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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 Ins t i tu te of Technology, 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 of Forest ry Ve accept t h i s thes i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l 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 Mfr>U c±f /?f/ DE-6 (2/88) i i ABSTRACT R e l i a b i l i t y l eve l s of Japanese 2x4 wood frame st ructures were evaluated using lumber property data der ived from eva luat ion of Canadian Spruce-Pine-Fir dimension lumber. The evaluat ions were made using the "Standard f o r L imi t States Design of S tee l Structures (D ra f t ) " , which was newly publ ished by the LRFD Subcommittee of A r ch i t e c tu r a l I ns t i tu te of Japan, and In-Grade Data obtained by a Canadian Wood Counci l research p ro jec t . These analyses were implemented using the computer program "RELAN" developed by Dr. R.O. Foschi at UBC and Monte Car lo s imula t ions . R e l i a b i l i t y l eve l s of current Japanese 2x4 wood frame s t ructures were a l so evaluated. Recommendations were made to encourage the app l i c a t i on of l i m i t s tates design i'n'to e x i s t i n g Japanese design methods. i i i TABLE DF CONTENTS Page ABSTRACT i i TABLE OF CONTENTS i i i LIST OF TABLES v i i LIST OF FIGURES ix LIST OF APPENDICES x LIST OF ABBREVIATIONS x i ACKNOWLEDGEMENTS x i i 1. INTRODUCTION 1 2. OBJECTIVES 7 3. CURRENT STRUCTURAL CALCULATION SYSTEM FOR JAPANESE TIMBER STRUCTURES 9 3.1 Bu i ld ing Codes and Standards 9 3.1.1 Bu i ld ing Standard Law 9 3.1.2 Bu i ld ing Standard Law Enforcement Order 9 3.1.3 Bu i ld ing N o t i f i c a t i o n 10 3.1.4 Standard f o r S t ruc tu ra l Ca l cu l a t i on of Timber Structures 10 3.1.5 GHLC Span Table 11 3.2 P r i n c i p l e s of S t ruc tu ra l Ca l cu l a t i on fo r Timber Structures 12 3.2.1 Design Requirements 12 3.2.2 Design Loads 12 3.2.3 Allowable Uni t Stress 13 i v 3.2.4 Working Stress 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 3.2.5 La te ra l Resistance fo r Ordinal Wooden Structures 16 4. JAPANESE LIMIT STATES DESIGN 19 4.1 New Japanese Standard f o r L imi t State Design of S tee l S t ructure (Draft ) 19 4.2 Proposed Load Combinations and Load Factors 20 5. JAPANESE FULL SIZE TEST PROGRAM FOR STRENGTH OF LUMBER . . 23 5.1 Bending 24 5.2 MOE 24 5.3 Moisture Content 24 5.4 Mater ia l Strength 25 5.5 Duration of 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. 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 9. PERFORMANCE FACTORS FOR JAPANESE 2x4 WOOD FRAME STRUCTURAL MEMBERS 40 9.1 Strength L imi t States 40 9.1.1 E f f e c t of Load Rat io 7 42 9.1.2 Resistance D i s t r i b u t i o n Model 43 9.1.3 Bending Performance Factor 44 8.1.4 Tension 48 9.1.5 Compression 49 9.2 S e r v i c e a b i l i t y L imi t states 51 10. DURATION OF LOAD EFFECTS 55 10.1 Damage Model 56 10.2 Load Case '58 10.3 S imulat ion 58 10.4 Duration of Load Results 60 11. ASSESSMENT OF RELIABILITY LEVELS ASSOCIATED WITH CURRENT WORKING STRESS DESIGN 63 11.1 Load 63 11.2 Allowable Unit. S t ress 64 11.3 R e l i a b i l i t y Levels in Bending (Short-Term Basis ) . . . 64 11.4 R e l i a b i l i t y Levels in De f l ec t ion 67 v i 11.5 R e l i a b i l i t y of Current Rafter Construct ion under Long-Term Loading 69 11.6 Discuss ion 74 12. DISCUSSION AND CONCLUSION 76 REFERENCES 82 v i i LIST OF TABLES Page Table 1. Design Requirements of the Bu i ld ing Codes 85 Table 2. Load Combinations fo r Working Stress Design 86 Table 3. Basic S t a t i s t i c a l Data f o r Safety Ana lys is of S tee l St ructure 87 Table 4. Occupancy Load (Extreme Type I D i s t r i bu t i on ) 88 Table 5. Japanese Snow Data 89 Table 6. Nominal Design Dead, Occupancy and Snow Load 90 Table 6a. Nominal Dead to L ive Design Load Rat ios 90 Table 7. Bending Performance Factors fo r S-P-F 91 Table 8. Mean /3-values Corresponding Given (j> in Bending 92 Table 9. S ize Factors and Cha rac t e r i s t i c Strengths R0, f o r Bending 93 Table 10a. Modi f ied /3-values in Bending ( 7 = 0.25) 94 Table 10b. Modif ied /3-values in Bending (Actual ja) 94 Table 11. Performance Factors in Tension fo r S-P-F 95 Table 12. Mean /3-values Corresponding Given <j> in Tension 96 Table 13. S ize Factors and Cha ra c t e r i s t i c Strengths RQ, f o r Tension 97 Table 14a. Modi f ied /3-values in Tension ( 7 = 0.25) 98 Table 14b. Modi f ied /3-values in Tension (Actual ja) 98 Table 15. Performance Factors in Compression fo r S-P-F 99 Table 16. Mean /3-values Corresponding Given <j> in Compression . . 100 Table 17. S ize Factors and Cha rac t e r i s t i c Strengths RQ, f o r Compression 101 Table 18a. Modi f ied /3-values in Compression ( 7 = 0.25) 102 Table 18b. Modi f ied /3-values in Compression (Actual ya) 102 Table 19. Performance Factors in S e r v i c e a b i l i t y f o r S-P-F . . . . 103 Table 20. S t a t i s t i c a l Data f o r Ana lys is of Duration of Load E f f e c t 104 Table 21. Duration of Load E f f e c t s f o r S-P-F Ql 105 Table 22. Duration of Load E f f e c t s f o r S-P-F Q2 106 V i i i Table 23. Bending R e l i a b i l i t y Levels fo r Current 2x4 Wood Frame Structures (Short-Term Basis ) 107 Table 24. De f l ec t ion L imi ts 108 Table 25. S e r v i c e a b i l i t y R e l i a b i l i t y Levels fo r Current 2x4 Wood Frame Structures 109 Table 26. Typ i ca l Rafter Span 110 Table 27. Recommended <j> and /^-values 78 Table 28. Duration of Load Factor KD f o r SPF Ql at 0T - 2.5 . . 79 Table 29. R e l i a b i l i t y Level /? in Current 2x4 Wood Frame Structure 80 Table 30. Rafter Span Comparison Using Current and New LSD Design Equation 81 ix LIST OF FIGURES Page Figure 1. Beta(/?) vs Phi(0) f o r Japanese Stee l Code I l l F igure 2. Occupancy Load Modeling 112 Figure 3. Japanese Occupancy Load 113 Figure 4. Snow Model in Sapporo 114 Figure 5. Snow Model in Tokyo 115 Figure 6. Locat ion and Snow data 116 Figure 7. Beta(/?) vs. Gamma(7) 117 Figure 8. Bending Beta(/?) vs Phi(<£) in Tokyo ( A l l Data) 118 Figure 9. 2P-Veibul l F i t s (1) 119 Figure 10. 2P-Weibull F i t s (2) 120 Figure 11. Bending Beta(/?) vs Phi(<£) in Tokyo (15% Truncat ion) . 121 Figure 12. Bending Beta(/?) vs Phi(^) SS vs No.2 (1) 122 Figure 13. Bending Beta(/?) vs Phi(^) SS vs No.2 (2) 123 Figure 14. Bending Beta(/?) vs Phi(<?!>) ( A l l Cases) 124 Figure 15. Bending Beta(/?) vs Phi(<^) ( A l l Cases, Actual Gamma) . 125 Figure 16. Tension Beta(/?) vs Phi(<£) ( A l l Cases) 126 Figure 17. Compression Beta(/3) vs Phi(^) ( A l l Cases) 127 Figure 18. Load and Stress Model f o r DOL 128 Figure 19. DOL Osaka 129 Figure 20. DOL Sapporo 130 Figure 21. Recommended Re la t ionsh ip between j and KD Factor . . . 131 Figure 22. Beta(/?) vs Span 132 Figure 23. Long-Term Beta(/?) vs Span Tokyo 1 133 Figure 24. Long-Term Beta(/?) vs Span Sapporo 134 Figure 25. Long-Term Beta(/?) vs Span N i iga ta 135 Figure 26. Long-Term Beta(/?) vs Span Tokyo 2 136 Figure 27. Long-Term Beta(/?) vs Span Osaka . 137 X LIST OF APPENDICES Page Appendix 1. Al lowable Unit Stress fo r Lumber f o r 2x4 Wood Frame Structure 138 Appendix 2. Measurement of Plumb Measure S ize 139 Appendix 3. Cha rac t e r i s t i c s of Bending Strength fo r S-P-F (100% Data) 140 Appendix 4. Cha rac t e r i s t i c s of Bending Strength fo r S-P-F (Lower 15% Da ta 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 fo r MOE fo r S-P-F 142 Appendix 6. Cha rac t e r i s t i c s of Tension Strength (Lower 15% Da ta f i t ) 143 Appendix 7. Cha rac t e r i s t i c s of Compression Strength (Lower 25% Data f i t ) 144 x i LIST OF ABBREVIATIONS A U A r ch i t e c tu ra l I ns t i tu te of Japan CMHC Canada Mortgage and Housing Corporat ion COV C o e f f i c i e n t of Va r i a t i on FFPRI Forest ry and Forest Products Research Ins t i tu te GHLC Government Housing Loan Corporat ion JAS Japanese A g r i c u l t u r a l Standard LRFD Load and Resistance Factored Design LSD L imi t States Design MOAFF M in i s t r y of A g r i c u l t u r a l , Forest ry and F i she r i e s MOC Min i s t r y of Construct ion NLGA Nat ional Lumber Grades Author i ty RBD Re l i ab i l i t y-Based Design S-P-F Spruce-Pine-Fir SS Se lec t S t ruc tu ra l VSD Working Stress Design ACKNDVLEDGEMENTS x i i I would l i k e to express my deepest gra t i tude to Dr. J .D . Barret t and Dr. R.O. Foschi f o r t he i r inva luable adv ice , and pat ient guidance throughout th i s study and in the presentat ion of t h i s t he s i s . I would a l so l i k e to thank my employer, Counci l of Forest Industr ies of B r i t i s h Columbia (COFI), who allowed me an educat ional leave and provided f i n a n c i a l support so that I could accept the opportunity to study at UBC and complete th i s t he s i s . 1. INTRODUCTION 1 L imi t States Design (LSD) codes incorporat ing safety assessments based on modern Re l i ab i l i t y-Based Design (RBD) p r i n c i p l e s are r ap id l y r ep lac ing the t r a d i t i o n a l Working Stress Design (WSD) phi losophy in s t ruc tu ra l mater ia ls design codes throughout the world. The transformation to the LSD or the Load and Resistance Factor Design (LRFD) format has l a rge l y been led by the s t e e l , concrete and other non-wood mater ia ls groups. Interest in developing LSD timber design codes i s expanding r ap id l y in order to keep timber s t ructures design on a bas is compatible with the other major s t ruc tu ra l mater ia l s . The Canadian Code f o r Engineering Design in Wood [1] was the f i r s t timber code to be converted to the LSD format. The 1984 r e v i s i on was l a rge l y a so f t conversion of the WSD code with the exception that new sawn lumber mater ia ls property data was incorporated into the LSD r e v i s i o n . The 1989 r e v i s i on of the Canadian Code [2] incorporates new design equations c a l i b r a t ed to provide minimum target safety l eve l s der ived using formal r e l i a b i l i t y assessment procedures. Applying r e l i a b i l i t y assessment procedures requi res knowledge of ac tua l loads ( e . g . , occupancy, snow, wind, earthquake), member s t ruc tu ra l behavior models and appropr iate mater ia ls strength data as wel l as the corresponding member design equations f o r the strength and s e r v i c e a b i l i t y l i m i t s ta tes . Th is information i s requi red f o r the ana l ys i s of the member r e l i a b i l i t y and the r e l a t i onsh ip between member safety and the performance f a c to r chosen fo r each design equat ion. The performance f ac to r in the design equations determines the l e ve l of safety assoc ia ted with the des ign. The r e l i a b i l i t y assessment framework and implementation methodology (Foschi [3]) developed fo r the Canadian LSD Code can be app l ied in other j u r i s d i c t i o n s once the design equations are s p e c i f i e d and when the appropr iate load data and mater ia ls proper t ies information are a v a i l a b l e . The Canadian f o r e s t products industry i s a major exporter of s t ruc tu ra l wood products. The continued acceptance of these products on an equi tab le bas is in the United S ta tes , Europe, Japan, A u s t r a l i a and other markets i s a major concern to the fo res t indust ry . The more or less common in te rna t iona l VSD phi losophy was a very s i g n i f i c a n t bene f i t in he lp ing the Canadian industry expand the use of Canadian timber products i n t e r n a t i o n a l l y . The VSD methodology was t r a d i t i o n a l l y based on design proper t ies developed from small c l ea r specimens. The t es t methods, procedures f o r data ana lys i s to convert t es t proper t ies to working s t resses were cons is tent in most countr ies with the exception of the choice of safety f a c t o r s . The general consistency in design property development al lowed shar ing of t es t data . The common design property development concepts were r ead i l y understood with in the techn ica l community. LSD timber codes are being invest igated in severa l of Canada's important timber markets inc lud ing the United States and the European Community. As a major export ing country Canada has a p a r t i c u l a r i n t e res t in working with the research community and codes committees in order to achieve as much uni formity in LSD code and support standards development as poss ib l e . LSD phi losophy provides a r a t i o n a l framework fo r spec i f y ing member safety which al lows a l l s t ruc tu ra l mater ia ls to be compared on an equi table bas i s . Th is presents a s i g n i f i c a n t chal lenge to the timber community to demonstrate that the t r a d i t i o n a l s o l i d sawn v i s u a l l y graded timber s t ruc tu ra l members, systems and s t ructures have adequate safety in r e l a t i o n to the competing non-wood and emerging engineered wood based products. Since the safety assessment system d i r e c t l y recognizes e f f e c t s of mater ia l v a r i a b i l i t y , products with lower v a r i a b i l i t y w i l l have an inherent advantage over higher v a r i a b i l i t y mate r i a l s . I n i t i a l concerns, within the timber community, about the long-term competi t ive pos i t i on of wood-based s t ru c tu r a l mater ia ls being a f f ec ted by the adoption of the LSD code framework s t i l l cont inue. Recent ly , with the expanding development of LSD timber codes, i t i s become evident that lack of cons is tent approaches in development of codes and standards could s i g n i f i c a n t l y impact lumber export ing countr ies such as Canada. New f u l l - s i z e mater ia l t es t methods, data i n te rp re ta t i on procedures, development of new member res i s tance models coupled with attempts to s imp l i f y design codes has created a need fo r the Canadian dimension lumber industry to mount add i t i ona l e f f o r t s to support development of cons is tent i n t e rna t i ona l l y accepted standards. With lack of a t ten t ion to these developments the industry w i l l r i s k s i g n i f i c a n t losses in s t ruc tu ra l e f f i c i e n c y and product value f o r Canadian s t ruc tu ra l wood products. The t r a d i t i o n a l products such as v i s u a l l y graded nominal 2-inch dimension lumber are under p a r t i c u l a r l y intense sc ru t iny in many market areas. The Canadian fo res t products industry has been successfu l in promoting the use of the North American 2x4 plat form const ruct ion system in Japan. The 2x4 wood frame system was o f f i c i a l l y adopted in Japan in 1974 when the M in i s t r y of Construct ion (MOC) publ ished the "2x4 Bu i ld ing Code". At the same time, the M in i s t r y of A g r i c u l t u r e , Forest ry and F i she r i e s (MOAFF) es tab l i shed the Japanese A g r i c u l t u r a l Standard (JAS) f o r approval of Canadian dimension lumber f o r the 2x4 wood frame system. The JAS standard fo r dimension lumber c l o se l y p a r a l l e l s the Nat ional Lumber Grades Author i ty (NLGA) dimension lumber grading ru les used by the Canadian 2-inch dimension lumber producers. Japanese 2x4 wood frame s t ructures are cur rent l y designed using VSD p r i n c i p l e s . For the convenience of a r c h i t e c t s , engineers and bu i lders the Government Housing Loan Corporat ion (GHLC) publ ishes span tables [4] and a design s p e c i f i c a t i o n manual f o r the 2x4 wood frame system. Since large amounts of Canadian dimension lumber are used in these s t ruc tu res , i t i s important to begin to understand how a code transformation from VSD to LSD w i l l impact the use of dimension lumber in the Japanese market. The A r ch i t e c tu r a l I ns t i tu te of Japan ( A U ) has studied the r e l i a b i l i t y of s t ee l s t ruc tu res . The Load and Resistance Factor Design (LRFD) Subcommittee of the AIJ issued the "Standard f o r L imi t States Design of S tee l Structures (Dra f t ) " [5] in February 1990. The d ra f t provides LRFD design equations with assoc ia ted target r e l i a b i l i t y l eve l s f o r strength and s e r v i c e a b i l i t y l i m i t s ta tes . Pub l i ca t ion of the d ra f t LSD S tee l Standard provided the opportunity to inves t igate r e l i a b i l i t y of Japanese timber s t ructures using the LRFD design phi losophy proposed fo r s t ee l s t ruc tu res . The r e l i a b i l i t y of the Japanese 2x4 wood frame const ruct ion system can be studied using r e l i a b i l i t y assessment and implementation methodologies developed in Canada (Foschi [3] ) . While most Japanese wooden s t ructures are b u i l t using the t r a d i t i o n a l post and beam system the mater ia l property information requi red f o r r e l i a b i l i t y s tudies of these s t ructures i s cur rent l y l a ck ing . However, the Japanese 2x4 wood frame system i s designed using Canadian nominal 2-inch dimension lumber f o r which mater ia l property data i s a v a i l ab l e . Therefore th i s study focuses on (1) eva luat ing r e l a t i onsh ips between safety l e ve l s and member performance f ac to rs f o r s ing le members designed according to the LSD code phi losophy and achiev ing the same target safety l eve l s proposed fo r the d ra f t LSD Stee l Standard and (2) assess ing the safety l eve l s assoc ia ted with members designed according to the current WSD code fo r 2x4 wood frame s t ruc tu res . The r e su l t s of the study w i l l provide the f i r s t i nd i ca t i on of the po ten t i a l impact of adopting an LSD code phi losophy f o r timber s t ructures in Japan. R e l i a b i l i t y s tudies undertaken in t h i s study are exc lus i ve l y based on mater ia l property information fo r two grades (Se lect S t ruc tu ra l (SS) and No.2) and three s izes (2x4, 2x8 and 2x10) of Spruce-Pine-Fir (S-P-F) nominal 2-inch dimension lumber. Since th i s species group i s the most widely used in 2x4 wood frame s t ructures in Japan these r e su l t s w i l l y i e l d the pre l iminary information on which to 6 base an ana l ys i s of the po ten t i a l impact of LSD on 2x4 wood frame housing design in Japan. 