RELIABILITY STUDY OF NORTH A M E R I C A N DIMENSION L U M B E R IN THE CHINESE TIMBER STRUCTURES DESIGN CODE by X I A O I U N Z H U A N G B.ENG., Shanghai University, 1997 A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF THE REQUIREMENT FOR THE DEGREE OF M A S T E R OF SCIENCE in THE F A C U L T Y OF G R A D U A T E STUDIES Department of Wood Science We accept this thesis as conforming to the required standard THE UNIYERISITY OF BRITISH C O L U M B I A September 2004 © Xiaojun Zhuang, 2004 JDBCL THE UNIVERSITY OF BRITISH COLUMBIA FACULTY OF GRADUATE STUDIES Library Authorization In present ing this thesis in part ial fulf i l lment of the requi rements for an advanced degree at the University of British Columbia, I agree that the Library shall m a k e it freely avai lable for reference and study. I further agree that permiss ion for extens ive copy ing of this thesis for scholar ly purposes may be granted by the head of my depar tment or by his or her representat ives. It is unders tood that copying or publ icat ion of this thesis for f inancial ga in shall not be a l lowed wi thout my wri t ten permiss ion. X i a o j u n Z h u a n g 0 8 / 1 0 / 2 0 0 4 Name of Author (please print) Date (dd/mm/yyyy) Title of Thesis: R e l i a b i l i t y s t u d y o f N o r t h A m e r i c a n d i m e n s i o n l u m b e r in t h e C h i n e s e t i m b e r s t r u c t u r e s d e s i g n c o d e Degree: M a s t e r o f S c i e n c e Year: 2 0 0 4 Depar tment of W o o d S c i e n c e The University of British Co lumb ia Vancouver , BC C a n a d a g rad .ubc .ca / fo rms/? fo rmlD=THS page 1 of 1 last updated: 20-Jul-04 ABSTRACT Reliability evaluation principles, procedures as applied in the Chinese timber structure design code were reviewed. The general method to establish the design values of Chinese wood strength properties was investigated. In particular, Chinese load information, including the statistical models and parameters, was analyzed. Also, the reliability associated with wood structural design requirements in Canada was studied. The emphasis was placed on the in-grade testing method, which is a more reliable method to get the lumber strength properties compared with small clear wood testing method used in China. Finally, Canadian procedures for establishing the design values of wood strength properties were reviewed. Using Chinese load information and Canadian in-grade testing data, reliability evaluations were conducted for the design values of common Canadian Species in the Chinese timber design code. These design values were previous soft converted from allowable stresses approved by the American Lumber Standards Committee. Reliability results were compared with the target reliability levels tabulated in the Chinese national unified reliability code. This reliability analysis was implemented by using the " R E L A N " (Reliability ANalysis) program developed by Dr. R.O. Foschi of UBC. Recommendations were made to develop a formal reliability evaluation of the performance of North American dimension lumber under the Chinese load conditions. ii TABLE OF CONTENTS A B S T R A C T ii T A B L E O F C O N T E N T S iii LIST O F T A B L E S vi LIST O F F I G U R E S vii LIST O F A P P E N D I C E S viii A C K N O W L E D G E M E N T S ix 1. Introduction 1 1.1 Background I 1.2 New Chinese timber design code 2 1.3 Design methods of the code 4 1.4 Reliability evaluation method 4 1.5 Reliability assessment procedure 5 1.6 Objectives 6 2. Limit states design in China 8 2.1 Limit states design equation 8 2.2 Target reliability. 10 2.2.1 Method 10 2.2.2 Load 11 2.2.3 Resistance 11 2.2.4 Results of target reliability analysis 13 2.3 Structural importance factors 14 2.4 Load effect factors 15 2.5 Resistance division coefficient. 16 3. Reliability Analys is of Chinese timber design code 18 3.1 Reliability evaluation 18 3.1.1 Load information 18 3.1.2 Member resistance 19 3.1.2.1 Small clear testing specimen strength 21 3.1.2.2 Quality variability factor KQ 23 3.1.2.3 Geometry variability factor KA 24 3.1.2.4 Analysis model variability KP 25 3.1.3 Results 25 3.2 Wood strength design values 26 3.2.1 Characteristic strength 27 3.2.2 Material property division coefficient 28 4. Chinese load models 31 iii 4.1 Dead load 31 4.2 Occupancy load 32 4.2.1 Sustained occupancy load 32 4.2.2 Extraordinary occupancy load 33 4.2.3 Maximum occupancy load in 50 years 34 4.3 Wind load , 36 4.3.1 The wind velocity and reference velocity pressure 37 4.3.2 The model of reference velocity pressure 37 4.3.3 The national reference velocity pressure 38 4.3.4 The national wind pressure statistical model 40 4.3.5 The national maximum wind pressure in 50 years 41 4.4 Snow Load 42 4.4.1 Annual maximum ground snow load data 42 4.4.2 The statistical model of ground show load 42 4.4.3 The national snow load statistical model 43 4.4.4 The snow load model in the code 44 4.5 Load models used in reliability analysis 45 5. Reliability study of wood in Canada 46 5.1 Material strength database. 46 5.1.1 Small clear wood testing 47 5.1.2 Shortcomings of small clear wood testing 48 5.1.3 In-grade testing 49 5.1.4 CWC lumber properties project 50 5.2 Reliability evaluation 50 5.2.1 Load information 51 5.2.2 Member resistance 52 5.2.3 Results 53 5.3 Specified strengths 55 5.4 Modification factors 56 6. Reliability evaluation of lumber Design Values in Chinese Code 59 . 6.1 Pedormance functions 60 6.1.1 Strength limit states 60 6.1.2 Serviceability limit states 61 6.2 Strength database 67 6.2.1 Species, grades and sizes 62 6.2.2 Resistance distribution model 62 6.3 Load information 6 5 6.3.1 Statistical parameters of load models 66 6.3.2 Load ratio 66 6.4 Bending 6 8 6.4.1 Original data 68 6.4.2 Effect of distribution types and load ratios 69 6.4.3 Target reliability evaluation results 72 6.5 Compression 7 3 6.5.'1 Original data 7 3 6.5.2 Effect of distribution types and load ratios 74 6.5.3 Target reliability evaluation results 77 i v 6.6 Tension 78 6.6.1 Original data. 78 6.6.2 Effect of distribution types and load ratios 79 6.6.3 Target reliability evaluation results 82 6.7 Serviceability 83 6.7.1 Original data 83 6.7.2 Effect of distribution types and load ratio 84 6.7.3 Target reliability evaluation results 87 7. Discussion and conclusion 88 7.1 Target reliability evaluation 89 7.2 Robustness of soft conversion method 90 7.3 Discussion 92 7.4 Conclusion 94 APPENDIX A: 95 REFERENCES 100 v L I S T O F T A B L E S Table 2-1 Load information used in target reliability assessment 11 Table 2-2 Resistance parameters for wood 13 Table 2-3 Existing reliability levels 13 Table 2-4 Target reliability levels 14 Table 2-5 Importance factors 14 Table 3-1 Load information used in wood reliability evaluation 19 Table 3-2 Statistical parameters for testing specimen strength 21 Table 3-3 Testing member strength parameters for Fir in different locations 22 Table 3-4 Statistical parameters for quality factors 23 Table 3-5 Statistical parameters for quality variability factor 24 Table 3-6 Statistical parameters for geometry variability factor 25 Table 3-7 Statistical parameters for model variability factor 25 Table 3-8 p value under dead load plus occupancy (office) load 26 Table 3-9 p value under dead load plus snow load 26 Table 3-10 p value published in the timber design code 26 Table 4-1 Statistical parameters of occupancy loads 35 Table 4-2 Statistical parameters of live loads 36 Table 4-3 Statistical Parameters and distribution types for loads (1984 version) 45 Table 5-1 Parameters for Canadian live load 52 Table 5-2 Snow load data for six Canadian cities 52 Table 6-1 Relationship between Chinese and North American grades 62 Table 6-2 Load statistical information for reliability evaluation 66 Table 6-3 Parameter estimates of Bending at 15% M . C 68 Table 6-4 2-P Weibull (Truncated at 15%) for snow load (bending) 70 Table 6-5 Lognormal (100% Data) for snow load (bending) 70 Table 6-6 Characteristics of the bending strength for S P F No.2 2x8 71 Table 6-7 B values for bending strength with Lognormal (entire data) distribution 72 Table 6-8 Parameter estimates of U C S at 15% M . C 73 Table 6-9 2-P Weibull (Truncated at 15%) for snow load (compression) 75 Table 6-10 Lognormal (100% Data) for snow load (compression) 75 Table 6-11 Characteristics of U C S for DF SS 2x10 76 Table 6-12 B values for compress ion strength with Lognormal (entire data) distribution ...77 Table 6-13 Parameter estimates of U T S at 15% M . C 78 Table 6-14 2-P Weibull (Truncated at 15%) under snow load (tension) 80 Table 6-15 Lognormal (100% Data) under snow load (compression) 80 Table 6-16 Characteristics of the U T S for S P F No.2 2x4 81 Table 6-17 p values for tension strength with Lognormal (entire data) distribution 82 Table 6-18 Parameter estimates of M O E at 15% M . C 83 Table 6-19 Lognormal under snow load (serviceability) 85 Table 6-20 2-P Weibull under snow load (serviceability) 85 Table 6-21 Characteristics of the M O E for HF No.2 2x4 86 Table 6-22 B values for serviceability with Lognormal distribution 87 Table 7-1 Target reliability evaluation 89 LIST OF FIGURES Figure 1-1 Yin Xian W o o d Tower 1 Figure 4-1 Dead load Model 31 Figure 4-2 Sustained live load model 33 Figure 4-3 Extraordinary occupancy load model 34 Figure 6-1 (S -<t> Relation for four distribution types (SPF No.2 2x8,100% data) 63 Figure 6-2 Lognormal fit to 2x4 D F entire test data (Bending) 64 Figure 6-3 Lognormal fit to 2x4 D F lower 100 test data (Bending) 65 Figure 6-4 j3 -<t> relations for four distribution types (bending) 71 Figure 6-5 /3 -<t> relations for four distribution types (compression) 76 Figure 6-6 (3 -<P relations for four distribution types (tension) 81 Figure 6-7 (3 -<P relations for three distribution types (serviceability) 86 Figure 7-1 Compar i son of reliability levels of load combinations 89 Figure 7-2 Reliability levels according to grades 90 Figure 7-3 Reliability levels according to species ....91 Figure 7-4 Reliability levels according to sizes 91 LIST OF APPENDICES Appendix A: Commentary on Dimension Lumber Design values for GBJ-5 code A C K N O W L E D G E M E N T S I would first like to thank my supervisors, Dr. J.D. Barrett and Dr. F. Lam, for their suggestions, support and encouragement throughout my graduate study and in the presentation of this thesis. I am also grateful to Dr. R.O. Foschi and Mr. F. Yao from Department of Civi l Engineering in the University of British Columbia. They gave me detail explanation and references for their work on the reliability study of wood products. The other two committee members also gave me a lot of help on this thesis. They are Dr. C. Ni of Forintek Canada Corporation, and Dr. M.J . He from Tongji University. Without the information they provided, this thesis never would have materialized. I also need to express my appreciation to my colleagues and fellow graduate students in our T E A M (Timber Engineering Applied Mechanics) group. They gave me so much help and encouragements during my courses study and thesis preparation. Finally, I would like to thank my wife Erlu for all of her love and understanding of my work. ix Chapter One Introduction 1. INTRODUCTION 1.1 Background Wood, as a natural building material, has a long history of application in China. From common residential buildings to royal palace and temples, wood was a common structural material for centuries. Figure 1-1 shows the oldest existing wood structure in China, Ying Xian wood tower. Built in 1056 A.D. , it is a symbol of Chinese ancient wood building technology [1]. Figure 1 - lYin X i a n W o o d T o w e r Source : htip://www.tvdao.com/sxscn/shuo/hou/muia.htm However, wood housing is rarely built in the current booming Chinese construction market. Comparing with the other buildings, wood building occupies very small market segment. Two key factors influence the Chinese housing market—limited land for housing and high population density. Although multi-story and high-rise buildings provide a solution for the high-density housing market, wood buildings are suitable for most of the low-density housing, such as the single family house, town house and three-or four-story apartment. But this market is also dominated by the concrete or masonry structures. 1 Chapter One Introduction In some cases, concrete is used to imitate wood even though wood is an acceptable solution. This phenomenon is caused by several reasons. The primary reason is the shortage of timber resources in China. Concerning the environmental protection issues, Chinese government strictly prohibits the harvesting of forest resources. With a huge population and limited wood resources, wood structures were not recommended as a structural solution for housing since the 1960s. In addition, the only available wood structural style in China is the post and beam structure, which typically consumes the restricted old growth timber. Therefore, government enacted a series of rules to limit the use of wood in construction. This out-of-date post and beam wood building technology also prohibits the wide application of wood structures in China. With the development of alternative modern materials, such as concrete and steel, wood has been replaced as the major construction material in China. With few applications for wood structures in the housing market, research and development activities for wood structures have been limited. This lack of knowledge further led to the misunderstandings that suggested wood as an inferior construction material and wood building as a less reliable structure. Furthermore the old Chinese timber design code GBJ 5-88 lacked state of the art wood technology. With the unnecessary safety considerations for wood, the old timber design code GBJ 5-88 could result in more consumption of wood resource, which in turn further restricts the development of wood buildings. With the development of the Chinese housing market, wood buildings, one of the best solutions for the residential housing, are gaining more and more attention. The best way to promote the use of wood as a structural building material in China is to accept the import of worldwide timber resource, implement advanced wood building technology and update the current out-of-date timber design code. 1.2 New Chinese timber design code The newly published "Code for design of timber structures" (GB 50005-2003) [2] supercedes GBJ5-88 [3]. One of the most important updates in this code is the implementation of North American's platform frame (2x4) building technology. 2 Chapter One Introduction The 2x4 platform frame structure1 is the most common structural style for the single family residence, town house and low-rise multi-family housing in North America. Also, it is commonly used in North American low-rise commercial and industrial construction. Compared with the post and beam construction, platform frame structure has the advantages of economy, strength and flexibility. It efficiently uses small wood members spaced closely together in load sharing arrangements. The resistance of this system not only comes from the combined action of the main structural framing members, but also from the sheathing and decking systems. Its inherent strength and durability is demonstrated by a long and proven performance history [4]. Compared with the post and beam structure, wood-frame structure is a totally new concept in China. In the new Chinese timber structure design code, there is a new wood frame construction chapter introducing the wood-frame design method used in North America. This chapter is developed primarily based on the Section 9.23 of the National Building code of Canada 1995. With the introduction of wood-frame structure in China, it is also the first time that the definition of "dimension lumber" appears in the glossary of Chinese timber design code. Normally, commercial dimension lumber, named with species, grades and sizes, refers to surfaced solid sawn wood in specialized size (less than 89mm in thickness) with specified depths. Dimension lumber, used as a stud, or a joist or rafter, is the main structural material in wood frame construction. Design properties of Canadian and U.S. dimension lumber are obtained from tests of full size dimension lumber. Strength properties of dimension lumber in the Chinese code are derived from soft conversion of the lumber properties published in the A F & P A codes, Structural Lumber Supplement to the A F & P A / A S C E 16-95 Standard for Load and Resistance Factor Design (LRFD) for Engineered Wood Construction. The basic purpose of this soft conversion is to arrive at the same member size using either the U.S. LRFD code or GB 50005 code under the same live load condition [5]. 1 The 2x4 platform frame construction system 2 American Forest & Paper Association 3 Chapter One Introduction 1.3 Design methods of the code Both the Chinese and Canadian codes use the Limit States Design method. The objective of Limit States Design is to develop safe design guidelines by considering the uncertainties involved in the design process. Moreover, the limit state design guidelines aim to satisfy the criteria of a target safety level 3 or "target probability of failure". Limit states of structural member can be classified in two categories. One is the strength limit states, which is concerned with the structural safety and corresponding capacity of the member. The other one is the serviceability limit states, which is concerned with non-safety related issues that restrict normal use of the structure. The design equation format in the Limit States Design format is Effect of factored load ^ Factored Resistance (1.1) Both sides of this equation involve several random variables with different degree of uncertainty, such as the load information and material strength. The most important advantage of the Limit States design method is it provides an equitable basis for comparing the member safety across all the structural materials. Although the material strength of wood tends to be generally more variable, it is possible to arrive at designs with similar performance compared to steel and concrete by calibrating the design procedures to recognize differences in the material variability. In the case the uncertainty of random variables are specified, a formal reliability evaluation can be conducted to get the probability of failure of the structural members by using principles of probability theory. Canadian code for Engineering Design in wood CSA 086-1 is the first wood structure design code to convert to the Limit States Method based on a formal reliability-based assessment. 1.4 Reliability evaluation method There are several methods to calculate the probability of failure or non-performance of structural members. One method is to calculate the probability of failure directly by using the Monte Carlo Method. Instead of direct calculation, another approach is to calculate the reliability index /?, which can be used to calculate probabilities of failure 3 The target safety level is measured by a safety index that can be related to notional probability of failure 4 Chapter One Introduction Pf by using the standard normal probability distribution function O(-) , where Pf = The key point of this method is to calculate the index /? in a geometric approach, in which P is the distance between the origin point and the design point. This problem can be solved by the optimization algorithms. The accuracy of the results, however, depends on several factors. For variables in the G functions, they need to be normally distributed and uncorrelated. For the G function, it needs to be linear. Although some of these conditions are difficult to meet, the result of this method provides an acceptable answer in most cases. The calculation of the index j5 is based on the First-order Second-Moment Theory. This method is referred as the "First-order Second-Moment method considering the distribution type of the variables" method in Chinese code [6]. In the Canadian approach, the "FORM" (First Order Reliability Method) in the RELAN (RELiability ANalysis) program, which was developed at the Civil Engineering Department of the University of British Columbia, was also developed from the First-order Second-Moment theory. The calculation methods used in China and Canada are based on the same theory and follow the same calculation process; therefore, the RELAN program is used in this study. 1.5 Reliability assessment procedure Applying reliability assessment procedures for code calibration requires knowledge of: • Loads (e.g., occupancy, snow, wind, earthquake) • Appropriate materials strength data • Member structural behavior models • Corresponding member design equations for the strength and serviceability limit states In China, the reliability assessment standard and analysis procedures are described in the national reliability code— "Unified standard for reliability design of building structures" (GB 50068-2001) [7]. Following the specified procedure, Chinese timber design code also went through a reliability assessment. The result of the assessment 5 Chapter One Introduction indicated that the reliability level of post and beam buildings in China meets the target reliability level, which are 3.2 for the ductile failure mode, 3.7 for the brittle failure mode and 0-1.5 for the serviceability mode [7]. Using the Canadian load information and material strength database, however, the reliability index level of members used in wood frame structures in Canada ranges from 2.5 to 3.0. The gap between the target reliability indices indicates that it is necessary to confirm the safety level of the Canadian dimension lumber for applications in China. 