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Reliability-based design for Japanese timber structures using Canadian S-P-F dimension lumber Tomoi, Masatoshi 1991

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RELIABILITY-BASED DESIGN FOR JAPANESE TIMBER STRUCTURES USING CANADIAN S-P-F  DIMENSION LUMBER  By MASATOSHI TOMOI B.Eng.,  Osaka I n s t i t u t e  o f T e c h n o l o g y , 1974  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS  FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES Department o f F o r e s t r y  Ve a c c e p t t h i s t h e s i s as conforming to the r e q u i r e d s t a n d a r d  THE UNIVERSITY OF BRITISH COLUMBIA April  1991  © Masatoshi Tomoi,  1991  In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree „ that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.  Department of  O^^yc^r^-  The University of British Columbia Vancouver, Canada Date  DE-6 (2/88)  Mfr>U  c±f  /?f/  ii ABSTRACT  Reliability evaluated  using  Canadian using  levels lumber  Spruce-Pine-Fir  the  (Draft)",  "Standard which  Architectural Canadian  current  at  UBC  dimension  lumber.  and  Japanese  Limit  Monte  2x4  Japan,  and  research  computer  by  The  the  LRFD  In-Grade  frame  simulations. structures  Steel  Data  These  were made Structures  obtained analyses  Reliability also  of  by  a  were  developed by D r .  were  of  Subcommittee  Recommendations were made to encourage the a p p l i c a t i o n of d e s i g n i'n'to e x i s t i n g Japanese d e s i g n methods.  were  evaluation  evaluations of  project.  structures  from  Design  program "RELAN"  Carlo  wood  derived  States  published  of  Council the  2x4 wood frame  data  newly  Institute  Wood  Japanese  property  for  was  implemented u s i n g Foschi  of  R.O.  levels  of  evaluated. limit  states  iii TABLE DF CONTENTS  Page ABSTRACT  ii  TABLE OF CONTENTS  iii  LIST OF TABLES  vii  LIST OF FIGURES  ix  LIST OF APPENDICES  x  LIST OF ABBREVIATIONS  xi  ACKNOWLEDGEMENTS  xii  1.  INTRODUCTION  1  2.  OBJECTIVES  7  3.  CURRENT STRUCTURAL CALCULATION SYSTEM FOR JAPANESE TIMBER STRUCTURES  9  3.1  B u i l d i n g Codes and Standards  9  3.1.1  B u i l d i n g Standard Law  9  3.1.2  B u i l d i n g Standard Law Enforcement Order  9  3.1.3  Building Notification  10  3.1.4  Standard f o r S t r u c t u r a l  3.1.5 3.2  C a l c u l a t i o n of  Timber S t r u c t u r e s  10  GHLC Span T a b l e  11  Principles  of S t r u c t u r a l  C a l c u l a t i o n f o r Timber  Structures  12  3.2.1  Design Requirements  12  3.2.2  Design Loads  12  3.2.3  Allowable Unit Stress  13  iv 3.2.4  3.2.5  Working S t r e s s Design C r i t e r i a  13  3.2.4.1  Bending  14  3.2.4.2  Shear  14  3.2.4.3  Tension  15  3.2.4.4  Compression  15  L a t e r a l R e s i s t a n c e f o r O r d i n a l Wooden Structures  4.  JAPANESE LIMIT STATES DESIGN 4.1  4.2  19  New Japanese Standard f o r L i m i t S t a t e Design o f Steel  5.  16  Structure  (Draft)  19  Proposed Load Combinations and Load F a c t o r s  JAPANESE FULL SIZE TEST PROGRAM FOR STRENGTH OF LUMBER  20 ..  23  5.1  Bending  24  5.2  MOE  24  5.3  M o i s t u r e Content  24  5.4  Material Strength  25  5.5  D u r a t i o n o f Load Adjustment  25  5.6  Tension  25  5.7  Compression  26  6.  CANADIAN FULL SIZE TEST PROGRAMS  27  7.  ADJUSTMENTS OF CANADIAN IN-GRADE DATA TO JAPANESE BASIS . .  29  7.1  MOR  29  7.2  MOE  29  7.3  Tension  30  7.4  Compression  30  V  8.  9.  DEVELOPMENTS OF LOAD MODEL AND LOAD PARAMETERS FOR JAPANESE BUILDINGS  32  8.1  Dead Load  32  8.2  Occupancy Load  33  8.3  Snow Load  36  PERFORMANCE FACTORS FOR JAPANESE 2x4 WOOD FRAME STRUCTURAL MEMBERS  40  9.1  Strength Limit States  40  9.1.1  E f f e c t o f Load R a t i o 7  42  9.1.2  R e s i s t a n c e D i s t r i b u t i o n Model  43  9.1.3  Bending Performance F a c t o r  44  8.1.4  Tension  48  9.1.5  Compression  49  9.2 10.  11.  Serviceability  Limit states  51  DURATION OF LOAD EFFECTS  55  10.1 Damage Model  56  10.2 Load Case  '58  10.3 S i m u l a t i o n  58  10.4 D u r a t i o n o f Load R e s u l t s  60  ASSESSMENT OF RELIABILITY  LEVELS  ASSOCIATED WITH CURRENT WORKING STRESS DESIGN  63  11.1 Load  63  11.2 A l l o w a b l e U n i t . S t r e s s  64  11.3 R e l i a b i l i t y L e v e l s  i n Bending (Short-Term B a s i s )  11.4 R e l i a b i l i t y  in Deflection  Levels  ...  64 67  vi 11.5 R e l i a b i l i t y  of Current Rafter  under Long-Term Loading  12.  Construction 69  11.6 D i s c u s s i o n  74  DISCUSSION AND CONCLUSION  76  REFERENCES  82  vii LIST OF TABLES Page T a b l e 1.  Design Requirements of the B u i l d i n g Codes  85  T a b l e 2.  Load Combinations f o r Working S t r e s s Design  86  T a b l e 3.  Basic S t a t i s t i c a l  Data f o r S a f e t y A n a l y s i s  of  Steel Structure  87  T a b l e 4.  Occupancy Load (Extreme Type I  Distribution)  88  T a b l e 5.  Japanese Snow Data  89  T a b l e 6.  Nominal Design Dead, Occupancy and Snow Load  90  Table 6a.  Nominal Dead to L i v e Design Load R a t i o s  90  T a b l e 7.  Bending Performance F a c t o r s  91  T a b l e 8.  Mean /3-values C o r r e s p o n d i n g Given (j> i n Bending  T a b l e 9.  S i z e F a c t o r s and C h a r a c t e r i s t i c  f o r S-P-F Strengths  92  R, 0  f o r Bending  93  T a b l e 10a. M o d i f i e d /3-values  i n Bending ( 7 = 0.25)  T a b l e 10b. M o d i f i e d /3-values i n Bending ( A c t u a l Factors  94  j)  94  i n T e n s i o n f o r S-P-F  95  a  T a b l e 11.  Performance  T a b l e 12.  Mean /3-values C o r r e s p o n d i n g Given <j> i n T e n s i o n  T a b l e 13.  S i z e F a c t o r s and C h a r a c t e r i s t i c  Strengths  96  R, Q  f o r Tension  97  T a b l e 14a. M o d i f i e d /3-values  in Tension  ( 7 = 0.25)  98  T a b l e 14b. M o d i f i e d /3-values  in Tension  (Actual  98  Factors  j) a  T a b l e 15.  Performance  i n Compression f o r S-P-F  T a b l e 16.  Mean /3-values C o r r e s p o n d i n g Given <j> i n Compression . . 100  T a b l e 17.  S i z e F a c t o r s and C h a r a c t e r i s t i c  Strengths  99  R, Q  f o r Compression  101  T a b l e 18a. M o d i f i e d /3-values  i n Compression ( 7 = 0.25)  102  T a b l e 18b. M o d i f i e d /3-values  i n Compression ( A c t u a l  102  T a b l e 19.  Performance F a c t o r s  T a b l e 20.  Statistical  Data f o r  in S e r v i c e a b i l i t y  y) a  f o r S-P-F  ....  103  Analysis  of D u r a t i o n of Load E f f e c t  104  Table 21.  D u r a t i o n of Load E f f e c t s  f o r S-P-F  Ql  105  T a b l e 22.  D u r a t i o n of Load E f f e c t s  f o r S-P-F  Q2  106  Viii T a b l e 23.  Bending R e l i a b i l i t y  L e v e l s f o r C u r r e n t 2x4  Wood Frame S t r u c t u r e s  (Short-Term B a s i s )  T a b l e 24.  Deflection Limits  Table 25.  Serviceability Reliability  107 108  Levels  for  C u r r e n t 2x4 Wood Frame S t r u c t u r e s  109  T a b l e 26.  Typical Rafter  110  T a b l e 27.  Recommended <j> and /^-values  T a b l e 28.  D u r a t i o n o f Load F a c t o r K  T a b l e 29.  Reliability  Span  D  f o r SPF Ql a t 0  T  - 2.5  ..  79  L e v e l /?  i n C u r r e n t 2x4 Wood Frame S t r u c t u r e T a b l e 30.  78  80  R a f t e r Span Comparison U s i n g C u r r e n t and New LSD Design E q u a t i o n  81  ix LIST OF FIGURES Page F i g u r e 1.  Beta(/?) vs Phi(0) f o r Japanese S t e e l Code  Ill  F i g u r e 2.  Occupancy Load Modeling  112  F i g u r e 3.  Japanese Occupancy Load  113  F i g u r e 4.  Snow Model i n Sapporo  114  F i g u r e 5.  Snow Model i n Tokyo  115  F i g u r e 6.  L o c a t i o n and Snow d a t a  116  F i g u r e 7.  Beta(/?) vs. Gamma(7)  117  F i g u r e 8.  Bending Beta(/?) vs Phi(<£) i n Tokyo ( A l l Data)  118  F i g u r e 9.  2 P - V e i b u l l F i t s (1)  119  F i g u r e 10. 2P-Weibull  Fits  (2)  120  F i g u r e 11. Bending Beta(/?) vs Phi(<£) i n Tokyo (15% T r u n c a t i o n )  . 121  F i g u r e 12. Bending Beta(/?) vs Phi(^) SS vs No.2 (1)  122  F i g u r e 13. Bending Beta(/?) vs Phi(^) SS vs No.2 (2)  123  F i g u r e 14. Bending Beta(/?) vs Phi(<?!>) ( A l l Cases)  124  F i g u r e 15. Bending Beta(/?) vs Phi(<^) ( A l l C a s e s , A c t u a l Gamma)  . 125  F i g u r e 16. T e n s i o n Beta(/?) vs Phi(<£) ( A l l Cases)  126  F i g u r e 17. Compression Beta(/3) vs Phi(^)  127  ( A l l Cases)  F i g u r e 18. Load and S t r e s s Model f o r DOL  128  F i g u r e 19. DOL Osaka  129  F i g u r e 20. DOL Sapporo  130  F i g u r e 2 1 . Recommended R e l a t i o n s h i p between j and K  D  Factor  ...  131  F i g u r e 22. Beta(/?) vs Span  132  F i g u r e 2 3 . Long-Term Beta(/?) vs Span Tokyo 1  133  F i g u r e 24. Long-Term Beta(/?) vs Span Sapporo  134  F i g u r e 2 5 . Long-Term Beta(/?) vs Span N i i g a t a  135  F i g u r e 2 6 . Long-Term Beta(/?) vs Span Tokyo 2  136  F i g u r e 2 7 . Long-Term Beta(/?) vs Span Osaka  .  137  X  LIST OF APPENDICES  Page Appendix 1. A l l o w a b l e U n i t S t r e s s f o r Lumber f o r 2x4 Wood Frame S t r u c t u r e Appendix 2. Measurement o f Plumb Measure S i z e  138 139  Appendix 3. C h a r a c t e r i s t i c s o f Bending S t r e n g t h f o r S-P-F  (100% Data)  140  Appendix 4. C h a r a c t e r i s t i c s o f Bending S t r e n g t h f o r S-P-F  (Lower 15% D a t a f i t )  141  Appendix 5. 2 Parameter V e i b u l l D i s t r i b u t i o n Parameters f o r MOE f o r S-P-F  142  Appendix 6. C h a r a c t e r i s t i c s o f T e n s i o n S t r e n g t h (Lower 15% D a t a f i t )  143  Appendix 7. C h a r a c t e r i s t i c s o f Compression S t r e n g t h (Lower 25% D a t a f i t )  144  xi LIST OF ABBREVIATIONS  AU  Architectural  I n s t i t u t e of Japan  CMHC  Canada Mortgage and Housing C o r p o r a t i o n  COV  C o e f f i c i e n t of  FFPRI  F o r e s t r y and F o r e s t Products Research  GHLC  Government Housing Loan C o r p o r a t i o n  JAS  Japanese A g r i c u l t u r a l  LRFD  Load and R e s i s t a n c e  LSD  L i m i t S t a t e s Design  MOAFF  M i n i s t r y of A g r i c u l t u r a l ,  MOC  M i n i s t r y of  NLGA  National  RBD  Reliability-Based  S-P-F  Spruce-Pine-Fir  SS  Select  VSD  Working S t r e s s Design  Variation Institute  Standard  F a c t o r e d Design  F o r e s t r y and  Construction  Lumber Grades  Authority  Design  Structural  Fisheries  xii ACKNDVLEDGEMENTS  I and Dr.  would l i k e R.O.  Foschi  throughout t h i s I  would  for  their  invaluable  advice,  to Dr.  also  of  British  leave  provided  like  to  thank  my  Columbia (COFI), financial  support  J.D.  and p a t i e n t  study and i n the p r e s e n t a t i o n o f t h i s  Industries and  to express my deepest g r a t i t u d e  Barrett guidance  thesis.  employer,  Council  who a l l o w e d  me an  educational  so  could  accept  o p p o r t u n i t y to study a t UBC and complete t h i s  that  I  thesis.  of  Forest  the  1 1.  Limit  INTRODUCTION  S t a t e s Design (LSD)  codes i n c o r p o r a t i n g s a f e t y  based on modern R e l i a b i l i t y - B a s e d replacing  the  structural  traditional  materials  transformation (LRFD)  format  to has  Working  design  the  LSD  the  been  Design  (WSD)  throughout  Load  led  principles  by  and the  world.  Resistance  other  on a b a s i s c o m p a t i b l e w i t h the o t h e r major s t r u c t u r a l  materials.  first was  Code  for  a soft  Engineering  c o n v e r s i o n of  new sawn lumber m a t e r i a l s revision. design  Design  in  Wood  using  reliability  and  appropriate member  serviceability  limit  analysis  the  [1]  was  the  to  provide  wind,  requires  earthquake),  design states.  o f the member r e l i a b i l i t y  and the performance f a c t o r  incorporates  new  safety  of  data for  information  as the  is  levels  Applying  actual  member s t r u c t u r a l  strength  equations This  LSD  procedures.  knowledge  that  the  minimum t a r g e t  assessment  materials  exception  incorporated into  Canadian Code [2]  procedures  snow,  corresponding  d a t a was  reliability  assessment  occupancy,  models  of  calibrated formal  the WSD code with the  property  The 1989 r e v i s i o n  equations  derived  safety  order  timber code t o be c o n v e r t e d to the LSD f o r m a t . The 1984 r e v i s i o n  largely  (e.g.,  to  and  design  Canadian  in  LSD  Design  structures  The  developing  concrete  The  keep timber  expanding r a p i d l y  in  Factor  in  design  is  Interest  rapidly  philosophy  the  steel,  are  timber  codes  groups.  (RBD)  Stress  codes  or  largely  non-wood m a t e r i a l s  Design  assessments  well  behavior as  strength  required  loads  for  the and the  and the r e l a t i o n s h i p between member chosen f o r each d e s i g n e q u a t i o n . The  performance safety  in  associated  framework the  factor  and  the  design  with  the  equations  design.  implementation  d e s i g n e q u a t i o n s are  Canadian  structural on an  and o t h e r or  less  basis  markets common  benefit  forest  in  is  The  in  the  a major  timber p r o d u c t s  the  to  stresses  exception of  the  design  property  design  property  the t e c h n i c a l  development  once  for the  load d a t a and  major of  industry  these  a  very  expand the  factors.  allowed  to c o n v e r t  concepts  were  of  Canadian  traditionally specimens.  test  test  readily  with  consistency  data.  The  properties  countries  The g e n e r a l  s h a r i n g of  The more  significant  use  clear  most  Australia  industry.  was  of  products  Japan,  The VSD methodology was  in  exporter  the in  The common  understood  within  community.  timber  markets  Community.  As  major  to  a  Europe,  philosophy  data a n a l y s i s  development  important  order  VSD  safety  codes a r e  in  is  States,  consistent  c h o i c e of  timber  in  jurisdictions  developed from s m a l l  were  LSD  interest  industry  United  internationally.  methods, procedures f o r working  other  of  assessment  developed  [3])  c o n t i n u e d acceptance  Canadian  based on d e s i g n p r o p e r t i e s test  (Foschi  concern t o the f o r e s t  international  helping  reliability  level  available.  products  wood p r o d u c t s .  equitable  in  the  s p e c i f i e d and when the a p p r o p r i a t e  m a t e r i a l s p r o p e r t i e s i n f o r m a t i o n are The  The  methodology  Canadian LSD Code can be a p p l i e d  determines  a  working  of  Canada's  i n c l u d i n g the U n i t e d S t a t e s and the  European  exporting  with  achieve  being  as  the  investigated  country  research  much  in  several  Canada  has  a  particular  community and codes  uniformity  in  LSD  code  committees  and  support  standards development as p o s s i b l e . LSD  philosophy  provides  a  rational  member s a f e t y  which a l l o w s  all  an  basis.  presents  equitable  timber  community  visually  to  demonstrate  graded timber  adequate  safety  engineered directly lower  This  in  wood  based  variability  variability  materials.  about  long-term  materials still  being  codes,  it  is  development exporting methods,  Recently, become  of  models  created  need  additional  internationally developments efficiency The  the  the  and  that  as  to  lumber  lack  Canada.  have  emerging system  products over  with higher  timber  community,  wood-based  structural  the  LSD  code  will  New  framework  such  under  to  lumber  industry  lack  of  of  structural  visually  graded  intense  test member  codes to  has  mount  consistent  attention losses  in  lumber  new  design  significant  particularly  of  simplify  development  Canadian  impact material  development  With  as  approaches  full-size  dimension  risk for  consistent  significantly  procedures,  support  value  products are  of  of  could  standards.  industry product  the  of  adoption  Canadian  accepted  traditional  dimension  such  efforts  sawn  assessment  advantage  within  coupled with attempts  for  the  with the expanding development of LSD timber  interpretation  resistance a  the  and  variability,  position  and standards  countries data  concerns,  evident  codes  to  solid  non-wood  safety  inherent  competitive by  challenge  traditional  the  material an  Initial  the  specifying  to be compared on  significant  competing  Since  of  have  affected  continue.  the  products.  will  materials  for  members, systems and s t r u c t u r e s  to  effects  a that  structural  relation  recognizes  the  structural  framework  to  these  in  structural  wood  products.  nominal  scrutiny  2-inch in  many  market  areas. The  Canadian  forest  products  promoting  the  of  North  system  Japan.  Japan "2x4  in in  use  Forestry  and  Standard  (JAS)  frame  parallels  American  The 2x4 wood frame  1974 when the  Building  wood  the  industry  Code".  Ministry  At  the  Fisheries for  (MOAFF)  approval  system.  The  the N a t i o n a l  time,  the  been  (MOC)  adopted  published  for  the  Agriculture,  Japanese  Agricultural  dimension  Lumber Grades A u t h o r i t y  in  of  Canadian dimension lumber f o r standard  in  construction  officially  Ministry the  successful  platform  Construction  established  of  JAS  2x4  system was  of  same  has  lumber  the  2x4  closely  (NLGA) dimension lumber  g r a d i n g r u l e s used by the Canadian 2-inch dimension lumber p r o d u c e r s . Japanese 2x4 wood frame VSD  principles.  builders tables  the  convenience  are  of  currently  designed u s i n g  architects,  engineers  and  the Government Housing Loan C o r p o r a t i o n (GHLC) p u b l i s h e s span  [4]  system. these  For  structures  and a  Since  design  large  structures,  specification  amounts  it  is  of  manual  for  the  2x4 wood  Canadian dimension lumber a r e  important  to  t r a n s f o r m a t i o n from VSD to LSD w i l l  begin  to  understand  frame  used  how a  in  code  impact the use o f dimension lumber  i n the Japanese market. The  Architectural  reliability  of s t e e l  (LRFD)  Subcommittee  Design  of  provides levels  Steel LRFD  for  Institute  structures. of  the  Structures design  strength  AIJ  Japan  (AU)  has  The Load and R e s i s t a n c e i s s u e d the  (Draft)"  equations  and  of  [5]  with  serviceability  "Standard in  for  February  associated limit  the  Factor  Design  Limit  States  1990. The  target  states.  studied  draft  reliability  Publication  of  the  draft  LSD  reliability  Steel  of  Standard  Japanese  timber  p h i l o s o p h y proposed f o r s t e e l The  reliability  provided  of  the  structures  developed  the  wooden s t r u c t u r e s the  material  these  built  property  structures  frame  system  lumber  for  study  are  is  is  Japanese  2x4  (1)  (Foschi  lacking.  using  levels code  the d r a f t  associated for  provide  2x4  factors  for  single  the  2-inch  the  first  structures.  indication  of  the  The  safety  Reliability based  on  Structural  studies  undertaken  material  property  (SS)  No.2)  Spruce-Pine-Fir s p e c i e s group i s  and  levels  a s s e s s i n g the  safety  (S-P-F)  nominal  the most w i d e l y  Japan these r e s u l t s  2-inch  of  impact  the the of  current  WSD  study  will  adopting  an  i n Japan.  