2. OBJECTIVES The general object ives of t h i s study are to apply RBD p r i n c i p l e s to assess safety l eve l s f o r Japanese 2x4 wood frame const ruct ion systems, designed using c r i t e r i a from the d ra f t LSD Stee l Standard [5 ] , and to assess the r e l i a b i l i t y l e ve l s assoc ia ted with current 2x4 wood frame cons t ruc t ion . S p e c i f i c ob jec t ives of the study are as fo l l ows : 1) To review the Japanese bu i l d ing code and the s t ruc tu ra l c a l cu l a t i on system as i t app l ies to 2x4 wood frame cons t ruc t ion . 2) To develop and present mater ia l property data fo r Canadian S-P-F dimension lumber on the bas is requi red by Japanese bu i l d ing codes. 3) To der ive load models f o r dead, occupancy and snow loads appropr iate f o r ana l ys i s of 2x4 s t ructures in Japan. 4) To study the r e l i a b i l i t y l eve l s fo r bending, tension and compression members using design c r i t e r i a taken from the Japanese d ra f t LSD S tee l Standard. 5) To der ive performance f ac to rs fo r 2x4 wood frame const ruct ion to y i e l d the target safety l e ve l s chosen fo r the d ra f t LSD S tee l Standard. To der ive durat ion of load adjustment f ac to rs fo r 2x4 wood frame const ruct ion using Japanese load models. To assess the r e l i a b i l i t y of current Japanese 2x4 wood frame s t ructures using S-P-F mater ia l property data . 3. CURRENT STRUCTURAL CALCULATION SYSTEM  FOR JAPANESE TIMBER STRUCTURES 9 3.1 BUILDING CODES AND STANDARDS With the exception of the strength data , the en t i r e study was based on the Japanese Bu i ld ing Codes and Standards. The Canadian Code requirements are d i f f e r e n t from those of the Japanese. The fo l low ing d iscuss ion h igh l igh t s the major elements of the Japanese bu i l d i ng code system re l a ted to 2x4 wood frame s t ruc tu res . 3.1.1 BUILDING STANDARD LAV This law mainly provides fundamental requirements fo r bu i ld ings in general [6 ] . The contents of t h i s law are s im i l a r to the Nat ional Bu i ld ing Code of Canada [7] . However, the Nat ional Bu i ld ing Code of Canada i s v a l i d only a f t e r acceptance by l o c a l a u t h o r i t i e s . Vhereas in Japan, genera l l y speaking, the Bu i ld ing Standard Law i s v a l i d throughout Japan at a l l t imes. 3.1.2 BUILDING STANDARD LAV ENFORCEMENT ORDER Bu i ld ing Standard Law Enforcement Orders [8] address more s p e c i f i c d e t a i l s in bu i ld ings such as strength proper t ies and design requirements. These Orders provide more complete gu ide l ines f o r enforcement au tho r i t i e s and des igners . 3.1.3 BUILDING NOTIFICATION Bu i ld ing n o t i f i c a t i o n s are supplements fo r the Bu i ld ing Codes. There are two types of Bu i ld ing N o t i f i c a t i o n s , 1) Bu i ld ing N o t i f i c a t i o n fo r the Pub l i c and 2) Bu i ld ing N o t i f i c a t i o n fo r Spec ia l Admin is t ra t ive Agency. The former Bu i ld ing N o t i f i c a t i o n i s a supplement to the Bu i ld ing Standard Law and Bu i ld ing Standard Law Enforcement Order. There are many Bu i ld ing N o t i f i c a t i o n s f o r the Pub l i c . Each n o t i f i c a t i o n deals with one s p e c i f i c t o p i c . For example, the so-ca l led "2x4 Bu i ld ing Code" [9] i s one of many such n o t i f i c a t i o n s . The l a t t e r Bu i ld ing N o t i f i c a t i o n i s a N o t i f i c a t i o n from the D i rec tor of the M in i s t r y of Construct ion (MOC) to the l o c a l Spec ia l Admin is t ra t ive Agency which has appointed bu i l d i ng o f f i c i a l s take charge of the a f f a i r s concerning bu i l d i ng conf i rmat ion . For example, a f t e r new methods or new mater ia ls are approved by the Min is te r of Const ruc t ion , or i f there i s a Bu i ld ing Code r e v i s i o n , a Bu i ld ing N o t i f i c a t i o n i s i ssued. For the 2x4 wood frame cons t ruc t ion , the Bu i ld ing N o t i f i c a t i o n fo r Spec ia l Admin is t ra t ive Agency [10] requi res e i the r s i m p l i f i e d s t ruc tu ra l member checking using GHLC's span tab les or de ta i l ed member s t ruc tu ra l c a l cu l a t i ons . 3.1.4 STANDARD FOR STRUCTURAL CALCULATION OF TIMBER STRUCTURES Current s t ruc tu ra l design of timber s t ructures i s based on VSD. Th is standard publ ished by AIJ [11] i s s im i l a r to the Canadian Code f o r Engineering Design in Vood (Vorking Stress Design)[12] . Deta i led design equations and strength proper t ies fo r lumber and glue-laminated lumber are spec i f i ed in th i s standard. The Japanese Bu i ld ing Standard Law was rev ised in 1987 to al low const ruct ion of higher and larger wooden s t ruc tu res . The Standard fo r S t ruc tu ra l Ca l cu l a t i on of Timber Structures was rev i sed in 1988. 3.1.5 GHLC SPAN TABLE GHLC i s s im i l a r to the Canada Mortgage and Housing Corporat ion (CMHC). GHLC publ ishes s p e c i f i c a t i o n s and span tab les [4] f o r 2x4 wood frame cons t ruc t ion , based on VSD c r i t e r i a [11]. Design proper t ies fo r lumber fo r 2x4 wood frame cons t ruc t ion , load data and design c r i t e r i a requi red fo r c a l cu l a t i on of member spans inc lude : Al lowable Unit Stresses fo r 2x4 Lumber and S t ruc tu ra l Glue-Laminated Lumber; De f l ec t ion L im i t s ; Uni t Shear Resistance fo r Common N a i l ; Nominal Dead Load; Nominal Occupancy Load f o r Res ident i a l Bu i l d i ng ; and Nominal Snow Load which are given in the GHLC's span t ab les . Span tab les are based on simply supported beam ana l y s i s . No composite ac t ion between the framing members and sheathing i s considered except fo r glued f l o o r s . 3.2 PRINCIPLES OF STRUCTURAL CALCULATION FOR TIMBER STRUCTURES 3.2.1 DESIGN REQUIREMENTS S t ruc tu ra l design requirements s p e c i f i e d in Japanese Bu i ld ing Codes vary depending on the type, s i ze and height of the s t ruc tu re . General ly speaking, timber s t ructures are c l a s s i f i e d into one of the fo l low ing f i v e ca tegor ies : General T r a d i t i o n a l Wooden Structures ( mainly housing ) 2x4 Wood Frame Structures ( mainly housing ) Log Construct ion Heavy Timber St ructures Spec ia l S t ruc tures . Japanese Bu i ld ing Codes have requirements fo r the design of i nd i v idua l members and fo r the ana l ys i s and design of the complete s t ruc tu re . Depending upon the type, s i ze and height of the s t ruc tu re , wooden s t ructures sha l l comply with some or a l l of the requirements of the items which are shown in Table 1. General ly speaking, f o r the common r e s i d e n t i a l 2x4 wood frame s t ructures of l ess than three s t o r i e s , i nd i v i dua l members are designed by using GHLC's span table or a l t e r n a t i v e l y by s t ruc tu ra l c a l cu l a t i on according to the Standard f o r Timber Design. The en t i r e s t ructure must s a t i s f y the e f f e c t i v e wal l length requirement explained in 3 .2 .5 . 3.2.2 DESIGN LOADS Loads and external forces are s p e c i f i e d in the Bu i ld ing Standard Law Enforcement Order. The load cases to be considered in design are shown in Table 2. Unl ike the VSD methods of Canada and the US which recognized d i f f e r e n t durat ion of load f ac to rs fo r the var ious load cases, the Japanese system has only two load durat ion ca tegor ies : sustained (normal durat ion) loading and temporary (short-term durat ion) load ing . Vhen temporary loads are cons idered, a l lowable un i t s t resses of lumber and s t ruc tu ra l glue-laminated timber become double those of sustained loads. 3.2.3 ALLOVABLE UNIT STRESS Allowable un i t s t resses fo r lumber and s t ruc tu ra l glue-laminated timber are s p e c i f i e d in the Bu i ld ing Standard Law Enforcement Order, Bu i ld ing N o t i f i c a t i o n s and/or A I J ' s "Standard fo r S t ruc tu ra l Ca l cu l a t i on of Timber S t ruc tu res " . Since th i s study p r imar i l y focuses on 2x4 wood frame s t ruc tu res , the al lowable un i t s t resses of lumber fo r 2x4 wood frame const ruct ion spec i f i ed in Bu i ld ing N o t i f i c a t i o n f o r Spec ia l Admin is t ra t ive Agency [13] are l i s t e d in Appendix 1. 3.2.4 VORKING STRESS DESIGN CRITERIA General ly speaking, s t ruc tu ra l ca l cu l a t i ons to determine the i nd i v idua l s i ze of s t ruc tu ra l wooden members s h a l l be based on the fo l low ing equat ions: 3.2.4.1 BENDING 14 where *b = °"6 M fb _ M < crfb ( 3. 1 ) : bending stress; : bending moment; : effect ive section modulus; : allowable bending stress; : s ize factor for glued-laminated timber determined by the fol lowing formula but not less than 1.0. The factor i s not applied for s o l i d lumber, therefore = 1.0 for s o l i d lumber, ( 3. 2 ) 3.2.4.2 SHEAR where d i s the depth of the member in cm. where r = a • Q I K < fs ( 3. 3 ) shear stress; allowable shear s tress; shape factor (rectangular cross sect ion, a shear force; effect ive area of cross sect ion. = 1.5); 3.2.4.3 TENSION 1) Tension P a r a l l e l to the Grain e where ~A~ - ft ( 3. 4 ) at : t e n s i l e s t r e s s ; ft : a l lowable t e n s i l e s t r e s s ; T : a x i a l tension force p a r a l l e l to g ra in ; A. : e f f e c t i v e area of cross sec t i on ; 2) Tension Perpendicular to the Grain In areas where a tension perpendicular to the gra in i s generated, an appropr iate reinforcement should be given in order to avoid an excessive s t ress in t h i s d i r e c t i o n . The al lowable t e n s i l e s t ress perpendicular to the gra in i s assumed to be 1/3 of the al lowable shear s t r e s s . 3 .2 .4 .4 COMPRESSION 1) Compression P a r a l l e l to the Grain °c = - f - < fk ( 3. 5 ) where ac : compression s t r e s s ; N : a x i a l compression force p a r a l l e l to the g r a i n ; A : area of cross sec t i on ; / f c : a l lowable compression s t ress obtained as fo l lows : i f A <30 : fk = fe ( 3. 6 ) i f 30 < A < 100 : fk = fc ( 1.3 - 0.01 A ) ( 3. 7 ) i f 100 < A : fk = 0.3 fc / ( A/100 ) 2 ( 3. 8 ) where fc : a l lowable short-member compression s t r e s s ; A : slenderness r a t i o of the compression member A = ^ ; where Le : e f f e c t i v e length ; ie : rad ius of gyra t ion of the column with respect to the ax is of buckl ing ie = ^—^~ where I : moment of i n e r t i a . 2) Compression Perpendicular to Grain „ - N c ~ ~A where < fc± or f ' c ± ( 3. 9 ) fc j_ : a l lowable compression s t ress perpendicular to the g r a i n ; f'c j_ : a l lowable bear ing s t r e s s ; A : support (bearing) a rea ; N : compression force perpendicular to g r a i n . 3.2.5 LATERAL RESISTANCE FOR RESIDENTIAL WOODEN STRUCTURES The " E f f e c t i v e Wall Length Methods" are app l ied fo r the s t ruc tu ra l c a l cu l a t i on of l a t e r a l loads fo r common r e s i d e n t i a l wooden s t ruc tu res . This method has two components: "Required Rat io of E f f e c t i v e V a i l length p" and "Resistance Factor of Bearing wal l q". The parameter p has two va lues , i . e . pe f o r seismic and pw f o r wind force ana l y s i s . Both p and q f o r the 2x4 wood frame st ructures are spec i f i ed in the Bu i ld ing N o t i f i c a t i o n [9] . The fo l low ing requirement should be s a t i s f i e d fo r l a t e r a l res i s tance fo r common r e s i d e n t i a l wooden s t ruc tu res : pA = £ ^ ( 3. 10 ) where pA : l a rger of e i the r peAj or pmAp ; pe : requi red r a t i o of e f f e c t i v e wal l length fo r seismic f o r c e ; Aj : f l o o r a rea ; pw : requi red r a t i o of e f f e c t i v e wal l length fo r wind fo r ce ; Ap : plumb measure area ; : r e a l length of the bear ing wall with res i s tance f a c to r 9t-. Appendix 2 shows measurement of the plumb measure s izes ( v e r t i c a l l y projected area) fo r the span or r idge d i r e c t i o n of a bear ing wa l l . The required r a t i o s of e f f e c t i v e wal l length pe and pw, and res i s tance f ac to rs fo r bear ing wal l q are given in the Bu i ld ing Standard Law Enforcement Order fo r t r a d i t i o n a l post and beam st ructures and Bu i ld ing N o t i f i c a t i o n fo r 2x4 wood frame s t ruc tu res . The parameters pe and pw were determined from the ana l ys i s of common r e s i d e n t i a l bu i ld ings subjected to seismic and wind f o r ce . Resistance f ac to rs fo r bear ing wal ls q, based on rack ing tes ts f o r bear ing wal ls with d i f f e r e n t sheathing mate r i a l s , are given in the Enforcement Order and Bu i ld ing N o t i f i c a t i o n . General ly speaking, the load at shear s t r a i n versus res i s tance of 1/120 radian f o r t r a d i t i o n a l post and beam st ruc tures and 1/300 radian fo r 2x4 wood frame s t ruc tures correspond to t he i r a l lowable s t rengths . I t i s important to note that although there are requirements to check s t ruc tu ra l safety against l a t e r a l loads such as wind and earthquake, most s t ruc tu ra l member s izes are determined by the g rav i t y loads fo r r e s i d e n t i a l wooden s t ructures inc lud ing 2x4 wood frame s t ruc tu res . Therefore only g rav i t y loads were considered in the ana lys i s of s t ruc tu ra l member in th i s study. 4. JAPANESE LIMIT STATES DESIGN There are two organizat ions in Japan that are s im i l a r to the Canadian C i v i l Engineering Soc ie ty . The A r ch i t e c tu ra l I ns t i tu te of Japan ( A U ) , and the Japan Society of C i v i l Engineering (JSCE). The JSCE deals with major const ruct ion pro jec ts such dams, b r idges , and highways. The AIJ deals with b u i l d i n g s , from l o ca l housing to large skyscrapers. Cur ren t l y , the AIJ has been cons ider ing adoption of the LSD approach fo r s t ee l and re in fo rced concrete s t ructures in Japan. An LSD standard fo r r e in fo rced concrete s t ructures has a lready been publ ished by the JSCE in 1986 however i t does not apply to the regular bu i l d i ngs . 4.1 NEW JAPANESE STANDARD FOR LIMIT STATE DESIGN OF STEEL STRUCTURE (DRAFT) The LRFD Subcommittee of AIJ publ ished the "Standard f o r L imi t State Design of S tee l Structures (Dra f t ) " [5] in February 1990. P r i o r to the d ra f t standard, the S tee l Structures Subcommittee of AIJ issued the "Load and Resistance Factor Design fo r S tee l Structures (Proposa l ) " [14] in March 1986 to examine a c c e p t a b i l i t y of RBD in s t ee l s t ruc tu res . Although the d ra f t LSD S tee l Standard has not o f f i c i a l l y been accepted, the content would be the gu ide l ine fo r the Japanese RBD c r i t e r i a . The fo l low ing requirements adopted from the d ra f t LSD S tee l Standard are used and re fe r red to in th i s study. 4.2 PROPOSED LOAD COMBINATION AND LOAD FACTORS The LSD equation genera l l y cons i s t s of the load e f f e c t s mu l t i p l i ed by load f ac to rs and the res i s tance to load expressed as a product of some chosen spec i f i ed strength (convent iona l l y , the lower 5th pe rcen t i l e fo r lumber) and a performance f ac to r <j>. Typ i ca l design c r i t e r i a i s expressed as : Factored Resistance > E f f e c t of fac tored load ( 4. 1 ) In the general case, the t o t a l load e f f e c t i s a l i nea r combination of i nd i v idua l load e f f e c t s which are r e l a t ed to the fac tored res i s tance according t o , *K > E T A - ( 4. 2 ) t = l where </> : performance f a c t o r ; Rn : s p e c i f i e d s t rength ; : i nd i v i dua l load f a c t o r ; Qt- : i nd i v i dua l load. The proposed e f f e c t of fac tored loads and load combinations f o r strength l i m i t s tates fo r s tee l s t ructures with the assoc ia ted target r e l i a b i l i t y index at performance f a c to r <j> - 0.9 are given as : 1.3Dn /? = 2.5 ( 4. 