1.6 Objectives The design values of dimension lumber published in the Chinese code were soft converted from the A F & P A L R F D resistance values. Although the same size member could be obtained under the same live load with a given live-to-dead load ratio, the reliability level of these members could vary with load conditions and design equations. Furthermore, the reliability level also varies according to species, grades and sizes. Therefore, it is important to evaluate the reliability levels of these values by using North American lumber strength database, Chinese load information and Chinese corresponding design equations. This work will include the study of load information and material strength. Since this study references the Chinese target reliability index, it is necessary to understand the principles of the Chinese reliability assessment procedures and the development of target reliability indices. Moreover, a clear understanding of the background information of the reliability assessment in the Chinese timber design code and the derivation of wood design properties are also needed. Therefore, the major objectives of this study are to: 1) Understand the application of the reliability-based limit states design method in the Chinese timber design code. 2) Evaluate the reliability level of North American dimension lumber design values published in the code. By realizing the first objective, the reliability study of Chinese timber design code can be compared with Canadian approach to reliability assessment. It is important to understand the Canadian reliability assessment procedure for the wood-frame structure, 6 Chapter One Introduction and then compare it with the Chinese procedure for the post and beam structure. Based on this knowledge, reliability levels of both the structural styles could achieve the uniformity in the limit states design. In turn, it will support the development of the wood-frame structure technology in China. The reliability evaluation of the design values could provide the reference for future updating of the dimension lumber strength values in the Chinese code. The development of appropriate strength values is central to the lumber marketing program in China. The appropriate strength values will increase the competition capacity in structural efficiency and product value for North American structural wood products in the Chinese market. 7 Chapter T w o Limit States Design in China 2. LIMIT STATES DESIGN IN CHINA The key issue in the design of a structure is how to deal with the uncertainty in the design process. Two methods are commonly applied, (1) working stress design method based on experience and (2) limit states design method based on the reliability theory, are the common ways to solve this problem. Before the application of limit states design method, working stress design methods were used in China. In 1980s, all structural design codes in China were transferred from working stress design to the limit states design method. The principles of reliability-based limit states design in China are specified by the national reliability code— "Unified standard for reliability design of building structures". The first version of code GBJ 68-84 [8], published in 1984, performed a reliability based code calibration to all structural design codes in China, and then unified the reliability-based design standard. The calibration procedure was a two-step procedure. In the first step, target reliabilities were specified on the basis of the old design codes. Then the corresponding partial factors and other safety elements were developed. This unified reliability code also provided the reliability index calculation method, modeling of load, and statistical information of material properties. Current version of reliability code is GB 50068-2001, which is an updated version of the old reliability code— GBJ 68-84. Based on the experience of the old reliability code and ISO 2394—"General principles on reliability for structures", GB 50068-2001 made modifications on some reliability standards. However, modeling of load and statistical information of material properties are no longer provided in this code. 2.1 Limit states design equation For a long time, the only design method used in China was the working stress design method using the characteristic material strength values and safety factor. A typical working stress design equation is K(SGK+SQk)<RK (2.1) where 8 Chapter T w o Limit States Design in China K : Safety factor RK : Member resistance Sr : Dead load effects " A T Sn : Live load effects Following the working stress design equation, limit states design also uses the characteristic material strength values and adjustment coefficients in its equation. The basic design equation of limit state design is expressed as 70S < R (2.2) where R : Design value, includes the resistance factor S : Design dead and live load effects y0 : Structure importance factor Design equation follows different load combinations. Under common load effects, the limit state design equation can be defined as f " ") To rGsGK+wY,yQisQlK zRirR'/k*"*'-) (2-3) V 1=1 ) where yG : Permanent load effect factor yQ : Live load effect factors SG : Permanent load effects of the nominal permanent load Gk SQ : Variable load effects according to the nominal variable load Qik. y/ : Combination factor for the variable loads, y/ = 0.9 in most cases. In the case there is only one variable load, y/ = 1.0. n : Number of the variable loads R(-) : Resistance functions of the structural member yR : Resistance division factor fk : Material characteristic strength ak : Characteristic value of a geometrical parameter 9 Chapter Two Limit States Design in China Although the form of the design equations is similar, the load effect factors as well as the resistance factor hidden in the strength design values are fundamentally different from the safety factor in the working stress design equation. The safety factor basically comes from the long-term engineering experience, while the factors in the limit states design equations come from the formal reliability assessment. Load and resistance are random variables and the reliability index is used to evaluate the safety level of the building members. 2.2 Target reliability The first step in developing a limit states design in a code is to define the target reliabilities. In China, target reliabilities of structural design codes for different materials are specified for all Chinese structural design codes. 2.2.1 Method In theory, target reliabilities are determined by the combined consideration of structural member importance, member failure characteristics and potential consequences of members' failure. For structural members under different load conditions, a series of reliability assessments with different load ratios and load combination effects are normally considered. Considering the compatibility with the existing design codes in China, calibration method was adopted to define the target reliabilities. The calibration method and the reliability analysis of existing codes is used to establish the target reliability in the future limit state design codes. The idea of this method is that the application of a new design method should not lead to large differences in member sizes or the reliability levels. In China, target reliability levels of different codes were unified. The unified target reliability should not only reach the compatibility with previous engineering experience, but also balance the reliability level of different materials under the same loading conditions. In this procedure, reliability levels of 14 structural members were calculated [8]. These members, with different load conditions, load ratios and load combination effects, were taken from 5 structural design codes, including steel, 10 Chapter Two Limit States Design in China light steel, concrete, masonry and wood structural design codes. For the wood members, only two load conditions, bending and compression parallel to grain, were considered in this target reliability assessment with live load to dead load ratios of 0.25, 0.5 and 1.5 [6 and 8]. 2.2.2 Load In the target reliability assessment, loads were taken as random variables. Statistical models of the loads in China are: • Dead Load— Normal Distribution • Occupancy Load— Extreme Type I Distribution • Snow Load— Extreme Type I Distribution • Wind Load— Extreme Type I Distribution The statistical parameters of the loads were given as the coefficient of variation and the ratio of mean value to nominal value shown in Table 2-1 [6 and 8]: Load types Mean/Nominal Coefficient of Variation Dead 1.06 0.07 Occupancy(office) 0.70 0.29 Occupancy( residential) 0.86 0.23 Wind 1.00 0.19 Snow 1.14 0.22 Table 2-1 Load information used in target reliability assessment In addition, load combination effects and live-to-dead load ratio were two important factors in the process of target reliability assessment. Three load combinations were used in the target reliability assessment, 1) Dead load plus occupancy load in office buildings 2) Dead load plus occupancy load in residential buildings 3) Dead load plus wind load In China, the live-to-dead load ratio is commonly taken as 0.25, 0.5, 1 and 2. 2.2.3 Resistance According to the Chinese code [8], the resistance of the structural member composed of one material can be expressed as 11 Chapter T w o Limit States Design in China R = KP-{KM- 0)Jk )-(KA-AK) = KPKM KAR (2.4) where KM : Material variability factor, random variable KA : Geometry variability factor, random variable KP : Analysis model variability factor, random variable RK : Resistance, RK = O)0fk • A K a)0 : Safety factor, which concerns the difference between the testing member and the full size member. fk : Characteristic strength A K : Characteristic value of geometry dimensions For the material variability factor KM , it can be further derived as K _ — • — - — K Q — U a>0 f fk o)a fk where fQ : Full size structural member strength f : Testing member strength KQ : Quality variability factor Finally, the resistance can be expressed as According to the theory of probability, if y = X , • X 2 - X 3 . . . . X l , , t h e n InF = l n X , + l n X 2 + l n X 3 +.... +InX„ (2.7) when n is large enough, In Y approaches a Normal distribution. Therefore, Y , as the resistance, approximately fits to Lognormal distribution. To evaluated target reliability in the existing code, statistical parameters of resistance were given as the coefficient of variation and the ratio of mean value to nominal value. For the wood structure members, previous code assumed that the variance of wood strength was only related to load conditions and had no difference between the species. Then the coefficient of variation was taken as the average of the R - KPKAAKKQf (2.6) 12 Chapter T w o Limit States Design in China f coefficient of variation across all the species. The final parameters used for wood structural member resistance are listed in the Table 2-2 [6]. Mean/Nominal Coefficient of variation Tension 1.42 0.33 Compression 1.23 0.23 Bending 1.38 0.27 Shear 1.23 0.25 Table 2-2 Resistance parameters for wood 2.2.4 Results of target reliability analysis The performance function used in the target reliability analysis was G = R-SG-SQ (2.8) where R : Member resistance Sc : Dead load effect SQ : Live load effect The reliability index ft could be calculated when the distribution type and statistical parameters of these three random variables are specified [8]. Average (3 under different load ratios Structural member Load conditions SG+ S u SG+ S L SG+ SW (live to dead load ratios) office residential Steel Compression 3.16 2.89 2.66 (0.25, 0.5, 1.0, 2.0) Compression & bending 3.29 3.04 2.83 Light steel Compression 3.42 3.16 2.94 (0.5, 1.0, 2.0, 3.0) Compression & bending 3.49 3.23 3.02 Masonry Compression 3.98 3.84 3.73 (0.1, 0.25, 0.5, 0.75) Compression & bending 3.45 3.32 3.22 Shear 3.34 3.21 3.09 Wood Compression 3.42 3.23 3.07 (0.25, 0.5, 1.5) Bending 3.54 3.37 3.22 Concrete Tension 3.34 3.10 2.91 (0.1, 0.25, 0.5, 1.0, 2.0) Compression 3.84 3.65 3.50 Compression & bending 3.84 3.63 3.47 Bending 3.51 3.28 3.09 Shear 3.24 3.04 2.88 Average 3.49 3.29 3.12 Total Average 3.30 Table 2-3 Existing reliability levels 13 Chapter T w o Limit States Design in China Based on the results of this analysis, it was concluded that the average reliability index in old codes was 3.30, which is illustrated in Table 2-3. For the ductile failure mode, the average reliability index value was 3.22. Finally, target reliability index were defined in Table 2-4, according to different building safety levels. In addition, target reliability index for the serviceability is taken as 0-1.5. F a i l u r e m o d e S a f e t y l e v e l s L e v e l I L e v e l II L e v e l III D u c t i l e 3.7 3.2 2.7 B r i t t l e 4.2 3.7 3.2 Table 2-4 Target reliability levels 2.3 Structural importance factors According to engineering experience in China, safety levels of the building can be divided into three levels. The incremental difference in reliability index between each safety level is a 0.5. In the design equation, structural important factor yo is used to express the difference between the safety levels. The result of target reliability analysis, which used fourteen different structural members, showed that when importance factor yo =1.1 was applied, the mean value of the reliability index of the fourteen structural members increased about 0.5. On the other side, when importance factory =0.9was applied, the value decreased about 0.5. Therefore, the structural importance factor in the unified reliability code is specified by Table 2-5. S a f e t y l e v e l F a i l u r e S e v e r i t y B u i l d i n g t y p e S a f e t y F a c t o r L e v e l I H i g h I m p o r t a n t 1.1 L e v e l I I N o r m a l N o r m a l 1.0 L e v e l I I I L o w T e m p o r a r y 0 . 9 Table 2-5 Importance factors In this table, the building types is defined according to the failure results, which are evaluated according to the life safety, economy lost and social effects of the building failures. In China, most of industrial and residential buildings belong to the safety level II. Some high-density population buildings, such as a cinema, stadium or high-rise building, are specified as important buildings. 14 Chapter T w o Limit States Design in China Structural members in one building should have the same safety levels as the building. Some critical structural members, however, could be designed for a high safety level. A typical example is the beam column connection design. On the other hand, if structural member is less important, the safety level of that member can be lower than the safety levels of the other members, but it should not be lower than the level III. 2.4 Load effect factors The load factors yG and yQ in the Chinese code were chosen such that the member resistance calculated according to limit states design equations has the least difference with those calculated according to target reliability index [8]. Minimum error theory is applied in this procedure. The function can be expressed as ff,=Efc-**J (2-9) j Where R*KiJ : Member resistance based on the target reliability RKij : Member resistance based on limit states design equation For the evaluation, the value of yG was taken as 1.1, 1.2 and 1.3, and the value of yQ was taken as 1.1, 1.2, 1.3, 1.4, 1.5, and 1.6. Therefore, there were 18 combinations of yG and yQ . For each combination, each structural member (i) can get an optimized resistance division c o e f f i c i e n t . Therefore, the best load factors and resistance division coefficients should minimize the I value below, where To define the value of dead load factor yc and live load factor yQ, a comprehensive calculation and analysis was conducted under three load combinations including dead load plus live load in office buildings, dead load plus live load in residential buildings and dead load plus wind load. In addition, load combination of dead load plus snow load 15 Chapter Two Limit States Design in China was also studied for reference to this study. For the other load combinations, the load factors were taken based on experience. When the dead load effect had the same sign as the live load effect, such as dead load plus live load in office buildings, the load factor is normally taken as ya=l.2, yQ=\A When the dead load effect had the different sign than the live load effect, such as the dead load minus wind load, the load factors can not be taken as the above values. The structure safety index decreased under such circumstance. After the comparison of the safety index ft of 14 structural members under different load combinations, such as SL ± SG (office building), SL ± SG (residential building) and Sw ± SG , the code takes the load factors as rG=i.o, YQ = \A 2.5 Resistance division coefficient In the process of choosing load effect factor, resistance division coefficient yR of each structural member, under three types of load combinations, can also be chosen based on the each combination of fixed load effect factor according to - R j =Zfc y -ns , ) 2 (2. i i) j J where V = K * W , + rAJ , ( 2- 1 2 ) dH To get the minimum of yR value, take - — - = 0 Then, yR, = (2.13) When all the values of R*KiJ and S • under three load combinations, SL + SG (office building), SL + SG (residential building) andSw +SG, are put into the above functions, the optimized resistance division coefficient according to the target reliability index can 16 Chapter T w o Limit States Design in China be derived. For example, the steel structural member has 3 x n ; =12 values of R*Kij andS ; . Then the steel structural member's optimized resistance division coefficient yR according to its target reliability index can be calculated by aforementioned function. The code also allows some adjustments of the yR value for the real application purposes. According to the reliability code, the reliability safety index could be bigger than the requirement of the reliability code. When the reliability safety index is changing, the optimized yR value is also changing. The adjustment principle is to fix the value of dead load factor yG and live load factor yQ, and then recalculate the yR value based on the minimum error theory. Based on the target reliability indices fi0, the resistance division coefficient of wood structural member yR was calculated by using the method illustrated in the unified reliability code. In this procedure, the permanent load effect factor yG was taken as 1.2 and variables load effect factor yQ was taken as 1. 4. The results of the resistant division coefficient based on the four variable load ratios p (0.2, 0.3, 0.5 and 1.5) are [9]: 1) Bending members, yR = 1.60 2) Compression member (parallel to grain), yR = 1.45 3) Tension member (parallel to grain), yR = 1.95 4) Shear member (parallel to grain), yR = 1.50 For the design equation of wood structural members, the yR was further transformed to the material division coefficient yfj. 17 Chapter Three Reliability Analysis of Chinese Timber Design Code 3. R E L I A B I L I T Y A N A L Y S I S O F C H I N E S E T I M B E R D E S I G N C O D E The initial reliability study of Chinese timber structure design code was performed in 1980s. The 1973 version of the code—GBJ 5-73 [10], a working stress design code, was used to evaluate the target reliability levels of wood members. The first reliability-based limit states design code published in 1988—GBJ5-88 [3]. In the reliability analysis of this code, reliability level of wood members was evaluated, and results were used to investigate the compatibility with the target reliability levels. Also, design values and stress class system for Chinese wood species were re-established based on the reliability study. With the update of load code and unified reliability code in 2001, the 2003 version of the timber design code— GB 50005-2003 [2] performed a reliability study to evaluate the reliability levels according to new load information and reliability requirements. 3.1 Reliability evaluation 3.1.1 Load information Currently, the most common use of wood as structural members in buildings in China is the roof system. The most popular wood roof style used in China is the pitched roof with a 30° slope. The load applied to the pitched roof was used in the reliability study by Mr. Wang Yongwei [11]. Roof loads were divided into two groups: the dead load, such as the weights of structural members, water-proofing material and other roof sheathing materials; the live load, which included occupancy load, snow load, wind load and temporary load during constructions. Following the unified reliability code, dead load data was fitted to the Normal distribution and all the live load data were fitted to the Extreme type I (Gumbel) distribution. Due to the revisions of the nominal loads in the new version of load code—GB50009—2001 [12], statistical parameters of loads used in this reliability assessment were not different from the old information [11]. Detailed explanation 18 Chapter Three Reliability Analysis of Chinese Timber Design Code of this issue will be discussed in next chapter. Table 3-1 lists the statistical parameters of loads used in this reliability evaluation. Load types Mean/Nominal Coefficient of variation Dead 1.060 0.070 Occupancy(office) 0.524 0.288 Occupancy(residential) 0.644 0.233 Snow 1.040 0.220 Table 3-1 Load information used in wood reliability evaluation Two load combinations were used in this reliability evaluation. 