in  three  levels  safety  results  this  information  and  this  members designed a c c o r d i n g  potential  LSD code p h i l o s o p h y f o r timber s t r u c t u r e s  of  dimension  Therefore  between  LSD S t e e l Standard and (2)  frame  studies  Japanese 2x4 wood  available.  relationships  Japanese  post and beam system  nominal  is  most  reliability  However,  data  implementation  While  with members designed a c c o r d i n g to  wood  design  construction  t o the LSD code p h i l o s o p h y and a c h i e v i n g the same t a r g e t proposed f o r  investigate LRFD  frame  [3]).  Canadian  property  evaluating  and member performance  the  assessment and  u s i n g the t r a d i t i o n a l  currently  material  on  Canada  wood  information required f o r  designed  which  focuses  in  using  to  structures.  system can be s t u d i e d u s i n g r e l i a b i l i t y methodologies  opportunity  study  for  sizes  two  (2x4,  dimension  are  exclusively  grades  2x8  and  lumber.  (Select 2x10)  Since  of this  used i n 2x4 wood frame s t r u c t u r e s  w i l l y i e l d the p r e l i m i n a r y  i n f o r m a t i o n on which  in to  6  base  an  analysis  housing d e s i g n i n  of  the  Japan.  potential  impact  of  LSD  on  2x4 wood  frame  2.  The g e n e r a l to  assess  systems, [5],  objectives  safety designed  and to a s s e s s  wood  frame  levels using  OBJECTIVES  of t h i s  for  Japanese  criteria  the r e l i a b i l i t y  construction.  study are to a p p l y RBD p r i n c i p l e s  Specific  from  2x4 the  levels  wood  frame  draft  LSD  construction  Steel  Standard  a s s o c i a t e d with c u r r e n t  objectives  of  the  study  2x4  are  as  follows:  1)  To review  the Japanese b u i l d i n g code and the  c a l c u l a t i o n system as i t  2)  structural  a p p l i e s to 2x4 wood frame c o n s t r u c t i o n .  To develop and p r e s e n t m a t e r i a l p r o p e r t y d a t a f o r Canadian  S-P-F  dimension lumber on the b a s i s r e q u i r e d by Japanese b u i l d i n g c o d e s .  3)  To d e r i v e  l o a d models f o r dead, occupancy and snow loads  a p p r o p r i a t e f o r a n a l y s i s o f 2x4 s t r u c t u r e s  4)  To study the r e l i a b i l i t y  levels  in  Japan.  f o r b e n d i n g , t e n s i o n and  compression members u s i n g d e s i g n c r i t e r i a taken from the Japanese d r a f t LSD S t e e l  5)  Standard.  To d e r i v e performance f a c t o r s f o r 2x4 wood frame c o n s t r u c t i o n to y i e l d the t a r g e t Standard.  safety  levels  chosen f o r the d r a f t LSD S t e e l  To d e r i v e d u r a t i o n o f l o a d adjustment f a c t o r s f o r 2x4 wood frame c o n s t r u c t i o n u s i n g Japanese l o a d models.  To a s s e s s the r e l i a b i l i t y s t r u c t u r e s u s i n g S-P-F  o f c u r r e n t Japanese 2x4 wood frame  material property data.  9 3. CURRENT STRUCTURAL CALCULATION SYSTEM FOR JAPANESE TIMBER STRUCTURES  3.1  BUILDING CODES AND STANDARDS With  the  exception  of  the  based on the  Japanese B u i l d i n g  requirements  are  different  discussion highlights  the  from those of  the major  the  entire  study  was  The Canadian Code  Japanese.  The  following  elements of the Japanese b u i l d i n g code structures.  BUILDING STANDARD LAV This  in  data,  Codes and S t a n d a r d s .  system r e l a t e d to 2x4 wood frame  3.1.1  strength  general  Building  mainly  [6].  provides  The c o n t e n t s  Code of  Canada i s Japan,  law  valid  Canada  [7].  only a f t e r  generally  of  this  However,  law  requirements are  the  similar  National  for  to  the  Building  buildings  the  National  Building  acceptance by l o c a l a u t h o r i t i e s .  speaking,  throughout Japan a t a l l  fundamental  Standard  Law  Code  of  Vhereas  in  is  valid  times.  3 . 1 . 2 BUILDING STANDARD LAV ENFORCEMENT ORDER Building specific  Standard  details  requirements.  in  These  Law  buildings Orders  Enforcement such as provide  enforcement a u t h o r i t i e s and d e s i g n e r s .  Orders  strength more  [8]  address  properties  complete  and  more design  guidelines  for  3 . 1 . 3 BUILDING NOTIFICATION Building There  are  notifications  two  Notification  for  Administrative supplement  Public. the  the  of  the  The  There  "2x4  Building  Law  many  and  Building  Code"  [9]  of  Special take  Administrative  charge  example,  of  after  the new  which  has  new  C o n s t r u c t i o n , or  if  there  Building  Notification  Building  is  issued.  Notification  either  simplified  for  For  one  structural  (MOC)  are  Law the  such  the  from local  officials  confirmation. approved  by  For the  Code r e v i s i o n ,  Administrative  span t a b l e s o r d e t a i l e d member s t r u c t u r a l  to  a  example,  many  building  a Building  member  is  for  For  of  the 2x4 wood frame  Special  Special  is a Notification  building  materials is  for  Standard  topic.  appointed  concerning or  of  requires  Agency  Construction  methods  Minister  the  of  affairs  Building  is  the  Ministry  Building  Notifications  The l a t t e r B u i l d i n g N o t i f i c a t i o n the  1)  Codes.  Notification  with one s p e c i f i c  Building  Building  Notification  notifications. Director  the  Building  Standard  deals  for  Notifications,  former  are  Each n o t i f i c a t i o n  so-called  and 2)  Building  Order.  supplements  Building  Public  Agency.  to  Enforcement  types  are  checking  a  construction, Agency using  [10] GHLC's  calculations.  3 . 1 . 4 STANDARD FOR STRUCTURAL CALCULATION OF TIMBER STRUCTURES Current This for  standard  structural  d e s i g n of  p u b l i s h e d by  Engineering  Design  in  AIJ  timber  [11]  is  Vood ( V o r k i n g  structures similar Stress  d e s i g n e q u a t i o n s and s t r e n g t h p r o p e r t i e s f o r  to  is  based on VSD.  the  Canadian Code  Design)[12].  Detailed  lumber and g l u e - l a m i n a t e d  lumber are Law  was  wooden  specified  revised  in  structures.  Structures  in  this  standard.  1987 to The  allow  Standard  The Japanese B u i l d i n g  construction  for  Structural  of  higher  Calculation  Standard  and  larger  of  Timber  was r e v i s e d i n 1988.  3 . 1 . 5 GHLC SPAN TABLE GHLC i s (CMHC). frame  similar  GHLC p u b l i s h e s  construction,  lumber f o r  to  the  Canada Mortgage  specifications  and span t a b l e s  based on VSD c r i t e r i a  2x4 wood frame  construction,  r e q u i r e d f o r c a l c u l a t i o n of member spans Allowable Unit Stresses  and Housing  [11].  [4]  Corporation f o r 2x4 wood  Design p r o p e r t i e s  l o a d d a t a and d e s i g n  for  criteria  include:  f o r 2x4 Lumber and S t r u c t u r a l  Glue-  Laminated Lumber; Deflection  Limits;  U n i t Shear R e s i s t a n c e  f o r Common N a i l ;  Nominal Dead L o a d ; Nominal Occupancy Load f o r R e s i d e n t i a l  Building;  and  Nominal Snow Load which are g i v e n i n the GHLC's span t a b l e s . Span composite  tables  are  based  action  between  on  the  simply  supported  framing  members  c o n s i d e r e d except f o r g l u e d f l o o r s .  beam and  analysis.  No  sheathing  is  3.2 PRINCIPLES OF STRUCTURAL CALCULATION FOR TIMBER STRUCTURES  3.2.1  DESIGN REQUIREMENTS Structural  Codes  vary  Generally  design  requirements  depending on the speaking,  following f i v e  timber  type,  specified  size  structures  in  Japanese  and h e i g h t  are  of  classified  the into  Building structure.  one of  the  categories:  General T r a d i t i o n a l Wooden S t r u c t u r e s 2x4 Wood Frame S t r u c t u r e s  ( mainly h o u s i n g )  ( mainly h o u s i n g )  Log C o n s t r u c t i o n Heavy Timber Special Japanese  Structures  Structures. Building  individual  members  structure.  Depending upon the  wooden s t r u c t u r e s the  items  common  which  are  for  the  requirements  analysis  type,  and  in  wood  for  s i z e and h e i g h t  Table frame  1.  the  design  comply with some or a l l  shown 2x4  have  of of  design  the the  of  complete structure,  of the requirements  Generally  structures  speaking,  of  less  for  than  Design.  by  structural  The  entire  calculation structure  a c c o r d i n g to  must  satisfy  the  the  three  Standard  effective  of the  i n d i v i d u a l members are designed by u s i n g GHLC's span t a b l e  alternatively Timber  shall  residential  stories,  and  Codes  or for  wall  l e n g t h requirement e x p l a i n e d i n 3 . 2 . 5 .  3.2.2 DESIGN LOADS Loads and e x t e r n a l  f o r c e s are  s p e c i f i e d i n the B u i l d i n g  Standard  Law Enforcement shown  in  Table  recognized cases,  2.  the  system  (normal  duration)  l o a d cases  of  has  load  be c o n s i d e r e d i n  duration)  two  loading  lumber and s t r u c t u r a l  for  load  and  loads a r e  design  Canada and the US  factors  only  l o a d i n g . Vhen temporary of  to  VSD methods o f  duration  Japanese  sustained  The  Unlike  different  the  stresses  Order.  the  which  various  duration  temporary  load  categories: (short-term  considered, allowable  glue-laminated  timber  are  unit  become double  those o f s u s t a i n e d l o a d s .  3 . 2 . 3 ALLOVABLE UNIT STRESS Allowable timber  are  Building  unit  stresses  specified  in  the  Notifications  C a l c u l a t i o n of Timber Since structures,  this the  construction  for  lumber and s t r u c t u r a l  Building  and/or  Standard  AIJ's  Law  glue-laminated  Enforcement  "Standard  for  Order,  Structural  Structures". study  allowable specified  A d m i n i s t r a t i v e Agency [13]  primarily  focuses  unit  stresses  in  Building  of  on  2x4  lumber f o r  wood  frame  2x4 wood frame  Notification  for  Special  are l i s t e d i n Appendix 1.  3 . 2 . 4 VORKING STRESS DESIGN CRITERIA Generally individual  size  speaking, of  following equations:  structural  structural  wooden  calculations members  shall  to be  determine based  on  the the  14 3.2.4.1 BENDING  _ M  *b =  <  ( 3. 1 )  cf r  b  where °"6  M  fb  :  bending s t r e s s ;  :  bending moment;  :  e f f e c t i v e section modulus;  :  allowable bending s t r e s s ;  :  s i z e factor for glued-laminated timber determined by the f o l l o w i n g formula but not less than 1.0. The factor i s not a p p l i e d for s o l i d lumber, therefore = 1.0 f o r s o l i d lumber,  ( 3. 2 )  where d i s the depth of the member i n cm.  3 . 2 . 4 . 2 SHEAR  r = a•  I K  <  ( 3. 3 )  fs  where shear  stress;  allowable shear  stress;  shape factor (rectangular cross s e c t i o n , a = 1.5); Q  shear force; e f f e c t i v e area of cross s e c t i o n .  3 . 2 . 4 . 3 TENSION 1)  T e n s i o n P a r a l l e l to the  ~A~  -  e  Grain  ( 3. 4 )  ft  where a  :  tensile  f  :  allowable  T  :  a x i a l tension force p a r a l l e l  A.  :  effective  t  2)  t  stress;  Tension Perpendicular In  generated, avoid stress  an  areas  where  an  appropriate  a  stress  perpendicular  to  shear  stress; to g r a i n ;  area of cross s e c t i o n ;  to the  excessive  allowable  tensile  Grain  tension  perpendicular  reinforcement in the  this grain  the  s h o u l d be g i v e n  direction. is  to  The  assumed  to  grain  in  order  allowable be  1/3  of  stress.  Compression P a r a l l e l t o the  °c  =  -f-  Grain  < fk  ( 3. 5 )  where a  :  compression s t r e s s ;  N  :  a x i a l compression f o r c e p a r a l l e l  A  :  a r e a of c r o s s s e c t i o n ;  /  :  allowable  c  fc  to the g r a i n ;  compression s t r e s s o b t a i n e d as  to  tensile  3 . 2 . 4 . 4 COMPRESSION 1)  is  follows:  the  if  A <30  :  f  k  = f  e  if  30 < A < 100  :  f  k  = f  c  if  100 < A  :  f  ( 3. 6 ) ( 1.3  = 0.3 f  k  -  ( A/100 )  /  c  0.01 A ) 2  ( 3. 7 ) ( 3. 8 )  where f  :  allowable  A  :  s l e n d e r n e s s r a t i o of the compression member A =  :  effective  :  r a d i u s o f g y r a t i o n of the column with r e s p e c t t o  c  short-member compression s t r e s s ; ^  ;  where L  e  i  e  length;  i  axis of buckling  e  the  = ^—^~  where  :  I  2)  moment o f  inertia.  Compression P e r p e n d i c u l a r  „  ~  c  N ~A  <  fc±  to G r a i n or  f'  ( 3. 9 )  c ±  where f j_ c  :  allowable  compression s t r e s s p e r p e n d i c u l a r to  the  grain; :  allowable bearing s t r e s s ;  A  :  support ( b e a r i n g )  N  :  compression f o r c e p e r p e n d i c u l a r to g r a i n .  f'  c  j_  area;  3 . 2 . 5 LATERAL RESISTANCE FOR RESIDENTIAL WOODEN STRUCTURES The structural  "Effective  Wall  calculation  of  Length  lateral  Methods"  loads  for  are  applied  for  common r e s i d e n t i a l  the  wooden  structures.  This  method  has  two  components:  l e n g t h p" and " R e s i s t a n c e  "Required  Ratio  of  F a c t o r of B e a r i n g w a l l q".  The  Effective  Vail  parameter  p has two v a l u e s ,  analysis.  Both p and q f o r the 2x4 wood frame s t r u c t u r e s are  i.e.  i n the B u i l d i n g N o t i f i c a t i o n The  following  for  p  e  s e i s m i c and p  f o r wind  w  force  specified  [9].  requirement  should  be  satisfied  for  lateral  r e s i s t a n c e f o r common r e s i d e n t i a l wooden s t r u c t u r e s :  £  pA =  ( 3. 10 )  ^  where pA  :  l a r g e r of e i t h e r  p  :  required r a t i o of e f f e c t i v e  e  p Aj e  or p A m  ;  p  wall length f o r  seismic  wall length f o r  wind  force; Aj  :  floor  p  :  r e q u i r e d r a t i o of e f f e c t i v e  w  area;  force; A  p  :  plumb measure a r e a ;  :  real  l e n g t h of the b e a r i n g w a l l with  factor Appendix (vertically  2  9 -. t  shows  projected  resistance  measurement  area)  for  the  of  the  span  or  plumb ridge  measure  sizes  direction  of  a  bearing wall. The resistance  required factors  ratios for  of  effective  bearing  wall  wall q  are  length given  p  e  in  and  p,  the  Building  w  and  Standard  Law  structures  and  The parameters  Enforcement Building p  e  and p  Order  Notification  b u i l d i n g s s u b j e c t e d to  factors  b e a r i n g w a l l s q,  with d i f f e r e n t and  Building  traditional  for  post  2x4 wood frame  based on r a c k i n g t e s t s  sheathing m a t e r i a l s , Notification.  are given  Generally  for  and 1/300  to t h e i r a l l o w a b l e It check  is  radian  for  o f common Resistance  bearing walls  i n the Enforcement Order  speaking,  the  2x4 wood frame  load  at  shear  p o s t and beam  structures  correspond  strengths.  important to note t h a t a l t h o u g h t h e r e a r e  structural  safety  against  lateral  loads  requirements  such  as  wind  earthquake, most s t r u c t u r a l member s i z e s a r e determined by the loads  for  structures.  beam  structures.  s e i s m i c and wind f o r c e .  s t r a i n v e r s u s r e s i s t a n c e o f 1/120 r a d i a n f o r t r a d i t i o n a l structures  and  were determined from the a n a l y s i s  w  residential for  for  residential Therefore  wooden only  structures  gravity  loads  a n a l y s i s o f s t r u c t u r a l member i n t h i s  study.  including were  2x4  and  gravity  wood  considered  to  in  frame the  4.  There Canadian Japan JSCE  are  Civil  (AU),  with  the  LSD approach f o r LSD  standard  steel  for  Society  with the  Japan The  of  construction  deals  Currently,  in  Society.  Japan  major  The AIJ  skyscrapers.  organizations  Engineering  and  deals  highways.  two  JAPANESE LIMIT STATES DESIGN  similar  such  from  dams,  local  the of  (JSCE).  The  bridges,  and  housing to  large  been c o n s i d e r i n g a d o p t i o n of  and r e i n f o r c e d c o n c r e t e s t r u c t u r e s  reinforced  to  Institute  Engineering  projects  has  are  Architectural  Civil  buildings,  AIJ  that  concrete  p u b l i s h e d by the JSCE i n 1986 however  structures  it  has  the  i n Japan. already  does not a p p l y to the  An  been  regular  buildings.  4.1 NEW JAPANESE STANDARD FOR LIMIT STATE DESIGN OF STEEL STRUCTURE  (DRAFT)  The LRFD  Subcommittee  S t a t e Design of S t e e l  of  AIJ  Structures  p u b l i s h e d the  (Draft)"  t o the d r a f t  s t a n d a r d , the S t e e l S t r u c t u r e s  the  "Load  and  Resistance  (Proposal)"  [14]  in  steel  structures.  officially Japanese  March  1986  Although  been a c c e p t e d , RBD  Factor  criteria.  the  the  The  to  [5]  draft  LSD  i n February  for  Limit  1990.  Prior  Subcommittee o f AIJ  Design examine  "Standard  for  Steel  Structures  acceptability Steel  content  would be the  following  requirements  of  Standard guideline adopted  d r a f t LSD S t e e l Standard are used and r e f e r r e d to i n t h i s  issued  RBD has  in not  for  the  from  the  study.  4.2 PROPOSED LOAD COMBINATION AND LOAD FACTORS The  LSD  multiplied product  by  of  equation load f a c t o r s  some chosen  5th p e r c e n t i l e criteria  generally  for  and the  specified  lumber)  consists  of  resistance  to  strength  the  load  effects  load expressed as  (conventionally,  and a performance f a c t o r  the  <j>. T y p i c a l  a  lower design  i s expressed a s :  Factored Resistance In  the  combination  general of  > Effect  case,  individual  the  load  of f a c t o r e d l o a d total  effects  load  ( 4. 1 )  effect  which  are  is  a  related  linear to  the  factored resistance according t o ,  *K  ETA-  >  (  t=l  where < / >  :  performance  R  :  specified strength;  :  i n d i v i d u a l load f a c t o r ;  :  individual  n  Qt  The proposed e f f e c t strength  limit  reliability  states  for  of  4. 2 )  factor;  load. factored  steel  loads and l o a d combinations  structures  with the a s s o c i a t e d  index a t performance f a c t o r <j> - 0.9 are g i v e n a s :  1.3Dn  /? = 2.5  ( 4. 3 )  l . l D n + 1.6In  /? = 2.5  ( 4. 4 )  /? = 2.0  ( 4. 5 )  l.lDn  + 1.6Sn  + 0.6In  for  target  l.lDn  + I.QEn  + O.ALn  0 =(1.5)  ( 4. 6 )  + 0.6In  0 = 2.0  ( 4. 7 )  0 = 2.0  ( 4. 8 )  l . l D n + 1.6Wn 0.9Dn  -  Following  1.6Wn load  combinations  shall  be  also  considered  in  heavy  snow a r e a s , l . l D n + l.bWn  + 0.55n + 0.4Ln  0 = 2.0  ( 4. 9 )  l . l D n + 1.7En  + 0.45n + 0.4In  /3 =(1.75)  ( 4. 10 )  Effect limit  of f a c t o r e d  states  with  the  loads and l o a d combination f o r associated  target  serviceability  reliability  index  at  performance f a c t o r <j> = 0.9 s h a l l be taken a s : l.ODn + l . O i n  ft = 1.0  ( 4. 11 )  l . O D n + 0.95n + 0.6In  j3 = 1.0  ( 4. 12 )  l . O D n + 0 . 4 £ n + 0.4In  0 = 1.0  ( 4. 13 )  l.ODn  + 0.9Wn + 0.6£n  0 =(-0.35)  ( 4. 14 )  l.ODn  -  0 = 1.0  ( 4. 15 )  Following  0.9W^n loads  combinations  shall  also  be  considered  in  snow a r e a s , l . O D n + 0.9Wn + 0.55n + 0 . 4 i n  0 = 1.0  ( 4. 16 )  l . O D n + 0 . 4 £ n + 0.45n + 0.4In  0 =(0.4)  ( 4. 