and diaphragm configurations that would be considered minimal

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lateral-force-resisting systems with a maximum demand. Reducing the number of vertical lateral-force-resisting elements, combined with multiple complicated load paths, and then designing to the maximum element capacity are neither suggested nor encouraged by the authors. In most cases, more direct, conservative, and simpler solutions to load paths are available. The examples included are intended to provide the design professional with reasonable and rational tools that can be used to solve complex problems, but do not represent the only methods available.

It has been the authors experience, from private design practice, teaching, and experience as a structural plans examiner, that the knowledge in the engineering and code administration communities regarding the analysis of wood diaphragms and shear walls varies greatly. More importantly, the art of understanding and establishing complete load paths appears to be diminishing due partly to an overreliance on computer programs and waning emphasis on mentoring. Although it is helpful to have a basic understanding of simple shear walls and diaphragms prior to reading this book, enough fundamental information is provided for the layperson to follow the complex examples. This book is based on the 2009 IBC,4 ASCE 7-05,5 the 2005 NDS,6 and the 2008 edition of the Special Design Provisions for Wind and Seismic (SDPWS-08).7 It is assumed that the reader has a good understanding of these codes and standards, including the applicable loads, load combinations, allowable stresses, and adjustment factors, as well as the methods of deriving wind and seismic forces and distributing them into the structure. Publications covering the basic concepts and methods of addressing analysis and design of wood structures can be found in Design of Wood Structures8 and SEAOCs Structural Seismic Design Manual, vol. 2,9 which provide comprehensive coverage of the fundamentals of wood lateral-force-resisting system analysis and design. Every effort has been made to conform to the referenced documents. The opinions and interpretations are those of the authors, based on experience, and are intended to reflect current structural practice.

Engineering judgment and experience has been used in establishing the procedures presented in this book when there was an absence of documentation or well-established procedures available. Although every attempt has been made to eliminate errors and to provide complete accuracy in this publication, it is the responsibility of the design professional or individual using these procedures to verify the results. Users of this information assume all liability arising from such use.

Comments or questions about the text, examples, or problems may be addressed to either of the authors.

References1. Applied Technology Council, 2471 E. Bayshore Rd., Suite 512, Palo Alto, CA 94303.2. APAThe Engineered Wood Association, P.O. Box 11700, Tacoma, WA 98411-0700.3. Edward F. Diekmann, M.S.E. (retired), formerly President of GFDS Engineers, Inc.,

San Francisco, Calif.4. International Building Code with Commentary 2009, International Code Council, Whittier,

Calif., 2009.5. Minimum Design Loads for Buildings and Other Structures, ASCE/SEI 7-05, American

Society of Civil Engineers, New York, 2005.6. National Design Specification for Wood Construction and Supplement, American Forest

and Paper Association, Washington, D.C., 2005.

P r e f a c e

7. Special Design Provisions for Wind and Seismic with Commentary, American Forest and Paper Association, Washington, D.C., 2008.

8. D. E. Breyer, J. F. Fridley, D. G. Pollock, and K. E. Cobeen, Design of Wood Structures ASD/LRFD, 6th ed., McGraw-Hill, New York, 2003.

9. 2006 IBC Structural/Seismic Design Manual, Vols. 1, 2, 3, Structural Engineers Association of California (SEAOC), Sacramento, 2006.

R. Terry Malone, P.E., S.E.Robert W. Rice, CBO

[email protected]

Nomenclature

OrganizationsAF&PA ICCAmerican Forest and Paper Association International Code Council1111 19th St. NW 5360 South Workman Mill Rd.Suite 800 Whittier, CA 90601Washington, DC 20036

APA PAAAPAThe Engineered Wood Association Plywood Association ofP.O. Box 11700 Australia, Ltd.Tacoma, WA 98411-0700 Fortitude Valley, MAC, Queensland

ASCE SEAOCAmerican Society of Civil Engineers Structural Engineers Association1801 Alexander Bell Dr. of CaliforniaReston, VA 20191 555 University Ave., Suite 126 Sacramento, CA 95825ATCApplied Technology Council USDA2471 E. Bayshore Rd. U.S. Department of AgricultureSuite 512 Forest Products LaboratoryPalo Alto, CA 94303 Madison, WI

Building Seismic Safety Council (a council of the National Institute of Building Safety)Washington, DC

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AbbreviationsAllow. allowable min. minimumASD allowable stress design N.A. neutral axisEcc. Eccentricity N.G. no goodFS factor of safety o.c. on centerI.P. inflection point reqd requiredLRFD load and resistance factor design trib. tributaryLFRS lateral-force-resisting system WSD working stress designmax. maximum

Unitsft foot, feet ksi kips per square inchft2 square foot, square feet pcf pounds per cubic footin inch, inches plf pounds per lineal footin2 square inch, square inches psf pounds per square footk kip, kips, 1000 lb psi pounds per square inch

SymbolsA area (in2, ft2)AfB area of bottom flange (in

2)AfT area of top flange (in

2)Anet net area (in

2, ft2)Apw area of parallel grain of plywood web or webs (in

2)A/R, A.R. aspect ratio (length to width or length to depth)As area of steel reinforcement (in

2)b length of shear wall parallel to lateral force, distance between chords of

shear wall (in or ft)b width or depth of diaphragm between chords of diaphragm (ft)b width of solid wood section (in)b shallower depth of diaphragm (ft)C compression force (lb or k)C1 distan ce to extreme outer fiber of composite section from neutral axis (in)Cb bearing length (in)CD load duration factorCdi diaphragm factor for nail connectionsCeg end grain factor for wood connectionsCf size factor for sawn lumberCL distance from face of hold-down to centerline of anchor bolt (in)Cs seismic response coefficientD dead load (lb, k, plf, klf, psf, ksf)D depth (ft)d depth of solid wood section (in)da vertical elongation of overturning anchorage (in)de depth of member less distance from connector to unloaded edge (in)

N o m e n c l a t u r e

diaph 2 diaphragm 2DL dead load (lb, k, plf, klf)dreqd depth required (ft)DTD , dTD depth of transfer diaphragm (ft)E modulus of elasticity (psi, ksi)e eccentricity (in, ft)en nail deformation (in)fa axial stress (psi, ksi)fb bending stress (psi, ksi)F b allowable bending stress, adjusted (psi, ksi)F9B force at grid line 9B (lb, k)fc compression stress in flanges (psi, ksi)FCL force at centerline (lb, k)F C allowa ble bearing stress perpendicular to grain, adjusted (psi, ksi)F c concrete compressive strength (psi, ksi)Fchord chord force (lb, k)Fcollector , Fcoll collector force (lb, k)Fmax maximum force (lb, k)Fo/t overturning force (lb, k)Fstrut strut force (lb, k)fs rolling shear stress (psi)ft tension stress in flanges (psi, ksi)ft feetft-lb foot-poundsft-k foot-kipsF v allowable shear stress, adjusted (psi, ksi)fv horizontal shear stress (psi)FV , FH vertical or horizontal force (lb, k)Fx , Fy force along x or y axis (lb, k)Fx axial force (lb, k)Fy steel yield strength (psi, ksi)Ga appar ent diaphragm shear stiffness from nail slip and panel shear

deformationGt panel rigidity through thickness (lb/in of panel width)H horizontal force (lb, k)h1 height of first story (ft)I moment of inertia (in4)I1 moment of inertia of section 1 (in