1) Dead load plus snow load 2) Dead load plus occupancy load in office buildings According to the survey which analyzed the 30 roof styles in China, the live-to-dead load ratio of these roofs arranged from 0.14 to 0.6, and most cases were specified to 0.2, 0.3 and 0.5. The load ratio for the office was roughly about 1.5. Therefore, load ratios used in the reliability analysis were For S S K / S G K : 0.2, 0.3 and 0.5 F o r S L K / S G K : 1.5 where SSK : Nominal show load SGK : Nominal dead load : Nominal occupancy (office) load 3.1.2 Member resistance In China, wood member resistance is based on the material strength of small clear wood specimen test results. The member resistance in the Chinese wood structures code is expressed as R = KpAfQ (3.1) where R : Member resistance K : Analysis model variability factor A : Standard dimension of the member 19 Chapter Three Reliability Analysis of Chinese Timber Design Code fQ : Full size structural member strength Because of the quality variability between full size member and small clear wood as well as the geometry variability of the testing specimen, the member material strength and the standard dimension of the member are adjusted to: fQ=KQf, A = KAAK (3.2) Then the resistance function can be represented by R — K PK AAKKQf (3.3) where Kp : Analysis model variability factor KA : Geometry variability factor AK : Nominal dimensions K~Q : Quality variability factor / : Small clear testing specimen strength The function is as same as the one discussed in the last chapter. AK is a constant, and the other parameters are all independent random variables. Therefore, the statistical parameters of resistance can be defined as mR - Kp • KA- KQ- mf • AK (3.4) and cov(R) = ^ jcov(Kp)2 + cov(KA)2 +cow(KQ)2 +cov(/) 2 (3.5) where mR,cov(R) : Mean value and coefficient of variation of member resistance Kp ,cov(Kp) : Mean value and coefficient of variation of analysis model variability factor KA ,co\(KA) : Mean value and coefficient of variation of geometry variability factor KQ,cov(KQ) : Mean value and coefficient of variation of quality variability factor 20 Chapter Three Reliability Analysis of Chinese Timber Design Code mf ,cov(/) : Mean value and coefficient of variation of test specimen strength Based on the above assumptions, wood member resistance was represented as a Lognormal distribution with the statistical parameters given above [11]. 3.1.2.1 Small clear testing specimen strength Small clear test specimen strength/can be obtained according to the national standard testing method—"Standard for methods testing of timber structures" (GB/T 50329-2002) [13]. Three distribution types, Normal, Lognormal and the Weibull distribution, were used to describe structural properties, including bending, tension parallel to grain, and compression parallel to grain as well as shear parallel to grain. Based on 73 groups of test results from 14 Chinese species which were collected from 20 sample sites, Normal distribution was chosen as the distribution model for the small clear test specimen strength [14]. Generally, material strength varies with wood species. Therefore, various wood species have their own statistical parameters. However, in the procedure of reliability evaluation in China, material strength of wood was assumed to be only related to load conditions instead of species dependent. As a result, material strengths of different wood species were represented by only one random variable with unified statistical parameters under one load condition. This method was not only used to specify the target reliability level, but also applied in the reliability analysis of the current timber design code. In China, statistical parameters of the material strength were referenced to the mean value and the coefficient of variation. However, only coefficient of variation, which was taken as the average of all species' coefficient of variation, was published [9]. The values of the average coefficient of variation of test specimen strength are listed in Table 3-2. C o m p r e s s i o n para l le l to gra in T e n s i o n paral le l to gra in B e n d i n g S h e a r paral le l to gra in cov 0.12 0.217 0.13 0.148 Table 3-2 Statistical parameters for testing specimen strength 21 Chapter Three Reliability Analysis of Chinese Timber Design Code In the Chinese procedure, wood strengths were considered as species dependent only when they were used to determine the stress class system and design values. Moreover, the reliability level for each wood species with its associated design values under a specified stress class must meet the reliability requirements specified in the unified reliability code [2]. Furthermore, the situation is complicated by the factor that the strength properties of a given species of wood in China are highly regional dependent. Table 3-3 shows the regional dependent strength data for Chinese Fir from several locations in China [11]. Tension Compression Bending Shear Location Parallel to grain Parallel to grain Parallel to grain m, cov(f) m, cov(f) m, cov(f) mf cov(f) kg/cm2 % kg/cm2 % kg/cm2 % kg/cm2 % Hu Nan 772.0 18.8 388.0 13.2 636.0 17.2 42.0 23.1 Gui Zhou 791.0 25.8 361.0 18.5 626.0 22.9 35.0 31.3 Si Chuan 935.0 27.0 391.0 15.8 684.0 19.3 59.0 21.7 An Hui 791.0 21.2 381.0 15.2 737.0 14.5 62.0 23.4 Guang Xi 724.0 21.2 368.0 15.5 725.0 19.9 51.0 17.6 Zhe Jiang 816.0 14.1 428.0 11.1 863.0 16.5 71.0 17.7 Fu Jian 861.0 21.2 356.0 17.3 652.0 19.2 61.0 20.1 Table 3-3 Testing member strength parameters for Fir in different locations For one species which has different strength properties in different locations, its mean value and coefficient of variation of the strength properties were calculated according to n i=i cov(/) = jj>,-covC/,) (3.7) where mf : Mean value of strength in one location cov(/ (.) : Coefficient of variation of strength in one location p{ : Ratio of the local amount of the species and the total amount of this species in the country. 22 Chapter Three Reliability Analysis of Chinese Timber Design Code 3.1.2.2 Quality variability factor KQ Small clear test specimen strength is different from full size member strength. This is caused by several reasons. First of all, the strength of full size specimen is governed by the natural strength reducing characteristics, including knots, cross grain and cracks, etc. Such defects do not exist in small clear specimens. Second, there may be additional strength reducing characteristics in full size specimens due to the drying process. A study of the quality variability factor was conducted through 132 locations in China. Testing specimens were divided into two groups according to sizes. For small clear specimen tests, 46750 testing data were recorded from 1182 samples of 22 softwood species and 1120 samples of hardwood species through tension, compression, bending and shear testing. In addition, 748 testing data of four species were taken from the full size testing members, which had knots and cracks [8]. Finally, the quality variability factor KQ was expressed as KQI ' K 0 2 • KQ3 • KQ4 (3.8) where K K 22 K G3 K 24 : Natural defects factor : Drying defects factor : Long term loading factor : Structural member size factor Statistical parameters of these random variables are listed in Table 3-4. Compression Tension Bending Shear parallel to grain parallel to grain parallel to grain KQI M E A N 0.80 0.66 0.75 -COV 0.14 0.19 0.16 --KQ2 M E A N - 0.90 0.85 0.82 COV — 0.04 0.04 0.10 KQ3 M E A N 0.72 0.72 0.72 0.72 COV 0.12 0.12 0.12 0.12 KQ4 M E A N - 0.75 0.89 0.90 COV - 0.07 0.06 0.06 Table 3-4 Statistical parameters for quality factors 23 Chapter Three Reliability Analysis of Chinese Timber Design Code Based on the assumption that all these random variables were independent, the mean value and coefficient of variation of KQ was expressed as _ and cov(KQ) = ^jcov(KQL)2 + cov(KQ2)2 + cov(KQI)2 +cow(KQ4)2 The results are listed in Table 3-5. (3.9) (3.10) C o m p r e s s i o n T e n s i o n B e n d i n g S h e a r para l le l to gra in paral le l to gra in para l le l to gra in K Q M E A N 0 . 5 8 0 . 3 2 0 . 4 1 0 . 5 3 C O V 0 . 1 8 0 . 2 4 0 . 2 1 0 . 1 7 Table 3-5 Statistical parameters for quality variability factor 3.1.2.3 Geometry variability factor KA Real geometry characteristics are not exactly as same as the nominal or design geometry characteristics. Generally, the variability of geometry characteristics is much smaller than the variability of load and material strength. This variability, however, still needs to be considered in developing a limit states design code. Based on a survey performed in 29 construction sites or manufactures plants of 7 provinces, 6556 testing data points were recorded from bending members of 344 wood trusses and 876 purlins. In addition, 2000 test data were recorded from members having the defects and dimension faults [8]. By the analysis of those data, the geometry variability was defined as a random variable: a ab (3.11) where a : Member geometry dimension value ak : Design or nominal member geometry dimension value The mean value of KA and coefficient of variation cov(K A ) were — a K A = — a,. (3.12) 24 Chap te r T h r e e Reliability Analysis of Chinese Timber Design Code cov(KA) = cow(a) (3.13) Table 3-6 shows the statistical parameters for geometry variability factor. Compression Tension Bending Shear parallel to grain parallel to grain parallel to grain K A MEAN 0.96 0.96 0.94 0.96 COV 0.06 0.06 0.08 0.06 Table 3 -6 Statistical parameters for geometry variability factor 3.1.2.4 Analysis model variability Kp The analysis model factor is defined as a ratio of the design equation result to the more accurate theoretical result. Or, it is a ratio of design equation results to experimental testing results. For this purpose, test data were recorded through the compression, shear experiments, as well as the combined bending and compression testing of 147 full size members [8]. Analysis model factor was expressed as: R" KP ~ R C where R" Rc (3.14) : Actual member resistance (testing results or accurate calculation results) : Member resistance calculated through code functions Table 3-7 shows the statistical parameters for model variability factor. Compression Tension Bending Shear parallel to grain parallel to grain parallel to grain K P MEAN 1.00 1.00 1.00 0.97 COV 0.05 0.05 0.05 0.08 Table 3 -7 Statistical parameters for model variability factor 3.1.3 Results The performance function used in the reliability calculation was G = R-SG -SQ (3.15) 25 Chapter Three Reliability Analysis of Chinese Timber Design Code This performance function included three random variables. After the statistical parameters of load and member resistance were determined the reliability index J3 was calculated according to the method specified in the unified reliability code. For different load ratios, the mean value of the reliability indices was taken as the final result in Table 3-9. For dead load plus occupancy load in office (load ratio: S L K / S G K = 1-5) Compression parallel to grain Tension parallel to grain Bending Shear parallel to grain p 4.29 4.72 4.26 4.36 Table 3-8 p value under dead load plus occupancy (office) load For dead load plus snow load (load ratio: S S K / S G K = 0.2, 0.3, 0.5) Compression jaarallel to grain Tension parallel to grain Bending Shear parallel to grain P 3.40 3.93 3.37 3.47 Table 3-9 p value under dead load plus snow load After adjustment, the target reliability indices adopted for reliability assessment of wood were 1) Bending and compression parallel to grain fio = 3.20 2) Tension parallel to grain and shear parallel to grain Bo = 3.70 The reliability level, which needs to meet the target reliability level, was taken as the average of reliability indices under two load combinations. Table 3-10 shows the results published in the timber design code commentary. A l l the reliability levels meet the requirements specified in the unified reliability code [11]. Compression parallel to grain Tension parallel to grain Bending Shear parallel to grain p 3.8 4.3 3.8 3.9 Table 3-10 B value published in the timber design code 3.2 Wood strength design values The establishment of wood strength design value is a complicated procedure in China. It is based on these studies: • Small clear wood testing database 26 Chapter Three Reliability Analysis of Chinese Timber Design Code Full size test database (limited specimens) National testing standard Design functions Reliability study Engineering experience According to the unified reliability code, material strength should be defined according to following requirements 1) Material strength fits to the Normal or Lognormal distribution. 2) Characteristic strength is the 5 t h percentile strength. The design equation in the Chinese timber structural code is expressed in a working stress design format and the performance factor is normally concealed in the design properties as 70<r<f (3.16) where yo '• Structure importance factor a : Design stress of the structure members, a = SI aK S : Design reaction force of structure members, to be calculated according to combinations of the loading effects specified in the load code. f : Wood strength design value aK : Geometry parameter characteristic value The wood strength design value is calculated according to f = fK/yf (3.17) where fK : Characteristic strength yf : Material property division coefficient 3.2.1 Characteristic strength Wood characteristic strength is usually determined in the following equations: (3.18) 27 Chapter Three Reliability Analysis of Chinese Timber Design Code or fK=uf(\-uaSf) (3.19) where Pk : Probability that wood strength / is lower than wood characteristic strength/^, here is 0.05. F~'(/> ): Value of the inverse function of the wood strength probability distribution function at point Pk juf : Mean strength based on small clear specimens testing o~f : Standard deviation of wood strength based on small clear specimens testing Sf : Coefficient of variation of wood strength based on small clear specimens ua : Coefficient determined based on wood strength distribution functions, obtained from the probability distribution chart For Normal distribution, ua at lower 5 t h percentile is 1.645, therefore characteristic strength can be rewritten as fK =uf ( l -1 .645^) (3.20) 3.2.2 Material property division coefficient Material property division coefficient y}- is defined as 7f =7R/MK,MKAMKQ (3-21) where yR : Resistance division coefficient of structural member jUKp : Mean value of analysis model variability JUKA : Mean value of geometry variability juK : Mean value of quality variability 28 Chapter Three Reliability Analysis of Chinese Timber Design Code Based on the target reliability indices the resistance division coefficient of wood structural member yR can be calculated by using the method illustrated in the unified reliability code. In this procedure, the permanent load effect factor yG is taken as 1.2 and variables load effect factor yQ is taken as 1.4. The results of the resistance division coefficient based on the four load ratios p (0.2, 0.3, 0.5 and 1.5) are: 5) Bending members, yR = 1.60 6) Compression member (parallel to grain), yR = 1.45 7) Tension member (parallel to grain), yR = 1.95 8) Shear member (parallel to grain), yR =1.50 Based on the information of yR and mean values of three variability factors, it is easy to get the material property division coefficient yf. 1) Bending, yf = 4.2 ; 2) Compression parallel to grain, yf = 2.6 ; 3) Tension parallel to grain, yf = 6.4; 4) Shear parallel to grain, yf = 3.0. After the characteristic value and material property division coefficient are specified, the design value of a species can be easily calculated. The value published in the code, however, might not totally agree with the calculated results [9]. This is caused by two reasons. First, the design values published in the code are based on stress class system. In the timber structural design code, there are four strength classes for softwood, and five strength classes for hardwood. Different species are classified into various stress classes. In this case, each stress class includes several species and these species share one set of design values. Moreover for all the species included in a specified strength class, their reliability indices under different load conditions should equal or exceed the target reliability indices. 29 Chapter Three Reliability Analysis of Chinese Timber Design Code S e c o n d , f o r s o m e s p e c i e s c h a r a c t e r i z e d w i t h m o r e n a t u r a l d e f e c t s , t he c l a s s i f i c a t i o n o f the s t ress c l a s s c a n n o t t o t a l l y d e p e n d o n the r e l i a b i l i t y s t u d y . I n s u c h c a s e , e n g i n e e r i n g e x p e r i e n c e w a s u s e d to d e t e r m i n e the d e s i g n v a l u e s o f s u c h s p e c i e s . 30 Chapter Four Chinese Load Models 4. CHINESE L O A D MODELS 4.1 Dead load Dead load includes the weight of structural members and the components that it supports permanently. It is commonly assumed to remain constant during the service life of a structure, as illustrated in Figure 4-1. Load level Time (years) Figure 4-1 Dead load Model The uncertainty of dead load is due to dimensional tolerances and the uncertainty of unit weights. In order to evaluate the uncertainty of the dead load and derive its statistical model in China, dead load data was collected from 17 provinces [8]. A normalized random variable Q G = GIGk was used to express the randomness in the dead loadG. Here, the nominal dead load Gk, based on the average weight of the material, was expressed as the product of the member's dimension and its material density. The density of common construction materials were listed in the load code. Based on results of the dead load analysis, the normalized random variable Qc was represented by Normal distribution. Its density function was given by far(*) = 1 exp (w-1.060)2 (4.1) 0.074V2/T "I 0.011 where the Mean=1.060, Standard Deviation=0.074. This Normal distribution can also be re-written as: x = 1.060 +0.074 •/? (4.2) 31 Chapter Four Chinese Load Models where R is a Standard Normal Variate with zero mean and standard deviation=l. Because the dead load in a building will not vary during the service life of the structure, the distribution model of maximum dead load in the structure's 50-year service life is the same as the annual dead load. 4.2 Occupancy load The occupancy load includes the weights of furniture, equipment, stored objects and persons. These loads vary randomly in time and space. Generally, occupancy load is divided into two load processes: sustained and extraordinary. The sustained load contains the weight of furniture and heavy equipments, which tends to have relatively long duration. It also depends on the use of building. The extraordinary load refers to the regular gathering of people, temporary stacking of furniture as well as crowded room for special events. Compared with the sustained load, the duration of the extraordinary load is relatively short. Occupancy load is distinguished according the intended user category of the building, such as the office, residential and commercial buildings. To get the statistical information of the occupancy load, surveys were conducted for these main types of buildings in China. Data were collected from 133 office buildings, 566 residential buildings and 20 commercial buildings in 25 cities in China [8]. According to the survey results and detail recorded history of changes of users and building purpose, the sustained and the extraordinary loads were both assumed to be represented by the Extreme Type I (Gumbel) distribution in this reliability analysis. 4.2.1 Sustained occupancy load In general, the period between changes of sustained occupancy load is a random variable. According to the survey results of the sustained load, however, the average period between the changes of the sustained load was approximately 10 years. Therefore, the return period of the sustained occupancy load was assumed to be 10 years, as illustrated in Figure 4-2. 32 Chapter Four Chinese Load Models 0 TD TO ^ T j W Time (years) TO T Figure 4-2 Sustained live load model The data obtained by survey showed that the sustained live load L, in a 10 year return period was fitted to Extreme Type I (Gumbel) Distribution according to (-ln(-lnp)) L. = B + - (4.3) The distribution parameters A and B were related to the mean value of the Li and coefficient of variation cov(L,) , where A = ].282/[cov(L,.)L~] , B = Z~-(0.577/A) A B Mean SD COV office residential 7.204 7.924 0.306 0.431 0.386 0.504 0.178 0.162 0.461 0.321 4.2.2 Extraordinary occupancy load It is difficult to get accurate information about the period between extraordinary occurrences and the duration of pulse for the extraordinary occupancy load, as illustrated in Figure 4-3. Therefore, all the data came directly from the survey of the people's memories about the variability of the extraordinary load in a 10-year period. Based on the analysis of the survey results, the extraordinary occupancy load in a 10-year return period was also assumed to follow the Extreme Type I (Gumbel) distribution. 