3 ) l . l D n + 1.6In /? = 2.5 ( 4. 4 ) l.lDn + 1.6Sn + 0.6In /? = 2.0 ( 4. 5 ) l.lDn + I.QEn + O.ALn l . l D n + 1.6Wn + 0.6In 0.9Dn - 1.6Wn 0 =(1.5) ( 4. 6 ) 0 = 2.0 ( 4. 7 ) 0 = 2.0 ( 4. 8 ) Fol lowing load combinations s h a l l be a l so considered in heavy snow areas, 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 ) E f f e c t of fac tored loads and load combination f o r s e r v i c e a b i l i t y l i m i t s tates with the assoc ia ted target r e l i a b i l i t y index at performance f a c to r <j> = 0.9 sha l l be taken as : l .ODn + l .O in ft = 1.0 ( 4. 11 ) l .ODn + 0.95n + 0.6In j3 = 1.0 ( 4. 12 ) l .ODn + 0.4£n + 0.4In 0 = 1.0 ( 4. 13 ) l.ODn + 0.9Wn + 0.6£n 0 =(-0.35) ( 4. 14 ) l .ODn - 0.9W^n 0 = 1.0 ( 4. 15 ) Fol lowing loads combinations s h a l l a l so be considered in heavy snow areas , l .ODn + 0.9Wn + 0.55n + 0 .4 in 0 = 1.0 ( 4. 16 ) l .ODn + 0.4£n + 0.45n + 0.4In 0 =(0.4) ( 4. 17 ) where Dn Ln Sn Wn En nominal dead load; nominal l i v e (occupancy) load ; nominal snow load; nominal wind load ; nominal earthquake load. Basic s t a t i s t i c a l data (means and c o e f f i c i e n t s of v a r i a t i on of lognormal d i s t r i b u t i o n ) assumed fo r the normalized load va r i ab les and the normalized mater ia l res i s tance in the d ra f t LSD Stee l Standard are shown in Table 3 . The j3 - <j> r e l a t i onsh ips of four combinations in s t ee l design were der ived using the bas ic s t a t i s t i c a l data obtained from Table 3 f o r two r a t i o s of nominal dead to nominal l i v e load ( 7 = 2.0 and 0.25) and two c o e f f i c i e n t s of v a r i a t i on of mater ia l strength (cov = 0.15 and 0.2) as shown in F igure 1. 5. JAPANESE FULL SIZE TEST PROGRAM FOR STRENGTH OF LUMBER Japanese strength proper t ies used fo r s t ruc tu ra l design of wood are der ived from small c l ea r wood specimens. Only a few f u l l s i ze tes t r e su l t s are a va i l ab l e . Among them, the fo l low ing two f u l l s i ze t es t reports review r e su l t s of the Japanese f u l l s i ze lumber t es t programs: 1) Forest ry Agency, Study on the Stress Grading in S t ruc tu ra l Lumber, Report No.25, 1985. [15] 2) Strength of Timber and Wood Based S t ruc tu ra l Group, Japan Wood Research Soc ie ty , S t ruc tu ra l Lumber - C o l l e c t i o n and Ana lys is of Strength Data, 1988. [16] The f i r s t report [15] summarizes r e su l t s of bending tes ts of square sect ions proposed by the Forest Agency and Forest ry and the Forest Products Research I ns t i tu te (FFPRI) which were ca r r i ed out by the nine p re fec tu ra l Research Ins t i tu tes throughout Japan. A l l tes ts were performed using the same t e s t i ng procedure. The s i ze of specimen was 10.5 x 10.5 x 300 cm. The t h i r d point load was app l ied with 270 cm tes t span. De f l ec t ion at mid-span was measured when a s p e c i f i e d load was app l i ed at the lumber yard in green moisture cond i t i on . A f te r a i r d r y ing , a bending tes t was conducted on the t e s t i ng machine to obtain bending strength (MDR) and modulus of e l a s t i c i t y (MOE). The second report [16] , the Strength of Timber and Wood Based S t ruc tu ra l Group of the Japan Wood Research Soc iety compiled and analyzed the f u l l s i ze lumber t es t data which had been ca r r i ed out by the 21 Research organ iza t ions . Since a f u l l s i ze t es t procedure i s not s tandard ized, these research organizat ions d id the tes ts d i f f e r e n t l y . The co l l e c t ed data was adjusted as descr ibed in the fo l low ing sec t ions . Although there i s no standard fo r f u l l s i ze tes ts f o r lumber, procedures descr ibed in the fo l low ing sect ions are considered to be reasonable in t h i s study. 5.1 BENDING A one-third point loading system s h a l l be used. The maximum strength a f f e c t i n g defect sha l l be randomly placed on the tension s ide between the tes t span. 5.2 MOE MOE values s h a l l be adjusted with a span depth r a t i o of 21 to 1 under an assumed uniform load as descr ibed in ASTM D2915 [17]. 5.3 MOISTURE CONTENT MOE and MOR values s h a l l be adjusted at target moisture content (MC) of 15%, as descr ibed in ASTM D 2915. The adjustment should not be app l ied where the d i f f e rence of moisture content i s la rger than f i v e percentage points from the chosen va lue . The ASTM D 2915 moisture adjustments are made: P 2 = P1 ( a - p-M2 ) / ( a - p-Mx ) ( 5. 1 ) where P1 : o r i g i n a l strength property at moisture content Mx\ P 2 : target strength property at moisture content Af 2 ; a and (3 are c o e f f i c i e n t s given in ASTM D 2915. 5.4 MATERIAL STRENGTH Bu i ld ing Standard Law Enforcement Order spec i f i e s mater ia l strengths of lumber and glued-laminated lumber. None of the pub l i ca t ions mention that mater ia l strength values are based on lower 5th pe r cen t i l e values of the mater ia l property d i s t r i b u t i o n . However AI J 's Standard fo r Timber Design expla ins that the l im i t ed Japanese in-grade tes t r e su l t s showed the mater ia l strengths are usua l l y l ess than or approximately equivalent to the 5th pe r cen t i l e of a va i l ab l e data se t s . General ly speaking, a l lowable un i t s t resses fo r timber are der ived by simply d i v i d i n g mater ia l strength by 3.0 fo r sustained load and 1.5 fo r temporary load. 5.5 DURATION OF LOAD ADJUSTMENT The tes t machine sha l l be adjusted so that f a i l u r e occurs several minutes a f t e r loading s t a r t s . Since al lowable un i t s t resses are co r re l a ted with e i ther sustained load or temporary load , data need not be adjusted using the safety and durat ion of load f ac to rs provided in ASTM D2555 [18]. 5.6 TENSION There i s no s p e c i f i c f u l l s i ze tension t e s t i ng procedure ava i l ab l e in Japan. 5.7 COMPRESSION There i s no s p e c i f i c f u l l s i ze compression t e s t i ng procedure a va i l ab l e in Japan. 6. CANADIAN FULL SIZE TEST PROGRAMS 27 T r a d i t i o n a l l y , strength proper t ies of Canadian v i s u a l l y graded lumber have a l so been determined by t e s t i ng small c l ea r wood specimens. In the la te 7 0 ' s , large sca le in-grade tes ts were conducted to f i n d the mechanical proper t ies of f u l l - s i z e , on-grade Canadian v i s u a l l y stress-graded lumber sampled from product ion. The tes ts conducted were mostly in bending with l im i t ed tension p a r a l l e l to the gra in eva luat ions . More than 55,000 f u l l s i ze samples were tes ted . At t h i s t ime, the proof loading concept was introduced to estimate lower 5th-percent i le values fo r a range of s ize/grade and species combinations without breaking the en t i r e t es t samples. The bending and tension r e su l t s were used to der ive new design p rope r t i e s , which were included in the CAN3-086-M84 vers ion [1 and 12]. Although the aforementioned in-grade tes ts were adequate f o r cha rac te r i z ing the t r a d i t i o n a l strength proper t ies of lumber, i . e . , the average bending modulus of e l a s t i c i t y , and the lower 5th-percen t i l e exc lus ion values of s t rength , a more de t a i l ed second phase of a major lumber research program was undertaken from 1983 to 1985. The major reason fo r fu r ther t e s t i ng was to provide information required fo r the p r o b a b i l i s t i c LSD format. The major species groups of Douglas F i r -La r ch , Hem-Fir and S-P-F with three s i zes 2x4, 2x8 and 2x10 and nine minor species with three s i zes of 2x4, 2x6 and 2x8 were tes ted . The in-grade tes ts were conducted to e s t ab l i sh bending s t rength , bending modulus of e l a s t i c i t y , tension p a r a l l e l to the gra in and compression p a r a l l e l to the gra in strength according to ASTM D 4761 [19]. The th i rd-po in t load was app l ied on the bending specimen with span to depth r a t i o of 17: 1. The maximum strength-reducing defect was randomly located with in the span fo r the bending t e s t . The gauge lengths of 2462mm fo r 2x4, 3683mm fo r 2x8 and 3683mm fo r 2x10 were se lec ted fo r the tension t e s t . The gauge lengths of 2438mm fo r 2x4, 3658mm fo r 2x8 and 4267mm fo r 2x10 were se lec ted fo r the compression t e s t . Compression specimens were l a t e r a l l y res t ra ined so that the t es t r e su l t s provide short column strength p roper t i es . The r e su l t s of these tes ts were included in CAN/CSA-086.1-M89 vers ion [2 and 20] . 7. ADJUSTMENTS OF CANADIAN IN-GRADE DATA TO JAPANESE BASIS In order to use Canadian tes t r e su l t s in t h i s study, appropr iate adjustments were necessary to compensate fo r the d i f f e rences between Canadian and Japanese t e s t i ng methods and data ana lyz ing procedures. 7.1 MQR The Canadian bending strength tes t data were obtained using the span to depth r a t i o of 17 to 1 and adjusted to 15% moisture content. The parameters f o r Normal, Lognormal, 2 Parameter V e i b u l l and 3 Parameter V e i b u l l d i s t r i b u t i o n s were developed f o r the strength data. Each data set was then truncated at the 15th pe r c en t i l e , and these lower t a i l data were f i t t e d with the same four d i s t r i b u t i o n types. Parameters shown in Appendix 3 and 4 were obtained using 100% data and using lower 15% data. 7.2 MOE Test MOE values were measured using the displacement of the loading cross-head and a span to depth r a t i o of 17 : 1. These data were subsequently adjusted to y i e l d MOE values which would be der ived using a f u l l span yoke to measure midspan de f l e c t i ons in accordance with ASTM D 2915 procedures. For Japanese code requirements, these data were fur ther adjusted to a span to depth r a t i o of 21 : 1. The obtained data were already adjusted to the target moisture content of 15 percent and MOE stroke to MOE yoke with span to depth r a t i o of 17: 1. The fo l low ing formulae [21] were developed to adjust to span to depth r a t i o of 17 : 1 to that of 21 : 1 f o r th i s study. where -J— = —fr1 0.00591 H x 1 0 - 6 ( 7. 1 ) A 1 7 &TLP -J— = - p ^ 0.00298 H x 1 0 ~ 6 ( 7. 2 ) •^21 &TLP E17 : M0Eyoke at span to depth r a t i o of 17 : 1; ETLP : m E l o a d i n g - head a t s P a n t o depth r a t i o of 17 : 1; E2i : M0E y o f c e at span to depth r a t i o of 21 : 1; H : nominal depth of the specimen. The 2 Parameter V e i b u l l d i s t r i b u t i o n parameters of the adjusted MOE d i s t r i b u t i o n are shown in Appendix 5. 7.3 TENSION Since there i s no Japanese tes t standards f o r f u l l s i ze tension tes ts of lumber, no adjustment was app l ied fo r the CVC tension data . The data f o r tension strength was taken from Re l i ab i l i t y-Based Design of Vood Structures S t ruc tu ra l Research Ser ies [3 ] . Parameters f o r 2P V e i b u l l with lower 15% f i t s are shown in Appendix 6. 7.4 COMPRESSION No adjustments were app l ied to the compression in-grade tes t r e su l t s f o r the same reason as the tens ion . The data f o r compression strength was a l so taken from Re l i ab i l i t y-Based Design of Wood Structures S t ruc tu ra l Research Se r i es . Parameters fo r 2P Ve i bu l l d i s t r i b u t i o n with lower 25% f i t s are shown in Appendix 7. 8.DEVELOPMENT OF LOAD MODEL AND LOAD PARAMETERS FOR JAPANESE BUILDINGS 8.1 DEAD LOAD Because the same values of the nominal load were used in the LSD and VSD fo r s t e e l , they too were u t i l i z e d in t h i s study f o r the 2x4. wood frame cons t ruc t ion . The design dead load i s based on the average weight of mate r i a l s . The de ta i l ed information of dead load i s a va i l ab l e in the A I J ' s "Recommendations f o r Bu i ld ing Design, Load" [22]. Since th i s study was intended to evaluate the r e l i a b i l i t y l eve l s fo r Japanese 2x4 wood frame s t ruc tu res , the design load values s p e c i f i e d in the GHLC's span table used fo r t h i s study are l i s t e d below. fo r F loor J o i s t s : Tatami Mat Gypsum Board Plywood Sheathing(15mm) 18 kgf/m 2 (177 N/m2) 10 kgf/m 2 (98 N/m2) 15 kgf/m 2 (147 N/m2) f o r Ra f te rs : Plywood Sheathing(9mm) 6 kgf/m 2 (59 N/m2) Plywood Sheathing(12mm) L ight Roofing Mater ia l Clay t i l e 8 kgf/m 2 (78 N/m2) 20 kgf/m 2 (196 N/m2) 60 kgf/m 2 (588 N/m2) fo r Lumber: 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 t h i s study, the normalized dead load random va r i ab le d = D/Dn> where D i s dead load (random va r i ab le ) and Dn i s the design dead load , was assumed Normally d i s t r i bu t ed with a mean of 1.0 and standard dev ia t ion of 0 .1 . 8.2 OCCUPANCY LOAD Occupancy loads are assumed to be the superpos i t ion of two l i v e load processes: sustained and extraordinary as shown in F igure 2. The magnitude of both the sustained and extraordinary components were assumed d i s t r i bu t ed according to a Gamma d i s t r i b u t i o n . The per iod between changes are assumed as Poisson processes. The fo l low ing load s t a t i s t i c s , taken from the d ra f t LSD S tee l Standard, were used to model occupancy loads fo r t h i s study. Sustained Load: mean 65 kgf/m 2 (637.4 N/m2) cov 0.40 mean return 8 years Extraordinary Load: mean cov mean return durat ion of loading 45 kgf/m 2 (441.3 N/m2) 0.55 1 year impulse For the sustained load , the load magnitude i s modeled using the Gamma d i s t r i b u t i o n : where: mean = - |- ; ( 8. 2 ) standard dev ia t ion = A 2 ( 8. 3 ) The parameters of k and A can be ca l cu la ted as : mean2 _ 65 2 (standard dev i a t i on ) 2 (65x0.42) 9 - > = 6.25 ( 8. 4 ) A = m e f n , -2 = = 9 . 615X10- 2 (standard deviat ion)^ (65x0.42)^ ( 8. 5 ) and the durat ion of the load i s modeled by the Exponential d i s t r i b u t i o n as : f(ta) = Xe~xt ( 8. 6 ) where U = 4 " 5 ( 8. 7 ) X = -T- = -7mm-= 1 . 427X10 " 5 ( 8. 8 ) 8 ( 8 years = 70080 hours ). S i m i l a r l y , the magnitude of extraordinary l i v e load can be modeled by the Gamma d i s t r i b u t i o n in Eq.8.1 and the parameters k and 7 are given by: k = ^ = 3.306 ( 8. 9 ) ( 45x0 .55 ) 2 v ; A = ^ -5 = 7.346x10"2 ( 8. 10 ) (45x0.55)2 V J and Exponentia l d i s t r i b u t i o n in Eq.8.6 f o r i t s time between events as : A = W = 1-142X10- 4 ( 8. 11 ) Maximum occupancy loads were determined f o r a 50 year load s imula t ion . F ive thousand r e a l i z a t i o n s of maximum sustained load plus extraordinary load fo r the 50-year per iod were generated by the Monte Car lo s imula t ion . The upper 10% of the maximum load data were f i t t e d (Figure 3) us ing Extreme Type I (Gumbel) d i s t r i b u t i o n model: 0ao = B • ( - 1 ' p ) } ( 8. 12 ) The parameter B f o r the 50-year model was adjusted fo r 8-year return per iods according to : Q s = B s + ( ( - l n P ) } ( 8. 13 ) where B8 = (B - -IlL_5P_ + ^ 8 _ ) ( 8. 14 ) The parameters fo r 50-year return were used in r e l i a b i l i t y ana lys i s fo r strength l i m i t states and the parameters fo r 8-year return were used fo r r e l i a b i l i t y ana l ys i s f o r s e r v i c e a b i l i t y l i m i t s ta tes . These parameters were used to der ive the normalized random va r i ab le q = Q/Qn, where Q i s e i the r Q50 or Qs and Qn i s the design l i v e load of 180 kgf/m 2 (1.765 KN/m2) f o r r e s i d e n t i a l bu i l d ing given in Bu i ld ing Standard Law Enforcement Order. Therefore , q = Q/Qn = Q/180 can be expressed as : q = B* + ( - l n P) ) ( 8 . 1 5 ) where B* : B I 180 A* : A x 180 where B i s given by Eq.8.12 or Eq.8.13 fo r the 50 year and 8 year re turn load models r e spec t i v e l y . These parameters were ca l cu la ted fo r 50 year and 8 year return loads which are shown in Table 4. 8.3 SNOW LOAD In Japan, geographical locat ions are designated e i the r l i g h t (general) snow areas or heavy snow areas. The l i g h t snow area i s def ined as an area with 50-year return snow height l ess than 100 cm. Locat ions with 50-year return snow heights greater than or equal to 100 cm are def ined as heavy snow area. The annual maximum snow height and annual average snow durat ion in Sapporo, N i i ga t a , Tokyo and Osaka were obtained from the l o ca l meteorologica l observator ies . Sapporo and N i iga ta belong to the heavy snow areas, whereas Tokyo and Osaka belong to the general snow areas. F igure 4 and 5 are samples of the snow data showing a snow height and an average annual snow durat ion with the same sca le in Sapporo and Tokyo f o r s i x successive years . Design snow load Sn, on a roof i s expressed in the AI J ' s "Recommendations fo r Bu i ld ing Design, Snow Load" [23] and d ra f t LSD S tee l Standard as the product of a se r i es of f a c t o r s : Sn = p-Za.Ea.Cr ( 8. 