4)IE , Ie importance factor for seismicIG , Ig gross moment of inertia (in

4)In , Inet net moment of inertia (in

4)Io moment of inertia of individual element about itself (in

4)It total moment of inertia (in

4)Iw importance factor for windJ polar moment of inertia (in4)k kip, 1000 lbk rigidityL length (in, ft)

xx N o m e n c l a t u r e

LL live load (lb, k, plf, klf)L1 length of section 1 (ft)L13 length of section from grid line 1 to 3 (ft)lbrg length of bearing (in)Lembed length of embedment (ft)Lhdr length of header (ft)Lr roof live load (psf)Lsw length of shear wall (ft)LTD length of transfer diaphragm (ft)lu unbraced length of bending member (in, ft)Lwall length of wall (ft)L/W length-to-width (or depth) ratioM bending moment (in-lb, in-k, ft-lb, ft-k)Mjnt bending moment at panel joint or chord joint (in-lb, in-k, ft-lb, ft-k)Mmax maximum bending moment (in-lb, in-k, ft-lb, ft-k)Mnet net bending moment (in-lb, in-k, ft-lb, ft-k)Mo overturning moment (ft-lb, ft-k)MR resisting moment (ft-lb, ft-k)Mx bending moment at distance x (in-lb, in-k, ft-lb, ft-k)Mu ultimate bending moment (in-lb, in-k, ft-lb, ft-k)M1 bending moment at grid line 1, or moment 1 (in-lb, in-k, ft-lb, ft-k)n number of fasteners in the same planeP concentrated load (lb, k)p, n wind pressure (psf)Qf first st atical moment about neutral axis (in

3) of all parallel-grain material in upper or lower flanges

Qt first st atical moment about neutral axis (in3) of all parallel-grain material

regardless of butt jointsR reaction (lb, k)R2L reaction on the left side of grid line 2 (lb, k)RA reaction at grid line A (lb, k)RL, RR left or right reaction (lb, k)S snow load (lb, k, plf, klf)S, Sx section modulus (in

3)SBP soil bearing pressureSDC seismic design categorySL snow load (psf)SW1 shear wall 1T tension force (lb, k)T fundamental period of vibration of structure (s)TD1 transfer diaphragm 1ts total thickness for shear through webs at composite section (in)V shear force (lb, k)V vertical force (lb, k)Vv , VH vertical or horizontal shear force (lb, k)Vh maximum allowable shear force for composite section (lb, k)Vmax maximum shear force (lb, k)Vn average uniform load per nail (lb)

N o m e n c l a t u r e

Vn average nonuniform load per nail (lb)Vsw2 shear force applied to shear wall 2 (lb, k)VTL , Vtotal total shear force (lb, k)Vu ultimate shear (lb, k)Vwall shear force applied to a wall (lb, k)Vx total shear force at distance x (lb, k)V2L shear force on left side of grid line 2 (lb, k)V3AB uniform unit shear at grid line 3, from A to B (plf, klf)v uniform unit shear (plf, klf) vdiaph uniform unit shear in diaphragm (plf, klf)vmax maximum uniform unit shear (plf, klf)vnet , vn net uniform unit shear (plf, klf)V r adjusted design shear based on effective depth (lb, k)Vsw2 uniform unit shear in shear wall 2 (plf, klf)vx uniform unit shear at distance x (plf, klf)v2L uniform unit shear on left side of grid line 2 (plf, klf)W lateral force due to wind (lb, k)w lateral uniform load (plf, klf)wlw lateral uniform load due to wind, leeward pressures (plf, klf)wwind lateral uniform load due to wind, windward and leeward pressures

combined (plf, klf)www lateral uniform load due to wind, windward pressures (plf, klf)w35 uniform load from grid line 3 to 5 (plf, klf)wE lateral uniform load due to seismic (plf, klf)wstrip uniform load applied to 1 ft wide strip across structure (plf, klf)wx uniform load applied along distance x (plf, klf)x distance x (ft)x distance to neutral axis (in, ft)x1 distance to centroid of an element from neutral axis (in)Z adjusted allowable load capacity of a single nail per NDS (lb)D deflection (in)DB deflection at grid line B (in)Db deflection due to bending (in)DC , Dcs deflection due to chord slip (in)De deflection due to elongation of steel strap (in)Dmax maximum deflection (in)Droot deflection due to rotation (in)Dns deflection due to nail slip (in)Ds deflection due to shear (in)Dstrap deflection due to strap elongation and nail slip (in)DT , DTL total deflection (in)dx story drift at level x (in)dxe deflection at location required determined by an elastic analysis (in) stability coefficient for p-delta effectsWo overstrength factor


Structures

1

CHAPTER 1Code Sections and Analysis

1.1 IntroductionFor centuries, building codes have been developed to define the standards for the design and construction of structures. Opinions are often expressed that code require-ments have become too complex; however, from the earliest of codes to our current standards, codes have changed in response to our increased understanding of materials and methods as well as our knowledge of the forces that are imposed on structures, particularly wind and seismic forces. This understanding has been greatly increased by past structural failures and from current state-of-the-art testing and research. In addi-tion, changes to the code have been brought about by the reality that structures have become increasingly complex compared to structures previously built.

The most widely used and accepted code for building design standards is the Inter-national Building Code (IBC), published by the International Code Council (ICC).1 The document references a compilation of design standards that have been developed through an open and transparent consensus process that represents all interested par-ties and stakeholders. ASCE/SEI 7-05, Minimum Design Loads for Buildings and Other Structures, is published by the American Society of Civil Engineers and the Structural Engineering Institute2 and is referenced from within the 2009 IBC. Wood lateral-force-resisting systems are addressed in the National Design Specification for Wood Con-struction (NDS-05) and Special Design Provisions for Wind and Seismic3 (SDPWS-08), which are published by the American Forest & Paper Association and the American Wood Council. The 2009 IBC, ASCE 7-05, NDS-05, and SDPWS-08 are codes and stan-dards that are discussed in the chapters that follow.