33 Chapter Four Chinese Load Models Lr{t) Time (years) T Figu re 4-3 E x t r a o r d i n a r y occupancy load model The distribution of Extraordinary Occupancy Load L r , in a 10-year return period was obtained according to ( - ln(- lnp)) Lrx=B + (4.4) The distribution parameters A and B were related to the Mean Value of the ^ and coefficient of variation cov(Z T j) where A = 1.282/[cov(L r t)-L rJ , B = ClLr -(0.577/A) A B Mean SD C O V office residential 5.257 5.092 0.245 0.355 0.355 0.468 0.244 0.252 0.687 0.538 4.2.3 Max imum occupancy load in 50 years To evaluate the building safety in a 50-year service life, the distribution of maximum sustained load in 50 years LiT and maximum extraordinary load in 50 years LrT needs to be calculated based on the distributions of the sustained occupancy load in 10-year period L. and extraordinary occupancy load in 10-year period LTs according to ^ W = KWj (4.5) F^AFJX)) (4.6) 34 Chapter Four Chinese Load Models Given the distribution of LiT and LTT, the distribution of the maximum combined load over a 50-year period LT was obtained by using Turkstra's rule. In the two load cases, the procedure can be summarized in following steps • Design for the largest lifetime maximum value of Load 1 plus the value of Load 2 that will occur when the maximum value of Load 1 is on. • Also design for the lifetime maximum of Load 2 plus the value of Load 1 that will occur when Load 2 is on. • Select the larger of these two designs. This procedure was conducted with four occupancy loads— Li, L n . , LiT and Finally, the statistical parameters of the maximum occupancy load was taken •'TT as o (4.7) •Lr -yI°i+°lT (4-8) Table 4-1 shows the statistical parameters corresponding to office and residential occupancy loads. office residentia Mean SD COV Mean SD COV u 0.386 0.178 0.461 0.504 0.162 0.321 0.355 0.244 0.687 0.468 0.252 0.538 LIT 0.610 0.178 0.292 0.707 0.162 0.229 Ln 0.661 0.244 0.369 0.784 0.252 0.321 Lj- 1.047 0.302 0.288 1.288 0.300 0.233 LK 1.5kN/m2 1.5kN/m2 Table 4-1 Statistical parameters of occupancy loads For the maximum occupancy load in 50 years, it was expressed as: For office: L? =0.91108 + For residential: L\ =1.15298 + (-ln(-lnp)) 4.24685 (-ln(-lnp)) 4.27517 (4.9) (4.10) 35 Chapter Four Chinese Load Models The random variable LT I Lk was used in the reliability analysis, where Lk was the nominal value of the occupancy load. Therefore, the statistical model was defined as: h L„ 1.5 For office: =0.607387 + For residential: 0.768653 + (-ln(-lnp)) 6.37028 (-ln(-lnp)) (4.11) (4.12) (4.13) 6.412755 The statistical parameters used in the reliability study are listed in Table 4-2 office residentia Mean SD COV Mean SD COV 0.70 0.203 0.29 0.86 0.198 0.23 u 1.5kN/m 2 1.5 kN/m2 Table 4-2 Statistical parameters of live loads 4.3 Wind load Wind load for the structures not only depends on the general wind climate at the site, the roughness of ground surface and the exposure of buildings, but also depends on the dynamic properties, the shape and dimensions of the building. In China, the annual wind velocity and wind directionality were recorded based on the local meteorological observations from 29 meteorological station located in 18 provinces. Totally 656 recorded data of annual wind velocity and wind directionality were used in the statistical analysis. In addition, 27 sets of wind tunnel experimental data were also recorded and analyzed [8]. Statistical analysis of the wind load needs three random variables: 1. Wind velocity 2. Reference velocity pressure 3. Wind pressure 36 Chapter Four Chinese Load Models The recorded wind velocity was used to calculate the reference velocity pressure, which depends on the climatic conditions of the site. It can be considered as a random process based on the assumption that all the climatic conditions are kept constant. The reference velocity pressure was transformed to wind pressure by using several coefficients, which were also considered to be time-independent random variables. In addition, the wind directionality was also considered in the statistical models of reference velocity pressure and wind pressure where two cases defined as "with directionality" and "without directionality" were considered. 4.3.1 T h e w i n d v e l o c i t y a n d r e f e r e n c e v e l o c i t y p r e s s u r e According to the Chinese load code [12], the average maximum wind velocity, recorded at the 10m reference height and in a 10-minute duration period, was used to calculate reference velocity pressure w as 1 7 2 w = -—v2 (4.14) 2 g where y : Gravity of unit volume air 0.012018kN/ m 3 for dry air at 15 °C and the atmospheric pressure at 101.325kPa 8 : Acceleration of gravity, 9.8 m/s2 v : Wind velocity (m/s) 4.3.2 T h e m o d e l o f r e f e r e n c e v e l o c i t y p r e s s u r e The first statistical model of wind load was based on statistical analysis of the annual maximum reference velocity pressure (without directionality) Woy . A normalized random variable Q.w, = Woy IWok was used to express the randomness in the annual maximum reference velocity pressure (without directionality) W , where W0k was the 30-year return reference velocity pressure. The annual maximum reference velocity pressure (with directionality) W(n. was taken as 90% ofWtn.. 1) Annual maximum reference pressure (without directionality) Wm 37 Chapter Four Chinese Load Models For each city, the random variable Woy was represented by Extreme Type I (Gumbel) distribution according to „,• _ (- ln(- lno)) Woy=B + - A (4.15) The distribution parameters A and B were related to the mean value of the Woy and coefficient of variation cov(w„'v), where A = 1.282/[cov(VV>W^] , B = W^-(0 .577/A) 2) 30-year return reference velocity pressure Wok The 30-year return reference velocity pressure W()k was calculated through using the statistical parameters of Wuy for each city with a probability of non-exceedance p=29/30, according to A 3) The normalized random variable Qw. Since Wok was a constant, the random variable Qw-=Woy/Wok was represented by an Extreme Type I distribution, according to q„. = F + ( - l n ( - l n p ) ) (4.i7) A' with a corresponding mean value of Q.w. and coefficient of variation cov(Qw.)for each city, where A = 1.282 /[cow(Qw.) • , B = - (0.577 / A) 4.3.3 The national reference velocity pressure The normalized random variable Cl\ of the national reference velocity pressure statistical model was obtained by calculating the average of each city's statistical parameters, which were the mean value of Q,w. and coefficient of variation cov(Q l v.) according to 38 Chapter Four Chinese Load Models W / i w n i C O V ( Q ; . ) = - X C O V ( Q , , ) (4.18) (4.19) The normalized random variable was expressed as an Extreme Type I (Gumbel) distribution according to g . t ( - ln(- lnp)) (4.20) The distribution parameters A*and B* were related to the mean value of Q.*w. and coefficient of variation cov^^ . ) , where A* = 1.282/[ cov(Q ; . ) ' f tT ) ] . 5* = O T - ( 0 . 5 7 7 / A * ) The normalized random variable £l*w, which reflected the randomness of the annual maximum reference velocity pressure (with directionality) Woy , was represented by the Extreme Type I distribution with its statistical parameters as n > o . 9 - n ^ (4.2i) cov(ft;) = 0.9cov(ft; .) (4.22) According to the "Chinese Unified Standard for Reliability Based Design of Building Structures" (GBJ 68-84), the distribution for the random variable Q.\ and Q*w were fitted to the Extreme Type I (Gumbel) distribution, according to: = fl. + ( - ln ( - ln„ ) ) A (4.23) A * B* Mean SD COV 1/0.157 0.364 0.455 0.202 0.444 ( - ln ( - ln A P)) A** g * * Mean SD C O V 1/0.142 0.328 0.410 0.182 0.444 (4.24) 39 Chapter Four Chinese Load Models 4.3.4 The national wind pressure statistical model The national annual maximum wind pressure (with directionality) Wy was calculated based on the annual maximum reference velocity pressure (with directionality) Wm. according to WY=KKzWoy (4.25) where K : External Pressure Coefficient, a random variable K Z : Exposure Factor, a random variable Both coefficients were random variables. The mean values of two factors were specified in the load code according to statistical analysis of the wind tunnel experimental data. The coefficients of variation were given as cov(y^) = 0.12 andcov(A\ ) = 0.10. Then the statistical parameters of the annual maximum wind pressure were calculated according to Without directionality: Mw- = • • MWm = 0-455 • fiK • fiKi • Wok = 0.455 • Wk (4.26) where juK • jUK^ : Mean value of K , K Z ju : Mean value of annual maximum reference pressure (without directionality), a = 0.455 • Wok Wk : Design or nominal wind pressure value in the load code, With directionality: juWy -=0.9MW = 0.410 (4.27) cov(lV;) = cov(W v) = J'COV(K)2 +cov(KZ)2 +cov(W„ v) 2 = 0.471 (4.28) The random variable Wy IWk was used in the reliability analysis, where Wk was the nominal wind pressure value. It was assumed that wind pressure model also was fitted to the Extreme Type I distribution according to 40 Chapter Four Chinese Load Models Without directionality: A* A* B * Mean SD COV 1/0.167 0.359 0.455 0.214 0.471 With directionality: A A * * g** Mean SD COV 1/0.151 0.323 0.410 0.193 0.471 4.3.5 The national maximum wind pressure in 50 years The design service life in China was stipulated as 50 years; therefore, the distribution of the maximum pressure that occurred over a given design service life was derived from the annual maximum pressure distribution according to Without directionality: Fn. (x) = [ F n . (x)]50 F n - (x) = expj-exp x-1.012 0.167 (4.31) A " B " Mean SD COV 1/0.167 1.012 1.109 0.214 0.193 With directionality: F n ^ ( x ) = [ F Q ; ( X ) ] 5 0 x-0.912" Fn- (*) = exp -exp 0.151 (4.32) A " B " Mean SD COV 1/0.151 0.912 1.000 0.193 0.193 41 Chapter Four Chinese Load Models 4.4 Snow Load The snow load has a very high variation across the different climate regions and geographical locations. Compared with the design snow load from 1.38kN/m2 to 3.10kN/m in different major cities in Canada, the design snow load in China seldom exceeds 1.00kN/m . In addition, the accumulation and depletion of snow on the roof are complex processes and depend on different factors, such as the ground snow load, wind exposure as well as the roof shape and type. The annual maximum ground snow was obtained based on the local meteorological observations from meteorological stations located in 16 provinces. A total of 384 recorded data of annual maximum ground snow were used in the statistical analysis. 4.4.1 Annual maximum ground snow load data The annual maximum ground snow height was recorded based on the local meteorological observations. The annual maximum ground snow load was expressed in the Chinese load code equation: S = hpg (kN/m2) (4.33) where h : Annual height of the snow accumulation (m) p : Average density of snow (kg/m3) • 150 kg/m3 for Northeast and Xinjiang area • 130 kg/m3 for North and Northwest area (120 kg/m 3 for Qin Hai Province) • 150 kg/m 3 for the south area of Wai River and Qin Lin (200 kg/m3 for Jiang X i and Zhe Jiang) g : Acceleration of gravity, 9.8 m/s2 4.4.2 The statistical model of ground snow load The snow load model was based on statistical analysis of the annual ground maximum snow load Soy. A normalized random variable Q.s = Soy I Sllk was used to express the randomness in the annual maximum ground snow load, where S(,k was the 30-year return snow load. 42 Chap te r F o u r Chinese Load Models 1) Annual maximum ground snow load Soy For each city, the random variable Soy was represented by an Extreme Type I (Gumbel) distribution according to _ (- ln(- lnp)) SOT=5 + - \ !> (4.34) A The distribution parameters A and B were related to the mean value of the Soy and coefficient of variation cov(5oy), where A = 1.282/[ cov(5 o y ) -5^ ], B = 5 ^ -(0.5771 A) 2) 30-year return snow load S„k The 30-year return snow load S(,k was calculated using statistical parameters of Soy for each city with a probability of non-exceedance p=29/30, according to ( - M - I . . 2 9 / 3 0 ) ) A 3) The normalized random variable Q ( Since S„k was a constant, the random variable Q.s = Soy I Sok was represented by an Extreme Type I (Gumbel) distribution, according to Q , = B ' + ( - l n ( - l n / ? ) ) (4.36) A' with a corresponding mean value of Q ? and coefficient of variation cov(Q 5) for each city, where A =1.282/[cov(Q ()-Q^], B = O j - (0.5771 A) 4.4.3 The national snow load statistical model The normalized random variable Q* for the national snow load statistical model were obtained by computing the mean value of each city's statistical parameters, the mean value of Q.s and coefficient of variation cov(Q s) according to Q > - y X (4.37) n , 43 Chapter Four Chinese Load Models 1 " C0v(O*) = — V cov(£2s) « i (4.38) The normalized random variable was expressed as an Extreme Type I (Gumbel) distribution according to n - = f l ' + (- l n(- l n*0) A* (4.39) The distribution parameters A*and B* were related to the mean value of Q] and coefficient of variation cov(Q*), where A* =1.282/[ cov(Q])-B* = Q*s - (0.5771 A*) 4 A A The snow load model in the code According to unified reliability code, the distribution for the random variable Q* was fitted to the Extreme Type I (Gumbel) distribution, according to ( - ln(- lnp)) Q =B +• (4.40) A * B * Mean SD C O V 1/0.221 0.271 0.399 0.284 0.712 For the structural design of buildings, the ground snow load must be adjusted to the roof snow load. However, the roof snow load information in China was poorly documented. The roof snow load Sy was taken 90% of the ground snow load Soy as Sy= 90%Soy. Accordingly, the distribution for the random variable =Sy/Sok introduced the randomness between the annual maximum roof snow load Sy and the 30-year return ground snow load Soy. Q* was fitted to Extreme Type I (Gumbel) distribution according to o: - 5 " + (-ln(-lnp)) (4.41) A * * Mean SD COV 1/0.199 0.244 0.359 0.256 0.713 44 Chapter Four Chinese Load Models Since the design reference period in China is 50 years, the maximum roof snow load in 50 years ST was calculated based on the annual maximum roof snow load SY according to FXT{x) = [FSy{x)]50 (4.42) For the purpose of the reliability analysis, the distribution for the random variable Q*7 =ST/SUK , which introduced the randomness between the annual maximum roof snow load in 50 years ST and 30-year return snow load S0k, was defined according to: l50 n* =B - ^ (ln50 + ( - l n ( - M ) ) = g „ , (- ln(-lnp)) A " (4.43) (4.44) where A"- A** , B"= B" + In 50 A ' B " Mean SD COV 1/0.199 1.024 1.139 0.256 0.225 4.5 Load models used in reliability analysis The 1984 version of the Chinese unified reliability code [8] provided the detailed information about the statistical model and parameters of the loads, which was also used in the reliability study of the 1988 version Chinese timber design code [9]. Detailed information is shown in Table 4-3. Load types Mean/Nominal Coefficient of variation Distribution Type Dead 1.06 0.07 Normal Occupancy(office) 0.70 0.29 Extreme Type I Occupancy(residential) 0.86 0.23 Extreme Type I Wind 1.00 0.19 Extreme Type I Snow 1.14 0.22 Extreme Type I Table 4-3 Statistical Parameters and distribution types for loads (1984 version) 45 Chapter Five Reliability Study of Wood in Canada 5. RELIABILITY STUDY OF WOOD IN CANADA Before the application of limit states design method, the timber design code in Canada was based on the working stress design method. While the first limit states design code CAN3-086-M84 was still a soft conversion of the old code, the second version— CAN/CSA-086.1-M89 incorporated formal reliability assessments in the development of the design equations and the specified strength properties for structural lumber. The main purpose of reliability evaluation was to calibrate design equations so that the structure members obtained by the limit states design equations can achieve a desired reliability level. This calibration work involved the establishment of the performance factors, load effect factors and other safety adjustment factors. The accuracy of the reliability evaluation depends on several factors, such as the quality of material strength database, the understanding of structural member behavior and structural analysis techniques. Because material strength of wood is more variable than other materials, the material strength database plays a key role in the whole reliability assessment procedure [15]. 5.1 Material strength database Material strength properties can be obtained by standardized testing methods. Before 1970s, small clear wood testing method was used to obtain wood strength properties in Canada. This method was also widely accepted all over the world because of its simplicity in testing and economy in cost. During the 1970s, however, Canadian and U.S. wood scientists revealed that the small clear testing was not an appropriate method to establish strength properties of full size visually-graded dimension lumber. For dimension lumber, instead, a more advanced test method—in-grade testing method was developed to establish the strength properties. Consequently, this method led to the Canadian in-grade testing program, which built a comprehensive database of structural properties for the commercially important species of Canadian dimension lumber. 46 Chapter Five Reliability Study of Wood in Canada Currently, both the small clear wood testing results and in-grade testing results are used to establish the strength properties of the wood in Canada. While the major dimension lumber properties such as modules of elasticity, bending strength, tensile strength and compressive strength are established from in-grade testing results, small clear wood testing results are still used to establish the strength properties such as the compression perpendicular to grain and horizontal shear strength [16]. 5.1.1 Small clear wood testing Small clear wood testing uses the small specimens of straight-grained and defect-free wood. It is assumed that full size member properties are proportional to the strength of small clear specimen with appropriate adjustments. In Canada, allowable design properties derived from the small clear wood testing are obtained according to A S T M standards. First, the small clear wood database is developed according to A S T M Standard D 1 4 3 (Standard Methods of Testing Small Clear Specimens of Timber), which describes test methods intended to evaluate the physical and mechanical properties of small clear specimens for different wood species. A S T M Standard D 2 5 5 5 (Standard Methods for Establishing Clear Wood Strength Values) provides an authoritative compilation of clear wood strength values for important species. It also aims to provide standardized procedures to establish the clear wood strength values and assign values to species combinations. A S T M Standard D 2 4 5 (Standard Methods for Establishing Structural Grades and Related Allowable Properties for Visually Graded Lumber) is used to establish grade rules for structural lumber and develop allowable design properties from the tests of small defect-free wood specimens. In Canada, N L G A (National Lumber Grades Atithority) Standard Grading rules were derived from A S T M Standard D 2 4 5 . For allowable properties for timber design, this standard describes the concept of the 5% exclusion limit. The 5% exclusion limit is the strength level that is exceeded by 9 5 % of the population. In addition, this standard provides a series of modification factors including the grade factor, size factor, seasoning factor, safety 47 Chapter Five Reliability Study of Wood in Canada and duration of load factor that are used to convert the small clear wood property to the strength of full-size lumber members. 5.1.2 Shortcomings of small clear wood testing In the early 1970s, Prof. Madsen and others wood science scientists in Canada found that the behavior of small clear specimens were quite different from behaviors of full size members. Studies in support of their opinion showed that using the small clear test results for scientific study of wood properties was one thing, using the results for the full size member structural properties was quite another [17]. One of the main shortcomings of small clear testing was that the small clear wood specimen and the full size member had quite different failure modes. For example, bending failure of the small clear specimen was initiated by the formation of winkles in the compression side, while the failure of full size member was normally caused by the tension perpendicular to the grain stresses around knots and the strength reducing effect of slope of grain. Moreover, the small clear wood specimen normally had a relatively constant strength along the length of the member. In the full size member, however, knots and the other strength reducing characteristics were distributed more discretely along the length of full size member. The availability of full size member test results further raised questions regarding the choice of statistical models to represent full size member strength as well as the appropriateness of the adjustment factors used to derive the full size member properties based on the small clear testing. While Normal distributions were always assumed to be an acceptable fit to the data from small clear wood specimens, research results showed that Weibull distribution fitted the result of full size testing better. In addition, studies also focused on the adjustment factors adopted by working stress design code. The result revealed that these factors, which related to the duration of load, moisture content, depth effects, grade effect and safety, were not appropriate in many cases. Consequently, it was concluded that the small clear specimen and the full-size structural member behaved as two different materials. It was agreed that the full 48 Chapter Five Reliability Study of Wood in Canada size tests provided the most reliable basis for deviation of characteristic properties for members used in structural applications. In order to improve the reliability of wood structures and promote the efficient use of wood resources, the full size in-grade testing method was adopted in the mid of 1970s to establish the strength properties for dimension lumber. Later, it evolved into In-grade test program for the dimension lumber products that was implemented in Canada and U.S. 5.1.3 In-grade testing The principle of in-grade testing was articulated in Professor Borg Madsen's book "Structural Behavior of Timber" [17]: "The test results should, as closely as possible, reflect the structural end use conditions to which the timber products would be subjected.". It means the testing has to emulate the end use conditions of the full size structural member as closely as possible. In-grade testing method was different from small clear wood testing from several aspects. First of all, a large sample size was taken to establish the characteristic values of different dimension lumber products. Second, major commercial species groups such as Douglas Fir-Larch, Hem-Fir, and Spruce-Pine-Fir, were evaluated as species groups rather than individual species. In addition, in order to facilitate the large number tests, a higher rate of loading was adopted and in some studies a proof loading method was promoted to save the manpower and cost of testing. Moreover, portable test equipment was developed in some studies to accommodate testing conducted in the mills. Also, new testing standards were developed according to the in-grade testing principle. In A S T M Standard D4761 (Standard Tests Methods for Mechanical Properties of Lumber and Wood-Base Structural Material), the mechanical properties test methods to be used on production sites for field testing and quality control were documented. This standard differs from the A S T M D198 (Standard Methods of Static Tests of Timbers in Structural Sizes) in terms of the testing speed, the deflection measuring procedures and the details of data reporting. In addition, it promoted the proof loading method. 