16 ) where p : un i t weight of snow 2.1 kg/m2/cm (20.6 N/m2/cm) fo r heavy snow area 2.0 kg/m2/cm (19.6 N/m2/cm) f o r l i g h t snow area Za : 50-year return height of snow accumulation (cm); Ea : environment f a c t o r ; Cr : roof shape f a c t o r . The snow load d i s t r i b u t i o n considered corresponds to those fo r the maximum in a per iod of 50 years . The annual maximum ground snow height i s represented by an Extreme Type I (Gumbel) d i s t r i b u t i o n : G = B - (-In (-In P ) ) A ( 8. 17 ) where A and B are model parameters. A corresponding d i s t r i b u t i o n of maximum snow height in N years can be expressed as : G = B - 1° N - In (-In P ) ( g _ l g } where p i s a p r o b a b i l i t y of non-exceedance and A and B are parameters of the Type I d i s t r i b u t i o n . The 50-year return snow height <750, corresponding to a p r o b a b i l i t y of non-exceedance of 49/50, can be obtained using Eq. 8.17. Also using Eq.8.17 and Eq .8 .18, the normalized g = G/G50 can be expressed as : 9 = B * + ( < - l n P ) ) ( 8. 19 ) where AB + 3.9019 R * - AB + ln N r Q on \ A* = AB + 3.9019 ( 8. 21 ) These parameters were ca l cu la ted f o r 50 year and 8 year return load . The parameters, the average annual snow durat ion and the design snow loads are shown in Table 5. The l o c a t i on , annual snow durat ion and design snow load f o r t h i s study are shown in F igure 6. 50-year return value was assumed in r e l i a b i l i t y ana lys i s fo r strength l i m i t s tates and 8 year-return value was assumed in r e l i a b i l i t y ana l ys i s fo r the s e r v i c e a b i l i t y l i m i t s t a tes , the same as occupancy load . The v a r i a b i l i t y of the environment, roof shape and snow densi ty f ac to rs in Eq.8.16 should be considered in the c a l cu l a t i on of the snow load from annual maximum snow he ight . However, t h i s study assumed that those f ac to rs were constant because of lack of a va i l ab l e informat ion. Therefore the normalized snow load s = S/Sn i s def ined as : s = S = G S n G5Q snow load; a design snow load; maximum snow he ight ; 50-year re turn snow height . ( 8. 22 ) where S sn G 9. PERFORMANCE FACTORS FOR JAPANESE 2x4 WOOD FRAME STRUCTURAL MEMBERS In genera l , the r e l i a b i l i t y l e ve l /? and corresponding d i f f e r e n t performance f ac to rs <f>, can be generated using the RELAN program [24] given the appropr iate performance funct ion G and required s t a t i s t i c a l data . The performance funct ions G are formulated using a s p e c i f i c design equat ion. Therefore the performance f ac to r <f> at the given target r e l i a b i l i t y /?r i s obtained from the r e su l t s of a j3 - <j> ana l y s i s . In t h i s chapter, design equations and target r e l i a b i l i t y l eve l s /?y from the d ra f t LSD Stee l Standard, strength data from CVC's research pro jec t and the aforementioned s t a t i s t i c a l data fo r loads are used to der ive the performance fac to rs at the given target r e l i a b i l i t y 0rp f o r t y p i c a l S-P-F members used in the 2x4 wood frame s t ruc tu res . Since the g rav i t y load cases i . e , dead, occupancy and snow load , govern in many p r a c t i c a l design s i tua t i ons and are considered to be of fundamental importance in the c a l i b r a t i o n work, the dead load and occupancy load case fo r bending, and the dead load and snow load cases fo r bending, tension and compression were considered in th i s study. 9.1 STRENGTH LIMIT STATES E f f e c t s of fac tored loads and the s p e c i f i c load combination fo r eva luat ion of the /? - <j> r e l a t i onsh ip fo r strength l i m i t states are obtained from the d ra f t LSD S tee l Standard. Analyses are performed fo r f l o o r and f l a t roof member des igns. For f l o o r j o i s t s , e f f e c t s of dead and occupancy load w i l l be compared with the fac tored res i s tance using the design equation 1.1 Dn + 1.6 L n < cf, i? 0 j 05 ( 9. 1 ) For r a f t e r s , e f f e c t s of dead load and snow load w i l l be evaluated us ing : 1.1 Dn + 1.6 Sn < <p R0t05 ( 9. 2 ) vfhere K <p •^0.05 e f f e c t of design dead load; e f f e c t of design l i v e load; e f f e c t of design snow load; performance f a c t o r ; s p e c i f i e d s t rength . The r e l a t i o n of /? - <f> can be ca l cu la ted using the performance func t ion G. For strength l i m i t s t a tes , the performance func t ion G f o r j o i s t s and r a f t e r s can be formulated as : G = R - ( D + L) ( 9 . 3 ) fo r f l o o r j o i s t and G = R - ( D + S) ( 9 . 4 ) f o r r a f t e r s in f l a t roo f , where R : strength (a random v a r i a b l e ) ; D : e f f e c t of the dead load (a random v a r i a b l e ) ; L : e f f e c t of the occupancy load (a random v a r i a b l e ) ; 5 : e f f e c t of the snow load (a random v a r i a b l e ) . By subs t i t u t i on of the appropr iate design equat ion, the performance funct ions can be expressed as : G = R - + ° f 6 (dy + I ) ( 9. 5 ) fo r j o i s t and G = R ~ l.l7R+°f.6 + s ) ( 9- 6 ) f o r r a f t e r . where 7 : DJLn f o r j o i s t s , Dn/Sn fo r r a f t e r s ; D/Dn; L/Ln; s/sn. d I 9.1.1 EFFECT OF LOAD RATIO 7 The de te rmin i s t i c value 7 = Dn/Ln or 7 = Dn/Sn was required as a load re l a ted input f o r the computation of /? - <j> r e l a t i ons using Eq.9.5 or Eq .9 .6 . A r a t i o 7 = 0.25 was chosen fo r i n i t i a l safety studies in th i s p ro jec t . In order to va l ida te the cho ice , ac tua l ja values were ca l cu la ted using GHLC's span table requirements. The r a t i o 7 = 0.25 was appropr iate in the heavy snow area and fo r occupancy load . However in the l i g h t snow area 7 was higher than 0.25 as shown in Table 6 and Table 6a. The e f f e c t of the choice of 7 on safety was studied f o r <f> -0.8, 0.9 and 1.0 in Sapporo and the same ^-values in Tokyo fo r 2x8 No.2 grade. Results in F igure 7 show that increas ing the r a t i o j = Dn/Sn tends to reduce safety l e v e l s , i f strength d i s t r i b u t i o n was assumed as a V e i b u l l d i s t r i b u t i o n ; therefore subsequent ana lys i s of the ac tua l values of 7 f o r heavy roo f ing j a i s a l so s tud ied . 9.1.2 RESISTANCE DISTRIBUTION MODEL The choice of the res i s tance d i s t r i b u t i o n model a f f e c t s the (5 -cp r e l a t i o n s h i p . F igure 8 shows /? - cp r e l a t i ons der ived using four d i f f e r e n t res i s tance d i s t r i b u t i o n models f i t t e d to the complete data se t s . F igure 8 shows the inf luence of the res i s tance d i s t r i b u t i o n model on the f3 - cp r e l a t i ons when the d i s t r i b u t i o n models are f i t to the complete data se t s . Foschi et a l . showed that the in f luence of the d i s t r i b u t i o n model was s i g n i f i c a n t l y reduced when the models were f i t t e d to lower t a i l res i s tance data [3] . F igure 9 compares the 2 Parameter V e i b u l l d i s t r i b u t i o n f i t s to the lower 15% of the data and en t i r e data se t s . F igure 10 compares the f i t t e d d i s t r i b u t i o n to the data f o r cumulative p r o b a b i l i t i e s less than 0.3 . The model f i t t e d to en t i re data range does not f i t the data wel l at the lower pe r cen t i l e s . In order to avoid these problems, the res i s tance d i s t r i b u t i o n models were f i t t e d to the lower 15 percent of the data (15% t runca t ion ) . F igure 11 shows the va r i a t i on in the P - cp r e l a t i onsh ip fo r four d i s t r i b u t i o n types when the d i s t r i b u t i o n parameters are determined by f i t t i n g to the lower 15% of the data. A l l four d i s t r i b u t i o n models were used to analyze P - cp r e l a t i onsh ips fo r each s i ze and grade combination. In most cases, the 2 Parameter V e i b u l l d i s t r i b u t i o n tended to g ive r e su l t s fo l low ing the average trend fo r the four d i s t r i b u t i o n s . Thus, the (3 - <f> r e su l t s obtained using 2 Parameter Weibul l d i s t r i b u t i o n and 15% t runcat ion were used in subsequent ana l y s i s . Results in F igure 12 and 13 show that the data f i t t i n g strategy a l so a f f e c t s the r e l i a b i l i t y ranking of data sets in a /? - <j> ana l y s i s . From Figure 12 using lower 15% data , the v i sua l lumber grade No.2 has a higher r e l i a b i l i t y index than SS, while F igure 13 showed the opposite r e s u l t when using the en t i re data set to ca l cu l a te d i s t r i b u t i o n parameters. 9.1.3 BENDING PERFORMANCE FACTOR Performance fac to rs are tabulated f o r four snow loads and the occupancy load case using j - 0.25 and the ac tua l ja f o r the load case taken from Tables 6 and 6a. Table T summarizes ^-values corresponding to three target ^-values (/?r = 3.0, 2.5 and 2.0) f o r the se lected s ize/grade combinations fo r S-P-F. The r e su l t s show the lower j3-values corresponding to given (^-values in Tokyo and Osaka which have s i g n i f i c a n t d i f f e rences between 7 = 0.25 and the ac tua l •ya va lues . F igure 14 shows the average f3 - <j> trends fo r f i v e load cases at 7 = 0.25. F igure 15 shows the average /? - <j> trends fo r f i v e load cases at the ac tua l ja. Table 8 g ives the approximate mean /3-values corresponding to s p e c i f i c <f> values at 7 = 0.25 and the ac tua l 7 . As explained in d ra f t LSD S tee l Standard, /? = 2.5 i s targeted fo r a load combination of dead load plus occupancy load (Eq.4.4) at <j> = 0.9 and j3 = 2.0 fo r a load combination of dead plus snow plus l i v e load in (Eq.4.5) at the same <j> = 0 .9 . In t h i s a n a l y s i s , l i v e load was assumed 0 fo r r a f t e r s of the r e s i d e n t i a l b u i l d i n g . I f Eq.4.5 from the d ra f t LSD Stee l Standard i s used fo r S-P-F lumber, Table 8 shows the r e s u l t i n g <0-value at /Jj. = 2.0 would be larger than 1.0. A l t e rna t i v e l y i f we adopt Eq.9.2 which requi res flj, = 2.5 then 4> - 0.95 f o r 7 = 0.25 and <j> = 0.9 f o r ac tua l ja va lues . Therefore the design equation (Eq.9.2) with <j> = 0.9 (f3T = 2.5) , has been adopted fo r the dead plus snow load combination fo r r a f t e r des ign. For t h i s case F i g . 1 shows that 2x4 wood frame st ructures have comparable <f> - (3 r e l a t i onsh ips to s tee l s t ruc tu res . Although a current Japanese design methods do not apply s i ze e f f e c t adjustments to design strength proper t ies of lumber ( s i ze e f f e c t s are app l ied to glued-laminated lumber fo r depth more than 30 cm), s i ze e f f e c t adjustments are required to s imp l i f y the presentat ion of the design strength proper t ies fo r dimension lumber. The s i ze e f f e c t adjustment equation re l a tes member strength to member dimensions according to ° i _ ( H2 L2 V T *2 " I, H1 L, ) where ax and o~2 a r e ^ n e strength corresponding to the lengths Lx and L2 and to the depths and E2 and k i s the parameter determining the magnitude of the s i ze e f f e c t . Using t h i s Eq .9 .7 , then Eq.9.1 can be expressed as ( 9. 7 ) 1.1 DN + 1.6 Ln = <p0 R0 ( g°LL° ( 9. 8 ) a lso Eq.9.2 can be expressed as 1.1 DN + 1.6 SN = <t>0 R0 ( H °L° ( 9- 9 ) where 4>Q i s the performance f ac to r assoc ia ted with RQ which i s the c h a r a c t e r i s t i c bending strength fo r a standardized 2x8 beam having a depth HQ = 184 mm and a length LQ - 3000 mm; H and L are the ac tua l depth and length of the member being evaluated; and fc i s the s i ze f ac to r parameter. The performance f a c to r <j>0, the strength R0 and parameter fc are obtained using leas t squares techniques to minimize the func t i on : r i F = ££E|^ V»W Roi ( - ^ i j p ' ) ( 9- 1 0 ) where i = 1,2 (one spec ies , two grades) ; j = 1 , . . ,3 (three s i z e s ) ; / . = 1, . . ,5 ( f i ve loading cond i t i ons ) . The minimizat ion was ca r r i ed out using the ac tua l <f> values fo r 7 = 0.25 and actua l ja at the 8 = 2.5 and adopting </>0 = 0.9 as shown in Table 7. The tes t spans fo r bending (span/depth r a t i o of 17:1) are 1511 mm fo r 2x4, 3131 mm fo r 2x8 and 3994 mm fo r 2x10. The bending s i ze e f f e c t parameter determined in the minimizat ion was approximately 4.5 in both 7 cases. Adjusted c h a r a c t e r i s t i c strength values R0, are shown in Table 9 with the corresponding non-parametric 5th pe rcen t i l e s fo r 2x8 ' s . The safety index 0 values assoc ia ted with the design Eqns. 9.8 and 9.9 were evaluated f o r the case j = 0.25 and the ac tua l j a , with <f>0 = 0.9 using the R0 and s i ze parameters k given in Table 9. The average 0 ca l cu la ted fo r the locat ions and s i ze grade combinations in Table 7 was approximately 2.5 fo r 7 = 0.25 but d id not achieve the target 0T = 2.5 f o r the ac tua l ya. The safety assessment was repeated with <f>Q = 0.85 fo r the case 7 = 0.25 and <j>0 = 0.85 and 0.8 fo r the ac tua l j a . Table 10a shows the r e su l t s of t h i s ana l ys i s fo r <f>0 = 0.9 and 0.85 when 7 = 0.25. Results obtained when the ac tua l ya i s used are given in Table 10b f o r <j>Q - 0.85 and 0.80. According to the Table 10a, fo r <j>0 = 0.9 and 7 = 0.25 the mean 0 i s 2.49 with a range from 2.31 to 2.69. For <j>0 = 0.85 and using the actua l 7 a the mean 0 i s 2.48 with a range from 2.13 to 2.80, and the mean 0 i s 2.59 with a range from 2.25 to 2.92 at <f>0 - 0.8 fo r the ac tua l 7 a in Table 10b. For bending strength l i m i t s tates Eq.9 .8 i s recommended f o r dead plus occupancy load and Eq.9.9 i s recommended as the design checking r e l a t i onsh ip fo r dead plus snow load. The s p e c i f i e d strength referenced to the 2x8 s i ze are given in Table 9. Using k = 4 .5 , 4>Q -0.85 and the ac tua l ja y i e l d s average safety ind ices 0 of approximately 0 = 2.5. I f the choice of 7 = 0.25 and the same 4>Q = 0.85 are adopted fo r c a l i b r a t i o n then the average safety ind ices 0 can be increased. 9.1.4 TENSION R e l i a b i l i t y l e ve l s f o r tension members were ca l cu la ted using the procedures prev ious ly descr ibed fo r bending members. However only one load case dead load plus snow load was considered. The r e l i a b i l i t y l eve l s fo r the four snow locat ions were studied using the mater ia l res i s tance d i s t r i b u t i o n der ived by f i t t i n g the 2 Parameter V e i b u l l to the lower 15% of the tes t data . Table 11 summarizes 0-values corresponding to three target 8-values (8T = 3.0, 2.5 and 2.0) f o r se lected s ize/grade combinations fo r four snow loads cases at 7 = 0.25 and the ac tua l ja f o r the l o c a t i on . The ca l cu la ted performance fac to rs are not s i g n i f i c a n t l y a f f ec ted by the choice of 7. However (^-values in Tokyo and Osaka are s l i g h t l y lower where the ac tua l ja values are greater than 1. F igure 16 shows the average 0 - <j> trends fo r four load cases at 7 = 0.25. Table 12 gives the approximate mean /3-values corresponding to s p e c i f i c 0 values fo r 7 = 0.25 and the ac tua l 7 a at each l o ca t i on . Average /?-values were not a f f ec ted by the choice of 7. The minimizat ion was ca r r i ed out assuming a standardized 2x8 tension member having a depth H0 = 184 mm and a length L0 = 3000 mm; using r e su l t s shown in Table 11 fo r 0T = 2.5 with <j>0 = 0.9 f o r 7 = 0.25 and the ac tua l ya. The gauge lengths of 2462mm fo r 2x4, 3683mm fo r 2x8 and 3683mm fo r 2x10 were used f o r the tension strength t e s t s . The r e s u l t i n g tension s i ze e f f e c t parameters were 8.9 fo r 7 = 0.25 and 9.5 fo r the ac tua l ya. Adjusted c h a r a c t e r i s t i c strength values RQ f o r the lumber grades SS and No.2 are shown in Table 13 with the corresponding non-parametric 5th pe rcen t i l e s fo r 2x8 ' s . Eq.9 .9 i s adopted f o r design checking fo r the tension strength l i m i t s ta te . Actual /?'s f o r the four load cases shown in Table 14a and Table 14b are der ived using 4>0 = 0.90 and 0.85 fo r j = 0.25 and the ac tua l 7 a with the corresponding s p e c i f i e d strengths R0 from Table 13. According to the Table 14a, the mean f3 i s 2.50 (range from 2.25 to 2.72) at <f>Q = 0.9 and the mean /? i s 2.61 (range from 2.39 to 2.83) at <j>0 = 0.85 f o r 7 = 0.25. The mean /? i s 2.50 (range from 2.21 to 2.77) at 4>Q = 0.9 f o r the ac tua l ja and the mean /? i s 2.61 with a range from 2.34 to 2.88 at 0O = 0.85 fo r the ac tua l ja from Table 14b. Eq.9.9 i s recommended f o r design checking fo r the tension strength l i m i t s tate with k = 9.5 , (j>0 = 0.90 and the adjusted 2x8 strength R0 f o r the actua l ja from Table 13. When 7 = 0.25, then k = 8.9, <j>Q = 0.90 when used with the adjusted 2x8 strength RQ f o r 7 = 0.25 from Table 13. In a l l cases t h i s design equation would lead to r e l i a b i l i t y l eve l s comparable to s t ee l s t ruc tu re . 