Most of the texts and publications today only address simple rectangular diaphragms, the analysis of which does not easily adapt to complex diaphragm and shear wall layouts. The layout of the lateral-force-resisting system shown in Fig. 1.1 demonstrates this problem. The vertical and horizontal offsets shown in the figure create disconti-nuities in the diaphragm, which require special collector and drag elements to establish complete load paths. Collectors and drag elements in diaphragms and in shear walls are a critical part of complex lateral-force-resisting systems. The analysis and design requirements for diaphragms under wind vs. seismic loading are topics that are often misunderstood. Some of the confusion has been brought about by the presentation of lateral-force-resisting systems and their elements within ASCE 7-05. Chapters 11 and 12 of that standard, which address seismic design, provide a complete and organized cover-age of lateral-force-resisting systems and their components under seismic loading conditions. Chapter 6 addresses the analysis and application of wind loads and pressures on structures with regard to the main-force-resisting system (MFRS) and on components

2 C h a p t e r O n e

and cladding. It does not, however, mention individual structural components or design requirements as the seismic design section does. Some designers may interpret the lack of discussion of structures and their components in those chapters to imply that drag struts and collectors are not required for wind design and that diaphragm discontinui-ties do not have to be addressed if wind controls. Section 1604.10 of the 2009 IBC addressing wind and seismic detailing says, Lateral-force-resisting systems shall meet seismic detailing requirements and limitations prescribed in this code and ASCE 7, excluding Chap. 14 and Appendix 11A, even when wind load effects are greater than seismic load effects. Diaphragms, drag struts, collectors, and shear walls function the same way regardless of whether loads applied to the diaphragm are from wind, seis-mic, soil, or other pressures. All irregularities and/or discontinuities within a system of diaphragms and shear walls must be addressed. It is easy to overlook the definitions section when thumbing through the codes and standards, believing that the contents therein are already understood. A quick review will show that the definitions actually

Figure 1.1 Continuous load path issues.

C o d e S e c t i o n s a n d A n a l y s i s

set the criteria and requirements for diaphragms, chords, collectors, and their design. Comparing the IBC, ASCE 7, and the SDPWS reveals that the definitions for a dia-phragm and its components under both wind and seismic loading are nearly identical. In practical terms, all diaphragms must have boundary members consisting of drag struts, chords, collectors, or other vertical lateral-force-resisting elements. Collectors are required at all offsets and areas of discontinuity within the diaphragm, including at openings. These requirements also apply to shear walls. Forces at all discontinuities and openings must be dissipated into the diaphragm or shear wall without exceeding its design capacity. The codes and standards specify that the sheathing shall not be used to splice boundary elements or collectors. Furthermore, all diaphragms and shear walls shall contain continuous load paths along all boundaries and lines of lateral force resis-tance and across all discontinuities.

The following sections are presented to show agreement between the codes and standards with regard to lateral-force-resisting systems that resist wind and seismic forces. These sections have been selected for their relevance to this book. These sections should be reviewed in their entirety when reading each chapter of the book.

1.2 IBC 2009 Code Sections Referencing Wind and Seismic1Chapter 16

1602.1 DefinitionsDiaphragm: A horizontal or sloped system acting to transmit lateral forces to the vertical-resisting elements. When the term diaphragm is used, it shall include horizontal bracing systems.Diaphragm Boundary: In light framed construction, a location where shear is trans-ferred into or out of the diaphragm sheathing. Transfer is to either a boundary element or to another force-resisting element.Diaphragm Chord: A diaphragm boundary element perpendicular to the applied load that is assumed to take axial stress due to the diaphragm movement.

1604.4 Analysis [partial quote]Load effects on structural members and their connections shall be determined by methods of structural analysis that take into account equilibrium, general stabil-ity, geometric compatibility, and both short- and long-term material properties.

Any system or method of construction to be used shall be based on a rational analysis in accordance with well-established principles of mechanics. Such analy-sis shall result in a system that provides a complete load path capable of transfer-ring loads from their point of origin to the load-resisting elements.

The total lateral force shall be distributed to the various vertical elements of the lateral-force-resisting system in proportion to their rigidities, considering the rigidity of the horizontal bracing system or diaphragm. Except where diaphragms are flexible, or are permitted to be analyzed as flexible, provisions shall be made for the increased forces induced on resisting elements of the structural system resulting from torsion due to eccentricity between the center of application of the lateral forces and the center of rigidity of the lateral-force-resisting system.

Every structure shall be designed to resist the overturning effects of the appli-cation of the lateral forces specified in this chapter. See Section 1609 for wind loads, Section 1610 for lateral soil loads, and Section 1613 for earthquake loads.


Chapter 222210.5 The design of cold-formed steel walls and diaphragms shall be in accordance with AISILateral.

Chapter 232302.1 DefinitionsCollector: A horizontal diaphragm element parallel and in line with the applied force that collects and transfers diaphragm shear forces to the vertical elements of the lateral-force-resisting system and/or distributes forces within the diaphragm.Drag Strut: See Collector.Sub-diaphragm: A portion of a larger wood diaphragm designed to anchor and transfer local forces to the primary diaphragm struts and the main diaphragm [also referred to as a transfer diaphragm in this book].Nailing, Boundary: A special nailing pattern required by design at the boundaries of diaphragms.Shear Wall: A wall designed to resist lateral forces parallel to the plane of the wall. Shear wall, perforatedA wood structural panel sheathed wall with open-

ings that has not been specifically designed and detailed for force transfer around openings.

Shear wall segment, perforatedA section of shear wall with full height sheathing that meets the height-to-width ratio limits of Section 4.3.4 of AF&PA SDPWS-08.

Sub-diaphragm: A portion of a larger wood (should also include steel deck) dia-phragm designed to anchor and transfer local forces to primary diaphragm struts and the main diaphragm.

2305 General design requirements for lateral-force-resisting systems

2305.1GeneralStructures using wood shear walls and diaphragms to resist wind, seis-mic, and other lateral loads shall be designed and constructed in accordance with AF&PA SDPWS and the provisions of Sections 2305, 2306, and 2307.

2305.1.1Openings in shear panels that materially affect their strength shall be fully detailed on the plans and shall have their edges adequately reinforced to transfer all shear stresses.

2306.2.1 Design of diaphragmsWood structural panel diaphragms shall be designed and constructed in accordance with AF&PA SDPWS. Wood structural panel diaphragms are permitted to resist horizontal forces using the allowable shear capacities set forth in Tables 2306.2.1(1) and 2306.2.1(2). The allowable shear capacities set forth in Tables 2306.2.1(1) and 2306.2.1(2) are permitted to be increased 40% for wind design.

2306.3Design of wood structural panel shear wallsWood structural panel shear walls shall be designed and constructed in accor-dance with AF&PA SDPWS. Wood structural panel shear walls are permitted to resist horizontal forces using the allowable capacities set forth in Table 2306.3.


The allowable capacities in Table 2306.3 are permitted to be increased 40% for wind design.

1.3 ASCE 7-05 Sections Referencing Seismic2Chapter 11

11.2 DefinitionsBoundary Elements: Diaphragm and shear wall boundary members to which the diaphragm transfers forces. Boundary members include chords and drag struts at diaphragms and shear wall perimeters, interior openings, discontinuities, and re-entrant corners.Boundary Members: Portions along wall and diaphragm edges strengthened by longitudinal and transverse reinforcement. Boundary members include chords and drag struts at diaphragm and shear wall perimeters, interior openings, dis-continuities, and re-entrant corners.Diaphragm Boundary: A location where shear is transferred into or out of the dia-phragm element. Transfer is either to a boundary element or to another force-re-sisting element.Drag Strut (Collector, Tie, Diaphragm Strut): A diaphragm or shear wall boundary element parallel to the applied load that collects and transfers diaphragm shear forces to the vertical force-resisting elements or distributes forces within the dia-phragm or shear walls.