49 Chapter Five Reliability Study of Wood in Canada Allowable properties can also be derived from in-grade tests by using either A S T M D2915 (Practice for Evaluating Allowable Properties for Grades of Structural Lumber) or A S T M D1990 (Practice for Establishing Allowable Properties for Visually Graded Dimension Lumber from In-grade Tests of Full-Size Specimens). The allowable properties for Canadian species used in United States were derived following the requirements of A S T M D1990-91. 5.1.4 CWC lumber properties project The first large scale in-grading testing program, which was organized by the N L G A (National Lumber Grades Authority) from 1977 to 1980, tested several important strength properties, including the mean modulus of elasticity and 5 t h percentile bending and tension strength properties. In this initial in-grade testing program, almost 60,000 bending and about 35,000 tension specimens were tested. As the extension studies of N L G A project, a more detailed second stage in-grade testing program was conducted from 1983 to 1985. This program, conducted in cooperation with U.S. researchers, was called the C W C (Canadian Wood Council) Lumber Properties Project. Its objective was to provide full size dimension lumber property data for deriving design properties for both limit state design and working stress design codes [18]. The results of two in-grade testing projects, N G L A and C W C Lumber Properties Project, had been used in the timber design codes since 1980. The 1989 edition of CAN/CSA-086.1 was the first timber design code based on a formal reliability analysis. In the development of this code, in-grade testing database of C W C Lumber Properties Project was used in the reliability assessment method established by Dr. Foschi and his colleagues at the University of British Columbia [16]. 5.2 Reliability evaluation To study the reliability of wood structure based on the in-grade testing database of the Canadian commercial dimension lumber, Dr. Foschi conducted a formal reliability 50 Chapter F ive Reliability Study of Wood in Canada analysis to wood structural members. Results of the study were implemented in the Canadian timber design code. The major work of this formal reliability evaluation was the calibration of performance factors for single members under short-term bending, tension or compression. In addition, the research covered the other reliability-based topics including the duration of load factors, system factors, behavior of columns and beam columns, design for ponding, serviceability limit states, shear design, as well as trusses and riveted connections [15]. 5.2.1 Load information Seven loading conditions, including snow loads, residential and office floor loads, were used in this study with the combination of dead load. Dead load was modeled as a random variable to account for the uncertainty of the dead load over the service life. It was assumed to be distributed normally, and the ratio of dead load to design load used in the reliability analysis can be expressed where d : Ratio of the dead load to the design load D : Dead load, random variable Dn : Design dead load, taken equal to the mean value Rn : Standard normal random variable Occupancy load was treated as a superposition of sustained and extraordinary load processes. Both load processes were assumed distributed according to Gamma distribution. The period between the changes of loads was assumed to be exponentially distributed in both load processes. For the extraordinary load processes, the duration of the pulse was modeled by a separate exponential distribution. Finally, computer simulation was used to get the maximum occupancy load in a 30 years service life. The simulated result for maximum load was fitted to Extreme Type I (Gumbel) distribution. Again, the load ratio, maximum load as 1.0 + 0.1/?, (5.1) 51 Chapter F ive Reliability Study of Wood in.Canada distribution model divided by design live load, was used in the reliability analysis. The statistical parameters are shown in Table 5-1. Occupancy Type Maxima 50 years Mean COV Qn(kPa) Residential Office 0.904 0.225 1.9 1.023 0.202 2.4 Table 5-1 Parameters for Canadian live load Snow loads, fitted to Extreme Type I (Gumbel) distribution, were taken from five cities in Canada. Table 5-2 shows the snow load data for six major Canadian cities. Location Mean COV 30-year return Vancouver 0.523 1.202 1.90 Halifax 1.199 0.498 2.50 Arvida 1.630 0.300 2.70 Ottawa 1.255 0.452 2.50 Saskatoon 0.903 0.401 1.70 Table 5-2 Snow load data for six Canadian cities The snow load model used in the reliability analysis was expressed as q = rg (5.2) where r : Roof load ratio, random variable g : Ratio of maximum load in 30 years to 30 year-return load, random variable 5.2.2 Member resistance Three major Canadian lumber species groups, Douglas-Fir, Hem-Fir and Spruce-Pine-Fir, were used in the reliability evaluation. Data was taken from three sizes, 2x4, 2x8 and 2x10. Results of C W C in-grade testing project used five different models to describe the property distribution. Four parametric models were Normal, Lognormal, two-parameter (2-P) Weibull and three-parameter (3-P) Weibull distributions. In addition, a non-parameter model, commonly used to describe the strength properties of wood products, was taken for reference. 52 Chapter Five Reliability Study of Wood in Canada Final results of the reliability analysis depended partly on the choice of the strength distribution type. In the case of bending strength, a reliability analysis was conducted by using the entire testing data. The relationship between performance factor 0 and reliability index (3 for four distribution types showed that Lognormal distribution resulted the least conservative and Normal distribution showed the most conservative results. Both Weibull distributions produced the intermediate results Further study revealed that distribution types with entire range of data could not represent the low 10% data well, which is more important for strength properties. Therefore, the lower tail of strength distribution was studies with a truncation at the 25 t h percentile and 15 th percentile. The result showed that the ambiguity caused by distributions types was decreased in the low tail of the data. Also, the 15 t h percentile showed good agreement with the 2-P Weibull distribution. Finally, 2-P Weibull with data truncated at the 15 t h percentile was chosen as the characteristic distribution mode. One reason for this was that it averaged the result of four distribution types. Another reason was that the Weibull distribution is an asymptotic representation for the distribution according to the minimum value among a large number samples. Therefore, it is suitable to represent material strength, especially for cases where the capacity of an assembly of many components is determined by the capacity of the weakest component in the assembly. 5.2.3 Results The performance function used in the reliability assessment, which was a combination of design equation and general performance function, was expressed as [15]. G = R-(1.25^+1.50) •(dy+q) (5.3) where 7 : Load ratio, Dn I Ql •n d : DID, n • QIQ, •n 53 Chapter F ive Reliability Study of Wood in Canada After the statistical parameters of load and resistance were determined, reliability index was calculated by F O R M (First Order Reliability Method), which was enrolled in the R E L A N program [15]. The initial study focused on the relationship of performance factor <p and reliability level J3. For a given reliability level, performance factors were obtained according to all the species, grades and sizes. The analysis of results showed that performance factors corresponding to a given reliability level did not have large difference between species, grades, sizes, as well as loading characteristics. It implied that a constant (j) could be used at different reliability level across all species, grades and sizes. In turn, for a given <p, the reliability level /? could vary with species, grades and sizes. Therefore, the non-parametric 5-th percentile R005 would also have different values according to species, grades and sizes. In the code format, however, it would be more appropriate to provide a characteristic strength only related to the variation of species and grades. A "smoothing" method, following the principle of minimum error, was used to calibrate the characteristic strength with the code performance factor and a size effect to account for the variation in member strength with member depth (or width). The main procedure of smoothing method was the minimization of the following function. r Ilk 2 (5.4) where : 1... 6 (three species, two grades) J : 1... 3 (three sizes) I : 1... 7 (seven loading conditions: five snow load cases plus residential and office loads) : Calculated resistance factor for each case o : Code resistance factor for property 54 Chapter Five Reliability Study of Wood in Canada R005 : Nonparametric 5 percentile for each cell Roi : Characteristic strength for a species-grade H0 : Standardized depth (184mm) L0 : Standardized length (3000mm) Hj : Test depth (for a given size) Lj : Test length (for a given size) k : Size effect parameter (resulting from method) In this procedure, the performance factor <j>o , the strengths Rni and the parameter k were calibrated by minimization of minimum error theory. This method was used to establish the characteristic values, which was adjusted to a 2x8 size with dry condition (15% moisture content), for bending, tension and compression parallel to grain. 5.3 Specified strengths Specified strength is the strength assigned for use in the prediction of member resistance. The value of the specified strength is published in the Canadian wood design code for engineering calculations [19]. Based on the characteristic strength, the specified strengths in bending can be expressed as fh=C(KD)(dJdsylk(Lc/Ls)m (5.5) where c : Characteristic bending value, MPa KD : 0.8 (duration of load factor) dc : 184mm (characteristic depth) ds : 286mm (specified depth) k : 3000mm (characteristic length) : 4862mm (specified length, at 17:1 span/depth ratio) k : Size factor, 4.3 55 Chapter Five Reliability Study of Wood in Canada In this function, size and duration of load adjustments are made to the characteristic properties to establish the specified strength values. The published strength value is based on the largest common dimension lumber size — 2 x 12 (38 x 286mm). Generally, the biggest size lumber has the lowest strength value. While the original characteristic strength value is based on the size 2x8, the adjustment is made to transfer it into 2x12. One reason for this adjustment is that the resulting factored resistance will still be safe if the designer does not apply the modification for size Kz. Duration of load must be considered in the design process. It is well known that wood, as a structural material, is stronger under the short-term duration load than the long-term load. In order to incorporate the factor for snow and occupancy loads directly into the specified strengths, the duration of load adjustment factor KD is applied to the specified strength. The duration of load factors were developed based on long-term loading tests conducted on full-size lumber. The duration of load factors were derived so as to achieve the same level of reliability under short-term and long-term loading. Similarly, the design procedures for tension strength fh, the compression parallel to grain strength fc and the longitudinal shear strength /„ were also established in reliability based approach. The mean strength of the compression perpendicular to grain / was set equal to characteristic values, while modulus of elasticity was set equal to characteristic mean M O E values for Select Structural, N o . l , No.2 and No.3 grades. 5.4 Modification factors The final factored resistance in the design equation is calculated with additional two groups of adjustment factors. The first group factors are related to material behavior. In the case of bending, bending resistance is expressed as Fh=fb{KDKHKshKT) (5.6) where KD : Duration of load factor KH : System factor 56 Chapter Five Reliability Study of Wood in Canada Ksb : Service condition factor for bending KT : Treatment factor The long term duration of load effect is directly incorporated in the specified strengths. The duration of load for the standard term is taken as 1.00. In the other two cases, KD is taken as 1.15 for short term and 0.65 for permanent duration of loading. The system factor KH is established to account for the high structural capacity of redundant of wood structural systems. A reliability study of the system modification factors was conducted for light frame floors and flat roofs. There are two different degrees of structural interaction (Case 1 and Case 2). Case 1 applies to systems of closely spaced structural components such as light-frame trusses. KH is taken as 1.10 for bending, shear, compression parallel to grain as well as tension parallel to grain. Case 2 includes the conventional wood frame floors, roofs and walls. Different system factors are applied for different materials used in the system. Studies of strength and stiffness changes of dimension lumber due to moisture content show that member capacities and stiffness are higher in dry service conditions than wet service conditions. The specified strengths are derived by assuming the structural member is used in the dry service condition. Therefore, service condition factor Ks is applied to adjust specified strength to the wet service condition in design calculations. Dimension lumber treatments, such as the preservative treatment and fire-retardant treatments, will reduce the strength of the lumber, especially for those small dimensions lumber. For this reason, the treatment factor KT is applied with dry or wet service conditions. The second group of adjustment factors involves the member geometry and configuration, as well as the resistance factor based on the reliability analysis. For the bending resistance moment, it can be expressed as: M^QF^K^K, (5.7) where <p : Resistance factor for bending S : Section modulus 57 Chapter Five Reliability Study of Wood in Canada : Size factor for bending KL : Lateral stability factor The resistance factors, based on the reliability study, are taken as 0.8 for compressive properties, and 0.9 for the other properties. Strength properties of lumber members vary by the member size. In order to maintain uniform reliability levels for all member sizes under all load cases, the size factor Kz is established under different load conditions. Size factors for bending and shear depend on the member width and thickness. For tension parallel to grain, it depends on the width. For compression parallel to grain, the size factor is a function of both column length and the member dimension in the direction of buckling. 58 Chapter Six Reliability Evaluation of Lumber Design Values in Chinese Code 6. RELIABILITY EVALUATION OF L U M B E R DESIGN VALUES IN CHINESE CODE The dimension lumber design values in the Chinese timber design code GB 50005-2003 were converted from the reference strength values specified in the A F & P A 16-95— Standard for Load and Resistance Factor Design (LRFD) for Engineering Wood Construction. The purpose of this soft conversion method was to obtain the same member sizes under the same live load at a live-to-dead load ratio 3 by either the LRFD or Chinese codes. Chinese timber design code is a limit states design code based on reliability analysis. Therefore, design parameters, especially design values of dimension lumber, should be established based on the reliability study. Although same member size under same load conditions could be obtained by both Chinese and North American codes, the reliability level could be different according to different reliability evaluation methods, load information and load combinations. Still, the Chinese timber design code needs to satisfy the reliability criteria specified in the Chinese unified reliability code. One of the most important requirements is the compatibility with target reliability levels. Although the current design values were obtained by the soft conversion method, it is important to evaluate their reliability levels and compare them with the target reliability levels. F O R M method in the R E L A N program was used to calculate the reliability level /3 under three load combinations, dead load plus occupancy load in office, dead load plus snow load and dead load plus wind load. And the average of reliability indices in three load combinations was taken as final result to compare with the target reliability index. In order to evaluate the reliability levels of design values in the Chinese code, appropriate performance functions, a material strength database and load information was developed and presented. Then the reliability levels of single members are evaluated under three load conditions, bending, compression and tension. Also, the reliability level of serviceability is also investigated. 59 Chapter Six Reliability Evaluation of Lumber Design Values in Chinese Code 6.1 Performance functions The performance functions G are formulated for specific design equations. The design equation is used to obtain structural dimensions using nominal loads and strengths. The G function includes random variables to represent the performance of the single member under the assumed load model. In this study, design equations and specific load combination are obtained from Chinese timber design code. 6.1.1 Strength limit states The design equation in the design code and the G function are 1.2-E{Dn) + lA-E{QN) = fKz (6.1) and G = R-[E(D) + E(Q)] (6.2) where E(Dn) : Nominal dead load effects E(QN) : Nominal live load effects E(D) : Dead load effects (random variable) E(Q) : Live load effects (random variable) / : Design value for dimension lumber published in the code Kz : Size effect for different lumber sizes R : Bending, compression or tension strength (random variable) If the design equation is incorporated into the performance function with the introduction of load ratio, the ratio of nominal dead load to nominal live load, the performance function can be rewritten as: G = R - f K z (dr+q) (6.3) (1.2/+1.4) where y : Load ratio, Dn I QN d : DI Dn, the ratio of dead load to nominal dead load q :QI' <2n, the ratio of live load to nominal live load 60 Chapter Six Reliability Evaluation of Lumber Design Values in Chinese Code 6.1.2 Serviceability limit states The reliability level of serviceability is also investigated in the study. The design equation in the design code and the performance function G are 5 (D+Q)s-L4 L A = — — = ^ < — (6 4) m a x 384 EI ~K { } L 5 (D + Q)sL4 G = -i ^ (6.5) K 384 EI K J where A m a x : Maximum transverse deflection D„,Qn '• Nominal dead load and live load s : Spacing between the beams L : Span of beam K : Limiting deflection factor, specified as 150, 200 and 250 according to different structural application E : Published modulus of elasticity E : Modulus of elasticity, random variable / : Moment of inertia of the beam cross-section If the design equation is incorporated into the performance function with the introduction of load ratio, the ratio of nominal dead load to nominal live load, the performance function can be rewritten as: G = 1_Z.fe±i) ( 6.6 ) E (r+D 6.2 Strength database Reference strength values in the L R F D code were converted from the design values of A F & P A National Design Specification (NDS) for Wood Construction. Originally, the NDS design values for lumber were derived from full size in-grade testing data. The in-grade testing results of Canadian commercial species, specified as Douglas Fir-larch (north), Hem-Fir (north), and Spruce-Pine-Fir in both the U.S. and Chinese codes, were introduced into the NDS design code in 1991 [18]. 