17 )  where Dn  nominal dead l o a d ;  Ln  nominal l i v e (occupancy)  Sn  nominal snow l o a d ;  Wn  nominal wind l o a d ;  En  nominal earthquake  load.  load;  heavy  Basic lognormal  statistical  distribution)  data  (means  assumed f o r  the n o r m a l i z e d m a t e r i a l  resistance  shown  in  j3 -  steel  design  Table  3 . The  were  from T a b l e 3 f o r 2.0  and 0.25)  derived  two r a t i o s  and two  (cov = 0.15 and 0.2)  and c o e f f i c i e n t s  <j> using  the  variation  normalized load v a r i a b l e s  i n the d r a f t  relationships the  of  basic  LSD S t e e l Standard of  four  statistical  of  as shown i n F i g u r e  variation 1.  of  and are  combinations data  of nominal dead to nominal l i v e  coefficients  of  material  in  obtained load ( 7 = strength  5.  JAPANESE FULL SIZE TEST PROGRAM FOR STRENGTH OF LUMBER  Japanese  strength  properties  are d e r i v e d from s m a l l c l e a r results  are  available.  r e p o r t s review  used f o r  structural  wood specimens. Only a few f u l l  Among them,  the  following  r e s u l t s of the Japanese f u l l  Lumber, Report N o . 2 5 , 1985.  two  Grading i n  Structural  report  [15]  square  sections  proposed by  Forest  Products  Research  size  of  applied  tests  with  270  testing  After  machine  elasticity The Structural  air to  Group, Japan  of  bending  tests  of  the  Agency  and  Forestry  and  the  Forest  (FFPRI)  which  were c a r r i e d  span.  same t e s t i n g  Deflection  drying, obtain  a  the  bending  bending  at  out  by  Japan.  10.5 x 10.5 x 300 cm. The t h i r d  when a s p e c i f i e d l o a d was a p p l i e d a t condition.  Structural  results  Institute  cm t e s t  test  summarizes  were performed u s i n g the  specimen was  size  [16]  the nine p r e f e c t u r a l Research I n s t i t u t e s throughout All  test  Lumber - C o l l e c t i o n and  A n a l y s i s of S t r e n g t h D a t a , 1988. first  size  [15]  2) S t r e n g t h of Timber and Wood Based S t r u c t u r a l Wood Research S o c i e t y ,  full  wood  s i z e lumber t e s t programs:  1) F o r e s t r y Agency, Study on the S t r e s s  The  design of  procedure.  The  point  was  mid-span  was  load  measured  lumber y a r d i n green moisture test  strength  was  conducted  (MDR)  and  on  the  modulus  of  (MOE). second r e p o r t Group  a n a l y z e d the  full  of  the  [16],  the  Japan  Strength  Wood  s i z e lumber t e s t  of  Research  Timber Society  and Wood  Based  compiled  and  d a t a which had been c a r r i e d out by  the 21 Research o r g a n i z a t i o n s . S i n c e a f u l l standardized, The  these  collected  sections. lumber,  research  data  Although  procedures  was  adjusted  there  is  no  described in  to be r e a s o n a b l e i n t h i s  5.1  organizations as  d i d the  for  following  procedure i s  tests  described  standard  the  size test  in  full  not  differently.  the size  following tests  sections are  for  considered  study.  BENDING A  one-third  point  strength a f f e c t i n g defect between the t e s t  loading shall  system  shall  be  used.  The  maximum  be randomly p l a c e d on the t e n s i o n  side  span.  5.2 MOE MOE v a l u e s  shall  be a d j u s t e d with a span depth r a t i o  of 21 to  1  under an assumed u n i f o r m l o a d as d e s c r i b e d i n ASTM D2915 [ 1 7 ] .  5.3 MOISTURE CONTENT MOE and MOR v a l u e s (MC)  shall  be a d j u s t e d a t  target  moisture  of 15%, as d e s c r i b e d i n ASTM D 2915. The adjustment  a p p l i e d where the  difference  percentage  from  points  the  of  moisture  chosen  content  value.  The  is  ASTM  content  s h o u l d not be  larger D 2915  than  five  moisture  adjustments are made: P  2  = P  ( a -  1  p-M  2  ) / ( a -  p-M  x  )  ( 5. 1 )  where  P  1  :  o r i g i n a l s t r e n g t h p r o p e r t y a t moisture c o n t e n t  M\ x  P  :  2  target  s t r e n g t h p r o p e r t y a t m o i s t u r e content  Af ; 2  a and (3 are c o e f f i c i e n t s g i v e n i n ASTM D 2915.  5.4 MATERIAL  STRENGTH  Building strengths  of  publications 5th  Standard lumber  values  Standard  in-grade  and  Enforcement  test  for  of  the  Timber  Order  glued-laminated  mention t h a t m a t e r i a l  percentile  AIJ's  Law  material  Design  property  explains  showed the  material  approximately  equivalent  to  or  data  sets.  Generally  the  speaking, allowable  d e r i v e d by s i m p l y d i v i d i n g m a t e r i a l and 1.5 f o r temporary  lumber.  strength values  results  than  specifies  that  unit  None  are  of  the  are  percentile  s t r e n g t h by 3.0 f o r  lower  However  limited  stresses  the  based on  distribution.  strengths 5th  material  Japanese  usually of  for  less  available timber  sustained  are load  load.  5.5 DURATION OF LOAD ADJUSTMENT The several are  test  minutes  machine after  shall  be  loading  c o r r e l a t e d with e i t h e r  adjusted  starts.  Since  so  that  allowable  failure unit  s u s t a i n e d l o a d or temporary l o a d ,  not be a d j u s t e d u s i n g the s a f e t y  and d u r a t i o n of  load f a c t o r s  occurs stresses  d a t a need provided  i n ASTM D2555 [ 1 8 ] .  5.6 TENSION There available  is  no  i n Japan.  specific  full  size  tension  testing  procedure  5.7 COMPRESSION There  is  no  a v a i l a b l e i n Japan.  specific  full  size  compression  testing  procedure  27 6. CANADIAN FULL SIZE TEST PROGRAMS  Traditionally, lumber  have  specimens. to  find  In  the  visually  strength  also the  been  stress-graded  conducted were mostly grain this  evaluations. time,  the  lumber  of  combinations without  Canadian  testing  a  sampled  range  b r e a k i n g the e n t i r e  were used to d e r i v e  small  full-size, from  graded  clear  wood  were conducted  on-grade  production.  Canadian  The  tests  tension p a r a l l e l  to  the  s i z e samples were t e s t e d .  l o a d i n g concept was for  visually  in-grade t e s t s  More than 55,000 f u l l  values  tension results  by  large scale  properties  of  i n bending w i t h l i m i t e d  proof  5th-percentile  determined  late 70's,  mechanical  properties  introduced to estimate of test  size/grade  and  At  lower  species  samples. The bending and  new d e s i g n p r o p e r t i e s ,  which were  i n c l u d e d i n the CAN3-086-M84 v e r s i o n [1 and 1 2 ] . Although  the  aforementioned  characterizing  the  traditional  the  average  percentile of The  a major major  bending  modulus  exclusion values lumber r e s e a r c h reason  for  of  in-grade  strength of  were  properties  elasticity,  strength,  program was  further  tests  of  and  adequate lumber,  i.e.,  lower  5th-  the  a more d e t a i l e d undertaken  testing  was  to  for  second phase  from 1983 to 1985. provide  information  r e q u i r e d f o r the p r o b a b i l i s t i c LSD f o r m a t . The major with t h r e e  s p e c i e s groups o f Douglas F i r - L a r c h ,  Hem-Fir and  s i z e s 2x4, 2x8 and 2x10 and nine minor s p e c i e s  with  S-P-F three  s i z e s of 2x4, 2x6 and 2x8 were t e s t e d . The in-grade t e s t s  were conducted to e s t a b l i s h bending s t r e n g t h ,  bending  modulus  compression  of  elasticity,  parallel  to  the  tension  grain  parallel  strength  to  according  the to  grain  and  ASTM D 4761  [19]. The  third-point  span to depth r a t i o randomly lengths  located of  selected  3658mm f o r test.  the  was  applied  on  the  bending  specimen  with  o f 17: 1. The maximum s t r e n g t h - r e d u c i n g d e f e c t  within  2462mm f o r  for  load  the  2x4,  tension  span  for  3683mm f o r  test.  2x8 and 4267mm f o r  the  bending  test.  2x8 and 3683mm f o r  The gauge  lengths  2x10 were s e l e c t e d  Compression specimens were l a t e r a l l y  of for  restrained  The  gauge  2x10 were  2438mm f o r the  was  2x4,  compression  so t h a t the  test  r e s u l t s p r o v i d e s h o r t column s t r e n g t h p r o p e r t i e s . The  results  v e r s i o n [2 and 2 0 ] .  of  these  tests  were  included  i n CAN/CSA-086.1-M89  7. ADJUSTMENTS  In  OF CANADIAN IN-GRADE DATA TO JAPANESE BASIS  o r d e r to use Canadian t e s t  adjustments  were n e c e s s a r y  to  results  compensate  in this  for  the  study,  appropriate  differences  between  Canadian and Japanese t e s t i n g methods and d a t a a n a l y z i n g p r o c e d u r e s .  7.1 MQR The Canadian bending s t r e n g t h span t o The  depth r a t i o  parameters  Parameter Each lower  for  Veibull  data tail  Parameters  set  of  17 to  Normal,  data  then  were  d a t a were o b t a i n e d u s i n g  1 and a d j u s t e d Lognormal,  distributions  was  test  15% moisture  Parameter  were developed f o r  truncated  fitted  2  to  at  with  the  the  15th  same  and  strength  percentile,  four  content.  Veibull  the  the  data.  and  distribution  3  these types.  shown i n Appendix 3 and 4 were o b t a i n e d u s i n g 100% d a t a and  u s i n g lower 15% d a t a .  7.2 MOE Test loading  MOE  values  were  cross-head and a  span  were s u b s e q u e n t l y a d j u s t e d using a  full  span yoke  measured  to  to  depth  to y i e l d measure  with  ASTM D 2915  procedures.  For  data  were f u r t h e r  adjusted  a  o b t a i n e d d a t a were a l r e a d y 15 p e r c e n t  and  MOE  to  to  the  ratio  MOE v a l u e s  displacement  of  17  :  1.  Japanese  code  depth  t o the  of  target  in  of  21  data  derived  accordance  requirements,  ratio  the  These  which would be  midspan d e f l e c t i o n s  span t o  adjusted  stroke  using  :  these 1.  moisture c o n t e n t  MOE yoke with span to  depth r a t i o  The of of  17:  1. The f o l l o w i n g formulae [21] were developed t o a d j u s t  depth r a t i o o f 17 : 1 t o t h a t o f 21 : 1 f o r t h i s  -J— A  = —fr  17  -J—  0.00591 H x 1 0  1  -  t o span t o  study.  ( 7. 1 )  6  &TLP  0.00298 H x 1 0 ~  =-p^  •^21  ( 7. 2 )  6  &TLP  where  E  :  17  TLP  E  :  M0E  a t span t o depth r a t i o o f 17 : 1;  yoke  m E  loadi  n g  - head  a  t  s  P  a n  t  depth r a t i o o f 17 : 1;  o  Ei  :  M0E  H  :  nominal depth o f t h e specimen.  2  The 2 Parameter  yofce  a t span t o depth r a t i o o f 21 : 1;  Veibull  distribution  parameters  o f the a d j u s t e d  MOE d i s t r i b u t i o n a r e shown i n Appendix 5.  7.3 TENSION Since tests  there  o f lumber,  i s no Japanese t e s t no adjustment  The d a t a f o r t e n s i o n of  Vood S t r u c t u r e s  standards  for full  size  was a p p l i e d f o r the CVC t e n s i o n  s t r e n g t h was taken from R e l i a b i l i t y - B a s e d  Structural  V e i b u l l with lower 15% f i t s  tension  Research  Series  [ 3 ] . Parameters  data. Design f o r 2P  a r e shown i n Appendix 6.  7.4 COMPRESSION No results  adjustments  were  applied  to  the compression  f o r the same reason as t h e t e n s i o n .  The d a t a  in-grade  test  f o r compression  strength Structures  was  also  Structural  taken  from  Research  Reliability-Based Series.  Parameters  Design for  d i s t r i b u t i o n with lower 25% f i t s a r e shown i n Appendix 7.  2P  of  Wood  Veibull  8.DEVELOPMENT OF LOAD MODEL AND LOAD PARAMETERS FOR JAPANESE BUILDINGS  8.1 DEAD LOAD Because  the same v a l u e s  and VSD f o r  steel,  they  of the nominal l o a d were used i n the  too were u t i l i z e d  in  this  study  for  LSD  the 2x4.  wood frame c o n s t r u c t i o n . The  design  materials.  dead  The d e t a i l e d  load  is  based  information  of  on  the  dead l o a d  A I J ' s "Recommendations f o r B u i l d i n g D e s i g n , L o a d " Since for  this  Japanese  study was  intended to e v a l u a t e  wood  frame  the  GHLC's  span  for Floor  Joists:  specified  in  2x4  structures, table  average  used  is  available  the r e l i a b i l i t y design  this  study  below.  Tatami Mat  18 kgf/m  2  (177  Plywood  10 kgf/m  2  (98  15 kgf/m  2  (147  Sheathing(15mm)  Gypsum Board  for  Sheathing(9mm)  6 kgf/m  Plywood  Sheathing(12mm)  8 kgf/m  Light Roofing Clay  N/m ) 2  N/m ) 2  N/m ) 2  Rafters:  Plywood  tile  Material  2  2  in  of the  [22].  the for  weight  (59  N/m )  (78  N/m )  2  2  20 kgf/m  2  (196  N/m )  60 kgf/m  2  (588  N/m )  2  2  levels  load  values  are  listed  for  2 x 4  4 kgf/m (39 N/m)  2 x 6  5 kgf/m (49 N/m)  2 x 8  6 kgf/m (59  N/m)  2 x 10  8 kgf/m (78  N/m)  2 x 12  9 kgf/m (88 N/m)  For D/D  this  where  n>  dead  Lumber:  load,  study,  D  was  is  the  dead  assumed  normalized  load  (random  Normally  dead  load  variable)  distributed  random v a r i a b l e and D  is  n  with  a  mean  the of  d  =  design 1.0  and  standard d e v i a t i o n of 0 . 1 .  8.2 OCCUPANCY LOAD Occupancy load processes: magnitude assumed  of  loads  assumed to be the  s u s t a i n e d and e x t r a o r d i n a r y  both  the  distributed  between changes statistics,  are  are  taken  sustained to  assumed as  Poisson  from  the  draft  a  as  Gamma  LSD  Standard,  Load: 65 kgf/m  cov  0.40  mean r e t u r n  8 years  2  (637.4  N/m ) 2  were  The were  period  The f o l l o w i n g  study.  mean  The  live  2.  components  distribution.  processes. Steel  two  shown i n F i g u r e  extraordinary  according  model occupancy loads f o r t h i s  Sustained  and  s u p e r p o s i t i o n of  load  used  to  Extraordinary  Load:  mean  45 kgf/m  cov  0.55  mean r e t u r n  1 year  d u r a t i o n of  For  the  N/m ) 2  impulse  loading  sustained  (441.3  2  load,  the  load  magnitude  is  modeled  using  the Gamma d i s t r i b u t i o n :  where: mean = - | - ;  ( 8. 2 )  standard d e v i a t i o n =  A  ( 8. 3 )  2  The parameters of k and A can be c a l c u l a t e d a s :  mean  _  2  (standard d e v i a t i o n )  A =  m  e  f  n  65  9 - >  2  (65x0.42)  2  -2 =  ,  (standard deviation)^  = 6.25  =  ( 8. 4 )  9.615X10-  2  (65x0.42)^ ( 8. 5 )  and  the  duration  of  the  load  is  modeled  by  the  Exponential  d i s t r i b u t i o n as: f(t ) a  = Xe~  (  xt  8.  6  )  where U = 4 " X  = -T-  ( 8. 7 )  5  = -7mm-=  1.427X10"  8  ( 8 y e a r s = 70080 hours  ).  5  ( 8. 8 )  Similarly,  the  magnitude  of  modeled by the Gamma d i s t r i b u t i o n  extraordinary  live  load  can  be  i n E q . 8 . 1 and the parameters k and 7  a r e g i v e n by:  k =  ^  = 3.306  (45x0.55)  A=  ( 8. 9 )  2  v  ^ -5 = 7.346x10" (45x0.55)  ( 8. 10 )  2  2  V  and E x p o n e n t i a l d i s t r i b u t i o n i n E q . 8 . 6 f o r i t s  = W  A  Maximum simulation.  1-142X10-  occupancy  Five  extraordinary Carlo  =  simulation.  were  the 50-year 10% of  ( F i g u r e 3) u s i n g Extreme Type I  0ao = B •  The  ( 8.  loads  The upper  (  parameter  -  1  '  p  B for  determined of  for  a  50  maximum s u s t a i n e d  the  year  load  load  fitted  d i s t r i b u t i o n model:  ( 8. 12 )  model was  adjusted  for  8-year  return periods according to:  Q s = B  s  +  (  (  -  l  n  P  )  }  (  8. 13  )  where B  8  = (B - -IlL_5P_  +  ^ 8 _ )  plus Monte  maximum l o a d d a t a were  }  50-year  as:  11 )  p e r i o d were generated by the  (Gumbel)  )  the  J  time between events  4  thousand r e a l i z a t i o n s  load f o r  ;  ( 8. 14 )  The analysis return  parameters for  for  strength  were  used  50-year  limit  for  return  states  reliability  were  and  used  the  analysis  in  reliability  parameters  for  for  8-year  serviceability  limit  states. These variable live  parameters  were  where Q  q = Q/Q , n  l o a d o f 180 kgf/m  B u i l d i n g Standard  2  used is  to  either  derive  the  or Q  Q  50  s  normalized  and Q  n  is  random  the  design  (1.765 KN/m ) f o r r e s i d e n t i a l b u i l d i n g g i v e n 2  Law Enforcement  Order.  Therefore,  q = Q/Q  =  n  in  Q/180  can be expressed a s :  q  B  =  *  ( -  +  l  P) )  n  (  8  .  1  )  5  where  B*  :  B I 180  A*  :  A x 180  where B  is  g i v e n by E q . 8 . 1 2 or E q . 8 . 1 3 f o r  the 50 year  and 8  year r e t u r n l o a d models r e s p e c t i v e l y . These parameters  were c a l c u l a t e d  for  50 year  and 8 year  return  loads which a r e shown i n T a b l e 4.  8.3 SNOW LOAD In  Japan,  (general) d e f i n e d as Locations  snow  geographical areas  or  locations  heavy  snow  an a r e a with 50-year with  50-year  return  are  areas.  return  The  light  snow h e i g h t  snow h e i g h t s  100 cm a r e d e f i n e d as heavy snow a r e a .  designated  greater  less than  either snow than or  light  area  is  100 cm. equal  to  The annual in  Sapporo,  Niigata,  meteorological snow a r e a s ,  maximum snow h e i g h t Tokyo  and  observatories.  whereas  an  snow  annual  Tokyo f o r s i x s u c c e s s i v e snow  "Recommendations  were  n  from  belong to  load  for  duration  with  the  same  scale  a  the  local  the  heavy  snow  in  areas.  Sapporo  and  years. on  S, n  Building  a  roof  Design,  is  expressed  Snow L o a d "  [23]  in  the  AIJ's  and  draft  LSD  factors:  ( 8. 16 )  = p-Z .E .C a  duration  snow d a t a showing a snow h e i g h t and  S t e e l Standard as the product of a s e r i e s of  S  obtained  snow  Tokyo and Osaka belong to the g e n e r a l samples o f the  Design  Osaka  Sapporo and N i i g a t a  F i g u r e 4 and 5 are average  and annual average  r  where :  p  u n i t weight of snow 2.1 kg/m /cm (20.6 N/m /cm) f o r heavy snow a r e a 2  2  2.0 kg/m /cm (19.6 N/m /cm) f o r l i g h t snow a r e a 2  2  :  50-year r e t u r n h e i g h t of snow a c c u m u l a t i o n  E  :  environment  C  :  r o o f shape f a c t o r .  Z  a  a  r  The  snow  load  (cm);  factor;  distribution  c o n s i d e r e d corresponds  to  those  for  the maximum i n a p e r i o d of 50 y e a r s . The  annual  Extreme Type I  G = B  maximum  (Gumbel)  -  (-In  ground  snow  height  is  represented  by  distribution:  (-In  A  P  ))  ( 8. 17 )  an  where A and B a r e model parameters. A corresponding d i s t r i b u t i o n  of  maximum snow h e i g h t  in  N years  can be e x p r e s s e d a s :  G = B  -  where  p  1° N -  is  a  In  (-In  P  probability  )  of  (  g  _  non-exceedance and A  l  g  }  and B  are  parameters o f the Type I d i s t r i b u t i o n . The  50-year  probability 8.17.  of  return  snow  non-exceedance  <7 ,  height  of  50  49/50,  can  corresponding  be  obtained  to  using  A l s o u s i n g E q . 8 . 1 7 and E q . 8 . 1 8 , the n o r m a l i z e d g = G/G  a Eq.  can be  50  expressed a s :  9 = B *  < -  (  +  l  n  P  )  ( 8. 19 )  )  where AB + l n N AB + 3.9019  r Q on \  A* = AB + 3.9019  ( 8. 21 )  R*  These load. snow and  -  parameters  The parameters, loads  design  are  shown  snow  load  was  were c a l c u l a t e d  50 year  and 8 year  return  the average annual snow d u r a t i o n and the d e s i g n in for  return  value  states  and 8 y e a r - r e t u r n  the s e r v i c e a b i l i t y  for  assumed  Table this in  5.  The  study  location, are  reliability  shown  annual in  analysis  snow  Figure for  50-year  strength  v a l u e was assumed i n r e l i a b i l i t y  limit states,  6.  duration  limit  analysis  the same as occupancy l o a d .  for  The v a r i a b i l i t y factors  of  the  environment,  roof  shape and snow  density  i n E q . 8 . 1 6 should be c o n s i d e r e d i n the c a l c u l a t i o n of the snow  l o a d from annual maximum snow h e i g h t . those f a c t o r s  were c o n s t a n t  However,  because o f  lack  T h e r e f o r e the n o r m a l i z e d snow l o a d s = S/S  n  s =  =  S S  n  s  G  information.  