9.1.5 COMPRESSION The approach adopted tension r e l i a b i l i t y s tudies was app l ied fo r r e l i a b i l i t y l e ve l ana lys i s fo r compression members. Analyses were performed fo r the four load cases (dead load plus snow load) used fo r tension s tud ies . Compression members are considered to be f u l l y res t ra ined against buck l ing ( i . e . short columns). Resistance parameters were obtained by f i t t i n g a 2 Parameter V e i b u l l to the lower 25% of the t es t data. Table 15 summarizes ^-values corresponding to three target 8-values (8T = 3.0, 2.5 and 2.0) f o r se lec ted size/grade combinations f o r four snow loads 7 = 0.25 and the ac tua l ya. The r e su l t s do not show s i g n i f i c a n t d i f f e rences with the choice of 7. Figure 17 shows the average 8 - <j> trends fo r four load cases at 7 = 0.25. Table 16 gives the approximate mean ^-values corresponding to s p e c i f i c <f> values at 7 = 0.25 and the ac tua l ya. The minimizat ion was ca r r i ed out assuming fo r a standardized 2x8 compression members having a depth H0 = 184 mm and a length LQ = 3000 mm; using r esu l t s shown in Table 15 fo r 8 = 2.5 with <j> - 0.9 at 7 = 0.25 and the ac tua l ja. The gauge lengths of 2438mm fo r 2x4, 3658mm fo r 2x8 and 4267mm fo r 2x10 were used fo r the compression t e s t . The r e s u l t i n g compression s i ze e f f e c t parameters were approximately 8.3 in 7 = 0.25 and 8.7 in the ac tua l ja, and adjusted c h a r a c t e r i s t i c strength values RQ are shown in Table 17 with the corresponding non-parametric 5th pe rcen t i l e s fo r 2x8 ' s . Using Eq.9.9 fo r design with <j>0 = 0.9 and 0.85 fo r 7 = 0.25 and the ac tua l ja, and the adjusted c h a r a c t e r i s t i c values R0, the safety index 8 are shown in Table 18a and Table 18b fo r s i z e , grade and load combination. According to the Table 18a and Tale 18b, the mean 8 i s 2.51 with a range from 2.15 to 3.11 at 0O = 0.9 and the mean 8 i s 2.65 with a range from 2.30 to 3.25 at <f>0 = 0.85 fo r 7 = 0.25, the mean 8 = 2.51 with a range from 2.09 to 3.15 at (f>0 = 0.9 and the mean 8 = 2.66 with a range from 2.23 to 3.29 at <f>0 = 0.85 fo r the ac tua l ja. Based on th i s ana l y s i s , i t i s recommended that k = 8 .7 , <j>0 = 0.9 with the adjusted 2x8 strength R0 f o r the actua l ja, or k = 8 .3 , (j)Q -0.9 with the adjusted 2x8 strength R0 f o r j = 0.25 would be comparable with s tee l s t ruc tu res . 9.2 SERVICEABILITY LIMIT STATES E f f e c t s of fac tored load and load combination f o r s e r v i c e a b i l i t y l i m i t states are obtained from the d ra f t LSD Stee l Standard in Sect ion 3.2. To fo l low th i s standard, the de f l e c t i on of the beam i s con t ro l l ed in terms of e i the r a proport ion of the span or spec i f i ed de f l e c t i on l i m i t expressed as : max — ^allow ( 9. 11 ) where A , allow L K d allow maximum d e f l e c t i o n ; a l lowable d e f l e c t i o n ; beam span; l i m i t i n g de f l e c t i on f a c t o r ; s p e c i f i e d de f l e c t i on l i m i t . The maximum de f l e c t i on can be ca l cu la ted fo r a s ing le j o i s t under uniformly d i s t r i b u t e d load as : 5-( Dn + Q!L)-s.L4 384 • <j> • E • I - \llow ( 9. 12 ) 52 where ^allov E maximum deflection corresponding to E; allowable deflection; design uniformly distributed dead load; design uniformly distributed occupancy load; spacing between members; mean modulus of elasticity for the population of lumber; moment of inertia of the member cross-section, whereas for rafters: 5-( Dn + 0.9-_S„ )-s-L4 384-<j>-E-I ^ 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 = A allou 5 • ( D + Q ) • s • L4 384-E-I ( 9. 14 ) where D Q E dead load (a random variable); occupancy load (a random variable); modulus of elasticity of the member (a random v a r i a b l e ) , whereas fo r the r a f t e r : G - Aallow ~ 3 8 4 . E • I ( 9. 15 ) where S : snow load (a random v a r i a b l e ) . By s u b s t i t u t i o n , the performance funct ion and design equation can be expressed f o r j o i s t as : (y + 1)• E v ' where d : D I Dn; 7 - DJ Qn; 1 : Q I Qn, and fo r the r a f t e r , the performance funct ion i s given by C - 1 ( dy + s ).<p.E . ° ~ 1 (7 + 0.9)- E ( 9- I 7 ) where 7 : DJ Sn; : S I Sn. The parameters fo r random var i ab les Q and S are assumed 8-year return loads fo r the s e r v i c e a b i l i t y l i m i t s ta tes . The performance funct ions of Eq. 9.16 and Eq. 9.17 were evaluated using the RELAN program. Table 19 summarizes ^-values corresponding to three target /?-values = 2.0, 1.5 and 1.0) f o r se lec ted size/grade combination fo r four snow loads j = 0.25 and the ac tua l ya. The r e su l t s do not show s i g n i f i c a n t d i f f e rences with the choice of 7. The r e su l t s d id not meet the s a t i s f a c t o r y r e l i a b i l i t y of f3T = 1.0 at 4> = 0.9 as was recommended by the d ra f t LSD Stee l Standard. In order to get f3T = 1.0, a performance f ac to r <j> = 0.85 should be used fo r the de f l e c t i on s e r v i c e a b i l i t y l i m i t s tates to y i e l d safety l eve l s comparable with s tee l s t ruc tu res . 10. DURATION OF LOAD EFFECTS Strength proper t ies of lumber depend on the durat ion of the load. Members subjected to short-term durat ion load have a higher strength than obtained fo r longer durat ion loads. In order to account fo r these c h a r a c t e r i s t i c s , the current Japanese standard regards snow load as the temporary (short-term) load in the l i g h t snow area , and sustained load (long-term) in the heavy snow area . The al lowable un i t s t resses fo r temporary load are two times the un i t s t resses fo r sustained load. In t h i s chapter, a newly developed damage accumulation model by Foschi et a l . [3 and 25] was used to evaluate Japanese p rac t i ce with respect to durat ion of load adjustments. Monte Car lo s imulat ion was app l ied to evaluate the e f f e c t of se lec ted load combination on the durat ion of load adjustments fo r two q u a l i t i e s of S-P-F dimension lumber (SPF Ql and SPF Q2). S-P-F Ql i s a high qua l i t y grade with a c o e f f i c i e n t of v a r i a t i on of approximately 20 percent. S-P-F Q2 i s a low qua l i t y grade with c o e f f i c i e n t of v a r i a t i on of approximately 28 percent. The ob jec t i ve of the durat ion of load ana l ys i s i s to develop durat ion of load adjustment f ac to rs KD such that the member r e l i a b i l i t y under short-term load i s maintained when durat ion of load e f f e c t s are considered. Since data of an average snow durat ion can be obtained from the l o c a l meteorologica l observa tor ies , simple snow load models were app l ied in th i s ana l y s i s . Snow load was assumed constant fo r the average durat ion of the ground snow load in each year in four l o ca t i ons . Duration of load response of two q u a l i t i e s of S-P-F lumber w i l l be evaluated in th i s study. 10.1 DAMAGE MODEL A nonl inear damage accumulation model expressed by the fo l low ing d i f f e r e n t i a l equation was developed by .Foschi et a l . [3 and 25] : & = a [ r ( t ) - <r0r8]6 + c [ r ( t ) - <r 0 r j " a ( 10. 1 ) where a : damage state va r i ab le (a = 0 in the i n i t i a l s tate and a = 1 at f a i l u r e ) ; a,b,c,n : model parameters; <T 0 : threshold s t ress r a t i o ; r ( t ) : s t ress h i s t o r y ; TS . standard short- term bending strength of the member obtained in a ramp tes t of one minute dura t ion . Only when T(t ) > o"0r s, w i l l there be damage accumulation. Since th i s d i f f e r e n t i a l equation model i s d i f f i c u l t to evaluate, the damage accumulation was ca l cu la ted step by step as shown in the fo l low ing procedures: ai = ai-l Ki + Li ( 10. 2 ) where K. = exp [c (r,- - <70r,) n A t ] ( 10. 3 ) ^ = (r4 - *0T8)b ~ » ( 1) ( 10. 4 ) Ks ( b + 1 ) where AT8 = median of r s x60 (MPa/Hour) and the damage a can be obtained at any time by the recurrence r e l a t i onsh ip of Eq .10.2 . The parameters 6, c, n, <r0 were assumed lognormally d i s t r i bu t ed and the d i s t r i b u t i o n of r s i s assumed lognormally d i s t r i b u t e d and known from the ana l ys i s of short-term t e s t s . The parameters obtained f o r the random values 6, c, n, aQ and rg f o r the S-P-F durat ion of loads studies fo r qua l i t y l e ve l 1 (SPF Ql) and qua l i t y l e ve l 2 mater ia l (SPF Q2) were taken from Re l i ab i l i t y-Based Design of Wood Structures S t ruc tu ra l Research Ser ies [3] . Those parameters are l i s t e d in Table 20. Damage i s def ined as a s tate va r i ab le taking the values a = 0 in the i n i t i a l s tate and a = 1 at f a i l u r e . The damage a i s a funct ion of the s t ress h i s to r y . For 50 years of serv ice l i f e , the performance funct ion i s expressed as : ( 10. 5 ) G - 1.0 - o(50) ( 10. 6 ) 10.2 LOAD CASE Duration of load e f f e c t s were evaluated fo r the dead load plus snow load combination. The dead load model assumed was as explained in Sec. 8 .1 . The annual snow load record was assumed as one rectangular d i s t r i b u t i o n in time with a durat ion At, equal to the annual average snow per iod as shown in Figure 18. Parameters fo r annual snow height d i s t r i b u t i o n used in th i s ana l ys i s are explained in Sec. 8.3. The t o t a l load i s the superpos i t ion of the dead load and the snow load. A load sequence fo r 50 years was considered. At any time t , ac tua l s t ress i s expressed as : o-(t) = ( D + 5(t) ) F ( 10. 7 ) where F : f a c to r to convert from load to s t r e s s . Since the design equation f o r combination of dead load and snow load i s expressed as : ( 1.1 D n + 1.6 S „ ) F = <fi R o m ( 10. 8 ) Eq. 10.7 can be rewr i t ten as : - T O T C «f * ) ( io. 9 ) 10.3 SIMULATION Monte Car lo s imulat ion was app l ied to obtain durat ion of load 59 f a c to rs as fo l l ows : 1) A value of performance funct ion <j> and a value of the r a t i o of the design dead load to the design l i v e load 7 were chosen. 2) A load sequence of 50 segments was created. a) A Uniformly d i s t r i bu t ed random number was chosen to ca l cu l a te the dead load d, which was taken as a constant f o r the 50 years . b) A Gumbel-distr ibuted random number fo r annual snow was chosen, which was taken as a constant fo r the whole year. I f the se lec ted Uniformly d i s t r i bu t ed random number was smal ler than p 0 = exp{- exp (AB)}, there was no snow in the year. c) The dead load and l i v e load were combined as Eq .10.9 . 3) The damage accumulated the 50 years fo r each sample was computed. a) F ive Uniformly d i s t r i b u t e d random numbers were chosen to obta in the values of 6, c, n, <TQ and ra from the i r Lognormal d i s t r i b u t i o n s from Table 20. b) Using the recurrence r e l a t i onsh ip in Eq .10 .2 , the accumulated damage a was ca l cu la ted f o r 50 c yc l e s . c) The performance funct ion G = 1.0 - a ( 10. 10 ) was then evaluated. I f G > 0, the sample surv ived , and i f G < 0, the sample f a i l e d . 4) Step 2 and 3 above were then repeated fo r 10,000 r e p l i c a t i o n s . 5) The number of f a i l u r e s occurr ing in 50 years was used to compute the p r o b a b i l i t y of f a i l u r e p _ number of f a i l u r e s ( 1 0 11 ) I number of r e p l i c a t i o n s (10000) ' 6) The assoc ia ted r e l i a b i l i t y index /? was obtained from /? = - 9~\ Pf ) 7) The above process, s t a r t i n g at step 1, was then repeated f o r d i f f e r e n t values of <j>. 10.4 DURATION OF LOAD RESULTS The r e l i a b i l i t y r e su l t s fo r SPF Ql and Q2 are l i s t e d in Table 21 and 22 which shows ^-values corresponding to d i f f e r e n t target /3-values fo r S-P-F Ql and S-P-F Q2 mater ia l with and without DOL e f f e c t . The durat ion of load adjustment f ac to r KD i s ca l cu la ted fo r the four l o ca t i ons , where KD i s def ined as — 7 — — yuk.—. These <j> and KD values ^without DOL were obtained from the ana lys i s us ing three combinations of 7 = 0.25 with an average annual snow durat ion in each l o ca t i on , an ac tua l ya with an average annual snow in each loca t ion and 7 = 0.25 with an annual snow durat ion of f i v e months (155 days)(D0L-5) in order to compare the e f f e c t s of those parameters. The trends in ^-values were cons is tent across d i f f e r e n t /? l e v e l s . But, <j> and KD values were in f luenced by the l o c a t i on , annual snow dura t ion , and 7-values. The d i f fe rences between </>-values obtained using the average annual snow durat ion and the assumed f i v e months snow durat ion are greater in the l i g h t snow areas but less in the heavy snow areas because heavy snow areas have a longer snow durat ion shown as F igure 19 and 20. For example, the annual snow durat ion in Osaka i s two days and that in Sapporo i s 136 days. Although the Canadian snow model was qui te d i f f e r e n t from the rectangular model, the snow durat ion of f i v e months was considered fo r the Canadian study of durat ion of load e f f e c t . I t i s too conservat ive to only use a snow durat ion of f i v e months fo r the rectangular model. Foschi et a l . s tates that the choice of 7 's has a s i g n i f i c a n t a f f e c t on the ca l cu la ted durat ion of load f a c to r KD [3] . D i f ferences between ^-values at 7 = 0.25 and at the ac tua l ja are la rger in the l i g h t snow areas but smal ler in the heavy snow areas. The ac tua l ja in Sapporo was 0.25, whereas that in Osaka was 4 .4 . From Table 21 and 22, the r e su l t s between SPF Ql and Q2 were qu i te d i f f e r e n t . However, the (^-values in both cases were c lose r in Osaka with 7 = 0.25 but were d i f f e r e n t with using the ac tua l ja. General ly speaking, r e su l t s of SPF Ql are c lose r to the r e su l t s obtained fo r Hem-Fir as explained in Re l i ab i l i t y-Based Design of Wood Structures S t ruc tu ra l Research Se r i e s , but qu i te d i f f e r e n t from those of SPF Q2. Since SPF Q2 i s a low qua l i t y grade and the KD f ac to rs fo r SPF Ql are s im i l a r to those of obtained f o r Hem-Fir the KD values der ived f o r SPF Ql are recommended f o r S-P-F lumber. The r e su l t s of the SPF Ql were p lo t ted in F igure 21. It can be seen that they correspond c l o se l y to the Canadian ana l y s i s . Where KD -0.8 when 0 < j < 1; KD = 0.8 - 0.431og(7) when 1 < 7 < 5; and KD = 0.5 when 7 > 5.0. Because only l im i t ed data were f e a s i b l e , i t seems reasonable to use the Canadian ana lys i s f o r the remainder of t h i s study, given the f a c t that the present data genera l l y have the same trend as the Canadian ana l y s i s . 11. ASSESSMENT OF RELIABILITY LEVELS  ASSOCIATED WITH CURRENT WORKING STRESS DESIGN WSD i s cur rent l y used f o r the Japanese timber des ign. The r e l i a b i l i t y assessment procedures used to study /? - <f> r e l a t i onsh ips f o r the LSD code format can a l so be used to study the r e l i a b i l i t y l eve l s in the WSD codes. The current r e l i a b i l i t y l eve l s fo r 2x4 wood frame const ruct ion are evaluated in th i s chapter. Typ i ca l f l o o r and roof systems were s tud ied . 11.1 LOAD Since th i s chapter i s intended to evaluate the r e l i a b i l i t y l e ve l f o r current Japanese 2x4 wood frame cons t ruc t ion , the nominal load values spec i f i ed in the GHLC's span tab les were used fo r t h i s eva lua t ion . The random va r i ab l e d = D/Dn was assumed to be Normally d i s t r i bu t ed with mean of 1.0 and standard dev ia t ion of 0 .1 . An ac tua l r a t i o 7 = Dn/Ln or 7 = Dn/Sn was ca l cu la ted at each loca t ion using data obtained from GHLC's span t ab le . The nominal occupancy load fo r r e s i d e n t i a l s t ructures of 180 kgf/m 2 (1.765 KN/m2) i s used fo r the span tab le c a l c u l a t i o n s . The normalized occupancy load i s explained in Sec .8 .2 . The 50-year return occupancy load was used the bending ana l y s i s . The annual maximum value was used fo r de f l e c t i on ana l y s i s . For the snow load , the random va r i ab les s = S/Sn in each loca t ion are explained in Sec .8 .3 . The 50-year re turn snow load was used as the nominal load fo r the bending ana l y s i s . The annual maximum value was used f o r de f l e c t i on ana l y s i s . 11.2 ALLOWABLE UNIT STRESS The al lowable un i t s t resses fo r lumber fo r 2x4 wood frame const ruct ion are s p e c i f i e d in the Bu i ld ing N o t i f i c a t i o n fo r Spec ia l Admin is t ra t ive Agency [13], explained in Sec .3 .2 .3 , and tabulated in Appendix 1. 11.3 RELIABILITY LEVELS IN BENDING (SHORT-TERM BASIS) WSD procedures taken from the Standard f o r Timber Design are used to develop span t ab les . For f l o o r j o i s t s : Dn + Ln < Ra ( 11. 1 ) For r a f t e r s : Dn < Ra. ( in l i g h t snow area) ( 11. 2 ) Dn + Sn < 2 Ra ( in l i g h t snow area) ( 11. 3 ) Dn + Sn < Ra ( in heavy snow area) ( 11. 