11.7.3 Load Path Connections [partial quote] All parts of the structure between separation joints shall be interconnected to form a continuous path to the lateral force resisting system, and the connections shall be capable of transmitting the lateral forces induced by the parts being connected.

Chapter 1212.1.3 Continuous load path and interconnection [partial quote]A continuous load path, or paths, with adequate strength and stiffness shall be provided to transfer all forces from the point of application to the final point of resistance.

12.3 Diaphragm flexibility, configuration irregularities, and redundancy

12.3.1 Diaphragm FlexibilityThe structural analysis shall consider the relative stiffnesses of diaphragms and the vertical elements of the lateral-force-resisting systems. Unless a diaphragm can be idealized as either flexible or rigid in accordance with Sections 12.3.1.1, 12.3.1.2, or 12.3.1.3, the structural analysis shall explicitly include consideration of the stiffness of the diaphragm (i.e., semi-rigid modeling assumption).

12.3.1.1 Flexible diaphragm condition Diaphragms constructed of untopped steel decking or wood structural panels are permitted to be idealized as flexible in structures in which the vertical elements are steel or composite steel and concrete braced frames, or concrete, masonry, steel or composite shear walls. Diaphragms of wood structural panel or untopped steel decks in one and two family residential buildings of light framed construc-tion shall also be permitted to be idealized as flexible.


12.3.1.2 Rigid diaphragm conditionDiaphragms of concrete slabs or concrete filled metal deck with span to depth ratios of 3 or less in structures that have no horizontal irregularities are permitted to be idealized as rigid.

12.3.1.3 Calculated flexible diaphragm conditionDiaphragms not satisfying the conditions of sections 12.3.1.1 or 12.3.1.2 are permit-ted to be idealized as flexible where the computed maximum in-plane deflection of the diaphragm under lateral load is more than two times the average story drift of adjoining vertical elements of the seismic force resisting system of the associated story under equivalent tributary lateral load, as shown in ASCE 7-05 Fig. 12.3-1.

12.10 Diaphragm chords and collectors

12.10.1 Diaphragm designDiaphragms shall be designed for both shear and bending stresses resulting from design forces. At diaphragm discontinuities, such as openings or re-entrant cor-ners, the design shall assure that the dissipation or transfer of edge (chord) forces combined with other forces in the diaphragm is within the shear and tension capacity of the diaphragm.

12.10.2 Collector elementsCollector elements shall be provided that are capable of transferring the seismic forces originating in other portions of the structure to the elements providing resistance to those forces (all seismic design categories).

12.10.2.1 Collectors in Seismic Design Categories C through FIn structures assigned to Seismic Design Categories C through F, collector ele-ments (see ASCE 7-05 Fig. 12.10-1), splices, and their connections to resisting ele-ments shall resist the load combinations with over-strength of Section 12.4.3.2. Exception: In structures or portions thereof braced entirely by light frame shear walls, collector elements, splices, and connections to resisting elements need only be designed to resist forces in accordance with 12.10.1.1.

1.4 AF&PA-SDPWS 2008 Sections Referencing Wind and Seismic32.2 TerminologyBoundary Element: Diaphragm and shear wall boundary members to which sheathing transfers forces. Boundary elements include chords and collectors at diaphragm and shear wall perimeters, interior openings, discontinuities, and re-entrant corners.Diaphragm Boundary: A location where shear is transferred into or out of the diaphragm sheathing. Transfer is either to a boundary element or to another force-resisting element.Collector: A diaphragm or shear wall element parallel and in line with the applied force that collects and transfers diaphragm shear forces to the vertical elements of the lateral-force-resisting system and/or distributes forces within the diaphragm.Chord: A diaphragm boundary element perpendicular to the applied load that resists axial stress due to the induced moment. Diaphragm: A roof, floor, or other membrane bracing system acting to transmit lateral forces to the vertical resisting elements. When the term diaphragm is used, it shall include horizontal bracing systems.


4.1.1 Design requirementsThe proportioning, design and detailing of engineered wood systems members, and connections in lateral resisting systems shall be in accordance with the refer-ence documents in Section 2.1.2 and the provisions of this chapter. A continuous load path, or paths, with adequate strength and stiffness shall be provided to transfer all forces from the point of application to the final point of resistance.

4.1.4 Boundary elementsShear wall and diaphragm boundary elements shall be provided to transfer the design tension and compression forces. Diaphragm and shear wall sheathing shall not be used to splice boundary elements. Diaphragm chords and collectors shall be placed in, or tangent to, the plane of the diaphragm framing unless it can be demonstrated the moments, shears, and deformations, considering eccentrici-ties resulting from other configurations can be tolerated without exceeding the framing capacity and drifts limits.

4.2.1 Application requirements [partial quote]Wood diaphragms shall be permitted to be used to resist lateral forces provided the deflection in the plane of the diaphragm, as determined by calculations, tests, or analogies drawn therefrom, does not exceed the maximum permissible deflec-tion limit of attached load distributing or resisting elements. Framing members, blocking, and connections shall extend into the diaphragm a sufficient distance to develop the force transferred into the diaphragm.

4.2.2 Deflections [partial quote]Alternatively, for wood structural panel diaphragms, deflection shall be permit-ted to be calculated using a rational analysis where apparent shear stiffness accounts for panel deformation and non-linear nail slip in the sheathing-to-framing connection.

1.5 Complete Load PathsIrregular-shaped structures similar to the one shown in Fig. 1.1 are commonly designed without properly addressing the irregularities contained therein. Tie straps with block-ing are often randomly placed throughout the structure without explicit purpose, in an ambiguous attempt to provide a solution to the irregularities, and are seldom supported by calculation. All the connections that are required to develop a complete load path are often ignored, even along straight lines of lateral resistance. ATC-74 noted that failures have occurred for the following reasons:

Connection failures were caused by incomplete load paths, incomplete designs, inadequate detailing, and inadequate installation (construction). Often, deter-mination of the size of wood chords for tension and compression forces is also ignored in the design, which ensures failure.

Designs included diaphragm shears and chord forces only, no connection designs.

Designs did not include load paths that continued down to the foundation and into the soil.

Designing to the maximum diaphragm and shear wall capacity (close nail-ing), while limiting the number of shear walls to a minimum (no redundancy),


provides no room for workmanship. This puts a high demand on diaphragms, shear walls, and connections.

Splitting, using gun-nails when common nails are specified, using different species of wood than specified, overdriving nails, and slack in light-gage metal straps lead to failures.