is defined as:  G  5Q  G  snow l o a d ; a  n  study assumed t h a t  of a v a i l a b l e  where  S  this  d e s i g n snow l o a d ; maximum snow h e i g h t ; 50-year r e t u r n snow h e i g h t .  ( 8. 22 )  9. PERFORMANCE FACTORS FOR JAPANESE 2x4 WOOD FRAME STRUCTURAL MEMBERS  In  general,  performance given  the  data.  The  the  factors  reliability  level  /? and c o r r e s p o n d i n g  <f>, can be generated  appropriate  u s i n g the  RELAN program  performance f u n c t i o n G and r e q u i r e d  performance  functions  are  G  different  formulated  using  [24]  statistical a  specific  d e s i g n e q u a t i o n . T h e r e f o r e the performance f a c t o r <f> a t the g i v e n reliability In /?y  /?  r  this  from  i s o b t a i n e d from the r e s u l t s of a j3 - <j> a n a l y s i s . chapter,  the  draft  research project used to d e r i v e  d e s i g n e q u a t i o n s and t a r g e t  LSD  Steel  Standard,  strength  and the aforementioned s t a t i s t i c a l  the performance f a c t o r s a t  0rp f o r t y p i c a l S-P-F  reliability data  l o a d cases  govern i n many p r a c t i c a l importance  i.e,  levels  from  data f o r  the g i v e n t a r g e t  members used i n the 2x4 wood frame  S i n c e the g r a v i t y  fundamental  target  CVC's  loads  are  reliability  structures.  dead, occupancy and snow  load,  d e s i g n s i t u a t i o n s and are c o n s i d e r e d to be of in  the  calibration  work,  the  dead  load  and  occupancy l o a d case f o r b e n d i n g , and the dead l o a d and snow l o a d cases f o r b e n d i n g , t e n s i o n and compression were c o n s i d e r e d i n t h i s  study.  9.1 STRENGTH LIMIT STATES Effects evaluation  of  of  factored  the  loads and the  /? - <j>  o b t a i n e d from the d r a f t  specific  relationship  for  LSD S t e e l S t a n d a r d .  l o a d combination  strength  limit  states  for are  A n a l y s e s a r e performed f o r  f l o o r and f l a t r o o f member d e s i g n s . For  floor  joists,  effects  of  dead  and  occupancy  load  will  be  compared with the f a c t o r e d r e s i s t a n c e u s i n g the d e s i g n e q u a t i o n  1.1 D + 1.6 L n  For evaluated  rafters,  n  ( 9. 1 )  < cf, i?05 0j  effects  of  dead  load  and  snow  load  will  be  using:  1.1  D  + 1.6 S  n  <  n  <p  R  ( 9. 2 )  0t05  vfhere e f f e c t of d e s i g n dead l o a d ; e f f e c t of d e s i g n l i v e  K  load;  e f f e c t o f d e s i g n snow l o a d ; <p  performance  •^0.05  specified strength.  The r e l a t i o n f u n c t i o n G.  For  of  be  states,  calculated  using  the  performance  the performance f u n c t i o n G  + L)  (9.  3)  + S)  (9.  4)  and  G = R - ( D for rafters  limit  can  can be f o r m u l a t e d a s :  G = R - ( D for floor joist  /? - <f>  strength  j o i s t s and r a f t e r s  factor;  in f l a t  roof,  where R  :  s t r e n g t h (a random v a r i a b l e ) ;  D  :  effect  L  :  effect  of the  5  :  effect  of the snow l o a d (a random v a r i a b l e ) .  of the dead l o a d (a random v a r i a b l e ) ; occupancy l o a d (a random v a r i a b l e ) ;  for  By  substitution  of  the  appropriate  design  equation,  the  performance f u n c t i o n s can be expressed a s :  G = R -  +  ° f  (dy + I )  6  ( 9. 5 )  f o r j o i s t and  G  for  =  ~ l.l °f.6  R  R  +  )  s  7 +  ( 9  )  6  rafter.  where 7  :  D  J  L  f  n  D /S n  D/D ;  I  L/L ;  r  joists,  for rafters;  n  d  o  n  n  s/s . n  9.1.1 EFFECT OF LOAD RATIO 7 The d e t e r m i n i s t i c v a l u e 7 = D /L n  load r e l a t e d  n  o r 7 = D /S n  was r e q u i r e d as a  n  i n p u t f o r the computation o f /? - <j> r e l a t i o n s  using Eq.9.5  or E q . 9 . 6 . A ratio project.  In  7 = 0.25 was chosen f o r i n i t i a l order  to  validate  the c h o i c e ,  safety actual  studies j  a  in this  values  were  c a l c u l a t e d u s i n g GHLC's span t a b l e r e q u i r e m e n t s . The r a t i o 7 = 0.25 was appropriate the  light  i n t h e heavy snow a r e a  T a b l e 6 a . The e f f e c t  snow a r e a and f o r occupancy l o a d .  7 was h i g h e r  than  0.25 as shown  o f t h e c h o i c e o f 7 on s a f e t y  However i n  i n Table  6 and  was s t u d i e d f o r <f> -  0.8,  0.9 and 1.0  grade.  Results  i n Sapporo and the same ^-values in  Figure  tends to reduce s a f e t y a  Veibull  7 show t h a t  levels,  distribution;  if  increasing  the  ratio  j  =  D /S n  n  s t r e n g t h d i s t r i b u t i o n was assumed as  therefore  v a l u e s of 7 f o r heavy r o o f i n g j  i n Tokyo f o r 2x8 No.2  subsequent  analysis  of  the  actual  is also studied.  a  9 . 1 . 2 RESISTANCE DISTRIBUTION MODEL The c h o i c e of cp r e l a t i o n s h i p . different sets.  the  Figure  resistance  Figure  8  model on the  resistance 8  the  the complete d a t a s e t s .  fitted  to  lower  Parameter entire data  data  for  entire In  Veibull  cumulative  to  avoid  fitted  Figure  11  to  fitting  to  used  to  variation  when the  lower analyze  In  15  most  -  Figure  the the  less  lower fitted  than  0.3.  the  the  of  the  the  P  -  data.  All  cp r e l a t i o n s h i p s  cases,  the  2  four  complete  data  distribution  models  the  Parameter  the were  the  lower  to  the  are  for  four  determined by  size  Veibull  models  truncation).  distribution each  to  percentiles.  distribution (15%  2  and  The model f i t t e d  cp r e l a t i o n s h i p  for  to  data  distribution  data  four  fit  compares  15% of  the  resistance  the 9  d i s t r i b u t i o n parameters  15% of P  [3].  percent in  using  influence of  when  the d a t a w e l l a t  problems,  lower  the  types the  combination.  these  the  shows  distribution  were  probabilities  the  resistance  reduced  to  10 compares  d a t a range does not f i t  order  were  Figure  to  showed t h a t the  data  fits  the  derived  the (5 -  d i s t r i b u t i o n models a r e  significantly  resistance  fitted  of  when the  distribution  sets.  cp r e l a t i o n s  models  F o s c h i et a l .  was  tail  -  influence  cp r e l a t i o n s  model  /?  distribution  shows  f3 -  distribution  shows  d i s t r i b u t i o n model a f f e c t s  and  models grade  distribution  tended  to  give  distributions. Weibull  results Thus,  following  the  distribution  average  <f> r e s u l t s  (3 -  and  the  15%  trend  obtained  truncation  were  for  using  used  the  2  in  four  Parameter subsequent  analysis. Results also affects  higher  12 and 13 show t h a t  the r e l i a b i l i t y  From F i g u r e a  in Figure  12 u s i n g lower reliability  opposite  result  ranking of data sets 15% d a t a ,  index  when  the d a t a f i t t i n g  than  using  the v i s u a l SS,  the  while  entire  strategy  i n a /? - <j> a n a l y s i s . lumber grade No.2 has  Figure  13  data  set  four  snow  showed  to  the  calculate  d i s t r i b u t i o n parameters.  9 . 1 . 3 BENDING PERFORMANCE FACTOR Performance occupancy taken to  factors  are  l o a d case u s i n g j  tabulated  for  0.25 and the a c t u a l  -  loads  f o r the  j  a  from T a b l e s 6 and 6 a . T a b l e T summarizes ^-values  three  target  size/grade values  ^-values  combinations  c o r r e s p o n d i n g to  (/?  = 3.0,  r  for  S-P-F.  given  2.5 The  (^-values  in  and  2.0)  results  14 shows the average  f3 -  7 = 0.25. Figure  15 shows the average  at  j.  the  actual  Table  a  8  gives  l o a d case  for  the  show  the  selected lower  Tokyo and Osaka which  <j> t r e n d s  for  the  corresponding  s i g n i f i c a n t d i f f e r e n c e s between 7 = 0.25 and the a c t u a l •y Figure  and  a  five  j3have  values. l o a d cases  at  /? - <j> t r e n d s f o r f i v e l o a d cases the  approximate  mean  /3-values  c o r r e s p o n d i n g to s p e c i f i c <f> v a l u e s a t 7 = 0.25 and the a c t u a l 7 . As  explained  in  draft  LSD  Steel  Standard,  /? = 2.5  is  targeted  f o r a l o a d combination of dead l o a d p l u s occupancy l o a d ( E q . 4 . 4 ) a t <j> =  0.9  and j3 = 2.0  load in  (Eq.4.5)  assumed 0 f o r draft  at  a  load  the  rafters  LSD S t e e l  resulting if  for  same <j> = 0 . 9 .  of  the  Standard at  <0-value  combination o f  residential  is  /Jj.  used f o r  <j> =  (Eq.9.2) snow  0.9  for  actual  with <j> = 0.9  load  steel  flj,  a  T  rafter  structures  the  T a b l e 8 shows  the  Alternatively  0.95 f o r 7 = 0.25  the  design  has been adopted f o r  design.  For  l o a d was  E q . 4 . 5 from  than 1.0.  Therefore  this  case  have comparable <f> -  a  current  Japanese  design  effect  adjustments  to  design  effects  are  to  glued-laminated  of  lumber,  live  live  equation  the  dead p l u s  Fig.  1 shows  (3 r e l a t i o n s h i p s  to  structures. Although  cm),  If  = 2.5 then 4> -  = 2.5),  (f3  snow p l u s  analysis,  building.  S-P-F  values.  j  combination f o r  t h a t 2x4 wood frame  this  = 2.0 would be l a r g e r  we adopt E q . 9 . 2 which r e q u i r e s  and  In  dead p l u s  applied  size effect the  design  effect  strength  methods  do  properties lumber f o r  not  of  adjustment  properties  equation  for  relates  dimension member  lumber  size (size  depth more than 30  adjustments are r e q u i r e d to s i m p l i f y the strength  apply  presentation  lumber.  strength  The to  size  member  dimensions a c c o r d i n g to  °i *2  where a and  to  x  _ (  " I,  and o~  2  the  2 2 VT H L, )  H  a  L  ( 9. 7 )  1  r  e  ^  depths  magnitude of the s i z e  n e  s t r e n g t h c o r r e s p o n d i n g to the and E  2  and k  is  the  parameter  lengths L  x  and  determining  effect.  U s i n g t h i s E q . 9 . 7 , then E q . 9 . 1 can be expressed as  L  2  the  1.1 D  + 1.6 L  N  = <p R (  n  0  ( 9. 8 )  g° ° L  0  L  a l s o E q . 9 . 2 can be expressed as  1.1  + 1.6  D  N  where 4>  Q  is  N  the  the c h a r a c t e r i s t i c  = <t>  S  R  0  (  0  performance  factor  bending s t r e n g t h  a depth H  = 184 mm and a l e n g t h L  depth  length  Q  factor  of  the  member  associated  with R  9- 9 )  which  Q  is  f o r a s t a n d a r d i z e d 2x8 beam h a v i n g 3000 mm; H and L a r e the  -  Q  and  (  H °L°  being  evaluated;  and fc i s  actual  the  size  parameter. The  performance  obtained using least  factor  strength  0  and parameter fc are  R  0  squares t e c h n i q u e s to minimize the f u n c t i o n :  r  F = ££E|^  <j> , the  i V»W  oi ( - ^ i j p '  R  )  ( 9  1 0  )  where i  =  1,2  j  =  1 , . . , 3 (three  / . =  (one s p e c i e s , two  grades);  sizes);  1,..,5 ( f i v e loading  conditions).  The m i n i m i z a t i o n was c a r r i e d out u s i n g the a c t u a l = 0.25 and a c t u a l Table  7.  The  1511 mm f o r size effect 4.5  in  both  test 2x4,  at  j  a  spans  8 = 2.5  for  3131 mm f o r  parameter 7  the  cases.  <f> v a l u e s  and a d o p t i n g </> = 0.9 as shown  bending  0  (span/depth  2x8 and 3994 mm f o r  ratio  of  2x10. The  determined i n the m i n i m i z a t i o n was Adjusted  characteristic  17:1)  strength  for in are  bending  approximately  values  R, 0  are  7  shown i n T a b l e 9 with the c o r r e s p o n d i n g non-parametric 5th for  2x8's. The s a f e t y  index 0 v a l u e s  a s s o c i a t e d with the  and 9.9 were e v a l u a t e d f o r the case j = 0.9 u s i n g the R calculated  for  d e s i g n Eqns.  = 0.25 and the a c t u a l  the  for  0.85  the  for  actual  the  case  The  y. a  safety  7 = 0.25 and <j>  assessment  = 0.25.  Results  T a b l e 10b f o r <j>  Q  obtained -  when the  2.49  actual mean 0  actual 7  a  the  is a  mean 0  2.59  from 2.31 is  for  with  the  =  T  <f>  =  Q  actual  j . a  0  y  a  is  used a r e  given  in  with  a  to  2.69.  0  = 0.9 and 7 = 0.25 the mean 0 For  <j>  0  = 0.85 and u s i n g  range  from 2.25  to  2.92  at  to 2 . 8 0 , <f>  0  -  and  0.8  the the  for  the  i n T a b l e 10b.  occupancy  for  referenced  the  to  dead  plus  2x8 s i z e are  0.85 and the a c t u a l j If  limit  l o a d and E q . 9 . 9  relationship  0 = 2.5.  the t a r g e t 0  repeated  2.48 with a range from 2.13  For bending s t r e n g t h plus  average  0.85 and 0 . 8 0 .  with a range 7  0  f o r <f> = 0.9 and 0.85 when  actual  A c c o r d i n g to the T a b l e 10a, f o r <j> is  was  = 0.85 and 0.8  0  T a b l e 10a shows the r e s u l t s of t h i s a n a l y s i s 7  a  l o c a t i o n s and s i z e grade combinations i n T a b l e 7  was a p p r o x i m a t e l y 2.5 f o r 7 = 0.25 but d i d not a c h i e v e 2.5  9.8  with <f>  j ,  and s i z e parameters k g i v e n i n T a b l e 9. The  0  0  percentiles  a  states is  Eq.9.8 is  recommended as  snow  load.  given  i n T a b l e 9.  y i e l d s average  safety  the c h o i c e of 7 = 0.25 and the  f o r c a l i b r a t i o n then the average  safety  The  recommended f o r the  design  specified  dead  checking strength  Using k = 4 . 5 ,  4>Q -  i n d i c e s 0 of a p p r o x i m a t e l y same 4> = 0.85 a r e Q  adopted  i n d i c e s 0 can be i n c r e a s e d .  9 . 1 . 4 TENSION Reliability  levels  procedures p r e v i o u s l y load  case  levels  for  described for  dead  load  plus  snow  the  four  snow  locations  for  resistance  distribution  Table  for  11  T  2.5  0-values  and 2.0)  four  snow  loads  location.  The  calculated  the  cases  at  7  slightly  lower where the a c t u a l j  = 0.25.  to  specific  of  12 g i v e s  0 values  studied  for  using  minimization  selected  = 0.25  a  and  factors  size/grade the  and  3683mm f o r  are  the a c t u a l  Veibull  to  target  8-  not  0 -  was  carried 0  j  7  assuming  the  significantly are  than 1.  <j> t r e n d s f o r  out  four  at  a  l o a d cases  each  location.  7. a  standardized 0  2x8  = 3000 mm;  = 2.5 with <j> = 0.9 f o r 7 = 0.25 0  The gauge l e n g t h s of 2462mm f o r 2x4, 3683mm f o r 2x8  y. a  2x10 were  used  y. a  for  the  tension  strength  tests.  The  parameters were 8.9 f o r 7 = 0.25 and 9.5  Adjusted c h a r a c t e r i s t i c  lumber grades SS and No.2 are  at  corresponding  = 184 mm and a l e n g t h L T  for  a  (^-values i n Tokyo and Osaka  7 = 0.25 and the a c t u a l  r e s u l t i n g tension size effect for  material  combinations  actual  values are greater  shown i n T a b l e 11 f o r 0  and the a c t u a l  the  three  the approximate mean /3-values  t e n s i o n member h a v i n g a depth H using r e s u l t s  one  reliability  the 2 Parameter  Average /?-values were not a f f e c t e d by the c h o i c e of The  The  c o r r e s p o n d i n g to  However  7.  16 shows the average  Table  considered.  were  performance  by  7  was  for  affected  Figure  choice  load  only  data.  summarizes  = 3.0,  (8  bending members. However  d e r i v e d by f i t t i n g  the lower 15% of the t e s t  values  t e n s i o n members were c a l c u l a t e d u s i n g the  strength values  R  Q  for  the  shown i n T a b l e 13 with the c o r r e s p o n d i n g  non-parametric 5th p e r c e n t i l e s f o r Eq.9.9 limit  is  state.  adopted f o r  Actual  /?'s  2x8's.  design  for  the  checking f o r four  the  l o a d cases  tension  shown i n  strength Table  14a  and T a b l e 14b are d e r i v e d u s i n g 4> = 0.90 and 0.85 f o r j = 0.25 and the 0  actual 7  a  with the c o r r e s p o n d i n g s p e c i f i e d s t r e n g t h s R  A c c o r d i n g t o the T a b l e 14a, the mean f3 i s to 2.72)  at  0.9 and the mean /? i s  = 0.85 f o r 7 = 0 . 2 5 . The mean /? i s 2.50 (range from 2.21 to  2.77)  <j>  at  4> = 0.9 f o r the a c t u a l O  Eq.9.9  is  strength  limit  strength  R  from  j  Q  2.34 to 2.88 a t 0  8.9,  (range from 2.25 2.83)  Q  0  <j>Q =  Table  reliability  and the mean /? i s 2.61 with a range from  a  = 0.85 f o r the a c t u a l j  from T a b l e 14b.  a  recommended state  for  2.61  2.50  (range from 2.39 to  <f> =  at  0  from T a b l e 13.  0  the  with actual  for  design  k = 9.5, j  (j> = 0.90 0  from T a b l e  a  checking and  for the  In  levels  all  cases  this  design  comparable t o s t e e l  equation  tension  adjusted  13. When 7 = 0 . 2 5 ,  0.90 when used with the a d j u s t e d 2x8 s t r e n g t h 13.  the  R  Q  2x8  then k =  f o r 7 = 0.25  would  lead  to  s t u d i e s was a p p l i e d  for  structure.  9 . 1 . 5 COMPRESSION The approach adopted t e n s i o n r e l i a b i l i t y reliability  level  performed f o r tension  the f o u r  studies.  restrained parameters  analysis  for  l o a d cases  Compression  against  buckling  compression  members.  (dead l o a d p l u s snow load)  members (i.e.  are  considered  short  were o b t a i n e d by f i t t i n g a 2 Parameter  25% of the t e s t  data.  Analyses  columns).  to  were  used f o r be  fully  Resistance  V e i b u l l to the  lower  Table values  (8  15 =  T  summarizes  3.0,  2.5  ^-values  and  2.0)  c o r r e s p o n d i n g to  for  selected  f o r f o u r snow loads 7 = 0.25 and the a c t u a l y . a  s i g n i f i c a n t d i f f e r e n c e s with the c h o i c e of Figure 7  = 0.25.  17 shows the average  Table  16 g i v e s  the  8  -  three  size/grade  target  8-  combinations  The r e s u l t s do not show  7.  <j> t r e n d s  for  four  approximate mean ^-values  to s p e c i f i c <f> v a l u e s a t 7 = 0.25 and the a c t u a l  l o a d cases  at  corresponding  y. a  The m i n i m i z a t i o n was c a r r i e d out assuming f o r a s t a n d a r d i z e d 2x8 compression members h a v i n g a depth H  0  mm; u s i n g r e s u l t s  shown i n T a b l e  0.25 and the a c t u a l j . and  4267mm f o r  2x10  were  used  r e s u l t i n g compression s i z e e f f e c t 7 = 0.25 and 8.7 i n the a c t u a l values  are  R  Q  shown i n T a b l e  5th p e r c e n t i l e s f o r  actual  index 8 are  j, a  = 2.5  8  with <j> -  0.9 a t  7 =  j, a  for  the  compression  test.  The  parameters were a p p r o x i m a t e l y 8.3 and a d j u s t e d c h a r a c t e r i s t i c  17 with the  in  strength  c o r r e s p o n d i n g non-parametric  2x8's.  Using Eq.9.9 f o r the  15 f o r  = 3000  Q  The gauge l e n g t h s of 2438mm f o r 2x4, 3658mm f o r  a  2x8  = 184 mm and a l e n g t h L  d e s i g n with <j>  and the  adjusted  0  = 0.9 and 0.85 f o r  characteristic  values  shown i n T a b l e 18a and T a b l e 18b f o r  R, 0  size,  7 = 0.25 and the  safety  grade and l o a d  combination. A c c o r d i n g to the T a b l e 18a and T a l e 18b, the mean 8 i s 2.51 a  range  from 2.15  to  3.11  range from 2.30 t o 3.25 a t  at  0  O  <f>  0  = 0.9 and the = 0.85 f o r  mean 8  7 = 0.25,  is  with  2.65 with a  the mean 8 = 2.51  with a range from 2.09 to 3.15 a t (f> = 0.9 and the mean 8 = 2.66 with a 0  range from 2.23 t o 3.29 a t <f> = 0.85 f o r the a c t u a l 0  j. a  Based on t h i s with the a d j u s t e d  analysis,  i t i s recommended t h a t k = 8 . 7 , <j>  2x8 s t r e n g t h R  f o r the a c t u a l  0  0.9 with the a d j u s t e d 2x8 s t r e n g t h R with s t e e l  for j  0  j, a  = 0.9  0  o r k = 8 . 3 , (j) Q  = 0.25 would be comparable  structures.  