4 ) where Dn : design dead load e f f e c t ; Ln : design l i v e load e f f e c t ; Sn : design snow load e f f e c t ; Ra : a l lowable un i t s t ress fo r sustained load. The eva luat ion of the r e l i a b i l i t y index 0, us ing the RELAN program requi res a performance funct ion G. The safety l eve l s fo r f l o o r j o i s t s under short-term loading are evaluated by determining the p r o b a b i l i t y that the performance funct ion G < 0. For the j o i s t , the performance funct ion i s : G = R - ( D + L) ( 11. 5 ) where R : strength (a random v a r i a b l e ) ; D : e f f e c t of the dead load (a random v a r i a b l e ) ; L : e f f e c t of the l i v e load (a random v a r i a b l e ) . Introducing the design equation in Eq.11.1 into the performance funct ion in Eq.11.5 y i e l d s : G = R - R a - ( d f + 0 ( 11. 6 ) (7+1) V ' wh< 7 '• Dn/Ln; d : D/Dn; I : L/Ln. In a l i g h t snow area , snow load i s regarded as the temporary load so that the al lowable un i t s t ress of a temporary load i s used, i . e . two times i t s sustained load . The f ac to r 2 takes account of a durat ion of load e f f e c t . However the s t ruc tu ra l member should a l so be checked fo r the dead load on ly . Therefore two performance funct ions must be considered in the l i g h t snow area. I f Dn > Sn, the governing design equation i s Dn < Ra. For r a f t e r s the performance funct ion G can be expressed as G = R - (D + S) ( 11. 7 ) Introducing the design* equation in Eq .11 .2 , the performance funct ion in Eq.11.7 can be expressed as : G = R - R a - ^ + S ) ( 11. 8 ) I f Sn > Dn, the governing design equation i s Dn + Sn < 2 Ra By s u b s t i t u t i o n , the performance func t ion in Eq.11.7 and the design equation in Eq.11.3 can be a l so expressed as : (7+1) For heavy snow areas , the snow load i s regarded as a sustained load. Therefore , the a l lowable s t ress fo r sustained load i s used. By s u b s t i t u t i o n , the performance funct ion Eq.11.7 and the design equation Eq.11.4 can be expressed as : G = R A«-0*7 + 0 ( 1 1 . 1 0 ) (7+1) v ' The short-term r e l i a b i l i t y of current const ruct ion was evaluated fo r bending fo r f l o o r j o i s t and r a f t e r systems. The r a t i o ' s 7 used fo r the ana lys i s were der ived using the mater ia l weights and nominal occupancy and snow load spec i f i ed in the GHLC span t ab les . Results of these ana l ys i s are summarized in Table 23. 11.4 RELIABILITY LEVELS IN DEFLECTION In the Standard fo r Timber Design, the al lowable de f l e c t i ons f o r s t ruc tu ra l members are s p e c i f i e d . GHLC's span table was app l ied to the requirements from the standard. The current s e r v i c e a b i l i t y l i m i t states ana l ys i s was performed f o r the short-term de f l e c t i on of a s ing le member f l a t roof and f l o o r . Fol lowing GHLC's requirement, the de f l e c t i on l i m i t as s p e c i f i e d as a proport ion of the span or a maximum al lowable de f l e c t i on expressed as : A m a x < ( U. U ) or A m a l < al lowable de f l e c t i on ( 11. 12 ) The de f l e c t i on l i m i t s f o r s t ruc tu ra l members f o r 2x4 wood frame s t ructure are summarized in Table 24. The maximum de f l e c t i on can be ca l cu la ted fo r s ing le lumber member under uniformly d i s t r i b u t e d load as : _ 5-( Dn + Qn ).S-L* ^max ~ 384-IS-1 ^allow \ iJ-- 1 6 ) where Am„„ : maximum d e f l e c t i o n : ^allow '• a l lowable d e f l e c t i o n ; Dn : design uniformly d i s t r i bu t ed dead load ; Qn : design uniformly d i s t r i bu t ed l i v e load; s : spacing between members; E : mean modulus of e l a s t i c i t y f o r the populat ion of lumber; I : moment of i n e r t i a of the member c ross-sec t ion . A performance funct ion f o r de f l e c t i on l i m i t s tate can be formulated as : 5 - ( D + Q )-s-L4 allow 3 8 4 . E • I where D : dead load (a random v a r i a b l e ) ; Q : l i v e load (a random va r i ab le ); E : modulus of e l a s t i c i t y of the member (a random v a r i a b l e ) . ( 11- 14 ) Introducing Eq.11.13 the performance funct ion can be expressed as : G = i _ ( d y \ } - \ ( i i . 1 5 ) ( 7 + 1 ) • E K ' where d : D/Dni 7 : DJQn; 3 : Q/Qn-The performance funct ion of Eq.11.15 was evaluated using the RELAN program and r e l i a b i l i t y l eve l s at the s e r v i c e a b i l i t y l i m i t s tate fo r current const ruct ion are shown in Table 25. 11.5 RELIABILITY OF CURRENT RAFTER CONSTRUCTIONS UNDER LONG-TERM LOADING The ac tua l r e l i a b i l i t y l e ve l s assoc ia ted with current const ruct ion w i l l vary depending on the design c r i t e r i a c o n t r o l l i n g the member des ign. The r e l i a b i l i t y l eve l s f o r bending members subjected to short-term loads have been evaluated fo r the bending strength l i m i t state (Sec.11.3) and fo r the de f l e c t i on s e r v i c e a b i l i t y l i m i t s tate (Sec.11.4) . The r e l i a b i l i t y l eve l s are ca l cu la ted fo r each l i m i t s tate separate ly . The purpose of th i s sect ion i s to evaluate the actua l r e l i a b i l i t y l e ve l s assoc ia ted with current construct ions fo r the bending strength l i m i t state us ing the ac tua l maximum spans permitted in the GHLC span t ab les . The f i r s t step in th i s ana lys i s i s to ca l cu la te the al lowable spans as governed by the bending, shear and de f l e c t i on design requirements. The ana lys i s i s undertaken f o r f i v e t y p i c a l r a f t e r systems fo r the four l o ca t i ons . In the l i g h t snow area , two times the al lowable un i t s t r e s s , 2-Ra, must be greater than or equal to the sum of the e f f e c t s of the uniformly d i s t r i bu t ed dead and snow load , when the uniformly snow load i s greater than the uniformly dead load. Thus, (Dn+Sn) < 2Ra, when Sn>Dn. When the uniformly d i s t r i bu t ed snow load i s less than the uniformly d i s t r i bu t ed dead load , the al lowable un i t s t r e s s , Ra, must be greater than the e f f e c t of d i s t r i b u t e d dead load. Dn < Ra, when Sn<Dn. For de f l e c t i on cons iderat ions of the r a f t e r s , both ^ T J Q A N < ^ 2 cm must not be exceeded. The governing span / i s the minimum value determined using the fo l low ing equat ions. De f l ec t ion 3 i _ 384 • E • I  1 ~ > 200-5-u; when 200 < 2cm ( 11. 16 ) W - N-2-384.E-1 w h e n _ A 5 • w 200 > 2cm ( 11. 17 ) Bending: 8-Z.fb •2 - \ w ( 11. 18 ) Shear: Where •3 = 4-A-/ a 3-w E h f. I Z span governed by d e f l e c t i o n ; span governed by bending; span governed by shear; modulus of e l a s t i c i t y ; a l lowable bending s t r e s s ; a l lowable shear s t r e s s ; moment of i n e r t i a ; sec t ion modulus; ( 11. 19 ) 71 A cross sect ion area ; w uniformly d i s t r i bu t ed load without safety f ac to r as with the LSD. Consider the fo l low ing example: g i ven : Tokyo, l i g h t roo f , spacing = 455mm, S-P-F, SS, 2x8 Dead load was ca l cu la ted from Table 6 DN = ( 20 + 6 )x .455 + 6 = 17.83 kg/m Snow load was obtained from Table 5 SN = 35.88 x 2 x.455 = 32.65 kg/m Since uniformly d i s t r i bu t ed snow load i s greater than uniformly d i s t r i bu t ed dead load , therefore the design equation (DN+SN) < 2Ra must be s a t i s f i e d . In order to use from Eq.11.16 to Eq.11.19 with RA (not 2-RA), nominal uniformly d i s t r i b u t e d dead plus nominal uniformly d i s t r i bu t ed snow load was d iv ided by two to get w (convert short-term to long-term) so that w can a l so be used fo r the de f l e c t i on checking equations on a long-term bas i s . w = (DN+Sn)/2 = 0.252 kg/cm ( 11. 20 ) Introducing w to the Eq.11.16 to Eq.11.19 4 2-384-85000-1972 5-0.252 = 565.1cm ( 11. 21 ) 72 8-214.4-110 0.252 = 864.6cm ( 11. 22 ) 4-69.9-6 = 2215.5cm ( 11. 23 ) 3-0.252 The al lowable span fo r th i s case was 5.56m, the span governed by d e f l e c t i o n . An ana l ys i s of r a f t e r spans as governed by d e f l e c t i o n , bending and shear i s summarized in Table 26. Genera l ly speaking, bending requirements governs in the heavy snow cases and de f l e c t i on governs in the l i g h t snow cases. When de f l e c t i on governs, the al lowable span w i l l be shorter than permitted by bending requirements. In these cases the actua l r e l i a b i l i t y l eve l s f o r the bending strength l i m i t state w i l l be greater than pred ic ted versus when the bending strength l i m i t s tate i s examined independently (Sec. 11.3) . The ac tua l r e l i a b i l i t y l e ve l s f o r the bending strength l i m i t state are evaluated in a two stage process. (1) evaluate the short-term r e l i a b i l i t y of the bending member and then (2) adjust the short-term r e l i a b i l i t y f o r durat ion of load e f f e c t s to get the ac tua l r e l i a b i l i t y under long-term load ing. The r e l a t i onsh ip between span and corresponding /? f o r bending can be obtained from the fo l low ing performance func t i on : G = R - (D+S)-p- 6L 2 ( 11. 24 ) 8BH2 = R - Sn(dy+s)-p- 6L2 ( 11. 25 ) 8BH2 where D : dead load; S : snow load; p : spacing between members; L : span; B : member width; H : member depth; Sn : nominal snow load; d : normalized dead load ; s : normalized snow load ; 7 : DjSn. The durat ion of load f a c to r fo r snow load cases, KD = 0.8 f o r Sapporo, N i i ga ta and Tokyo and KD = 0.52 fo r Osaka were app l ied f o r the r e su l t s from the short-term r e l i a b i l i t y ana lys i s to obtain the long-term bas i s . Since the durat ion of load f ac to r i s def ined as KD = L 2 ( l°n9 - t e r m — \ bending a n a l y s i s , an adjustment span from the ^ short — term ' short-term r e l i a b i l i t y to the long-term r e l i a b i l i t y can be obtained as Llong-term = Lshort - t e r m x V^D a t t h e s a m e r e l i a b i l i t y l e v e l . F igure 22 shows the r e l a t i onsh ip between member span and corresponding 0 values fo r a l i g h t roof case and Tokyo snow load fo r the short-term (without DOL) and long-term (with DOL) cases. In t h i s case, the maximum ca lcu la ted span due to short-term bending was 8.64 m (Table 26) with a /?-value of 1.566. This same /3-value was obtained in the ana lys i s of the r e l i a b i l i t y of current const ruct ion summarized in Table 23. Because the governing f ac to r in the example was d e f l e c t i o n , the governing span was then reduced to 5.65. At t h i s span the /?-value i s found to be : 0 = 3.01 fo r the short-term bas is and 0 = 2.68 fo r the long-term bas i s . S i m i l a r l y , d i f f e r e n t member s i z e s , grades and spac ing; snow loads of d i f f e r e n t geographic l o ca t i ons ; and d i f f e r e n t roo f ing mater ia l commonly used in the se lec ted regions were incorporated to generate F igures 23, 24, 25, 26, and 27. Since the strength d i s t r i b u t i o n parameters of 2x6 were not a v a i l a b l e , those of 2x8 were t en ta t i v e l y used f o r t h i s ana l y s i s . 11.6 DISCUSSION The short-term r e l i a b i l i t y l eve l s fo r f l o o r j o i s t s in bending range are from 2.68 to 3.03. However the safety l eve l s fo r r a f t e r s range from 1.40 to 3.63 depending on l o c a t i o n , 7, nominal dead load and nominal snow load r a t i o . In heavy snow area i e . , Sapporo and N i i ga t a , they range from 2.67 to 3.63. In l i g h t snow areas i e . , Tokyo and Osaka, i f r a f t e r spans are determined by Dn, when Dn > Sn or 7 > 1.0, then r e l i a b i l i t y ind ices range from 1.63 to 3.35. However i f r a f t e r s are determined by Dn + Sn, when Sn > Dn or 7 < 1.0, r e l i a b i l i t y l eve l s drop to range from 1.38 to 2.40. This i s because al lowable s t resses fo r temporary load (twice as much as the a l lowable un i t s t ress f o r sustained load) are used fo r the snow load in l i g h t snow areas. The r e l i a b i l i t y l eve l s in bending f o r r a f t e r design in the l i g h t snow area are very low, i f they were considered i n d i v i d u a l l y . Since r a f t e r s i zes are determined not only by bending strength but shear strength and s t i f f n e s s of the lumber, the r e l i a b i l i t y l eve l s of ac tua l roof member in long-term bending were evaluated assuming KD = 0.8 fo r f i v e cases. From the f i v e cases, the minimum and mean-/? values were 2.35 and 2.78 r e spec t i v e l y , which i s qu i te acceptable fo r the bending strength l i m i t s ta tes . The values fo r 2x6 were not inves t iga ted . 12. DISCUSSION AND CONCLUSION Most timber s t ructures in Japan are of the so-ca l led t r a d i t i o n a l post and beam const ruct ion and u t i l i z e var ious t r a d i t i o n a l s i zes of sawn lumber. Introduced in to Japan in 1974, 2x4 wood frame const ruct ion makes up approximately 3% of t o t a l housing un i ts constructed in 1989. The current s t ruc tu ra l design method fo r a l l types of wood s t ructures i s based on VSD. I t i s h igh ly recommended that the design of 2x4 wood frame system be converted to the LSD format as a tes t case fo r development of LSD codes f o r a l l timber s t ruc tu res . It would be idea l f o r Japanese bu i l d i ng codes to be converted from the WSD to the LSD fo r a l l types of s t ruc tu res . Although intens ive in-grade tes t r e su l t s from CWC's research pro ject are ava i l ab l e fo r the dimension lumber used fo r 2x4 wood frame s t ruc tu res , cur rent l y there i s no standard fo r eva luat ing f u l l - s i z e lumber and very l i t t l e data i s a va i l ab l e fo r the lumber used fo r t r a d i t i o n a l post and beam st ructures in Japan. The ana lys i s and r e su l t s obtained in th i s study were e n t i r e l y based on an ana lys i s of lumber used f o r the 2x4 wood frame s t ruc tu res . However, due to the l im i t ed a v a i l a b i l i t y of re levant strength data fo r other wood s t ruc tu ra l systems, i t i s important to develop a standard tes t method to evaluate f u l l - s i z e lumber fo r the r e l i a b i l i t y ana l y s i s . Therefore , the development of LSD codes fo r a l l timber s t ructures requi res a tremendous amount of co l l abo ra t i ve work among designers and engineers in the fu tu re . In t h i s study, r e l i a b i l i t y l e ve l s were evaluated mainly in bending. The species se lec ted throughout th i s study was S-P-F which const i tu tes more than two th i rds of t o t a l lumber used fo r 2x4 wood frame const ruct ion in Japan. The four locat ions of sno(w load chosen fo r the ana lys i s represent t yp i c a l Japanese snow cond i t ions . The performance fac to rs fo r LSD equations have been ca l i b ra ted fo r 2x4 wood frame st ructures using d ra f t LSD S tee l Standard requirements fo r r e l i a b i l i t y l e v e l s . The outcome from th i s study shows that the 2x4 wood frame system y i e l d s performance fac to rs <p of 0.85 f o r bending and 0.9 f o r tension and compression at the target r e l i a b i l i t y of 8T = 2.5 which i s compatible with s tee l s t ruc tu res . Ratio of nominal dead to l i v e load 7, of 0.25 and the ac tua l dead to l i v e load r a t i o s ja were used in th i s ana l y s i s . The 7 = 0.25 was chosen fo r r e l i a b i l i t y s tudies of wooden s t ructures in Canada. The ac tua l 7Q value resu l ted in lower r e l i a b i l i t y l e ve l s fo r bending design in ce r ta in areas of Japan where snow accumulations are not as severe. However the r e l i a b i l i t y l eve l s fo r tension and compression d id not show s i g n i f i c a n t d i f f e rences with the choice of 7. Therefore , r e su l t s ind ica te that the ac tua l dead to l i v e load r a t i o ja should be used f o r the c a l i b r a t i o n s tud ies . S ize e f f e c t s are cur rent l y not considered in non-glulam timber s t ructures in Japan. To achieve a bet ter strength p red i c t i on of the non-glulam t imber, s i ze e f f e c t s should be incorporated into design procedure fo r 2x4 wood frame cons t ruc t ion . The recommended ^-values and the corresponding average /? and range of 8 were evaluated tak ing in to account s i z e e f f e c t s are summarized in table 27. Table 27. Recommended <f> and /^ -values 7 0 Min. 0 Mean p Max. 0 Bending 7 = 0.25 0.9 2.31 2.49 2.69 Actual 7 a 0.85 2.13 2.48 2.80 Tension 7 = 0.25 0.9 2.25 2.50 2.72 Actual 7 a 0.9 2.21 2.50 2.77 Compression 7 = 0.25 0.9 2.15 2.51 3.11 Actual 7 a 0.9 2.09 2.51 3.15 Based on the study of durat ion of load e f f e c t s , the r e su l t s from SPF Ql were c lose to those obtained from Hem-Fir f o r the Canadian study. The durat ion of load e f f e c t var ies with the choice of dead to l i v e load r a t i o . In the Canadian case, regard less of the l i v e load a f ac to r of Kj-) = 0.80 can be used where 7 i s less than or equal to 1.0. Where 7 i s greater than 5.0, a f ac to r of KD = 0.50 can be app l i