61 Chapter S ix Reliability Evaluation of Lumber Design Values in Chinese Code 6.2.1 Species, grades and sizes Canadian in-grade testing results of three major commercial species, Douglas Fir-Larch, Hem-Fir and Spruce-Pine-Fir are used in this study. They are specified as Douglas Fir-Larch (North), Hem-Fir (North) and Spruce-Pine-Fir in the Chinese code. The lumber properties study in Canada showed that no consistent differences could be found between the No. l and No.2 grades; therefore, identical design values were assigned to those grades. In this study, only two grades, Select Structural and No.2, which are specified as grades I c and IIIC in the Chinese code, were used in the reliability study. Table 6-1 shows the relationship between the Chinese and North American grades. GB50005 Grades North American Grades l c Select Structural He No.1 IIIc No.2 r v c No.3 V c Stud Vic Construction v n c Standard Table 6-1 Relationship between Chinese and North American grades Three sizes of dimension lumber are used in this study. Lumber sizes used in Chinese code, 40mm X 90mm, 40mm x 185mm and 40mm x 235mm, are deemed identical to 2x4, 2x8 and 2x10 of North American commercial lumber sizes. 6.2.2 Resistance distribution model Reliability study in Canada shows that resistance different distribution models of full size member strength properties significantly affect reliability levels. In order to study this effect in the Chinese code, the relationship between the reliability index and performance factor 0 is studied by using Chinese design equations. Then the performance function is written as: 0-^ 0.05 G = R — (1.2y+1.4) (dy+q) (6.7) where 62 Chapter Six Reliability Evaluation of Lumber Design Values in Chinese Code R : Bending strength, random variable A ' 0 0 5 : Nonparametric 5 t h percentile y : Load ratio, DJQn d : DI Dn, the ratio of dead load to nominal dead load 1 '• QIQ„ > the ratio of live load to nominal live load <p : Performance factor Using the entire data range of SPF No.2 2x8 and Chinese dead plus snow load model, the difference between four distribution types under a bending strength case is illustrated in the Figure 6-1. It shows Lognormal distribution has the relatively higher reliability level, and Normal distribution has the least reliability level. Both Weibull distributions produced the intermediate results. The final result shows the same trend illustrated in the Dr. Foschi's study. FORM Load ratio 0.25 7.0 -| 6.5 -6.0 -1.0 H 1 1 1 1 1 1 1 1 1 1 1 1 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 P e r f o r m a n c e F a c t o r Figure 6-1 /3 - 0 Relation for four distribution types (SPF No.2 2x8,100% data) In Canada, Dr. Foschi chose 2-P Weibull distribution as the distribution model for lumber. Also, his study illustrated that the lower 15 percent of the data can effectively reduce the variability between the different distribution models [15]. 63 Chapter Six Reliability Evaluation of Lumber Design Values in Chinese Code Considering the distribution model of lumber strength properties used in Canadian wood structure reliability study, 2P-Weibull distribution fitted to the lower 15 percentile of the data is taken in this study. On the other side, Chinese national unified reliability code suggests that the material strength should be fitted to either Normal distribution or Lognormal distribution. Wood strength, coming from the small clear testing, is fitted to the Normal distribution in China. Then the resistance of wood, which is a combination of small clear wood strength and several random variables used to convert the small clear strength to full size member strength, is represented by Lognormal distribution. Also, the data used to fit this Lognormal distribution model is entire range data. Figure 6-2 shows the Lognormal distribution does not represent the full distribution of test data very well. And Figure 6-3 shows that the lower tail fit, which is the most important part of the strength distribution for reliability analysis, does not show good agreement with the test data. 0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0 Bending Strength, R(MPa) Figure 6-2 Lognormal fit to 2x4 DF entire test data (Bending) 64 Chapter S ix Reliability Evaluation of Lumber Design Values in Chinese Code 0.4 T - - - In-Grade Test Data 100% Data Fit Lognormal o 0.2 --> 0.0 0.0 10.0 20.0 30.0 40.0 50.0 60.0 Bending Strength, R(MPa) Figure 6-3 Lognormal fit to 2x4 DF lower 100 test data (Bending) Considering the target reliability indices specified in the reliability code were calculated based on the Lognormal distribution, the entire date range fitted to Lognormal distribution is also studied. In sum, two distribution models are chosen in the current study of strength limit states: 2P-Weibull distribution fitted to the 15 percent of the lower tail and the Lognormal distribution fitted to the entire data range. In the serviceability limit states, 2P-Weibull distribution and Lognormal distribution fitted to the entire range data were used. Two different sets of reliability index results in bending, compression and tension, as well as the serviceability case will show us the effect of distribution models. These results could be the reference for the future reliability study. Finally, only one distribution model is used to investigate the reliability levels of design value published in the wood design code. 6.3 Load information Although the new national unified reliability code [7] did not publish detailed information for load models, two important adjustments were explained in the code. First, 65 Chapter Six Reliability Evaluation of Lumber Design Values in Chinese Code the 30-year return period for wind and snow load was updated to 50-year return period, which means, according to this update, the wind and snow load model should be updated. Second, the design occupancy load was increased from 1.5 kN/m 2 to 2.0 kN/m 2 , therefore the occupancy load model also needs to be modified according to this change. 6.3.1 Statistical parameters of load models In this study, the load distribution model and statistical parameters are taken from the Chinese wood reliability evaluation paper [11]. In this paper, the updated distribution models were given to the snow load and occupancy load. Because the wind load was not considered in the reliability study of Chinese wood structures, the distribution model of wind load was not listed. Therefore, the wind load model for the current study is based on the old version 30-year return period model. Detailed load information is shown in Table 6-2. Load Types Mean/Nominal Coefficient of variation Distribution Type Dead 1.060 0.070 Normal Occupancy(office) 0.524 0.288 Extreme Type I Occupancy( residential) 0.644 0.233 Extreme Type I Wind(30-year return) 1.000 0.190 Extreme Type I Snow(30-year return) 1.140 0.220 Extreme Type I Snow(50-year return) 1.040 0.220 Extreme Type I Table 6-2 Load statistical information for reliability evaluation 6.3.2 Load ratio Load ratio is defined as the ratio of nominal dead load to nominal live load in North America. In China, the load ratio is expressed, in reverse, as the ratio of nominal live load to nominal dead load. The typical dead-to-live load ratio for a wood-frame house in Canada was taken as 0.25, which was used in the reliability study for the CSA 086-1. In the Chinese soft conversion method, the dead-to-live ratio was assumed as 0.33. A research of more than 30 roof types in China showed that the live-to-dead ratio of wood roof ranges from 0.14 to 0.6. For the floors in office building, the live-to-dead ratio was about 1.5. In the reliability study, the live-to-dead load ratio 66 Chapter Six Reliability Evaluation of Lumber Design Values in Chinese Code 0.2, 0.3 and 0.5 were taken for the roof. Also, 1.5 was taken for the office building floor case. Given the load ratio definition in North America, the dead-to-live ratio was taken as 5, 3.3, and 2 for roof and 0.67 for the office building floor. The major difference of load ratios between Canada and China are basically caused by two facts. First, different styles of roof structure lead to different definitions of nominal dead loads. Instead of the light trusses in Canada, wood roofs are traditionally constructed using heavy timber in China. In addition, most of wood roofs are finally covered by cement roof tiles, which are much heavier than the weight of roof material typically used in Canada. This partly explains the higher dead load ratio adopted in China. Second, design live loads, such as snow load, are significantly different between two countries. Due to the different weather conditions as well as the snow accumulation level and time, the design snow loads in China are much less than the design snow loads of the major Canadian cities. Considering the variation of the load ratios, several load ratios are used to study the load ratio effect on the reliability levels. First of all, dead-to-live ratio is taken as 0.33, which was also used in the soft conversion procedure adopted in the current Chinese code. In addition, the dead-to-live ratio 0.25 used in the Canadian reliability analysis is also used for reference. A more consistent approach is to define the term "load ratio" as the ratio of dead-to-live loads based on the Canadian definition. In the reliability study of the Canadian code, the dead-to-live load ratio is taken as 0.25. Since the average design snow load in Canada is approximately 2.0 kN/m 2 , it indicates that the typical Canadian design dead load is about 0.5 kN/m 2 . On the other side, the design snow load in most of Chinese cities ranges from 0.2-0.5 kN/m 2 . Assuming the same light roof structure is used in both Canada and China, the dead load of both roofs would be 0.5 kN/m 2 . Therefore, dead-to-live load ratio of light roof system in China could be taken as 1 and 2.5. In the case of office floor loads, the dead-to-live load ratio is taken as 0.25, 0.33 and 0.67, which are consistent with the ones adopted in the Canadian reliability study, and also consistent with the assumption in the soft conversion method and the ratio adopted in the Chinese traditional wood structure. 67 Chapter S ix Reliability Evaluation of Lumber Design Values in Chinese Code 6.4 Bending 6.4.1 Or ig ina l data Table 6-3 lists the statistical information for bending strength according to different combinations of all the species, grades and sizes. These parameters are directly taken from the Appendix of Canadian Lumber Properties [18]. It includes: • Parameters of 2-P Weibull distribution (truncated at 15% Percentile) • Parameters of Lognormal distribution (100% data) • Design values fm in Chinese code • Size factor Kz 2-P Weibull(15%) Lognormal Species Grade Size Scale m (MPa) Shape k Mean Standard Deviation fm (MPa) K 2 DF SS 2x10 44.13 4.31 3.77 0.37 15.00 1.10 DF SS 2x8 50.88 4.46 3.97 0.39 15.00 1.20 DF SS 2x4 61.36 5.51 4.15 0.33 15.00 1.50 DF No.2 2x10 27.44 4.68 3.44 0.47 9.10 1.10 DF No.2 2x8 33.23 4.19 3.58 0.48 9.10 1.20 DF No.2 2x4 46.40 3.80 3.86 0.46 9.10 1.50 HF SS 2x10 42.13 4.44 3.68 0.33 14.00 1.10 HF SS 2x8 52.40 4.21 3.88 0.34 14.00 1.20 HF SS 2x4 68.88 4.75 4.15 0.31 14.00 1.50 HF No.2 2x10 32.54 4.30 3.46 0.39 11.00 1.10 HF No.2 2x8 44.26 3.45 3.70 0.43 11.00 1.20 HF No.2 2x4 52.61 4.04 3.96 0.40 11.00 1.50 SPF SS 2x10 38.82 4.77 3.55 0.28 13.00 1.10 SPF SS 2x8 43.44 4.72 3.68 0.29 13.00 1.20 SPF SS 2x4 55.30 5.77 3.97 0.28 13.00 1.50 SPF No.2 2x10 26.41 5.40 3.35 0.36 9.40 1.10 SPF No.2 2x8 34.13 4.41 3.53 0.38 9.40 1.20 SPF No.2 2x4 45.16 4.19 3.76 0.37 9.40 1.50 Table 6-3 Parameter estimates of Bending at 15% M.C. 68 Chapter S ix Reliability Evaluation of Lumber Design Values in Chinese Code 6.4.2 Effect of distribution types and load ratios To further illustrate the difference between bending strength distribution types and load ratios, a reliability index comparison study is conducted. By using the dead load plus snow load (30-year return) combination, reliability indices are calculated by G function 6.7 with two distribution models, 2-P Weibull (15%) and Lognormal (100% Data), each with four load ratios, 0.25, 0.33, 1 and 2.5. Table 6-4 and Table 6-5 show the results of the combination of all species, grades and sizes. Comparing the results in Table 6-4 and Table 6-5, significant difference is found between two distribution types. The Lognormal distribution with entire data results in an approximately 25% higher reliability index (3 than the Weibull distribution. To illustrate this relationship, R-<f> curve, which is similar to Dr. Foschi's study in Canada [15], is developed for SPF No.2 2x8 lumber under the dead load plus snow load (30-year return). Statistical parameters for the four distribution types are listed in Table 6-6. Figure 6-4 shows a graphic illustration of the trend of the results in Table 6-4 and Table 6-5, where the Lognormal distribution produces the relatively higher reliability indices than the others. Considering the requirement of Chinese unified reliability code and Chinese wood reliability study, the resistance needs to be fitted to Lognormal distribution. Finally, Lognormal distribution with entire data range is used in the further study. Table 6-4 and Table 6-5 also compare the reliability results obtained by using different load ratios. It is apparent that the reliability levels do not vary substantially with load ratios. Thus, this effect could be disregarded in the bending case. Since the dead-to-live load ratio 0.33 was used in the soft conversion method to derive the design values, reliability indices of load ratio 0.33 are used in the further study. 69 Chapter Six Reliability Evaluation of Lumber Design Values in Chinese Code Reliability index p Species Grade Size (load ratio) Average (0.25) (0.33) (1) (2.5) P DF SS 2x10 2.449 2.451 2.449 2.429 2.445 DF SS 2x8 2.591 2.593 2.593 2.575 2.588 DF SS 2x4 2.903 2.909 2.925 2.913 2.913 DF No.2 2x10 2.626 2.629 2.632 2.614 2.625 DF No.2 2x8 2.592 2.594 2.591 2.572 2.587 DF No.2 2x4 2.574 2.574 2.568 2.549 2.566 HF SS 2x10 2.534 2.536 2.535 2.516 2.530 HF SS 2x8 2.636 2.637 2.635 2.616 2.631 HF SS 2x4 2.925 2.928 2.933 2.917 2.926 HF No.2 2x10 2.454 2.456 2.453 2.433 2.449 HF No.2 2x8 2.392 2.391 2.381 2.361 2.381 HF No.2 2x4 2.595 2.596 2.591 2.573 2.589 SPF SS 2x10 2.643 2.647 2.651 2.633 2.644 SPF SS 2x8 2.665 2.669 2.672 2.655 2.665 SPF SS 2x4 3.053 3.061 3.082 3.071 3.067 SPF No.2 2x10 2.755 2.761 2.775 2.760 2.763 SPF No.2 2x8 2.673 2.675 2.675 2.657 2.670 SPF No.2 2x4 2.665 2.666 2.663 2.645 2.660 Table 6-4 2-P Weibull (Truncated at 15%) for snow load (bending) Species Grade Size Reliability index (3 (load ratio) Average (0.25) (0.33) (D (2.5) P DF SS 2x10 2.859 2.878 2.959 2.976 2.918 DF SS 2x8 3.001 3.020 3.098 3.114 3.058 DF SS 2x4 3.279 3.309 3.459 3.520 3.392 DF No.2 2x10 2.691 2.700 2.729 2.720 2.710 DF No.2 2x8 2.746 2.754 2.783 2.774 2.764 DF No.2 2x4 2.959 2.971 3.014 3.012 2.989 HF SS 2x10 3.051 3.079 3.207 3.254 3.148 HF SS 2x8 3.266 3.295 3.433 3.486 3.370 HF SS 2x4 3.594 3.633 3.839 3.945 3.753 HF No.2 2x10 2.747 2.763 2.825 2.831 2.792 HF No.2 2x8 2.862 2.876 2.926 2.927 2.898 HF No.2 2x4 3.113 3.132 3.211 3.227 3.171 SPF SS 2x10 3.234 3.274 3.483 3.596 3.397 SPF SS 2x8 3.283 3.321 3.521 3.625 3.438 SPF SS 2x4 3.535 3.579 3.823 3.969 3.727 SPF No.2 2x10 3.031 3.053 3.154 3.183 3.105 SPF No.2 2x8 3.124 3.145 3.238 3.262 3.192 1 SPF No.2 2x4 3.202 3.226 3.332 3.364 3.281 Table 6-5 Lognormal (100% Data) for snow load (bending) 70 Chapter S ix Reliability Evaluation of Lumber Design Values in Chinese Code 2-P Weibull 15% Lognormal 2-P Weibull 100% Normal 5-th Percentile (MPa) Scale m Shape k Mean Standard Deviation Scale m Shape k Mean Standard Deviation 34.13 4.41 3.53 0.38 40.68 3.08 36.37 12.78 17.24 Table 6-6 Characteristics of the bending strength for SPF No.2 2x8 FORM Load ratio 0.25 1 .o -I 1 1 1 1 1 1 1 1 1 1 1 1 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 Performance Factor Figure 6-4 j8 -<P relations for four distribution types (bending) 71 Chap te r S ix Reliability Evaluation of Lumber Design Values in Chinese Code 6.4.3 Target reliability evaluation results The reliability level under certain load condition needs to meet the target reliability level. For the bending strength, a ductile failure model, the target reliability level specified in the Chinese reliability code is 3.2. Three load combinations, dead load plus snow load, dead load plus wind load and dead load plus occupancy (office) load, are implemented in performance function 6.3 to calculate the reliability index. Theoretically, snow load and wind load used here should be the updated 50-year return model. However, the official published 50-year return load model is not available. Therefore, the updated 50-year return snow load model used in this study referenced the snow load model published in the Chinese wood design code reliability study paper [11]. Grades DF 2x10 2x8 2x4 HF 2x10 2x8 2x4 SPF 2x10 2x8 2x4 Snow Load SS No.2 3.054 3.188 3.501 2.843 2.895 3.117 3.270 3.482 3.833 2.931 3.031 3.297 3.487 3.529 3.792 3.232 3.317 3.401 Wind Load SS No.2 3.194 3.322 3.679 2.940 2.990 3.222 3.440 3.654 4.039 3.058 3.144 3.429 3.703 3.739 4.021 3.385 3.460 3.552 Occupancy (office) Load SS No.2 4.104 4.198 4.612 3.733 3.769 4.016 4.389 4.575 4.973 3.948 3.978 4.287 4.702 4.721 4.997 4.295 4.341 4.441 Mean =3.690, Range in (3: 2.843 - 4.997 Table 6-7 B values for bending strength with Lognormal (entire data) distribution Following the method used in the Chinese reliability evaluation, the mean value of the reliability indices in all of the combinations is taken as the final result. Table 6-7 shows the average reliability index is 3.690, which meets the target reliability level 3.2. 72 Chapter S ix Reliability Evaluation of Lumber Design Values in Chinese Code 6.5 Compression 6.5.1 Original data Table 6-8 lists the statistical information for ultimate compression strength according to different combinations of all the species, grades and sizes. These parameters are directly taken from the Appendix of Canadian Lumber Properties [18]. It includes: • Parameters of 2-P Weibull distribution (truncated at 15% Percentile) • Parameters of Lognormal distribution (100% data) • Design values fc in the Chinese code • Size factor Kz 2-P Weibull Lo gnormal Species Grade Size Scale m (MPa) Shape k Mean Standard Deviation fc (MPa) K z DF SS 2x10 34.56 10.00 3.57 0.22 20.00 1.00 DF SS 2x8 35.29 10.23 3.59 0.21 20.00 1.05 DF SS 2x4 39.31 11.09 3.70 0.20 20.00 1.15 DF No.2 2x10 30.49 6.38 3.39 0.27 15.00 1.00 DF No.2 2x8 28.50 7.87 3.39 0.26 15.00 1.05 DF No.2 2x4 31.92 8.81 3.49 0.23 15.00 1.15 HF SS 2x10 30.55 9.28 3.49 0.23 18.00 1.00 HF SS 2x8 31.66 10.39 3.52 0.22 18.00 1.05 HF SS 2x4 39.27 8.85 3.69 0.21 18.00 1.15 HF No.2 2x10 28.72 8.12 3.38 0.24 16.00 1.00 HF No.2 2x8 30.07 7.52 3.42 0.25 16.00 1.05 HF No.2 2x4 30.67 9.75 3.50 0.24 16.00 1.15 SPF SS 2x10 24.23 11.25 3.24 0.20 15.00 1.00 SPF SS 2x8 27.81 8.20 3.30 0.20 15.00 1.05 SPF SS 2x4 31.54 9.97 3.47 0.19 15.00 1.15 SPF No.2 2x10 22.93 6.90 3.13 0.25 12.00 1.00 SPF No.2 2x8 25.17 9.15 3.23 0.21 12.00 1.05 SPF No.2 2x4 27.09 7.36 3.31 0.25 12.00 1.15 Table 6-8 Parameter estimates of UCS at 15% M.C. 73 Chapter S ix Reliability Evaluation of Lumber Design Values in Chinese Code 6.5.2 Effect of distribution types and load ratios By using the dead load plus snow load combination, reliability indices are calculated by G function 6.7 with the two distribution types, 2-P Weibull (15%) and Lognormal (100% Data), each with four load ratios, 0.25, 0.33, 1 and 2.5. Table 6-9 and Table 6-10 show the results of the combinations of all species, grades and sizes. The results show that no significant difference is found between using the Lognormal distribution with entire data or using the Weibull distribution fitted to the lower 15% of the data. To illustrate this relationship, /? - <p relationship is studied on the case of DF SS 2x10 lumber under the dead load plus snow load. Statistical parameters for the four distribution types are listed in Table 6-11. Results from Figure 6-5 and Table 6-9 and Table 6-10 show the similar trends where the Lognormal distribution produces similar results compared with the 2-P Weibull(truncated in 15%), especially in the reliability index ranging from 3.0 to 4.0. Because of the requirement of the Chinese unified reliability code and reliability study in the Chinese timber design code, the resistance needs to be fitted to Lognormal distribution. Therefore, Lognormal distribution with entire data range is used in further study. Table 6-9 and Table 6-10 also show the reliability results obtained by using different load ratios. It is apparent that reliability levels varied with load ratios between load ratio 0.33 and 1.0. The reliability level under load ratio 1.0 is higher than the reliability indices under load ratio 0.33. Because the load ratio 0.33 is the assumption of the soft conversion method, the reliability indices of load ratio 0.33 are used in further study. 