Edward F. Diekmann provided an interesting note in his engineering module Design of Wood Diaphragms5 regarding a misconception for the requirement of wood diaphragms and shear walls. He noted that it was unfortunate that interest in diaphragms and shear walls was developed primarily on the West Coast, which gave rise to an impression that they were required only because of the earthquakes that occur in that region. Experience has shown that most wood-framed structures on the West Coast are governed by wind forces which are larger than seismic forces. Because of this misconception, it appears that a large number of wood-framed structures in many other regions of the country are apparently erected without thought as to how they are to be braced against wind forces. Another problem noted in ATC 7-16 was the lack of provi-sion of complete load paths and detailing. Engineering has become a highly competi-tive business. ATC 7-1 noted, Nothing is more discouraging to the conscientious engineer endeavoring to deal with lateral forces with all the detailing requirements on diaphragms and shear walls than to contemplate the absence of attention paid by some of his fellow engineers to the most basic shear transfer problems. It is a sobering experi-ence to see structural plans for a wood-framed apartment complex without a single wood-framing detail and to realize that you were not given the job because your pro-posed fee was too high. It is hoped that the information provided in this chapter and the remainder of this book will provide clarity to the importance of complete load paths and designs.

The diaphragm and shear wall layout shown in Fig. 1.1 is a good example of structures currently being designed and built. The code and standards definitions and sections just presented should be carefully reviewed for applicability to each irregularity discussed for this structure. In the transverse direction, two diaphragms exist. Diaphragm 1 is supported by the first-floor shear walls along grid line 1 and at grid line 6. Diaphragm 2 is supported by the shear walls located at grid line 6 and at grid line 7. Diaphragm 1 has multiple discontinuities and irregularities within the span that must be resolved. Starting at grid line 1A, it can be seen that a two-story entry con-dition exists, which typically occurs in many office or shopping center complexes. The upper level is usually an architectural feature commonly referred to as a pop-up. The shear walls at grid line 1A are two stories in height and support the pop-up roof. The walls at grid line 2 and grid line B also support the pop-up roof but are discontinuous shear walls because they are supported by the main roof and do not continue to the founda-tion. The pop-up section should be designed as a second story that transfers its forces as a concentrated load into the main diaphragm. The diaphragm sheathing and framing is often omitted below the pop-up section at the main roof level. Diaphragm boundary members are not allowed at the main diaphragm level at grid line A from 1 to 2 or at line 1 from A to B, due to architectural constraints. This condition creates a horizontal offset in the roof diaphragm in the transverse and longitudinal directions. The offset disrupts the diaphragm chords, creating a notched diaphragm effect. Because of the offset, the question arises as to how to provide continuity in the chord members and transfer its disrupted force across the offset. It also raises the question of how to


dissipate the disrupted chord force into the main diaphragm, at grid line 2B. Creating complete load paths to transfer all the discontinuous forces into the main diaphragm can be very complex and challenging. There are multiple offsets at grid lines C, D, and E between 3 and 6. These offsets also cause a disruption in the diaphragm chords and struts, and must also have their disrupted chord forces transferred into the main dia-phragm by special means. The large opening in the diaphragm in-line with grid line 5 causes a disruption in the diaphragm web and requires the transfer of concentrated forces into the main diaphragm at each corner of the opening. The opening reduces the stiffness of the diaphragm because of its proximity to the multiple offsets near grid line D. Diaphragm shears will increase at all areas of discontinuities because of the addi-tional shears that are created by the transfer of the disrupted chord forces into the main diaphragm. Diaphragm 2, which is located between grid lines 6 and 7 from C to E, is offset vertically from the main diaphragm. The low roof is supported on three sides by shear walls. The diaphragm boundary along grid line C is unsupported unless the boundary member along that line is transferred into the main diaphragm by a vertical bending element and collector that extends into the main diaphragm. This example may appear to be extreme to some; however, such structures are becoming more com-monplace in current practice and design.

The establishment of a complete load path does not end by providing boundary members along the entire length of the lateral-force-resisting line. It must also include all the connections necessary to make members in the line of lateral force resistance act as a unit and transfer the shears and forces from the diaphragm sheathing into the boundary elements, then into the vertical force-resisting elements, and finally down into the foundation. The lateral forces must then be transferred safely into the soil with-out exceeding the soil capacity. The drawings and calculations must be complete and clear so that the engineer can ensure that the load paths are complete from the point of application of the loads to the foundation. In addition, clearly defined load paths, sup-porting calculations, and drawings assist the plans examiner in an efficient and accu-rate review of the documents. It also provides the contractor with the details necessary to construct the structure per the design, and the building inspector to verify its compli-ance with the construction documents. Clear and thorough documentation of load paths can save countless hours of misunderstanding, construction errors, and revisions. In some cases, those errors may not even be realized because of the lack of clarity, and the final structure may not meet the intended design.

Figures 1.2 through 1.5 provide examples of maintaining complete load paths through various framing configurations. Figure 1.2 shows sloped roof trusses connected to exterior wood walls. In configuration A, the diaphragm shears are transferred into full-depth solid blocking installed between the trusses, next into the double wall plate by shear clips or toenailing, then from the double plate into the wall sheathing. Figure 1.3 is a photograph of framing that is similar to configuration A. The photograph shows that the blocking between the trusses is not the full depth of the trusses at the point of bearing. This is often done by the contractor as a way to provide roof ventilation. How-ever, this prevents the installation of the boundary nailing for the diaphragm, because the nails at this location cannot transfer shear across the air gap. Boundary nailing is required for all engineered diaphragm designs, as verified by diaphragm testing and the principles of mechanics. It is also required by code and must be installed. In addi-tion, the roof sheathing is not supported by the blocking at the wall location to prevent its buckling under lateral shear forces (in-plane axial force applied to the sheathing).


It should also be pointed out that code does not allow the diaphragm sheathing to act as the boundary element or to act as the splice for a boundary element. Since boundary nailing cannot be installed in the aforementioned configuration to transfer the shear forces into the wall top plate, the diaphragm shears would be transferred into the truss top chord at the first nail located back from the blocking. The effective nail spacing at that location would be one nail at 24 o.c. It should be obvious that this excessive nail spacing would not be capable of resisting the applied shears. Therefore, a complete load path does not exist, and the transfer of diaphragm shears into a boundary element can-not be achieved. The structural detailing for the shear transfer at this location was cor-rectly shown on the drawings, but was ignored during construction by the contractor.

Figure 1.2 Example of complete load paths, wood roof sections.

Figure 1.3 Photograph of incomplete load path, blocking issue.

Figure 1.5 Example of complete load paths, floor/roof sections.

Figure 1.4 Example of complete load paths, low roof sections.