ed . In th i s study, a simple snow load model was used fo r S-P-F durat ion of load ana l y s i s . Results were r e l a t i v e l y c lose that obtained in the more de ta i l ed Canadian s tud ies . The fac to rs KD at 7 = 0.25 and the actua l 7 a are summarized in Table 28 fo r four locat ions in Japan. The bending r e l i a b i l i t y l eve l s of current 2x4 wood frame fo r r a f t e r design were found to be qui te comparable with s t ee l s t ruc tu res . The r e l i a b i l i t y l e ve l s f o r bending strength in the l i g h t snow area are very low. In order to ca l cu l a te the ac tua l r e l i a b i l i t y l eve l s in Table 28. Duration of Load Factor KD for SPF Ql at 0T = 2.5 # £ ( 7 = 0.25) Actual 7 a KD(Actual 7 a ) Sapporo 0.70 7„ = 0.25 0.70 Niigata 0.78 7 a = 0-41 0.77 Tokyo 0.87 7 a = 1-22 0.81 Osaka 0.90 7 a = 4-40 0.57 r a f t e r s , we take the r e l i a b i l i t y l e ve l as a func t ion of span. The r a f t e r span i s determined by bending, shear and de f l e c t i on requirements. General ly speaking, the r a f t e r spans in the l i g h t snow area are governed by d e f l e c t i o n . Therefore , the ca l cu la ted bending spans are reduced to the governing de f l e c t i on spans and the r e l i a b i l i t y l eve l s fo r the strength l i m i t s tates are increased. The durat ion of load adjustment f ac to r KD = 0.8 fo r Sapporo, N i i ga ta and Tokyo and KD = 0.52 f o r Osaka were app l i ed to assess r e l i a b i l i t y under long-term load ing . The ac tua l minimum r e l i a b i l i t y l eve l s fo r the strength l i m i t s tates in long-term bending and short-term bending were summarized in Table 29. Table 30 compares r a f t e r spans using the new LSD equations vs . the current design procedures and shows the corresponding long-term r e l i a b i l i t y l e v e l s . F ive d i f f e r e n t condi t ions and three s i ze combinations were used in the comparison. The r e su l t s from the new LSD equations (using <j>0 - 0.85 and the ac tua l ja) show cons is tent r e l i a b i l i t y l eve l s above 2.5. The span values from the new LSD equations do not deviate too much from the current design spans. Only when the r e l i a b i l i t y l e ve l goes below 2.5 in the current design Table 29. Reliability Level P in Current 2x4 Wood Frame Structure Short-Term Bending Final Long-Term Bending Min. P Max. p Min. P 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 method, w i l l we witness a decrease in span. The table shows the LSD method provides more cons is tent r e l i a b i l i t y l eve l s than the current design method where the range of /?-values var ies cons iderably . This study i s ca r r i ed out mainly in bending with the load combination of dead plus occupancy load and dead plus snow load using S-P-F strength data . Therefore fu r ther s tudies w i l l be required in areas such as load combinations with wind and earthquake load and fo r other species and other strength l i m i t states in order to develop a complete LSD code. For example, Japanese s t ruc tu ra l design i s based on s ing le members and design proper t ies are not adjusted by system modi f i ca t ion f a c t o r s . Although system modi f i ca t ion f ac to rs were not considered in th i s study, and probably not app l i cab le in the t r a d i t i o n a l post and beam st ructures (due to the extens ive ly long spacing between members), they should be considered when c a l c u l a t i n g the r e l i a b i l i t y l eve l s in s t ructures made up of r e p e t i t i v e s ing le members such as the 2x4 wood frame system. By incorporat ing these modi f i ca t ion fac to rs the safety l e ve l s P, would represent more c l ose l y ac tua l behavior and al low fo r more e f f i c i e n t use of mater ia ls [3 ] . Table 30. Rafter Span Comparison Using Current and New LSD Design Equation Tokyo, Light Roofing, Spacing=455mm 2x4 2x8 2x10 unit: m Grade Current New Current New Current New SS D-Span 3.10 3.18 5.65 5.75 6.72 6.85 B-Span 4.26 3.19 8.64 5.71 10.82 6.94 Span 3.10 3.18 5.65 5.71 6.72 6.85 P 3.14 3.05 2.68 2.63 2.74 2.69 Sapporo, Light Roofing, Spacing=303mm 2x4 2x8 2x10 unit: m Grade Current New Current New Current New No.2 D-Span 1.75 1.84 3.61 3.83 4.43 4.59 B-Span 1.59 1.81 3.26 3.24 4.14 3.95 Span 1.59 1.81 3.26 3.24 4.14 3.95 P 3.09 2.66 2.65 2.66 2.63 2.81 Niigata, Heavy Roofing, Spacing=455mm 2x4 2x8 2x10 unit: m Grade Current New Current New Current New No.2 D-Span 1.68 1.73 3.47 3.61 4.30 4.38 B-Span 1.50 1.73 3.08 3.10 3.90 3.77 Span 1.50 1.73 3.08 3.10 3.90 3.77 P 3.08 2.59 2.63 2.61 2.60 2.72 Tokyo, Light Roofing, Spacing=455 2x4 2x8 2x10 unit: m Grade Current New Current New Current New No.2 D-Span 2.98 3.06 5.47 5.66 6.51 6.70 B-Span 3.52 2.76 7.13 4.94 8.94 6.00 Span 2.98 2.76 5.47 4.94 6.51 6.00 P 2.46 2.71 2.35 2.68 2.45 2.77 Osaka, Heavy Roofing, Spacing=455mm 2x4 2x8 2x10 unit: m Grade Current New Current New Current New No.2 D-Span 2.63 3.03 4.97 5.63 5.90 6.66 B-Span 2.93 2.49 5.90 4.46 7.34 5.42 Span 2.63 2.49 4.97 4.46 5.90 5.42 P 2.42 2.61 2.20 2.56 2.29 2.64 where D-Span ; Span Calculated by Deflection Requirement B-Span ; Span Calculated by Bending Requirement Span ; Minimum of Above Two Calculated Span P ; Bending (Long-Term) Reliability Level at Allowable Span REFERENCES Canadian Standard Assoc i a t i on . 1984. 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[19] American Society of Tes t ing and Ma te r i a l . 1990. Standard Test Methods f o r Mechanical Propert ies of Lumber and Wood-Base S t ruc tu ra l Ma te r i a l . ASTM D4761-88. ASTM, Ph i l ade lph i a , Pa. Fouquet, R.J .M., and Ba r re t t , J .D . 1989. Phys ica l and Mechanical Propert ies of Canadian V i s u a l l y Stress-Graded Lumber Es tab l i shed by In-Grade Tes t i ng . Counci l of Forest Industr ies of B r i t i s h Columbia, Vancouver, B.C. Pa lka , L.C. and Bar re t t , J .D . 1985. E f f e c t of Span-Depth Rat io on Apparent S t i f f n e s s of Dimension Lumber. Contact No. 02-50-10-019. For intek Canada Corp. Western Laboratory, Vancouver, B.C. A r ch i t e c tu ra l I ns t i tu te of Japan. 1981. Recommendations fo r Bu i ld ing Design - Load, ( in Japanese) A r ch i t e c tu ra l I ns t i tu te of Japan. 1986. Recommendations fo r Bu i ld ing Design - Snow Load, ( in Japanese) Fosch i , R.O. 1988. User ' s Manual: RELAN (REL i ab i l i t y ANa lys i s ) . Department of C i v i l Engineer ing, Un i ve rs i t y of B r i t i s h Columbia, Vancouver, B.C. Yao, Z .C. 1987. R e l i a b i l i t y of Structures with Load H is tory -Dependent Strength and an App l i ca t i on to Wood Members, M.A.Sc. Thes i s . Department of C i v i l Engineer ing, Un i ve rs i t y of B r i t i s h Columbia, Vancouver, B.C. 85 Table 1. Design Requirements of the Japanese Building Codes Allowable Unit Relative story Dlaplacement Angle Rigidity and Eccentricity Retained Horizontal Strength Remarks Stories of 2 or less, Total Floor Area of 500 maor less, Building Height of 13 m or less, and Eaves Height of 9 m or less N/A N/A N/A N/A Traditional Post and Beam Stories of 3 or more * N/A N/A N/A Effective Wall Length Building Standard Law Enforcement Order Article 46 Structure Total Floor Area of more than 500 m2 * N/A N/A N/A Building Height of more than 13 m or Eaves Height of More than 9 m Prohibited Building Standard Law Enforcement Order Article 129 2x4 Wood Frame Stories of 2 or less and Total Floor Area of 500 m2 or less 1) N/A N/A N/A Effective Wall Length Notification No.56 Structure 3 Stories or more or Total Floor Area of more than 500 m2 * N/A N/A N/A Effective Wall Length Notification No.56 Log House Maximum 2 Stories with Maxlmun Height of 8.5 m and Total Floor Area of 300 m2 N/A N/A N/A N/A Notification No.1126 Stories of 2 or less, Total Floor Area of 500 m2or 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 Building Height of 13 m Heavy Timber Total Floor Area of more than 500 m2 * * * N/A or less and Eaves Height of 9 m or less Structure Total Floor Area of more than 500 m2 * * * * Building Height of 31 m Building Height of more than 13 m or Eaves Height of more than 9 m * * * * or less Building Height of more than 31 m * * * * Special Structure N/A Building Standard Law Article 38 N/A ; 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 Kinds of stress Possible conditions regarding loads and external forces General cases In heavy snow areas designated by the Special Administrative Agency under the provision to Article 86 Paragraph 2 Remarks Stress due to sustained loads Normal time D + L D + L + S Stress due to temporary loads Snow season D + L + S D + L + S Storm D + L + W D + L + W 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 + 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 u X/Xn Vx Remarks D - 1.0 0.10 LS 1/8 8 0.36 0.40 sustained load LE 1 0.25 0.55 extraordinary load S 1 1/3 0.45 0.48 heavy snow area w 1 1 0.42 0.47 annual maxima E 1/3 0.42 0.80 /Resistance 1.10 0.15 ~ 0.20 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 ~1); A* duration of tenancy ( year ); X mean in variable X; 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 q A B A* B* (kg/m2)"1 (kg/m2) 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 Annual Snow Duration (days) 132 61 5 2 A Annual Snow Height (cm"1) 0.04677 0.05534 0.13291 0.38919 Gumbel Distribution B (cm) 83.92 32.66 6.52 0.023 50 Years Return Snow Height (cm) 167 103 36 10 Design Snow Load ( kg/m2 ) 351 216 72 20 Normalized 50 Years Return Snow Height A 7.8267 5.7091 4.7686 3.9111 Distribution Gumbel Distribution B 1.0013 1.0018 1.0021 1.0026 Normalized 8 Years Return Snow Height A 7.8267 5.7091 4.7686 3.9111 Distribution Gumbel Distribution B 0.7671 0.6808 0.6178 0.5340 Table 6. Nominal Design Dead, Occupancy and Snow Load Dead Load Floor Joists Tatami Mat 18 kgf/m* Plywood Sheathing (12 mm) 8 kgf/m2 Gypsum Board 15 kgf/m2 Joist (2x8 455mm spacing) 13 kgf/m2 Total 54 kgf/m* Rafters Light Roofing Material Light Roofing Material 20 kgf/m2 Plywood Sheathing (9 mm) 6 kgf/m2 Rafter (2x8 455mm spacing) 13 kgf/m2 Total 39 kgf/m* Heavy Roofing Material Heavy Roofing Material (Clay Tile) 60 kgf/m2 Plywood Sheathing (9 mm) 8 kgf/m2 Rafter (2x8 303mm spacing) 20 kgf/m2 Total 88 kgf/m* Design Occupancy Load Residential Type 180 kgf/m* Design Snow Load Sapporo 350 kgf/m* Niigata 216 kgf/m2 Tokyo 72 kgf/m2 Osaka 20 kgf/m2 Table 6a. Nominal Dead to Live Design Load Ratio 7 = Dn/Ln 0.30 7 = Dn I Sn Light Roofing Heavy Roofing ( 7 J Sapporo 0.11 0.25 Niigata 0.18 0.41 Tokyo 0.54 1.22 Osaka 1.95 4.40 Table 7. Bending Performance Factors for S-P-F (^ -values Corresponding Target /3-values) Sapporo £=3.0 £=2.5 £=2.0 7=0.25 7„=0.25 7=0.25 7„=0.25 7=0.25 7„=0.25 2x4 SS 0.77 - 1.01 1.28 -No2 0.72 - 0.98 - 1.28 -2x8 SS 0.65 - 0.90 - 1.20 -No2 0.67 - 0.94 - 1.24 -2x10 SS 0.68 - 0.94 - 1.24 -No2 0.81 - 1.04 - 1.30 -Average 0.72 - 0.97 - 1.26 -Niigata £=3.0 £=2.5 £=2.0 7=0.25 7„=0.41 7=0.25 7„=0.41 7=0.25 7„=0.41 2x4 SS 0.76 0.74 1.00 0.98 1.26 1.23 No2 0.71 0.70 0.97 0.95 1.26 1.23 2x8 SS 0.64 0.62 0.89 0.87 1.19 1.16 No2 0.67 0.65 0.93 0.90 1.23 1.19 2x10 SS 0.67 0.65 0.93 0.90 1.22 1.19 No2 0.80 0.78 1.03 1.00 1.28 1.25 Average 0.71 0.69 0.96 0.93 1.24 1.21 Tokyo £=3.0 £=2.5 £=2.0 7=0.25 7„=1.22 7=0.25 7„=1.22 7=0.25 7„=1.22 2x4 SS 0.76 0.69 0.99 0.90 1.25 1.14 No2 0.71 0.64 0.96 0.87 1.25 1.13 2x8 SS 0.63 0.57 0.88 0.80 1.17 1.07 No2 0.66 0.59 0.92 0.83 1.21 1.10 2x10 SS 0.66 0.60 0.92 0.83 1.21 1.10 No2 0.79 0.72 1.02 0.93 1.27 1.15 Average 0.70 0.64 0.95 0.86 1.23 1.12 Osaka £=3.0 £=2.5 £=2.0 7=0.25 7„=4.40 7=0.25 7„=4.40 7=0.25 7„=4.40 2x4 SS 0.75 0.63 0.98 0.82 1.24 1.04 No2 0.70 0.58 0.95 0.80 1.24 1.04 2x8 SS 0.62 0.53 0.87 0.73 1.16 0.97 No2 0.65 0.55 0.90 0.76 1.20 1.01 2x10 SS 0.65 0.55 0.90 0.76 1.19 1.00 No2 0.78 0.66 1.01 0.85 1.25 1.05 Average 0.69 0.58 0.93 0.79 1.21 1.02 Occupancy £=3.0 £=2.5 £=2.0 7=0.25 7„=0.28 7=0.25 7„=0.28 7=0.25 7„=0.28 2x4 SS 0.73 0.73 0.96 0.95 1.21 1.20 No2 0.69 0.69 0.93 0.92 1.21 1.20 2x8 SS 0.61 0.61 0.85 0.85 1.13. 1.13 No2 0.63 0.63 0.88 0.88 1.17 1.17 2x10 SS 0.64 0.64 0.88 0.88 1.17 1.16 No2 0.76 0.76 0.98 0.98 1.22 1.22 Average 0.68 0.68 0.91 0.91 1.19 1.18 Total Average 0.70 0.66 0.94 0.89 1.22 1.16 Table 8. Mean /?-values Corresponding to Given 4> in Bending Performance Factor <j> Mean j3 Mean Q 7=0.25 Actual ja 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 Table 9. Size Factor and Standard Strength R0 for Bending P - 2.5 at , 4>0 = 0.9 unit : MPa 7 Size Factor Grade R0 ^0.05 0.25 4.495 SS 24.358 23.050 No.2 17.666 16.890 Actual1) 4.483 SS 22.744 23.050 No.2 16.491 16.890 1) see Table 6a 94 Table 10a. Modified ^ -values in Bending at 0O=O.9 and 0O=O.85 (7=0.25) Size Grade Sapporo Niigata Tokyo Osaka Occupancy 00 0.9 0.85 0.9 0.85 0.9 0.85 0.9 0.85 0.9 0.85 2x4 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 2x8 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 2x10 SS 2.49 2.58 2.47 2.56 2.45 2.54 2.43 2.52 2.39 2.49 No.2 2.69 2.80 2.66 2.77 2.64 2.75 2.61 2.73 2.57 2.69 0O=O.9 Maximum=2.69 Minimum=2.31 Average J=2.49 0O=O.85 Maximum=2.80 Minimum=2.42 Average 5=2.59 Table 10b. Modified /9-values in Bending at 0O=O.85 and 0O=O.8O (Actual ya) Size Grade Sapporo Niigata Tokyo Osaka Occupancy <t>Q 0.85 0.8 0.85 0.8 0.85 0.8 0.85 0.8 0.85 0.8 2x4 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 2x8 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 2x10 SS 2.58 2.68 2.52 2.62 2.38 2.48 2.23 2.33 2.48 2.58 No.2 2.80 2.92 2.72 2.82 2.56 2.68 2.37 2.50 2.68 2.80 00=0.85 Maximum=2.80 Minimum=2.13 Average 5=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 0=2.0 7=0.25 7=0.25 7=0.25 7=0.25 7=0.25 7=0.25 2x4 SS 0.64 - 0.91 - 1.16 -No2 0.64 - 0.90 - 1.20 -2x8 SS 0.81 - 1.02 - 1.25 -No2 0.80 - 1.03 - 1.28 -2x10 SS 0.80 - 1.02 - 1.26 -No2 0.71 - 0.95 - 1.23 -Average 0.73 - 0.97 - 1.23 -Niigata 0=3.0 0=2.5 0=2.0 7=0.25 7=0.41 7=0.25 7=0.41 7=0.25 7=0.41 2x4 SS 0.65 0.64 0.87 0.86 1.12 1.10 No2 0.61 0.64 0.87 0.85 1.16 1.14 2x8 SS 0.77 0.76 0.97 0.96 1.19 1.17 No2 0.76 0.75 0.98 0.97 1.22 1.21 2x10 SS 0.76 0.75 0.97 0.96 1.20 1.19 No2 0.68 0.68 0.92 0.90 1.18 1.16 Average 0.71 0.70 0.93 0.92 1.18 1.16 Tokyo 0=3.0 0=2.5 0=2.0 7=0.25 7=1.22 7=0.25 7=1.22 7=0.25 7=1.22 2x4 SS 0.63 0.60 0.84 0.80 1.08 1.03 No2 0.59 0.57 0.84 0.80 1.13 1.07 2x8 SS 0.73 0.72 0.93 0.91 1.14 1.10 No2 0.73 0.71 0.94 0.91 1.18 1.13 2x10 SS 0.73 0.71 0.93 0.90 1.15 1.11 No2 0.66 0.63 0.88 0.85 1.14 1.09 Average 0.68 0.66 0.89 0.86 1.14 1.09 Osaka 0=3.0 0=2.5 0=2.0 7=0.25 7=4.40 7=0.25 7=4.40 7=0.25 7=4.40 2x4 SS 0.59 0.56 0.80 0.75 1.03 0.96 No2 0.57 0.53 0.80 0.74 1.08 0.99 2x8 SS 0.69 0.67 0.87 0.84 1.08 1.03 No2 0.69 0.66 0.89 0.85 1.12 1.05 2x10 SS 0.69 0.66 0.88 0.84 1.09 1.04 No2 0.62 0.59 0.84 0.78 1.09 1.01 Average 0.64 0.61 0.85 0.80 1.08 1.01 Total Average 0.69 0.68 0.91 0.89 1.16 1.12 Table 12. Mean /3-values Corresponding to Given <j> in Tension Performance Factor <j> Mean /? Mean /? 7=0.25 Actual ja 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 Table 13. Size Factor and Standard Strength R0 for Tension (3 = 2.5 at <j>Q = 0.9 unit : MPa 7 Size Factor Grade RQ •^0.05 0.25 8.864 SS 13.628 12.27 • No.2 8.8125 8.320 Actual l ) 9.543 SS 13.317 12.27 No.2 8.5487 8.320 1) see Table 6a Table 14a. Modified /3-values in Tension at 0O=O.9 and 0O=O.85 (7=0.25) Size Grade Sapporo Niigata Tokyo Osaka ^0 0.9 0.85 0.9 0.85 0.9 0.85 0.9 0.85 2x4 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 2x8 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 2x10 SS 2.62 2.74 2.51 2.63 2.42 2.54 2.29 2.41 No.2 2.63 2.73 2.55 2.65 2.49 2.59 2.40 2.50 0O=O.9 Maximum=2.72 Minimum=2.25 Average=2.50 0O=O.85 Maximum=2.83 Minimum=2.39 Average ;=2.61 Table 14b. Modified /3-values in Tension at 0O=O.9 and 0o=O.85(Actual ja) Size Grade Sapporo Niigata Tokyo Osaka 00 0.9 0.85 0.9 0.85 0.9 0.85 0.9 0.85 2x4 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 2x8 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 2x10 SS 2.66 2.78 2.53 2.65 2.39 2.52 2.22 2.36 No.2 2.68 2.77 2.58 2.68 2.46 2.56 2.32 2.43 00=0.9 Maximum=2.77 Minimum=2.21 Averag< j=2.50 00=0.85 Maximum=2.8J i 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 0=2.0 7=0.25 7=0.25 7=0.25 7=0.25 7=0.25 7=0.25 2x4 SS 0.90 - 1.08 - 1.26 -No2 0.72 - 0.94 - 1.17 -2x8 SS 0.86 - 1.05 - 1.24 -No2 0.90 - 1.05 - 1.23 -2x10 SS 0.90 - 1.06 - 1.23 -No2 0.79 - 1.01 - 1.24 -Average 0.84 - 1.03 - 1.23 -Niigata /?