9.2 SERVICEABILITY LIMIT STATES Effects limit  states  of factored  l o a d and l o a d combination f o r s e r v i c e a b i l i t y  a r e o b t a i n e d from the d r a f t  LSD S t e e l Standard  in Section  3.2. To  follow  controlled  this  i n terms  standard,  of e i t h e r  the  deflection  of  the  a p r o p o r t i o n o f the span o r  beam  is  specified  d e f l e c t i o n l i m i t expressed a s :  max  —  ( 9. 11 )  ^allow  where maximum d e f l e c t i o n ;  A,  allowable  allow  deflection;  L  beam span;  K  limiting deflection  dallow  specified deflection  The  maximum  deflection  factor; limit.  can be c a l c u l a t e d  for a  single  under u n i f o r m l y d i s t r i b u t e d l o a d a s :  5-( D  n  +  Q )-s.L  4  !L  384 • <j> • E • I  -  \llow  ( 9. 12 )  joist  52  where maximum deflection corresponding to E; allowable deflection;  ^allov  design uniformly distributed dead load; design uniformly distributed occupancy load; spacing between members; mean modulus of elasticity for the population of  E  lumber; moment of inertia of the member cross-section,  whereas for rafters:  5-(  D  n  + 0.9-_S„ 384-<j>-E-I  )-s-L  4  ^  A  a//ou>  ( 9. 13 )  where design uniformly distributed snow load.  A performance function for deflection limit state of a joist can be formulated as:  G  =  Aallou  5• ( D + Q ) • s•L  4  384-E-I  ( 9. 14 )  where D  dead load (a random variable);  Q  occupancy load (a random variable);  E  modulus of elasticity of the member (a random  variable), whereas f o r the G  -  rafter:  ( 9. 15 )  384. E • I  allow ~  A  where S  By  :  snow l o a d (a random v a r i a b l e ) .  substitution,  the  can be expressed f o r j o i s t  performance  function  and  design  as:  + 1)• E  (y  equation  '  v  where  d  :  D I  D;  7  -  DJ  Q;  1  :  Q I  Q,  and f o r the r a f t e r ,  C -  °  ~  1  n  n  n  the performance f u n c t i o n i s g i v e n by  ( dy + s ).<p.E (7 + 0.9)- E  1  ( 9- I  .  7  )  where  7  :  DJ  S;  :  S I  S.  The parameters  n  n  for  random v a r i a b l e s  Q and S are  assumed 8-year  r e t u r n loads f o r the s e r v i c e a b i l i t y The  performance  functions  limit of  states.  Eq.  9.16  and  Eq.  9.17  were  e v a l u a t e d u s i n g the RELAN program. Table values four  19  summarizes  = 2.0,  snow  loads  ^-values  1.5 and 1.0)  j  c o r r e s p o n d i n g to  1.0 a t order for  results  = 0.25 and the  did  not  actual  meet  the  The r e s u l t s  y. a  the  f3  T  = 1.0,  deflection  satisfactory  a performance f a c t o r  serviceability  comparable with s t e e l  /?-  structures.  limit  do not  show  7.  4> = 0.9 as was recommended by the d r a f t to g e t  target  f o r s e l e c t e d s i z e / g r a d e combination f o r  s i g n i f i c a n t d i f f e r e n c e s with the c h o i c e o f The  three  reliability  f3  LSD S t e e l S t a n d a r d .  <j> = 0.85  states  of  to y i e l d  T  = In  s h o u l d be used safety  levels  10. DURATION OF LOAD EFFECTS  Strength load.  Members  strength for  as  subjected  the  temporary  load  stresses  for  by  Foschi  practice  with  this et  simulation  was  combination  on the  S-P-F  applied  load  are  two  is  a  to  25]  of  of  in  the  order  a to  the  higher account  unit  the  snow  snow a r e a ,  times  and unit  stresses  for  developed damage a c c u m u l a t i o n used  the  to  evaluate  adjustments. effect  Q2). S-P-F  of v a r i a t i o n  light  The a l l o w a b l e  l o a d adjustments  grade  In  have  of  snow a r e a .  load  Ql and SPF  quality  duration  load  loads.  was  evaluate  duration  low  a newly  duration  dimension lumber (SPF  Q2  load heavy  to  the  Japanese s t a n d a r d r e g a r d s  the  and  on  duration  current  in  [3  grade with a c o e f f i c i e n t P-F  the  chapter,  al.  respect  short-term  (short-term)  temporary In  depend  longer duration  (long-term)  sustained load.  lumber  to  characteristics,  sustained  model  of  than o b t a i n e d f o r  these  load  properties  of  for  Japanese  Monte  Carlo  selected  load  two  qualities  Ql i s a h i g h  of  quality  of a p p r o x i m a t e l y 20 p e r c e n t .  with  coefficient  of  variation  Sof  a p p r o x i m a t e l y 28 p e r c e n t . The duration  objective  of  of  adjustment  reliability  load under  the  short-term  duration  of  factors  load  is  load  analysis  K  such  D  is  that  to  develop  the  member  maintained when d u r a t i o n of  load  e f f e c t s are considered. S i n c e d a t a of an average local applied  meteorological in  this  snow d u r a t i o n can be o b t a i n e d from the  observatories,  analysis.  Snow  load  simple was  snow assumed  load  models  constant  for  were the  average  duration  of  the  ground  snow  load  in  each  year  in  four  locations. D u r a t i o n of be e v a l u a t e d  l o a d response of two q u a l i t i e s  in this  o f S-P-F  lumber  will  study.  10.1 DAMAGE MODEL A n o n l i n e a r damage a c c u m u l a t i o n model expressed by the differential  e q u a t i o n was developed by . F o s c h i e t a l .  &  = a [r(t)  a  :  -  <r r ] 0  8  6  + c [r(t)  -  following  [3 and 2 5 ] :  <r rj" a  ( 10. 1 )  0  where damage s t a t e v a r i a b l e and a = 1 a t a,b,c,n  (a = 0 i n the i n i t i a l  state  failure);  model parameters;  : :  threshold stress  r(t)  :  stress  T  .  s t a n d a r d s h o r t - term bending s t r e n g t h of the member  <T  0  S  ratio;  history;  o b t a i n e d i n a ramp t e s t of one minute d u r a t i o n . Only when Since damage  this  T(t)  > o" r , w i l l t h e r e be damage a c c u m u l a t i o n . 0  differential  accumulation  was  s  equation  model  calculated  is  step  difficult by  step  to as  evaluate,  the  shown  the  in  following procedures:  a  i  = i-l a  K  i  +  i  L  (  10. 2 )  where K. = exp [c (r,- -  ^  =  (r  K  AT  8  0  - *T)  4  0  n  A t ]  ( 10. 3 )  ~ » (  b  8  1)  ( 10. 4 )  ( b + 1 )  s  where  <7 r,)  = median  of  (  r  x60  s  (MPa/Hour)  and  the  10. 5 )  damage  can  a  be  o b t a i n e d a t any time by the r e c u r r e n c e r e l a t i o n s h i p o f E q . 1 0 . 2 . The parameters  6,  c,  and the d i s t r i b u t i o n o f r  n,  <r  were assumed l o g n o r m a l l y  0  i s assumed l o g n o r m a l l y d i s t r i b u t e d and known  s  from the a n a l y s i s  of  short-term t e s t s .  random  c,  n,  values  studies Q2)  for  were  Structural  6,  quality taken  a  level  from  Research  distributed  and  Q  1 (SPF  r  The parameters  for  g  Ql)  the  and q u a l i t y  Reliability-Based Series  [3].  S-P-F  Design  Those  obtained f o r  duration  level of  parameters  of  loads  2 material Wood are  the  (SPF  Structures listed  in  T a b l e 20. Damage i s  d e f i n e d as a s t a t e  the  initial  state  and a = 1 a t  the  stress  history.  For  50  variable  failure.  years  of  t a k i n g the v a l u e s  The damage a i s service  life,  a = 0 in  a function  the  performance  f u n c t i o n i s expressed a s :  G - 1.0  -  o(50)  of  (  10. 6 )  10.2 LOAD CASE Duration  of  load  effects  were e v a l u a t e d  for  the  dead l o a d  plus  snow load c o m b i n a t i o n . The dead l o a d model assumed was as e x p l a i n e d Sec.  8.1.  The annual  distribution  in  snow p e r i o d as  time  snow  l o a d r e c o r d was  with a d u r a t i o n  shown i n  Figure  18.  assumed as equal  At,  Parameters  to for  one  the  d i s t r i b u t i o n used i n t h i s a n a l y s i s a r e e x p l a i n e d i n Sec. The  total  snow l o a d .  load  is  the  superposition  of  the  dead  rectangular  annual  annual  in  average  snow  height  8.3. load  and  the  A load sequence f o r 50 y e a r s was c o n s i d e r e d .  At any time t ,  o-(t)  actual  = ( D + 5(t)  stress  i s expressed a s :  ) F  ( 10. 7 )  where :  F  f a c t o r to c o n v e r t from l o a d to  S i n c e the  design equation f o r  stress.  combination of  dead l o a d and snow  l o a d i s expressed a s :  (  Eq.  1.1  D  n  + 1.6 S „ ) F = <fi R  ( 10. 8 )  o m  10.7 can be r e w r i t t e n a s :  -  T  O  T  C «f *  ( io.  )  9 )  10.3 SIMULATION Monte  Carlo  simulation  was  applied  to  obtain  duration  of  load  59 f a c t o r s as 1)  follows:  A v a l u e o f performance f u n c t i o n <j> and a v a l u e o f the r a t i o  of  the d e s i g n dead l o a d to the d e s i g n l i v e l o a d 7 were chosen. 2)  A l o a d sequence of 50 segments was c r e a t e d . a)  A U n i f o r m l y d i s t r i b u t e d random number was chosen to calculate  the dead load d,  which was taken as a  c o n s t a n t f o r the 50 y e a r s . b)  A G u m b e l - d i s t r i b u t e d random number f o r annual snow was c h o s e n , which was taken as a c o n s t a n t f o r whole y e a r .  If  the s e l e c t e d U n i f o r m l y  random number was s m a l l e r than p  0  the  distributed  = exp{-  exp  (AB)},  t h e r e was no snow i n the y e a r . c)  The dead l o a d and l i v e l o a d were combined as Eq.10.9.  3)  The damage accumulated the 50 y e a r s f o r each sample was computed. a)  F i v e U n i f o r m l y d i s t r i b u t e d random numbers were chosen to o b t a i n the v a l u e s of 6, c, n,  <T and r Q  a  from  t h e i r Lognormal d i s t r i b u t i o n s from T a b l e 20. b)  U s i n g the r e c u r r e n c e r e l a t i o n s h i p i n E q . 1 0 . 2 ,  the  accumulated damage a was c a l c u l a t e d f o r 50 c y c l e s . c)  The performance f u n c t i o n  G = 1.0  -  ( 10. 10 )  a  was then e v a l u a t e d .  If  G > 0, the sample s u r v i v e d ,  and i f G < 0, the sample f a i l e d . 4)  Step 2 and 3 above were then r e p e a t e d f o r 10,000 r e p l i c a t i o n s .  5)  The number o f f a i l u r e s o c c u r r i n g i n 50 years was used t o compute the p r o b a b i l i t y o f  _  p  number of f a i l u r e s  number o f r e p l i c a t i o n s  I  6)  The a s s o c i a t e d r e l i a b i l i t y /? = - 9~\  7)  failure  P  (10  (10000)  11  )  '  index /? was o b t a i n e d from  )  f  The above p r o c e s s , s t a r t i n g a t step 1, was then r e p e a t e d f o r d i f f e r e n t v a l u e s of <j>.  10.4 DURATION OF LOAD RESULTS The r e l i a b i l i t y  r e s u l t s f o r SPF Ql and Q2 are  and 22 which shows ^-values for  S-P-F  Ql  duration  of  locations,  and S-P-F load  c o r r e s p o n d i n g to d i f f e r e n t  Q2 m a t e r i a l  adjustment  where K  D  l i s t e d i n T a b l e 21  with and without  factor  is  K  D  i s d e f i n e d as — 7 — —  target  /3-values  DOL e f f e c t .  calculated  for  the  The four  yuk.—. These <j> and K  D  values  ^without DOL  were o b t a i n e d from the  analysis  using three  combinations of  with an average  annual  snow d u r a t i o n  in  with  annual  snow  location  an  annual  average snow  duration  of  in  five  each  months  each  (155  location, and 7  an a c t u a l  = 0.25  days)(D0L-5)  7 = 0.25  in  y  a  with  an  order  to  compare the e f f e c t s of those parameters. The levels.  trends  But,  in  ^-values  <j> and K  D  values  were  consistent  across  were i n f l u e n c e d by the  different location,  /?  annual  snow d u r a t i o n , and 7-values. The annual  differences  snow  duration  greater  in  because  heavy  the  quite  light  different was  effect.  It  the  snow  is  areas  have a  from the  but  too  for  et  the  using  five  months  less  in  the  snow d u r a t i o n  heavy  model,  to  only  the  The a c t u a l j  quite  a  light  that  snow areas  study use  the  choice  but  smaller  i n Sapporo was 0 . 2 5 , whereas 21 and  different.  However,  shown as  of  obtained f o r  22,  the  the  Structures of SPF SPF  Ql  Structural  Q2. S i n c e SPF are  similar  a  snow  duration  of  has  7's  five  of  load  of  five  in  a  significant  [3].  the  the a c t u a l j  a  heavy  between in  both  SPF cases  of SPF  Ql are  closer  explained in Reliability-Based  Research  Series,  but q u i t e  Q2 i s a low q u a l i t y to  days  snow  those  of  are  areas.  t h a t i n Osaka was 4 . 4 .  results  (^-values  speaking, r e s u l t s  Hem-Fir as  Figure  two  duration  Ql  and  to  d e r i v e d f o r SPF Ql are recommended f o r S-P-F  for  different  Hem-Fir  lumber.  in  j. a  the  results  Design of Wood  grade and the K  obtained  Q2 were  were c l o s e r  Osaka with 7 = 0.25 but were d i f f e r e n t with u s i n g the a c t u a l Generally  areas  model.  states  From T a b l e  snow  are  snow d u r a t i o n o f  D i f f e r e n c e s between ^-values a t 7 = 0.25 and a t the  duration  Although the Canadian snow model was  D  in  average  i n Osaka i s  a f f e c t on the c a l c u l a t e d d u r a t i o n of l o a d f a c t o r K  larger  the  snow  snow d u r a t i o n  Canadian  conservative  al.  obtained  longer  rectangular  months f o r the r e c t a n g u l a r Foschi  assumed  136 days.  considered is  </>-values  example, the annual  i n Sapporo  months  and  snow areas  19 and 20. For and t h a t  between  D  the  from  those  factors K  D  for  values  The r e s u l t s  of  the  SPF  Ql were p l o t t e d  in Figure  21.  seen t h a t they correspond c l o s e l y t o the Canadian a n a l y s i s . 0.8 when 0  < j  0.5  > 5.0.  Because  to  the  when 7  reasonable study,  given  <  use the  1; K  fact  D  = 0.8 - 0.431og(7) when 1 < 7 only  Canadian that  the  t r e n d as the Canadian a n a l y s i s .  limited analysis present  <  It  Where K 5; and K  d a t a were f e a s i b l e , for data  the  remainder  generally  can be  have  it  D  -  D  =  seems  of  this  the  same  11. ASSESSMENT OF RELIABILITY LEVELS ASSOCIATED WITH CURRENT WORKING STRESS DESIGN  WSD  is  reliability for  the  levels frame  currently  assessment  LSD in  code  the  used  the  procedures  format  can  WSD c o d e s .  construction  for  are  used  to  study  be  used  to  also  The c u r r e n t  evaluated  Japanese  in  timber /? - <f>  study  reliability this  design.  chapter.  relationships  the  levels  The  reliability for  Typical  2x4 wood floor  and  r o o f systems were s t u d i e d .  11.1 LOAD Since t h i s for  current  values  chapter  Japanese  specified  evaluation.  is  2x4  in  7 =  wood  the  frame  GHLC's  The random v a r i a b l e  d i s t r i b u t e d with mean of ratio  intended to e v a l u a t e  D /L n  n  or  1.0  construction,  span  tables  d = D/D  n  was  the  were  n  n  was  calculated  at  used  load  for  be  of 0.1.  each  level  nominal  assumed to  and standard d e v i a t i o n  D /S  7 =  the r e l i a b i l i t y  this  Normally An a c t u a l  location  using  d a t a o b t a i n e d from GHLC's span t a b l e . The kgf/m  2  nominal  (1.765  occupancy  KN/m ) 2  n o r m a l i z e d occupancy  is  load  used  load  is  for  for the  explained  residential span  was used f o r d e f l e c t i o n  of  180  calculations.  The  The 50-year  return  The annual maximum v a l u e  analysis.  For the snow l o a d , are  table  in Sec.8.2.  occupancy l o a d was used the bending a n a l y s i s .  structures  explained in Sec.8.3.  the random v a r i a b l e s  s = S/S  n  i n each  location  The 50-year r e t u r n snow l o a d was used as  the  nominal  load  for  the  used f o r d e f l e c t i o n  bending a n a l y s i s .  The annual  maximum v a l u e  was  analysis.  11.2 ALLOWABLE UNIT STRESS The  allowable  construction  are  Administrative  unit  stresses  specified  Agency  [13],  in  the  for  lumber  Building  explained  in  for  2x4  Notification  Sec.3.2.3,  wood for  frame Special  and t a b u l a t e d  in  Appendix 1.  11.3 RELIABILITY LEVELS IN BENDING (SHORT-TERM BASIS) WSD  procedures  taken  from  the  Standard  for  Timber  Design  are  used to develop span t a b l e s . For f l o o r  joists:  D For  n  + L  n  <  ( 11. 1 )  Ra  rafters: D  n  <  D  n  + S  n  <  D  n  + S  n  <  (in  l i g h t snow a r e a )  ( 11. 2 )  2 Ra  (in  l i g h t snow a r e a )  ( 11. 3 )  Ra  (in  heavy snow a r e a )  ( 11. 4 )  Ra.  where :  d e s i g n dead l o a d  effect;  :  design l i v e load  effect;  S  n  :  d e s i g n snow l o a d  effect;  Ra  :  allowable  D  n  L  n  The  evaluation  of  unit stress for sustained  the  reliability  program r e q u i r e s a performance f u n c t i o n G.  index  0,  The s a f e t y  load. using levels  the for  RELAN floor  joists  under  short-term  loading  are  evaluated  by  determining  the  p r o b a b i l i t y t h a t the performance f u n c t i o n G < 0. For the j o i s t ,  the performance f u n c t i o n  G = R - ( D  is:  ( 11. 5 )  + L)  where R  :  s t r e n g t h (a random v a r i a b l e ) ;  D  :  e f f e c t o f the dead l o a d (a random v a r i a b l e ) ;  L  :  e f f e c t of the l i v e l o a d (a random v a r i a b l e ) .  Introducing  the  design equation  in Eq.11.1 into  the  performance  function in Eq.11.5 y i e l d s :  G  = R  -  R  a  - (  f  d  (  0  +  (7+1)  11.  6  )  V  '  wh< 7  '•  d  :  D/D ;  I  :  L/L .  In load  so  i.e.  two  a  n  that  n  the  times  for  n  n  light  duration of checked  D /L ;  snow  area,  allowable  its  unit  sustained  load e f f e c t . the  snow  dead  load  is  regarded  stress  of  a  load.  However the  load  only.  The  the  temporary  factor  structural  Therefore  as  two  load  2 takes  D  n  >  S, n  is  account  used, of  member s h o u l d a l s o performance  must be c o n s i d e r e d i n the l i g h t snow a r e a . If  temporary  the g o v e r n i n g d e s i g n e q u a t i o n i s D  n  <  Ra.  a be  functions  For r a f t e r s  the performance f u n c t i o n G can be expressed as  G = R -  Introducing  the  ( 11. 7 )  (D + S)  design* equation  in  Eq.11.2,  the  performance  function  i n E q . 1 1 . 7 can be expressed a s :  G = R -  If  S  By  n  >  R  a  - ^  +  ( 11. 8 )  S )  the g o v e r n i n g d e s i g n equation i s D  D, n  n  substitution,  the  performance  function  in  + S  n  Eq.11.7  <  2 Ra and  the  design  equation i n E q . 1 1 . 3 can be a l s o expressed a s :  (7+1)  For  heavy  snow a r e a s ,  the  l o a d . T h e r e f o r e , the a l l o w a b l e By  substitution,  the  snow  load  is  regarded as a  s t r e s s f o r sustained load i s  performance  function  Eq.11.7  and  sustained  used. the  design  equation E q . 1 1 . 4 can be expressed a s :  G  =  A«-0*7 + 0  R  (11.10)  (7+1)  The short-term r e l i a b i l i t y f o r bending f o r f l o o r the  analysis  were  joist  derived  '  v  of c u r r e n t  and r a f t e r using  the  c o n s t r u c t i o n was  systems. The r a t i o ' s material  weights  evaluated 7 used f o r  and  nominal  occupancy and snow l o a d s p e c i f i e d  i n the GHLC span t a b l e s .  Results of  these a n a l y s i s a r e summarized i n T a b l e 2 3 .  11.4 RELIABILITY LEVELS IN DEFLECTION In the Standard structural  members a r e s p e c i f i e d .  requirements states  f o r Timber D e s i g n , the a l l o w a b l e  from  analysis  the  GHLC's span t a b l e was a p p l i e d t o t h e  standard.  was performed  deflections for  The c u r r e n t  for  the  serviceability  short-term  limit  deflection  of  a  s i n g l e member f l a t r o o f and f l o o r . Following as  a  GHLC's  proportion  of  requirement, the  span  or  the d e f l e c t i o n a  maximum  limit  as  allowable  specified deflection  expressed a s :  A  m a x  <  ( U. U )  or A  m  a  l  < allowable  The d e f l e c t i o n  deflection  limits  ( 11. 