11


There have been many debates on the necessity of full-depth blocking at exterior wall lines, especially in areas of low to moderate seismicity. Some stakeholders are pushing for half-height blocking or to eliminate the blocking entirely. These efforts are not consistent with the goal of providing a complete load path and should be scruti-nized for rationality and substantiation. Attempting to transfer diaphragm shears through the truss top chord would put the truss top chord in cross-grain bending at the truss heel joint if partial-height blocking were used and could potentially pull off the gang-nail plate. This type of failure has been observed in the field. In the case where blocking is eliminated, the truss would have to transfer the shears into the wall top plate by roll over action. The APA has conducted tests on sloped mobile home roof diaphragms. An interesting mode of failure was that the gang-nail plates at the ridge line joint of the trusses were pulled apart by opposing shear forces in the diaphragm sheathing because blocking was not provided for the sheathing at the ridge joint. Substantial testing for gravity plus torsion (rollover) or gravity plus cross-grain forces would have to be con-ducted on gang-nail trusses before serious consideration could be given to reducing the full-depth blocking requirements. Also, trusses would have to include these rotational forces in their design. Configuration B is the same framing condition, but the truss is a deep heel configuration. Under this condition, a prefabricated shear panel consisting of 2 members with plywood sheathing replaces the solid blocking. The load path is the same regardless of the blocking material installed.

Figure 1.4 shows the condition where low roofs frame into the walls at midheight of the studs. Configuration A shows the condition where the ledger is attached directly to the wall studs. The exterior wall sheathing is terminated at the low roof elevation, and the shear wall sheathing is continued on the inside of the wall. The upper wall shears are transferred into the double blocking, through the nailing connecting the dou-ble blocking together and then into the inside wall sheathing. The lower roof shears are transferred from the diaphragm sheathing into the ledger, into the double wall blocking, and then into the inside wall sheathing. A more direct load path would be to continue the exterior wall sheathing full height of the wall and attach the ledger on the outside of the sheathing. Configuration B shows the condition where the wall sheathing is dis-rupted at the interface of the wall and ledger. The shear from the upper wall sheathing is transferred into the blocking, into the ledger, back into the lower blocking, and then back into the wall sheathing. The low roof shears are transferred into the ledger, then into the lower blocking and wall sheathing.

Figure 1.5 shows two floor framing sections. Joints in the wall sheathing can occur at many locations in the floor framing area. There are no guarantees where these joints will occur unless the joint locations are specifically detailed in the drawings. The nail-ing required to establish a complete load path should be based on the worst-case sce-nario, assuming that the joints will fall at the locations shown in configuration B and that the sheathing will not be lapped onto the rim joist. Configuration A is somewhat unconventional because the floor joists are hangered off of the wall instead of being in direct bearing, as shown in configuration B. The wall shear is transferred from the upper wall into the wall double top plate below and then back into the outer sheath-ing. The floor shears are transferred from the floor sheathing into the double top plate, then into the wall sheathing. In both cases, the shears are then transferred into the lower floor or roof through the blocking that is nailed to the edge joist. The low floor or roof sheathing is nailed to the edge joist, which completes the load path. Configura-tion B represents the common method of framing a floor onto a bearing wall. Since


sheathing joints usually occur at the upper wall bottom plate and lower wall top plate locations, the upper wall and floor shears must be transferred by nailing into the rim joist, then down into the lower wall top plate by toenailing or shear clips. All these figures should call out the complete nailing, clip, splice straps, and blocking neces-sary to provide a continuous load path. Calculations should be completed to verify the adequate transfer of all forces and shears. A mistake commonly made occurs when a detail is taken from a typical detail book and applied to a set of drawings without verifying that the capacity of the connections will actually meet or exceed the applied shears. It is sometimes assumed that the detail will work for any load that is applied. Sometimes too much trust is given to the details that are devel-oped by others.

Figure 1.6 shows the condition where roof or floor joists bear directly over a masonry wall. In-plane shears from the diaphragm sheathing are transferred into the blocking or rim joist by boundary nailing, then into the sill plate by shear clips or toenails. The 4 sill plate transfers its shear into the masonry wall through the anchor bolts. The most overlooked calculation for the sill plate design is for out-of-plane loading. Typically the anchor bolt size and spacing are based on the bolt shear capacity parallel to the grain, when the lateral forces are applied parallel to the wall. The bolt shear capacity perpen-dicular to the grain and sill plate shear capacity for wall out-of-plane loads are seldom checked. From the plan view shown above the section, it can be seen that the section of the plate on the left side of the anchor bolt opposite to the applied force is not supported and therefore cannot resist shear. The effective depth de on the load side of the anchor bolt is the only part of the sill plate that can resist shear. The sill plate must be designed for a reduced shear capacity based on NDS 7 Section 3.4.3, the same as for a wood ledger supporting gravity loads. Section 3.4.3 addresses shear in bending members. It has been argued that the sill plates are not bending members, and therefore the code equations do not apply. This is only true if the spacing of the anchor bolts is close enough to trans-fer the forces directly into the anchor bolts without bending (i.e., spacing = 2de). The shear capacity of the reduced depth is noted as follows:

For bolt less than five times the depth of the member from the end of the ledger,

=

V F bdddr V ee2

3

2

NDS Eq. 3.4-6

For bolt location greater than five times the depth of the member from the end of the ledger,

= V F bdr V e

23

NDS Eq. 3.4-7

The reduced depth shear capacity usually controls the anchor bolt spacing. The effective shear capacity is further reduced when a single 2 plate is used in lieu of a 3 or 4 plate or when countersinking is used (net thickness for bearing perpendicular-to-grain bolt values). Placement of the shear clips is important. It can be seen that if only one clip is installed under the direction of the load shown, cross-grain tension will occur, which is not allowed by code. Placing a clip on each side of the anchor bolt cen-terline will transfer the out-of-plane forces into the anchor bolts without causing cross-grain tension. It is important to remember when transferring in-plane lateral forces into a sill plate and anchor bolt of a concrete or masonry wall, where soil pressures are


applied normal to the wall, that in-plane and out-of-plane shear forces applied to the anchor bolt and plate must be resolved into resultant forces.

Figure 1.7 is a typical interior or exterior shear wall elevation along a line of lateral force resistance. In this case, the load path under discussion is the transfer of shears and lateral forces from the roof diaphragm down to the soil. The continuous rim joist or the wall top plates and beams can be used as the diaphragm boundary elements (drag struts). Assuming that blocking occurs between the joists in lieu of a continuous rim

Figure 1.6 Example of complete load paths, masonry wall/floor sections.


joist, the diaphragm shears are transferred through the blocking into the drag members and shear wall at the wall top plate level. All the nailing, clips, splice straps, and block-ing necessary to provide a complete continuous load path along the drag line must be detailed and installed. The wall shears are transferred into the foundation by anchor bolts. The wall overturning forces are resisted by dead loads and/or hold-downs that are embedded into the foundation. The foundation must be designed to have the strength necessary to transfer all these forces plus gravity loads into the soil without exceeding the allowable soil-bearing pressures. The load path is not complete until the forces are completely transferred into the soil. Figure 1.8 shows the condition where the roof diaphragms are vertically offset. If drag forces are applied in the same direction along this line of lateral resistance, the shear and overturning moment caused by the upper roof must be added to the shear and overturning moment caused by the low roof. When loads are applied to the diaphragm perpendicular to the wall line, the boundary members act as a diaphragm chord. Under this loading condition, it is usually not obvi-ous to the engineer that the wall at the vertical offset will act as a shear wall. Figure 1.8 shows chord forces applied to the wall at the offset. The chord forces are equal at the offset location, but act at different heights. This causes a counterclockwise moment that is larger than the clockwise moment. A net moment will result acting in the counteclockwise direction, which must be resisted by a hold-down anchor.