=3.0 0=2.5 0=2.0 7=0.25 7=0.41 7=0.25 7=0.41 7=0.25 7=0.41 2x4 SS 0.84 0.84 1.01 1.00 1.18 1.18 No2 0.69 0.68 0.89 0.88 1.12 1.10 2x8 SS 0.81 0.80 0.98 0.98 1.17 1.16 No2 0.81 0.81 0.98 0.98 1.16 1.15 2x10 SS 0.83 - 0.84 0.99 0.99 1.15 1.15 No2 0.75 0.75 0.96 0.95 1.18 1.17 Average 0.79 0.79 0.97 0.96 1.16 1.15 Tokyo 0=3.0 0=2.5 0=2.0 7=0.25 7=1.22 7=0.25 7=1.22 7=0.25 7=1.22 2x4 SS 0.79 0.80 0.95 0.96 1.13 1.11 No2 0.66 0.64 0.86 0.83 1.08 1.03 2x8 SS 0.77 0.76 0.94 0.93 1.12 1.10 No2 0.77 0.77 0.93 0.93 1.10 1.09 2x10 SS 0.78 0.80 0.93 0.95 1.09 1.09 No2 0.72 0.70 0.92 0.89 1.14 1.10 Average 0.75 0.75 0.92 0.92 1.11 1.09 Osaka 0=3.0 0=2.5 0=2.0 7=0.25 7=4.40 7=0.25 7=4.40 7=0.25 7=4.40 2x4 SS 0.73 0.76 0.74 0.90 0.91 1.05 No2 0.62 0.60 0.71 0.77 0.88 0.96 2x8 SS 0.71 0.72 0.75 0.87 0.91 1.03 No2 0.71 0.73 0.73 0.87 0.89 1.02 2x10 SS 0.72 0.76 0.75 0.89 0.91 1.03 No2 0.68 0.66 0.72 0.83 0.89 1.02 Average 0.70 0.71 0.73 0.86 0.90 1.02 Total Average 0.77 0.77 0.95 0.94 1.14 1.12 Table 16. Mean /?-values Corresponding to Given <j> in Compression Performance Factor <fi Mean /? Mean ft 7=0.25 Actual ya 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 Table 17. Size Factor and Standard Strength R0 for Compression /? = 2.5 at , <j>0 = 0.9 unit : MPa 7 Size Factor Grade RQ •^0.05 0.25 8.312 SS 21.676 19.32 No.2 17.232 18.20 Actual x ) 8.675 SS 21.784 19.32 No.2 16.967 18.20 1) see Table 6a Table 18a. Modified /?-values in Compression at 0O=O.9 and 0O=O.85 (7=0.25) Size Grade Sapporo Niigata Tokyo Osaka <t>0 0.9 0.85 0.9 0.85 0.9 0.85 0.9 0.85 2x4 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 2x8 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 2x10 SS 2.78 2.95 2.55 2.73 2.37 2.55 2.15 2.32 No.2 2.51 2.64 2.40 2.53 2.30 2.43 2.17 2.30 0O=O.9 Maximum=3.11 Minimum=2.15 Average j=2.51 0o=O.85 Maximum=3.25 Minimum=2.30 Average ;=2.65 Table 18b. Modified /?-values in Compression at 0O=O.9 and 0O=O.85 (Actual ja) Size Grade Sapporo Niigata Tokyo Osaka <t>Q 0.9 0.85 0.9 0.85 0.9 0.85 0.9 0.85 2x4 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 2x8 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 2x10 SS 2.76 2.93 2.53 2.71 2.38 2.57 2.18 2.38 No.2 2.54 2.66 2.40 2.53 2.26 2.40 2.09 2.23 00=0.9 Maximum=3.15 Minimum=2.09 Average ;=2.51 00=0.85 Maximum=3.29 Minimum=2.23 Average 2=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 0=1.0 7=0.25 7=0.25 7=0.25 7=0.25 7=0.25 7=0.25 2x4 SS 0.63 - 0.75 - 0.86 -No2 0.56 - 0.69 - 0.82 -2x8 SS 0.64 - 0.75 - 0.87 -No2 0.59 - 0.71 - 0.84 -2x10 SS 0.64 - 0.76 - 0.87 -No2 0.58 - 0.71 - 0.83 -Average 0.61 - 0.73 - 0.85 -Niigata 0=2.0 0=1.5 0=1.0 7=0.25 7=0.41 7=0.25 7=0.41 7=0.25 7=0.41 2x4 SS 0.63 0.64 0.75 0.76 0.88 0.88 No2 0.57 0.57 0.70 0.71 0.85 0.85 2x8 SS 0.64 0.65 0.76 0.76 0.89 0.89 No2 0.59 0.60 0.73 0.73 0.86 0.86 2x10 SS 0.64 0.65 0.76 0.77 0.89 0.89 No2 0.58 0.59 0.72 0.72 0.86 0.86 Average 0.61 0.62 0.74 0.74 0.87 0.87 Tokyo 0=2.0 0=1.5 0=1.0 7=0.25 7=1.22 7=0.25 7=1.22 7=0.25 7=1.22 2x4 SS 0.62 0.65 0.75 0.77 0.89 0.88 No2 0.56 0.58 0.71 0.71 0.86 0.84 2x8 SS 0.63 0.66 0.76 0.77 0.90 0.89 No2 0.59 0.61 0.73 0.73 0.88 0.86 2x10 SS 0.63 0.66 0.76 0.78 0.90 0.89 No2 0.58 0.60 0.72 0.72 0.87 0.85 Average 0.60 0.63 0.74 0.75 0.88 0.87 Osaka 0=2.0 0=1.5 0=1.0 7=0.25 7=4.40 7=0.25 7=4.40 7=0.25 7=4.40 2x4 SS 0.60 0.64 0.74 0.75 0.91 0.86 No2 0.56 0.56 0.71 0.69 0.88 0.86 2x8 SS 0.61 0.65 0.75 0.76 0.91 0.86 No2 0.58 0.59 0.73 0.71 0.89 0.83 2x10 SS 0.61 0.65 0.75 0.76 0.91 0.87 No2 0.57 0.58 0.72 0.71 0.89 0.83 Average 0.59 0.61 0.73 0.73 0.90 0.85 Occupancy 0=2.0 0=1.5 0=1.0 7=0.25 7=0.28 7=0.25 7=0.28 7=0.25 7=0.28 2x4 SS 0.63 0.63 0.74 0.74 0.85 0.85 No2 0.56 0.56 0.68 0.68 0.81 0.81 2x8 SS 0.64 0.64 0.75 0.75 0.86 0.86 No2 0.59 0.59 0.71 0.71 0.83 0.83 2x10 SS 0.65 0.65 0.75 0.75 0.86 0.86 No2 0.58 0.58 0.70 0.70 0.82 0.82 Average 0.61 0.61 0.72 0.72 0.84 0.84 Total Average 0.60 0.61 0.73 0.73 0.87 0.86 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 n <r0 Mean COV Mean COV Mean COV Mean COV SPF Q l 77.392 0.174 2.810 xio"6 0.057 1.162 0.231 0.420 0.038 SPF Q2 158.656 0.009 7.525 xio' 7 0.042 1.285 0.170 0.365 0.562 Table 21. Duration of Load Effects for S-P-F Ql Sapporo 0 = 3.0 0 = 2.5 =2.0 7 <f> KD <f> KD «D 0.25 No-DOL 0.96 1.10 1.25 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 Niigata 0 = 3.0 0 = 2.5 0 =2.0 7 <t> KD <t> Kn 4> KD 0.25 No-DOL 0.87 1.01 1.16 DOL 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 0.41 No-DOL 0.88 1.01 1.16 DOL 0.70 0.80 0.78 . 0.77 0.89 0.77 Tokyo 0 = 3.0 0 = 2.5 0 =2.0 7 KD KD <!> KD 0.25 No-DOL 0.80 0.95 l . n 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 1.22 No-DOL 0.86 0.98 1.11 DOL 0.72 0.84 0.79 0.81 0.90 0.81 Osaka 0 = 3.0 0 = 2.5 0 =2.0 7 <t> KD 4> KD 4> KD 0.25 No-DOL 0.74 0.87 1.03 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 4.40 No-DOL 0.84 0.94 1.05 DOL 0.48 0.57 0.54 0.57 0.60 0.57 Table 22. Duration of Load Effects for S-P-F Q2 Sapporo 0 = 3.0 0 = 2.5 0 =2.0 7 <P KD <f> KD KD 0.25 No-DOL 0.91 1.07 1.24 DOL 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 Niigata 0 = 3.0 0 = 2.5 0 =2.0 7 <P KD 4> KD <P KD 0.25 No-DOL 0.84 0.99 1.17 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 0.41 No-DOL 0.84 0.99 1.16 DOL 0.57 0.68 0.67 0.68 0.78 0.67 Tokyo 0 = 3.0 0 = 2.5 0 =2.0 7 4> KD <t> KD 4> KD 0.25 No-DOL 0.78 0.94 1.12 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 1.22 No-DOL 0.81 0.95 1.10 DOL 0.39 0.48 0.46 0.48 0.54 0.49 Osaka 0 = 3.0 P = 2.5 0 =2.0 7 <t> KD 4> KD <P KD 0.25 No-DOL 0.73 0.88 1.06 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 4.40 No-DOL 0.78 0.90 1.03 DOL 0.25 0.32 0.30 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 7 P 2x8 SS 455 mm 0.30 2.778 303 0.34 2.782 No2 405 0.30 2.938 303 0.34 2.942 2x10 SS 455 0.33 2.680 303 0.37 2.686 No2 455 0.33 3.021 303 0.37 3.028 Rafters ( light weight roofing material ) Sapporo Niigata Tokyo Osaka Size Grade Spacing 7 P 7 P 7 P 7 P 2x4 SS 455 mm 0.10 3.608 0.17 3.542 0.48 2.382 1.74 2.921 303 0.12 3.610 0.19 3.547 0.54 2.396* 1.96 3.003 No2 405 0.10 3.387 0.17 3.332 0.48 2.258 1.74 2.476 303 0.12 3.389 0.19 3.337 0.54 2.269 1.96 2.821 2x8 SS 455 0.12 2.817 0.19 2.765 0.54 1.566 1.96 2.189 303 0.14 2.820 0.22 2.771 0.64 1.580 2.29 2.286 No2 455 0.12 2.976 0.19 2.925 0.54 1.780 1.96 2.373 303 0.14 2.978 0.22 2.930 0.64 1.795 2.29 2.466 2x10 SS 455 0.13 2.720 0.21 2.666* 0.61 1.384* 2.18 2.121 303 0.16 2.723 0.25 2.674 0.73 1.402 2.62 2.232 No2 455 0.13 3.051 0.21 2.973 0.61 1.456 2.18 2.360 303 0.16 3.056 0.25 2.985 0.73 1.482 2.62 2.493 Rafters ( Heavy weight roofing material ) Sapporo Niigata Tokyo Osaka Size Grade Spacing 7 P 7 P 7 P 7 P 2x4 SS 455 mm 0.22 3.626 0.36 3.581 1.07 2.532 3.84 3.335 303 0.23 3.628* 0.38 3.585 1.13 2.588 4.06 3.354* No2 405 0.22 3.402 0.36 3.365 1.07 2.387 3.84 3.127 303 0.23 3.404 0.38 3.368 1.13 2.438 4.06 3.145 2x8 SS 455 0.23 2.832 0.38 2.796 1.13 1.753 4.06 2.547 303 0.25 2.834 0.41 2.800 1.22 1.831 4.39 2.573 No2 455 0.23 2.990 0.38 2.955 1.13 1.959 4.06 2.715 303 0.25 2.992 0.41 2.959 1.22 2.033 4.39 2.740 2x10 SS 455 0.24 2.735 0.40 2.698 1.19 1.634* 4.28 2.450 303 0.27 2.737 0.44 2.704 1.31 1.735 4.72 2.483 No2 455 0.24 3.073 0.40 3.020 1.19 1.775 4.28 2.751 303 0.27 3.077 0.44 3.028 1.31 1.899 4.72 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 Rafter Beam Header L/300 and 1.0cm L/150 and 2.0 cm Table 25. Serviceability Reliability Levels for Current 2x4 Wood Frame Structures Floor Joist Size Grade Spacing 7 0 2x8 SS 455 mm 0.30 1.143 303 0.34 1.167 No2 405 0.30 1.200 303 0.34 1.219 2x10 SS 455 0.33 1.041 303 0.37 1.073 No2 455 0.33 0.995 303 0.37 1.020 Rafters ( light weight roofing material ) Sapporo Niigata Tokyo Osaka Size Grade Spacing 7 0 7 0 7 0 7 0 2x4 SS 455 mm 0.10 1.210 0.17 1.389 0.48 1.893 1.74 2.325 303 0.12 1.228 0.19 1.423 0.54 1.974 1.96 2.329 No2 405 0.10 1.011 0.17 1.165 0.48 1.619 1.74 2.167 303 0.12 1.027 0.19 1.194 0.54 1.672 1.96 2.182 2x8 SS 455 0.12 1.085 0.19 1.296 0.54 1.857 1.96 2.255 303 0.14 1.114 0.22 1.348 0.64 1.929 2.29 2.260 No2 455 0.12 1.153 0.19 1.328 0.54 1.818 1.96 2.273 303 0.14 1.177 0.22 1.372 0.64 1.886 2.29 2.283 2x10 SS 455 0.13 0.985 0.21 1.222 0.61 1.824 2.18 2.200 303 0.16 1.024 0.25 1.291 0.73 1.907 2.62 2.205 No2 455 0.13 0.951 0.21 1.147 0.61 1.681 2.18 2.155 303 0.16 0.983 0.25 1.205 0.73 1.764 2.62 2.169 Rafters ( Heavy weight roofing material ) Sapporo Niigata Tokyo Osaka Size Grade Spacing 7 0 7 0 7 0 7 0 2x4 SS 455 mm 0.22 1.363 0.36 1.651 1.07 2.197 3.84 2.334 303 0.23 1.377 0.38 1.674 1.13 2.211 4.06 2.334 No2 405 0.22 1.140 0.36 1.394 1.07 1.946 3.84 2.227 303 0.23 1.153 0.38 1.414 1.13 1.964 4.06 2.228 2x8 SS 455 0.23 1.246 0.38 1.566 1.13 2.131 4.06 2.265 303 0.25 1.270 0.41 1.601 1.22 2.150 4.39 2.265 No2 455 0.23 1.286 0.38 1.557 1.13 2.098 4.06 2.300 303 0.25 1.305 0.41 1.587 1.22 2.120 4.39 2.301 2x10 SS 455 0.24 1.149 0.40 1.493 1.19 2.072 4.28 2.212 303 0.27 1.181 0.44 1.539 1.31 2.094 4.72 2.212 No2 455 0.24 1.085 0.40 1.377 1.19 1.951 4.28 2.190 303 0.27 1.111 0.44 1.418 1.31 1.979 4.72 2.192 Table 26. Typical Rafter Span Tokyo, Light Roofing, Spacing=455mm Grade 2x4 2x6 2x8 2x10 unit SS D-Span 310.81 462.75 565.13 672.46 cm B-Span 426.47 664.39 864.58 1082.9 cm S-Span 1115.5 1720.3 2215.5 2722.5 cm Span 3.10 4.62 5.65 6.72 m Sapporo, Light Roofing, Spacing: =303mm Grade 2x4 2x6 2x8 2x10 unit No.2 D-Span 175.72 275.74 361.35 443.51 cm B-Span 159.36 249.76 326.92 414.09 cm S-Span 228.45 356.55 464.59 583.83 cm Span 1.59 2.49 3.26 4.14 m Niigata, Heavy Roofing, Spacing: =455mm Grade 2x4 2x6 2x8 2x10 unit No.2 D-Span 168.79 264.97 347.32 430.73 cm B-Span 150.02 235.27 308.06 390.56 cm S-Span 202.47 316.38 412.54 519.38 cm Span 1.50 2.35 3.08 3.90 m Tokyo, Light Roofing, Spacing=' 455 Grade 2x4 2x6 2x8 2x10 unit No.2 D-Span 298.11 448.50 547.72 651.74 cm B-Span 352.14 548.60 713.90 894.20 cm S-Span 1115.5 1720.3 2215.5 2722.5 cm Span 2.98 4.48 5.47 6.51 m Osaka, Heavy Roofing, Spacing= :455mm Grade 2x4 2x6 2x8 2x10 unit No.2 D-Span 263.91 408.52 497.98 590.50 cm B-Span 293.31 455.16 590.11 734.04 cm S-Span 773.89 1184.2 1513.8 1834.6 cm Span 2.63 4.08 4.97 5.90 m where D-Span ; Span Calculated by Allowable Deflection B-Span ; Span Calculated by Allowable Bending Unit Stress S-Span ; Span Calculated by Allowable Shearing Unit Stress Span ; Minimum of Above Three Calculated Span Figure 1. Beta vs Phi for Japanese Steel Code LOAD L E V E L X (D SUSTAINED LOAD T IME LOAD L E V E L X (2) EXTRAORDINARY LOAD LOAD L E V E L X (1)*X (2) Maximum TOTAL OCCUPANCY LOAD T IME T I M E 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/m2) SIMULATION UPPER 10% DATAFIT Figure 3. Japanese Occupancy Load (50-Year Return) 140 SNOW HEIGHT (cm) Figure 4. Snow Model in Sapporo 140 120 100 -SNOW HEIGHT (cm) Figure 5. Snow Model in Tokyo CHINA KOREA ASD : 2 days NSH : 10 cm Figure 6. Location and Snow Data SAPPOR ASD : 132 days NSH : 167 cm JAPAN OKYO 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 0.5 1 1.5 2 GAMMA • Dn / Sn — SAPPORO Cp =0.8 -B- TOKYO ()9 =0.8 SAPPOROC/J =0.9 TOKYO CP =0.9 -5K-2.5 3 SAPPORO CP =1.0 TOKYO <P -1.0 Figure 7. Beta vs Gamma (2x8, No.2) 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 8. Bending Beta vs Phi in Tokyo (2x8, No.2, All Data) CUMULATIVE PROBABILITY 0 2 4 6 8 10 12 BENDING STRENGTH (psi) (Thousands) TEST DATA LOWER 15% DATAFIT - *- 100% DATAFIT Figure 9. 2P Weibull Datafit (1) (2x8, No.2, CWC Test Data) CUMULATIVE PROBABILITY 0.25 0.15 0.05 -1 1.5 2 2.5 3 3.5 4 BENDING STRENGTH (psi) (Thousands) 4.5 TEST DATA LOWER 15% DATAFIT -*~ 100% DATAFIT Figure 10. 2P Weibull Datafit (2) (2x8, No.2, CWC Test Data) to o BETA 4 2 -1 -B-2P-WEIBULL 3P-WEIBULL LOGNORMAL NORMAL J L J L J L 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 11. Bending Beta vs Phi in Tokyo (2x8, No.2, 15% Truncation) BETA 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 PHI Figure 12. Bending Beta vs Phi (SS-No.2) (Tokyo, 2x10, 15% Truncation) 1.4 1.5 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 BETA 3.5 2.5 1.5 SAPPORO NIIGATA TOKYO - B - OSAKA OCCUPANCY 1 0.4 0.5 0.6 0.7 0.8 0.9 PHI 1.1 1.2 1.3 1.4 Figure 14. Bending Beta vs Phi (All Cases) BETA 3.5 2.5 1.5 1 SAPPORO - f - NIIGATA TOKYO - s - OSAKA OCCUPANCY 1 0.4 0.5 0.6 0.7 0.8 0.9 PHI Figure 15. Bending Beta vs Phi (All Cases, Actual Gamma) 1.1 1.2 1.3 1.4 BETA 3.5 2.5 1.5 1 SAPPORO NIIGATA TOKYO - B - OSAKA 0.4 0.5 0.6 0.7 0.8 0.9 PHI Figure 16. Beta vs Phi in Tension (All Cases) 1.1 1.2 1.3 1.4 to BETA 3.5 I 3 -2.5 -2 -1.5 -SAPPORO - f - NIIGATA - * - TOKYO - B - OSAKA 0.4 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 LOAD T IME D(t) DEAD LOAD T IME a(t) _n_ Jl n . S T R E S S T IME Figure 18. Load and Stress Model for DOL to OO BETA 4 i 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 19. DOL in Osaka (SPF Q1, Gamma = 0.25) 1 K D Factor 0 . 8 0 .6 0 . 4 0 .2 x J_L 0.1 10 GAMMA 1 0 0 1 0 0 0 Figure 21. Recomended Relationship between GAMMA and K D Factor BETA 3 . 5 I 3 -2 .5 -2 -1.5 -4 5 5 6 5 6 7 8 8 6 4 9 10 11 12 SPAN (m) Figure 22. Bending Beta vs Span (Tokyo, 2x8, SS, Light Roof) BETA SPAN (m) 2 x 4 2 x 6 - * - 2 x 8 2 x 1 0 Figure 23. Long-Term Bending Beta vs Span (Tokyo 1, SS, 455mm, Light Roof) CO CO BETA .8 5 SPAN (m) 2 x 4 2 x 6 - ^ 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 2.35 2 2 .5 SPAN (m) 3.08 3 3 . 5 3.90 4 . 5 2 x 4 2 x 6 2 x 8 2 x 1 0 Figure 25. Long-Term Bending Beta vs Span (Niigata, No.2, 455mm, Heavy Roof) CO BETA SPAN (m) 2 x 4 2 x 6 2 x 8 2 x 1 0 Figure 26. Long-Term Bending Beta vs Span (Tokyo 2, No.2, 455mm, Light Roof) BETA 6 . 5 SPAN (m) 2 x 4 2 x 6 - * - 2 x 8 -B- 2 x 1 0 Figure 27. Long-Term Bending Beta vs Span (Osaka, No.2, 455mm, Heavy Roof) CO 138 Appendix 1. Allowable Unit Stress for Lumber for 2x4 Wood Frame Structure Allowable Unit Stress Allowable Unit Stress for Sustained Loads for Temporary Loads Modulus of Elasticity Species Grade (unit: MPa) (unit: MPa) Group Compression Tension Bending Shear Compression Tension Bending Shear (unit: MPa) S.S. 9.8 8.3 13.7 0.78 10800 No.1 9.3 6.9 11.8 0.78 10800 No.2 7.4 5.9 9.8 0.78 9800 DFir-L No.3 4.4 3.4 5.4 0.78 8800 Construction 8.3 4.4 7.4 0.78 8800 Standard 6.9 2.5 3.9 0.78 8800 Utility 4.4 1.0 2.0 0.78 8800 S.S. 8.8 7.8 12.7 0.69 9800 No.1 7.8 6.4 10.8 0.69 9800 Hem-Tarn No.2 No.3 6.4 3.9 5.4 2.9 8.8 4.9 0.69 0.69 2 times the values of allowable unit stress for compression, tension, bend 8800 7800 Construction 7.4 3.9 6.9 0.69 ng 7800 Standard 5.9 2.5 3.9 0.69 or shear for sustained loads, 7800 Utility 3.9 1.0 2.0 0.69 respectively 7800 S.S. 8.8 6.9 11.8 0.69 8800 No.1 7.8 5.9 9.8 0.69 8800 No.2 6.4 5.4 8.8 0.69 7800 Hem-Fir No.3 3.9 2.9 4.9 0.69 6900 Construction 7.4 3.9 6.4 0.69 6900 Standard 5.9 2.0 3.4 0.69 6900 Utility 3.9 1.0 1.5 0.69 6900 S.S. 7.4 6.4 10.8 0.59 8300 No.1 6.4 5.4 9.3 0.59 8300 No.2 4.9 4.4 7.4 0.59 7400 S-P-F No.3 2.9 2.5 4.4 0.59 6900 Construction 5.9 3.4 5.9 0.59 6900 Standard 4.9 2.0 3.4 0.59 6900 Utility 2.9 1.0 1.5 0.59 6900 S.S. 7.4 5.9 9.8 0.59 7800 No.1 6.4 5.4 8.8 0.59 7800 No.2 5.4 4.4 7.4 0.59 6900 W Cedar No.3 2.9 2.5 4.4 0.59 6400 Construction 5.9 3.4 5.4 0.59 6400 Standard 4.9 2.0 2.9 0.59 6400 Utility 2.9 1.0 1.5 0.59 6400 Plumb Measure Size 1.3<im 1.35m 2F 1F 1.35m 1.35m 1st Floor 2nd Floor Against Ridge Direction 1st Floor 2nd Floor Against Span Direction Appendix 2. Measurement of Plumb Measure Size Appendix 3. Characteristics of the Bending Strength (100% Data) unit : MPa Size 2x4 2x8 2x10 Grade SS No2 SS No2 SS No2 Normal 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 Lognormal 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 2P Weibull 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 3P Weibull Location 14.09 8.94 3.35 6.72 1.35 7.26 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 Non-Parametric 5th Percentile 32.77 21.17 23.05 16.89 20.71 14.86 Appendix 4. Characteristics of the Bending Strength (Lower 15% Datafit) unit : MPa Size 2x4 2x8 2x10 Grade SS No2 SS No2 SS No2 Normal 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 Lognormal 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 2P Weibull 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 3P Weibull 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 Non-Parametric 5th Percentile 32.77 21.17' 23.05 16.89 20.71 14.86 Appendix 5. 2 Parameter Weibull Distribution Parameters for MOE for S-P-F Size Grade Mean COV Scale m Shape k (xlO4 MPa) (xlO4 MPa) 2x4 SS 1.029 0.167 1.100 7.056 No.2 0.910 0.210 0.986 5.499 2x8 SS 0.984 0.161 1.049 7.326 No.2 0.923 0.192 0.994 6.070 2x10 SS 0.954 0.160 1.017 7.403 N0.2 0.872 0.198 0.941 5.868 Appendix 6. Parameters for Tension Strength (Lower 15% Datafit) 2-P Weibull Parameters Non-parametric Size Grade Mean COV Scale m Shape k 5-th Percentile ( MPa) ( MPa ) ( MPa) 2x4 SS 25.83 0.22 28.04 5.30 16.53 No.2 17.73 0.25 19.43 4.49 9.80 2x8 SS 18.21 0.18 19.52 6.62 12.27 No.2 13.19 0.19 14.21 6.09 8.32 2x10 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 Non-parametric Size Grade Mean COV Scale m Shape k 5-th Percentile ( MPa) ( MPa) ( MPa) 2x4 SS 31.19 0.14 32.97 8.81 23.28 No.2 27.01 0.19 29.12 5.97 18.48 2x8 SS 26.54 0.15 28.20 7.88 19.32 No.2 24.15 0.14 25.57 8.46 18.20 2x10 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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