74 Chapter S ix Reliability Evaluation of Lumber Design Values in Chinese Code Reliability index p Species Grade Size (load ratio) (0.25) (0.33) (D (2.5) DF SS 2x10 2.804 2.842 3.005 3.050 DF SS 2x8 2.745 2.785 2.958 3.009 DF SS 2x4 2.884 2.931 3.145 3.218 DF No.2 2x10 2.587 2.598 2.632 2.623 DF No.2 2x8 2.624 2.645 2.722 2.729 DF No.2 2x4 2.838 2.866 2.977 2.999 HF SS 2x10 2.663 2.695 2.826 2.856 HF SS 2x8 2.752 2.793 2.974 3.028 HF SS 2x4 2.911 2.939 3.051 3.074 HF No.2 2x10 2.646 2.669 2.755 2.765 HF No.2 2x8 2.534 2.552 2.617 2.619 HF No.2 2x4 2.667 2.703 2.854 2.893 SPF SS 2x10 2.716 2.763 2.985 3.062 SPF SS 2x8 2.616 2.639 2.728 2.739 SPF SS 2x4 2.966 3.004 3.164 3.209 SPF No.2 2x10 2.568 2.582 2.630 2.625 SPF No.2 2x8 3.094 3.124 3.247 3.275 SPF No.2 2x4 2.727 2.745 2.805 2.806 Table 6-9 2-P Weibull (Truncated at 15%) for snow load (compression) Reliability index p Species Grade Size (load ratio) (0.25) (0.33) (D (2.5) DF SS 2x10 2.692 2.734 2.970 3.122 DF SS 2x8 2.658 2.702 2.951 3.122 DF SS 2x4 2.778 2.826 3.115 3.336 DF No.2 2x10 2.717 2.749 2.911 2.985 DF No.2 2x8 2.636 2.668 2.833 2.911 DF No.2 2x4 2.842 2.885 3.126 3.280 HF SS 2x10 2.712 2.752 2.973 3.108 HF SS 2x8 2.712 2.755 2.994 3.150 HF SS 2x4 3.022 3.074 3.380 3.618 HF No.2 2x10 2.676 2.714 2.914 3.025 HF No.2 2x8 2.592 2.625 2.799 2.884 HF No.2 2x4 2.616 2.652 2.844 2.948 SPF SS 2x10 2.672 2.718 2.989 3.189 SPF SS 2x8 2.708 2.755 3.032 3.240 SPF SS 2x4 3.026 3.082 3.432 3.744 SPF No.2 2x10 2.730 2.766 2.958 3.060 SPF No.2 2x8 3.137 3.191 3.514 3.775 SPF No.2 2x4 2.849 2.887 3.095 3.211 Table 6-10 Lognormal (100% Data) for snow load (compression) 75 Chapter S ix Reliability Evaluation of Lumber Design Values in Chinese Code 2-P Weibull 15% Lognormal 2-P Wei bull 100% Normal 5-th Percentile (Mpa) Scale m Shape k Mean Standard Deviation Scale m Shape k Mean Standard Deviation 34.56 10.00 3.57 0.22 39.71 4.52 36.45 8.05 26.14 Table 6-11 Characteristics of UCS for DF SS 2x10 FORM Load ratio 0.25 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 Performance Factor Figure 6-5 /3 -<P relations for four distribution types (compression) 76 Chapter Six Reliability Evaluation of Lumber Design Values in Chinese Code 6.5.3 Target reliability evaluation results For the compression strength, a ductile failure, the target reliability level is 3.2. Three load combinations, dead load plus snow load, dead load plus wind load and dead load plus occupancy (office) load, are applied in performance function 6.3 to calculate the reliability index. This study uses the updated 50-year return period snow load model. Grades DF 2x10 2x8 2x4 HF 2x10 2x8 2x4 SPF 2x10 2x8 2x4 Snow Load SS No.2 2.977 2.951 3.080 2.968 2.891 3.123 2.990 2.998 3.322 2.947 2.854 2.886 2.972 3.010 3.341 2.994 3.439 3.115 Wind Load SS No.2 3.225 3.207 3.353 3.170 3.098 3.369 3.229 3.247 3.597 3.174 3.067 3.110 3.240 3.279 3.639 3.215 3.720 3.341 Occupancy (office) Load SS No.2 4.355 4.354 4.502 4.227 4.178 4.469 4.343 4.375 4.708 4.278 4.165 4.220 4.400 4.435 4.777 4.299 4.820 4.414 Mean =3.583, Range in 3: 2.854 - 4.820 Table 6-12 6 values for compression strength with Lognormal (entire data) distribution Following the method used in the Chinese reliability evaluation, the mean value of the reliability indices for all of the combinations is taken as the final result. Table 6-12 shows the average reliability index is 3.582, which meets the target reliability level. 77 Chap te r S ix Reliability Evaluation of Lumber Design Values in Chinese Code 6.6 Tension 6.6.1 Original data Table 6-13 lists the statistical information for ultimate tensile strength according to different combinations of all the species, grades and sizes. These parameters are directly taken from the Appendix of Canadian Lumber Properties [18]. It includes: • Parameters of 2-P Weibull distribution (truncated at 15% Percentile) • Parameters of Lognormal distribution (100% data) • Design values / , in the Chinese code • Size factor Kz 2-P Weibull Lognormal Species Grade Size Scale m (MPa) Shape k Mean Standard Deviation f, (MPa) K z DF SS 2x10 22.71 6.53 3.28 0.37 8.80 1.10 DF SS 2x8 25.34 6.16 3.33 0.37 8.80 1.20 DF SS 2x4 30.96 6.00 3.49 0.36 8.80 1.50 DF No.2 2x10 16.08 4.78 2.90 0.48 5.40 1.10 DF No.2 2x8 17.55 4.83 2.95 0.46 5.40 1.20 DF No.2 2x4 21.83 4.51 3.10 0.44 5.40 1.50 HF SS 2x10 22.51 5.68 3.23 0.39 8.30 1.10 HF SS 2x8 22.27 6.93 3.29 0.39 8.30 1.20 HF SS 2x4 33.35 All 3.53 0.41 8.30 1.50 HF No.2 2x10 16.59 5.25 2.95 0.45 6.20 1.10 HF No.2 2x8 19.40 4.65 3.02 0.44 6.20 1.20 HF No.2 2x4 21.97 5.49 3.24 0.46 6.20 1.50 SPF SS 2x10 21.85 5.24 3.10 0.37 7.50 1.10 SPF SS 2x8 21.46 5.20 3.14 0.39 7.50 1.20 SPF SS 2x4 26.76 5.88 3.37 0.35 7.50 1.50 SPF No.2 2x10 16.22 4.59 2.86 0.44 4.80 1.10 SPF No.2 2x8 15.84 4.75 2.86 0.46 4.80 1.20 SPF No.2 2x4 19.61 4.39 3.05 0.45 4.80 1.50 Table 6-13 Parameter estimates of UTS at 15% M.C. 78 Chapter S ix Reliability Evaluation of Lumber Design Values in Chinese Code 6.6.2 Effect of distribution types and load ratios Using the dead load plus snow load combination, reliability indices are calculated by G function 6.7 with the two distribution types, 2-P Weibull (15%) and Lognormal (100% Data), each with four load ratios, 0.25, 0.33, 1 and 2.5. Table 6-14 and Table 6-15 show the results of the combination of all species, grades and sizes. As shown in Table 6-14 and Table 6-15, small difference is found between the Lognormal distribution with the entire data and the Weibull distribution fitted to the lower 15% of the data. The Lognormal case tends to provide slightly higher p values compared to the 2P Weibull (15% case). The j3 - (f> curve is developed for the SPF No.2 2x4 lumber under the dead load plus snow load to illustrate the situation. Statistical parameters for the four distribution types are listed in Table 6-16. Figure 6-6 and Table 6-14 and Table 6-15 show the same trend where the results of Lognormal distribution show a slightly higher reliability level than the results of the 2-P Weibull (truncated in 15%). Because of the requirement of the Chinese unified reliability code and reliability study in the Chinese timber design code, the resistance needs to be fitted to the Lognormal distribution. Therefore, the Lognormal distribution with entire data range is used in further study. Table 6-14 and Table 6-15 also show the reliability results obtained using different load ratios. It is apparent that the reliability levels do not vary substantially with load ratios. Thus, this effect could be disregarded in the tension strength. Because the load ratio 0.33 is the assumption of the soft conversion method, the reliability indices of load ratio 0.33 are used for further study. 79 Chapter S ix Reliability Evaluation of Lumber Design Values in Chinese Code Reliability index p Species Grade Size (load ratio) (0.25) (0.33) (D (2.5) DF SS 2x10 2.922 2.933 2.971 2.965 DF SS 2x8 2.866 2.876 2.905 2.896 DF SS 2x4 2.778 2.787 2.812 2.802 DF No.2 2x10 2.642 2.646 2.650 2.633 DF No.2 2x8 2.661 2.665 2.669 2.653 DF No.2 2x4 2.537 2.539 2.539 2.521 HF SS 2x10 2.778 2.786 2.805 2.792 HF SS 2x8 2.922 2.937 2.984 2.982 HF SS 2x4 2.622 2.625 2.629 2.612 HF No.2 2x10 2.621 2.627 2.638 2.622 HF No.2 2x8 2.673 2.676 2.678 2.661 HF No.2 2x4 2.643 2.650 2.665 2.650 SPF SS 2x10 2.765 2.770 2.781 2.767 SPF SS 2x8 2.570 2.575 2.586 2.569 SPF SS 2x4 2.771 2.779 2.802 2.791 SPF No.2 2x10 2.766 2.769 2.771 2.754 SPF No.2 2x8 2.657 2.660 2.664 2.647 SPF No.2 2x4 2.508 2.510 2.509 2.490 Table 6-14 2-P Weibull (Truncated at 15%) under snow load (tension) Reliability index p Species Grade Size (load ratio) (0.25) (0.33) (1) (2.5) DF SS 2x10 2.960 2.981 3.069 3.090 DF SS 2x8 2.874 2.893 2.975 2.993 DF SS 2x4 2.782 2.802 2.884 2.901 DF No.2 2x10 2.609 2.617 2.639 2.628 DF No.2 2x8 2.631 2.640 2.669 2.659 DF No.2 2x4 2.579 2.589 2.621 2.613 HF SS 2x10 2.864 2.881 2.950 2.960 HF SS 2x8 2.803 2.819 2.884 2.892 HF SS 2x4 2.731 2.745 2.796 2.797 HF No.2 2x10 2.576 2.585 2.614 2.605 HF No.2 2x8 2.589 2.599 2.632 2.624 HF No.2 2x4 2.489 2.496 2.519 2.507 SPF SS 2x10 2.913 2.933 3.018 3.037 SPF SS 2x8 2.693 2.708 2.766 2.770 SPF SS 2x4 2.937 2.960 3.061 2.090 SPF No.2 2x10 2.787 2.799 2.841 2.838 SPF No.2 2x8 2.686 2.696 2.727 2.719 SPF No.2 2x4 2.669 2.679 2.712 2.705 Table 6-15 Lognormal (100% Data) under snow load (compression) 80 Chapter S ix Reliability Evaluation of Lumber Design Values in Chinese Code 2-P Weibull 15% Lognormal 2-P Weibull 100% Normal 5-th Percentile (Mpa) Scale m Shape k Mean Standard Deviation Scale m Shape k Mean Standard Deviation 19.61 4.39 3.05 0.45 26.34 2.39 23.27 10.37 9.69 Table 6-16 Characteristics of the UTS for SPF No.2 2x4 x 0) •o c n .3 "35 OC 7.0 6.5 6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 FORM Load ratio 0.25 2P Weibull 15% Lognormal 2P Weibull Normal 1 1 1 1 1 1 1 1 1 1 1 1 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 P e r f o r m a n c e F a c t o r Figure 6-6 j8 -<P relations for four distribution types (tension) 81 Chapter Six Reliability Evaluation of Lumber Design Values in Chinese Code 6.6.3 Target reliability evaluation results For the tension strength, a brittle failure mode, the target reliability level is 3.7. Three load combinations, dead load plus snow load, dead load plus wind load and dead load plus occupancy (office) load, are used in performance function 6.3 to calculate the reliability index. This study uses the updated 50-year return snow load model. Grades DF 2x10 2x8 2x4 HF 2x10 2x8 2x4 SPF 2x10 2x8 2x4 Snow Load SS No.2 3.156 3.069 2.981 2.757 2.786 2.740 3.049 2.987 2.906 2.733 2.751 2.642 3.109 2.876 3.143 3.132 2.841 2.827 Wind Load SS No.2 3.299 3.209 3.124 2.849 2.884 2.844 3.179 3.116 3.024 2.834 2.854 2.737 3.250 3.001 3.297 3.244 2.941 2.929 Occupancy (office) Load SS No.2 4.203 4.118 4.052 3.633 3.691 3.678 4.063 4.003 3.890 3.656 3.688 3.550 4.157 3.895 4.228 4.061 3.746 3.748 Mean =3.281, Range in 8: 2.733 - 4.228 Table 6-17 B values for tension strength with Lognormal (entire data) distribution Following the method used in the Chinese reliability evaluation, the mean value of the reliability indices in all of the combinations is taken as the final result. Table 6-17 shows the average reliability index is 3.281, which is lower than the target reliability level. 82 Chapter Six Reliability Evaluation of Lumber Design Values in Chinese Code 6.7 Serviceability 6.7.1 Original data Table 6-18 lists the statistical information for M O E according to combination of all the species, grades and sizes. The statistical parameters are taken from a' database developed by Dr. Barrett of University of British Columbia [19]. It includes • Parameters of 2-P Weibull distribution (100% data) • Parameters of Lognormal distribution (100% data) • Design M O E values in the Chinese code Lognormal 2-P Weibull MOE Species Grade Size A <; m k Chinese code (MPa) DF SS 2x10 9.44 0.21 14021.19 5.29 13000 DF SS 2x8 9.50 0.21 14734.33 5.51 13000 DF SS 2x4 9.39 0.20 13169.40 5.86 13000 DF No.2 2x10 9.28 0.25 12097.99 4.50 11000 DF No.2 2x8 9.31 0.24 12398.26 4.59 11000 DF No.2 2x4 9.25 0.25 11717.95 4.45 11000 HF SS 2x10 9.37 0.18 12779.30 6.38 12000 HF SS 2x8 9.39 0.18 13045.40 6.30 12000 HF SS 2x4 9.35 0.19 12618.85 5.93 12000 HF No.2 2x10 9.29 0.20 11910.77 5.86 11000 HF No.2 2x8 9.31 0.20 12145.15 5.62 11000 HF No.2 2x4 9.26 0.21 11712.02 5.38 11000 SPF SS 2x10 9.22 0.18 10950.03 6.59 10300 SPF SS 2x8 .9.24 0.17 11157.09 6.67 10300 SPF SS 2x4 9.27 0.17 11495.35 6.67 10300 SPF No.2 2x10 9.12 0.21 10101.22 5.31 9700 SPF No.2 2x8 9.16 0.21 10560.10 5.50 9700 SPF No.2 2x4 9.13 0.22 10317.28 5.08 9700 Table 6-18 Parameter estimates of M O E at 15% M . C . 83 Chapter Six Reliability Evaluation of Lumber Design Values in Chinese Code 6.7.2 Effect of distribution types and load ratio Using the dead load plus snow load combination, reliability indices are calculated with two distribution types, 2-P Weibull and Lognormal distribution, each with four load ratios, 0.25, 0.33, 1 and 2.5. Table 6-19 and Table 6-20 show the results of the combination of all species, grades and sizes. Between two tables, small difference is found between the distribution types. The Lognormal distribution results in slightly lower reliability levels than the Weibull distribution case. To further illustrate the difference between two models, f5 - (j) relationship is studied for the HF No.2 2x4 lumber under the dead load plus snow load. Statistical parameters for the three distribution types are listed in Table 6-21. Figure 6-7 and Table 6-19 and Table 6-20 show the same trend where the Lognormal distribution results agree with the result of the 2-P Weibull, especially around the reliability level 1.0. Because of the requirement of the Chinese unified reliability code, Lognormal distribution is used in further study. Table 6-19 and Table 6-20 also show the reliability results obtained using different load ratios. It is apparent that reliability levels varied with load ratios between load ratio 0.33 and 1.0. Because the load ratio 0.33 is the assumption of the soft conversion method, the reliability indices of load ratio 0.33 are used for further study. 84 Chapter Six Reliability Evaluation of Lumber Design Values in Chinese Code Reliability index (3 Species Grade Size (load ratio) (0.25) (0.33) (1) (2.5) DF SS 2x10 -0.176 -0.190 -0 .270 -0.338 DF SS 2x8 0.051 0.041 -0.015 -0.069 DF SS 2x4 -0.378 -0.398 -0.504 -0.587 DF No.2 2x10 -0.133 -0.144 -0.208 -0.261 DF No.2 2x8 -0.033 -0.043 -0.101 -0.152 DF No.2 2x4 -0.234 -0.247 -0.319 -0.376 HF SS 2x10 -0.151 -0.167 -0.256 -0 .335 HF SS 2x8 -0.068 -0.082 -0.160 -0.232 HF SS 2x4 -0.227 -0.244 -0 .339 -0.417 HF No.2 2x10 -0.115 -0.128 -0 .205 -0 .273 HF No.2 2x8 -0.037 -0.049 -0.117 -0 .179 HF No.2 2x4 -0.225 -0.241 -0.326 -0.396 SPF SS 2x10 -0.140 -0.155 -0.243 -0 .320 SPF SS 2x8 -0.058 -0.072 -0.153 -0 .229 SPF SS 2x4 0.069 0.059 -0.003 -0.067 SPF No.2 2x10 -0.279 -0.296 -0.387 -0.459 SPF No.2 2x8 -0.127 -0.141 -0.216 -0 .280 SPF No.2 2x4 -0.234 -0.249 -0.331 -0.398 Tab le 6-19 L o g n o r m a l under snow load (serviceabili ty) Reliability index p Species Grade Size (load ratio) (0.25) (0.33) (D (2.5) DF SS 2x10 -0.028 -0.039 -0.102 -0.161 DF SS 2x8 0.167 0.160 0.118 0.072 DF SS 2x4 -0.255 -0.274 -0.377 -0.467 DF No.2 2x10 0.000 -0.009 -0.062 -0 .110 DF No.2 2x8 0.086 0.078 0.033 -0.011 DF No.2 2x4 -0.109 -0.121 -0.183 -0.238 HF SS 2x10 -0.034 -0.047 -0.122 -0.195 HF SS 2x8 0.047 0.037 -0.026 -0.089 HF SS 2x4 -0.101 -0.115 -0 .196 -0 .270 HF No.2 2x10 0.012 0.002 , -0 .062 -0.124 HF No.2 2x8 0.076 0.067 0.013 -0.041 HF No.2 2x4 -0.072 -0.084 -0 .155 -0 .219 SPF SS 2x10 -0.035 -0.048 -0.125 -0 .200 SPF SS 2x8 0.047 0.036 -0.028 -0 .095 SPF SS 2x4 0.170 0.163 0.118 0.064 SPF No.2 2x10 -0.159 -0.173 -0.254 -0.325 SPF No.2 2x8 0.017 0.007 -0.053 -0.111 SPF No.2 2x4 -0.088 -0.100 -0.168 -0 .230 Tab le 6-20 2-P W e i b u l l under snow load (serviceabili ty) 85 Chapter Six Reliability Evaluation of Lumber Design Values in Chinese Code Lognormal 2-P Weibull 100% Normal Species Grade Size Mean Standard Deviation Scale m (MPa) Shape k Mean Standard Deviation HF No.2 2x4 9.26 0.21 11712.02 5.38 10798.90 2311.99 Table 6-21 Characteristics of the MOE for HF No.2 2x4 FORM Load ratio 0.25 4.0 -i 3.5 --0.5 \ -1.0 'i 1 1 1 1 1 1 1 1 1 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 P e r f o r m a n c e F a c t o r Figure 6-7 j8 -0 relations for three distribution types (serviceability) 86 Chapter S ix Reliability Evaluation of Lumber Design Values in Chinese Code 6.7.3 Target reliability evaluation results For the serviceability, the target reliability level is between 0 and 1.5. Three load combinations, dead load plus snow load (50-year return), dead load plus wind load and dead load plus occupancy (office) load, are implemented in performance function 6.6 to calculate the reliability index. Grades DF HF SPF 2x10 2x8 2x4 2x10 2x8 2x4 2x10 2x8 2x4 Snow Load SS -0.190 0.041 -0.398 -0.167 -0.082 -0.244 -0.155 -0.072 0.059 No.2 -0.144 -0.043 -0.247 -0.128 -0.049 -0.241 -0.296 -0.141 -0.249 Wind Load SS -0.098 0.145 -0.312 -0.063 0.027 -0.148 -0.051 0.041 0.180 No.2 -0.060 0.047 -0.167 -0.029 0.054 -0.150 -0.208 -0.046 -0.162 Mean = -0.104, Range in B: -0.398-0.145 Occupancy (office) Load SS 1.513 1.721 1.373 1.669 1.742 1.555 1.679 1.795 1.906 No.2 1.388 1.522 1.292 1.613 1.683 1.468 1.418 1.558 1.416 Mean =1.573, Range in 0: 1.388-1.906 Table 6-22 B values for serviceability with Lognormal distribution Table 6-22 shows results of the reliability evaluation. For the roof, the average value of dead load plus snow load and dead load plus wind load is -0.104, which can not meet the target reliability level. Here, the negative values of reliability indices close to 0 indicate that the probability of failure will be slightly higher than 50%. For the floor system, the mean value of dead load plus occupancy (office) load is 1.573, which meets the target reliability level. In the reliability index calculation of this case, only the single member performance is considered in this study. However, in the service case of floor or roof system, the deflection in the whole system should be much smaller and actual reliability index will be much higher than the value of single member case. 87 Chapter Seven Discussion and Conclusion 7. DISCUSSION AND CONCLUSION Traditional Chinese timber structures are based on the post and beam system, which needs large timbers. For a country short of forestry resources, the traditional structural system limits the application of wood structure in the Chinese housing market. The 2x4 wood frame structural system, as a relatively new structural style accepted in the Chinese code, provides a good opportunity for the development of wood building in China. An important advantage of wood frame structure is that it uses the relatively small sized wood structural members such as dimension lumber. The reliability-based limit states design method is applied in both the Chinese and Canadian wood structural design codes. Despite the same philosophy, differences of the material database, load information and target reliability levels lead to the different reliability results. One of the most critical issues is the difference in procedures for establishing design values for the Canadian and Chinese code. Currently, design values of dimension lumber in the Chinese code are based on the soft conversion method. These design values are calibrated to achieve the same member cross sections with the U.S. code4 under the same load ratio and live load. Although it is a feasible method to establish the design values, it does not match the reliability-based principle of the limit states design method. Although the same cross section is achieved by using this method; the reliability levels of members could be different than would be predicted using different reliability analysis procedures, design equations, and the appropriate database for loads and member resistance. This could cause the inappropriate definition of North American dimension lumber design value. Possibly, it would cause inefficient use of wood and limit the application and development of wood frame structural system in China. Therefore, it is necessary to evaluate the reliability levels of the published design values in the code. In this study, reliability levels are evaluated mainly in bending, compression and tension. Also, the serviceability is investigated. The species selected are Douglas-Fir, Hem-Fir and Spruce-Pine-Fir, which are the major commercial products of Canadian lumber industry. There are two major targets for this reliability evaluation. One is to 4 AF&PA LRFD code 8 8 Chapter Seven Discussion and Conclusion evaluate the compatibility with the target reliability levels. Another is to study the robustness of the soft conversion method. 7.1 Target reliability evaluation The mean values of the reliability levels of three load conditions are compared with the target reliability specified in the Chinese unified reliability code. Table 7-1 lists the reliability levels with the load conditions, load combinations and target reliability level. Bending Compression Tension Serviceability Dead + Snow 3.289 3.048 2.916 -0.153 Dead + Wind 3.443 3.293 3.034 -0.056 Dead + Office 4.338 4.407 3.892 1.573 Average 3.690 3.583 3.281 Target Reliability 3.200 3.200 3.700 1.500 Table 7-1 Target reliability evaluation The outcome of this study shows that reliability levels of bending and compression exceeded the target reliability levels, which are 3.2 for the ductile failure. The reliability level of tension, as a brittle failure model, does not match the target reliability 3.7. Figure 7-1 shows the comparison of reliability levels under different load conditions. Load Combinations Reliability Leve l s 4.338 4.407 3.443 3.293 3.892 3.034 ^ • Snow • Wind • Office Bending Compression Load Conditions Tension Figure 7-1 Comparison of reliability levels of load combinations 89 Chapter Seven Discussion and Conclusion In the serviceability study, only the office load combination applied to the joist in the floor system meets the target reliability. However, this reliability analysis is based on the single member study. For the roof system or floor system, system performance must be studied and appropriate system modification factor must be introduced into the reliability study. 7.2 Robustness of soft conversion method Reliability levels vary with the species, grade and size. Although it is impossible to reach a constant reliability level across species, grades, sizes and even load conditions, the appropriate definition of the design values and adjustment factors could balance the reliability level so that it does not have a wide fluctuation. So, another objective in this study is to investigate the reliability levels within the species, grades and sizes, and then evaluate the robustness of the soft conversion method. The reliability levels between grades reveal that Select Structural generally has a higher level than the No.2, as it is illustrated in Figure 7-2. Despite the relatively wide fluctuation in the bending case, the difference of the reliability level within grades is not significant in all of the load conditions. Grades Reliability Levels 4.0-1 3.896 « 3.5 Q> > 0) 1" 3.0 !5 .S "35 DC 2.5 2.0 3.626 3.484 3.539 3.422 3.140 SS • No.2 — i 1 Bending Compression Tension Load Conditions Figure 7-2 Reliability levels according to grades 90 Chapter Seven Discussion and Conclusion Figure 7-3 shows the reliability levels among the species, in which Spruce-Pine-Fir species has a higher reliability level than the other two species. The biggest fluctuation happened in the bending case. But the level of variation is deemed to be acceptable. Species Reliability Levels Bending Compression Tension Load Conditions Figure 7-3 Reliability levels according to species Figure 7-4 illustrates the variability of the reliability level within sizes is deemed to be not significant. Sizes Reliability Levels 4.0 w 3.5 H 2.0 3.901 3.539 3.630 3 . 