Figure 1.7 Complete load path to foundation, roof at same elevation.


Assuming no dead load (for clarity)

M T h

M T h

FM M

Lo t

1 1

2 2

1 2

=

=

=

( )

( )

/wall

The actual force transfer through this wall is somewhat complicated and is addressed in detail in Chap. 7. The complete load path must also continue into the soil.

It is important to provide documents that can verify that a complete load path has been provided. The engineer, building official, plans examiner, contractor, and building inspector must all be able to understand and verify these load paths. Most structural drawings combine the gravity system with the lateral system. Looking at the framing plans, the sections cuts are indistinguishable between lateral and gravity details. Per-sonal experience has shown that lateral load paths are often framed incomplete in the field because a detail has been overlooked or is hidden in the drawings. Although it is

Figure 1.8 Complete load path to foundation, roof at different elevations.


not required by code, the authors personal preference is to separate the gravity system from the lateral system. In some cases it can cause additional work and potentially increase the number of drawing sheets; however, the results are well worth the effort because it ensures that a part of the lateral system will not be overlooked. For the engi-neer, the clutter and confusion are reduced because only one system is being concen-trated on at a time, thereby ensuring that a complete lateral system has been provided. This also simplifies the plan review process and improves the quality control for the project. For the code official, it significantly reduces the time required for a plan review. The contractor can give a framer the lateral system sheets to complete that portion of the structure, which reduces the chance for missed details and critical framing or con-nections. The benefits for the building inspector are the same as for the engineer. The lateral drawings should include a simple key plan to show the diaphragm boundaries and required nailing. The framing plan should also call out all drag struts, collectors, splice connections, special nailing requirements, shear walls, frames, and structural sec-tions. All strut and collector forces should be called out on the plans. Grid lines should be used for ease of communication over the phone or in written forms to identify spe-cific locations. Wall elevations should be provided when walls contain openings that require special force transfer connections or anchoring information. Inclusion of a lat-eral system narrative and design criteria in the calculations is useful for the plan review process, especially when the system contains complicated load paths.

1.6 Methods of AnalysisThe examples in this book provide methods of analyzing complex diaphragms and shear walls. Each chapter contains one or two examples that demonstrate the method or methods being discussed in the chapter. Problems, located at the end of each chapter, are variations of the examples, each of which has a special lesson or point of interest. As shown in those examples, the relocation of a single shear wall can significantly change the distribution of forces through a structure. The lateral loads used in the examples are generalized and can represent wind, seismic, or soil loads at either an allowable stress design (ASD) or ultimate strength (LRFD) design level. The applied loads are assumed to be the results of the individuals generation of forces to the structure, which are appropriately factored up or down to fit the load combination and design method being used. The number of decimal places typically used for most calculations varies from one to two significant figures. Some of the examples are carried out using more signifi-cant figures than would be normally be used in common practice. The intent is to pro-vide better closure of the diaphragm chord and collector force diagrams.

The typical sign convention used in this book is shown Fig. 1.9. One-foot by one-foot square sheathing elements are used to show the direction of the shears acting on the sheathing or collectors and chords. The figure shows typical positive and negative sheathing elements when loaded in the transverse and longitudinal directions. The figure also shows representative portions of force diagrams for collectors, struts, and chords. For transverse loading, a positive force is drawn above the line representing tension. A negative force is drawn below the line representing compression. In reality, it does not make a difference on which side of the line the forces are drawn as long as the construction of these diagrams is consistent throughout the analysis. This is so because the force in a member will change from tension to compression upon the reversal of the direction of the loads.


As a prerequisite, the reader should have a working knowledge of the analysis and design of simple rectangular diaphragms and simple shear walls and should know how to calculate wind and seismic forces to structures. The methods for calculating wind and seismic forces are not included in this book. A cursory review of the analysis of simple diaphragms and shear walls is presented as an introduction or refresher before tackling the more advanced examples contained in this book.

The examples and methodology presented should be verified by the reader for its accuracy and applicability prior to use on a project.

1.7 References Containing Analysis Methods for Complex Diaphragms and Shear Walls

Edward F. Diekmann, Design of Wood Diaphragms, Journal of Materials Education, University of Wisconsin, Madison, August 1982.

This paper (Ref. 5) is one of a set of modules on Wood: Engineering Design Concepts that was prepared for the Fourth Clark C. Heritage Memorial Workshop at the University of Wisconsin, Madison, August 1982, published seriatim in the Journal of Materials Educa-tion. The paper is a very important document, which provides a fairly comprehensive

Figure 1.9 Sign convention.


coverage of basic diaphragm and shear wall analysis and connection design. Of greater importance and relevance to this book are the presentations on

Diaphragm continuity issues Diaphragms with openings Diaphragms with horizontal offsets (notches) Diaphragms with vertical offsets Collector analysis at diaphragm discontinuities Transfer of disrupted chord forces within the diaphragm Shear walls with openings

The examples are clear and easy to follow. It is surprising, and at the same time unfortunate, that this paper was not provided in a major publication where it could have been more readily accessed by the engineering community.

Edward F. Diekmann, Diaphragms and Shear Walls, Chap. 8, Wood Engineering and Construction Handbook, K. F. Faherty and T. G. Williamson (eds.), McGraw-Hill, New York, 1995.

Chapter 8 of the above book8 is devoted to simple diaphragms and shear walls. Most of the material on basic diaphragms and shear walls that was included in Ref. 5 has been repeated here. Diaphragms with openings, covered in Ref. 5, have also been included in the chapter. The information is comprehensive for its coverage of simple systems, but limited with regard to complex systems.

Proceedings of a Workshop on Design of Horizontal Diaphragms, ATC 7-1, Applied Technology Council, Redwood, Calif., 1980.

The objective of the workshop6 was to evaluate current knowledge and practice in the design and construction of horizontal wood diaphragms, to examine the needs and priorities for immediate and long-range research required to minimize gaps in current knowledge, to improve current practice, and to provide state-of-the-art practice papers for the development of a guideline for the design of horizontal wood diaphragms. The document included several case studies on (1) the field performance of wood diaphragms subjected to wind and seismic loading conditions, (2) the performance of mechanical fasteners in wood diaphragms, (3) analysis methods for horizontal diaphragms, (4) a very basic discussion of irregular-shaped diaphragms, and (5) details for the transfer of forces from the diaphragm to the vertical resisting elements. A final list of some of the recommendations developed from the workshop included these items:

Develop mathematical models and analysis methods to predict the inelastic response of diaphragms.