12 )  for structural  members f o r 2x4 wood frame  s t r u c t u r e a r e summarized i n T a b l e 2 4 . The  maximum  deflection  can be  calculated  for  single  lumber  member under u n i f o r m l y d i s t r i b u t e d l o a d a s :  _ ^max ~  5-( D Q ). -L* 384-IS-1 n  +  n  S  where  A „„ m  :  maximum d e f l e c t i o n :  ^allow  \ -iJ  1  6  )  ^allow  '•  allowable  deflection;  D  n  :  d e s i g n u n i f o r m l y d i s t r i b u t e d dead l o a d ;  Q  n  :  design uniformly d i s t r i b u t e d l i v e  s  :  s p a c i n g between members;  E  :  mean modulus o f e l a s t i c i t y  load;  f o r the p o p u l a t i o n o f  lumber; I A  :  moment o f i n e r t i a o f the member c r o s s - s e c t i o n .  performance  function  for  deflection  limit  state  can  be  f o r m u l a t e d as :  5 - ( D + Q )-s-L 384. E• I  4  allow  ( 11- 14 )  where D  :  dead l o a d (a random  variable);  Q  :  l i v e l o a d (a random v a r i a b l e  E  :  modulus o f e l a s t i c i t y  );  o f the member (a random  variable).  Introducing as  Eq.11.13 the performance  function  can be expressed  :  = i _ ( y\}-\ d  G  + 1 ) •  (7  where  d  :  D/D  7  :  DJQ ;  ni  n  E  ( K  ii. 15) '  3  Q/Q -  :  The  n  performance  function  RELAN program and r e l i a b i l i t y  of  Eq.11.15  levels  was  evaluated  a t the s e r v i c e a b i l i t y  using limit  the state  f o r c u r r e n t c o n s t r u c t i o n a r e shown i n T a b l e 25.  11.5 RELIABILITY OF CURRENT RAFTER CONSTRUCTIONS UNDER LONG-TERM LOADING The  actual  reliability  construction  will  the  design.  member  subjected strength  to  vary  The  state  associated  depending on the d e s i g n  short-term  limit  levels  reliability loads  have  (Sec.11.3)  levels  been  (Sec.11.4).  The r e l i a b i l i t y  limit  state  separately.  The purpose o f t h i s  the  bending  levels  strength  associated  limit  for  state  levels  with  using  current  controlling  bending  members  for  bending  and f o r the d e f l e c t i o n  state  reliability  criteria  evaluated  limit  actual  with  the  serviceability  a r e c a l c u l a t e d f o r each  section i s to evaluate  the  current  for  the  constructions  actual  maximum  spans  p e r m i t t e d i n the GHLC span t a b l e s . The spans  first  as  step  governed  requirements.  The  in by  this  analysis  is  the  bending,  shear  analysis  is  to  undertaken  calculate and  for  the  allowable  deflection  five  design  typical  rafter  systems f o r the f o u r l o c a t i o n s . In 2-R , a  the  light  snow  must be g r e a t e r  area,  two times  greater  than  unit  stress,  than or equal t o the sum o f the e f f e c t s  u n i f o r m l y d i s t r i b u t e d dead and snow l o a d , is  the a l l o w a b l e  the u n i f o r m l y  dead l o a d .  of the  when the u n i f o r m l y snow l o a d Thus,  (D +S ) n  n  <  2R , a  when  S >D . n  When  n  uniformly  the u n i f o r m l y  distributed  be g r e a t e r  than  dead  For d e f l e c t i o n  cm must  not be exceeded.  n  load,  the e f f e c t  S <D . n  distributed  snow  the a l l o w a b l e  of distributed  considerations  is  unit  dead  span  load.  / is  less  stress,  o f the r a f t e r s ,  The g o v e r n i n g  determined u s i n g the f o l l o w i n g  load  D  n  <  both  than  the  R,  must  R,  when  a  a  ^TJQ  the minimum  A  N  <  ^  value  equations.  Deflection 3  i 1  _ 384 • E • ~ > 200-5-u;  I  2-384.E-1  W - -  5•  N  w  when  w h e n  200  _A  200  < 2cm  ( 11. 16 )  > 2cm  ( 11. 17 )  Bending: 8-Z.f •2 -  \  ( 1 1 . 18 )  b  w  Shear: •3 =  4-A-/  ( 1 1 . 19 )  a  3-w  Where span governed by d e f l e c t i o n ; span governed by b e n d i n g ; span governed by s h e a r ; E  modulus o f  elasticity;  h  allowable  bending s t r e s s ;  f.  allowable  shear  I  moment o f  Z  s e c t i o n modulus;  stress;  inertia;  2  71 A  cross section area;  w  u n i f o r m l y d i s t r i b u t e d l o a d without s a f e t y  f a c t o r as  with the LSD. C o n s i d e r the f o l l o w i n g example:  given:  Tokyo, l i g h t r o o f ,  s p a c i n g = 455mm, S-P-F, SS, 2x8  Dead l o a d was c a l c u l a t e d from T a b l e 6 D  N  = ( 20 + 6 ) x . 4 5 5 + 6 = 17.83 kg/m  Snow load was o b t a i n e d from T a b l e 5 S  N  = 35.88 x 2 x . 4 5 5 = 32.65 kg/m  Since uniformly distributed  dead  load,  must be s a t i s f i e d . (not  2-R ), A  distributed to  distributed therefore  In o r d e r  snow l o a d i s g r e a t e r the d e s i g n  equation  than  (D +S ) N  N  <  t o use from E q . 1 1 . 1 6 t o E q . 1 1 . 1 9 with  nominal u n i f o r m l y  distributed  dead p l u s nominal  snow l o a d was d i v i d e d by two t o g e t w ( c o n v e r t  long-term)  uniformly  so t h a t w can a l s o  N  n  2-384-85000-1972 5-0.252  = 565.1cm  A  checking  ( 11. 20 )  I n t r o d u c i n g w t o the E q . 1 1 . 1 6 t o E q . 1 1 . 1 9  4  R  short-term  be used f o r the d e f l e c t i o n  = 0.252 kg/cm  a  uniformly  equations on a long-term b a s i s .  w = (D +S )/2  2R  ( 11. 21 )  72  8-214.4-110 0.252  4-69.9-6 3-0.252 The a l l o w a b l e  = 864.6cm  ( 11. 22 )  ( 11. 23 )  = 2215.5cm  span f o r t h i s  case was 5.56m, the span governed by  deflection. An a n a l y s i s and  shear  is  of r a f t e r  summarized  requirements governs the  light  Table  i n the heavy  26. Generally  levels  bending  speaking,  bending  snow cases and d e f l e c t i o n governs i n the a l l o w a b l e  than p e r m i t t e d by bending r e q u i r e m e n t s .  reliability  greater  in  snow c a s e s . When d e f l e c t i o n g o v e r n s ,  be s h o r t e r actual  spans as governed by d e f l e c t i o n ,  span w i l l  In these  f o r the bending s t r e n g t h l i m i t  cases the  s t a t e w i l l be  than p r e d i c t e d v e r s u s when the bending s t r e n g t h l i m i t  state i s  examined i n d e p e n d e n t l y ( S e c . 1 1 . 3 ) . The state  actual  are evaluated  term r e l i a b i l i t y term  reliability  The  i n a two stage  f o r the bending process.  f o r duration  of  load  strength  (1) e v a l u a t e  o f the bending member and then  reliability  reliability  levels  effects  (2) a d j u s t to  limit  the s h o r t the s h o r t -  g e t the  actual  under long-term l o a d i n g . relationship  between  span  and c o r r e s p o n d i n g /? f o r bending  can be o b t a i n e d from the f o l l o w i n g performance f u n c t i o n :  G = R - (D+S)-p- 6 L 8BH 2  ( 1 1 . 24 )  2  = R - S (dy+s)-p- 6L 8BH 2  n  where  2  ( 1 1 . 25 )  D  :  dead l o a d ;  S  :  snow l o a d ;  p  :  s p a c i n g between members;  L  :  span;  B  :  member w i d t h ;  H  :  member d e p t h ;  S  :  nominal snow l o a d ;  d  :  n o r m a l i z e d dead l o a d ;  s  :  n o r m a l i z e d snow l o a d ;  7  :  n  DjS . n  The d u r a t i o n Sapporo, the  Niigata  results  L  the  l° 9 - t e r m — \  short — term '  shows the for DOL)  short - t e r m  =  L  and  a  for  reliability  = 0.8  for  Osaka were a p p l i e d  for  analysis  load f a c t o r  is  t  t  h  e  s  a  m  e  D  to  obtain  d e f i n e d as K  an adjustment  long-term r e l i a b i l i t y  K  span from  level.  Figure  between member span and c o r r e s p o n d i n g 0  (with  DOL)  cases.  In  short-term  this  =  D  the  can be o b t a i n e d as  reliability  the  the  case,  the  22  values  (without maximum  span due to short-term bending was 8.64 m ( T a b l e 26) with a  /?-value of  1.566.  reliability  Because  V^D  x  load cases,  r o o f case and Tokyo snow l o a d f o r  long-term  calculated  the  t o the  relationship  a light  = 0.52  D  bending a n a l y s i s ,  n  long-term  snow  S i n c e the d u r a t i o n of  short-term r e l i a b i l i t y L  for  short-term  2  ( ^  load f a c t o r  and Tokyo and K  from  long-term b a s i s .  of  the  This of  same /3-value  current  governing  factor  was  obtained  construction in  the  g o v e r n i n g span was then reduced to 5.65.  in  summarized  example At t h i s  was  the in  analysis  of  Table  23.  deflection,  the  span the /?-value  is  found t o be long-term  : 0 = 3.01 basis.  snow  roofing  material  strength  loads  to  the  Similarly,  spacing;  incorporated  for  of  different  different  commonly  generate  distribution  2x8 were t e n t a t i v e l y  s h o r t - t e r m b a s i s and 0 = 2.68 f o r member  geographic  used  Figures  in 23,  parameters  of  used f o r t h i s  locations;  the 24,  sizes,  25,  26,  2x6 were not  grades and  selected  and  different  regions  and  the  27.  were  Since  available,  the  those  of  analysis.  11.6 DISCUSSION The range  short-term  reliability  from  to  are  2.68  3.03.  levels  However  for the  floor safety  range from 1.40 to 3.63 depending on l o c a t i o n , 7, nominal snow l o a d r a t i o . they  range  Osaka, 1.0,  if  from rafter  then  rafters  reliability  unit  to  for  In  light  determined range  D  + S,  by  n  drop to  stresses for  3.63.  snow a r e a  indices  determined levels  stress  heavy  spans are  reliability  are  allowable  2.67  In  range  temporary  sustained  by D ,  bending  for  rafters  Sapporo and N i i g a t a , areas  ie. ,  >  n  1.63  to  3.35.  S  >  D  to  2.40.  n  n  Tokyo  S  7  >  However  if  n  or  This  <  7 is  1.0,  because allowable  load  in  light  i n bending f o r r a f t e r  d e s i g n i n the  light  they  were c o n s i d e r e d  individually.  Since  only  strength  but  shear  of  actual  are  ( t w i c e as much as  or  and  the  load)  load  1.38  in  nominal dead l o a d and  when D  n  when  from  levels  ie.,  snow  from  n  joists  used f o r  the  snow  snow a r e a s . The r e l i a b i l i t y snow a r e a rafter  are  sizes  very are  levels low,  if  determined  s t r e n g t h and s t i f f n e s s  of the  not  by  bending  lumber, the r e l i a b i l i t y  levels  r o o f member i n five  cases.  long-term bending were e v a l u a t e d assuming K  From the  D  five  2.35 and 2.78 r e s p e c t i v e l y , strength l i m i t states.  cases, which  the is  minimum and mean-/? quite  acceptable  The v a l u e s f o r 2x6 were not  for  = 0.8 values the  investigated.  for were  bending  12. DISCUSSION AND CONCLUSION  Most timber post  and  sawn  Introduced  construction constructed of  that  the  format  i n Japan a r e o f the s o - c a l l e d  beam c o n s t r u c t i o n  lumber.  types  structures  makes in  wood  1989.  a  structures.  of  test It  The  2x4  case  would  utilize  into  Japan  approximately  structures  design  as  up  and  current is  for be  3%  for  project  intensive  are a v a i l a b l e currently  lumber  very  traditional results lumber limited  obtained used  the  for  evaluate  and in  tremendous amount of i n the  future.  test  beam  no  frame  housing  units  method  is  be  converted  LSD  highly  codes  results  for  all  recommended to  for  building  types of  of  wood  It  is  standard  available  structures  study  it  of  relevant  is  important  lumber f o r  LSD  codes  in  for for  the  all  LSD  timber  codes  to  be  structures. from  CWC's  research  collaborative  full-size  the  used  lumber The  strength  analysis  However,  data  for  due other  to develop a standard t e s t reliability  all  for and  based on an a n a l y s i s  structures.  the  for  evaluating  Japan.  were e n t i r e l y  2x4 wood frame  full-size of  is  data  this  the  systems,  development  there  little  availability  structural to  post  design  sizes  f o r the dimension lumber used f o r 2x4 wood frame  structures, and  in-grade  of  2x4  total  Japanese  c o n v e r t e d from the WSD to the LSD f o r a l l Although  of  system  development  traditional  1974,  on VSD.  frame  ideal  in  structural  based  wood  various  traditional  timber  analysis. structures  to  of the  wood method  Therefore, requires  work among d e s i g n e r s and  a  engineers  In  this  bending.  The  constitutes frame  study,  reliability  species more  selected  than  construction  two  in  thirds  Japan.  for  performance  2x4  wood  The  factors  frame  that  T  live  chosen  four  study  lumber  locations  was  used  of  mainly S-P-F  for  snow (  in  which  2x4 wood  load  chosen  Japanese snow c o n d i t i o n s .  for  LSD  equations  using  levels.  have  been  LSD  Steel  draft  The outcome from t h i s  t e n s i o n and compression a t  calibrated Standard  study  shows  load r a t i o s  7  a  reliability  studies  in  of  areas  the  that  levels  differences  the a c t u a l  the c a l i b r a t i o n Size  Japan where  reliability  show s i g n i f i c a n t indicate  of  target  this  analysis.  wooden  structures levels  tension  with the  and  dead  The 7 = 0.25 in  Canada.  was The  f o r bending d e s i g n  snow accumulations are for  reliability  of 0.25 and the a c t u a l  v a l u e r e s u l t e d i n lower r e l i a b i l i t y  Q  certain  However  were used  j  the  structures.  of nominal dead to l i v e l o a d 7,  for  actual in  total  = 2.5 which i s compatible with s t e e l Ratio  to  this  evaluated  the 2x4 wood frame system y i e l d s performance f a c t o r s <p of 0.85 f o r  bending and 0.9 f o r of 8  of  structures  requirements f o r r e l i a b i l i t y  were  throughout  f o r the a n a l y s i s r e p r e s e n t t y p i c a l The  levels  not as  compression  severe. did  not  c h o i c e of  7.  Therefore,  j  should be used f o r  dead to  live  load r a t i o  currently  not  considered  a  results  studies.  effects  structures  in  non-glulam  timber,  are  Japan.  To a c h i e v e size  effects  a  better  should  in  strength be  non-glulam prediction  incorporated  into  timber of  the  design  procedure f o r 2x4 wood frame c o n s t r u c t i o n . The  recommended  ^-values  and  the  c o r r e s p o n d i n g average  /?  and  range  of  were  8  evaluated  taking  into  account  size  effects  are  the r e s u l t s  from  summarized i n t a b l e 2 7 .  Table 27. Recommended <f> and /^-values  7  0  Min. 0  Mean p  Max. 0  7 = 0.25  0.9  2.31  2.49  2.69  0.85  2.13  2.48  2.80  0.9  2.25  2.50  2.72  0.9  2.21  2.50  2.77  0.9  2.15  2.51  3.11  0.9  2.09  2.51  3.15  Bending  Actual 7 Tension  a  7 = 0.25 Actual 7  a  Compression 7 = 0.25 Actual 7  a  Based on the study o f d u r a t i o n o f l o a d e f f e c t s , SPF  Ql  study. live  were  close  The d u r a t i o n  load r a t i o .  factor  study,  detailed a  obtained  from  varies  the Canadian c a s e ,  Hem-Fir  for  the  Canadian  with the c h o i c e o f dead t o  regardless  o f the l i v e  load a  o f Kj-) = 0.80 can be used where 7 i s l e s s than or equal t o 1.0.  a  load a n a l y s i s .  7  those  of load e f f e c t  In  Where 7 i s g r e a t e r this  to  than 5 . 0 , a f a c t o r  simple Results  snow  of K  = 0.50 can be a p p l i e d .  l o a d model was used f o r S-P-F  were r e l a t i v e l y  Canadian s t u d i e s .  D  close that  The f a c t o r s  In  duration of  o b t a i n e d i n the more  a t 7 = 0.25 and the a c t u a l  K  D  a r e summarized i n T a b l e 28 f o r f o u r l o c a t i o n s i n Japan. The  rafter  bending  levels  of  current  2x4 wood  d e s i g n were found t o be q u i t e comparable w i t h s t e e l  The r e l i a b i l i t y very  reliability  low.  In  levels order  f o r bending s t r e n g t h to  calculate  the  i n the l i g h t  actual  frame  for  structures.  snow a r e a a r e  reliability  levels  in  Table 28. Duration of Load Factor K  # £ ( 7  7„ = 0.25  0.70  Niigata  0.78  7 = 0-41  0.77  Tokyo  0.87  7 = 1-22  0.81  Osaka  0.90  7 = 4-40  0.57  we  take  span  are  a  reliability  determined  Generally  governed  are  a  the  is  requirements.  a  to  duration  l o a d adjustment  strength  for  the  levels  long-term  the  the  as  a  rafter  function  strength factor  shear  D  in  states  = 0.8 f o r  span.  the  light  spans  are  loading. limit  The  states  actual  minimum  and  the  increased.  Sapporo,  reliability  snow  bending  The  Niigata  = 0.52 f o r Osaka were a p p l i e d to a s s e s s r e l i a b i l i t y  D  The  deflection  calculated  deflection  limit  K  the  of  and  spans  Therefore,  governing  = 2.5  a  bending,  deflection.  reliability  Tokyo and K  by  speaking,  by  reduced  of  level  T  7 )  D  0.70  rafter  spans  K (Actual  a  Sapporo  rafters,  area  Actual 7  0.25)  =  for SPF Ql at 0  D  levels  and  under  for  the  i n long-term bending and s h o r t - t e r m bending were  summarized i n T a b l e 29. Table the  current  reliability  30 compares design  rafter  spans  procedures  levels.  Five  and  u s i n g the  shows  different  the  new LSD  corresponding  conditions  and  combinations were used i n the comparison. The r e s u l t s equations  (using  reliability equations when  the  levels  <j> -  0.85  0  above  do not d e v i a t e reliability  and  2.5.  The  the  actual  span  too much from the level  goes  below  equations  a  long-term  three  size  from the new LSD show  j)  consistent  values  from  current  d e s i g n spans.  2.5 i n the  vs.  the  current  new  LSD Only  design  Table 29. Reliability Level P in Current 2x4 Wood Frame Structure Short-Term Bending Min.  method,  Max. p  Min.  Sapporo  2.72  3.63  2.63  Niigata  2.67  3.59  2.60  Tokyo  1.38  2.59  2.35  Osaka  2.12  3.35  2.20  will  method  P  Final Long-Term Bending  we witness  provides  more  a decrease  consistent  in  span.  P  The t a b l e  reliability  levels  d e s i g n method where the range of /?-values v a r i e s This  study  combination of  is  carried  out  dead p l u s occupancy data.  Therefore  mainly  in  than  bending  areas  such as  l o a d combinations with wind and earthquake  other  species  and o t h e r  studies  states  will  in  members  modification  in  traditional  post  the  this  between  reliability  members  design  factors.  considered  spacing  and  such  as  Although study,  and  beam  members), levels the  modification factors  properties  2x4 the  and  safety  to  to  develop  a  by  factors  of  system  were  not  in  the  extensively  long  calculating  repetitive  single  frame  system.  levels  P, would r e p r e s e n t more c l o s e l y  a c t u a l b e h a v i o r and a l l o w f o r more e f f i c i e n t  By  in  l o a d and f o r  applicable the  up  load  required  c o n s i d e r e d when  made  the  adjusted  not  (due  current  d e s i g n i s based on  modification  should be  structures wood  not  probably  structures they  in  system  are  be  order  complete LSD code. For example, Japanese s t r u c t u r a l single  LSD  snow l o a d u s i n g  strength  limit  the  with  S-P-F  strength  the  considerably.  l o a d and dead p l u s  further  shows  incorporating  use of m a t e r i a l s  [3].  