6 8 7 , 3.560 12x10 3.354 3-248 3.241 D 2 x 8 • 2x4 Bending Compression Tension Load Conditions Figure 7-4 Reliability levels according to sizes 91 Chapter Seven Discussion and Conclusion This study shows that there is no significant difference in the reliability levels across the grades, species and sizes. This means that the design values published in the Chinese code basically can achieve a fairly balanced the reliability levels across the species, grades and sizes. 7.3 Discussion For a limit states code, the design value should come from a reliability-based calibration procedure, which will lead to a consistent reliability level among species, grades and sizes. Therefore, a formal reliability assessment procedure should be developed to establish the design values of dimension lumber in the Chinese code. To perform this formal reliability assessment, the following issues should be addressed: 1) Testing standard: The current testing standard for wood structure in China is GB/T 50239-2002 "Standard for methods testing of timber structures". However, this test method is based on small clear wood testing and is mainly intended for the quality control of wood structural members. The "2x4" wood frame structure is a relatively new structural system, and the dimension lumber is also a new structural product in China. For this reason, there is no full size in-grade testing method standard for the dimension lumber yet. One way to solve this problem is to reference international testing standard, such as ISO standard. However, it is important to establish this full size in-grade testing method standard. And test standard should be suitable for the Chinese limit states design; because some test details can significantly affect the final reliability levels. For example, in the full size tension test, the member length has a significant effect to tension strength properties that would be used in the reliability analysis. 2) Material database: The distribution model of the strength properties has significant impact on the reliability levels. It is critical to choose the appropriate distribution model for material strength. The study in Canada showed that the effect of the distribution on calculation reliability was very significant when using the entire data set. Instead, using the 92 Chapter Seven Discussion and Conclusion distribution model with data truncated at 15% lower tail could almost eliminate the influence of the distribution models. Also, the lower 15% value, which is the weak part of the design data, is the most important part data for reliability study. Chinese unified reliability code stipulates that a Normal or Lognormal distribution must be used represent the material strength. Also, the entire data is suggested. However, the study in Chapter 6 shows that the lower tail of Lognormal does not show good agreement with the test data. For this reason, Lognormal distribution with 15% lower tail is recommended for any future study. 3) Load information: Load information is another issue in the reliability evaluation. Although the national snow and wind load models are used in this study, statistical information is not complete. This is due to the lack of statistical information on snow load and wind load for a 30-year to a 50-year return period. This return period change could have significant effect to the reliability levels. For this reason, more accurate load models and statistical parameters need to be obtained for future studies. Moreover, the load ratio needs to be clarified for Chinese structures. Various load ratios under the same load combinations can also produce different reliability levels. The study in the Chapter 6 shows that the dead-to-live load ratio =1 is more suitable for Chinese loads conditions. 4) Adjustment factors: Adjustment factors are important tools to balance the reliability levels. Currently, the adjustment factors considered in timber structure design code only include system factor for bending strength and size factors. These values cannot be taken directly from the North American codes. For the "2x4" wood frame structure, most of single members are working in a system. In all of the analysis, however, system effects are ignored. Including the system factor could contribute to a significant increase in the loading carrying capacities of the members in tension, bending or compression. Due to natural defects such as big knots in the full size single testing member, the common failure mode for these single members is brittle mode. However, if the member is in a floor or roof system, the most common system failure could be considered as a ductile failure 93 Chapter Seven Discussion and Conclusion mode. For example, the tension reliability index seems to be lower than the targeted value, but there is reserve conservation if the single tension member is working in a system. In addition, the failure of matching the serviceability target reliability indicates that the appropriate system effect factor needs to be studied in the future study. Therefore, it is important to develop the system effect factors for the Chinese code. Another important adjustment factor, duration of load factor, was assumed as 1 in the soft conversion method used to convert the design properties for North American lumber to the properties in the Chinese code. However, a more rational approach is to establish the duration of load factor through the reliability study based on Chinese load case. Also, the failure of serviceability target reliability indicates that the appropriate system effect factor needs to be studied. 7.4 Conclusion Based on this study, it has been shown that design values established by the soft conversion method can meet the Chinese target reliability in the bending and compression cases, but fail to achieve the target reliability levels in the tension and serviceability cases. It also shows that the soft conversion approach could be used to establish the design values in this initial step of introducing the dimension lumber into Chinese code. A formal reliability calibration procedure is proposed to develop the design values in the future reversions of Chinese timber structure design code. The reliability assessment framework and methodology used in the Canadian limit states timber design code can be applied in the reliability assessment of the Chinese code when the appropriate material properties and load information are specified. To establish a formal reliability evaluation with the study of adjustment factors will not only explore a more appropriate way to establish design values of dimension lumber, but also achieve the reliability-based limit states design of "2x4" wood frame structure in the Chinese timber design code, which will technically support the development of wood frame building in China. 94 Appendices APPENDIX A: Commentary on Dimension Lumber Design Values for the GBJ-5 Code 1. B A C K G R O U N D The proposed dimension lumber design values in GBJ-5 are based on the reference strength values found in the latest edition of the Structural Lumber Supplement to the A F & P A / A S C E 16-95 Standard for Load and Resistance Factor Design (LRFD) for Engineered Wood Construction. These L R F D reference strength values for lumber are, in turn, derived from the design values published with the ANSI /AF&PA National Design Specification (NDS) for Wood Construction. The LRFD code follows a limit states format, while the NDS code follows an allowable stress design format. Both are recognized for used with US building codes and contain design values for US, Canadian and, more recently, other foreign wood species. 2. D E V E L O P M E N T O F T H E NDS A L L O W A B L E STRESS DESIGN V A L U E S The NDS design values for the major commercial dimension lumber species are based on tests carried out on full-size in-grade lumber sampled from production. The main motivation for adopting the in-grade lumber testing approach was to more accurately characterize the relative strength of the various grades and species of dimension lumber. This would ultimately lead to better understanding of the strength of lumber used in engineered wood-frame construction, the performance of wood-frame construction, and facilitate the harmonisation of dimension lumber design with not only other wood products, but also non-wood products. For modulus of elasticity, bending, tension parallel-to-grain and compression parallel to grain, data are developed from tests on full-size lumber carried out in accordance with either A S T M D198 or A S T M D4761. Characteristic values are then derived in accordance with A S T M D1990. For the bending, tension and compression strength properties, the characteristic values are derived from the 5 t h percentile statistic, while for modulus of elasticity, the characteristic value is based on the mean statistic. 95 Appendices Although A S T M D1990 permits the development of characteristic values for a single grade or size, the major species or North American dimension lumber were sampled as a "full matrix". A full matrix consisted of at least two grades and three sizes, and a target sample size of 360 pieces was sampled for each test cell within the test matrix. For the other properties (longitudinal shear and compression perpendicular-to-grain), data are developed from tests carried out in accordance with A S T M D143 on small clear wood samples. Characteristic values are then derived in accordance with A S T M D2555 and A S T M D245. The characteristic value for longitudinal shear is derived from the 5 t h percentile statistic, and the compression-perpendicular-to-grain property is derived from the mean stress corresponding to a 1-mm deformation. A l l test properties must be adjusted to the reference moisture content of 15%. Characteristic values for bending, tension parallel-to-grain and compression parallel-to-grain need to be further adjusted to the reference sizes before applying the factor to convert the characteristic values to the Allowable Stress Design values. The reference size for Select Structural, No. 1, No. 2 and No. 3 grades is 2x12 (286 mm) at a span corresponding to 17 times the depth (4.9m). The reference size for Construction and Standard grades is 2x4 (89 mm) at a span of 3.7m. A S T M D1990 provides the adjustment equations for moisture content and size; however, any technically supported adjustment equation may be used. Table 1 summarizes the factors to convert the characteristic properties to allowable stress design values. Table 1: Fac tors to C o n v e r t Charac ter i s t ic Propert ies to A l l o w a b l e Stress Design Va lues ( A S T M D1990 & D245) Property and Statistic"1 Standards Factor Bending strength (5* percentile) ASTM D476112'/ ASTM D1990 2.1 Compression parallel-to-grain (5m percentile) ASTM D476112' / ASTM D1990 1.9 Tension parallel-to-grain (5"1 percentile) ASTM D4761'21/ ASTM D1990 2.1 Longitudinal shear (5th percentile) ASTM D142 / ASTM D2555 / ASTM D245 4.2131 Compression perpendicular-to-grain (mean) ASTM D142 / ASTM D2555 / ASTM D245 1.67141 Bending modulus of elasticity (mean) ASTM D4761121 / ASTM D1990 1.0 Notes: 96 Appendices [1 ] Characteristic values should be at the standard moisture content of 15% and the reference size before applying the reduction factor. [2 ] ASTM D198 may also be used. [3] This adjustment includes a strength ratio adjustment of 0.5 to account for the presence of fissures. [4] ASTM D143 tests are carried out with the growth rings parallel to the loading direction. This reduction is to account for most unfavourable ring orientation (45° to the loading direction). 3. DEVELOPMENT OF THE LRFD VALUES The L R F D design values are based on a soft conversion process described in A S T M D5457. Section 6.7 of the Standard provides a procedure for generating L R F D reference resistance values based on format conversion from code-recognized allowable stress design. where K — ^ l l ^ . 5 for bending, compression, tension and shear <P K = h^H.; for compression perpendicular - to - grain (P Table 2: Factors to Convert Allowable Stress Design Values to LRFD Reference Values (ASTM D5457) Bending Compression Tension Shear Comp-Perp R e s i s t a n c e f a c l o r , (p 0 . 8 5 0 . 9 0 0 . 8 0 0 . 7 5 0 . 9 0 A S T M D 5 4 5 7 c o n s t a n t 2 . 1 6 0 2 . 1 6 0 2 . 1 6 0 2 . 1 6 0 1 . 8 7 5 K r 2 . 5 4 1 2 . 4 0 0 2 . 7 0 0 2 . 8 8 0 2 . 0 8 3 4. DEVELOPMENT OF THE GBJ-5 DESIGN VALUES The GBJ-5 and L R F D codes use different load and resistance factors. The GBJ-5 design values were soft converted from the US LRFD values using the following procedures: 1. A live-to-dead load ratio of 3 was assumed. 2. "Standard term" loading was assumed. This would be the duration of load typically assigned to roof snow loading and floor live loading. 97 Appendices 3. The L R F D resistance values were soft converted to a GBJ-5 resistance value at this level of live-to-dead load such that under the same live load, the same size member would be obtained using either the LRFD and GBJ-5 codes. The basic equation used to soft convert the L R F D design values was derived as follows: aL = live load factor aD = dead load factor L = specified live load D = specified dead load cp = resistance factor (phi factor) KD = duration of load factor for standard term R = reference or specified strength (standard term loading) y = dead to live load ratio = 1 to 3 (assumed) aLL + apD <<pKDR ,oeL+aD-- <(pKDR V L ) L L(aL+aDy)<cpKDR <pKDR L< {aL+aDy) Assuming the same load for both the LRFD and GBJ-5 codes: ,-LRFD LRFD n ,nGBJ-5 r^GBJ-5 n <P KD LRFD _<P KD KGBJ-5 (a?m+aF"r) (aGLBJ-'+acDBJ-5y) KGBJ-5 LRFD „GBJ-5 ,„GBJ-5 I-.LRFD , LRFD \ KD <p \aL +aD y) or -GBJ-5 _ K o F D <p mFD (<BJ-^<BJ-5r) WFD K™- 5 <p GBJ- 5 (a?n>+a?fDr) • Values of the conversion factor, , used are summarized in Table 3. 98 Appendices Table 3:Strength Conversion Factors to Account for Code Format LRFD and GBJ -5 Design Code Factors Duration of load KD = Dead load factor \ D = Live load factor XL = Resistance factor = Bending O i n 2 - J U Compression Q m 2 CC CQ - 1 U Tension Q i o CC CQ - J O Shear Q i n CC CQ - I O Comp-Perp Q to 2 CC CQ _i a M O E O i n 2 CC CQ -i a 0.80 1.00 1.20 1.20 1.60 1.40 0.85 1.00 0.80 1.00 1.20 1.20 1.60 1.40 0.90 1.00 0.80 1.00 1.20 1.20 1.60 1.40 0.80 1.00 0.80 1.00 1.20 1.20 1.60 1.40 0.75 1.00 1.00 1.00 1.20 1.20 1.60 1.40 0.90 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Dead.Live ratio y = 0.333 Unit conversion k = 6.895 (KSI to MPa) LRFD to GBJ -5 Reference or Specified Strength Conversion Factors Bending Compression Tension Shear Comp-Prep MOE js GBJ - 5 A IJtFD 4.220 4.468 3.971 3.723 5.585 6.895 5. REFERENCES American Forest & Paper Association; American Society of Civil Engineers. A F & P A / A S C E 16-95. Standard for Load and Resistance Factor Design (LRFD) for Engineered Wood Construction. American Forest & Paper Association; American Wood Council. ANSI /AF&PA NDS-1997. National Design Specification for Wood Construction. A S T M D198. Standard Test Methods of Static Tests of Lumber in Structural Sizes A S T M D245. Standard Practice for Establishing Structural Grades and Related Allowable Properties for Visually Graded Lumber A S T M D1990. Standard Practice for Establishing Allowable Properties for Visually-Graded Dimension Lumber from In-Grade Tests of Full-Size Specimens A S T M D2555. Standard Test Methods for Establishing Clear Wood Strength Properties. A S T M D5457. Standard Specification for Computing the Reference Resistance of Wood-Based Materials and Structural Connections for Load and Resistance Factor Design A S T M D4761. Standard Test Methods for Mechanical Properties of Lumber and Wood-Base Stnictural Materials. Supplement: Structural Lumber. Load and Resistance Factor Design Manual for Engineered Wood Construction. 99 References REFERENCES [I] Wu, Xirong, 1995. History of Shu Zhou. Shu Hai Press. Beijing, China, (in Chinese) [2] Ministry of Construction, China. 2003. Code for design of timber structures (GB 50005-2003). China Architecture& Building Press, Beijing, China, (in Chinese) [3] Ministry of Construction, China. 1989. Code for design of timber structure (GBJ 5-88). China Architecture& Building Press, Beijing, China, (in Chinese) [4] Canadian Wood Council. 2002. Introduction to Wood Design. Canadian Wood Council, Ottawa, Ontario, Canada. [5] Anonymous, 2003. Commentary on dimension lumber design values for the GBJ-5 code. Forintek Canada Corp. Vancouver, Canada. [6] Yang, Weijun, Zhao, Chuanzhi, 1998. Reliability-based theory and design for civil engineering. Renmin Transportation Press, Beijin, China, (in Chinese) [7] Ministry of Construction, China. 2001. Unified standard for reliability design of building structures (GB 50068-2001). China Architecture& Building Press, Beijing, China, (in Chinese) [8] Ministry of Construction, China. 1984. Unified standard for reliability design of building structures (GBJ 68-84). China Architecture& Building Press, Beijing, China, (in Chinese) [9] Chinese Southwest Architectural Design Institute. 1993. Wood Structure Design Handbook. China Architecture& Building Press, Beijing, China, (in Chinese) [10] Ministry of Construction, China. 1973. Code for design of timber structure (GBJ 5-73). China Architecture& Building Press, Beijing, China, (in Chinese) [II] Wang, Yongwei. 2002. Reliability Analysis of Wood Structure. Building Science Research of Shichuan. Vol.28, No.2. Cheng Du, China, (in Chinese) [12] Ministry of Construction, China. 2002. Load code for the design of building structures (GB 50009-2002). China Architecture& Building Press, Beijing, China, (in Chinese) 100 References [ 13] Ministry of Construction, China. 2002. Standard for methods testing of timber structures (GB/T 50329-2002). China Architecture& Building Press, Beijing, China, (in Chinese) [14] Ni , Shizhu, Chen, Rongcai. 1980. Distribution types of wood strength as building material. Chinese wood structure technology committee meeting document. Beijing, China, (in Chinese) [15] Foschi, R.O., Folz, B.R., and Yao, F.Z. 1989. Reliability-Based Design of Wood structures. Structural Research Series, Report No.34. Department of Civi l Engineering, University of British Columbia, Vancouver, B.C. [16] Canadian Wood Council. 2001. Wood Design Manual. Canadian Wood Council, Ottawa, Ontario, Canada. [17] Madsen, Borg. 1992. Structural Behavior of Timber. Timber Engineering LTD, North Vancouver, British Columbia, Canada. [18] Barrett, J.D., Lau, W., 1994. Canada Lumber Properties. Canadian Wood Council, Ottawa, Ontario, Canada. [19] Barrett, J.D., Lau, W., Bernaldez. J, 1999. UBC Data viewing program, version 1.1.0 (Software). University of British Columbia, Department of Wood Science, British Columbia, Canada. 101
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Reliability study of North American dimension lumber in the Chinese timber structures design code Zhuang, Xiaojun 2004
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Title | Reliability study of North American dimension lumber in the Chinese timber structures design code |
Creator |
Zhuang, Xiaojun |
Date Issued | 2004 |
Description | Reliability evaluation principles, procedures as applied in the Chinese timber structure design code were reviewed. The general method to establish the design values of Chinese wood strength properties was investigated. In particular, Chinese load information, including the statistical models and parameters, was analyzed. Also, the reliability associated with wood structural design requirements in Canada was studied. The emphasis was placed on the in-grade testing method, which is a more reliable method to get the lumber strength properties compared with small clear wood testing method used in China. Finally, Canadian procedures for establishing the design values of wood strength properties were reviewed. Using Chinese load information and Canadian in-grade testing data, reliability evaluations were conducted for the design values of common Canadian Species in the Chinese timber design code. These design values were previous soft converted from allowable stresses approved by the American Lumber Standards Committee. Reliability results were compared with the target reliability levels tabulated in the Chinese national unified reliability code. This reliability analysis was implemented by using the "RELAN" (Reliability ANalysis) program developed by Dr. R.O. Foschi of UBC. Recommendations were made to develop a formal reliability evaluation of the performance of North American dimension lumber under the Chinese load conditions. |
Extent | 6285008 bytes |
Genre |
Thesis/Dissertation |
Type |
Text |
FileFormat | application/pdf |
Language | eng |
Date Available | 2009-11-27 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
IsShownAt | 10.14288/1.0075016 |
URI | http://hdl.handle.net/2429/15856 |
Degree |
Master of Science - MSc |
Program |
Forestry |
Affiliation |
Forestry, Faculty of |
Degree Grantor | University of British Columbia |
GraduationDate | 2004-11 |
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Scholarly Level | Graduate |
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