Develop a simplified analytical model to predict deflections of diaphragms. Perform additional dynamic tests using either cyclic loads or input from realis-

tic earthquake motions.

Determine what, if any, size effects exist in the performance of diaphragm tests.


Determine by tests the distances required for ties and collectors to spread loads into the diaphragm.

Evaluate by tests the current assumptions associated with subdiaphragms. Determine the effects of the size and location of openings on the force distribu-

tion and deformation of diaphragms.

Determine the necessity of code-enforced aspect ratios.

Guidelines for the Design of Horizontal Wood Diaphragms, ATC-7, Applied Technol-ogy Council, Redwood, Calif., 1981.

The guideline4 was prepared by H. J. Brunnier Associates and guided by an advi-sory panel comprised of Noel R. Adams, Edward F. Diekmann, Byrne Eggenberger, Ronald L. Meyes, Roland L. Sharpe, and Edward J. Teal.

The document was considered to be the state of the art at the time of publication. Most of the information contained in the guideline continues to be of value and rele-vance today. Twelve design examples are included in the guide, in addition to discus-sions of the topics listed below. Some of the concepts are not fully developed; however, there is a considerable amount of information contained there for both the novice and the experienced professional.

Basic diaphragm discussions1. Basic components and stresses

2. Girder analogy

3. Truss analogy

4. Moment couple series

Diaphragms with openings Continuous diaphragms Subdiaphragms Irregular diaphragms Diagonal and straight sheathed diaphragms Diaphragm deflections Load transfer through the diaphragm

John R. Tissell and James R. Elliott, APA Research Report 138, Plywood Diaphragms, APA from E315H, APAThe Engineered Wood Association, Engineering Wood Systems, Tacoma, Wash., 2000.

The report9 included 11 tests of diaphragms on panelized systems, high-load dia-phragms, diaphragms with openings, field-glued diaphragms, and diaphragms with framing spaced at 5 ft. Of particular interest is Appendix E, which provided an example of the analysis of a diaphragm with openings. The example was based on the design method described in ATC-7, which was developed by Edward F. Diekmann, S.E.

D. E. Breyer, J. F. Fridley, D. G. Pollock, and K. E. Cobeen, Design of Wood Structures ASD, McGraw-Hill, New York, 2003.


This book10 is perhaps the best known and most widely used book on the design of wood members, connections, diaphragms, and shear walls. It provides a very compre-hensive coverage of the design of simple wood structures.

Structural/Seismic Design Manual, vol. 2, Structural Engineers Association of Califor-nia, Sacramento, Calif., 2006.

Volume 2 of this series11 provides some of the most comprehensive and state-of-the-art coverage of the analysis and design of light-framed structures as well as masonry and concrete tilt-up walls with flexible diaphragms. All the design examples are located in high seismic zones.

Uno Kula, Diaphragms and Diaphragm Chords, SEAOC 2001 70th Annual Conven-tion Proceedings, Structural Engineers Association of California, Sacramento, 2001.

The paper12 was a short abstract on the analysis of irregular-shaped diaphragms containing openings and horizontal offsets of the diaphragm chords. Although the number of examples was limited, the method described for analyzing chord and collec-tor forces was fairly clear and complete. The analytical method was consistent with the method developed by Edward F. Diekmann, as presented in ATC-7.

Design/Construction Guide-Diaphragms and Shear Walls, APA Form L350, APAThe Engineered Wood Association, Tacoma, Wash., 2004.

This Guide13 provides current state-of-the-art design and construction requirements for simple rectangular diaphragms and shear walls.

Dr. Tim Mays, Guide to the Design of Diaphragms, Chords and Collectors, National Council of Structural Engineers Association, 2009.

This guide14 provides examples for the analysis and design of multistory rectangu-lar diaphragms with cantilever sections and interior openings.

Four-story concrete diaphragm with concrete collectors Three-story wood diaphragm with wood collectors Four-story flexible steel deck diaphragm with steel beam collectors Four-story concrete-filled steel deck diaphragm with steel beam collectors

Clear, thorough examples are provided for the design of the chords and collectors. The guide is based on the 2006 IBC and ASCE/SEI 7-05.

1.8 References 1. International Building Code 2009 with Commentary, International Code Council,

Whittier, Calif., 2009. 2. Minimum Design Loads for Buildings and Other Structures, ASCE/SEI 7-05, American

Society of Civil Engineers, New York, 2005. 3. Special Design Provisions for Wind and Seismic with Commentary, SDPWS-08, American

Forest and Paper Association, Washington, D.C., 2008.


4. Guidelines for Design of Horizontal Wood Diaphragms, ATC-7, Applied Technology Council, Redwood, Calif., 1981.

5. Edward F. Diekmann, Design of Wood Diaphragms, Journal of Materials Education, University of Wisconsin, Madison, August 1982.

6. Proceedings of a Workshop on Design of Horizontal Wood Diaphragms, ATC 7-1, Applied Technology Council, Redwood, Calif., 1980.

7. National Design Specification for Wood Construction and Supplement, American Forest and Paper Association, Washington, D.C., 2005.

8. Edward Diekmann, Diagrams and Shear Walls, Chap. 8, Wood Engineering and Construction Handbook, K. F. Faherty and T. G. Williamson (eds.), McGraw-Hill, New York, 1995.

9. Plywood Diaphragms, APA Form E315H, APAThe Engineered Wood Association, Engineering Wood Systems, Tacoma, Wash., 2000.

10. D. E. Breyer, J. F. Fridley, D. G. Pollock, and K. E. Cobeen, Design of Wood Structures ASD, McGraw-Hill, New York, 2003.

11. Structural/Seismic Design Manual, vol. 2, Structural Engineers Association of California, Sacramento, 2006.

12. Uno Kula, Diaphragms and Diaphragm Chords, SEAOC 2001 70th Annual Convention Proceedings, Structural Engineers Association of California, Sacramento, 2001.

13. Design/Construction GuideDiaphragms and Shear Walls, APA Form L350, APAThe Engineered Wood Association, Engineering Wood Systems, Tacoma, Wash., 2004.

14. Dr. Tim Mays, Guide to the Design of Diaphragms, Chords and Collectors Based on the 2006 IBC and ASCE/SEI 7-05, National Council of Structural Engineers Association, Country Club Hills, IL, 2009.

23

CHAPTER 2Diaphragm Basics

2.1 IntroductionThe methods for analyzing and designing simple rectangular box systems have been common knowledge for decades. A number of publications and textbooks that have been written to date provide a fairly complete coverage of the topic. However, a natural progression of architectural creativity has taken structures from simple rectangular floor plans to ones that contain horizontal and vertical offsets and other irregularities that complicate load paths. Because of time constraints, the length of undergraduate classes on wood design often limits the coverage of diaphragms to simple rectangular sections. The extent of mentoring after graduation varies greatly, and because there are very few books or examples that explain how to analyze complex diaphragms and structures, some individuals may not have an in-depth understanding about how

analysis irregular shaped structures diaphandshearwalls

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