these  Table 30. Rafter Span Comparison Using Current and New LSD Design Equation Tokyo, Light Roofing, Spacing=455mm 2x4 Grade Current New SS D-Span 3.10 3.18 B-Span 4.26 3.19 Span 3.10 3.18 3.14 3.05 P  2x8 Current 5.65 8.64 5.65 2.68  New 5.75 5.71 5.71 2.63  2x10 Current 6.72 10.82 6.72 2.74  unit: m New 6.85 6.94 6.85 2.69  Sapporo, Light Roofing, Spacing=303mm 2x4 2x8 Grade Current New Current No.2 D-Span 1.75 1.84 3.61 B-Span 1.59 3.26 1.81 Span 1.59 1.81 3.26 3.09 2.66 2.65 P  New 3.83 3.24 3.24 2.66  2x10 Current 4.43 4.14 4.14 2.63  unit: m New 4.59 3.95 3.95 2.81  Niigata, Heavy Roofing, Spacing=455mm 2x4 2x8 Grade Current New Current No.2 D-Span 1.68 1.73 3.47 B-Span 1.50 1.73 3.08 Span 1.50 1.73 3.08 3.08 2.59 2.63 P  New 3.61 3.10 3.10 2.61  2x10 Current 4.30 3.90 3.90 2.60  unit: m New 4.38 3.77 3.77 2.72  Tokyo, Light Roofing, Spacing=455 2x4 Grade Current New No.2 D-Span 2.98 3.06 B-Span 3.52 2.76 Span 2.98 2.76 2.46 2.71 P  2x8 Current 5.47 7.13 5.47 2.35  New 5.66 4.94 4.94 2.68  2x10 Current 6.51 8.94 6.51 2.45  unit: m New 6.70 6.00 6.00 2.77  Osaka, Heavy Roofing, Spacing=455mm 2x4 2x8 Grade Current New Current No.2 D-Span 2.63 3.03 4.97 B-Span 2.93 2.49 5.90 Span 2.63 2.49 4.97 2.42 2.61 2.20 P  New 5.63 4.46 4.46 2.56  2x10 Current 5.90 7.34 5.90 2.29  unit: m New 6.66 5.42 5.42 2.64  where D-Span B-Span Span P  ; ; ; ;  Span Calculated by Deflection Requirement Span Calculated by Bending Requirement Minimum of Above Two Calculated Span Bending (Long-Term) Reliability Level at Allowable Span  REFERENCES  Canadian Standard A s s o c i a t i o n . 1984. CAN3-086-M84. E n g i n e e r i n g Design i n Wood ( L i m i t S t a t e s D e s i g n ) . Canadian Standard A s s o c i a t i o n , Rexdale,  Ont.  Canadian Standard A s s o c i a t i o n . 1989. CAN/CSA-086.1-M89. E n g i n e e r i n g Design i n Wood ( L i m i t S t a t e s S t r e s s Canadian Standard A s s o c i a t i o n , R e x d a l e ,  Ont.  F o s c h i , R.O.,  1989.  Folz,  B.R.,  and Yao, F . Z .  Based Design of Wood S t r u c t u r e s .  Structural  Design).  Reliability-  Research  Series,  Report No.34. Department of C i v i l E n g i n e e r i n g , U n i v e r s i t y British  C o l u m b i a , Vancouver,  of  B.C.  Japanese Government Housing Loan C o r p o r a t i o n . 1990. Span T a b l e s f o r 2x4 Wood Frame H o u s i n g , ( i n Architectural  I n s t i t u t e o f Japan.  S t a t e Design of S t e e l S t r u c t u r e s The B u i l d i n g Standard Law.  Japanese)  1990. Standard f o r (Draft),  1989. ( i n  (in  Japanese)  Japanese)  N a t i o n a l B u i l d i n g Code of Canada. 1990. N a t i o n a l C o u n c i l o f Canada, Ottawa,  Limit  Research  Ont.  The B u i l d i n g Standard Law Enforcement O r d e r . 1989.  (in  Japanese) E s t a b l i s h m e n t of T e c h n i c a l Standards f o r E n s u r i n g S a f e t y of Wood Frame C o n s t r u c t i o n . B u i l d i n g No.56, November 13, 1987. ( i n  Structural  Notification  Japanese)  N o t i f i c a t i o n of Procedure f o r E s t a b l i s h m e n t of T e c h n i c a l Standards f o r E n s u r i n g S t r u c t u r a l  S a f e t y of Wood Frame  83 C o n s t r u c t i o n . N o t i f i c a t i o n f o r S p e c i a l A d m i n i s t r a t i v e Agency No.19, February 5, [11]  Architectural Structural  [12]  1982. ( i n  Japanese)  I n s t i t u t e of Japan.  C a l c u l a t i o n of Timber S t r u c t u r e s ,  A s s o c i a t i o n , Rexdale,  N o t i f i c a t i o n of procedure f o r E s t a b l i s h m e n t of T e c h n i c a l  No.112, A p r i l 1,  S a f e t y of Wood Frame  Architectural  1988. ( i n  I n s t i t u t e of Japan.  1986. Load and R e s i s t a n c e (Proposal),  Lumber. Report No.25.  (in  1988. S t r u c t u r a l  A n a l y s i s of S t r e n g t h Data, American S o c i e t y  (in  Grading in  Group. Japan Wood  Lumber - C o l l e c t i o n and  Japanese)  of T e s t i n g and M a t e r i a l .  1990. Standard  Methods f o r E v a l u a t i n g A l l o w a b l e P r o p e r t i e s Structural  Japanese)  Japanese)  S t r e n g t h o f Timber and Wood Based S t r u c t u r a l Research S o c i e t y .  [18]  (in  Japanese F o r e s t r y Agency. 1985. Study on the S t r e s s Structural  [17]  A d m i n i s t r a t i v e Agency  Japanese)  F a c t o r Design f o r S t e e l S t r u c t u r e s  [16]  Engineering  Ont.  Construction. Notification for Special  [15]  Japanese)  D e s i g n ) . Canadian Standard  Standards f o r E n s u r i n g S t r u c t u r a l  [14]  (in  for  Canadian Standard A s s o c i a t i o n . 1984. CAN3-086-M84, Design i n Wood (Working S t r e s s  [13]  1988. Standard  f o r Grades of  Lumber. ASTM D2915-90. ASTM, P h i l a d e l p h i a ,  American S o c i e t y  of T e s t i n g and M a t e r i a l .  Pa.  1990. Standard T e s t  Methods f o r E s t a b l i s h i n g C l e a r Wood S t r e n g t h V a l u e s . ASTM D2555-88. ASTM, P h i l a d e l p h i a , [19]  American S o c i e t y  Pa.  o f T e s t i n g and M a t e r i a l .  Methods f o r Mechanical P r o p e r t i e s  1990. Standard T e s t  of Lumber and Wood-Base  Structural  Material.  ASTM D4761-88. ASTM, P h i l a d e l p h i a ,  Fouquet, R . J . M . , and B a r r e t t , J . D . Mechanical P r o p e r t i e s  1989. P h y s i c a l  of Canadian V i s u a l l y  Palka,  of B r i t i s h  L.C.  Columbia, Vancouver,  and B a r r e t t ,  on Apparent S t i f f n e s s  J.D.  1985. E f f e c t  and  Stress-Graded  Lumber E s t a b l i s h e d by In-Grade T e s t i n g . C o u n c i l o f Industries  Pa.  Forest  B.C. of Span-Depth  Ratio  of Dimension Lumber. C o n t a c t No. 02-50-  10-019. F o r i n t e k Canada C o r p . Western L a b o r a t o r y ,  Vancouver,  B.C. Architectural  I n s t i t u t e o f Japan.  B u i l d i n g Design - Load, ( i n Architectural  Japanese)  I n s t i t u t e of Japan.  B u i l d i n g Design - Snow Load, ( i n F o s c h i , R.O. ANalysis). British  1981. Recommendations f o r  1986. Recommendations f o r Japanese)  1988. U s e r ' s Manual: RELAN  (RELiability  Department of C i v i l E n g i n e e r i n g , U n i v e r s i t y  Columbia, Vancouver,  Yao, Z . C . 1987. R e l i a b i l i t y  of  B.C. of S t r u c t u r e s  with Load H i s t o r y  -Dependent S t r e n g t h and an A p p l i c a t i o n to Wood Members, M.A.Sc.  T h e s i s . Department o f C i v i l E n g i n e e r i n g , U n i v e r s i t y  British  C o l u m b i a , Vancouver,  B.C.  of  85 Table 1. Design Requirements of the Japanese Building Codes  Stories of 2 or less, Total Floor Area of 500 m or less, Building Height of 13 m or less, and Eaves Height of 9 m or less a  Stories of 3 or more  Traditional Post and Beam Structure  Total Floor Area of more than 500 m  2  Allowable  Relative story  Rigidity  Retained  Unit  Dlaplacement  and  Horizontal  Angle  Eccentricity  Strength  N/A  N/A  N/A  N/A  *  N/A  N/A  N/A  *  N/A  N/A  N/A  Building Height of more than 13 m or Eaves Height of More than 9 m Stories of 2 or less and Total Floor  N/A  N/A  Effective Wall Length Notification No.56  *  N/A  N/A  N/A  Effective Wall Length Notification No.56  N/A  N/A  N/A  N/A  Notification No.1126  Stories of 2 or less, Total Floor Area of 500 m or less, Building Height of 13 m or less, and Eaves Height of 9 m or less  *  *  N/A  N/A  Stories of 3 or more  *  *  N/A  N/A  3 Stories or more or Total Floor Area 2  Maximum 2 Stories with Maxlmun Height of 8.5 m and Total Floor Area of 300 m  2  2  Heavy Timber  Building Standard Law Enforcement Order Article 129  Prohibited  N/A  2  of more than 500 m Log House  Effective Wall Length Building Standard Law Enforcement Order Article 46  1)  Area of 500 m or less  2x4 Wood Frame  Structure  Remarks  Total Floor Area of more than 500 m  2  Structure Total Floor Area of more than 500 m  2  Building Height of 13 m or less and Eaves Height  *  *  *  N/A  *  *  *  *  of 9 m or less  Building Height of 31 m Building Height of more than 13 m or Eaves Height of more than 9 m  Building Height of more than 31 m  Special Structure N/A  *  *  *  *  *  *  *  *  N/A  or less  Building Standard Law Article 38  ; Not Applicable  *  ; Must Check Conditions  -J\  ; Notification for Special Administrative Agency Requires Simplified Structural Member Check  86  Table 2.  Load Combinations for Working Stress Design  regarding loads and  General cases  In heavy snow areas designated by the Special Administrative Agency under the provision to Article 86 Paragraph 2  Normal time  D+ L  D+ L+S  Snow season  D+ L+S  D+L+S  Possible conditions  Kinds of stress  external forces  Stress due to sustained loads  Remarks  Safety In case of overturning of buildings or pulling out of columns. L shall be a value obtained by reducing the live load according to the actual conditions of the building concerned  D+ L+W  Stress due to temporary loads  Storm  D+L+W D+L+S+W  Earthquake  D+ L+ E  D+L+S+E  where D ; Stresses due to dead load L ; Stresses due to live (occupancy) load S ; Stresses due to snow load W ; Stresses due to wind pressure E  ; Stresses due to seismic force  —  Table 3. Basic Statistical Data for Safety Analysis of Steel Structures Load  7  D  -  LS  1/8  LE  1  S  1  w  1  E  1/3  u  X/Xn  Vx  1.0  0.10  0.36  0.40  sustained load  0.25  0.55  extraordinary load  1/3  0.45  0.48  heavy snow area  1  0.42  0.47  annual maxima  0.42  0.80  1.10  0.15 ~ 0.20  8  /Resistance  Remarks  where D  dead load effect;  L  maximum values of live load effect in 50-Year return period;  LS  sustained live load effect;  LE  extraordinary live load;  S  maximum values of snow load effect in 50-Year return period;  W  maximum values of wind load effect in 50-Year return period;  E  maximum values of earthquake load effect in 50-Year return period;  7  the time between events ( year ~ );  A*  duration of tenancy ( year );  X  mean in variable X;  1  Xn  :  nominal value in variable X;  VX  :  coefficient of variation in variable X;  .Resistance :  material strength.  ( All data are assumed Lognormal distribution)  Table 4. Occupancy Load ( Extreme Type I Distribution)  Q  A  q  B  (kg/m )" 2  1  A*  B*  (kg/m ) 2  50-Y Return  0.0578493  196.272  10.41287  1.09040  8-Y Return  0.0578493  164.594  10.41287  0.91441  Annual  0.0578493  128.468  10.41287  0.71471  Table 5. Japanese Snow Data Location  Sapporo  Niigata  Tokyo  Osaka  132  61  5  2  0.05534  0.13291  0.38919  Annual Snow Duration (days) A Annual Snow Height Gumbel Distribution  (cm" ) 0.04677 1  B (cm)  83.92  32.66  6.52  0.023  (cm)  167  103  36  10  216  72  20  50 Years Return Snow Height Design Snow Load ( kg/m ) 351 2  Normalized 50 Years Return Snow Height  A  7.8267  5.7091  4.7686  3.9111  B  1.0013  1.0018  1.0021  1.0026  A  7.8267  5.7091  4.7686  3.9111  B  0.7671  0.6808  0.6178  0.5340  Distribution Gumbel Distribution Normalized 8 Years Return Snow Height Distribution Gumbel Distribution  Table 6. Nominal Design Dead, Occupancy and Snow Load Dead Load Floor Joists Tatami Mat Plywood Sheathing (12 mm) Gypsum Board Joist (2x8 455mm spacing) Total Rafters Light Roofing Material Light Roofing Material Plywood Sheathing (9 mm) Rafter (2x8 455mm spacing) Total Heavy Roofing Material Heavy Roofing Material (Clay Tile) Plywood Sheathing (9 mm) Rafter (2x8 303mm spacing) Total Design Occupancy Load Residential Type  18 8 15 13 54  kgf/m* kgf/m kgf/m kgf/m kgf/m*  20 6 13 39  kgf/m kgf/m kgf/m kgf/m*  60 8 20 88  kgf/m kgf/m kgf/m kgf/m*  180  kgf/m*  350 216 72 20  kgf/m* kgf/m kgf/m kgf/m  2 2 2  2 2 2  2  2  2  Design Snow Load Sapporo Niigata Tokyo Osaka  Table 6a. Nominal Dead to Live Design Load Ratio  7 = D /L n  7= D  n  I S  0.30  n  n  Sapporo Niigata Tokyo Osaka  Light Roofing 0.11 0.18 0.54 1.95  Heavy Roofing ( 7 J 0.25 0.41 1.22 4.40  2 2 2  Table 7. Bending Performance Factors for S-P-F (^-values Corresponding Target /3-values) Sapporo £=3.0 £=2.5 7=0.25 7„=0.25 7=0.25 7„=0.25 2x4 SS 0.77 1.01 No2 0.72 0.98 2x8 SS 0.65 0.90 No2 0.67 0.94 2x10 SS 0.68 0.94 No2 0.81 1.04 Average 0.72 0.97 Niigata 2x4  SS No2 2x8 SS No2 2x10 SS No2 Average Tokyo 2x4  SS No2 2x8 SS No2 2x10 SS No2 Average Osaka 2x4  SS No2 2x8 SS No2 2x10 SS No2 Average Occupancy 2x4  SS No2 2x8 SS No2 2x10 SS No2 Average  £=2.0 7=0.25 7„=0.25 1.28 1.28 1.20 1.24 1.24 1.30 1.26 -  £=3.0 7=0.25 0.76 0.71 0.64 0.67 0.67 0.80 0.71  7„=0.41 0.74 0.70 0.62 0.65 0.65 0.78 0.69  £=2.5 7=0.25 1.00 0.97 0.89 0.93 0.93 1.03 0.96  7„=0.41 0.98 0.95 0.87 0.90 0.90 1.00 0.93  £=2.0 7=0.25 1.26 1.26 1.19 1.23 1.22 1.28 1.24  7„=0.41 1.23 1.23 1.16 1.19 1.19 1.25 1.21  £=3.0 7=0.25 0.76 0.71 0.63 0.66 0.66 0.79 0.70  7„=1.22 0.69 0.64 0.57 0.59 0.60 0.72 0.64  £=2.5 7=0.25 0.99 0.96 0.88 0.92 0.92 1.02 0.95  7„=1.22 0.90 0.87 0.80 0.83 0.83 0.93 0.86  £=2.0 7=0.25 1.25 1.25 1.17 1.21 1.21 1.27 1.23  7„=1.22 1.14 1.13 1.07 1.10 1.10 1.15 1.12  £=3.0 7=0.25 0.75 0.70 0.62 0.65 0.65 0.78 0.69  7„=4.40 0.63 0.58 0.53 0.55 0.55 0.66 0.58  £=2.5 7=0.25 0.98 0.95 0.87 0.90 0.90 1.01 0.93  7„=4.40 0.82 0.80 0.73 0.76 0.76 0.85 0.79  £=2.0 7=0.25 1.24 1.24 1.16 1.20 1.19 1.25 1.21  7„=4.40 1.04 1.04 0.97 1.01 1.00 1.05 1.02  £=3.0 7=0.25 0.73 0.69 0.61 0.63 0.64 0.76 0.68  7„=0.28 0.73 0.69 0.61 0.63 0.64 0.76 0.68  £=2.5 7=0.25 0.96 0.93 0.85 0.88 0.88 0.98 0.91  7„=0.28 0.95 0.92 0.85 0.88 0.88 0.98 0.91  £=2.0 7=0.25 1.21 1.21 1.13. 1.17 1.17 1.22 1.19  7„=0.28 1.20 1.20 1.13 1.17 1.16 1.22 1.18  0.66  0.94  0.89  1.22  1.16  Total Average 0.70  Table 8. Mean /?-values Corresponding to Given 4> in Bending Performance Factor <j>  Mean j3  Mean Q  7=0.25  Actual j  0.6  3.2  3.1  0.7  3.0  2.9  0.8  2.8  2.7  0.9  2.6  2.5  1.0  2.4  2.3  a  Table 9. Size Factor and Standard Strength R for Bending 0  P -  2.5 at 4> , = 0.9  unit : MPa  0  7  Size Factor  Grade  R  0.25  4.495  SS  24.358  23.050  No.2  17.666  16.890  SS  22.744  23.050  No.2  16.491  16.890  Actual ) 1  4.483  1) see Table 6a  0  ^0.05  94  Table 10a. Modified ^-values in Bending at 0 =O.9 and 0 =O.85 (7=0.25) O  Size 2x4  2x8  Grade Sapporo  Niigata  O  Tokyo  Osaka  Occupancy  00  0.9  0.85  0.9  0.85  0.9  0.85  0.9  0.85  0.9  0.85  SS  2.69  2.80  2.67  2.77  2.65  2.75  2.62  2.73  2.58  2.69  No.2  2.42  2.52  2.39  2.49  2.37  2.48  2.35  2.45  2.31  2.42  SS  2.43  2.52  2.41  2.50  2.39  2.48  2.37  2.46  2.33  2.43  No.2  2.50  2.59  2.48  2.57  2.47  2.56  2.44  2.54  2.41  2.50  2.49  2.58  2.47  2.56  2.45  2.54  2.43  2.52  2.39  2.49  2.69  2.80  2.66  2.77  2.64  2.75  2.61  2.73  2.57  2.69  2x10 SS No.2 0 =O.9  Maximum=2.69  Minimum=2.31  AverageJ=2.49  0 =O.85  Maximum=2.80  Minimum=2.42  Average5=2.59  O  O  Table 10b. Modified /9-values in Bending at 0 =O.85 and 0 =O.8O (Actual y ) O  Size 2x4 2x8  Grade Sapporo  Niigata  O  Tokyo  a  Occupancy  Osaka  <t>Q  0.85  0.8  0.85  0.8  0.85  0.8  0.85  0.8  0.85  0.8  SS  2.80  2.90  2.73  2.84  2.57  2.69  2.40  2.52  2.68  2.79  No.2  2.52  2.62  2.45  2.55  2.30  2.41  2.13  2.25  2.40  2.51  SS  2.52  2.62  2.46  2.55  2.32  2.42  2.17  2.27  2.42  2.52  No.2  2.59  2.69  2.53  2.63  2.40  2.50  2.25  2.35  2.50  2.59  2.58  2.68  2.52  2.62  2.38  2.48  2.23  2.33  2.48  2.58  2.80  2.92  2.72  2.82  2.56  2.68  2.37  2.50  2.68  2.80  2x10 SS No.2  00=0.85  Maximum=2.80  Minimum=2.13  Average5=2.48  0o=O.8O  Maximum=2.92  Minimum=2.25  Average=2.59  Table 11. Performance Factors in Tension for S-P-F (0-values Corresponding to Target 0-values) Sapporo 0=3.0 0=2.5 7=0.25 7=0.25 7=0.25 2x4 SS 0.64 0.91 No2 0.64 0.90 2x8 SS 0.81 1.02 No2 0.80 1.03 2x10 SS 0.80 1.02 No2 0.71 0.95 Average 0.73 0.97 Niigata 2x4  SS No2 2x8 SS No2 2x10 SS No2 Average Tokyo 2x4  SS No2 2x8 SS No2 2x10 SS No2 Average Osaka 2x4  SS No2 2x8 SS No2 2x10 SS No2 Average  -  0=2.0 7=0.25 1.16 1.20 1.25 1.28 1.26 1.23 1.23  -  7=0.25  7=0.25  0=3.0 7=0.25 0.65 0.61 0.77 0.76 0.76 0.68 0.71  7=0.41 0.64 0.64 0.76 0.75 0.75 0.68 0.70  0=2.5 7=0.25 0.87 0.87 0.97 0.98 0.97 0.92 0.93  7=0.41 0.86 0.85 0.96 0.97 0.96 0.90 0.92  0=2.0 7=0.25 1.12 1.16 1.19 1.22 1.20 1.18 1.18  7=0.41 1.10 1.14 1.17 1.21 1.19 1.16 1.16  0=3.0 7=0.25 0.63 0.59 0.73 0.73 0.73 0.66 0.68  7=1.22 0.60 0.57 0.72 0.71 0.71 0.63 0.66  0=2.5 7=0.25 0.84 0.84 0.93 0.94 0.93 0.88 0.89  7=1.22 0.80 0.80 0.91 0.91 0.90 0.85 0.86  0=2.0 7=0.25 1.08 1.13 1.14 1.18 1.15 1.14 1.14  7=1.22 1.03 1.07 1.10 1.13 1.11 1.09 1.09  0=3.0 7=0.25 0.59 0.57 0.69 0.69 0.69 0.62 0.64  7=4.40 0.56 0.53 0.67 0.66 0.66 0.59 0.61  0=2.5 7=0.25 0.80 0.80 0.87 0.89 0.88 0.84 0.85  7=4.40 0.75 0.74 0.84 0.85 0.84 0.78 0.80  0=2.0 7=0.25 1.03 1.08 1.08 1.12 1.09 1.09 1.08  7=4.40 0.96 0.99 1.03 1.05 1.04 1.01 1.01  0.68  0.91  0.89  1.16  1.12  Total Average 0.69  Table 12. Mean /3-values Corresponding to Given <j> in Tension Performance Factor <j>  Mean /?  Mean /?  7=0.25  Actual j  0.6  3.2  3.2  0.7  3.0  3.0  0.8  2.7  2.7  0.9  2.5  2.5  1.0  2.3  2.3  a  Table 13. Size Factor and Standard Strength R for Tension 0  (3 = 2.5 at <j> = 0.9  unit : MPa  Q  7  Size Factor  Grade  RQ  •^0.05  0.25  8.864  SS  13.628  12.27 •  No.2  8.8125  8.320  SS  13.317  12.27  No.2  8.5487  8.320  Actual  l)  9.543  1) see Table 6a  Table 14a. Modified /3-values in Tension at 0 =O.9 and 0 =O.85 (7=0.25) O  Size 2x4  2x8  Grade Sapporo  Niigata  O  Tokyo  Osaka  ^0  0.9  0.85  0.9  0.85  0.9  0.85  0.9  0.85  SS  2.69  2.79  2.61  2.71  2.55  2.65  2.45  2.56  No.2  2.51  2.60  2.45  2.54  2.40  2.49  2.33  2.42  SS  2.61  2.74  2.49  2.62  2.39  2.52  2.25  2.39  No.2  2.72  2.83  2.62  2.73  2.55  2.62  2.41  2.53  2.62  2.74  2.51  2.63  2.42  2.54  2.29  2.41  2.63  2.73  2.55  2.65  2.49  2.59  2.40  2.50  2x10 SS No.2 0 =O.9  Maximum=2.72  Minimum=2.25  Average=2.50  0 =O.85  Maximum=2.83  Minimum=2.39  Average;=2.61  O  O  Table 14b. Modified /3-values in Tension at 0 =O.9 and 0 =O.85(Actual j ) O  o  Tokyo  Osaka  Size  Grade Sapporo 0.9  0.85  0.9  0.85  0.9  0.85  0.9  0.85  2x4  00 SS  2.74  2.84  2.64  2.74  2.53  2.63  2.38  2.49  No.2  2.57  2.66  2.49  2.58  2.38  2.47  2.25  2.34  SS  2.66  2.78  2.52  2.65  2.38  2.52  2.21  2.35  No.2  2.77  2.88  2.65  2.77  2.53  2.65  2.37  2.50  2.66  2.78  2.53  2.65  2.39  2.52  2.22  2.36  2.68  2.77  2.58  2.68  2.46  2.56  2.32  2.43  2x8  2x10 SS No.2  Niigata  a  00=0.9  Maximum=2.77  Minimum=2.21  Averag<j=2.50  00=0.85  Maximum=2.8Ji  Minimum=2.34  Average=2.61  Table 15. Performance Factors in Compression for S-P-F (0-values Corresponding to Target 0-values) Sapporo 0=3.0 0=2.5 7=0.25 7=0.25 7=0.25 2x4 SS 0.90 1.08 No2 0.72 0.94 2x8 SS 0.86 1.05 No2 0.90 1.05 2x10 SS 0.90 1.06 No2 0.79 1.01 Average 0.84 1.03 Niigata 2x4  SS No2 2x8 SS No2 2x10 SS No2 Average Tokyo 2x4  SS No2 2x8 SS No2 2x10 SS No2 Average Osaka 2x4  SS No2 2x8 SS No2 2x10 SS No2 Average  -  0=2.0 7=0.25 1.26 1.17 1.24 1.23 1.23 1.24 1.23  -  7=0.25  7=0.25  /?=3.0 7=0.25 0.84 0.69 0.81 0.81 0.83 0.75 0.79  7=0.41 0.84 0.68 0.80 0.81 0.84 0.75 0.79  0=2.5 7=0.25 1.01 0.89 0.98 0.98 0.99 0.96 0.97  7=0.41 1.00 0.88 0.98 0.98 0.99 0.95 0.96  0=2.0 7=0.25 1.18 1.12 1.17 1.16 1.15 1.18 1.16  7=0.41 1.18 1.10 1.16 1.15 1.15 1.17 1.15  0=3.0 7=0.25 0.79 0.66 0.77 0.77 0.78 0.72 0.75  7=1.22 0.80 0.64 0.76 0.77 0.80 0.70 0.75  0=2.5 7=0.25 0.95 0.86 0.94 0.93 0.93 0.92 0.92  7=1.22 0.96 0.83 0.93 0.93 0.95 0.89 0.92  0=2.0 7=0.25 1.13 1.08 1.12 1.10 1.09 1.14 1.11  7=1.22 1.11 1.03 1.10 1.09 1.09 1.10 1.09  0=3.0 7=0.25 0.73 0.62 0.71 0.71 0.72 0.68 0.70  7=4.40 0.76 0.60 0.72 0.73 0.76 0.66 0.71  0=2.5 7=0.25 0.74 0.71 0.75 0.73 0.75 0.72 0.73  7=4.40 0.90 0.77 0.87 0.87 0.89 0.83 0.86  0=2.0 7=0.25 0.91 0.88 0.91 0.89 0.91 0.89 0.90  7=4.40 1.05 0.96 1.03 1.02 1.03 1.02 1.02  0.77  0.95  0.94  1.14  1.12  Total Average 0.77  Table 16. Mean /?-values Corresponding to Given <j> in Compression  Performance Factor <fi  Mean /?  Mean ft  7=0.25  Actual y  0.6  3.5  3.6  0.7  3.2  3.2  0.8  2.9  2.9  0.9  2.6  2.6  1.0  2.4  2.3  a  Table 17. Size Factor and Standard Strength R for Compression 0  /? = 2.5 at <j> , = 0.9  unit : MPa  0  7  Size Factor  Grade  RQ  •^0.05  0.25  8.312  SS  21.676  19.32  No.2  17.232  18.20  SS  21.784  19.32  No.2  16.967  18.20  Actual  x )  8.675  1) see Table 6a  Table 18a. Modified /?-values in Compression at 0 =O.9 and 0 =O.85 (7=0.25) O  Size  Grade Sapporo  2x8  Tokyo  Osaka  0.9  0.85  0.9  0.85  0.9  0.85  0.9  0.85  SS  2.90  3.05  2.70  2.86  2.54  2.70  2.33  2.49  No.2  2.49  2.61  2.39  2.51  2.30  2.43  2.18  2.31  SS  2.66  2.80  2.49  2.64  2.36  2.51  2.18  2.33  No.2  3.11  3.25  2.94  3.08  2.80  2.94  2.60  2.75  2.78  2.95  2.55  2.73  2.37  2.55  2.15  2.32  2.51  2.64  2.40  2.53  2.30  2.43  2.17  2.30  <t>0  2x4  Niigata  O  2x10 SS No.2 0 =O.9  Maximum=3.11  Minimum=2.15  Averagej=2.51  0o=O.85  Maximum=3.25  Minimum=2.30  Average;=2.65  O  Table 18b. Modified /?-values in Compression at 0 =O.9 and 0 =O.85 (Actual j ) O  Size 2x4 2x8  Grade Sapporo  Niigata  O  Tokyo  a  Osaka  <t>Q  0.9  0.85  0.9  0.85  0.9  0.85  0.9  0.85  SS  2.90  3.05  2.70  2.86  2.56  2.73  2.37  2.55  No.2  2.53  2.65  2.41  2.53  2.27  2.40  2.10  2.24  SS  2.62  2.79  2.46  2.62  2.31  2.47  2.12  2.29  No.2  3.15  3.29  2.97  3.12  2.85  3.00  2.68  2.84  2.76  2.93  2.53  2.71  2.38  2.57  2.18  2.38  2.54  2.66  2.40  2.53  2.26  2.40  2.09  2.23  2x10 SS No.2 00=0.9  Maximum=3.15  Minimum=2.09  Average;=2.51  00=0.85  Maximum=3.29  Minimum=2.23  Average2=2.66  Table 19. Performance Factors in Serviceability for S-P-F (0-values Corresponding to Target 0-values) Sapporo 0=2.0 0=1.5 7=0.25 7=0.25 7=0.25 2x4 SS 0.63 0.75 No2 0.56 0.69 0.64 0.75 2x8 SS No2 0.59 0.71 0.64 2x10 SS 0.76 No2 0.58 0.71 Average 0.61 0.73 Niigata 2x4  SS No2 2x8 SS No2 2x10 SS No2 Average  Tokyo 2x4  SS No2 2x8 SS No2 2x10 SS No2 Average Osaka 2x4  SS No2 2x8 SS No2 2x10 SS No2 Average Occupancy 2x4  SS No2 2x8 SS No2 2x10 SS No2 Average  -  0=1.0 7=0.25 0.86 0.82 0.87 0.84 0.87 0.83 0.85  -  7=0.25  7=0.25  0=2.0 7=0.25 0.63 0.57 0.64 0.59 0.64 0.58 0.61  7=0.41 0.64 0.57 0.65 0.60 0.65 0.59 0.62  0=1.5 7=0.25 0.75 0.70 0.76 0.73 0.76 0.72 0.74  7=0.41 0.76 0.71 0.76 0.73 0.77 0.72 0.74  0=1.0 7=0.25 0.88 0.85 0.89 0.86 0.89 0.86 0.87  7=0.41 0.88 0.85 0.89 0.86 0.89 0.86 0.87  0=2.0 7=0.25 0.62 0.56 0.63 0.59 0.63 0.58 0.60  7=1.22 0.65 0.58 0.66 0.61 0.66 0.60 0.63  0=1.5 7=0.25 0.75 0.71 0.76 0.73 0.76 0.72 0.74  7=1.22 0.77 0.71 0.77 0.73 0.78 0.72 0.75  0=1.0 7=0.25 0.89 0.86 0.90 0.88 0.90 0.87 0.88  7=1.22 0.88 0.84 0.89 0.86 0.89 0.85 0.87  0=2.0 7=0.25 0.60 0.56 0.61 0.58 0.61 0.57 0.59  7=4.40 0.64 0.56 0.65 0.59 0.65 0.58 0.61  0=1.5 7=0.25 0.74 0.71 0.75 0.73 0.75 0.72 0.73  7=4.40 0.75 0.69 0.76 0.71 0.76 0.71 0.73  0=1.0 7=0.25 0.91 0.88 0.91 0.89 0.91 0.89 0.90  7=4.40 0.86 0.86 0.86 0.83 0.87 0.83 0.85  0=2.0 7=0.25 0.63 0.56 0.64 0.59 0.65 0.58 0.61  7=0.28 0.63 0.56 0.64 0.59 0.65 0.58 0.61  0=1.5 7=0.25 0.74 0.68 0.75 0.71 0.75 0.70 0.72  7=0.28 0.74 0.68 0.75 0.71 0.75 0.70 0.72  0=1.0 7=0.25 0.85 0.81 0.86 0.83 0.86 0.82 0.84  7=0.28 0.85 0.81 0.86 0.83 0.86 0.82 0.84  0.61  0.73  0.73  0.87  0.86  Total Average 0.60  Table 20. Statistical Data for Analysis of Duration of Load Effect  Short Term Strength Mean (MPa) S.D. (MPa) SPF Q l  48.90  9.83  SPF Q2  25.77  7.09  Parameters of Damage Accumulation Model b  c  Mean  C O V Mean  SPF Q l  77.392  0.174  2.810 xio"  SPF Q2  158.656 0.009  7.525 x i o '  n  <r  0  COV  Mean  COV  Mean C O V  6  0.057  1.162  0.231  0.420  0.038  7  0.042  1.285  0.170  0.365  0.562  Table 21. Duration of Load Effects for S-P-F Ql Sapporo  0 = 2.5  0 = 3.0  7 0.25  <f>  K  D  DOL  0.69  0.72  0.77  0.70  0.87  0.70  DOL-5  0.70  0.73  0.77  0.70  0.85  0.68  7  <t>  1.10  0 = 2.5  K  D  4>  K  D  0.70  0.80  0.79  0.78  0.91  0.78  DOL-5  0.65  0.75  0.74  0.73  0.84  0.72  No-DOL  0.88  DOL  0.70  1.01  1.16  1.16  1.01 0.80  0.78  . 0.77  0.89  K  D  0.77  0 =2.0  0 = 2.5  K  D  K  <!>  D  l.n  No-DOL  0.80  DOL  0.73  0.91  0.83  0.87  0.98  0.88  DOL-5  0.62  0.77  0.72  0.76  0.82  0.74  No-DOL  0.86  DOL  0.72  Osaka  0.95  7  <t>  1.11  0.98 0.84  0.79  0.81  0.90  0 = 2.5  0 = 3.0  4.40  Kn  DOL  7  0.25  <t>  0 =2.0  0.87  0 = 3.0  1.22  1.25  No-DOL  Tokyo 0.25  «D  D  0.96  0 = 3.0  0.41  K  No-DOL  Niigata 0.25  <f>  =2.0  K  D  4>  0.81  0 =2.0  K  D  4>  K  D  No-DOL  0.74  DOL  0.69  0.93  0.78  0.90  0.93  0.90  DOL-5  0.56  0.76  0.66  0.76  0.77  0.75  No-DOL  0.84  DOL  0.48  0.87  1.03  0.94 0.57  0.54  1.05 0.57  0.60  0.57  Table 22. Duration of Load Effects for S-P-F Q2 Sapporo  0 = 3.0 7  0.25  <P  0 = 2.5  K  D  0.51  0.56  0.58  0.54  0.68  0.55  DOL-5  0.48  0.53  0.56  0.52  0.65  0.52  <P  1.07  0 = 2.5  K  D  K  D  K  <P  D  DOL  0.63  0.75  0.73  0.74  0.85  0.73  DOL-5  0.51  0.61  0.61  0.62  0.72  0.62  No-DOL  0.84  DOL  0.57  4>  7  0.99  1.17  0.99 0.68  0.67  1.16 0.68  0.78  0 = 2.5  K  D  <t>  0.67  0 =2.0  K  D  4>  K  D  No-DOL  0.78  DOL  0.72  0.92  0.87  0.93  1.01  0.90  DOL-5  0.54  0.69  0.64  0.68  0.75  0.67  No-DOL  0.81  DOL  0.39  Osaka  0.94  7  <t>  1.12  0.95 0.48  0 = 3.0  4.40  4>  0 =2.0  0.84  0 = 3.0  0.25  1.24  No-DOL  Tokyo  1.22  D  DOL  7  0.25  K  D  0.91  0 = 3.0  0.41  K  No-DOL  Niigata 0.25  <f>  0 =2.0  0.46  1.10 0.48  0.54  P = 2.5  K  D  4>  0.49  0 =2.0  K  D  <P  K  D  No-DOL  0.73  DOL  0.67  0.92  0.83  0.94  0.98  0.92  DOL-5  0.54  0.74  0.65  0.74  0.77  0.73  No-DOL  0.78  DOL  0.25  0.88  1.06  0.90 0.32  0.30  1.03 0.33  0.36  0.35  107  Table 23. Bending Reliability Levels for Current 2x4 Wood Frame Structure (Short-Term Basis) Floor Joist Size Grade Spacing 2x8 SS 455 mm 303 No2 405 303 2x10 SS 455 303 No2 455 303  7 0.30 0.34 0.30 0.34 0.33 0.37 0.33 0.37  P  2.778 2.782 2.938 2.942 2.680 2.686 3.021 3.028  Rafters ( light weight roofing material ) Sapporo Size Grade Spacing 7 P 2x4 SS 455 mm 0.10 3.608 303 0.12 3.610 No2 405 0.10 3.387 303 0.12 3.389 2x8 SS 455 0.12 2.817 303 0.14 2.820 No2 455 0.12 2.976 303 0.14 2.978 2x10 SS 455 0.13 2.720 303 0.16 2.723 No2 455 0.13 3.051 303 0.16 3.056  Niigata 7 0.17 0.19 0.17 0.19 0.19 0.22 0.19 0.22 0.21 0.25 0.21 0.25  Rafters ( Heavy weight roofing material ) Sapporo Niigata Size Grade Spacing 7 P 7 2x4 SS 455 mm 0.22 3.626 0.36 303 0.23 3.628* 0.38 No2 405 0.22 3.402 0.36 303 3.404 0.23 0.38 2x8 SS 455 0.23 2.832 0.38 303 2.834 0.25 0.41 No2 455 0.23 2.990 0.38 303 2.992 0.25 0.41 2x10 SS 455 0.24 2.735 0.40 303 0.27 2.737 0.44 No2 455 0.24 3.073 0.40 303 0.27 3.077 0.44  P  3.542 3.547 3.332 3.337 2.765 2.771 2.925 2.930 2.666* 2.674 2.973 2.985  P  3.581 3.585 3.365 3.368 2.796 2.800 2.955 2.959 2.698 2.704 3.020 3.028  Tokyo 7 0.48 0.54 0.48 0.54 0.54 0.64 0.54 0.64 0.61 0.73 0.61 0.73 Tokyo 7 1.07 1.13 1.07 1.13 1.13 1.22 1.13 1.22 1.19 1.31 1.19 1.31  P  2.382 2.396* 2.258 2.269 1.566 1.580 1.780 1.795 1.384* 1.402 1.456 1.482  P  2.532 2.588 2.387 2.438 1.753 1.831 1.959 2.033 1.634* 1.735 1.775 1.899  Osaka 7 1.74 1.96 1.74 1.96 1.96 2.29 1.96 2.29 2.18 2.62 2.18 2.62 Osaka 7 3.84 4.06 3.84 4.06 4.06 4.39 4.06 4.39 4.28 4.72 4.28 4.72  P  2.921 3.003 2.476 2.821 2.189 2.286 2.373 2.466 2.121 2.232 2.360 2.493  P  3.335 3.354* 3.127 3.145 2.547 2.573 2.715 2.740 2.450 2.483 2.751 2.790  Table 24.  Deflection Limits Allowable Deflection  Member  (Long-Term)  (Short-Term)  Floor Joist Floor Beam  L/300 and 2.0 cm  N/A  Ceiling Joist Flat Roof Joist Rafter  L/200 and 2.0 cm  L/100 and 4.0 cm  L/300 and 1.0cm  L/150 and 2.0 cm  Rafter Beam Header  Table 25. Serviceability Reliability Levels for Current 2x4 Wood Frame Structures Floor Joist Size Grade Spacing 2x8 SS 455 mm 303 No2 405 303 2x10 SS 455 303 No2 455 303  7 0.30 0.34 0.30 0.34 0.33 0.37 0.33 0.37  0 1.143 1.167 1.200 1.219 1.041 1.073 0.995 1.020  Rafters ( light weight roofing material ) Sapporo Size Grade Spacing 7 0 2x4 SS 455 mm 0.10 1.210 303 0.12 1.228 No2 405 0.10 1.011 303 0.12 1.027 2x8 SS 455 0.12 1.085 303 0.14 1.114 No2 455 0.12 1.153 303 0.14 1.177 2x10 SS 455 0.13 0.985 303 0.16 1.024 No2 455 0.13 0.951 303 0.16 0.983  Niigata 7 0.17 0.19 0.17 0.19 0.19 0.22 0.19 0.22 0.21 0.25 0.21 0.25  Rafters ( Heavy weight roofing material ) Sapporo Niigata Size Grade Spacing 7 0 7 2x4 SS 455 mm 0.22 1.363 0.36 303 0.23 1.377 0.38 No2 405 0.22 1.140 0.36 303 0.23 1.153 0.38 2x8 SS 455 0.23 1.246 0.38 303 0.25 0.41 1.270 No2 455 0.23 1.286 0.38 303 0.25 1.305 0.41 2x10 SS 455 0.24 1.149 0.40 303 0.27 0.44 1.181 No2 455 0.24 1.085 0.40 303 0.27 1.111 0.44  0  1.389 1.423 1.165 1.194 1.296 1.348 1.328 1.372 1.222 1.291 1.147 1.205  0  1.651 1.674 1.394 1.414 1.566 1.601 1.557 1.587 1.493 1.539 1.377 1.418  Tokyo 7 0.48 0.54 0.48 0.54 0.54 0.64 0.54 0.64 0.61 0.73 0.61 0.73 Tokyo 7 1.07 1.13 1.07 1.13 1.13 1.22 1.13 1.22 1.19 1.31 1.19 1.31  0  1.893 1.974 1.619 1.672 1.857 1.929 1.818 1.886 1.824 1.907 1.681 1.764  0  2.197 2.211 1.946 1.964 2.131 2.150 2.098 2.120 2.072 2.094 1.951 1.979  Osaka 7 1.74 1.96 1.74 1.96 1.96 2.29 1.96 2.29 2.18 2.62 2.18 2.62 Osaka 7 3.84 4.06 3.84 4.06 4.06 4.39 4.06 4.39 4.28 4.72 4.28 4.72  0  2.325 2.329 2.167 2.182 2.255 2.260 2.273 2.283 2.200 2.205 2.155 2.169  0  2.334 2.334 2.227 2.228 2.265 2.265 2.300 2.301 2.212 2.212 2.190 2.192  Table 26. Typical Rafter Span Tokyo, Light Roofing, Spacing=455mm Grade 2x4 2x6 SS D-Span 310.81 462.75 B-Span 426.47 664.39 1115.5 S-Span 1720.3 Span 3.10 4.62  2x8 565.13 864.58 2215.5 5.65  2x10 672.46 1082.9 2722.5 6.72  unit cm cm cm m  Sapporo, Light Roofing, Spacing:=303mm Grade 2x4 2x6 No.2 D-Span 175.72 275.74 B-Span 159.36 249.76 S-Span 228.45 356.55 Span 1.59 2.49  2x8 361.35 326.92 464.59 3.26  2x10 443.51 414.09 583.83 4.14  unit cm cm cm m  Niigata, Heavy Roofing, Spacing:=455mm Grade 2x4 2x6 No.2 D-Span 168.79 264.97 B-Span 150.02 235.27 S-Span 202.47 316.38 Span 1.50 2.35  2x8 347.32 308.06 412.54 3.08  2x10 430.73 390.56 519.38 3.90  unit cm cm cm m  Tokyo, Light Roofing, Spacing='455 Grade 2x4 2x6 No.2 D-Span 298.11 448.50 352.14 B-Span 548.60 S-Span 1115.5 1720.3 Span 2.98 4.48  2x8 547.72 713.90 2215.5 5.47  2x10 651.74 894.20 2722.5 6.51  unit cm cm cm m  Osaka, Heavy Roofing, Spacing=:455mm Grade 2x4 2x6 No.2 D-Span 263.91 408.52 293.31 B-Span 455.16 1184.2 S-Span 773.89 Span 2.63 4.08  2x8 497.98 590.11 1513.8 4.97  2x10 590.50 734.04 1834.6 5.90  unit cm cm cm m  where D-Span ; B-Span ; S-Span ; Span ;  Span Calculated by Allowable Deflection Span Calculated by Allowable Bending Unit Stress Span Calculated by Allowable Shearing Unit Stress Minimum of Above Three Calculated Span  Figure 1. Beta vs Phi for Japanese Steel C o d e  LOAD LEVEL X (D  SUSTAINED  TIME  LOAD  LOAD LEVEL X(2)  EXTRAORDINARY  LOAD  TIME  Maximum LOAD LEVEL X(1)*X(2)  TOTAL O C C U P A N C Y  LOAD  TIME  Figure 2. Occupancy Load Model  r-* to  CUMULATIVE FREQUENCY  100  120  140  160  180 200 220 240 260 280 300 320 340  OCCUPANCY LOAD (Kg/m ) 2  SIMULATION  UPPER 10% DATAFIT  Figure 3. Japanese Occupancy Load (50-Year Return)  140  SNOW HEIGHT (cm)  Figure 4. Snow Model in Sapporo  140  SNOW HEIGHT (cm)  120 100 -  Figure 5. Snow Model in Tokyo  CHINA  KOREA  SAPPOR ASD : 132 days NSH : 167 cm  JAPAN OKYO ASD : 2 days NSH : 10 cm  Figure 6. Location and Snow Data  ASD : 5 days NSH : 36 cm  ASD: Annual Snow Duration NSH: Nominal Snow Height  BETA 2.9 2.7 2.5 2.3 2.1 1.9 1.7 1.5  1  0.5  —  2.5  2  3  GAMMA • Dn / Sn  SAPPORO Cp =0.8  -B- TOKYO  1.5  ()9 =0.8  Figure 7. Beta vs Gamma (2x8, No.2)  SAPPOROC/J =0.9 TOKYO  CP =0.9  -5K-  SAPPORO CP =1.0 TOKYO  <P -1.0  BETA  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  PHI  1  Figure 8. Bending Beta vs Phi in Tokyo (2x8, No.2, All Data)  1.1  1.2  1.3  1.4  1.5  CUMULATIVE PROBABILITY  0  2  4  6  8  10  BENDING STRENGTH (psi) (Thousands) TEST DATA  LOWER 15% DATAFIT  Figure 9. 2P Weibull Datafit (1) (2x8, No.2, CWC Test Data)  - * - 100% DATAFIT  12  CUMULATIVE PROBABILITY  0.25  0.15  0.05 -  1  1.5  2  2.5  3  3.5  4  BENDING STRENGTH (psi) (Thousands) TEST DATA  LOWER 15% DATAFIT  4.5  - * ~ 100% DATAFIT  Figure 10. 2P Weibull Datafit (2) (2x8, No.2, CWC Test Data) to o  BETA 2P-WEIBULL 3P-WEIBULL LOGNORMAL -B-  NORMAL  4  2 -  1 0.2  J  0.3  0.4  J  L  0.5  0.6  0.7  0.8  0.9  PHI  J  L  1  1.1  1.2  Figure 11. Bending Beta vs Phi in Tokyo (2x8, No.2, 15% Truncation)  1.3  L  1.4  1.5  BETA  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  PHI  1  1.1  1.2  1.3  1.4  1.5  Figure 12. Bending Beta vs Phi (SS-No.2) (Tokyo, 2x10, 15% Truncation) to to  BETA  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  1  1.1  1.2  1.3  1.4  1.5  PHI Figure 13. Bending Beta vs Phi (SS-No.2) (Tokyo, 2x10, All Data) to co  3.5  BETA  2.5  SAPPORO NIIGATA  1.5  TOKYO -B-  OSAKA OCCUPANCY  1 0.4  0.5  0.6  0.7  0.8  Figure 14. Bending Beta vs Phi (All Cases)  0.9  PHI  1.1  1.2  1.3  1.4  3.5  BETA  2.5  SAPPORO -f-  1.5  NIIGATA TOKYO  -s-  OSAKA OCCUPANCY  1 0.4  0.5  0.6  0.7  Figure 15. Bending Beta vs Phi  0.8  0.9  1  PHI  (All Cases, Actual Gamma)  1.1  1.2  1.3  1.4  3.5  BETA  2.5  SAPPORO NIIGATA  1.5  TOKYO -B-  1 0.4  OSAKA  0.5  0.6  0.7  0.8  0.9  1.1  1.2  1.3  1.4  PHI Figure 16. Beta vs Phi in Tension (All Cases) to  BETA 3.5  I  3 -  2.5 -  2 SAPPORO  1.5 -  NIIGATA  -f-  - * - TOKYO -B-  0.4  OSAKA  0.5  0.6  0.7  0.8  0.9  1  1.1  1.2  1.3  1.4  PHI Figure 17. Beta vs Phi in Compression (All Cases) to -a  S(t)  n  n SNOW  TIME  LOAD  D(t)  DEAD  a(t)  _n_  TIME  LOAD  Jl STRESS  n . TIME  Figure 18. Load and Stress Model for DOL to OO  4  BETA i  0.4  0.5  0.6  0.7  0.8  0.9  PHI  Figure 19. DOL in Osaka (SPF Q1, Gamma = 0.25)  1  1.1  1.2  1.3  1.4  1.5  1  K  D  Factor  x 0.8  0.6  0.4  0.2  J_L  0.1  10  100  GAMMA  Figure 21. Recomended Relationship between GAMMA and K Factor D  1000  3.5  BETA I  3 2.5 2 1.5 -  4  5  5  6  5  6  7  8  8  6  4  9  SPAN (m) Figure 22. Bending Beta vs Span (Tokyo, 2x8, S S , Light Roof)  10  11  12  BETA  SPAN (m) 2x4  2x6  - * - 2x8  2x10  Figure 23. Long-Term Bending Beta vs Span (Tokyo 1, SS, 455mm, Light Roof) CO CO  BETA  .8  5  SPAN (m) 2x4  2x6  - ^ 2 x 8^ 2 x 1 0  Figure 24. Long-Term Bending Beta vs Span (Sapporo, No.2, 303mm, Light Roof)  BETA  0.5  1  1.50 1.5  2x4  2  2.35 2.5  SPAN (m) 2x6  3  3.08  2x8  3.5  3.90  4.5  2x10  Figure 25. Long-Term Bending Beta vs Span (Niigata, No.2, 455mm, Heavy Roof) CO  BETA  SPAN (m) 2x4  2x6  2x8  2x10  Figure 26. Long-Term Bending Beta vs Span (Tokyo 2, No.2, 455mm, Light Roof)  BETA  6.5  SPAN (m) 2x4  2x6  -*-  2x8  -B- 2 x 1 0  Figure 27. Long-Term Bending Beta vs Span (Osaka, No.2, 455mm, Heavy Roof) CO  138  Appendix 1.  Species  Allowable Unit Stress for Lumber for 2x4 Wood Frame Structure  Grade  Group  DFir-L  Hem-Tarn  S.S.  9.8  8.3  13.7  0.78  9.3  6.9  11.8  0.78  No.2  7.4  5.9  9.8  0.78  No.3  4.4  3.4  5.4  0.78  Construction  8.3  4.4  7.4  0.78  6.9  2.5  8800  Standard  3.9  0.78  Utility  4.4  1.0  2.0  8800  0.78  8800  7.8  12.7  0.69  9800  S.S.  8.8  No.1  7.8  6.4  No.2  6.4  10.8  0.69  5.4  8.8  0.69  2.9  4.9  0.69  No.3  3.9  Construction  7.4  3.9  6.9  0.69  Standard  5.9  2.5  3.9  0.69  Utility  3.9  1.0  2.0  0.69  S.S.  8.8  6.9  11.8  0.69  No.1  7.8  5.9  9.8  6.4  5.4  0.69  No.3  2.9  0.69  3.9  8.8  Construction  7.4  3.9  5.9  2.0  Utility  3.9  1.0  10800 10800 9800 8800  9800 2 times the values of allowable unit stress for compression, tension, bend ng or shear for sustained loads, respectively  8800 7800 7800 7800 7800 8800 8800 7800  4.9  0.69  6.4  0.69  3.4  0.69  1.5  0.69  10.8  0.59  8300  9.3  0.59  8300  7.4  0.59  7400  4.4  0.59  6900 6900  S.S.  7.4  6.4  No.1  6.4  5.4  No.2  4.9  4.4  No.3  2.9  2.5  Construction  5.9  3.4  5.9  0.59  Standard  4.9  2.0  0.59  Utility  2.9  1.0  3.4 1.5  0.59  S.S.  7.4  5.9  9.8  0.59  No.1 W Cedar  Shear  Modulus of Elasticity (unit: MPa)  No.1  Standard  S-P-F  Allowable Unit Stress for Temporary Loads (unit: MPa)  Compression Tension Bending Shear Compression Tension Bending  No.2 Hem-Fir  Allowable Unit Stress for Sustained Loads (unit: MPa)  6900 6900 6900 6900  6900 6900  0.59  7800 7800  7.4  0.59  6900  4.4  0.59  6400  3.4  5.4  0.59  6400  2.0  2.9  0.59  6400  0.59  6400  6.4  5.4  No.2  5.4  4.4  No.3  2.9  2.5  Construction  5.9  Standard  4.9  Utility  2.9  1.0  8.8  1.5  Plumb Measure Size  1.35m  1.3<im  1st Floor  2nd Floor  Against Ridge Direction  1.35m  2F 1F  1.35m  1st Floor  Appendix 2. Measurement of Plumb Measure Size  2nd Floor  Against Span Direction  Appendix 3. Characteristics of the Bending Strength (100% Data) unit : MPa  Normal Lognormal  2P Weibull 3P Weibull  Size  2x4  Grade  SS  No2  SS  No2  SS  No2  Mean  55.43  45.78  41.71  36.32  37.15  30.68  S.D.  13.50  14.37  11.27  11.38  9.61  9.52  Mean  55.41  46.05  41.53  38.16  37.01  30.88  S.D.  14.70  17.22  12.38  14.37  10.52  11.27  Scale  60.51  51.47  45.90  41.00  40.70  34.47  Shape  4.765  3.335  4.215  3.272  4.481  3.382  Location 14.09  8.94  3.35  6.72  1.35  7.26  2x8  2x10  Scale  46.18  42.19  42.50  34.06  39.33  26.88  Shape  3.303  2.491  3.792  2.460  4.278  2.368  32.77  21.17  23.05  16.89  20.71  14.86  Non-Parametric 5th Percentile  Appendix 4. Characteristics of the Bending Strength (Lower 15% Datafit) unit : MPa  Normal Lognormal 2P Weibull 3P Weibull  Size  2x4  Grade  SS  No2  SS  No2  SS  No2  Mean  54.05  36.99  39.68  29.61  36.39  23.85  S.D.  12.44  9.01  10.15  7.43  9.26  5.22  Mean  68.58  50.82  56.00  42.69  50.46  29.75  S.D.  28.24  24.29  28.79  22.16  25.35  11.45  Scale  57.12  40.42  43.91  32.96  39.71  25.07  Shape  5.578  4.912  4.548  4.598  4.674  5.979  Location 3.66  12.62  3.68  4.86  0.00  10.04  Scale  54.57  45.92  42.26  31.84  39.71  26.88  Shape  4.912  1.792  3.730  3.102  4.674  1.713  32.77  21.17'  23.05  16.89  20.71  14.86  2x8  2x10  Non-Parametric 5th Percentile  Appendix 5. 2 Parameter Weibull Distribution Parameters for MOE for S-P-F Size  Grade  Mean  COV  2x4 2x8 2x10  Scale m  Shape k  (xlO MPa)  (xlO MPa)  SS  1.029  0.167  1.100  7.056  No.2  0.910  0.210  0.986  5.499  SS  0.984  0.161  1.049  7.326  No.2  0.923  0.192  0.994  6.070  SS  0.954  0.160  1.017  7.403  N0.2  0.872  0.198  0.941  5.868  4  4  Appendix 6. Parameters for Tension Strength (Lower 15% Datafit)  2-P Weibull Parameters Size  Grade  Mean  COV  ( MPa) 2x4  2x8  2x10  Scale m  Shape k  ( MPa )  Non-parametric 5-th Percentile ( MPa)  SS  25.83  0.22  28.04  5.30  16.53  No.2  17.73  0.25  19.43  4.49  9.80  SS  18.21  0.18  19.52  6.62  12.27  No.2  13.19  0.19  14.21  6.09  8.32  SS  18.45  0.18  19.83  6.33  12.07  No.2  14.11  0.22  15.33  5.23  8.50  Appendix 7. Parameters for Compression Strength (Lower 25% Datafit)  2-P Weibull Parameters Size  Grade  Mean  COV  ( MPa) 2x4  2x8  2x10  Scale m  Shape k  ( MPa)  Non-parametric 5-th Percentile ( MPa)  SS  31.19  0.14  32.97  8.81  23.28  No.2  27.01  0.19  29.12  5.97  18.48  SS  26.54  0.15  28.20  7.88  19.32  No.2  24.15  0.14  25.57  8.46  18.20  SS  23.96  0.13  25.24  9.50  18.69  No.2  21.69  0.18  23.31  6.36  14.40  

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